id	sid	tid	token	lemma	pos
easat-8674	1	1	edelweiss	edelweiss	PROPN
easat-8674	1	2	applied	apply	VERB
easat-8674	1	3	science	science	NOUN
easat-8674	1	4	and	and	CCONJ
easat-8674	1	5	technology	technology	NOUN
easat-8674	1	6	issn	issn	PROPN
easat-8674	1	7	:	:	PUNCT
easat-8674	1	8	2576	2576	NUM
easat-8674	1	9	-	-	SYM
easat-8674	1	10	8484	8484	NUM
easat-8674	1	11	vol	vol	NOUN
easat-8674	1	12	.	.	PROPN
easat-8674	2	1	9	9	NUM
easat-8674	2	2	,	,	PUNCT
easat-8674	2	3	no	no	INTJ
easat-8674	2	4	.	.	NOUN
easat-8674	2	5	7	7	NUM
easat-8674	2	6	,	,	PUNCT
easat-8674	2	7	580	580	NUM
easat-8674	2	8	-	-	SYM
easat-8674	2	9	594	594	NUM
easat-8674	2	10	2025	2025	NUM
easat-8674	2	11	publisher	publisher	NOUN
easat-8674	2	12	:	:	PUNCT
easat-8674	2	13	learning	learn	VERB
easat-8674	2	14	gate	gate	NOUN
easat-8674	2	15	doi	doi	PROPN
easat-8674	2	16	:	:	PUNCT
easat-8674	2	17	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	2	18	©	©	PROPN
easat-8674	2	19	2025	2025	NUM
easat-8674	2	20	by	by	ADP
easat-8674	2	21	the	the	DET
easat-8674	2	22	authors	author	NOUN
easat-8674	2	23	;	;	PUNCT
easat-8674	2	24	licensee	licensee	PROPN
easat-8674	2	25	learning	learning	NOUN
easat-8674	2	26	gate	gate	NOUN
easat-8674	3	1	©	©	PROPN
easat-8674	3	2	2025	2025	NUM
easat-8674	3	3	by	by	ADP
easat-8674	3	4	the	the	DET
easat-8674	3	5	authors	author	NOUN
easat-8674	3	6	;	;	PUNCT
easat-8674	3	7	licensee	licensee	PROPN
easat-8674	3	8	learning	learning	NOUN
easat-8674	3	9	gate	gate	NOUN
easat-8674	3	10	history	history	NOUN
easat-8674	3	11	:	:	PUNCT
easat-8674	3	12	received	receive	VERB
easat-8674	3	13	:	:	PUNCT
easat-8674	3	14	8	8	NUM
easat-8674	3	15	april	april	PROPN
easat-8674	3	16	2025	2025	NUM
easat-8674	3	17	;	;	PUNCT
easat-8674	3	18	revised	revise	VERB
easat-8674	3	19	:	:	PUNCT
easat-8674	3	20	16	16	NUM
easat-8674	3	21	june	june	PROPN
easat-8674	3	22	2025	2025	NUM
easat-8674	3	23	;	;	PUNCT
easat-8674	3	24	accepted	accept	VERB
easat-8674	3	25	:	:	PUNCT
easat-8674	3	26	19	19	NUM
easat-8674	3	27	june	june	PROPN
easat-8674	3	28	2025	2025	NUM
easat-8674	3	29	;	;	PUNCT
easat-8674	3	30	published	publish	VERB
easat-8674	3	31	:	:	PUNCT
easat-8674	3	32	3	3	NUM
easat-8674	3	33	july	july	PROPN
easat-8674	3	34	2025	2025	NUM
easat-8674	3	35	*	*	PUNCT
easat-8674	3	36	correspondence	correspondence	NOUN
easat-8674	3	37	:	:	PUNCT
easat-8674	3	38	yusuffuad@unesa.ac.id	yusuffuad@unesa.ac.id	PROPN
easat-8674	3	39	content	content	NOUN
easat-8674	3	40	knowledge	knowledge	NOUN
easat-8674	3	41	of	of	ADP
easat-8674	3	42	undergraduate	undergraduate	ADJ
easat-8674	3	43	students	student	NOUN
easat-8674	3	44	in	in	ADP
easat-8674	3	45	solving	solve	VERB
easat-8674	3	46	the	the	DET
easat-8674	3	47	algebra	algebra	NOUN
easat-8674	3	48	’s	’s	PART
easat-8674	3	49	problem	problem	NOUN
easat-8674	3	50	blandina	blandina	PROPN
easat-8674	3	51	seko	seko	PROPN
easat-8674	3	52	bani1	bani1	PROPN
easat-8674	3	53	,	,	PUNCT
easat-8674	3	54	yusuf	yusuf	PROPN
easat-8674	3	55	fuad2	fuad2	PROPN
easat-8674	3	56	*	*	PUNCT
easat-8674	3	57	,	,	PUNCT
easat-8674	3	58	rooselyna	rooselyna	NOUN
easat-8674	3	59	ekawati3	ekawati3	NOUN
easat-8674	3	60	1doctoral	1doctoral	NUM
easat-8674	3	61	program	program	NOUN
easat-8674	3	62	of	of	ADP
easat-8674	3	63	mathematics	mathematic	NOUN
easat-8674	3	64	education	education	NOUN
easat-8674	3	65	,	,	PUNCT
easat-8674	3	66	universitas	universitas	PROPN
easat-8674	3	67	negeri	negeri	PROPN
easat-8674	3	68	surabaya	surabaya	PROPN
easat-8674	3	69	,	,	PUNCT
easat-8674	3	70	surabaya	surabaya	PROPN
easat-8674	3	71	,	,	PUNCT
easat-8674	3	72	indonesia	indonesia	PROPN
easat-8674	3	73	;	;	PUNCT
easat-8674	3	74	blandina.21020@mhs.unesa.ac.id	blandina.21020@mhs.unesa.ac.id	PROPN
easat-8674	3	75	(	(	PUNCT
easat-8674	3	76	b.s.b	b.s.b	ADV
easat-8674	3	77	)	)	PUNCT
easat-8674	3	78	2,3department	2,3department	NUM
easat-8674	3	79	of	of	ADP
easat-8674	3	80	mathematics	mathematics	PROPN
easat-8674	3	81	education	education	NOUN
easat-8674	3	82	,	,	PUNCT
easat-8674	3	83	universitas	universitas	PROPN
easat-8674	3	84	negeri	negeri	PROPN
easat-8674	3	85	surabaya	surabaya	PROPN
easat-8674	3	86	,	,	PUNCT
easat-8674	3	87	surabaya	surabaya	PROPN
easat-8674	3	88	,	,	PUNCT
easat-8674	3	89	indonesia	indonesia	PROPN
easat-8674	3	90	;	;	PUNCT
easat-8674	3	91	yusuffuad@unesa.ac.id	yusuffuad@unesa.ac.id	PROPN
easat-8674	3	92	(	(	PUNCT
easat-8674	3	93	y.f	y.f	NOUN
easat-8674	3	94	)	)	PUNCT
easat-8674	3	95	rooselynaekawati@unesa.ac.id	rooselynaekawati@unesa.ac.id	NOUN
easat-8674	3	96	(	(	PUNCT
easat-8674	3	97	r.e	r.e	PROPN
easat-8674	3	98	)	)	PUNCT
easat-8674	3	99	.	.	PUNCT
easat-8674	4	1	abstract	abstract	ADJ
easat-8674	4	2	:	:	PUNCT
easat-8674	4	3	content	content	NOUN
easat-8674	4	4	knowledge	knowledge	NOUN
easat-8674	4	5	(	(	PUNCT
easat-8674	4	6	ck	ck	NOUN
easat-8674	4	7	)	)	PUNCT
easat-8674	4	8	is	be	AUX
easat-8674	4	9	essential	essential	ADJ
easat-8674	4	10	in	in	ADP
easat-8674	4	11	mathematics	mathematic	NOUN
easat-8674	4	12	education	education	NOUN
easat-8674	4	13	,	,	PUNCT
easat-8674	4	14	particularly	particularly	ADV
easat-8674	4	15	for	for	ADP
easat-8674	4	16	understanding	understand	VERB
easat-8674	4	17	algebraic	algebraic	ADJ
easat-8674	4	18	concepts	concept	NOUN
easat-8674	4	19	.	.	PUNCT
easat-8674	5	1	this	this	DET
easat-8674	5	2	study	study	NOUN
easat-8674	5	3	explores	explore	VERB
easat-8674	5	4	the	the	DET
easat-8674	5	5	algebraic	algebraic	ADJ
easat-8674	5	6	content	content	NOUN
easat-8674	5	7	knowledge	knowledge	NOUN
easat-8674	5	8	of	of	ADP
easat-8674	5	9	undergraduate	undergraduate	ADJ
easat-8674	5	10	mathematics	mathematic	NOUN
easat-8674	5	11	education	education	NOUN
easat-8674	5	12	students	student	NOUN
easat-8674	5	13	.	.	PUNCT
easat-8674	6	1	using	use	VERB
easat-8674	6	2	a	a	DET
easat-8674	6	3	descriptive	descriptive	ADJ
easat-8674	6	4	qualitative	qualitative	ADJ
easat-8674	6	5	approach	approach	NOUN
easat-8674	6	6	,	,	PUNCT
easat-8674	6	7	the	the	DET
easat-8674	6	8	research	research	NOUN
easat-8674	6	9	involved	involve	VERB
easat-8674	6	10	third	third	ADJ
easat-8674	6	11	-	-	PUNCT
easat-8674	6	12	year	year	NOUN
easat-8674	6	13	students	student	NOUN
easat-8674	6	14	from	from	ADP
easat-8674	6	15	a	a	DET
easat-8674	6	16	private	private	ADJ
easat-8674	6	17	university	university	NOUN
easat-8674	6	18	in	in	ADP
easat-8674	6	19	east	east	PROPN
easat-8674	6	20	nusa	nusa	PROPN
easat-8674	6	21	tenggara	tenggara	PROPN
easat-8674	6	22	,	,	PUNCT
easat-8674	6	23	indonesia	indonesia	PROPN
easat-8674	6	24	.	.	PUNCT
easat-8674	7	1	two	two	NUM
easat-8674	7	2	validated	validate	VERB
easat-8674	7	3	instruments	instrument	NOUN
easat-8674	7	4	,	,	PUNCT
easat-8674	7	5	the	the	DET
easat-8674	7	6	diagnostic	diagnostic	ADJ
easat-8674	7	7	test	test	NOUN
easat-8674	7	8	(	(	PUNCT
easat-8674	7	9	td	td	NOUN
easat-8674	7	10	)	)	PUNCT
easat-8674	7	11	and	and	CCONJ
easat-8674	7	12	the	the	DET
easat-8674	7	13	content	content	NOUN
easat-8674	7	14	knowledge	knowledge	PROPN
easat-8674	7	15	test	test	PROPN
easat-8674	7	16	(	(	PUNCT
easat-8674	7	17	tck	tck	PROPN
easat-8674	7	18	)	)	PUNCT
easat-8674	7	19	,	,	PUNCT
easat-8674	7	20	were	be	AUX
easat-8674	7	21	employed	employ	VERB
easat-8674	7	22	to	to	PART
easat-8674	7	23	assess	assess	VERB
easat-8674	7	24	students	student	NOUN
easat-8674	7	25	'	'	PART
easat-8674	7	26	understanding	understanding	NOUN
easat-8674	7	27	.	.	PUNCT
easat-8674	8	1	the	the	DET
easat-8674	8	2	instruments	instrument	NOUN
easat-8674	8	3	showed	show	VERB
easat-8674	8	4	strong	strong	ADJ
easat-8674	8	5	validity	validity	NOUN
easat-8674	8	6	scores	score	NOUN
easat-8674	8	7	,	,	PUNCT
easat-8674	8	8	with	with	ADP
easat-8674	8	9	4.6	4.6	NUM
easat-8674	8	10	for	for	ADP
easat-8674	8	11	the	the	DET
easat-8674	8	12	td	td	NOUN
easat-8674	8	13	and	and	CCONJ
easat-8674	8	14	4.0	4.0	NUM
easat-8674	8	15	for	for	ADP
easat-8674	8	16	the	the	DET
easat-8674	8	17	tck	tck	PROPN
easat-8674	8	18	(	(	PUNCT
easat-8674	8	19	on	on	ADP
easat-8674	8	20	a	a	DET
easat-8674	8	21	5	5	NUM
easat-8674	8	22	-	-	PUNCT
easat-8674	8	23	point	point	NOUN
easat-8674	8	24	scale	scale	NOUN
easat-8674	8	25	)	)	PUNCT
easat-8674	8	26	,	,	PUNCT
easat-8674	8	27	and	and	CCONJ
easat-8674	8	28	reliability	reliability	NOUN
easat-8674	8	29	scores	score	NOUN
easat-8674	8	30	of	of	ADP
easat-8674	8	31	0.9993	0.9993	NUM
easat-8674	8	32	for	for	ADP
easat-8674	8	33	the	the	DET
easat-8674	8	34	td	td	NOUN
easat-8674	8	35	and	and	CCONJ
easat-8674	8	36	0.9983	0.9983	NUM
easat-8674	8	37	for	for	ADP
easat-8674	8	38	the	the	DET
easat-8674	8	39	tck	tck	PROPN
easat-8674	8	40	.	.	PROPN
easat-8674	8	41	data	datum	NOUN
easat-8674	8	42	were	be	AUX
easat-8674	8	43	analyzed	analyze	VERB
easat-8674	8	44	using	use	VERB
easat-8674	8	45	two	two	NUM
easat-8674	8	46	frameworks	framework	NOUN
easat-8674	8	47	:	:	PUNCT
easat-8674	8	48	the	the	DET
easat-8674	8	49	direct	direct	ADJ
easat-8674	8	50	translation	translation	NOUN
easat-8674	8	51	approach	approach	NOUN
easat-8674	8	52	(	(	PUNCT
easat-8674	8	53	dta	dta	PROPN
easat-8674	8	54	)	)	PUNCT
easat-8674	8	55	and	and	CCONJ
easat-8674	8	56	the	the	DET
easat-8674	8	57	meaningbased	meaningbase	VERB
easat-8674	8	58	approach	approach	NOUN
easat-8674	8	59	(	(	PUNCT
easat-8674	8	60	mba	mba	NOUN
easat-8674	8	61	)	)	PUNCT
easat-8674	8	62	.	.	PUNCT
easat-8674	9	1	findings	finding	NOUN
easat-8674	9	2	revealed	reveal	VERB
easat-8674	9	3	varied	varied	ADJ
easat-8674	9	4	levels	level	NOUN
easat-8674	9	5	of	of	ADP
easat-8674	9	6	ck	ck	NOUN
easat-8674	9	7	:	:	PUNCT
easat-8674	9	8	some	some	DET
easat-8674	9	9	students	student	NOUN
easat-8674	9	10	demonstrated	demonstrate	VERB
easat-8674	9	11	procedural	procedural	ADJ
easat-8674	9	12	fluency	fluency	NOUN
easat-8674	9	13	and	and	CCONJ
easat-8674	9	14	the	the	DET
easat-8674	9	15	ability	ability	NOUN
easat-8674	9	16	to	to	PART
easat-8674	9	17	relate	relate	VERB
easat-8674	9	18	symbolic	symbolic	ADJ
easat-8674	9	19	representations	representation	NOUN
easat-8674	9	20	to	to	ADP
easat-8674	9	21	contextual	contextual	ADJ
easat-8674	9	22	meaning	meaning	NOUN
easat-8674	9	23	(	(	PUNCT
easat-8674	9	24	mba	mba	NOUN
easat-8674	9	25	)	)	PUNCT
easat-8674	9	26	,	,	PUNCT
easat-8674	9	27	while	while	SCONJ
easat-8674	9	28	others	other	NOUN
easat-8674	9	29	exhibited	exhibit	VERB
easat-8674	9	30	difficulties	difficulty	NOUN
easat-8674	9	31	in	in	ADP
easat-8674	9	32	applying	apply	VERB
easat-8674	9	33	concepts	concept	NOUN
easat-8674	9	34	flexibly	flexibly	ADV
easat-8674	9	35	,	,	PUNCT
easat-8674	9	36	leading	lead	VERB
easat-8674	9	37	to	to	ADP
easat-8674	9	38	illogical	illogical	ADJ
easat-8674	9	39	reasoning	reasoning	NOUN
easat-8674	9	40	(	(	PUNCT
easat-8674	9	41	dta	dta	PROPN
easat-8674	9	42	)	)	PUNCT
easat-8674	9	43	.	.	PUNCT
easat-8674	10	1	these	these	DET
easat-8674	10	2	outcomes	outcome	NOUN
easat-8674	10	3	highlight	highlight	VERB
easat-8674	10	4	the	the	DET
easat-8674	10	5	need	need	NOUN
easat-8674	10	6	to	to	PART
easat-8674	10	7	strengthen	strengthen	VERB
easat-8674	10	8	conceptual	conceptual	ADJ
easat-8674	10	9	understanding	understanding	NOUN
easat-8674	10	10	and	and	CCONJ
easat-8674	10	11	reflective	reflective	ADJ
easat-8674	10	12	thinking	thinking	NOUN
easat-8674	10	13	among	among	ADP
easat-8674	10	14	pre	pre	ADJ
easat-8674	10	15	-	-	ADJ
easat-8674	10	16	service	service	ADJ
easat-8674	10	17	teachers	teacher	NOUN
easat-8674	10	18	.	.	PUNCT
easat-8674	11	1	the	the	DET
easat-8674	11	2	study	study	NOUN
easat-8674	11	3	recommends	recommend	VERB
easat-8674	11	4	instructional	instructional	ADJ
easat-8674	11	5	strategies	strategy	NOUN
easat-8674	11	6	that	that	PRON
easat-8674	11	7	integrate	integrate	VERB
easat-8674	11	8	symbols	symbol	NOUN
easat-8674	11	9	,	,	PUNCT
easat-8674	11	10	context	context	NOUN
easat-8674	11	11	,	,	PUNCT
easat-8674	11	12	and	and	CCONJ
easat-8674	11	13	meaning	mean	VERB
easat-8674	11	14	to	to	PART
easat-8674	11	15	enhance	enhance	VERB
easat-8674	11	16	students	student	NOUN
easat-8674	11	17	'	'	PART
easat-8674	11	18	ability	ability	NOUN
easat-8674	11	19	to	to	PART
easat-8674	11	20	solve	solve	VERB
easat-8674	11	21	algebraic	algebraic	ADJ
easat-8674	11	22	problems	problem	NOUN
easat-8674	11	23	effectively	effectively	ADV
easat-8674	11	24	.	.	PUNCT
easat-8674	12	1	such	such	ADJ
easat-8674	12	2	approaches	approach	NOUN
easat-8674	12	3	are	be	AUX
easat-8674	12	4	crucial	crucial	ADJ
easat-8674	12	5	for	for	ADP
easat-8674	12	6	preparing	prepare	VERB
easat-8674	12	7	future	future	ADJ
easat-8674	12	8	mathematics	mathematic	NOUN
easat-8674	12	9	teachers	teacher	NOUN
easat-8674	12	10	capable	capable	ADJ
easat-8674	12	11	of	of	ADP
easat-8674	12	12	connecting	connect	VERB
easat-8674	12	13	mathematical	mathematical	ADJ
easat-8674	12	14	reasoning	reasoning	NOUN
easat-8674	12	15	to	to	ADP
easat-8674	12	16	realworld	realworld	PROPN
easat-8674	12	17	contexts	contexts	PROPN
easat-8674	12	18	.	.	PUNCT
easat-8674	13	1	keywords	keyword	NOUN
easat-8674	13	2	:	:	PUNCT
easat-8674	13	3	algebra	algebra	NOUN
easat-8674	13	4	,	,	PUNCT
easat-8674	13	5	pedagogical	pedagogical	ADJ
easat-8674	13	6	content	content	NOUN
easat-8674	13	7	knowledge	knowledge	NOUN
easat-8674	13	8	,	,	PUNCT
easat-8674	13	9	problem	problem	NOUN
easat-8674	13	10	solving	solving	NOUN
easat-8674	13	11	.	.	PUNCT
easat-8674	14	1	1	1	X
easat-8674	14	2	.	.	X
easat-8674	14	3	introduction	introduction	NOUN
easat-8674	14	4	pedagogical	pedagogical	ADJ
easat-8674	14	5	content	content	NOUN
easat-8674	14	6	knowledge	knowledge	NOUN
easat-8674	14	7	(	(	PUNCT
easat-8674	14	8	pck	pck	PROPN
easat-8674	14	9	)	)	PUNCT
easat-8674	14	10	refers	refer	VERB
easat-8674	14	11	to	to	ADP
easat-8674	14	12	the	the	DET
easat-8674	14	13	integration	integration	NOUN
easat-8674	14	14	of	of	ADP
easat-8674	14	15	content	content	ADJ
easat-8674	14	16	knowledge	knowledge	NOUN
easat-8674	14	17	(	(	PUNCT
easat-8674	14	18	ck	ck	NOUN
easat-8674	14	19	)	)	PUNCT
easat-8674	14	20	and	and	CCONJ
easat-8674	14	21	pedagogical	pedagogical	ADJ
easat-8674	14	22	knowledge	knowledge	NOUN
easat-8674	14	23	(	(	PUNCT
easat-8674	14	24	pk	pk	NOUN
easat-8674	14	25	)	)	PUNCT
easat-8674	14	26	,	,	PUNCT
easat-8674	14	27	both	both	PRON
easat-8674	14	28	of	of	ADP
easat-8674	14	29	which	which	PRON
easat-8674	14	30	are	be	AUX
easat-8674	14	31	essential	essential	ADJ
easat-8674	14	32	for	for	ADP
easat-8674	14	33	effective	effective	ADJ
easat-8674	14	34	teaching	teaching	NOUN
easat-8674	14	35	and	and	CCONJ
easat-8674	14	36	learning	learn	VERB
easat-8674	14	37	[	[	X
easat-8674	14	38	1	1	NUM
easat-8674	14	39	-	-	SYM
easat-8674	14	40	7	7	NUM
easat-8674	14	41	]	]	PUNCT
easat-8674	14	42	.	.	PUNCT
easat-8674	15	1	ck	ck	PROPN
easat-8674	15	2	encompasses	encompass	VERB
easat-8674	15	3	the	the	DET
easat-8674	15	4	understanding	understanding	NOUN
easat-8674	15	5	of	of	ADP
easat-8674	15	6	concepts	concept	NOUN
easat-8674	15	7	,	,	PUNCT
easat-8674	15	8	theories	theory	NOUN
easat-8674	15	9	,	,	PUNCT
easat-8674	15	10	rules	rule	NOUN
easat-8674	15	11	,	,	PUNCT
easat-8674	15	12	and	and	CCONJ
easat-8674	15	13	procedures	procedure	NOUN
easat-8674	15	14	related	relate	VERB
easat-8674	15	15	to	to	ADP
easat-8674	15	16	the	the	DET
easat-8674	15	17	subject	subject	NOUN
easat-8674	15	18	matter	matter	NOUN
easat-8674	15	19	,	,	PUNCT
easat-8674	15	20	while	while	SCONJ
easat-8674	15	21	pk	pk	NOUN
easat-8674	15	22	pertains	pertain	NOUN
easat-8674	15	23	to	to	ADP
easat-8674	15	24	instructional	instructional	ADJ
easat-8674	15	25	strategies	strategy	NOUN
easat-8674	15	26	that	that	PRON
easat-8674	15	27	help	help	VERB
easat-8674	15	28	students	student	NOUN
easat-8674	15	29	learn	learn	VERB
easat-8674	15	30	and	and	CCONJ
easat-8674	15	31	apply	apply	VERB
easat-8674	15	32	this	this	DET
easat-8674	15	33	knowledge	knowledge	NOUN
easat-8674	15	34	to	to	PART
easat-8674	15	35	solve	solve	VERB
easat-8674	15	36	mathematical	mathematical	ADJ
easat-8674	15	37	problems	problem	NOUN
easat-8674	15	38	.	.	PUNCT
easat-8674	16	1	this	this	DET
easat-8674	16	2	conceptual	conceptual	ADJ
easat-8674	16	3	framework	framework	NOUN
easat-8674	16	4	,	,	PUNCT
easat-8674	16	5	introduced	introduce	VERB
easat-8674	16	6	[	[	X
easat-8674	16	7	7	7	NUM
easat-8674	16	8	]	]	PUNCT
easat-8674	16	9	emphasizes	emphasize	VERB
easat-8674	16	10	that	that	SCONJ
easat-8674	16	11	teachers	teacher	NOUN
easat-8674	16	12	must	must	AUX
easat-8674	16	13	not	not	PART
easat-8674	16	14	only	only	ADV
easat-8674	16	15	understand	understand	VERB
easat-8674	16	16	what	what	PRON
easat-8674	16	17	to	to	PART
easat-8674	16	18	teach	teach	VERB
easat-8674	16	19	but	but	CCONJ
easat-8674	16	20	also	also	ADV
easat-8674	16	21	why	why	SCONJ
easat-8674	16	22	a	a	DET
easat-8674	16	23	concept	concept	NOUN
easat-8674	16	24	works	work	VERB
easat-8674	16	25	the	the	DET
easat-8674	16	26	way	way	NOUN
easat-8674	16	27	it	it	PRON
easat-8674	16	28	does	do	VERB
easat-8674	16	29	.	.	PUNCT
easat-8674	17	1	as	as	ADP
easat-8674	17	2	such	such	ADJ
easat-8674	17	3	,	,	PUNCT
easat-8674	17	4	they	they	PRON
easat-8674	17	5	are	be	AUX
easat-8674	17	6	expected	expect	VERB
easat-8674	17	7	to	to	PART
easat-8674	17	8	deliver	deliver	VERB
easat-8674	17	9	instruction	instruction	NOUN
easat-8674	17	10	and	and	CCONJ
easat-8674	17	11	address	address	NOUN
easat-8674	17	12	mathematical	mathematical	ADJ
easat-8674	17	13	problems	problem	NOUN
easat-8674	17	14	in	in	ADP
easat-8674	17	15	ways	way	NOUN
easat-8674	17	16	that	that	PRON
easat-8674	17	17	align	align	VERB
easat-8674	17	18	with	with	ADP
easat-8674	17	19	students	student	NOUN
easat-8674	17	20	’	’	PART
easat-8674	17	21	developmental	developmental	ADJ
easat-8674	17	22	levels	level	NOUN
easat-8674	17	23	,	,	PUNCT
easat-8674	17	24	especially	especially	ADV
easat-8674	17	25	in	in	ADP
easat-8674	17	26	the	the	DET
easat-8674	17	27	domain	domain	NOUN
easat-8674	17	28	of	of	ADP
easat-8674	17	29	algebra	algebra	PROPN
easat-8674	17	30	.	.	PUNCT
easat-8674	18	1	algebra	algebra	NOUN
easat-8674	18	2	is	be	AUX
easat-8674	18	3	not	not	PART
easat-8674	18	4	only	only	ADV
easat-8674	18	5	a	a	DET
easat-8674	18	6	component	component	NOUN
easat-8674	18	7	of	of	ADP
easat-8674	18	8	higher	high	ADJ
easat-8674	18	9	education	education	NOUN
easat-8674	18	10	curricula	curricula	NOUN
easat-8674	18	11	but	but	CCONJ
easat-8674	18	12	is	be	AUX
easat-8674	18	13	also	also	ADV
easat-8674	18	14	taught	teach	VERB
easat-8674	18	15	from	from	ADP
easat-8674	18	16	lower	low	ADJ
easat-8674	18	17	secondary	secondary	ADJ
easat-8674	18	18	school	school	NOUN
easat-8674	18	19	onwards	onwards	ADV
easat-8674	18	20	[	[	X
easat-8674	18	21	3	3	NUM
easat-8674	18	22	]	]	PUNCT
easat-8674	18	23	.	.	PUNCT
easat-8674	19	1	at	at	ADP
easat-8674	19	2	the	the	DET
easat-8674	19	3	secondary	secondary	ADJ
easat-8674	19	4	level	level	NOUN
easat-8674	19	5	,	,	PUNCT
easat-8674	19	6	algebraic	algebraic	ADJ
easat-8674	19	7	content	content	NOUN
easat-8674	19	8	includes	include	VERB
easat-8674	19	9	topics	topic	NOUN
easat-8674	19	10	such	such	ADJ
easat-8674	19	11	as	as	ADP
easat-8674	19	12	algebraic	algebraic	ADJ
easat-8674	19	13	expressions	expression	NOUN
easat-8674	19	14	,	,	PUNCT
easat-8674	19	15	operations	operation	NOUN
easat-8674	19	16	,	,	PUNCT
easat-8674	19	17	and	and	CCONJ
easat-8674	19	18	relationships	relationship	NOUN
easat-8674	19	19	within	within	ADP
easat-8674	19	20	contextual	contextual	ADJ
easat-8674	19	21	problems	problem	NOUN
easat-8674	19	22	.	.	PUNCT
easat-8674	20	1	algebra	algebra	NOUN
easat-8674	20	2	learning	learning	NOUN
easat-8674	20	3	is	be	AUX
easat-8674	20	4	crucial	crucial	ADJ
easat-8674	20	5	for	for	ADP
easat-8674	20	6	developing	develop	VERB
easat-8674	20	7	students	student	NOUN
easat-8674	20	8	’	'	PUNCT
easat-8674	20	9	critical	critical	ADJ
easat-8674	20	10	thinking	thinking	NOUN
easat-8674	20	11	skills	skill	NOUN
easat-8674	20	12	.	.	PUNCT
easat-8674	21	1	however	however	ADV
easat-8674	21	2	,	,	PUNCT
easat-8674	21	3	in	in	ADP
easat-8674	21	4	indonesia	indonesia	PROPN
easat-8674	21	5	,	,	PUNCT
easat-8674	21	6	fewer	few	ADJ
easat-8674	21	7	than	than	ADP
easat-8674	21	8	5	5	NUM
easat-8674	21	9	%	%	NOUN
easat-8674	21	10	of	of	ADP
easat-8674	21	11	secondary	secondary	ADJ
easat-8674	21	12	school	school	NOUN
easat-8674	21	13	students	student	NOUN
easat-8674	21	14	can	can	AUX
easat-8674	21	15	solve	solve	VERB
easat-8674	21	16	contextual	contextual	ADJ
easat-8674	21	17	problems	problem	NOUN
easat-8674	21	18	related	relate	VERB
easat-8674	21	19	to	to	ADP
easat-8674	21	20	real	real	ADJ
easat-8674	21	21	-	-	PUNCT
easat-8674	21	22	life	life	NOUN
easat-8674	21	23	situations	situation	NOUN
easat-8674	21	24	[	[	X
easat-8674	21	25	8	8	NUM
easat-8674	21	26	]	]	PUNCT
easat-8674	21	27	.	.	PUNCT
easat-8674	22	1	one	one	NUM
easat-8674	22	2	major	major	ADJ
easat-8674	22	3	factor	factor	NOUN
easat-8674	22	4	contributing	contribute	VERB
easat-8674	22	5	to	to	ADP
easat-8674	22	6	this	this	DET
easat-8674	22	7	issue	issue	NOUN
easat-8674	22	8	is	be	AUX
easat-8674	22	9	the	the	DET
easat-8674	22	10	lack	lack	NOUN
easat-8674	22	11	of	of	ADP
easat-8674	22	12	content	content	ADJ
easat-8674	22	13	mastery	mastery	NOUN
easat-8674	22	14	in	in	ADP
easat-8674	22	15	algebra	algebra	NOUN
easat-8674	22	16	among	among	ADP
easat-8674	22	17	teachers	teacher	NOUN
easat-8674	22	18	.	.	PUNCT
easat-8674	23	1	previous	previous	ADJ
easat-8674	23	2	studies	study	NOUN
easat-8674	23	3	indicate	indicate	VERB
easat-8674	23	4	that	that	SCONJ
easat-8674	23	5	many	many	ADJ
easat-8674	23	6	teachers	teacher	NOUN
easat-8674	23	7	struggle	struggle	VERB
easat-8674	23	8	to	to	PART
easat-8674	23	9	grasp	grasp	VERB
easat-8674	23	10	fundamental	fundamental	ADJ
easat-8674	23	11	algebraic	algebraic	ADJ
easat-8674	23	12	concepts	concept	NOUN
easat-8674	23	13	[	[	X
easat-8674	23	14	8	8	NUM
easat-8674	23	15	]	]	PUNCT
easat-8674	23	16	.	.	PUNCT
easat-8674	24	1	https://orcid.org/0009-0002-8874-7928	https://orcid.org/0009-0002-8874-7928	PROPN
easat-8674	24	2	https://orcid.org/0000-0002-9589-7839	https://orcid.org/0000-0002-9589-7839	PROPN
easat-8674	24	3	https://orcid.org/0000-0002-2646-9064	https://orcid.org/0000-0002-2646-9064	PROPN
easat-8674	24	4	581	581	NUM
easat-8674	24	5	edelweiss	edelweiss	PROPN
easat-8674	24	6	applied	apply	VERB
easat-8674	24	7	science	science	NOUN
easat-8674	24	8	and	and	CCONJ
easat-8674	24	9	technology	technology	NOUN
easat-8674	24	10	issn	issn	PROPN
easat-8674	24	11	:	:	PUNCT
easat-8674	24	12	2576	2576	NUM
easat-8674	24	13	-	-	SYM
easat-8674	24	14	8484	8484	NUM
easat-8674	24	15	vol	vol	NOUN
easat-8674	24	16	.	.	PROPN
easat-8674	25	1	9	9	NUM
easat-8674	25	2	,	,	PUNCT
easat-8674	25	3	no	no	INTJ
easat-8674	25	4	.	.	NOUN
easat-8674	26	1	7	7	NUM
easat-8674	26	2	:	:	SYM
easat-8674	26	3	580	580	NUM
easat-8674	26	4	-	-	SYM
easat-8674	26	5	594	594	NUM
easat-8674	26	6	,	,	PUNCT
easat-8674	26	7	2025	2025	NUM
easat-8674	26	8	doi	doi	NOUN
easat-8674	26	9	:	:	PUNCT
easat-8674	26	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	26	11	©	©	PROPN
easat-8674	26	12	2025	2025	NUM
easat-8674	26	13	by	by	ADP
easat-8674	26	14	the	the	DET
easat-8674	26	15	authors	author	NOUN
easat-8674	26	16	;	;	PUNCT
easat-8674	26	17	licensee	licensee	PROPN
easat-8674	26	18	learning	learning	NOUN
easat-8674	26	19	gate	gate	VERB
easat-8674	26	20	a	a	DET
easat-8674	26	21	systematic	systematic	ADJ
easat-8674	26	22	review	review	NOUN
easat-8674	26	23	of	of	ADP
easat-8674	26	24	237	237	NUM
easat-8674	26	25	mathematics	mathematic	NOUN
easat-8674	26	26	pck	pck	NOUN
easat-8674	26	27	studies	study	NOUN
easat-8674	26	28	conducted	conduct	VERB
easat-8674	26	29	over	over	ADP
easat-8674	26	30	the	the	DET
easat-8674	26	31	past	past	ADJ
easat-8674	26	32	decade	decade	NOUN
easat-8674	26	33	identified	identify	VERB
easat-8674	26	34	algebra	algebra	NOUN
easat-8674	26	35	as	as	ADP
easat-8674	26	36	one	one	NUM
easat-8674	26	37	of	of	ADP
easat-8674	26	38	the	the	DET
easat-8674	26	39	most	most	ADV
easat-8674	26	40	frequently	frequently	ADV
easat-8674	26	41	examined	examine	VERB
easat-8674	26	42	topics	topic	NOUN
easat-8674	26	43	,	,	PUNCT
easat-8674	26	44	highlighting	highlight	VERB
easat-8674	26	45	83	83	NUM
easat-8674	26	46	learning	learning	NOUN
easat-8674	26	47	obstacles	obstacle	NOUN
easat-8674	26	48	.	.	PUNCT
easat-8674	27	1	these	these	PRON
easat-8674	27	2	include	include	VERB
easat-8674	27	3	both	both	CCONJ
easat-8674	27	4	conceptual	conceptual	ADJ
easat-8674	27	5	and	and	CCONJ
easat-8674	27	6	procedural	procedural	ADJ
easat-8674	27	7	difficulties	difficulty	NOUN
easat-8674	27	8	commonly	commonly	ADV
easat-8674	27	9	encountered	encounter	VERB
easat-8674	27	10	by	by	ADP
easat-8674	27	11	students	student	NOUN
easat-8674	27	12	,	,	PUNCT
easat-8674	27	13	as	as	ADV
easat-8674	27	14	well	well	ADV
easat-8674	27	15	as	as	ADP
easat-8674	27	16	a	a	DET
easat-8674	27	17	lack	lack	NOUN
easat-8674	27	18	of	of	ADP
easat-8674	27	19	appropriate	appropriate	ADJ
easat-8674	27	20	pedagogical	pedagogical	ADJ
easat-8674	27	21	strategies	strategy	NOUN
easat-8674	27	22	to	to	PART
easat-8674	27	23	address	address	VERB
easat-8674	27	24	them	they	PRON
easat-8674	27	25	[	[	X
easat-8674	27	26	9	9	NUM
easat-8674	27	27	]	]	PUNCT
easat-8674	27	28	.	.	PUNCT
easat-8674	28	1	the	the	DET
easat-8674	28	2	review	review	NOUN
easat-8674	28	3	recommends	recommend	VERB
easat-8674	28	4	the	the	DET
easat-8674	28	5	use	use	NOUN
easat-8674	28	6	of	of	ADP
easat-8674	28	7	manipulative	manipulative	ADJ
easat-8674	28	8	tools	tool	NOUN
easat-8674	28	9	and	and	CCONJ
easat-8674	28	10	visualization	visualization	NOUN
easat-8674	28	11	-	-	PUNCT
easat-8674	28	12	based	base	VERB
easat-8674	28	13	approaches	approach	NOUN
easat-8674	28	14	to	to	PART
easat-8674	28	15	strengthen	strengthen	VERB
easat-8674	28	16	teachers	teacher	NOUN
easat-8674	28	17	’	'	PUNCT
easat-8674	28	18	pck	pck	PROPN
easat-8674	28	19	.	.	PUNCT
easat-8674	29	1	the	the	DET
easat-8674	29	2	problem	problem	NOUN
easat-8674	29	3	of	of	ADP
easat-8674	29	4	limited	limited	ADJ
easat-8674	29	5	algebraic	algebraic	PROPN
easat-8674	29	6	content	content	PROPN
easat-8674	29	7	mastery	mastery	NOUN
easat-8674	29	8	is	be	AUX
easat-8674	29	9	not	not	PART
easat-8674	29	10	confined	confine	VERB
easat-8674	29	11	to	to	ADP
easat-8674	29	12	in	in	ADP
easat-8674	29	13	-	-	PUNCT
easat-8674	29	14	service	service	NOUN
easat-8674	29	15	teachers	teacher	NOUN
easat-8674	29	16	;	;	PUNCT
easat-8674	29	17	it	it	PRON
easat-8674	29	18	also	also	ADV
easat-8674	29	19	affects	affect	VERB
easat-8674	29	20	prospective	prospective	ADJ
easat-8674	29	21	teachers	teacher	NOUN
easat-8674	29	22	.	.	PUNCT
easat-8674	30	1	a	a	DET
easat-8674	30	2	study	study	NOUN
easat-8674	30	3	rupasinghe	rupasinghe	NOUN
easat-8674	30	4	[	[	X
easat-8674	30	5	10	10	NUM
easat-8674	30	6	]	]	PUNCT
easat-8674	30	7	revealed	reveal	VERB
easat-8674	30	8	that	that	SCONJ
easat-8674	30	9	lower	low	ADJ
easat-8674	30	10	secondary	secondary	ADJ
easat-8674	30	11	mathematics	mathematic	NOUN
easat-8674	30	12	teachers	teacher	NOUN
easat-8674	30	13	in	in	ADP
easat-8674	30	14	sri	sri	PROPN
easat-8674	30	15	lanka	lanka	PROPN
easat-8674	30	16	still	still	ADV
easat-8674	30	17	show	show	VERB
easat-8674	30	18	low	low	ADJ
easat-8674	30	19	levels	level	NOUN
easat-8674	30	20	of	of	ADP
easat-8674	30	21	pck	pck	NOUN
easat-8674	30	22	,	,	PUNCT
easat-8674	30	23	particularly	particularly	ADV
easat-8674	30	24	in	in	ADP
easat-8674	30	25	interpreting	interpret	VERB
easat-8674	30	26	algebraic	algebraic	ADJ
easat-8674	30	27	symbols	symbol	NOUN
easat-8674	30	28	and	and	CCONJ
easat-8674	30	29	addressing	address	VERB
easat-8674	30	30	student	student	NOUN
easat-8674	30	31	misconceptions	misconception	NOUN
easat-8674	30	32	.	.	PUNCT
easat-8674	31	1	similar	similar	ADJ
easat-8674	31	2	patterns	pattern	NOUN
easat-8674	31	3	have	have	AUX
easat-8674	31	4	been	be	AUX
easat-8674	31	5	observed	observe	VERB
easat-8674	31	6	in	in	ADP
easat-8674	31	7	indonesia	indonesia	PROPN
easat-8674	31	8	,	,	PUNCT
easat-8674	31	9	where	where	SCONJ
easat-8674	31	10	pre	pre	ADJ
easat-8674	31	11	-	-	ADJ
easat-8674	31	12	service	service	ADJ
easat-8674	31	13	mathematics	mathematic	NOUN
easat-8674	31	14	teachers	teacher	NOUN
easat-8674	31	15	often	often	ADV
easat-8674	31	16	make	make	VERB
easat-8674	31	17	fundamental	fundamental	ADJ
easat-8674	31	18	errors	error	NOUN
easat-8674	31	19	in	in	ADP
easat-8674	31	20	algebraic	algebraic	ADJ
easat-8674	31	21	operations	operation	NOUN
easat-8674	31	22	.	.	PUNCT
easat-8674	32	1	for	for	ADP
easat-8674	32	2	example	example	NOUN
easat-8674	32	3	,	,	PUNCT
easat-8674	32	4	some	some	DET
easat-8674	32	5	students	student	NOUN
easat-8674	32	6	misinterpret	misinterpret	VERB
easat-8674	32	7	expressions	expression	NOUN
easat-8674	32	8	within	within	ADP
easat-8674	32	9	parentheses	parenthesis	NOUN
easat-8674	32	10	during	during	ADP
easat-8674	32	11	multiplication	multiplication	NOUN
easat-8674	32	12	operations	operation	NOUN
easat-8674	32	13	due	due	ADP
easat-8674	32	14	to	to	ADP
easat-8674	32	15	a	a	DET
easat-8674	32	16	poor	poor	ADJ
easat-8674	32	17	understanding	understanding	NOUN
easat-8674	32	18	of	of	ADP
easat-8674	32	19	structural	structural	ADJ
easat-8674	32	20	components	component	NOUN
easat-8674	32	21	[	[	X
easat-8674	32	22	2	2	NUM
easat-8674	32	23	]	]	PUNCT
easat-8674	32	24	.	.	PUNCT
easat-8674	33	1	observations	observation	NOUN
easat-8674	33	2	during	during	ADP
easat-8674	33	3	microteaching	microteache	VERB
easat-8674	33	4	sessions	session	NOUN
easat-8674	33	5	which	which	PRON
easat-8674	33	6	serve	serve	VERB
easat-8674	33	7	as	as	ADP
easat-8674	33	8	a	a	DET
easat-8674	33	9	prerequisite	prerequisite	NOUN
easat-8674	33	10	for	for	ADP
easat-8674	33	11	teaching	teach	VERB
easat-8674	33	12	internships	internship	NOUN
easat-8674	33	13	,	,	PUNCT
easat-8674	33	14	reveal	reveal	VERB
easat-8674	33	15	that	that	SCONJ
easat-8674	33	16	many	many	ADJ
easat-8674	33	17	students	student	NOUN
easat-8674	33	18	incorrectly	incorrectly	ADV
easat-8674	33	19	factor	factor	VERB
easat-8674	33	20	expressions	expression	NOUN
easat-8674	33	21	such	such	ADJ
easat-8674	33	22	as	as	ADP
easat-8674	33	23	𝑎2	𝑎2	NOUN
easat-8674	33	24	−	−	PROPN
easat-8674	33	25	25𝑏2	25𝑏2	NUM
easat-8674	33	26	,	,	PUNCT
easat-8674	33	27	by	by	ADP
easat-8674	33	28	providing	provide	VERB
easat-8674	33	29	flawed	flawed	ADJ
easat-8674	33	30	solutions	solution	NOUN
easat-8674	33	31	like	like	ADP
easat-8674	33	32	(	(	PUNCT
easat-8674	33	33	𝑎	𝑎	NOUN
easat-8674	33	34	−	−	NUM
easat-8674	33	35	25𝑏)(𝑎	25𝑏)(𝑎	NUM
easat-8674	33	36	−	−	PROPN
easat-8674	33	37	25𝑏	25𝑏	NUM
easat-8674	33	38	)	)	PUNCT
easat-8674	33	39	,	,	PUNCT
easat-8674	33	40	indicating	indicate	VERB
easat-8674	33	41	a	a	DET
easat-8674	33	42	lack	lack	NOUN
easat-8674	33	43	of	of	ADP
easat-8674	33	44	understanding	understanding	NOUN
easat-8674	33	45	of	of	ADP
easat-8674	33	46	the	the	DET
easat-8674	33	47	difference	difference	NOUN
easat-8674	33	48	of	of	ADP
easat-8674	33	49	squares	square	NOUN
easat-8674	33	50	.	.	PUNCT
easat-8674	34	1	this	this	DET
easat-8674	34	2	finding	finding	NOUN
easat-8674	34	3	echoes	echo	VERB
easat-8674	34	4	the	the	DET
easat-8674	34	5	results	result	NOUN
easat-8674	34	6	of	of	ADP
easat-8674	34	7	a	a	DET
easat-8674	34	8	recent	recent	ADJ
easat-8674	34	9	meta	meta	ADJ
easat-8674	34	10	-	-	PUNCT
easat-8674	34	11	analysis	analysis	NOUN
easat-8674	34	12	that	that	PRON
easat-8674	34	13	identified	identify	VERB
easat-8674	34	14	conceptual	conceptual	ADJ
easat-8674	34	15	misunderstandings	misunderstanding	NOUN
easat-8674	34	16	in	in	ADP
easat-8674	34	17	algebra	algebra	NOUN
easat-8674	34	18	as	as	ADP
easat-8674	34	19	a	a	DET
easat-8674	34	20	common	common	ADJ
easat-8674	34	21	issue	issue	NOUN
easat-8674	34	22	among	among	ADP
easat-8674	34	23	pre	pre	ADJ
easat-8674	34	24	-	-	ADJ
easat-8674	34	25	service	service	ADJ
easat-8674	34	26	teachers	teacher	NOUN
easat-8674	34	27	across	across	ADP
easat-8674	34	28	various	various	ADJ
easat-8674	34	29	regions	region	NOUN
easat-8674	34	30	[	[	X
easat-8674	34	31	11	11	NUM
easat-8674	34	32	]	]	PUNCT
easat-8674	34	33	.	.	PUNCT
easat-8674	35	1	additionally	additionally	ADV
easat-8674	35	2	,	,	PUNCT
easat-8674	35	3	studies	study	NOUN
easat-8674	35	4	have	have	AUX
easat-8674	35	5	shown	show	VERB
easat-8674	35	6	that	that	SCONJ
easat-8674	35	7	a	a	DET
easat-8674	35	8	significant	significant	ADJ
easat-8674	35	9	portion	portion	NOUN
easat-8674	35	10	of	of	ADP
easat-8674	35	11	mathematics	mathematic	NOUN
easat-8674	35	12	education	education	NOUN
easat-8674	35	13	undergraduates	undergraduate	NOUN
easat-8674	35	14	in	in	ADP
easat-8674	35	15	jombang	jombang	NOUN
easat-8674	35	16	are	be	AUX
easat-8674	35	17	unable	unable	ADJ
easat-8674	35	18	to	to	PART
easat-8674	35	19	solve	solve	VERB
easat-8674	35	20	mathematical	mathematical	ADJ
easat-8674	35	21	problems	problem	NOUN
easat-8674	35	22	conceptually	conceptually	ADV
easat-8674	35	23	[	[	X
easat-8674	35	24	8	8	NUM
easat-8674	35	25	]	]	PUNCT
easat-8674	35	26	.	.	PUNCT
easat-8674	36	1	to	to	PART
easat-8674	36	2	address	address	VERB
easat-8674	36	3	this	this	DET
easat-8674	36	4	gap	gap	NOUN
easat-8674	36	5	,	,	PUNCT
easat-8674	36	6	it	it	PRON
easat-8674	36	7	is	be	AUX
easat-8674	36	8	important	important	ADJ
easat-8674	36	9	to	to	PART
easat-8674	36	10	assess	assess	VERB
easat-8674	36	11	students	student	NOUN
easat-8674	36	12	’	'	PUNCT
easat-8674	36	13	conceptual	conceptual	ADJ
easat-8674	36	14	understanding	understanding	NOUN
easat-8674	36	15	through	through	ADP
easat-8674	36	16	the	the	DET
easat-8674	36	17	content	content	NOUN
easat-8674	36	18	knowledge	knowledge	NOUN
easat-8674	36	19	test	test	PROPN
easat-8674	36	20	(	(	PUNCT
easat-8674	36	21	tck	tck	PROPN
easat-8674	36	22	)	)	PUNCT
easat-8674	36	23	,	,	PUNCT
easat-8674	36	24	which	which	PRON
easat-8674	36	25	evaluates	evaluate	VERB
easat-8674	36	26	their	their	PRON
easat-8674	36	27	ability	ability	NOUN
easat-8674	36	28	to	to	PART
easat-8674	36	29	solve	solve	VERB
easat-8674	36	30	algebraic	algebraic	ADJ
easat-8674	36	31	problems	problem	NOUN
easat-8674	36	32	[	[	X
easat-8674	36	33	12	12	NUM
easat-8674	36	34	]	]	PUNCT
easat-8674	36	35	.	.	PUNCT
easat-8674	37	1	the	the	DET
easat-8674	37	2	tck	tck	PROPN
easat-8674	37	3	serves	serve	VERB
easat-8674	37	4	as	as	ADP
easat-8674	37	5	a	a	DET
easat-8674	37	6	foundational	foundational	ADJ
easat-8674	37	7	assessment	assessment	NOUN
easat-8674	37	8	for	for	ADP
easat-8674	37	9	undergraduate	undergraduate	ADJ
easat-8674	37	10	students	student	NOUN
easat-8674	37	11	before	before	SCONJ
easat-8674	37	12	they	they	PRON
easat-8674	37	13	begin	begin	VERB
easat-8674	37	14	teaching	teach	VERB
easat-8674	37	15	internships	internship	NOUN
easat-8674	37	16	in	in	ADP
easat-8674	37	17	junior	junior	ADJ
easat-8674	37	18	secondary	secondary	ADJ
easat-8674	37	19	schools	school	NOUN
easat-8674	37	20	,	,	PUNCT
easat-8674	37	21	allowing	allow	VERB
easat-8674	37	22	educators	educator	NOUN
easat-8674	37	23	to	to	PART
easat-8674	37	24	infer	infer	VERB
easat-8674	37	25	the	the	DET
easat-8674	37	26	depth	depth	NOUN
easat-8674	37	27	and	and	CCONJ
easat-8674	37	28	diversity	diversity	NOUN
easat-8674	37	29	of	of	ADP
easat-8674	37	30	students	student	NOUN
easat-8674	37	31	’	'	PUNCT
easat-8674	37	32	mathematical	mathematical	ADJ
easat-8674	37	33	understanding	understanding	NOUN
easat-8674	37	34	even	even	ADV
easat-8674	37	35	when	when	SCONJ
easat-8674	37	36	it	it	PRON
easat-8674	37	37	is	be	AUX
easat-8674	37	38	not	not	PART
easat-8674	37	39	directly	directly	ADV
easat-8674	37	40	observable	observable	ADJ
easat-8674	37	41	.	.	PUNCT
easat-8674	38	1	the	the	DET
easat-8674	38	2	tck	tck	PROPN
easat-8674	38	3	used	use	VERB
easat-8674	38	4	in	in	ADP
easat-8674	38	5	this	this	DET
easat-8674	38	6	study	study	NOUN
easat-8674	38	7	consisted	consist	VERB
easat-8674	38	8	of	of	ADP
easat-8674	38	9	three	three	NUM
easat-8674	38	10	algebra	algebra	NOUN
easat-8674	38	11	-	-	PUNCT
easat-8674	38	12	based	base	VERB
easat-8674	38	13	problems	problem	NOUN
easat-8674	38	14	designed	design	VERB
easat-8674	38	15	to	to	PART
easat-8674	38	16	explore	explore	VERB
easat-8674	38	17	students	student	NOUN
easat-8674	38	18	’	’	PART
easat-8674	38	19	problem	problem	NOUN
easat-8674	38	20	-	-	PUNCT
easat-8674	38	21	solving	solve	VERB
easat-8674	38	22	abilities	ability	NOUN
easat-8674	38	23	.	.	PUNCT
easat-8674	39	1	problem	problem	NOUN
easat-8674	39	2	-	-	PUNCT
easat-8674	39	3	solving	solve	VERB
easat-8674	39	4	[	[	X
easat-8674	39	5	13	13	NUM
easat-8674	39	6	]	]	PUNCT
easat-8674	39	7	involves	involve	VERB
easat-8674	39	8	applying	apply	VERB
easat-8674	39	9	concepts	concept	NOUN
easat-8674	39	10	and	and	CCONJ
easat-8674	39	11	skills	skill	NOUN
easat-8674	39	12	to	to	PART
easat-8674	39	13	achieve	achieve	VERB
easat-8674	39	14	specific	specific	ADJ
easat-8674	39	15	goals	goal	NOUN
easat-8674	39	16	.	.	PUNCT
easat-8674	40	1	successful	successful	ADJ
easat-8674	40	2	problem	problem	NOUN
easat-8674	40	3	-	-	PUNCT
easat-8674	40	4	solving	solving	NOUN
easat-8674	40	5	requires	require	VERB
easat-8674	40	6	multiple	multiple	ADJ
easat-8674	40	7	cognitive	cognitive	ADJ
easat-8674	40	8	processes	process	NOUN
easat-8674	40	9	,	,	PUNCT
easat-8674	40	10	including	include	VERB
easat-8674	40	11	understanding	understand	VERB
easat-8674	40	12	the	the	DET
easat-8674	40	13	problem	problem	NOUN
easat-8674	40	14	,	,	PUNCT
easat-8674	40	15	organizing	organize	VERB
easat-8674	40	16	information	information	NOUN
easat-8674	40	17	,	,	PUNCT
easat-8674	40	18	identifying	identify	VERB
easat-8674	40	19	relationships	relationship	NOUN
easat-8674	40	20	,	,	PUNCT
easat-8674	40	21	selecting	select	VERB
easat-8674	40	22	strategies	strategy	NOUN
easat-8674	40	23	,	,	PUNCT
easat-8674	40	24	monitoring	monitor	VERB
easat-8674	40	25	progress	progress	NOUN
easat-8674	40	26	,	,	PUNCT
easat-8674	40	27	and	and	CCONJ
easat-8674	40	28	interpreting	interpret	VERB
easat-8674	40	29	mathematical	mathematical	ADJ
easat-8674	40	30	meaning	meaning	NOUN
easat-8674	40	31	.	.	PUNCT
easat-8674	41	1	according	accord	VERB
easat-8674	41	2	pape	pape	NOUN
easat-8674	41	3	[	[	X
easat-8674	41	4	14	14	NUM
easat-8674	41	5	]	]	PUNCT
easat-8674	41	6	students	student	NOUN
easat-8674	41	7	’	'	PUNCT
easat-8674	41	8	problem	problem	NOUN
easat-8674	41	9	-	-	PUNCT
easat-8674	41	10	solving	solve	VERB
easat-8674	41	11	strategies	strategy	NOUN
easat-8674	41	12	can	can	AUX
easat-8674	41	13	be	be	AUX
easat-8674	41	14	categorized	categorize	VERB
easat-8674	41	15	into	into	ADP
easat-8674	41	16	five	five	NUM
easat-8674	41	17	approaches	approach	NOUN
easat-8674	41	18	:	:	PUNCT
easat-8674	41	19	direct	direct	ADJ
easat-8674	41	20	translation	translation	NOUN
easat-8674	41	21	approach	approach	NOUN
easat-8674	41	22	proficient	proficient	ADJ
easat-8674	41	23	(	(	PUNCT
easat-8674	41	24	dta	dta	PROPN
easat-8674	41	25	-	-	PUNCT
easat-8674	41	26	p	p	NOUN
easat-8674	41	27	)	)	PUNCT
easat-8674	41	28	,	,	PUNCT
easat-8674	41	29	direct	direct	ADJ
easat-8674	41	30	translation	translation	NOUN
easat-8674	41	31	approach	approach	NOUN
easat-8674	41	32	nonproficient	nonproficient	NOUN
easat-8674	41	33	(	(	PUNCT
easat-8674	41	34	dta	dta	PROPN
easat-8674	41	35	-	-	PUNCT
easat-8674	41	36	np	np	NOUN
easat-8674	41	37	)	)	PUNCT
easat-8674	41	38	,	,	PUNCT
easat-8674	41	39	direct	direct	ADJ
easat-8674	41	40	translation	translation	NOUN
easat-8674	41	41	approach	approach	NOUN
easat-8674	41	42	limited	limit	VERB
easat-8674	41	43	context	context	NOUN
easat-8674	41	44	(	(	PUNCT
easat-8674	41	45	dta	dta	PROPN
easat-8674	41	46	-	-	PUNCT
easat-8674	41	47	lc	lc	NOUN
easat-8674	41	48	)	)	PUNCT
easat-8674	41	49	,	,	PUNCT
easat-8674	41	50	meaning	meaning	NOUN
easat-8674	41	51	-	-	PUNCT
easat-8674	41	52	based	base	VERB
easat-8674	41	53	approach	approach	NOUN
easat-8674	41	54	full	full	ADJ
easat-8674	41	55	context	context	NOUN
easat-8674	41	56	(	(	PUNCT
easat-8674	41	57	mba	mba	NOUN
easat-8674	41	58	-	-	PUNCT
easat-8674	41	59	fc	fc	NOUN
easat-8674	41	60	)	)	PUNCT
easat-8674	41	61	,	,	PUNCT
easat-8674	41	62	and	and	CCONJ
easat-8674	41	63	meaning	meaning	NOUN
easat-8674	41	64	-	-	PUNCT
easat-8674	41	65	based	base	VERB
easat-8674	41	66	approach	approach	NOUN
easat-8674	41	67	justification	justification	NOUN
easat-8674	41	68	(	(	PUNCT
easat-8674	41	69	mba	mba	NOUN
easat-8674	41	70	-	-	PUNCT
easat-8674	41	71	j	j	NOUN
easat-8674	41	72	)	)	PUNCT
easat-8674	41	73	.	.	PUNCT
easat-8674	42	1	therefore	therefore	ADV
easat-8674	42	2	,	,	PUNCT
easat-8674	42	3	this	this	DET
easat-8674	42	4	study	study	NOUN
easat-8674	42	5	aims	aim	VERB
easat-8674	42	6	to	to	PART
easat-8674	42	7	explore	explore	VERB
easat-8674	42	8	the	the	DET
easat-8674	42	9	content	content	ADJ
easat-8674	42	10	knowledge	knowledge	NOUN
easat-8674	42	11	of	of	ADP
easat-8674	42	12	undergraduate	undergraduate	ADJ
easat-8674	42	13	students	student	NOUN
easat-8674	42	14	in	in	ADP
easat-8674	42	15	solving	solve	VERB
easat-8674	42	16	algebraic	algebraic	ADJ
easat-8674	42	17	problems	problem	NOUN
easat-8674	42	18	.	.	PUNCT
easat-8674	43	1	2	2	X
easat-8674	43	2	.	.	X
easat-8674	43	3	theoretical	theoretical	ADJ
easat-8674	43	4	framework	framework	NOUN
easat-8674	43	5	content	content	NOUN
easat-8674	43	6	knowledge	knowledge	NOUN
easat-8674	43	7	(	(	PUNCT
easat-8674	43	8	ck	ck	NOUN
easat-8674	43	9	)	)	PUNCT
easat-8674	43	10	is	be	AUX
easat-8674	43	11	one	one	NUM
easat-8674	43	12	of	of	ADP
easat-8674	43	13	the	the	DET
easat-8674	43	14	foundational	foundational	ADJ
easat-8674	43	15	components	component	NOUN
easat-8674	43	16	of	of	ADP
easat-8674	43	17	effective	effective	ADJ
easat-8674	43	18	mathematics	mathematic	NOUN
easat-8674	43	19	instruction	instruction	NOUN
easat-8674	43	20	,	,	PUNCT
easat-8674	43	21	particularly	particularly	ADV
easat-8674	43	22	within	within	ADP
easat-8674	43	23	the	the	DET
easat-8674	43	24	context	context	NOUN
easat-8674	43	25	of	of	ADP
easat-8674	43	26	teacher	teacher	NOUN
easat-8674	43	27	education	education	NOUN
easat-8674	43	28	.	.	PUNCT
easat-8674	44	1	this	this	DET
easat-8674	44	2	concept	concept	NOUN
easat-8674	44	3	was	be	AUX
easat-8674	44	4	first	first	ADV
easat-8674	44	5	comprehensively	comprehensively	ADV
easat-8674	44	6	introduced	introduce	VERB
easat-8674	44	7	by	by	ADP
easat-8674	44	8	shulman	shulman	NOUN
easat-8674	44	9	[	[	X
easat-8674	44	10	7	7	NUM
easat-8674	44	11	]	]	PUNCT
easat-8674	44	12	who	who	PRON
easat-8674	44	13	distinguished	distinguish	VERB
easat-8674	44	14	between	between	ADP
easat-8674	44	15	content	content	NOUN
easat-8674	44	16	knowledge	knowledge	NOUN
easat-8674	44	17	and	and	CCONJ
easat-8674	44	18	pedagogical	pedagogical	ADJ
easat-8674	44	19	content	content	NOUN
easat-8674	44	20	knowledge	knowledge	NOUN
easat-8674	44	21	.	.	PUNCT
easat-8674	45	1	ck	ck	PROPN
easat-8674	45	2	refers	refer	VERB
easat-8674	45	3	to	to	ADP
easat-8674	45	4	the	the	DET
easat-8674	45	5	knowledge	knowledge	NOUN
easat-8674	45	6	necessary	necessary	ADJ
easat-8674	45	7	to	to	PART
easat-8674	45	8	understand	understand	VERB
easat-8674	45	9	the	the	DET
easat-8674	45	10	curriculum	curriculum	NOUN
easat-8674	45	11	and	and	CCONJ
easat-8674	45	12	integrate	integrate	VERB
easat-8674	45	13	it	it	PRON
easat-8674	45	14	into	into	ADP
easat-8674	45	15	instruction	instruction	NOUN
easat-8674	45	16	,	,	PUNCT
easat-8674	45	17	particularly	particularly	ADV
easat-8674	45	18	in	in	ADP
easat-8674	45	19	relation	relation	NOUN
easat-8674	45	20	to	to	ADP
easat-8674	45	21	specific	specific	ADJ
easat-8674	45	22	subject	subject	NOUN
easat-8674	45	23	matter	matter	NOUN
easat-8674	45	24	aligned	align	VERB
easat-8674	45	25	with	with	ADP
easat-8674	45	26	grade	grade	NOUN
easat-8674	45	27	-	-	PUNCT
easat-8674	45	28	level	level	NOUN
easat-8674	45	29	expectations	expectation	NOUN
easat-8674	45	30	[	[	X
easat-8674	45	31	15	15	NUM
easat-8674	45	32	]	]	PUNCT
easat-8674	45	33	.	.	PUNCT
easat-8674	46	1	in	in	ADP
easat-8674	46	2	mathematics	mathematic	NOUN
easat-8674	46	3	,	,	PUNCT
easat-8674	46	4	content	content	NOUN
easat-8674	46	5	knowledge	knowledge	NOUN
easat-8674	46	6	encompasses	encompass	VERB
easat-8674	46	7	the	the	DET
easat-8674	46	8	understanding	understanding	NOUN
easat-8674	46	9	of	of	ADP
easat-8674	46	10	concepts	concept	NOUN
easat-8674	46	11	,	,	PUNCT
easat-8674	46	12	rules	rule	NOUN
easat-8674	46	13	,	,	PUNCT
easat-8674	46	14	theorems	theorem	NOUN
easat-8674	46	15	,	,	PUNCT
easat-8674	46	16	and	and	CCONJ
easat-8674	46	17	properties	property	NOUN
easat-8674	46	18	.	.	PUNCT
easat-8674	47	1	it	it	PRON
easat-8674	47	2	includes	include	VERB
easat-8674	47	3	knowledge	knowledge	NOUN
easat-8674	47	4	of	of	ADP
easat-8674	47	5	fundamental	fundamental	ADJ
easat-8674	47	6	mathematical	mathematical	ADJ
easat-8674	47	7	concepts	concept	NOUN
easat-8674	47	8	,	,	PUNCT
easat-8674	47	9	procedural	procedural	ADJ
easat-8674	47	10	fluency	fluency	NOUN
easat-8674	47	11	,	,	PUNCT
easat-8674	47	12	the	the	DET
easat-8674	47	13	interrelation	interrelation	NOUN
easat-8674	47	14	among	among	ADP
easat-8674	47	15	concepts	concept	NOUN
easat-8674	47	16	,	,	PUNCT
easat-8674	47	17	and	and	CCONJ
easat-8674	47	18	various	various	ADJ
easat-8674	47	19	mathematical	mathematical	ADJ
easat-8674	47	20	representations	representation	NOUN
easat-8674	47	21	hill	hill	PROPN
easat-8674	47	22	,	,	PUNCT
easat-8674	47	23	et	et	PROPN
easat-8674	47	24	al	al	PROPN
easat-8674	47	25	.	.	PUNCT
easat-8674	48	1	[	[	X
easat-8674	48	2	5	5	NUM
easat-8674	48	3	]	]	PUNCT
easat-8674	48	4	.	.	PUNCT
easat-8674	49	1	hill	hill	PROPN
easat-8674	49	2	,	,	PUNCT
easat-8674	49	3	et	et	PROPN
easat-8674	49	4	al	al	PROPN
easat-8674	49	5	.	.	PUNCT
easat-8674	50	1	[	[	X
easat-8674	50	2	16	16	NUM
easat-8674	50	3	]	]	PUNCT
easat-8674	50	4	further	far	ADV
easat-8674	50	5	categorize	categorize	VERB
easat-8674	50	6	content	content	ADJ
easat-8674	50	7	knowledge	knowledge	NOUN
easat-8674	50	8	into	into	ADP
easat-8674	50	9	two	two	NUM
easat-8674	50	10	essential	essential	ADJ
easat-8674	50	11	domains	domain	NOUN
easat-8674	50	12	:	:	PUNCT
easat-8674	50	13	common	common	ADJ
easat-8674	50	14	content	content	NOUN
easat-8674	50	15	knowledge	knowledge	NOUN
easat-8674	50	16	(	(	PUNCT
easat-8674	50	17	cck	cck	NOUN
easat-8674	50	18	)	)	PUNCT
easat-8674	50	19	and	and	CCONJ
easat-8674	50	20	specialized	specialized	ADJ
easat-8674	50	21	content	content	NOUN
easat-8674	50	22	knowledge	knowledge	NOUN
easat-8674	50	23	(	(	PUNCT
easat-8674	50	24	sck	sck	PROPN
easat-8674	50	25	)	)	PUNCT
easat-8674	50	26	.	.	PUNCT
easat-8674	51	1	cck	cck	PROPN
easat-8674	51	2	refers	refer	VERB
easat-8674	51	3	to	to	ADP
easat-8674	51	4	the	the	DET
easat-8674	51	5	mathematical	mathematical	ADJ
easat-8674	51	6	knowledge	knowledge	NOUN
easat-8674	51	7	that	that	PRON
easat-8674	51	8	is	be	AUX
easat-8674	51	9	generally	generally	ADV
easat-8674	51	10	accessible	accessible	ADJ
easat-8674	51	11	to	to	ADP
easat-8674	51	12	all	all	DET
easat-8674	51	13	individuals	individual	NOUN
easat-8674	51	14	,	,	PUNCT
easat-8674	51	15	whereas	whereas	SCONJ
easat-8674	51	16	sck	sck	PROPN
easat-8674	51	17	is	be	AUX
easat-8674	51	18	specific	specific	ADJ
easat-8674	51	19	to	to	ADP
easat-8674	51	20	teachers	teacher	NOUN
easat-8674	51	21	and	and	CCONJ
easat-8674	51	22	pertains	pertain	NOUN
easat-8674	51	23	to	to	ADP
easat-8674	51	24	instructional	instructional	ADJ
easat-8674	51	25	contexts	context	NOUN
easat-8674	51	26	for	for	ADP
easat-8674	51	27	instance	instance	NOUN
easat-8674	51	28	,	,	PUNCT
easat-8674	51	29	the	the	DET
easat-8674	51	30	ability	ability	NOUN
easat-8674	51	31	to	to	PART
easat-8674	51	32	identify	identify	VERB
easat-8674	51	33	and	and	CCONJ
easat-8674	51	34	explain	explain	VERB
easat-8674	51	35	students	student	NOUN
easat-8674	51	36	’	’	PART
easat-8674	51	37	mathematical	mathematical	ADJ
easat-8674	51	38	errors	error	NOUN
easat-8674	51	39	.	.	PUNCT
easat-8674	52	1	582	582	NUM
easat-8674	52	2	edelweiss	edelweiss	PROPN
easat-8674	52	3	applied	apply	VERB
easat-8674	52	4	science	science	NOUN
easat-8674	52	5	and	and	CCONJ
easat-8674	52	6	technology	technology	NOUN
easat-8674	52	7	issn	issn	PROPN
easat-8674	52	8	:	:	PUNCT
easat-8674	52	9	2576	2576	NUM
easat-8674	52	10	-	-	SYM
easat-8674	52	11	8484	8484	NUM
easat-8674	52	12	vol	vol	NOUN
easat-8674	52	13	.	.	PROPN
easat-8674	53	1	9	9	NUM
easat-8674	53	2	,	,	PUNCT
easat-8674	53	3	no	no	INTJ
easat-8674	53	4	.	.	NOUN
easat-8674	54	1	7	7	NUM
easat-8674	54	2	:	:	SYM
easat-8674	54	3	580	580	NUM
easat-8674	54	4	-	-	SYM
easat-8674	54	5	594	594	NUM
easat-8674	54	6	,	,	PUNCT
easat-8674	54	7	2025	2025	NUM
easat-8674	54	8	doi	doi	NOUN
easat-8674	54	9	:	:	PUNCT
easat-8674	54	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	54	11	©	©	PROPN
easat-8674	54	12	2025	2025	NUM
easat-8674	54	13	by	by	ADP
easat-8674	54	14	the	the	DET
easat-8674	54	15	authors	author	NOUN
easat-8674	54	16	;	;	PUNCT
easat-8674	54	17	licensee	licensee	PROPN
easat-8674	54	18	learning	learning	NOUN
easat-8674	54	19	gate	gate	NOUN
easat-8674	54	20	therefore	therefore	ADV
easat-8674	54	21	,	,	PUNCT
easat-8674	54	22	the	the	DET
easat-8674	54	23	content	content	NOUN
easat-8674	54	24	knowledge	knowledge	NOUN
easat-8674	54	25	possessed	possess	VERB
easat-8674	54	26	by	by	ADP
easat-8674	54	27	undergraduate	undergraduate	ADJ
easat-8674	54	28	pre	pre	ADJ
easat-8674	54	29	-	-	ADJ
easat-8674	54	30	service	service	ADJ
easat-8674	54	31	teachers	teacher	NOUN
easat-8674	54	32	becomes	become	VERB
easat-8674	54	33	a	a	DET
easat-8674	54	34	critical	critical	ADJ
easat-8674	54	35	prerequisite	prerequisite	NOUN
easat-8674	54	36	for	for	ADP
easat-8674	54	37	conducting	conduct	VERB
easat-8674	54	38	reflective	reflective	ADJ
easat-8674	54	39	and	and	CCONJ
easat-8674	54	40	adaptive	adaptive	ADJ
easat-8674	54	41	teaching	teaching	NOUN
easat-8674	54	42	practices	practice	NOUN
easat-8674	54	43	.	.	PUNCT
easat-8674	55	1	during	during	ADP
easat-8674	55	2	instruction	instruction	NOUN
easat-8674	55	3	,	,	PUNCT
easat-8674	55	4	preservice	preservice	NOUN
easat-8674	55	5	teachers	teacher	NOUN
easat-8674	55	6	are	be	AUX
easat-8674	55	7	required	require	VERB
easat-8674	55	8	to	to	PART
easat-8674	55	9	demonstrate	demonstrate	VERB
easat-8674	55	10	both	both	CCONJ
easat-8674	55	11	conceptual	conceptual	ADJ
easat-8674	55	12	and	and	CCONJ
easat-8674	55	13	procedural	procedural	ADJ
easat-8674	55	14	knowledge	knowledge	NOUN
easat-8674	55	15	,	,	PUNCT
easat-8674	55	16	which	which	PRON
easat-8674	55	17	enables	enable	VERB
easat-8674	55	18	them	they	PRON
easat-8674	55	19	to	to	PART
easat-8674	55	20	solve	solve	VERB
easat-8674	55	21	problems	problem	NOUN
easat-8674	55	22	effectively	effectively	ADV
easat-8674	55	23	and	and	CCONJ
easat-8674	55	24	provide	provide	VERB
easat-8674	55	25	accurate	accurate	ADJ
easat-8674	55	26	explanations	explanation	NOUN
easat-8674	55	27	to	to	ADP
easat-8674	55	28	students	student	NOUN
easat-8674	55	29	[	[	X
easat-8674	55	30	16	16	NUM
easat-8674	55	31	]	]	PUNCT
easat-8674	55	32	.	.	PUNCT
easat-8674	56	1	a	a	DET
easat-8674	56	2	problem	problem	NOUN
easat-8674	56	3	is	be	AUX
easat-8674	56	4	a	a	DET
easat-8674	56	5	theoretical	theoretical	ADJ
easat-8674	56	6	or	or	CCONJ
easat-8674	56	7	practical	practical	ADJ
easat-8674	56	8	difficulty	difficulty	NOUN
easat-8674	56	9	that	that	PRON
easat-8674	56	10	stimulates	stimulate	VERB
easat-8674	56	11	curiosity	curiosity	NOUN
easat-8674	56	12	[	[	X
easat-8674	56	13	17	17	NUM
easat-8674	56	14	]	]	PUNCT
easat-8674	56	15	.	.	PUNCT
easat-8674	57	1	in	in	ADP
easat-8674	57	2	the	the	DET
easat-8674	57	3	context	context	NOUN
easat-8674	57	4	of	of	ADP
easat-8674	57	5	mathematics	mathematics	PROPN
easat-8674	57	6	education	education	NOUN
easat-8674	57	7	,	,	PUNCT
easat-8674	57	8	a	a	DET
easat-8674	57	9	problem	problem	NOUN
easat-8674	57	10	refers	refer	VERB
easat-8674	57	11	to	to	ADP
easat-8674	57	12	a	a	DET
easat-8674	57	13	question	question	NOUN
easat-8674	57	14	or	or	CCONJ
easat-8674	57	15	task	task	NOUN
easat-8674	57	16	drawn	draw	VERB
easat-8674	57	17	from	from	ADP
easat-8674	57	18	everyday	everyday	ADJ
easat-8674	57	19	life	life	NOUN
easat-8674	57	20	that	that	PRON
easat-8674	57	21	requires	require	VERB
easat-8674	57	22	non	non	ADJ
easat-8674	57	23	-	-	ADJ
easat-8674	57	24	routine	routine	ADJ
easat-8674	57	25	procedures	procedure	NOUN
easat-8674	57	26	to	to	PART
easat-8674	57	27	solve	solve	AUX
easat-8674	57	28	typically	typically	ADV
easat-8674	57	29	involving	involve	VERB
easat-8674	57	30	more	more	ADJ
easat-8674	57	31	than	than	ADP
easat-8674	57	32	one	one	NUM
easat-8674	57	33	mathematical	mathematical	ADJ
easat-8674	57	34	operation	operation	NOUN
easat-8674	57	35	,	,	PUNCT
easat-8674	57	36	systematic	systematic	ADJ
easat-8674	57	37	problem	problem	NOUN
easat-8674	57	38	-	-	PUNCT
easat-8674	57	39	solving	solve	VERB
easat-8674	57	40	steps	step	NOUN
easat-8674	57	41	,	,	PUNCT
easat-8674	57	42	in	in	ADP
easat-8674	57	43	-	-	PUNCT
easat-8674	57	44	depth	depth	NOUN
easat-8674	57	45	analysis	analysis	NOUN
easat-8674	57	46	,	,	PUNCT
easat-8674	57	47	and	and	CCONJ
easat-8674	57	48	the	the	DET
easat-8674	57	49	application	application	NOUN
easat-8674	57	50	of	of	ADP
easat-8674	57	51	different	different	ADJ
easat-8674	57	52	procedures	procedure	NOUN
easat-8674	57	53	to	to	PART
easat-8674	57	54	arrive	arrive	VERB
easat-8674	57	55	at	at	ADP
easat-8674	57	56	a	a	DET
easat-8674	57	57	solution	solution	NOUN
easat-8674	57	58	[	[	X
easat-8674	57	59	18	18	NUM
easat-8674	57	60	]	]	PUNCT
easat-8674	57	61	.	.	PUNCT
easat-8674	58	1	problems	problem	NOUN
easat-8674	58	2	used	use	VERB
easat-8674	58	3	in	in	ADP
easat-8674	58	4	mathematics	mathematics	NOUN
easat-8674	58	5	instruction	instruction	NOUN
easat-8674	58	6	are	be	AUX
easat-8674	58	7	often	often	ADV
easat-8674	58	8	contextualized	contextualize	VERB
easat-8674	58	9	within	within	ADP
easat-8674	58	10	daily	daily	ADJ
easat-8674	58	11	experiences	experience	NOUN
easat-8674	58	12	and	and	CCONJ
easat-8674	58	13	necessitate	necessitate	ADJ
easat-8674	58	14	non	non	ADJ
easat-8674	58	15	-	-	ADJ
easat-8674	58	16	routine	routine	ADJ
easat-8674	58	17	strategies	strategy	NOUN
easat-8674	58	18	for	for	ADP
easat-8674	58	19	resolution	resolution	NOUN
easat-8674	58	20	.	.	PUNCT
easat-8674	59	1	therefore	therefore	ADV
easat-8674	59	2	,	,	PUNCT
easat-8674	59	3	problem	problem	NOUN
easat-8674	59	4	-	-	PUNCT
easat-8674	59	5	solving	solving	NOUN
easat-8674	59	6	is	be	AUX
easat-8674	59	7	regarded	regard	VERB
easat-8674	59	8	as	as	ADP
easat-8674	59	9	a	a	DET
easat-8674	59	10	central	central	ADJ
easat-8674	59	11	component	component	NOUN
easat-8674	59	12	of	of	ADP
easat-8674	59	13	mathematics	mathematic	NOUN
easat-8674	59	14	learning	learn	VERB
easat-8674	59	15	[	[	X
easat-8674	59	16	17	17	NUM
easat-8674	59	17	]	]	PUNCT
easat-8674	59	18	.	.	PUNCT
easat-8674	60	1	problem	problem	NOUN
easat-8674	60	2	-	-	PUNCT
easat-8674	60	3	solving	solve	VERB
easat-8674	60	4	approaches	approach	NOUN
easat-8674	60	5	can	can	AUX
easat-8674	60	6	be	be	AUX
easat-8674	60	7	categorized	categorize	VERB
easat-8674	60	8	into	into	ADP
easat-8674	60	9	two	two	NUM
easat-8674	60	10	major	major	ADJ
easat-8674	60	11	types	type	NOUN
easat-8674	60	12	[	[	X
easat-8674	60	13	14	14	NUM
easat-8674	60	14	]	]	X
easat-8674	60	15	:	:	PUNCT
easat-8674	60	16	the	the	DET
easat-8674	60	17	direct	direct	ADJ
easat-8674	60	18	translation	translation	NOUN
easat-8674	60	19	approach	approach	NOUN
easat-8674	60	20	(	(	PUNCT
easat-8674	60	21	dta	dta	PROPN
easat-8674	60	22	)	)	PUNCT
easat-8674	60	23	and	and	CCONJ
easat-8674	60	24	the	the	DET
easat-8674	60	25	meaningbased	meaningbase	VERB
easat-8674	60	26	approach	approach	NOUN
easat-8674	60	27	(	(	PUNCT
easat-8674	60	28	mba	mba	NOUN
easat-8674	60	29	)	)	PUNCT
easat-8674	60	30	.	.	PUNCT
easat-8674	61	1	the	the	DET
easat-8674	61	2	direct	direct	ADJ
easat-8674	61	3	translation	translation	NOUN
easat-8674	61	4	approach	approach	NOUN
easat-8674	61	5	is	be	AUX
easat-8674	61	6	characterized	characterize	VERB
easat-8674	61	7	by	by	ADP
easat-8674	61	8	a	a	DET
easat-8674	61	9	limited	limited	ADJ
easat-8674	61	10	ability	ability	NOUN
easat-8674	61	11	among	among	ADP
easat-8674	61	12	students	student	NOUN
easat-8674	61	13	to	to	PART
easat-8674	61	14	transform	transform	VERB
easat-8674	61	15	the	the	DET
easat-8674	61	16	information	information	NOUN
easat-8674	61	17	presented	present	VERB
easat-8674	61	18	in	in	ADP
easat-8674	61	19	a	a	DET
easat-8674	61	20	problem	problem	NOUN
easat-8674	61	21	into	into	ADP
easat-8674	61	22	mathematical	mathematical	ADJ
easat-8674	61	23	expressions	expression	NOUN
easat-8674	61	24	.	.	PUNCT
easat-8674	62	1	this	this	PRON
easat-8674	62	2	includes	include	VERB
easat-8674	62	3	a	a	DET
easat-8674	62	4	lack	lack	NOUN
easat-8674	62	5	of	of	ADP
easat-8674	62	6	context	context	NOUN
easat-8674	62	7	integration	integration	NOUN
easat-8674	62	8	,	,	PUNCT
easat-8674	62	9	insufficient	insufficient	ADJ
easat-8674	62	10	use	use	NOUN
easat-8674	62	11	of	of	ADP
easat-8674	62	12	relevant	relevant	ADJ
easat-8674	62	13	mathematical	mathematical	ADJ
easat-8674	62	14	concepts	concept	NOUN
easat-8674	62	15	,	,	PUNCT
easat-8674	62	16	and	and	CCONJ
easat-8674	62	17	difficulty	difficulty	NOUN
easat-8674	62	18	in	in	ADP
easat-8674	62	19	connecting	connect	VERB
easat-8674	62	20	various	various	ADJ
easat-8674	62	21	pieces	piece	NOUN
easat-8674	62	22	of	of	ADP
easat-8674	62	23	information	information	NOUN
easat-8674	62	24	within	within	ADP
easat-8674	62	25	the	the	DET
easat-8674	62	26	problem	problem	NOUN
easat-8674	62	27	.	.	PUNCT
easat-8674	63	1	dta	dta	PROPN
easat-8674	63	2	is	be	AUX
easat-8674	63	3	further	far	ADV
easat-8674	63	4	divided	divide	VERB
easat-8674	63	5	into	into	ADP
easat-8674	63	6	three	three	NUM
easat-8674	63	7	subcategories	subcategorie	NOUN
easat-8674	63	8	:	:	PUNCT
easat-8674	63	9	dta	dta	NOUN
easat-8674	63	10	-	-	PUNCT
easat-8674	63	11	proficient	proficient	ADJ
easat-8674	63	12	(	(	PUNCT
easat-8674	63	13	dta	dta	PROPN
easat-8674	63	14	-	-	PUNCT
easat-8674	63	15	p	p	NOUN
easat-8674	63	16	):	):	PUNCT
easat-8674	63	17	students	student	NOUN
easat-8674	63	18	in	in	ADP
easat-8674	63	19	this	this	DET
easat-8674	63	20	category	category	NOUN
easat-8674	63	21	utilize	utilize	VERB
easat-8674	63	22	the	the	DET
easat-8674	63	23	given	give	VERB
easat-8674	63	24	information	information	NOUN
easat-8674	63	25	automatically	automatically	ADV
easat-8674	63	26	and	and	CCONJ
easat-8674	63	27	efficiently	efficiently	ADV
easat-8674	63	28	in	in	ADP
easat-8674	63	29	mathematical	mathematical	ADJ
easat-8674	63	30	computations	computation	NOUN
easat-8674	63	31	,	,	PUNCT
easat-8674	63	32	typically	typically	ADV
easat-8674	63	33	relying	rely	VERB
easat-8674	63	34	on	on	ADP
easat-8674	63	35	their	their	PRON
easat-8674	63	36	initial	initial	ADJ
easat-8674	63	37	reading	reading	NOUN
easat-8674	63	38	of	of	ADP
easat-8674	63	39	the	the	DET
easat-8674	63	40	problem	problem	NOUN
easat-8674	63	41	without	without	ADP
easat-8674	63	42	needing	need	VERB
easat-8674	63	43	to	to	PART
easat-8674	63	44	reread	reread	VERB
easat-8674	63	45	it	it	PRON
easat-8674	63	46	.	.	PUNCT
easat-8674	64	1	dta	dta	PROPN
easat-8674	64	2	-	-	PUNCT
easat-8674	64	3	non	non	ADJ
easat-8674	64	4	-	-	ADJ
easat-8674	64	5	proficient	proficient	ADJ
easat-8674	64	6	(	(	PUNCT
easat-8674	64	7	dta	dta	PROPN
easat-8674	64	8	-	-	PUNCT
easat-8674	64	9	np	np	INTJ
easat-8674	64	10	):	):	PUNCT
easat-8674	64	11	students	student	NOUN
easat-8674	64	12	exhibit	exhibit	VERB
easat-8674	64	13	low	low	ADJ
easat-8674	64	14	competence	competence	NOUN
easat-8674	64	15	in	in	ADP
easat-8674	64	16	reading	read	VERB
easat-8674	64	17	comprehension	comprehension	NOUN
easat-8674	64	18	,	,	PUNCT
easat-8674	64	19	problem	problem	NOUN
easat-8674	64	20	understanding	understanding	NOUN
easat-8674	64	21	,	,	PUNCT
easat-8674	64	22	solution	solution	NOUN
easat-8674	64	23	planning	planning	NOUN
easat-8674	64	24	,	,	PUNCT
easat-8674	64	25	and	and	CCONJ
easat-8674	64	26	mathematical	mathematical	ADJ
easat-8674	64	27	computation	computation	NOUN
easat-8674	64	28	.	.	PUNCT
easat-8674	65	1	dta	dta	PROPN
easat-8674	65	2	-	-	PUNCT
easat-8674	65	3	limited	limit	VERB
easat-8674	65	4	context	context	NOUN
easat-8674	65	5	(	(	PUNCT
easat-8674	65	6	dta	dta	PROPN
easat-8674	65	7	-	-	PUNCT
easat-8674	65	8	lc	lc	NOUN
easat-8674	66	1	):	):	PUNCT
easat-8674	66	2	students	student	NOUN
easat-8674	66	3	apply	apply	VERB
easat-8674	66	4	the	the	DET
easat-8674	66	5	given	give	VERB
easat-8674	66	6	data	datum	NOUN
easat-8674	66	7	directly	directly	ADV
easat-8674	66	8	into	into	ADP
easat-8674	66	9	computations	computation	NOUN
easat-8674	66	10	but	but	CCONJ
easat-8674	66	11	provide	provide	VERB
easat-8674	66	12	minimal	minimal	ADJ
easat-8674	66	13	contextual	contextual	ADJ
easat-8674	66	14	explanation	explanation	NOUN
easat-8674	66	15	related	relate	VERB
easat-8674	66	16	to	to	ADP
easat-8674	66	17	the	the	DET
easat-8674	66	18	problem	problem	NOUN
easat-8674	66	19	.	.	PUNCT
easat-8674	67	1	in	in	ADP
easat-8674	67	2	contrast	contrast	NOUN
easat-8674	67	3	,	,	PUNCT
easat-8674	67	4	the	the	DET
easat-8674	67	5	meaning	meaning	NOUN
easat-8674	67	6	-	-	PUNCT
easat-8674	67	7	based	base	VERB
easat-8674	67	8	approach	approach	NOUN
easat-8674	67	9	(	(	PUNCT
easat-8674	67	10	mba	mba	NOUN
easat-8674	67	11	)	)	PUNCT
easat-8674	67	12	is	be	AUX
easat-8674	67	13	marked	mark	VERB
easat-8674	67	14	by	by	ADP
easat-8674	67	15	three	three	NUM
easat-8674	67	16	key	key	ADJ
easat-8674	67	17	features	feature	NOUN
easat-8674	67	18	:	:	PUNCT
easat-8674	67	19	documenting	document	VERB
easat-8674	67	20	given	give	VERB
easat-8674	67	21	information	information	NOUN
easat-8674	67	22	,	,	PUNCT
easat-8674	67	23	utilizing	utilize	VERB
easat-8674	67	24	the	the	DET
easat-8674	67	25	context	context	NOUN
easat-8674	67	26	of	of	ADP
easat-8674	67	27	the	the	DET
easat-8674	67	28	problem	problem	NOUN
easat-8674	67	29	,	,	PUNCT
easat-8674	67	30	and	and	CCONJ
easat-8674	67	31	offering	offer	VERB
easat-8674	67	32	logical	logical	ADJ
easat-8674	67	33	justifications	justification	NOUN
easat-8674	67	34	for	for	ADP
easat-8674	67	35	the	the	DET
easat-8674	67	36	mathematical	mathematical	ADJ
easat-8674	67	37	operations	operation	NOUN
easat-8674	67	38	employed	employ	VERB
easat-8674	67	39	.	.	PUNCT
easat-8674	68	1	mba	mba	NOUN
easat-8674	68	2	is	be	AUX
easat-8674	68	3	divided	divide	VERB
easat-8674	68	4	into	into	ADP
easat-8674	68	5	two	two	NUM
easat-8674	68	6	subcategories	subcategorie	NOUN
easat-8674	68	7	:	:	PUNCT
easat-8674	68	8	mba	mba	ADJ
easat-8674	68	9	-	-	PUNCT
easat-8674	68	10	full	full	ADJ
easat-8674	68	11	context	context	NOUN
easat-8674	68	12	(	(	PUNCT
easat-8674	68	13	mba	mba	NOUN
easat-8674	68	14	-	-	PUNCT
easat-8674	68	15	fc	fc	PROPN
easat-8674	68	16	):	):	PUNCT
easat-8674	68	17	students	student	NOUN
easat-8674	68	18	carefully	carefully	ADV
easat-8674	68	19	read	read	VERB
easat-8674	68	20	each	each	DET
easat-8674	68	21	sentence	sentence	NOUN
easat-8674	68	22	of	of	ADP
easat-8674	68	23	the	the	DET
easat-8674	68	24	problem	problem	NOUN
easat-8674	68	25	and	and	CCONJ
easat-8674	68	26	fully	fully	ADV
easat-8674	68	27	consider	consider	VERB
easat-8674	68	28	the	the	DET
easat-8674	68	29	context	context	NOUN
easat-8674	68	30	in	in	ADP
easat-8674	68	31	their	their	PRON
easat-8674	68	32	problem	problem	NOUN
easat-8674	68	33	-	-	PUNCT
easat-8674	68	34	solving	solve	VERB
easat-8674	68	35	process	process	NOUN
easat-8674	68	36	.	.	PUNCT
easat-8674	69	1	mba	mba	NOUN
easat-8674	69	2	-	-	PUNCT
easat-8674	69	3	justification	justification	NOUN
easat-8674	69	4	(	(	PUNCT
easat-8674	69	5	mba	mba	NOUN
easat-8674	69	6	-	-	PUNCT
easat-8674	69	7	j	j	NOUN
easat-8674	69	8	):	):	PUNCT
easat-8674	69	9	students	student	NOUN
easat-8674	69	10	approach	approach	VERB
easat-8674	69	11	each	each	DET
easat-8674	69	12	problem	problem	NOUN
easat-8674	69	13	using	use	VERB
easat-8674	69	14	a	a	DET
easat-8674	69	15	structured	structured	ADJ
easat-8674	69	16	schema	schema	NOUN
easat-8674	69	17	,	,	PUNCT
easat-8674	69	18	incorporating	incorporate	VERB
easat-8674	69	19	logical	logical	ADJ
easat-8674	69	20	reasoning	reasoning	NOUN
easat-8674	69	21	and	and	CCONJ
easat-8674	69	22	contextual	contextual	ADJ
easat-8674	69	23	interpretation	interpretation	NOUN
easat-8674	69	24	.	.	PUNCT
easat-8674	70	1	several	several	ADJ
easat-8674	70	2	studies	study	NOUN
easat-8674	70	3	have	have	AUX
easat-8674	70	4	highlighted	highlight	VERB
easat-8674	70	5	the	the	DET
easat-8674	70	6	lack	lack	NOUN
easat-8674	70	7	of	of	ADP
easat-8674	70	8	content	content	ADJ
easat-8674	70	9	knowledge	knowledge	NOUN
easat-8674	70	10	among	among	ADP
easat-8674	70	11	undergraduate	undergraduate	ADJ
easat-8674	70	12	students	student	NOUN
easat-8674	70	13	when	when	SCONJ
easat-8674	70	14	engaging	engage	VERB
easat-8674	70	15	in	in	ADP
easat-8674	70	16	conventional	conventional	ADJ
easat-8674	70	17	instructional	instructional	ADJ
easat-8674	70	18	settings	setting	NOUN
easat-8674	70	19	,	,	PUNCT
easat-8674	70	20	particularly	particularly	ADV
easat-8674	70	21	in	in	ADP
easat-8674	70	22	solving	solve	VERB
easat-8674	70	23	algebraic	algebraic	ADJ
easat-8674	70	24	problems	problem	NOUN
easat-8674	70	25	[	[	X
easat-8674	70	26	3	3	NUM
easat-8674	70	27	]	]	PUNCT
easat-8674	70	28	.	.	PUNCT
easat-8674	71	1	this	this	DET
easat-8674	71	2	gap	gap	NOUN
easat-8674	71	3	in	in	ADP
easat-8674	71	4	content	content	NOUN
easat-8674	71	5	understanding	understanding	NOUN
easat-8674	71	6	underscores	underscore	VERB
easat-8674	71	7	the	the	DET
easat-8674	71	8	necessity	necessity	NOUN
easat-8674	71	9	of	of	ADP
easat-8674	71	10	equipping	equip	VERB
easat-8674	71	11	preservice	preservice	NOUN
easat-8674	71	12	teachers	teacher	NOUN
easat-8674	71	13	with	with	ADP
easat-8674	71	14	both	both	CCONJ
easat-8674	71	15	conceptual	conceptual	ADJ
easat-8674	71	16	and	and	CCONJ
easat-8674	71	17	procedural	procedural	ADJ
easat-8674	71	18	knowledge	knowledge	NOUN
easat-8674	71	19	to	to	PART
easat-8674	71	20	enhance	enhance	VERB
easat-8674	71	21	their	their	PRON
easat-8674	71	22	problem	problem	NOUN
easat-8674	71	23	-	-	PUNCT
easat-8674	71	24	solving	solve	VERB
easat-8674	71	25	competence	competence	NOUN
easat-8674	71	26	in	in	ADP
easat-8674	71	27	mathematics	mathematics	NOUN
easat-8674	71	28	education	education	NOUN
easat-8674	71	29	algebra	algebra	NOUN
easat-8674	71	30	is	be	AUX
easat-8674	71	31	a	a	DET
easat-8674	71	32	branch	branch	NOUN
easat-8674	71	33	of	of	ADP
easat-8674	71	34	mathematics	mathematic	NOUN
easat-8674	71	35	concerned	concern	VERB
easat-8674	71	36	with	with	ADP
easat-8674	71	37	the	the	DET
easat-8674	71	38	use	use	NOUN
easat-8674	71	39	of	of	ADP
easat-8674	71	40	symbols	symbol	NOUN
easat-8674	71	41	and	and	CCONJ
easat-8674	71	42	rules	rule	NOUN
easat-8674	71	43	to	to	PART
easat-8674	71	44	achieve	achieve	VERB
easat-8674	71	45	specific	specific	ADJ
easat-8674	71	46	objectives	objective	NOUN
easat-8674	71	47	[	[	X
easat-8674	71	48	19	19	NUM
easat-8674	71	49	]	]	PUNCT
easat-8674	71	50	.	.	PUNCT
easat-8674	72	1	the	the	DET
easat-8674	72	2	nature	nature	NOUN
easat-8674	72	3	of	of	ADP
easat-8674	72	4	algebra	algebra	NOUN
easat-8674	72	5	at	at	ADP
easat-8674	72	6	the	the	DET
easat-8674	72	7	university	university	NOUN
easat-8674	72	8	level	level	NOUN
easat-8674	72	9	differs	differ	VERB
easat-8674	72	10	significantly	significantly	ADV
easat-8674	72	11	from	from	ADP
easat-8674	72	12	the	the	DET
easat-8674	72	13	algebra	algebra	NOUN
easat-8674	72	14	taught	teach	VERB
easat-8674	72	15	in	in	ADP
easat-8674	72	16	school	school	NOUN
easat-8674	72	17	settings	setting	NOUN
easat-8674	72	18	.	.	PUNCT
easat-8674	73	1	at	at	ADP
easat-8674	73	2	the	the	DET
easat-8674	73	3	school	school	NOUN
easat-8674	73	4	level	level	NOUN
easat-8674	73	5	,	,	PUNCT
easat-8674	73	6	algebra	algebra	NOUN
easat-8674	73	7	primarily	primarily	ADV
easat-8674	73	8	involves	involve	VERB
easat-8674	73	9	the	the	DET
easat-8674	73	10	understanding	understanding	NOUN
easat-8674	73	11	of	of	ADP
easat-8674	73	12	variables	variable	NOUN
easat-8674	73	13	and	and	CCONJ
easat-8674	73	14	the	the	DET
easat-8674	73	15	operations	operation	NOUN
easat-8674	73	16	associated	associate	VERB
easat-8674	73	17	with	with	ADP
easat-8674	73	18	them	they	PRON
easat-8674	73	19	[	[	X
easat-8674	73	20	20	20	NUM
easat-8674	73	21	]	]	PUNCT
easat-8674	73	22	.	.	PUNCT
easat-8674	74	1	algebraic	algebraic	ADJ
easat-8674	74	2	problems	problem	NOUN
easat-8674	74	3	frequently	frequently	ADV
easat-8674	74	4	require	require	VERB
easat-8674	74	5	generalization	generalization	NOUN
easat-8674	74	6	,	,	PUNCT
easat-8674	74	7	symbolic	symbolic	ADJ
easat-8674	74	8	manipulation	manipulation	NOUN
easat-8674	74	9	,	,	PUNCT
easat-8674	74	10	as	as	ADV
easat-8674	74	11	well	well	ADV
easat-8674	74	12	as	as	ADP
easat-8674	74	13	numerical	numerical	ADJ
easat-8674	74	14	and	and	CCONJ
easat-8674	74	15	graphical	graphical	ADJ
easat-8674	74	16	representations	representation	NOUN
easat-8674	74	17	[	[	X
easat-8674	74	18	21	21	NUM
easat-8674	74	19	]	]	PUNCT
easat-8674	74	20	.	.	PUNCT
easat-8674	75	1	these	these	DET
easat-8674	75	2	problems	problem	NOUN
easat-8674	75	3	can	can	AUX
easat-8674	75	4	be	be	AUX
easat-8674	75	5	broadly	broadly	ADV
easat-8674	75	6	classified	classify	VERB
easat-8674	75	7	into	into	ADP
easat-8674	75	8	three	three	NUM
easat-8674	75	9	categories	category	NOUN
easat-8674	75	10	:	:	PUNCT
easat-8674	75	11	(	(	PUNCT
easat-8674	75	12	1	1	X
easat-8674	75	13	)	)	PUNCT
easat-8674	75	14	routine	routine	ADJ
easat-8674	75	15	problems	problem	NOUN
easat-8674	75	16	,	,	PUNCT
easat-8674	75	17	which	which	PRON
easat-8674	75	18	emphasize	emphasize	VERB
easat-8674	75	19	the	the	DET
easat-8674	75	20	application	application	NOUN
easat-8674	75	21	of	of	ADP
easat-8674	75	22	specific	specific	ADJ
easat-8674	75	23	algorithms	algorithm	NOUN
easat-8674	75	24	;	;	PUNCT
easat-8674	75	25	(	(	PUNCT
easat-8674	75	26	2	2	X
easat-8674	75	27	)	)	PUNCT
easat-8674	75	28	non	non	ADJ
easat-8674	75	29	-	-	ADJ
easat-8674	75	30	routine	routine	ADJ
easat-8674	75	31	problems	problem	NOUN
easat-8674	75	32	,	,	PUNCT
easat-8674	75	33	which	which	PRON
easat-8674	75	34	demand	demand	VERB
easat-8674	75	35	flexible	flexible	ADJ
easat-8674	75	36	and	and	CCONJ
easat-8674	75	37	strategic	strategic	ADJ
easat-8674	75	38	problem	problem	NOUN
easat-8674	75	39	-	-	PUNCT
easat-8674	75	40	solving	solve	VERB
easat-8674	75	41	approaches	approach	NOUN
easat-8674	75	42	;	;	PUNCT
easat-8674	75	43	and	and	CCONJ
easat-8674	75	44	(	(	PUNCT
easat-8674	75	45	3	3	X
easat-8674	75	46	)	)	PUNCT
easat-8674	75	47	contextual	contextual	ADJ
easat-8674	75	48	problems	problem	NOUN
easat-8674	75	49	,	,	PUNCT
easat-8674	75	50	which	which	PRON
easat-8674	75	51	incorporate	incorporate	VERB
easat-8674	75	52	real	real	ADJ
easat-8674	75	53	-	-	PUNCT
easat-8674	75	54	world	world	NOUN
easat-8674	75	55	situations	situation	NOUN
easat-8674	75	56	.	.	PUNCT
easat-8674	76	1	solving	solve	VERB
easat-8674	76	2	algebraic	algebraic	ADJ
easat-8674	76	3	problems	problem	NOUN
easat-8674	76	4	necessitates	necessitate	VERB
easat-8674	76	5	mastery	mastery	NOUN
easat-8674	76	6	of	of	ADP
easat-8674	76	7	fundamental	fundamental	ADJ
easat-8674	76	8	concepts	concept	NOUN
easat-8674	76	9	,	,	PUNCT
easat-8674	76	10	along	along	ADP
easat-8674	76	11	with	with	ADP
easat-8674	76	12	the	the	DET
easat-8674	76	13	capacity	capacity	NOUN
easat-8674	76	14	for	for	ADP
easat-8674	76	15	abstract	abstract	ADJ
easat-8674	76	16	and	and	CCONJ
easat-8674	76	17	symbolic	symbolic	ADJ
easat-8674	76	18	reasoning	reasoning	NOUN
easat-8674	76	19	—	—	PUNCT
easat-8674	76	20	skills	skill	NOUN
easat-8674	76	21	that	that	PRON
easat-8674	76	22	often	often	ADV
easat-8674	76	23	present	present	VERB
easat-8674	76	24	challenges	challenge	NOUN
easat-8674	76	25	for	for	ADP
easat-8674	76	26	undergraduate	undergraduate	ADJ
easat-8674	76	27	students	student	NOUN
easat-8674	76	28	[	[	X
easat-8674	76	29	22	22	NUM
easat-8674	76	30	]	]	PUNCT
easat-8674	76	31	.	.	PUNCT
easat-8674	77	1	students	student	NOUN
easat-8674	77	2	with	with	ADP
easat-8674	77	3	strong	strong	ADJ
easat-8674	77	4	content	content	NOUN
easat-8674	77	5	knowledge	knowledge	NOUN
easat-8674	77	6	tend	tend	VERB
easat-8674	77	7	to	to	PART
easat-8674	77	8	recognize	recognize	VERB
easat-8674	77	9	mathematical	mathematical	ADJ
easat-8674	77	10	structures	structure	NOUN
easat-8674	77	11	within	within	ADP
easat-8674	77	12	algebraic	algebraic	ADJ
easat-8674	77	13	problems	problem	NOUN
easat-8674	77	14	and	and	CCONJ
easat-8674	77	15	employ	employ	VERB
easat-8674	77	16	appropriate	appropriate	ADJ
easat-8674	77	17	solution	solution	NOUN
easat-8674	77	18	strategies	strategy	NOUN
easat-8674	77	19	.	.	PUNCT
easat-8674	78	1	in	in	ADP
easat-8674	78	2	contrast	contrast	NOUN
easat-8674	78	3	,	,	PUNCT
easat-8674	78	4	limited	limited	ADJ
easat-8674	78	5	conceptual	conceptual	ADJ
easat-8674	78	6	understanding	understanding	NOUN
easat-8674	78	7	often	often	ADV
easat-8674	78	8	results	result	VERB
easat-8674	78	9	in	in	ADP
easat-8674	78	10	systematic	systematic	ADJ
easat-8674	78	11	errors	error	NOUN
easat-8674	78	12	,	,	PUNCT
easat-8674	78	13	such	such	ADJ
easat-8674	78	14	as	as	ADP
easat-8674	78	15	mistakes	mistake	NOUN
easat-8674	78	16	in	in	ADP
easat-8674	78	17	symbolic	symbolic	ADJ
easat-8674	78	18	manipulation	manipulation	NOUN
easat-8674	78	19	,	,	PUNCT
easat-8674	78	20	misapplication	misapplication	NOUN
easat-8674	78	21	of	of	ADP
easat-8674	78	22	operational	operational	ADJ
easat-8674	78	23	rules	rule	NOUN
easat-8674	78	24	,	,	PUNCT
easat-8674	78	25	or	or	CCONJ
easat-8674	78	26	misconceptions	misconception	NOUN
easat-8674	78	27	regarding	regard	VERB
easat-8674	78	28	the	the	DET
easat-8674	78	29	meaning	meaning	NOUN
easat-8674	78	30	of	of	ADP
easat-8674	78	31	variables	variable	NOUN
easat-8674	78	32	[	[	X
easat-8674	78	33	23	23	NUM
easat-8674	78	34	]	]	PUNCT
easat-8674	78	35	.	.	PUNCT
easat-8674	79	1	as	as	ADP
easat-8674	79	2	such	such	ADJ
easat-8674	79	3	,	,	PUNCT
easat-8674	79	4	the	the	DET
easat-8674	79	5	algebraic	algebraic	ADJ
easat-8674	79	6	content	content	NOUN
easat-8674	79	7	knowledge	knowledge	NOUN
easat-8674	79	8	of	of	ADP
easat-8674	79	9	undergraduate	undergraduate	ADJ
easat-8674	79	10	students	student	NOUN
easat-8674	79	11	has	have	AUX
easat-8674	79	12	become	become	VERB
easat-8674	79	13	a	a	DET
easat-8674	79	14	focal	focal	ADJ
easat-8674	79	15	point	point	NOUN
easat-8674	79	16	in	in	ADP
easat-8674	79	17	studies	study	NOUN
easat-8674	79	18	examining	examine	VERB
easat-8674	79	19	the	the	DET
easat-8674	79	20	readiness	readiness	NOUN
easat-8674	79	21	of	of	ADP
easat-8674	79	22	prospective	prospective	ADJ
easat-8674	79	23	mathematics	mathematic	NOUN
easat-8674	79	24	teachers	teacher	NOUN
easat-8674	79	25	to	to	PART
easat-8674	79	26	meet	meet	VERB
easat-8674	79	27	the	the	DET
easat-8674	79	28	demands	demand	NOUN
easat-8674	79	29	of	of	ADP
easat-8674	79	30	curriculum	curriculum	NOUN
easat-8674	79	31	reform	reform	NOUN
easat-8674	79	32	and	and	CCONJ
easat-8674	79	33	problem	problem	NOUN
easat-8674	79	34	-	-	PUNCT
easat-8674	79	35	based	base	VERB
easat-8674	79	36	instruction	instruction	NOUN
easat-8674	79	37	.	.	PUNCT
easat-8674	80	1	zazkis	zazki	NOUN
easat-8674	80	2	and	and	CCONJ
easat-8674	80	3	leikin	leikin	VERB
easat-8674	80	4	[	[	X
easat-8674	80	5	23	23	NUM
easat-8674	80	6	]	]	PUNCT
easat-8674	80	7	noted	note	VERB
easat-8674	80	8	that	that	SCONJ
easat-8674	80	9	prospective	prospective	ADJ
easat-8674	80	10	teachers	teacher	NOUN
easat-8674	80	11	frequently	frequently	ADV
easat-8674	80	12	exhibit	exhibit	VERB
easat-8674	80	13	a	a	DET
easat-8674	80	14	gap	gap	NOUN
easat-8674	80	15	between	between	ADP
easat-8674	80	16	procedural	procedural	ADJ
easat-8674	80	17	fluency	fluency	NOUN
easat-8674	80	18	and	and	CCONJ
easat-8674	80	19	conceptual	conceptual	ADJ
easat-8674	80	20	understanding	understanding	NOUN
easat-8674	80	21	when	when	SCONJ
easat-8674	80	22	solving	solve	VERB
easat-8674	80	23	583	583	NUM
easat-8674	80	24	edelweiss	edelweiss	PROPN
easat-8674	80	25	applied	apply	VERB
easat-8674	80	26	science	science	NOUN
easat-8674	80	27	and	and	CCONJ
easat-8674	80	28	technology	technology	NOUN
easat-8674	80	29	issn	issn	PROPN
easat-8674	80	30	:	:	PUNCT
easat-8674	80	31	2576	2576	NUM
easat-8674	80	32	-	-	SYM
easat-8674	80	33	8484	8484	NUM
easat-8674	80	34	vol	vol	NOUN
easat-8674	80	35	.	.	PROPN
easat-8674	81	1	9	9	NUM
easat-8674	81	2	,	,	PUNCT
easat-8674	81	3	no	no	INTJ
easat-8674	81	4	.	.	NOUN
easat-8674	82	1	7	7	NUM
easat-8674	82	2	:	:	SYM
easat-8674	82	3	580	580	NUM
easat-8674	82	4	-	-	SYM
easat-8674	82	5	594	594	NUM
easat-8674	82	6	,	,	PUNCT
easat-8674	82	7	2025	2025	NUM
easat-8674	82	8	doi	doi	NOUN
easat-8674	82	9	:	:	PUNCT
easat-8674	82	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	82	11	©	©	PROPN
easat-8674	82	12	2025	2025	NUM
easat-8674	82	13	by	by	ADP
easat-8674	82	14	the	the	DET
easat-8674	82	15	authors	author	NOUN
easat-8674	82	16	;	;	PUNCT
easat-8674	82	17	licensee	licensee	PROPN
easat-8674	82	18	learning	learning	NOUN
easat-8674	82	19	gate	gate	VERB
easat-8674	82	20	algebraic	algebraic	ADJ
easat-8674	82	21	tasks	task	NOUN
easat-8674	82	22	.	.	PUNCT
easat-8674	83	1	they	they	PRON
easat-8674	83	2	may	may	AUX
easat-8674	83	3	be	be	AUX
easat-8674	83	4	able	able	ADJ
easat-8674	83	5	to	to	PART
easat-8674	83	6	perform	perform	VERB
easat-8674	83	7	correct	correct	ADJ
easat-8674	83	8	procedures	procedure	NOUN
easat-8674	83	9	,	,	PUNCT
easat-8674	83	10	yet	yet	CCONJ
easat-8674	83	11	struggle	struggle	VERB
easat-8674	83	12	to	to	PART
easat-8674	83	13	articulate	articulate	VERB
easat-8674	83	14	the	the	DET
easat-8674	83	15	rationale	rationale	NOUN
easat-8674	83	16	behind	behind	ADP
easat-8674	83	17	their	their	PRON
easat-8674	83	18	steps	step	NOUN
easat-8674	83	19	.	.	PUNCT
easat-8674	84	1	further	further	ADJ
easat-8674	84	2	evidence	evidence	NOUN
easat-8674	84	3	from	from	ADP
easat-8674	84	4	stephens	stephen	NOUN
easat-8674	84	5	,	,	PUNCT
easat-8674	84	6	et	et	PROPN
easat-8674	84	7	al	al	PROPN
easat-8674	84	8	.	.	PUNCT
easat-8674	85	1	[	[	X
easat-8674	85	2	24	24	NUM
easat-8674	85	3	]	]	PUNCT
easat-8674	85	4	suggests	suggest	VERB
easat-8674	85	5	that	that	SCONJ
easat-8674	85	6	many	many	ADJ
easat-8674	85	7	students	student	NOUN
easat-8674	85	8	demonstrate	demonstrate	VERB
easat-8674	85	9	difficulties	difficulty	NOUN
easat-8674	85	10	in	in	ADP
easat-8674	85	11	flexibly	flexibly	ADV
easat-8674	85	12	interpreting	interpret	VERB
easat-8674	85	13	algebraic	algebraic	ADJ
easat-8674	85	14	representations	representation	NOUN
easat-8674	85	15	.	.	PUNCT
easat-8674	86	1	for	for	ADP
easat-8674	86	2	example	example	NOUN
easat-8674	86	3	,	,	PUNCT
easat-8674	86	4	students	student	NOUN
easat-8674	86	5	often	often	ADV
easat-8674	86	6	struggle	struggle	VERB
easat-8674	86	7	to	to	ADP
easat-8674	86	8	transition	transition	NOUN
easat-8674	86	9	between	between	ADP
easat-8674	86	10	symbolic	symbolic	ADJ
easat-8674	86	11	and	and	CCONJ
easat-8674	86	12	graphical	graphical	ADJ
easat-8674	86	13	forms	form	NOUN
easat-8674	86	14	or	or	CCONJ
easat-8674	86	15	fail	fail	VERB
easat-8674	86	16	to	to	PART
easat-8674	86	17	grasp	grasp	VERB
easat-8674	86	18	the	the	DET
easat-8674	86	19	role	role	NOUN
easat-8674	86	20	of	of	ADP
easat-8674	86	21	parameters	parameter	NOUN
easat-8674	86	22	in	in	ADP
easat-8674	86	23	linear	linear	ADJ
easat-8674	86	24	and	and	CCONJ
easat-8674	86	25	quadratic	quadratic	ADJ
easat-8674	86	26	functions	function	NOUN
easat-8674	86	27	.	.	PUNCT
easat-8674	87	1	these	these	DET
easat-8674	87	2	challenges	challenge	NOUN
easat-8674	87	3	indicate	indicate	VERB
easat-8674	87	4	that	that	SCONJ
easat-8674	87	5	their	their	PRON
easat-8674	87	6	existing	exist	VERB
easat-8674	87	7	content	content	NOUN
easat-8674	87	8	knowledge	knowledge	NOUN
easat-8674	87	9	is	be	AUX
easat-8674	87	10	insufficient	insufficient	ADJ
easat-8674	87	11	to	to	PART
easat-8674	87	12	support	support	VERB
easat-8674	87	13	conceptual	conceptual	ADJ
easat-8674	87	14	problem	problem	NOUN
easat-8674	87	15	-	-	PUNCT
easat-8674	87	16	solving	solving	NOUN
easat-8674	87	17	in	in	ADP
easat-8674	87	18	algebra	algebra	NOUN
easat-8674	87	19	.	.	PUNCT
easat-8674	88	1	moreover	moreover	ADV
easat-8674	88	2	,	,	PUNCT
easat-8674	88	3	research	research	NOUN
easat-8674	88	4	has	have	AUX
easat-8674	88	5	shown	show	VERB
easat-8674	88	6	that	that	SCONJ
easat-8674	88	7	students	student	NOUN
easat-8674	88	8	’	'	PUNCT
easat-8674	88	9	abilities	ability	NOUN
easat-8674	88	10	in	in	ADP
easat-8674	88	11	solving	solve	VERB
easat-8674	88	12	algebraic	algebraic	ADJ
easat-8674	88	13	problems	problem	NOUN
easat-8674	88	14	are	be	AUX
easat-8674	88	15	strongly	strongly	ADV
easat-8674	88	16	influenced	influence	VERB
easat-8674	88	17	by	by	ADP
easat-8674	88	18	their	their	PRON
easat-8674	88	19	prior	prior	ADJ
easat-8674	88	20	learning	learn	VERB
easat-8674	88	21	experiences	experience	NOUN
easat-8674	88	22	,	,	PUNCT
easat-8674	88	23	the	the	DET
easat-8674	88	24	quality	quality	NOUN
easat-8674	88	25	of	of	ADP
easat-8674	88	26	instruction	instruction	NOUN
easat-8674	88	27	received	receive	VERB
easat-8674	88	28	,	,	PUNCT
easat-8674	88	29	and	and	CCONJ
easat-8674	88	30	the	the	DET
easat-8674	88	31	extent	extent	NOUN
easat-8674	88	32	to	to	PART
easat-8674	88	33	which	which	PRON
easat-8674	88	34	they	they	PRON
easat-8674	88	35	are	be	AUX
easat-8674	88	36	given	give	VERB
easat-8674	88	37	opportunities	opportunity	NOUN
easat-8674	88	38	to	to	PART
easat-8674	88	39	reflect	reflect	VERB
easat-8674	88	40	on	on	ADP
easat-8674	88	41	their	their	PRON
easat-8674	88	42	mathematical	mathematical	ADJ
easat-8674	88	43	thinking	thinking	NOUN
easat-8674	88	44	.	.	PUNCT
easat-8674	89	1	therefore	therefore	ADV
easat-8674	89	2	,	,	PUNCT
easat-8674	89	3	it	it	PRON
easat-8674	89	4	is	be	AUX
easat-8674	89	5	essential	essential	ADJ
easat-8674	89	6	to	to	PART
easat-8674	89	7	explore	explore	VERB
easat-8674	89	8	the	the	DET
easat-8674	89	9	nature	nature	NOUN
easat-8674	89	10	of	of	ADP
easat-8674	89	11	undergraduate	undergraduate	ADJ
easat-8674	89	12	students	student	NOUN
easat-8674	89	13	’	'	PUNCT
easat-8674	89	14	content	content	NOUN
easat-8674	89	15	knowledge	knowledge	NOUN
easat-8674	89	16	in	in	ADP
easat-8674	89	17	algebra	algebra	NOUN
easat-8674	89	18	as	as	ADP
easat-8674	89	19	a	a	DET
easat-8674	89	20	foundation	foundation	NOUN
easat-8674	89	21	for	for	ADP
easat-8674	89	22	explicitly	explicitly	ADV
easat-8674	89	23	developing	develop	VERB
easat-8674	89	24	this	this	DET
easat-8674	89	25	knowledge	knowledge	NOUN
easat-8674	89	26	in	in	ADP
easat-8674	89	27	teacher	teacher	NOUN
easat-8674	89	28	education	education	NOUN
easat-8674	89	29	programs	program	NOUN
easat-8674	89	30	.	.	PUNCT
easat-8674	90	1	such	such	ADJ
easat-8674	90	2	development	development	NOUN
easat-8674	90	3	can	can	AUX
easat-8674	90	4	be	be	AUX
easat-8674	90	5	fostered	foster	VERB
easat-8674	90	6	through	through	ADP
easat-8674	90	7	problem	problem	NOUN
easat-8674	90	8	-	-	PUNCT
easat-8674	90	9	solving	solve	VERB
easat-8674	90	10	tasks	task	NOUN
easat-8674	90	11	,	,	PUNCT
easat-8674	90	12	reflective	reflective	ADJ
easat-8674	90	13	discussions	discussion	NOUN
easat-8674	90	14	,	,	PUNCT
easat-8674	90	15	and	and	CCONJ
easat-8674	90	16	in	in	ADP
easat-8674	90	17	-	-	PUNCT
easat-8674	90	18	depth	depth	NOUN
easat-8674	90	19	exploration	exploration	NOUN
easat-8674	90	20	of	of	ADP
easat-8674	90	21	core	core	NOUN
easat-8674	90	22	algebraic	algebraic	ADJ
easat-8674	90	23	concepts	concept	NOUN
easat-8674	90	24	3	3	NUM
easat-8674	90	25	.	.	PUNCT
easat-8674	90	26	research	research	NOUN
easat-8674	90	27	methodology	methodology	NOUN
easat-8674	90	28	this	this	DET
easat-8674	90	29	study	study	NOUN
easat-8674	90	30	employed	employ	VERB
easat-8674	90	31	a	a	DET
easat-8674	90	32	descriptive	descriptive	ADJ
easat-8674	90	33	qualitative	qualitative	ADJ
easat-8674	90	34	approach	approach	NOUN
easat-8674	90	35	to	to	PART
easat-8674	90	36	explore	explore	VERB
easat-8674	90	37	the	the	DET
easat-8674	90	38	content	content	NOUN
easat-8674	90	39	knowledge	knowledge	NOUN
easat-8674	90	40	abilities	ability	NOUN
easat-8674	90	41	of	of	ADP
easat-8674	90	42	third	third	ADJ
easat-8674	90	43	-	-	PUNCT
easat-8674	90	44	year	year	NOUN
easat-8674	90	45	undergraduate	undergraduate	NOUN
easat-8674	90	46	students	student	NOUN
easat-8674	90	47	in	in	ADP
easat-8674	90	48	mathematics	mathematic	NOUN
easat-8674	90	49	education	education	NOUN
easat-8674	90	50	.	.	PUNCT
easat-8674	91	1	participants	participant	NOUN
easat-8674	91	2	were	be	AUX
easat-8674	91	3	selected	select	VERB
easat-8674	91	4	from	from	ADP
easat-8674	91	5	a	a	DET
easat-8674	91	6	private	private	ADJ
easat-8674	91	7	university	university	NOUN
easat-8674	91	8	in	in	ADP
easat-8674	91	9	east	east	PROPN
easat-8674	91	10	nusa	nusa	PROPN
easat-8674	91	11	tenggara	tenggara	PROPN
easat-8674	91	12	,	,	PUNCT
easat-8674	91	13	indonesia	indonesia	PROPN
easat-8674	91	14	,	,	PUNCT
easat-8674	91	15	specifically	specifically	ADV
easat-8674	91	16	from	from	ADP
easat-8674	91	17	the	the	DET
easat-8674	91	18	2019	2019	NUM
easat-8674	91	19	cohort	cohort	NOUN
easat-8674	91	20	:	:	PUNCT
easat-8674	91	21	class	class	NOUN
easat-8674	91	22	a	a	PRON
easat-8674	91	23	(	(	PUNCT
easat-8674	91	24	10	10	NUM
easat-8674	91	25	students	student	NOUN
easat-8674	91	26	)	)	PUNCT
easat-8674	91	27	and	and	CCONJ
easat-8674	91	28	class	class	PROPN
easat-8674	91	29	b	b	PROPN
easat-8674	91	30	(	(	PUNCT
easat-8674	91	31	15	15	NUM
easat-8674	91	32	students	student	NOUN
easat-8674	91	33	)	)	PUNCT
easat-8674	91	34	.	.	PUNCT
easat-8674	92	1	for	for	ADP
easat-8674	92	2	the	the	DET
easat-8674	92	3	purpose	purpose	NOUN
easat-8674	92	4	of	of	ADP
easat-8674	92	5	this	this	DET
easat-8674	92	6	research	research	NOUN
easat-8674	92	7	,	,	PUNCT
easat-8674	92	8	class	class	NOUN
easat-8674	92	9	a	a	DET
easat-8674	92	10	comprising	comprise	VERB
easat-8674	92	11	10	10	NUM
easat-8674	92	12	female	female	ADJ
easat-8674	92	13	students	student	NOUN
easat-8674	92	14	was	be	AUX
easat-8674	92	15	chosen	choose	VERB
easat-8674	92	16	due	due	ADP
easat-8674	92	17	to	to	ADP
easat-8674	92	18	their	their	PRON
easat-8674	92	19	active	active	ADJ
easat-8674	92	20	participation	participation	NOUN
easat-8674	92	21	and	and	CCONJ
easat-8674	92	22	communicative	communicative	ADJ
easat-8674	92	23	learning	learn	VERB
easat-8674	92	24	behavior	behavior	NOUN
easat-8674	92	25	observed	observe	VERB
easat-8674	92	26	during	during	ADP
easat-8674	92	27	the	the	DET
easat-8674	92	28	sixth	sixth	ADJ
easat-8674	92	29	semester	semester	NOUN
easat-8674	92	30	.	.	PUNCT
easat-8674	93	1	two	two	NUM
easat-8674	93	2	primary	primary	ADJ
easat-8674	93	3	instruments	instrument	NOUN
easat-8674	93	4	were	be	AUX
easat-8674	93	5	utilized	utilize	VERB
easat-8674	93	6	in	in	ADP
easat-8674	93	7	the	the	DET
easat-8674	93	8	study	study	NOUN
easat-8674	93	9	:	:	PUNCT
easat-8674	93	10	diagnostic	diagnostic	ADJ
easat-8674	93	11	test	test	NOUN
easat-8674	93	12	(	(	PUNCT
easat-8674	93	13	td):consisted	td):consiste	VERB
easat-8674	93	14	of	of	ADP
easat-8674	93	15	five	five	NUM
easat-8674	93	16	open	open	ADV
easat-8674	93	17	-	-	PUNCT
easat-8674	93	18	ended	end	VERB
easat-8674	93	19	questions	question	NOUN
easat-8674	93	20	covering	cover	VERB
easat-8674	93	21	foundational	foundational	ADJ
easat-8674	93	22	mathematical	mathematical	ADJ
easat-8674	93	23	topics	topic	NOUN
easat-8674	93	24	such	such	ADJ
easat-8674	93	25	as	as	ADP
easat-8674	93	26	numbers	number	NOUN
easat-8674	93	27	,	,	PUNCT
easat-8674	93	28	sets	set	NOUN
easat-8674	93	29	,	,	PUNCT
easat-8674	93	30	algebra	algebra	NOUN
easat-8674	93	31	,	,	PUNCT
easat-8674	93	32	and	and	CCONJ
easat-8674	93	33	linear	linear	ADJ
easat-8674	93	34	equations	equation	NOUN
easat-8674	93	35	.	.	PUNCT
easat-8674	94	1	content	content	NOUN
easat-8674	94	2	knowledge	knowledge	PROPN
easat-8674	94	3	test	test	PROPN
easat-8674	94	4	(	(	PUNCT
easat-8674	94	5	tck	tck	PROPN
easat-8674	94	6	):	):	PUNCT
easat-8674	94	7	included	include	VERB
easat-8674	94	8	three	three	NUM
easat-8674	94	9	open	open	ADV
easat-8674	94	10	-	-	PUNCT
easat-8674	94	11	ended	end	VERB
easat-8674	94	12	questions	question	NOUN
easat-8674	94	13	focused	focus	VERB
easat-8674	94	14	specifically	specifically	ADV
easat-8674	94	15	on	on	ADP
easat-8674	94	16	algebraic	algebraic	ADJ
easat-8674	94	17	concepts	concept	NOUN
easat-8674	94	18	.	.	PUNCT
easat-8674	95	1	both	both	DET
easat-8674	95	2	instruments	instrument	NOUN
easat-8674	95	3	were	be	AUX
easat-8674	95	4	validated	validate	VERB
easat-8674	95	5	by	by	ADP
easat-8674	95	6	three	three	NUM
easat-8674	95	7	assistant	assistant	ADJ
easat-8674	95	8	professors	professor	NOUN
easat-8674	95	9	in	in	ADP
easat-8674	95	10	mathematics	mathematics	NOUN
easat-8674	95	11	education	education	NOUN
easat-8674	95	12	using	use	VERB
easat-8674	95	13	a	a	DET
easat-8674	95	14	five	five	NUM
easat-8674	95	15	-	-	PUNCT
easat-8674	95	16	point	point	NOUN
easat-8674	95	17	likert	likert	ADJ
easat-8674	95	18	scale	scale	NOUN
easat-8674	95	19	[	[	X
easat-8674	95	20	25	25	NUM
easat-8674	95	21	]	]	PUNCT
easat-8674	95	22	.	.	PUNCT
easat-8674	96	1	the	the	DET
easat-8674	96	2	validation	validation	NOUN
easat-8674	96	3	process	process	NOUN
easat-8674	96	4	produced	produce	VERB
easat-8674	96	5	strong	strong	ADJ
easat-8674	96	6	results	result	NOUN
easat-8674	96	7	,	,	PUNCT
easat-8674	96	8	with	with	ADP
easat-8674	96	9	average	average	ADJ
easat-8674	96	10	validity	validity	NOUN
easat-8674	96	11	scores	score	NOUN
easat-8674	96	12	of	of	ADP
easat-8674	96	13	4.6	4.6	NUM
easat-8674	96	14	for	for	ADP
easat-8674	96	15	the	the	DET
easat-8674	96	16	diagnostic	diagnostic	ADJ
easat-8674	96	17	test	test	NOUN
easat-8674	96	18	(	(	PUNCT
easat-8674	96	19	td	td	NOUN
easat-8674	96	20	)	)	PUNCT
easat-8674	96	21	and	and	CCONJ
easat-8674	96	22	4.0	4.0	NUM
easat-8674	96	23	for	for	ADP
easat-8674	96	24	the	the	DET
easat-8674	96	25	content	content	NOUN
easat-8674	96	26	knowledge	knowledge	NOUN
easat-8674	96	27	test	test	PROPN
easat-8674	96	28	(	(	PUNCT
easat-8674	96	29	tck	tck	PROPN
easat-8674	96	30	)	)	PUNCT
easat-8674	96	31	(	(	PUNCT
easat-8674	96	32	on	on	ADP
easat-8674	96	33	a	a	DET
easat-8674	96	34	maximum	maximum	ADJ
easat-8674	96	35	scale	scale	NOUN
easat-8674	96	36	of	of	ADP
easat-8674	96	37	5.0	5.0	NUM
easat-8674	96	38	)	)	PUNCT
easat-8674	96	39	,	,	PUNCT
easat-8674	96	40	indicating	indicate	VERB
easat-8674	96	41	a	a	DET
easat-8674	96	42	high	high	ADJ
easat-8674	96	43	level	level	NOUN
easat-8674	96	44	of	of	ADP
easat-8674	96	45	content	content	NOUN
easat-8674	96	46	and	and	CCONJ
easat-8674	96	47	construct	construct	VERB
easat-8674	96	48	validity	validity	NOUN
easat-8674	96	49	.	.	PUNCT
easat-8674	97	1	reliability	reliability	NOUN
easat-8674	97	2	coefficients	coefficient	NOUN
easat-8674	97	3	were	be	AUX
easat-8674	97	4	also	also	ADV
easat-8674	97	5	high	high	ADJ
easat-8674	97	6	:	:	PUNCT
easat-8674	97	7	0.9993	0.9993	NUM
easat-8674	97	8	for	for	ADP
easat-8674	97	9	the	the	DET
easat-8674	97	10	td	td	NOUN
easat-8674	97	11	and	and	CCONJ
easat-8674	97	12	0.9983	0.9983	NUM
easat-8674	97	13	for	for	ADP
easat-8674	97	14	the	the	DET
easat-8674	97	15	tck	tck	PROPN
easat-8674	97	16	.	.	PUNCT
easat-8674	98	1	students	student	NOUN
easat-8674	98	2	were	be	AUX
easat-8674	98	3	allotted	allot	VERB
easat-8674	98	4	a	a	DET
easat-8674	98	5	total	total	NOUN
easat-8674	98	6	of	of	ADP
easat-8674	98	7	100	100	NUM
easat-8674	98	8	minutes	minute	NOUN
easat-8674	98	9	to	to	PART
easat-8674	98	10	complete	complete	VERB
easat-8674	98	11	both	both	DET
easat-8674	98	12	tests	test	NOUN
easat-8674	98	13	.	.	PUNCT
easat-8674	99	1	all	all	DET
easat-8674	99	2	10	10	NUM
easat-8674	99	3	students	student	NOUN
easat-8674	99	4	from	from	ADP
easat-8674	99	5	class	class	NOUN
easat-8674	99	6	a	a	DET
easat-8674	99	7	completed	complete	VERB
easat-8674	99	8	the	the	DET
easat-8674	99	9	td	td	NOUN
easat-8674	99	10	and	and	CCONJ
easat-8674	99	11	tck	tck	PROPN
easat-8674	99	12	.	.	PUNCT
easat-8674	100	1	their	their	PRON
easat-8674	100	2	responses	response	NOUN
easat-8674	100	3	to	to	ADP
easat-8674	100	4	the	the	DET
easat-8674	100	5	tck	tck	PROPN
easat-8674	100	6	were	be	AUX
easat-8674	100	7	analyzed	analyze	VERB
easat-8674	100	8	using	use	VERB
easat-8674	100	9	two	two	NUM
easat-8674	100	10	theoretical	theoretical	ADJ
easat-8674	100	11	frameworks	framework	NOUN
easat-8674	100	12	:	:	PUNCT
easat-8674	100	13	the	the	DET
easat-8674	100	14	direct	direct	ADJ
easat-8674	100	15	translation	translation	NOUN
easat-8674	100	16	approach	approach	NOUN
easat-8674	100	17	(	(	PUNCT
easat-8674	100	18	dta	dta	PROPN
easat-8674	100	19	)	)	PUNCT
easat-8674	100	20	and	and	CCONJ
easat-8674	100	21	the	the	DET
easat-8674	100	22	meaning	meaning	NOUN
easat-8674	100	23	-	-	PUNCT
easat-8674	100	24	based	base	VERB
easat-8674	100	25	approach	approach	NOUN
easat-8674	100	26	(	(	PUNCT
easat-8674	100	27	mba	mba	NOUN
easat-8674	100	28	)	)	PUNCT
easat-8674	101	1	[	[	X
easat-8674	101	2	14	14	NUM
easat-8674	101	3	]	]	PUNCT
easat-8674	101	4	.	.	PUNCT
easat-8674	102	1	these	these	PRON
easat-8674	102	2	were	be	AUX
easat-8674	102	3	further	far	ADV
easat-8674	102	4	broken	break	VERB
easat-8674	102	5	down	down	ADP
easat-8674	102	6	into	into	ADP
easat-8674	102	7	subcategories	subcategorie	NOUN
easat-8674	102	8	:	:	PUNCT
easat-8674	102	9	dta	dta	PROPN
easat-8674	102	10	subcategories	subcategorie	NOUN
easat-8674	102	11	:	:	PUNCT
easat-8674	102	12	dta	dta	NOUN
easat-8674	102	13	-	-	PUNCT
easat-8674	102	14	proficient	proficient	ADJ
easat-8674	102	15	(	(	PUNCT
easat-8674	102	16	dta	dta	PROPN
easat-8674	102	17	-	-	PUNCT
easat-8674	102	18	p	p	NOUN
easat-8674	102	19	)	)	PUNCT
easat-8674	102	20	,	,	PUNCT
easat-8674	102	21	dta	dta	PROPN
easat-8674	102	22	-	-	PUNCT
easat-8674	102	23	non	non	ADJ
easat-8674	102	24	-	-	ADJ
easat-8674	102	25	proficient	proficient	ADJ
easat-8674	102	26	(	(	PUNCT
easat-8674	102	27	dta	dta	PROPN
easat-8674	102	28	-	-	PUNCT
easat-8674	102	29	np	np	NOUN
easat-8674	102	30	)	)	PUNCT
easat-8674	102	31	,	,	PUNCT
easat-8674	102	32	dta	dta	PROPN
easat-8674	102	33	-	-	PUNCT
easat-8674	102	34	limited	limit	VERB
easat-8674	102	35	context	context	NOUN
easat-8674	102	36	(	(	PUNCT
easat-8674	102	37	dta	dta	PROPN
easat-8674	102	38	-	-	PUNCT
easat-8674	102	39	lc	lc	NOUN
easat-8674	102	40	)	)	PUNCT
easat-8674	102	41	.	.	PUNCT
easat-8674	103	1	mba	mba	NOUN
easat-8674	103	2	subcategories	subcategorie	NOUN
easat-8674	103	3	:	:	PUNCT
easat-8674	103	4	mba	mba	ADJ
easat-8674	103	5	-	-	PUNCT
easat-8674	103	6	full	full	ADJ
easat-8674	103	7	context	context	NOUN
easat-8674	103	8	(	(	PUNCT
easat-8674	103	9	mba	mba	NOUN
easat-8674	103	10	-	-	PUNCT
easat-8674	103	11	fc	fc	NOUN
easat-8674	103	12	)	)	PUNCT
easat-8674	103	13	and	and	CCONJ
easat-8674	103	14	mba	mba	NOUN
easat-8674	103	15	-	-	PUNCT
easat-8674	103	16	justification	justification	NOUN
easat-8674	103	17	(	(	PUNCT
easat-8674	103	18	mba	mba	NOUN
easat-8674	103	19	-	-	PUNCT
easat-8674	103	20	j	j	NOUN
easat-8674	103	21	)	)	PUNCT
easat-8674	104	1	[	[	X
easat-8674	104	2	14	14	NUM
easat-8674	104	3	]	]	PUNCT
easat-8674	104	4	.	.	PUNCT
easat-8674	105	1	the	the	DET
easat-8674	105	2	empirical	empirical	ADJ
easat-8674	105	3	testing	testing	NOUN
easat-8674	105	4	results	result	NOUN
easat-8674	105	5	are	be	AUX
easat-8674	105	6	summarized	summarize	VERB
easat-8674	105	7	in	in	ADP
easat-8674	105	8	table	table	NOUN
easat-8674	105	9	1	1	NUM
easat-8674	105	10	.	.	PUNCT
easat-8674	105	11	table	table	NOUN
easat-8674	105	12	1	1	NUM
easat-8674	105	13	.	.	PUNCT
easat-8674	105	14	empirical	empirical	ADJ
easat-8674	105	15	test	test	NOUN
easat-8674	105	16	results	result	NOUN
easat-8674	105	17	of	of	ADP
easat-8674	105	18	the	the	DET
easat-8674	105	19	diagnostic	diagnostic	ADJ
easat-8674	105	20	test	test	NOUN
easat-8674	105	21	(	(	PUNCT
easat-8674	105	22	td	td	NOUN
easat-8674	105	23	)	)	PUNCT
easat-8674	105	24	and	and	CCONJ
easat-8674	105	25	the	the	DET
easat-8674	105	26	content	content	NOUN
easat-8674	105	27	knowledge	knowledge	PROPN
easat-8674	105	28	test	test	PROPN
easat-8674	105	29	(	(	PUNCT
easat-8674	105	30	tck	tck	PROPN
easat-8674	105	31	)	)	PUNCT
easat-8674	105	32	.	.	PUNCT
easat-8674	106	1	validation	validation	NOUN
easat-8674	106	2	aspect	aspect	PROPN
easat-8674	106	3	td	td	PROPN
easat-8674	106	4	tck	tck	PROPN
easat-8674	106	5	difficulty	difficulty	PROPN
easat-8674	106	6	level	level	NOUN
easat-8674	106	7	0.69	0.69	NUM
easat-8674	106	8	0.69	0.69	NUM
easat-8674	106	9	discriminating	discriminate	VERB
easat-8674	106	10	power	power	NOUN
easat-8674	106	11	0.58	0.58	NUM
easat-8674	106	12	0.60	0.60	NUM
easat-8674	106	13	empirical	empirical	ADJ
easat-8674	106	14	validity	validity	NOUN
easat-8674	106	15	0.99	0.99	NUM
easat-8674	106	16	0.99	0.99	NUM
easat-8674	106	17	reliability	reliability	NOUN
easat-8674	106	18	1.00	1.00	NUM
easat-8674	106	19	0.99	0.99	NUM
easat-8674	106	20	584	584	NUM
easat-8674	106	21	edelweiss	edelweiss	PROPN
easat-8674	106	22	applied	apply	VERB
easat-8674	106	23	science	science	NOUN
easat-8674	106	24	and	and	CCONJ
easat-8674	106	25	technology	technology	NOUN
easat-8674	106	26	issn	issn	PROPN
easat-8674	106	27	:	:	PUNCT
easat-8674	106	28	2576	2576	NUM
easat-8674	106	29	-	-	SYM
easat-8674	106	30	8484	8484	NUM
easat-8674	106	31	vol	vol	NOUN
easat-8674	106	32	.	.	PROPN
easat-8674	107	1	9	9	NUM
easat-8674	107	2	,	,	PUNCT
easat-8674	107	3	no	no	INTJ
easat-8674	107	4	.	.	NOUN
easat-8674	108	1	7	7	NUM
easat-8674	108	2	:	:	SYM
easat-8674	108	3	580	580	NUM
easat-8674	108	4	-	-	SYM
easat-8674	108	5	594	594	NUM
easat-8674	108	6	,	,	PUNCT
easat-8674	108	7	2025	2025	NUM
easat-8674	108	8	doi	doi	NOUN
easat-8674	108	9	:	:	PUNCT
easat-8674	108	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	108	11	©	©	PROPN
easat-8674	108	12	2025	2025	NUM
easat-8674	108	13	by	by	ADP
easat-8674	108	14	the	the	DET
easat-8674	108	15	authors	author	NOUN
easat-8674	108	16	;	;	PUNCT
easat-8674	108	17	licensee	licensee	PROPN
easat-8674	108	18	learning	learn	VERB
easat-8674	108	19	gate	gate	NOUN
easat-8674	108	20	table	table	NOUN
easat-8674	108	21	2	2	NUM
easat-8674	108	22	.	.	X
easat-8674	109	1	recapitulation	recapitulation	NOUN
easat-8674	109	2	of	of	ADP
easat-8674	109	3	diagnostic	diagnostic	ADJ
easat-8674	109	4	test	test	NOUN
easat-8674	109	5	(	(	PUNCT
easat-8674	109	6	td	td	NOUN
easat-8674	109	7	)	)	PUNCT
easat-8674	109	8	and	and	CCONJ
easat-8674	109	9	content	content	NOUN
easat-8674	109	10	knowledge	knowledge	NOUN
easat-8674	109	11	test	test	NOUN
easat-8674	109	12	(	(	PUNCT
easat-8674	109	13	tck	tck	PROPN
easat-8674	109	14	)	)	PUNCT
easat-8674	109	15	.	.	PUNCT
easat-8674	110	1	no	no	DET
easat-8674	110	2	initials	initial	NOUN
easat-8674	110	3	gender	gender	NOUN
easat-8674	110	4	td	td	NOUN
easat-8674	110	5	1	1	NUM
easat-8674	110	6	td2	td2	NOUN
easat-8674	110	7	td3	td3	NOUN
easat-8674	110	8	td4	td4	PROPN
easat-8674	110	9	td5	td5	PROPN
easat-8674	110	10	td	td	PROPN
easat-8674	110	11	score	score	PROPN
easat-8674	110	12	tck	tck	PROPN
easat-8674	110	13	1	1	NUM
easat-8674	110	14	tck	tck	PROPN
easat-8674	110	15	2	2	PROPN
easat-8674	110	16	tck	tck	PROPN
easat-8674	110	17	3	3	NUM
easat-8674	110	18	tck	tck	PROPN
easat-8674	110	19	score	score	NOUN
easat-8674	110	20	1	1	NUM
easat-8674	110	21	mp	mp	NOUN
easat-8674	110	22	f	f	PROPN
easat-8674	110	23	14	14	NUM
easat-8674	110	24	12	12	NUM
easat-8674	110	25	16	16	NUM
easat-8674	110	26	16	16	NUM
easat-8674	110	27	22	22	NUM
easat-8674	110	28	80	80	NUM
easat-8674	110	29	5	5	NUM
easat-8674	110	30	6	6	NUM
easat-8674	110	31	9	9	NUM
easat-8674	110	32	67	67	NUM
easat-8674	110	33	2	2	NUM
easat-8674	110	34	yb	yb	PROPN
easat-8674	110	35	f	f	PROPN
easat-8674	110	36	16	16	NUM
easat-8674	110	37	12	12	NUM
easat-8674	110	38	16	16	NUM
easat-8674	110	39	20	20	NUM
easat-8674	110	40	16	16	NUM
easat-8674	110	41	80	80	NUM
easat-8674	110	42	4	4	NUM
easat-8674	110	43	10	10	NUM
easat-8674	110	44	9	9	NUM
easat-8674	110	45	77	77	NUM
easat-8674	110	46	3	3	NUM
easat-8674	110	47	kw	kw	NOUN
easat-8674	110	48	f	f	NOUN
easat-8674	110	49	12	12	NUM
easat-8674	110	50	12	12	NUM
easat-8674	110	51	10	10	NUM
easat-8674	110	52	20	20	NUM
easat-8674	110	53	20	20	NUM
easat-8674	110	54	74	74	NUM
easat-8674	110	55	8	8	NUM
easat-8674	110	56	7	7	NUM
easat-8674	110	57	10	10	NUM
easat-8674	110	58	83	83	NUM
easat-8674	110	59	4	4	NUM
easat-8674	110	60	em	em	PRON
easat-8674	110	61	f	f	PROPN
easat-8674	110	62	10	10	NUM
easat-8674	110	63	12	12	NUM
easat-8674	110	64	18	18	NUM
easat-8674	110	65	20	20	NUM
easat-8674	110	66	8	8	NUM
easat-8674	110	67	68	68	NUM
easat-8674	110	68	7	7	NUM
easat-8674	110	69	9	9	NUM
easat-8674	110	70	10	10	NUM
easat-8674	110	71	87	87	NUM
easat-8674	110	72	5	5	NUM
easat-8674	110	73	ms	ms	PROPN
easat-8674	110	74	f	f	PROPN
easat-8674	110	75	14	14	NUM
easat-8674	110	76	8	8	NUM
easat-8674	110	77	12	12	NUM
easat-8674	110	78	10	10	NUM
easat-8674	110	79	16	16	NUM
easat-8674	110	80	60	60	NUM
easat-8674	110	81	3	3	NUM
easat-8674	110	82	7	7	NUM
easat-8674	110	83	10	10	NUM
easat-8674	110	84	67	67	NUM
easat-8674	110	85	6	6	NUM
easat-8674	110	86	my	my	PRON
easat-8674	110	87	f	f	PROPN
easat-8674	110	88	10	10	NUM
easat-8674	110	89	12	12	NUM
easat-8674	110	90	20	20	NUM
easat-8674	110	91	20	20	NUM
easat-8674	110	92	28	28	NUM
easat-8674	110	93	90	90	NUM
easat-8674	110	94	10	10	NUM
easat-8674	110	95	10	10	NUM
easat-8674	110	96	9	9	NUM
easat-8674	110	97	97	97	NUM
easat-8674	110	98	7	7	NUM
easat-8674	110	99	ma	ma	PROPN
easat-8674	110	100	f	f	PROPN
easat-8674	110	101	16	16	NUM
easat-8674	110	102	12	12	NUM
easat-8674	110	103	20	20	NUM
easat-8674	110	104	18	18	NUM
easat-8674	110	105	12	12	NUM
easat-8674	110	106	78	78	NUM
easat-8674	110	107	3	3	NUM
easat-8674	110	108	5	5	NUM
easat-8674	110	109	9	9	NUM
easat-8674	110	110	57	57	NUM
easat-8674	110	111	8	8	NUM
easat-8674	110	112	mm	mm	NOUN
easat-8674	110	113	f	f	NOUN
easat-8674	110	114	20	20	NUM
easat-8674	110	115	12	12	NUM
easat-8674	110	116	18	18	NUM
easat-8674	110	117	18	18	NUM
easat-8674	110	118	26	26	NUM
easat-8674	110	119	94	94	NUM
easat-8674	110	120	7	7	NUM
easat-8674	110	121	6	6	NUM
easat-8674	110	122	10	10	NUM
easat-8674	110	123	77	77	NUM
easat-8674	110	124	9	9	NUM
easat-8674	110	125	tr	tr	NOUN
easat-8674	110	126	f	f	PROPN
easat-8674	110	127	16	16	NUM
easat-8674	110	128	12	12	NUM
easat-8674	110	129	16	16	NUM
easat-8674	110	130	18	18	NUM
easat-8674	110	131	6	6	NUM
easat-8674	110	132	68	68	NUM
easat-8674	110	133	5	5	NUM
easat-8674	110	134	9	9	NUM
easat-8674	110	135	8	8	NUM
easat-8674	110	136	73	73	NUM
easat-8674	110	137	10	10	NUM
easat-8674	110	138	fa	fa	NOUN
easat-8674	110	139	f	f	PROPN
easat-8674	110	140	10	10	NUM
easat-8674	110	141	12	12	NUM
easat-8674	110	142	18	18	NUM
easat-8674	110	143	18	18	NUM
easat-8674	110	144	4	4	NUM
easat-8674	110	145	66	66	NUM
easat-8674	110	146	2	2	NUM
easat-8674	110	147	9	9	NUM
easat-8674	110	148	8	8	NUM
easat-8674	110	149	63	63	NUM
easat-8674	110	150	based	base	VERB
easat-8674	110	151	on	on	ADP
easat-8674	110	152	the	the	DET
easat-8674	110	153	results	result	NOUN
easat-8674	110	154	in	in	ADP
easat-8674	110	155	table	table	NOUN
easat-8674	110	156	2	2	NUM
easat-8674	110	157	,	,	PUNCT
easat-8674	110	158	three	three	NUM
easat-8674	110	159	students	student	NOUN
easat-8674	110	160	were	be	AUX
easat-8674	110	161	purposively	purposively	ADV
easat-8674	110	162	selected	select	VERB
easat-8674	110	163	for	for	ADP
easat-8674	110	164	interviews	interview	NOUN
easat-8674	110	165	according	accord	VERB
easat-8674	110	166	to	to	ADP
easat-8674	110	167	the	the	DET
easat-8674	110	168	following	follow	VERB
easat-8674	110	169	criteria	criterion	NOUN
easat-8674	110	170	:	:	PUNCT
easat-8674	110	171	(	(	PUNCT
easat-8674	110	172	i	i	NOUN
easat-8674	110	173	)	)	PUNCT
easat-8674	110	174	their	their	PRON
easat-8674	110	175	tck	tck	PROPN
easat-8674	110	176	responses	response	NOUN
easat-8674	110	177	demonstrated	demonstrate	VERB
easat-8674	110	178	distinctive	distinctive	ADJ
easat-8674	110	179	patterns	pattern	NOUN
easat-8674	110	180	or	or	CCONJ
easat-8674	110	181	unique	unique	ADJ
easat-8674	110	182	characteristics	characteristic	NOUN
easat-8674	110	183	;	;	PUNCT
easat-8674	110	184	(	(	PUNCT
easat-8674	110	185	ii	ii	X
easat-8674	110	186	)	)	PUNCT
easat-8674	110	187	their	their	PRON
easat-8674	110	188	answers	answer	NOUN
easat-8674	110	189	addressed	address	VERB
easat-8674	110	190	at	at	ADP
easat-8674	110	191	least	least	ADV
easat-8674	110	192	three	three	NUM
easat-8674	110	193	out	out	ADP
easat-8674	110	194	of	of	ADP
easat-8674	110	195	four	four	NUM
easat-8674	110	196	problem	problem	NOUN
easat-8674	110	197	-	-	PUNCT
easat-8674	110	198	solving	solve	VERB
easat-8674	110	199	components	component	NOUN
easat-8674	110	200	:	:	PUNCT
easat-8674	110	201	networking	networking	NOUN
easat-8674	110	202	,	,	PUNCT
easat-8674	110	203	extraction	extraction	NOUN
easat-8674	110	204	,	,	PUNCT
easat-8674	110	205	monitoring	monitoring	NOUN
easat-8674	110	206	,	,	PUNCT
easat-8674	110	207	and	and	CCONJ
easat-8674	110	208	strategy	strategy	NOUN
easat-8674	110	209	;	;	PUNCT
easat-8674	110	210	and	and	CCONJ
easat-8674	110	211	(	(	PUNCT
easat-8674	110	212	iii	iii	X
easat-8674	110	213	)	)	PUNCT
easat-8674	110	214	they	they	PRON
easat-8674	110	215	voluntarily	voluntarily	ADV
easat-8674	110	216	agreed	agree	VERB
easat-8674	110	217	to	to	PART
easat-8674	110	218	participate	participate	VERB
easat-8674	110	219	in	in	ADP
easat-8674	110	220	interviews	interview	NOUN
easat-8674	110	221	conducted	conduct	VERB
easat-8674	110	222	outside	outside	ADP
easat-8674	110	223	of	of	ADP
easat-8674	110	224	class	class	NOUN
easat-8674	110	225	hours	hour	NOUN
easat-8674	110	226	.	.	PUNCT
easat-8674	111	1	the	the	DET
easat-8674	111	2	interviews	interview	NOUN
easat-8674	111	3	were	be	AUX
easat-8674	111	4	conducted	conduct	VERB
easat-8674	111	5	in	in	ADP
easat-8674	111	6	a	a	DET
easat-8674	111	7	calm	calm	ADJ
easat-8674	111	8	and	and	CCONJ
easat-8674	111	9	supportive	supportive	ADJ
easat-8674	111	10	environment	environment	NOUN
easat-8674	111	11	to	to	PART
easat-8674	111	12	encourage	encourage	VERB
easat-8674	111	13	thoughtful	thoughtful	ADJ
easat-8674	111	14	and	and	CCONJ
easat-8674	111	15	reflective	reflective	ADJ
easat-8674	111	16	responses	response	NOUN
easat-8674	111	17	from	from	ADP
easat-8674	111	18	participants	participant	NOUN
easat-8674	111	19	.	.	PUNCT
easat-8674	112	1	3.1	3.1	NUM
easat-8674	112	2	.	.	PUNCT
easat-8674	112	3	content	content	PROPN
easat-8674	112	4	knowledge	knowledge	PROPN
easat-8674	112	5	test	test	PROPN
easat-8674	112	6	(	(	PUNCT
easat-8674	112	7	tck	tck	PROPN
easat-8674	112	8	)	)	PUNCT
easat-8674	112	9	3.1.1	3.1.1	NUM
easat-8674	112	10	.	.	PUNCT
easat-8674	113	1	problem	problem	NOUN
easat-8674	113	2	1	1	NUM
easat-8674	113	3	(	(	PUNCT
easat-8674	113	4	40	40	NUM
easat-8674	113	5	minutes	minute	NOUN
easat-8674	113	6	)	)	PUNCT
easat-8674	113	7	in	in	ADP
easat-8674	113	8	1963	1963	NUM
easat-8674	113	9	,	,	PUNCT
easat-8674	113	10	indonesia	indonesia	PROPN
easat-8674	113	11	first	first	ADV
easat-8674	113	12	launched	launch	VERB
easat-8674	113	13	two	two	NUM
easat-8674	113	14	rockets	rocket	NOUN
easat-8674	113	15	from	from	ADP
easat-8674	113	16	the	the	DET
easat-8674	113	17	sanden	sanden	PROPN
easat-8674	113	18	beach	beach	PROPN
easat-8674	113	19	,	,	PUNCT
easat-8674	113	20	bantul	bantul	NOUN
easat-8674	113	21	,	,	PUNCT
easat-8674	113	22	yogyakarta	yogyakarta	PROPN
easat-8674	113	23	students	student	NOUN
easat-8674	113	24	of	of	ADP
easat-8674	113	25	gajah	gajah	PROPN
easat-8674	113	26	mada	mada	PROPN
easat-8674	113	27	university	university	PROPN
easat-8674	113	28	(	(	PUNCT
easat-8674	113	29	ugm	ugm	PROPN
easat-8674	113	30	)	)	PUNCT
easat-8674	113	31	.	.	PUNCT
easat-8674	114	1	the	the	DET
easat-8674	114	2	rockets	rocket	NOUN
easat-8674	114	3	were	be	AUX
easat-8674	114	4	gama	gama	PROPN
easat-8674	114	5	ii	ii	PROPN
easat-8674	114	6	a	a	PROPN
easat-8674	114	7	and	and	CCONJ
easat-8674	114	8	ii	ii	PROPN
easat-8674	114	9	b	b	PROPN
easat-8674	114	10	with	with	ADP
easat-8674	114	11	454	454	NUM
easat-8674	114	12	kg	kg	NOUN
easat-8674	114	13	of	of	ADP
easat-8674	114	14	solid	solid	ADJ
easat-8674	114	15	fuel	fuel	NOUN
easat-8674	114	16	,	,	PUNCT
easat-8674	114	17	shaped	shape	VERB
easat-8674	114	18	as	as	ADP
easat-8674	114	19	below	below	ADP
easat-8674	114	20	the	the	DET
easat-8674	114	21	rocket	rocket	NOUN
easat-8674	114	22	is	be	AUX
easat-8674	114	23	launched	launch	VERB
easat-8674	114	24	from	from	ADP
easat-8674	114	25	the	the	DET
easat-8674	114	26	earth	earth	NOUN
easat-8674	114	27	to	to	ADP
easat-8674	114	28	the	the	DET
easat-8674	114	29	moon	moon	NOUN
easat-8674	114	30	and	and	CCONJ
easat-8674	114	31	is	be	AUX
easat-8674	114	32	scheduled	schedule	VERB
easat-8674	114	33	to	to	PART
easat-8674	114	34	enter	enter	VERB
easat-8674	114	35	the	the	DET
easat-8674	114	36	mesosphere	mesosphere	NOUN
easat-8674	114	37	layer	layer	NOUN
easat-8674	114	38	(	(	PUNCT
easat-8674	114	39	the	the	DET
easat-8674	114	40	third	third	ADJ
easat-8674	114	41	layer	layer	NOUN
easat-8674	114	42	of	of	ADP
easat-8674	114	43	air	air	NOUN
easat-8674	114	44	from	from	ADP
easat-8674	114	45	the	the	DET
easat-8674	114	46	earth	earth	NOUN
easat-8674	114	47	as	as	ADP
easat-8674	114	48	a	a	DET
easat-8674	114	49	constituent	constituent	NOUN
easat-8674	114	50	of	of	ADP
easat-8674	114	51	the	the	DET
easat-8674	114	52	atmosphere	atmosphere	NOUN
easat-8674	114	53	)	)	PUNCT
easat-8674	114	54	at	at	ADP
easat-8674	114	55	7:00	7:00	NUM
easat-8674	114	56	am	am	NOUN
easat-8674	114	57	.	.	PUNCT
easat-8674	115	1	if	if	SCONJ
easat-8674	115	2	the	the	DET
easat-8674	115	3	rocket	rocket	NOUN
easat-8674	115	4	is	be	AUX
easat-8674	115	5	launched	launch	VERB
easat-8674	115	6	at	at	ADP
easat-8674	115	7	40	40	NUM
easat-8674	115	8	𝑘𝑚/ℎ	𝑘𝑚/ℎ	NOUN
easat-8674	115	9	,	,	PUNCT
easat-8674	115	10	it	it	PRON
easat-8674	115	11	will	will	AUX
easat-8674	115	12	enter	enter	VERB
easat-8674	115	13	the	the	DET
easat-8674	115	14	mesosphere	mesosphere	NOUN
easat-8674	115	15	10	10	NUM
easat-8674	115	16	minutes	minute	NOUN
easat-8674	115	17	late	late	ADV
easat-8674	115	18	from	from	ADP
easat-8674	115	19	7	7	NUM
easat-8674	115	20	am	am	NOUN
easat-8674	115	21	.	.	PUNCT
easat-8674	116	1	if	if	SCONJ
easat-8674	116	2	the	the	DET
easat-8674	116	3	rocket	rocket	NOUN
easat-8674	116	4	is	be	AUX
easat-8674	116	5	launched	launch	VERB
easat-8674	116	6	at	at	ADP
easat-8674	116	7	60	60	NUM
easat-8674	116	8	𝑘𝑚/ℎ	𝑘𝑚/ℎ	NOUN
easat-8674	116	9	,	,	PUNCT
easat-8674	116	10	it	it	PRON
easat-8674	116	11	will	will	AUX
easat-8674	116	12	enter	enter	VERB
easat-8674	116	13	the	the	DET
easat-8674	116	14	mesosphere	mesosphere	NOUN
easat-8674	116	15	layer	layer	NOUN
easat-8674	116	16	20	20	NUM
easat-8674	116	17	minutes	minute	NOUN
easat-8674	116	18	before	before	ADP
easat-8674	116	19	7	7	NUM
easat-8674	116	20	am	be	AUX
easat-8674	116	21	.	.	PUNCT
easat-8674	117	1	what	what	PRON
easat-8674	117	2	is	be	AUX
easat-8674	117	3	the	the	DET
easat-8674	117	4	distance	distance	NOUN
easat-8674	117	5	between	between	ADP
easat-8674	117	6	the	the	DET
easat-8674	117	7	earth	earth	NOUN
easat-8674	117	8	and	and	CCONJ
easat-8674	117	9	the	the	DET
easat-8674	117	10	mesosphere	mesosphere	NOUN
easat-8674	117	11	layer	layer	NOUN
easat-8674	117	12	?	?	PUNCT
easat-8674	118	1	3.1.2	3.1.2	X
easat-8674	118	2	.	.	PUNCT
easat-8674	118	3	problem	problem	NOUN
easat-8674	118	4	2	2	NUM
easat-8674	118	5	(	(	PUNCT
easat-8674	118	6	30	30	NUM
easat-8674	118	7	minutes	minute	NOUN
easat-8674	118	8	)	)	PUNCT
easat-8674	118	9	below	below	ADP
easat-8674	118	10	are	be	AUX
easat-8674	118	11	3	3	NUM
easat-8674	118	12	wooden	wooden	ADJ
easat-8674	118	13	block	block	NOUN
easat-8674	118	14	arrangements	arrangement	NOUN
easat-8674	118	15	that	that	PRON
easat-8674	118	16	have	have	VERB
easat-8674	118	17	different	different	ADJ
easat-8674	118	18	heights	height	NOUN
easat-8674	118	19	and	and	CCONJ
easat-8674	118	20	are	be	AUX
easat-8674	118	21	composed	compose	VERB
easat-8674	118	22	of	of	ADP
easat-8674	118	23	two	two	NUM
easat-8674	118	24	different	different	ADJ
easat-8674	118	25	shapes	shape	NOUN
easat-8674	118	26	,	,	PUNCT
easat-8674	118	27	namely	namely	ADV
easat-8674	118	28	a	a	DET
easat-8674	118	29	block	block	NOUN
easat-8674	118	30	and	and	CCONJ
easat-8674	118	31	a	a	DET
easat-8674	118	32	tube	tube	NOUN
easat-8674	118	33	:	:	PUNCT
easat-8674	118	34	figure	figure	NOUN
easat-8674	118	35	1	1	NUM
easat-8674	118	36	.	.	PUNCT
easat-8674	118	37	three	three	NUM
easat-8674	118	38	wooden	wooden	ADJ
easat-8674	118	39	block	block	NOUN
easat-8674	118	40	.	.	PUNCT
easat-8674	119	1	what	what	PRON
easat-8674	119	2	is	be	AUX
easat-8674	119	3	the	the	DET
easat-8674	119	4	height	height	NOUN
easat-8674	119	5	of	of	ADP
easat-8674	119	6	the	the	DET
easat-8674	119	7	third	third	ADJ
easat-8674	119	8	wooden	wooden	ADJ
easat-8674	119	9	block	block	NOUN
easat-8674	119	10	arrangement	arrangement	NOUN
easat-8674	119	11	?	?	PUNCT
easat-8674	120	1	explain	explain	VERB
easat-8674	120	2	how	how	SCONJ
easat-8674	120	3	you	you	PRON
easat-8674	120	4	got	get	VERB
easat-8674	120	5	the	the	DET
easat-8674	120	6	result	result	NOUN
easat-8674	120	7	with	with	ADP
easat-8674	120	8	a	a	DET
easat-8674	120	9	rational	rational	ADJ
easat-8674	120	10	argument	argument	NOUN
easat-8674	120	11	!	!	PUNCT
easat-8674	121	1	3.1.3	3.1.3	X
easat-8674	121	2	.	.	PUNCT
easat-8674	121	3	problem	problem	NOUN
easat-8674	121	4	3	3	NUM
easat-8674	121	5	(	(	PUNCT
easat-8674	121	6	30	30	NUM
easat-8674	121	7	minutes	minute	NOUN
easat-8674	121	8	)	)	PUNCT
easat-8674	121	9	amin	amin	NOUN
easat-8674	121	10	and	and	CCONJ
easat-8674	121	11	dimas	dima	NOUN
easat-8674	121	12	each	each	PRON
easat-8674	121	13	have	have	VERB
easat-8674	121	14	a	a	DET
easat-8674	121	15	lucky	lucky	ADJ
easat-8674	121	16	number	number	NOUN
easat-8674	121	17	.	.	PUNCT
easat-8674	122	1	amin	amin	PROPN
easat-8674	122	2	’s	’s	PART
easat-8674	122	3	lucky	lucky	ADJ
easat-8674	122	4	number	number	NOUN
easat-8674	122	5	is	be	AUX
easat-8674	122	6	3	3	NUM
easat-8674	122	7	more	more	ADJ
easat-8674	122	8	than	than	ADP
easat-8674	122	9	dimas	dimas	PROPN
easat-8674	122	10	’s	’s	PART
easat-8674	122	11	lucky	lucky	ADJ
easat-8674	122	12	number	number	NOUN
easat-8674	122	13	.	.	PUNCT
easat-8674	123	1	if	if	SCONJ
easat-8674	123	2	the	the	DET
easat-8674	123	3	difference	difference	NOUN
easat-8674	123	4	between	between	ADP
easat-8674	123	5	the	the	DET
easat-8674	123	6	squares	square	NOUN
easat-8674	123	7	of	of	ADP
easat-8674	123	8	their	their	PRON
easat-8674	123	9	lucky	lucky	ADJ
easat-8674	123	10	numbers	number	NOUN
easat-8674	123	11	is	be	AUX
easat-8674	123	12	45	45	NUM
easat-8674	123	13	,	,	PUNCT
easat-8674	123	14	what	what	PRON
easat-8674	123	15	is	be	AUX
easat-8674	123	16	dimas	dimas	PROPN
easat-8674	123	17	’s	’s	PART
easat-8674	123	18	lucky	lucky	ADJ
easat-8674	123	19	585	585	NUM
easat-8674	123	20	edelweiss	edelweiss	PROPN
easat-8674	123	21	applied	apply	VERB
easat-8674	123	22	science	science	NOUN
easat-8674	123	23	and	and	CCONJ
easat-8674	123	24	technology	technology	NOUN
easat-8674	123	25	issn	issn	PROPN
easat-8674	123	26	:	:	PUNCT
easat-8674	123	27	2576	2576	NUM
easat-8674	123	28	-	-	SYM
easat-8674	123	29	8484	8484	NUM
easat-8674	123	30	vol	vol	NOUN
easat-8674	123	31	.	.	PROPN
easat-8674	124	1	9	9	NUM
easat-8674	124	2	,	,	PUNCT
easat-8674	124	3	no	no	INTJ
easat-8674	124	4	.	.	NOUN
easat-8674	125	1	7	7	NUM
easat-8674	125	2	:	:	SYM
easat-8674	125	3	580	580	NUM
easat-8674	125	4	-	-	SYM
easat-8674	125	5	594	594	NUM
easat-8674	125	6	,	,	PUNCT
easat-8674	125	7	2025	2025	NUM
easat-8674	125	8	doi	doi	NOUN
easat-8674	125	9	:	:	PUNCT
easat-8674	125	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	125	11	©	©	PROPN
easat-8674	125	12	2025	2025	NUM
easat-8674	125	13	by	by	ADP
easat-8674	125	14	the	the	DET
easat-8674	125	15	authors	author	NOUN
easat-8674	125	16	;	;	PUNCT
easat-8674	125	17	licensee	licensee	PROPN
easat-8674	125	18	learning	learning	NOUN
easat-8674	125	19	gate	gate	NOUN
easat-8674	125	20	number?"question	number?"question	PROPN
easat-8674	125	21	:	:	PUNCT
easat-8674	125	22	explain	explain	VERB
easat-8674	125	23	the	the	DET
easat-8674	125	24	steps	step	NOUN
easat-8674	125	25	of	of	ADP
easat-8674	125	26	the	the	DET
easat-8674	125	27	problem	problem	NOUN
easat-8674	125	28	solving	solving	NOUN
easat-8674	125	29	process	process	NOUN
easat-8674	125	30	above	above	ADV
easat-8674	125	31	for	for	SCONJ
easat-8674	125	32	junior	junior	ADJ
easat-8674	125	33	high	high	ADJ
easat-8674	125	34	students	student	NOUN
easat-8674	125	35	to	to	PART
easat-8674	125	36	easily	easily	ADV
easat-8674	125	37	understand	understand	VERB
easat-8674	125	38	?	?	PUNCT
easat-8674	126	1	4	4	X
easat-8674	126	2	.	.	X
easat-8674	126	3	results	result	VERB
easat-8674	126	4	4.1	4.1	NUM
easat-8674	126	5	.	.	PUNCT
easat-8674	126	6	case	case	NOUN
easat-8674	126	7	one	one	NUM
easat-8674	126	8	:	:	PUNCT
easat-8674	126	9	subject	subject	ADJ
easat-8674	126	10	s01	s01	NOUN
easat-8674	126	11	and	and	CCONJ
easat-8674	126	12	s02	s02	PROPN
easat-8674	126	13	subject	subject	ADJ
easat-8674	126	14	s01	s01	NOUN
easat-8674	126	15	provided	provide	VERB
easat-8674	126	16	a	a	DET
easat-8674	126	17	comprehensive	comprehensive	ADJ
easat-8674	126	18	response	response	NOUN
easat-8674	126	19	to	to	PART
easat-8674	126	20	question	question	VERB
easat-8674	126	21	1	1	NUM
easat-8674	126	22	.	.	PUNCT
easat-8674	127	1	the	the	DET
easat-8674	127	2	student	student	NOUN
easat-8674	127	3	systematically	systematically	ADV
easat-8674	127	4	identified	identify	VERB
easat-8674	127	5	the	the	DET
easat-8674	127	6	distance	distance	NOUN
easat-8674	127	7	between	between	ADP
easat-8674	127	8	the	the	DET
easat-8674	127	9	earth	earth	NOUN
easat-8674	127	10	and	and	CCONJ
easat-8674	127	11	the	the	DET
easat-8674	127	12	mesosphere	mesosphere	NOUN
easat-8674	127	13	layer	layer	NOUN
easat-8674	127	14	by	by	ADP
easat-8674	127	15	integrating	integrate	VERB
easat-8674	127	16	the	the	DET
easat-8674	127	17	information	information	NOUN
easat-8674	127	18	given	give	VERB
easat-8674	127	19	in	in	ADP
easat-8674	127	20	the	the	DET
easat-8674	127	21	problem	problem	NOUN
easat-8674	127	22	and	and	CCONJ
easat-8674	127	23	representing	represent	VERB
easat-8674	127	24	it	it	PRON
easat-8674	127	25	mathematically	mathematically	ADV
easat-8674	127	26	.	.	PUNCT
easat-8674	128	1	s01	s01	PROPN
easat-8674	128	2	successfully	successfully	ADV
easat-8674	128	3	connected	connect	VERB
easat-8674	128	4	this	this	DET
easat-8674	128	5	representation	representation	NOUN
easat-8674	128	6	to	to	ADP
easat-8674	128	7	fundamental	fundamental	ADJ
easat-8674	128	8	concepts	concept	NOUN
easat-8674	128	9	,	,	PUNCT
easat-8674	128	10	such	such	ADJ
easat-8674	128	11	as	as	ADP
easat-8674	128	12	the	the	DET
easat-8674	128	13	relationship	relationship	NOUN
easat-8674	128	14	between	between	ADP
easat-8674	128	15	speed	speed	NOUN
easat-8674	128	16	,	,	PUNCT
easat-8674	128	17	distance	distance	NOUN
easat-8674	128	18	,	,	PUNCT
easat-8674	128	19	and	and	CCONJ
easat-8674	128	20	time	time	NOUN
easat-8674	128	21	.	.	PUNCT
easat-8674	129	1	the	the	DET
easat-8674	129	2	student	student	NOUN
easat-8674	129	3	correctly	correctly	ADV
easat-8674	129	4	applied	apply	VERB
easat-8674	129	5	time	time	NOUN
easat-8674	129	6	unit	unit	NOUN
easat-8674	129	7	conversions	conversion	NOUN
easat-8674	129	8	and	and	CCONJ
easat-8674	129	9	clearly	clearly	ADV
easat-8674	129	10	wrote	write	VERB
easat-8674	129	11	the	the	DET
easat-8674	129	12	relevant	relevant	ADJ
easat-8674	129	13	speed	speed	NOUN
easat-8674	129	14	formula	formula	NOUN
easat-8674	129	15	on	on	ADP
easat-8674	129	16	the	the	DET
easat-8674	129	17	answer	answer	NOUN
easat-8674	129	18	sheet	sheet	NOUN
easat-8674	129	19	.	.	PUNCT
easat-8674	130	1	figure	figure	NOUN
easat-8674	130	2	2	2	NUM
easat-8674	130	3	.	.	PUNCT
easat-8674	130	4	response	response	NOUN
easat-8674	130	5	sheets	sheet	NOUN
easat-8674	130	6	of	of	ADP
easat-8674	130	7	s01	s01	NOUN
easat-8674	130	8	.	.	PUNCT
easat-8674	131	1	subject	subject	PROPN
easat-8674	131	2	s02	s02	PROPN
easat-8674	131	3	also	also	ADV
easat-8674	131	4	provided	provide	VERB
easat-8674	131	5	a	a	DET
easat-8674	131	6	complete	complete	ADJ
easat-8674	131	7	response	response	NOUN
easat-8674	131	8	to	to	PART
easat-8674	131	9	question	question	NOUN
easat-8674	131	10	1	1	NUM
easat-8674	131	11	but	but	CCONJ
easat-8674	131	12	demonstrated	demonstrate	VERB
easat-8674	131	13	a	a	DET
easat-8674	131	14	limited	limited	ADJ
easat-8674	131	15	understanding	understanding	NOUN
easat-8674	131	16	of	of	ADP
easat-8674	131	17	the	the	DET
easat-8674	131	18	problem	problem	NOUN
easat-8674	131	19	.	.	PUNCT
easat-8674	132	1	although	although	SCONJ
easat-8674	132	2	the	the	DET
easat-8674	132	3	student	student	NOUN
easat-8674	132	4	applied	apply	VERB
easat-8674	132	5	the	the	DET
easat-8674	132	6	speed	speed	NOUN
easat-8674	132	7	-	-	PUNCT
easat-8674	132	8	distance	distance	NOUN
easat-8674	132	9	-	-	PUNCT
easat-8674	132	10	time	time	NOUN
easat-8674	132	11	relationship	relationship	NOUN
easat-8674	132	12	,	,	PUNCT
easat-8674	132	13	there	there	PRON
easat-8674	132	14	was	be	VERB
easat-8674	132	15	a	a	DET
easat-8674	132	16	misunderstanding	misunderstanding	NOUN
easat-8674	132	17	regarding	regard	VERB
easat-8674	132	18	the	the	DET
easat-8674	132	19	conversion	conversion	NOUN
easat-8674	132	20	of	of	ADP
easat-8674	132	21	time	time	NOUN
easat-8674	132	22	units	unit	NOUN
easat-8674	132	23	,	,	PUNCT
easat-8674	132	24	as	as	SCONJ
easat-8674	132	25	shown	show	VERB
easat-8674	132	26	in	in	ADP
easat-8674	132	27	the	the	DET
easat-8674	132	28	student	student	NOUN
easat-8674	132	29	’s	’s	PART
easat-8674	132	30	answer	answer	NOUN
easat-8674	132	31	sheet	sheet	NOUN
easat-8674	132	32	(	(	PUNCT
easat-8674	132	33	figure	figure	NOUN
easat-8674	132	34	3	3	NUM
easat-8674	132	35	)	)	PUNCT
easat-8674	132	36	.	.	PUNCT
easat-8674	133	1	586	586	NUM
easat-8674	133	2	edelweiss	edelweiss	PROPN
easat-8674	133	3	applied	apply	VERB
easat-8674	133	4	science	science	NOUN
easat-8674	133	5	and	and	CCONJ
easat-8674	133	6	technology	technology	NOUN
easat-8674	133	7	issn	issn	PROPN
easat-8674	133	8	:	:	PUNCT
easat-8674	133	9	2576	2576	NUM
easat-8674	133	10	-	-	SYM
easat-8674	133	11	8484	8484	NUM
easat-8674	133	12	vol	vol	NOUN
easat-8674	133	13	.	.	PROPN
easat-8674	134	1	9	9	NUM
easat-8674	134	2	,	,	PUNCT
easat-8674	134	3	no	no	INTJ
easat-8674	134	4	.	.	NOUN
easat-8674	135	1	7	7	NUM
easat-8674	135	2	:	:	SYM
easat-8674	135	3	580	580	NUM
easat-8674	135	4	-	-	SYM
easat-8674	135	5	594	594	NUM
easat-8674	135	6	,	,	PUNCT
easat-8674	135	7	2025	2025	NUM
easat-8674	135	8	doi	doi	NOUN
easat-8674	135	9	:	:	PUNCT
easat-8674	135	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	135	11	©	©	PROPN
easat-8674	135	12	2025	2025	NUM
easat-8674	135	13	by	by	ADP
easat-8674	135	14	the	the	DET
easat-8674	135	15	authors	author	NOUN
easat-8674	135	16	;	;	PUNCT
easat-8674	135	17	licensee	licensee	PROPN
easat-8674	135	18	learning	learn	VERB
easat-8674	135	19	gate	gate	PROPN
easat-8674	135	20	figure	figure	NOUN
easat-8674	135	21	3	3	NUM
easat-8674	135	22	.	.	PUNCT
easat-8674	135	23	response	response	NOUN
easat-8674	135	24	sheets	sheet	NOUN
easat-8674	135	25	of	of	ADP
easat-8674	135	26	s02	s02	PROPN
easat-8674	135	27	.	.	PUNCT
easat-8674	136	1	based	base	VERB
easat-8674	136	2	on	on	ADP
easat-8674	136	3	figure	figure	NOUN
easat-8674	136	4	2	2	NUM
easat-8674	136	5	and	and	CCONJ
easat-8674	136	6	figure	figure	VERB
easat-8674	136	7	3	3	NUM
easat-8674	136	8	,	,	PUNCT
easat-8674	136	9	the	the	DET
easat-8674	136	10	answer	answer	NOUN
easat-8674	136	11	sheets	sheet	NOUN
easat-8674	136	12	of	of	ADP
easat-8674	136	13	s01	s01	NOUN
easat-8674	136	14	and	and	CCONJ
easat-8674	136	15	s02	s02	PROPN
easat-8674	136	16	demonstrate	demonstrate	VERB
easat-8674	136	17	their	their	PRON
easat-8674	136	18	ability	ability	NOUN
easat-8674	136	19	to	to	PART
easat-8674	136	20	represent	represent	VERB
easat-8674	136	21	content	content	NOUN
easat-8674	136	22	knowledge	knowledge	NOUN
easat-8674	136	23	in	in	ADP
easat-8674	136	24	solving	solve	VERB
easat-8674	136	25	the	the	DET
easat-8674	136	26	problem	problem	NOUN
easat-8674	136	27	.	.	PUNCT
easat-8674	137	1	however	however	ADV
easat-8674	137	2	,	,	PUNCT
easat-8674	137	3	to	to	PART
easat-8674	137	4	clarify	clarify	VERB
easat-8674	137	5	certain	certain	ADJ
easat-8674	137	6	aspects	aspect	NOUN
easat-8674	137	7	that	that	PRON
easat-8674	137	8	remained	remain	VERB
easat-8674	137	9	unclear	unclear	ADJ
easat-8674	137	10	such	such	ADJ
easat-8674	137	11	as	as	ADP
easat-8674	137	12	s01	s01	NOUN
easat-8674	137	13	’s	’s	PART
easat-8674	137	14	process	process	NOUN
easat-8674	137	15	of	of	ADP
easat-8674	137	16	converting	convert	VERB
easat-8674	137	17	time	time	NOUN
easat-8674	137	18	units	unit	NOUN
easat-8674	137	19	and	and	CCONJ
easat-8674	137	20	s02	s02	PROPN
easat-8674	137	21	’s	’s	PART
easat-8674	137	22	justification	justification	NOUN
easat-8674	137	23	of	of	ADP
easat-8674	137	24	the	the	DET
easat-8674	137	25	correctness	correctness	NOUN
easat-8674	137	26	of	of	ADP
easat-8674	137	27	the	the	DET
easat-8674	137	28	answer	answer	NOUN
easat-8674	137	29	the	the	DET
easat-8674	137	30	researcher	researcher	NOUN
easat-8674	137	31	conducted	conduct	VERB
easat-8674	137	32	follow	follow	NOUN
easat-8674	137	33	-	-	PUNCT
easat-8674	137	34	up	up	ADP
easat-8674	137	35	interviews	interview	NOUN
easat-8674	137	36	with	with	ADP
easat-8674	137	37	both	both	DET
easat-8674	137	38	students	student	NOUN
easat-8674	137	39	.	.	PUNCT
easat-8674	138	1	the	the	DET
easat-8674	138	2	following	follow	VERB
easat-8674	138	3	are	be	AUX
easat-8674	138	4	excerpts	excerpt	NOUN
easat-8674	138	5	from	from	ADP
easat-8674	138	6	the	the	DET
easat-8674	138	7	interviews	interview	NOUN
easat-8674	138	8	with	with	ADP
easat-8674	138	9	s01	s01	NOUN
easat-8674	138	10	and	and	CCONJ
easat-8674	138	11	s02	s02	PROPN
easat-8674	138	12	regarding	regard	VERB
easat-8674	138	13	question	question	NOUN
easat-8674	138	14	number	number	NOUN
easat-8674	138	15	1	1	NUM
easat-8674	138	16	r	r	NOUN
easat-8674	138	17	please	please	INTJ
easat-8674	138	18	explain	explain	VERB
easat-8674	138	19	where	where	SCONJ
easat-8674	138	20	you	you	PRON
easat-8674	138	21	got	get	VERB
easat-8674	138	22	the	the	DET
easat-8674	138	23	value	value	NOUN
easat-8674	138	24	1/6	1/6	NUM
easat-8674	138	25	.	.	PUNCT
easat-8674	139	1	what	what	PRON
easat-8674	139	2	does	do	AUX
easat-8674	139	3	it	it	PRON
easat-8674	139	4	represent	represent	VERB
easat-8674	139	5	?	?	PUNCT
easat-8674	140	1	s01	s01	NOUN
easat-8674	140	2	i	i	PRON
easat-8674	140	3	converted	convert	VERB
easat-8674	140	4	the	the	DET
easat-8674	140	5	rocket	rocket	NOUN
easat-8674	140	6	’s	’s	PART
easat-8674	140	7	arrival	arrival	NOUN
easat-8674	140	8	time	time	NOUN
easat-8674	140	9	,	,	PUNCT
easat-8674	140	10	which	which	PRON
easat-8674	140	11	is	be	AUX
easat-8674	140	12	less	less	ADJ
easat-8674	140	13	than	than	ADP
easat-8674	140	14	10	10	NUM
easat-8674	140	15	minutes	minute	NOUN
easat-8674	140	16	.	.	PUNCT
easat-8674	141	1	since	since	SCONJ
easat-8674	141	2	1	1	NUM
easat-8674	141	3	hour	hour	NOUN
easat-8674	141	4	=	=	SYM
easat-8674	141	5	60	60	NUM
easat-8674	141	6	minutes	minute	NOUN
easat-8674	141	7	,	,	PUNCT
easat-8674	141	8	then	then	ADV
easat-8674	141	9	10/60	10/60	NUM
easat-8674	141	10	=	=	SYM
easat-8674	141	11	1/6	1/6	NUM
easat-8674	141	12	hour	hour	NOUN
easat-8674	141	13	.	.	PUNCT
easat-8674	141	14	s02	s02	PROPN
easat-8674	141	15	because	because	SCONJ
easat-8674	141	16	1	1	NUM
easat-8674	141	17	hour	hour	NOUN
easat-8674	141	18	=	=	SYM
easat-8674	141	19	60	60	NUM
easat-8674	141	20	minutes	minute	NOUN
easat-8674	141	21	and	and	CCONJ
easat-8674	141	22	the	the	DET
easat-8674	141	23	time	time	NOUN
easat-8674	141	24	was	be	AUX
easat-8674	141	25	more	more	ADJ
easat-8674	141	26	than	than	ADP
easat-8674	141	27	10	10	NUM
easat-8674	141	28	minutes	minute	NOUN
easat-8674	141	29	,	,	PUNCT
easat-8674	141	30	i	i	PRON
easat-8674	141	31	used	use	VERB
easat-8674	141	32	70	70	NUM
easat-8674	141	33	minutes	minute	NOUN
easat-8674	141	34	.	.	PUNCT
easat-8674	142	1	r	r	NOUN
easat-8674	142	2	how	how	SCONJ
easat-8674	142	3	can	can	AUX
easat-8674	142	4	you	you	PRON
easat-8674	142	5	prove	prove	VERB
easat-8674	142	6	that	that	SCONJ
easat-8674	142	7	your	your	PRON
easat-8674	142	8	answer	answer	NOUN
easat-8674	142	9	is	be	AUX
easat-8674	142	10	correct	correct	ADJ
easat-8674	142	11	?	?	PUNCT
easat-8674	143	1	s02	s02	PROPN
easat-8674	143	2	because	because	SCONJ
easat-8674	143	3	i	i	PRON
easat-8674	143	4	used	use	VERB
easat-8674	143	5	the	the	DET
easat-8674	143	6	formula	formula	NOUN
easat-8674	143	7	for	for	ADP
easat-8674	143	8	speed	speed	NOUN
easat-8674	143	9	,	,	PUNCT
easat-8674	143	10	s	s	NOUN
easat-8674	143	11	=	=	X
easat-8674	143	12	v	v	X
easat-8674	143	13	×	×	PROPN
easat-8674	143	14	t	t	NOUN
easat-8674	143	15	in	in	ADP
easat-8674	143	16	solving	solve	VERB
easat-8674	143	17	the	the	DET
easat-8674	143	18	first	first	ADJ
easat-8674	143	19	problem	problem	NOUN
easat-8674	143	20	,	,	PUNCT
easat-8674	143	21	the	the	DET
easat-8674	143	22	two	two	NUM
easat-8674	143	23	subjects	subject	NOUN
easat-8674	143	24	demonstrated	demonstrate	VERB
easat-8674	143	25	different	different	ADJ
easat-8674	143	26	approaches	approach	NOUN
easat-8674	143	27	in	in	ADP
easat-8674	143	28	interpreting	interpret	VERB
easat-8674	143	29	and	and	CCONJ
easat-8674	143	30	representing	represent	VERB
easat-8674	143	31	time	time	NOUN
easat-8674	143	32	information	information	NOUN
easat-8674	143	33	algebraically	algebraically	ADV
easat-8674	143	34	.	.	PUNCT
easat-8674	144	1	this	this	DET
easat-8674	144	2	analysis	analysis	NOUN
easat-8674	144	3	focuses	focus	VERB
easat-8674	144	4	on	on	ADP
easat-8674	144	5	how	how	SCONJ
easat-8674	144	6	they	they	PRON
easat-8674	144	7	converted	convert	VERB
easat-8674	144	8	time	time	NOUN
easat-8674	144	9	units	unit	NOUN
easat-8674	144	10	and	and	CCONJ
easat-8674	144	11	applied	apply	VERB
easat-8674	144	12	algebraic	algebraic	ADJ
easat-8674	144	13	concepts	concept	NOUN
easat-8674	144	14	in	in	ADP
easat-8674	144	15	solving	solve	VERB
easat-8674	144	16	for	for	ADP
easat-8674	144	17	speed	speed	NOUN
easat-8674	144	18	.	.	PUNCT
easat-8674	145	1	subject	subject	ADJ
easat-8674	145	2	s01	s01	PROPN
easat-8674	145	3	demonstrated	demonstrate	VERB
easat-8674	145	4	a	a	DET
easat-8674	145	5	sound	sound	ADJ
easat-8674	145	6	conceptual	conceptual	ADJ
easat-8674	145	7	understanding	understanding	NOUN
easat-8674	145	8	of	of	ADP
easat-8674	145	9	time	time	NOUN
easat-8674	145	10	unit	unit	NOUN
easat-8674	145	11	conversion	conversion	NOUN
easat-8674	145	12	from	from	ADP
easat-8674	145	13	minutes	minute	NOUN
easat-8674	145	14	to	to	ADP
easat-8674	145	15	hours	hour	NOUN
easat-8674	145	16	.	.	PUNCT
easat-8674	146	1	by	by	ADP
easat-8674	146	2	recognizing	recognize	VERB
easat-8674	146	3	that	that	SCONJ
easat-8674	146	4	10	10	NUM
easat-8674	146	5	minutes	minute	NOUN
easat-8674	146	6	equals	equal	VERB
easat-8674	146	7	10	10	NUM
easat-8674	146	8	60	60	NUM
easat-8674	146	9	=	=	SYM
easat-8674	146	10	1	1	NUM
easat-8674	146	11	6	6	NUM
easat-8674	146	12	hour	hour	NOUN
easat-8674	146	13	,	,	PUNCT
easat-8674	146	14	s01	s01	NOUN
easat-8674	146	15	ensured	ensure	VERB
easat-8674	146	16	consistency	consistency	NOUN
easat-8674	146	17	in	in	ADP
easat-8674	146	18	units	unit	NOUN
easat-8674	146	19	within	within	ADP
easat-8674	146	20	the	the	DET
easat-8674	146	21	formula	formula	NOUN
easat-8674	146	22	𝑠	𝑠	NOUN
easat-8674	146	23	=	=	SYM
easat-8674	146	24	𝑣	𝑣	PART
easat-8674	146	25	×	×	NOUN
easat-8674	146	26	𝑡	𝑡	NOUN
easat-8674	146	27	particularly	particularly	ADV
easat-8674	146	28	when	when	SCONJ
easat-8674	146	29	speed	speed	NOUN
easat-8674	146	30	is	be	AUX
easat-8674	146	31	given	give	VERB
easat-8674	146	32	in	in	ADP
easat-8674	146	33	km	km	PROPN
easat-8674	146	34	/	/	SYM
easat-8674	146	35	h.	h.	NOUN
easat-8674	146	36	this	this	DET
easat-8674	146	37	representation	representation	NOUN
easat-8674	146	38	indicates	indicate	VERB
easat-8674	146	39	an	an	DET
easat-8674	146	40	appropriate	appropriate	ADJ
easat-8674	146	41	functional	functional	ADJ
easat-8674	146	42	understanding	understanding	NOUN
easat-8674	146	43	of	of	ADP
easat-8674	146	44	algebra	algebra	NOUN
easat-8674	146	45	.	.	PUNCT
easat-8674	147	1	conversely	conversely	ADV
easat-8674	147	2	,	,	PUNCT
easat-8674	147	3	subject	subject	ADJ
easat-8674	147	4	s02	s02	PROPN
easat-8674	147	5	exhibited	exhibit	VERB
easat-8674	147	6	a	a	DET
easat-8674	147	7	misconception	misconception	NOUN
easat-8674	147	8	by	by	ADP
easat-8674	147	9	assuming	assume	VERB
easat-8674	147	10	the	the	DET
easat-8674	147	11	time	time	NOUN
easat-8674	147	12	duration	duration	NOUN
easat-8674	147	13	was	be	AUX
easat-8674	147	14	70	70	NUM
easat-8674	147	15	minutes	minute	NOUN
easat-8674	147	16	without	without	ADP
easat-8674	147	17	clear	clear	ADJ
easat-8674	147	18	justification	justification	NOUN
easat-8674	147	19	.	.	PUNCT
easat-8674	148	1	this	this	DET
easat-8674	148	2	response	response	NOUN
easat-8674	148	3	highlights	highlight	VERB
easat-8674	148	4	a	a	DET
easat-8674	148	5	failure	failure	NOUN
easat-8674	148	6	to	to	PART
easat-8674	148	7	apply	apply	VERB
easat-8674	148	8	proper	proper	ADJ
easat-8674	148	9	unit	unit	NOUN
easat-8674	148	10	conversion	conversion	NOUN
easat-8674	148	11	and	and	CCONJ
easat-8674	148	12	a	a	DET
easat-8674	148	13	disregard	disregard	NOUN
easat-8674	148	14	for	for	ADP
easat-8674	148	15	consistency	consistency	NOUN
easat-8674	148	16	in	in	ADP
easat-8674	148	17	mathematical	mathematical	ADJ
easat-8674	148	18	representation	representation	NOUN
easat-8674	148	19	.	.	PUNCT
easat-8674	149	1	although	although	SCONJ
easat-8674	149	2	s02	s02	NOUN
easat-8674	149	3	referenced	reference	VERB
easat-8674	149	4	the	the	DET
easat-8674	149	5	speed	speed	NOUN
easat-8674	149	6	formula	formula	NOUN
easat-8674	149	7	,	,	PUNCT
easat-8674	149	8	there	there	PRON
easat-8674	149	9	was	be	VERB
easat-8674	149	10	no	no	DET
easat-8674	149	11	elaboration	elaboration	NOUN
easat-8674	149	12	587	587	NUM
easat-8674	149	13	edelweiss	edelweiss	PROPN
easat-8674	149	14	applied	apply	VERB
easat-8674	149	15	science	science	NOUN
easat-8674	149	16	and	and	CCONJ
easat-8674	149	17	technology	technology	NOUN
easat-8674	149	18	issn	issn	PROPN
easat-8674	149	19	:	:	PUNCT
easat-8674	149	20	2576	2576	NUM
easat-8674	149	21	-	-	SYM
easat-8674	149	22	8484	8484	NUM
easat-8674	149	23	vol	vol	NOUN
easat-8674	149	24	.	.	PROPN
easat-8674	150	1	9	9	NUM
easat-8674	150	2	,	,	PUNCT
easat-8674	150	3	no	no	INTJ
easat-8674	150	4	.	.	NOUN
easat-8674	151	1	7	7	NUM
easat-8674	151	2	:	:	SYM
easat-8674	151	3	580	580	NUM
easat-8674	151	4	-	-	SYM
easat-8674	151	5	594	594	NUM
easat-8674	151	6	,	,	PUNCT
easat-8674	151	7	2025	2025	NUM
easat-8674	151	8	doi	doi	NOUN
easat-8674	151	9	:	:	PUNCT
easat-8674	151	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	151	11	©	©	PROPN
easat-8674	151	12	2025	2025	NUM
easat-8674	151	13	by	by	ADP
easat-8674	151	14	the	the	DET
easat-8674	151	15	authors	author	NOUN
easat-8674	151	16	;	;	PUNCT
easat-8674	151	17	licensee	licensee	PROPN
easat-8674	151	18	learning	learning	NOUN
easat-8674	151	19	gate	gate	NOUN
easat-8674	151	20	on	on	ADP
easat-8674	151	21	how	how	SCONJ
easat-8674	151	22	values	value	NOUN
easat-8674	151	23	were	be	AUX
easat-8674	151	24	substituted	substitute	VERB
easat-8674	151	25	or	or	CCONJ
easat-8674	151	26	calculated	calculate	VERB
easat-8674	151	27	,	,	PUNCT
easat-8674	151	28	indicating	indicate	VERB
easat-8674	151	29	a	a	DET
easat-8674	151	30	procedural	procedural	ADJ
easat-8674	151	31	but	but	CCONJ
easat-8674	151	32	not	not	PART
easat-8674	151	33	conceptual	conceptual	ADJ
easat-8674	151	34	application	application	NOUN
easat-8674	151	35	of	of	ADP
easat-8674	151	36	algebra	algebra	PROPN
easat-8674	151	37	.	.	PUNCT
easat-8674	152	1	thus	thus	ADV
easat-8674	152	2	,	,	PUNCT
easat-8674	152	3	s01	s01	NOUN
easat-8674	152	4	falls	fall	VERB
easat-8674	152	5	under	under	ADP
easat-8674	152	6	the	the	DET
easat-8674	152	7	mba	mba	PROPN
easat-8674	152	8	-	-	PUNCT
easat-8674	152	9	j	j	NOUN
easat-8674	152	10	category	category	NOUN
easat-8674	152	11	,	,	PUNCT
easat-8674	152	12	while	while	SCONJ
easat-8674	152	13	s02	s02	PROPN
easat-8674	152	14	is	be	AUX
easat-8674	152	15	classified	classify	VERB
easat-8674	152	16	as	as	ADP
easat-8674	152	17	dta	dta	PROPN
easat-8674	152	18	-	-	PUNCT
easat-8674	152	19	lc	lc	NOUN
easat-8674	152	20	.	.	PROPN
easat-8674	153	1	4.2	4.2	NUM
easat-8674	153	2	.	.	PUNCT
easat-8674	153	3	case	case	NOUN
easat-8674	153	4	two	two	NUM
easat-8674	153	5	:	:	PUNCT
easat-8674	153	6	subject	subject	ADJ
easat-8674	153	7	s04	s04	NOUN
easat-8674	153	8	and	and	CCONJ
easat-8674	153	9	s06	s06	PROPN
easat-8674	153	10	s04	s04	NOUN
easat-8674	153	11	was	be	AUX
easat-8674	153	12	not	not	PART
easat-8674	153	13	able	able	ADJ
easat-8674	153	14	to	to	PART
easat-8674	153	15	provide	provide	VERB
easat-8674	153	16	a	a	DET
easat-8674	153	17	complete	complete	ADJ
easat-8674	153	18	answer	answer	NOUN
easat-8674	153	19	to	to	PART
easat-8674	153	20	question	question	VERB
easat-8674	153	21	number	number	NOUN
easat-8674	153	22	2	2	NUM
easat-8674	153	23	due	due	ADP
easat-8674	153	24	to	to	ADP
easat-8674	153	25	the	the	DET
easat-8674	153	26	omission	omission	NOUN
easat-8674	153	27	of	of	ADP
easat-8674	153	28	key	key	ADJ
easat-8674	153	29	information	information	NOUN
easat-8674	153	30	from	from	ADP
easat-8674	153	31	the	the	DET
easat-8674	153	32	problem	problem	NOUN
easat-8674	153	33	.	.	PUNCT
easat-8674	154	1	although	although	SCONJ
easat-8674	154	2	s04	s04	NOUN
easat-8674	154	3	correctly	correctly	ADV
easat-8674	154	4	applied	apply	VERB
easat-8674	154	5	the	the	DET
easat-8674	154	6	difference	difference	NOUN
easat-8674	154	7	of	of	ADP
easat-8674	154	8	squares	square	NOUN
easat-8674	154	9	formula	formula	NOUN
easat-8674	154	10	,	,	PUNCT
easat-8674	154	11	the	the	DET
easat-8674	154	12	response	response	NOUN
easat-8674	154	13	did	do	AUX
easat-8674	154	14	not	not	PART
easat-8674	154	15	fully	fully	ADV
easat-8674	154	16	address	address	VERB
easat-8674	154	17	the	the	DET
easat-8674	154	18	question	question	NOUN
easat-8674	154	19	,	,	PUNCT
easat-8674	154	20	indicating	indicate	VERB
easat-8674	154	21	a	a	DET
easat-8674	154	22	lack	lack	NOUN
easat-8674	154	23	of	of	ADP
easat-8674	154	24	understanding	understanding	NOUN
easat-8674	154	25	of	of	ADP
easat-8674	154	26	the	the	DET
easat-8674	154	27	given	give	VERB
easat-8674	154	28	information	information	NOUN
easat-8674	154	29	.	.	PUNCT
easat-8674	155	1	furthermore	furthermore	ADV
easat-8674	155	2	,	,	PUNCT
easat-8674	155	3	s04	s04	PROPN
easat-8674	155	4	did	do	AUX
easat-8674	155	5	not	not	PART
easat-8674	155	6	include	include	VERB
easat-8674	155	7	a	a	DET
easat-8674	155	8	final	final	ADJ
easat-8674	155	9	conclusion	conclusion	NOUN
easat-8674	155	10	in	in	ADP
easat-8674	155	11	the	the	DET
easat-8674	155	12	answer	answer	NOUN
easat-8674	155	13	(	(	PUNCT
easat-8674	155	14	see	see	VERB
easat-8674	155	15	figure	figure	NOUN
easat-8674	155	16	4	4	NUM
easat-8674	155	17	)	)	PUNCT
easat-8674	155	18	.	.	PUNCT
easat-8674	156	1	figure	figure	VERB
easat-8674	156	2	4	4	NUM
easat-8674	156	3	.	.	PUNCT
easat-8674	157	1	response	response	NOUN
easat-8674	157	2	sheets	sheet	NOUN
easat-8674	157	3	of	of	ADP
easat-8674	157	4	s04	s04	PROPN
easat-8674	157	5	.	.	PUNCT
easat-8674	158	1	s06	s06	PROPN
easat-8674	158	2	completed	complete	VERB
easat-8674	158	3	question	question	NOUN
easat-8674	158	4	number	number	NOUN
easat-8674	158	5	2	2	NUM
easat-8674	158	6	adequately	adequately	ADV
easat-8674	158	7	,	,	PUNCT
easat-8674	158	8	although	although	SCONJ
easat-8674	158	9	not	not	PART
easat-8674	158	10	all	all	PRON
easat-8674	158	11	of	of	ADP
easat-8674	158	12	the	the	DET
easat-8674	158	13	information	information	NOUN
easat-8674	158	14	from	from	ADP
easat-8674	158	15	the	the	DET
easat-8674	158	16	problem	problem	NOUN
easat-8674	158	17	was	be	AUX
easat-8674	158	18	fully	fully	ADV
easat-8674	158	19	written	write	VERB
easat-8674	158	20	.	.	PUNCT
easat-8674	159	1	s06	s06	PROPN
easat-8674	159	2	was	be	AUX
easat-8674	159	3	able	able	ADJ
easat-8674	159	4	to	to	PART
easat-8674	159	5	use	use	VERB
easat-8674	159	6	the	the	DET
easat-8674	159	7	difference	difference	NOUN
easat-8674	159	8	of	of	ADP
easat-8674	159	9	squares	square	NOUN
easat-8674	159	10	formula	formula	NOUN
easat-8674	159	11	and	and	CCONJ
easat-8674	159	12	algebraic	algebraic	ADJ
easat-8674	159	13	operations	operation	NOUN
easat-8674	159	14	to	to	PART
easat-8674	159	15	determine	determine	VERB
easat-8674	159	16	the	the	DET
easat-8674	159	17	lucky	lucky	ADJ
easat-8674	159	18	number	number	NOUN
easat-8674	159	19	,	,	PUNCT
easat-8674	159	20	and	and	CCONJ
easat-8674	159	21	provided	provide	VERB
easat-8674	159	22	an	an	DET
easat-8674	159	23	accurate	accurate	ADJ
easat-8674	159	24	answer	answer	NOUN
easat-8674	159	25	and	and	CCONJ
easat-8674	159	26	conclusion	conclusion	NOUN
easat-8674	159	27	(	(	PUNCT
easat-8674	159	28	see	see	VERB
easat-8674	159	29	figure	figure	NOUN
easat-8674	159	30	5	5	NUM
easat-8674	159	31	)	)	PUNCT
easat-8674	159	32	.	.	PUNCT
easat-8674	160	1	588	588	NUM
easat-8674	160	2	edelweiss	edelweiss	PROPN
easat-8674	160	3	applied	apply	VERB
easat-8674	160	4	science	science	NOUN
easat-8674	160	5	and	and	CCONJ
easat-8674	160	6	technology	technology	NOUN
easat-8674	160	7	issn	issn	PROPN
easat-8674	160	8	:	:	PUNCT
easat-8674	160	9	2576	2576	NUM
easat-8674	160	10	-	-	SYM
easat-8674	160	11	8484	8484	NUM
easat-8674	160	12	vol	vol	NOUN
easat-8674	160	13	.	.	PROPN
easat-8674	161	1	9	9	NUM
easat-8674	161	2	,	,	PUNCT
easat-8674	161	3	no	no	INTJ
easat-8674	161	4	.	.	NOUN
easat-8674	162	1	7	7	NUM
easat-8674	162	2	:	:	SYM
easat-8674	162	3	580	580	NUM
easat-8674	162	4	-	-	SYM
easat-8674	162	5	594	594	NUM
easat-8674	162	6	,	,	PUNCT
easat-8674	162	7	2025	2025	NUM
easat-8674	162	8	doi	doi	NOUN
easat-8674	162	9	:	:	PUNCT
easat-8674	162	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	162	11	©	©	PROPN
easat-8674	162	12	2025	2025	NUM
easat-8674	162	13	by	by	ADP
easat-8674	162	14	the	the	DET
easat-8674	162	15	authors	author	NOUN
easat-8674	162	16	;	;	PUNCT
easat-8674	162	17	licensee	licensee	PROPN
easat-8674	162	18	learning	learn	VERB
easat-8674	162	19	gate	gate	PROPN
easat-8674	162	20	figure	figure	NOUN
easat-8674	162	21	5	5	NUM
easat-8674	162	22	.	.	PUNCT
easat-8674	162	23	response	response	NOUN
easat-8674	162	24	sheets	sheet	NOUN
easat-8674	162	25	of	of	ADP
easat-8674	162	26	s06	s06	NOUN
easat-8674	162	27	.	.	PUNCT
easat-8674	163	1	based	base	VERB
easat-8674	163	2	on	on	ADP
easat-8674	163	3	figures	figure	NOUN
easat-8674	163	4	4	4	NUM
easat-8674	163	5	and	and	CCONJ
easat-8674	163	6	5	5	NUM
easat-8674	163	7	,	,	PUNCT
easat-8674	163	8	the	the	DET
easat-8674	163	9	answer	answer	NOUN
easat-8674	163	10	sheets	sheet	NOUN
easat-8674	163	11	of	of	ADP
easat-8674	163	12	s04	s04	NOUN
easat-8674	163	13	and	and	CCONJ
easat-8674	163	14	s06	s06	NOUN
easat-8674	163	15	reflect	reflect	VERB
easat-8674	163	16	their	their	PRON
easat-8674	163	17	content	content	NOUN
easat-8674	163	18	knowledge	knowledge	NOUN
easat-8674	163	19	in	in	ADP
easat-8674	163	20	solving	solve	VERB
easat-8674	163	21	the	the	DET
easat-8674	163	22	problem	problem	NOUN
easat-8674	163	23	.	.	PUNCT
easat-8674	164	1	however	however	ADV
easat-8674	164	2	,	,	PUNCT
easat-8674	164	3	to	to	PART
easat-8674	164	4	clarify	clarify	VERB
easat-8674	164	5	certain	certain	ADJ
easat-8674	164	6	aspects	aspect	NOUN
easat-8674	164	7	such	such	ADJ
easat-8674	164	8	as	as	ADP
easat-8674	164	9	the	the	DET
easat-8674	164	10	meaning	meaning	NOUN
easat-8674	164	11	of	of	ADP
easat-8674	164	12	the	the	DET
easat-8674	164	13	equations	equation	NOUN
easat-8674	164	14	they	they	PRON
easat-8674	164	15	constructed	construct	VERB
easat-8674	164	16	and	and	CCONJ
easat-8674	164	17	the	the	DET
easat-8674	164	18	justification	justification	NOUN
easat-8674	164	19	of	of	ADP
easat-8674	164	20	their	their	PRON
easat-8674	164	21	answers	answer	NOUN
easat-8674	164	22	the	the	DET
easat-8674	164	23	researcher	researcher	NOUN
easat-8674	164	24	conducted	conduct	VERB
easat-8674	164	25	follow	follow	NOUN
easat-8674	164	26	-	-	PUNCT
easat-8674	164	27	up	up	ADP
easat-8674	164	28	interviews	interview	NOUN
easat-8674	164	29	with	with	ADP
easat-8674	164	30	both	both	DET
easat-8674	164	31	participants	participant	NOUN
easat-8674	164	32	.	.	PUNCT
easat-8674	165	1	the	the	DET
easat-8674	165	2	following	follow	VERB
easat-8674	165	3	are	be	AUX
easat-8674	165	4	excerpts	excerpt	NOUN
easat-8674	165	5	from	from	ADP
easat-8674	165	6	the	the	DET
easat-8674	165	7	interviews	interview	NOUN
easat-8674	165	8	with	with	ADP
easat-8674	165	9	s04	s04	NOUN
easat-8674	165	10	and	and	CCONJ
easat-8674	165	11	s06	s06	NOUN
easat-8674	165	12	regarding	regard	VERB
easat-8674	165	13	question	question	NOUN
easat-8674	165	14	number	number	NOUN
easat-8674	165	15	2	2	NUM
easat-8674	165	16	.	.	PUNCT
easat-8674	166	1	r	r	NOUN
easat-8674	166	2	can	can	AUX
easat-8674	166	3	you	you	PRON
easat-8674	166	4	explain	explain	VERB
easat-8674	166	5	the	the	DET
easat-8674	166	6	meaning	meaning	NOUN
easat-8674	166	7	of	of	ADP
easat-8674	166	8	the	the	DET
easat-8674	166	9	equation	equation	NOUN
easat-8674	166	10	you	you	PRON
easat-8674	166	11	constructed	construct	VERB
easat-8674	166	12	?	?	PUNCT
easat-8674	167	1	s06	s06	AUX
easat-8674	167	2	the	the	DET
easat-8674	167	3	equation	equation	NOUN
easat-8674	167	4	𝑎2	𝑎2	NOUN
easat-8674	167	5	−	−	PROPN
easat-8674	167	6	𝑏2	𝑏2	PROPN
easat-8674	167	7	=	=	NOUN
easat-8674	167	8	𝑐2	𝑐2	NOUN
easat-8674	167	9	represents	represent	VERB
easat-8674	167	10	the	the	DET
easat-8674	167	11	difference	difference	NOUN
easat-8674	167	12	in	in	ADP
easat-8674	167	13	“	"	PUNCT
easat-8674	167	14	lucky	lucky	ADJ
easat-8674	167	15	numbers	number	NOUN
easat-8674	167	16	”	"	PUNCT
easat-8674	167	17	between	between	ADP
easat-8674	167	18	amin	amin	NOUN
easat-8674	167	19	and	and	CCONJ
easat-8674	167	20	dimas	dimas	PROPN
easat-8674	167	21	,	,	PUNCT
easat-8674	167	22	which	which	PRON
easat-8674	167	23	differ	differ	VERB
easat-8674	167	24	by	by	ADP
easat-8674	167	25	three	three	NUM
easat-8674	167	26	units	unit	NOUN
easat-8674	167	27	and	and	CCONJ
easat-8674	167	28	are	be	AUX
easat-8674	167	29	represented	represent	VERB
easat-8674	167	30	by	by	ADP
easat-8674	167	31	𝑎	𝑎	PROPN
easat-8674	167	32	,	,	PUNCT
easat-8674	167	33	𝑏	𝑏	NOUN
easat-8674	167	34	,	,	PUNCT
easat-8674	167	35	and	and	CCONJ
easat-8674	167	36	𝑐.	𝑐.	PROPN
easat-8674	167	37	s04	s04	NOUN
easat-8674	168	1	i	i	PRON
easat-8674	168	2	assigned	assign	VERB
easat-8674	168	3	𝑥	𝑥	PRON
easat-8674	168	4	to	to	ADP
easat-8674	168	5	amin	amin	PROPN
easat-8674	168	6	and	and	CCONJ
easat-8674	168	7	y	y	PROPN
easat-8674	168	8	to	to	ADP
easat-8674	168	9	dimas	dimas	PROPN
easat-8674	168	10	.	.	PUNCT
easat-8674	169	1	since	since	SCONJ
easat-8674	169	2	amin	amin	NOUN
easat-8674	169	3	’s	’s	PART
easat-8674	169	4	lucky	lucky	ADJ
easat-8674	169	5	number	number	NOUN
easat-8674	169	6	is	be	AUX
easat-8674	169	7	three	three	NUM
easat-8674	169	8	more	more	ADJ
easat-8674	169	9	than	than	ADP
easat-8674	169	10	dimas	dimas	PROPN
easat-8674	169	11	’	'	PUNCT
easat-8674	169	12	,	,	PUNCT
easat-8674	169	13	i	i	PRON
easat-8674	169	14	wrote	write	VERB
easat-8674	169	15	𝑥	𝑥	X
easat-8674	169	16	=	=	SYM
easat-8674	169	17	𝑦	𝑦	PROPN
easat-8674	169	18	+	+	NOUN
easat-8674	169	19	3	3	NUM
easat-8674	169	20	,	,	PUNCT
easat-8674	169	21	and	and	CCONJ
easat-8674	169	22	the	the	DET
easat-8674	169	23	difference	difference	NOUN
easat-8674	169	24	of	of	ADP
easat-8674	169	25	their	their	PRON
easat-8674	169	26	squared	square	VERB
easat-8674	169	27	lucky	lucky	ADJ
easat-8674	169	28	numbers	number	NOUN
easat-8674	169	29	is	be	AUX
easat-8674	169	30	45	45	NUM
easat-8674	169	31	,	,	PUNCT
easat-8674	169	32	thus	thus	ADV
easat-8674	169	33	𝑥2	𝑥2	NOUN
easat-8674	169	34	−	−	PROPN
easat-8674	169	35	𝑦2	𝑦2	NOUN
easat-8674	169	36	=	=	PUNCT
easat-8674	169	37	45	45	NUM
easat-8674	169	38	this	this	DET
easat-8674	169	39	problem	problem	NOUN
easat-8674	169	40	required	require	VERB
easat-8674	169	41	students	student	NOUN
easat-8674	169	42	to	to	PART
easat-8674	169	43	represent	represent	VERB
easat-8674	169	44	the	the	DET
easat-8674	169	45	relationship	relationship	NOUN
easat-8674	169	46	between	between	ADP
easat-8674	169	47	two	two	NUM
easat-8674	169	48	quantities	quantity	NOUN
easat-8674	169	49	using	use	VERB
easat-8674	169	50	an	an	DET
easat-8674	169	51	algebraic	algebraic	ADJ
easat-8674	169	52	equation	equation	NOUN
easat-8674	169	53	involving	involve	VERB
easat-8674	169	54	the	the	DET
easat-8674	169	55	difference	difference	NOUN
easat-8674	169	56	of	of	ADP
easat-8674	169	57	squares	square	NOUN
easat-8674	169	58	.	.	PUNCT
easat-8674	170	1	symbolic	symbolic	ADJ
easat-8674	170	2	representation	representation	NOUN
easat-8674	170	3	and	and	CCONJ
easat-8674	170	4	equation	equation	NOUN
easat-8674	170	5	structure	structure	NOUN
easat-8674	170	6	were	be	AUX
easat-8674	170	7	key	key	ADJ
easat-8674	170	8	indicators	indicator	NOUN
easat-8674	170	9	of	of	ADP
easat-8674	170	10	their	their	PRON
easat-8674	170	11	understanding	understanding	NOUN
easat-8674	170	12	of	of	ADP
easat-8674	170	13	advanced	advanced	ADJ
easat-8674	170	14	algebraic	algebraic	ADJ
easat-8674	170	15	concepts	concept	NOUN
easat-8674	170	16	,	,	PUNCT
easat-8674	170	17	particularly	particularly	ADV
easat-8674	170	18	the	the	DET
easat-8674	170	19	identity	identity	NOUN
easat-8674	170	20	𝑎2	𝑎2	NOUN
easat-8674	170	21	−	−	PROPN
easat-8674	170	22	𝑏2	𝑏2	PROPN
easat-8674	170	23	=	=	PUNCT
easat-8674	170	24	(	(	PUNCT
easat-8674	170	25	𝑎	𝑎	PROPN
easat-8674	170	26	−	−	PROPN
easat-8674	170	27	𝑏)(𝑎	𝑏)(𝑎	NOUN
easat-8674	170	28	+	+	ADP
easat-8674	170	29	𝑏	𝑏	NOUN
easat-8674	170	30	)	)	PUNCT
easat-8674	170	31	s04	s04	NOUN
easat-8674	170	32	showed	show	VERB
easat-8674	170	33	clear	clear	ADJ
easat-8674	170	34	and	and	CCONJ
easat-8674	170	35	consistent	consistent	ADJ
easat-8674	170	36	symbolic	symbolic	ADJ
easat-8674	170	37	representation	representation	NOUN
easat-8674	170	38	.	.	PUNCT
easat-8674	171	1	by	by	ADP
easat-8674	171	2	assigning	assign	VERB
easat-8674	171	3	𝑥	𝑥	X
easat-8674	171	4	=	=	PUNCT
easat-8674	171	5	𝑦	𝑦	NOUN
easat-8674	171	6	+	+	CCONJ
easat-8674	171	7	3	3	NUM
easat-8674	171	8	and	and	CCONJ
easat-8674	171	9	constructing	construct	VERB
easat-8674	171	10	the	the	DET
easat-8674	171	11	equation	equation	NOUN
easat-8674	171	12	𝑥2	𝑥2	NOUN
easat-8674	171	13	−	−	PROPN
easat-8674	171	14	𝑦2	𝑦2	PROPN
easat-8674	171	15	=	=	SYM
easat-8674	171	16	45	45	NUM
easat-8674	171	17	,	,	PUNCT
easat-8674	171	18	s04	s04	PROPN
easat-8674	171	19	demonstrated	demonstrate	VERB
easat-8674	171	20	an	an	DET
easat-8674	171	21	understanding	understanding	NOUN
easat-8674	171	22	of	of	ADP
easat-8674	171	23	algebraic	algebraic	ADJ
easat-8674	171	24	structure	structure	NOUN
easat-8674	171	25	and	and	CCONJ
easat-8674	171	26	successfully	successfully	ADV
easat-8674	171	27	translated	translate	VERB
easat-8674	171	28	verbal	verbal	ADJ
easat-8674	171	29	information	information	NOUN
easat-8674	171	30	into	into	ADP
easat-8674	171	31	logical	logical	ADJ
easat-8674	171	32	symbolic	symbolic	ADJ
easat-8674	171	33	form	form	NOUN
easat-8674	171	34	.	.	PUNCT
easat-8674	172	1	although	although	SCONJ
easat-8674	172	2	the	the	DET
easat-8674	172	3	identity	identity	NOUN
easat-8674	172	4	was	be	AUX
easat-8674	172	5	not	not	PART
easat-8674	172	6	explicitly	explicitly	ADV
easat-8674	172	7	stated	state	VERB
easat-8674	172	8	,	,	PUNCT
easat-8674	172	9	the	the	DET
easat-8674	172	10	combined	combined	ADJ
easat-8674	172	11	use	use	NOUN
easat-8674	172	12	of	of	ADP
easat-8674	172	13	linear	linear	ADJ
easat-8674	172	14	and	and	CCONJ
easat-8674	172	15	quadratic	quadratic	ADJ
easat-8674	172	16	relations	relation	NOUN
easat-8674	172	17	indicates	indicate	VERB
easat-8674	172	18	a	a	DET
easat-8674	172	19	solid	solid	ADJ
easat-8674	172	20	grasp	grasp	NOUN
easat-8674	172	21	of	of	ADP
easat-8674	172	22	mathematical	mathematical	ADJ
easat-8674	172	23	modeling	modeling	NOUN
easat-8674	172	24	.	.	PUNCT
easat-8674	173	1	in	in	ADP
easat-8674	173	2	contrast	contrast	NOUN
easat-8674	173	3	,	,	PUNCT
easat-8674	173	4	s06	s06	NOUN
easat-8674	173	5	showed	show	VERB
easat-8674	173	6	confusion	confusion	NOUN
easat-8674	173	7	in	in	ADP
easat-8674	173	8	constructing	construct	VERB
easat-8674	173	9	a	a	DET
easat-8674	173	10	suitable	suitable	ADJ
easat-8674	173	11	equation	equation	NOUN
easat-8674	173	12	.	.	PUNCT
easat-8674	174	1	the	the	DET
easat-8674	174	2	equation	equation	NOUN
easat-8674	174	3	𝑎2	𝑎2	NOUN
easat-8674	174	4	−	−	PROPN
easat-8674	174	5	𝑏2	𝑏2	PROPN
easat-8674	174	6	=	=	NOUN
easat-8674	174	7	𝑐2	𝑐2	PROPN
easat-8674	174	8	reflects	reflect	VERB
easat-8674	174	9	a	a	DET
easat-8674	174	10	misunderstanding	misunderstanding	NOUN
easat-8674	174	11	,	,	PUNCT
easat-8674	174	12	likely	likely	ADV
easat-8674	174	13	confusing	confuse	VERB
easat-8674	174	14	the	the	DET
easat-8674	174	15	identity	identity	NOUN
easat-8674	174	16	of	of	ADP
easat-8674	174	17	the	the	DET
easat-8674	174	18	difference	difference	NOUN
easat-8674	174	19	of	of	ADP
easat-8674	174	20	squares	square	NOUN
easat-8674	174	21	with	with	ADP
easat-8674	174	22	the	the	DET
easat-8674	174	23	pythagorean	pythagorean	PROPN
easat-8674	174	24	theorem	theorem	VERB
easat-8674	174	25	𝑎2	𝑎2	PROPN
easat-8674	174	26	+	+	CCONJ
easat-8674	174	27	𝑏2	𝑏2	PROPN
easat-8674	174	28	=	=	SYM
easat-8674	174	29	𝑐2	𝑐2	PROPN
easat-8674	174	30	.	.	PUNCT
easat-8674	175	1	this	this	PRON
easat-8674	175	2	indicates	indicate	VERB
easat-8674	175	3	that	that	SCONJ
easat-8674	175	4	s06	s06	NOUN
easat-8674	175	5	lacks	lack	VERB
easat-8674	175	6	clarity	clarity	NOUN
easat-8674	175	7	in	in	ADP
easat-8674	175	8	distinguishing	distinguish	VERB
easat-8674	175	9	between	between	ADP
easat-8674	175	10	algebraic	algebraic	ADJ
easat-8674	175	11	identities	identity	NOUN
easat-8674	175	12	and	and	CCONJ
easat-8674	175	13	their	their	PRON
easat-8674	175	14	appropriate	appropriate	ADJ
easat-8674	175	15	contexts	contexts	NOUN
easat-8674	175	16	.	.	PUNCT
easat-8674	176	1	therefore	therefore	ADV
easat-8674	176	2	,	,	PUNCT
easat-8674	176	3	s04	s04	PROPN
easat-8674	176	4	is	be	AUX
easat-8674	176	5	categorized	categorize	VERB
easat-8674	176	6	under	under	ADP
easat-8674	176	7	dta	dta	PROPN
easat-8674	176	8	-	-	PUNCT
easat-8674	176	9	np	np	NOUN
easat-8674	176	10	,	,	PUNCT
easat-8674	176	11	while	while	SCONJ
easat-8674	176	12	s06	s06	NOUN
easat-8674	176	13	falls	fall	VERB
easat-8674	176	14	under	under	ADP
easat-8674	176	15	the	the	DET
easat-8674	176	16	mba	mba	PROPN
easat-8674	176	17	-	-	PUNCT
easat-8674	176	18	j	j	NOUN
easat-8674	176	19	category	category	NOUN
easat-8674	176	20	.	.	PUNCT
easat-8674	177	1	4.3	4.3	NUM
easat-8674	177	2	.	.	PUNCT
easat-8674	177	3	case	case	NOUN
easat-8674	177	4	three	three	NUM
easat-8674	177	5	:	:	PUNCT
easat-8674	177	6	subject	subject	ADJ
easat-8674	177	7	s09	s09	NOUN
easat-8674	177	8	and	and	CCONJ
easat-8674	177	9	s10	s10	PROPN
easat-8674	177	10	s09	s09	NOUN
easat-8674	177	11	did	do	AUX
easat-8674	177	12	not	not	PART
easat-8674	177	13	answer	answer	VERB
easat-8674	177	14	question	question	NOUN
easat-8674	177	15	number	number	NOUN
easat-8674	177	16	3	3	NUM
easat-8674	177	17	completely	completely	ADV
easat-8674	177	18	.	.	PUNCT
easat-8674	178	1	the	the	DET
easat-8674	178	2	student	student	NOUN
easat-8674	178	3	's	's	PART
easat-8674	178	4	lack	lack	NOUN
easat-8674	178	5	of	of	ADP
easat-8674	178	6	understanding	understanding	NOUN
easat-8674	178	7	of	of	ADP
easat-8674	178	8	the	the	DET
easat-8674	178	9	information	information	NOUN
easat-8674	178	10	in	in	ADP
easat-8674	178	11	the	the	DET
easat-8674	178	12	problem	problem	NOUN
easat-8674	178	13	is	be	AUX
easat-8674	178	14	evident	evident	ADJ
easat-8674	178	15	from	from	ADP
easat-8674	178	16	the	the	DET
easat-8674	178	17	work	work	NOUN
easat-8674	178	18	shown	show	VERB
easat-8674	178	19	.	.	PUNCT
easat-8674	179	1	s09	s09	NOUN
easat-8674	179	2	concluded	conclude	VERB
easat-8674	179	3	that	that	SCONJ
easat-8674	179	4	the	the	DET
easat-8674	179	5	length	length	NOUN
easat-8674	179	6	of	of	ADP
easat-8674	179	7	the	the	DET
easat-8674	179	8	589	589	NUM
easat-8674	179	9	edelweiss	edelweiss	PROPN
easat-8674	179	10	applied	apply	VERB
easat-8674	179	11	science	science	NOUN
easat-8674	179	12	and	and	CCONJ
easat-8674	179	13	technology	technology	NOUN
easat-8674	179	14	issn	issn	PROPN
easat-8674	179	15	:	:	PUNCT
easat-8674	179	16	2576	2576	NUM
easat-8674	179	17	-	-	SYM
easat-8674	179	18	8484	8484	NUM
easat-8674	179	19	vol	vol	NOUN
easat-8674	179	20	.	.	PROPN
easat-8674	179	21	9	9	NUM
easat-8674	179	22	,	,	PUNCT
easat-8674	179	23	no	no	INTJ
easat-8674	179	24	.	.	NOUN
easat-8674	180	1	7	7	NUM
easat-8674	180	2	:	:	SYM
easat-8674	180	3	580	580	NUM
easat-8674	180	4	-	-	SYM
easat-8674	180	5	594	594	NUM
easat-8674	180	6	,	,	PUNCT
easat-8674	180	7	2025	2025	NUM
easat-8674	180	8	doi	doi	NOUN
easat-8674	180	9	:	:	PUNCT
easat-8674	180	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	180	11	©	©	PROPN
easat-8674	180	12	2025	2025	NUM
easat-8674	180	13	by	by	ADP
easat-8674	180	14	the	the	DET
easat-8674	180	15	authors	author	NOUN
easat-8674	180	16	;	;	PUNCT
easat-8674	180	17	licensee	licensee	PROPN
easat-8674	180	18	learning	learn	VERB
easat-8674	180	19	gate	gate	NOUN
easat-8674	180	20	block	block	NOUN
easat-8674	180	21	is	be	AUX
easat-8674	180	22	21	21	NUM
easat-8674	180	23	cm	cm	NOUN
easat-8674	180	24	and	and	CCONJ
easat-8674	180	25	the	the	DET
easat-8674	180	26	cylinder	cylinder	NOUN
easat-8674	180	27	is	be	AUX
easat-8674	180	28	19	19	NUM
easat-8674	180	29	cm	cm	NOUN
easat-8674	180	30	,	,	PUNCT
easat-8674	180	31	whereas	whereas	SCONJ
easat-8674	180	32	the	the	DET
easat-8674	180	33	problem	problem	NOUN
easat-8674	180	34	clearly	clearly	ADV
easat-8674	180	35	states	state	VERB
easat-8674	180	36	that	that	SCONJ
easat-8674	180	37	each	each	DET
easat-8674	180	38	block	block	NOUN
easat-8674	180	39	has	have	VERB
easat-8674	180	40	a	a	DET
easat-8674	180	41	different	different	ADJ
easat-8674	180	42	height	height	NOUN
easat-8674	180	43	.	.	PUNCT
easat-8674	181	1	each	each	DET
easat-8674	181	2	stack	stack	NOUN
easat-8674	181	3	of	of	ADP
easat-8674	181	4	blocks	block	NOUN
easat-8674	181	5	consists	consist	VERB
easat-8674	181	6	of	of	ADP
easat-8674	181	7	a	a	DET
easat-8674	181	8	square	square	NOUN
easat-8674	181	9	and	and	CCONJ
easat-8674	181	10	a	a	DET
easat-8674	181	11	cylinder	cylinder	NOUN
easat-8674	181	12	.	.	PUNCT
easat-8674	182	1	s09	s09	NOUN
easat-8674	182	2	used	use	VERB
easat-8674	182	3	subtraction	subtraction	NOUN
easat-8674	182	4	to	to	PART
easat-8674	182	5	determine	determine	VERB
easat-8674	182	6	the	the	DET
easat-8674	182	7	height	height	NOUN
easat-8674	182	8	of	of	ADP
easat-8674	182	9	the	the	DET
easat-8674	182	10	third	third	ADJ
easat-8674	182	11	block	block	NOUN
easat-8674	182	12	but	but	CCONJ
easat-8674	182	13	failed	fail	VERB
easat-8674	182	14	to	to	PART
easat-8674	182	15	connect	connect	VERB
easat-8674	182	16	the	the	DET
easat-8674	182	17	information	information	NOUN
easat-8674	182	18	from	from	ADP
easat-8674	182	19	the	the	DET
easat-8674	182	20	problem	problem	NOUN
easat-8674	182	21	with	with	ADP
easat-8674	182	22	the	the	DET
easat-8674	182	23	appropriate	appropriate	ADJ
easat-8674	182	24	rules	rule	NOUN
easat-8674	182	25	,	,	PUNCT
easat-8674	182	26	formulas	formula	NOUN
easat-8674	182	27	,	,	PUNCT
easat-8674	182	28	and	and	CCONJ
easat-8674	182	29	procedures	procedure	NOUN
easat-8674	182	30	,	,	PUNCT
easat-8674	182	31	resulting	result	VERB
easat-8674	182	32	in	in	ADP
easat-8674	182	33	an	an	DET
easat-8674	182	34	incorrect	incorrect	ADJ
easat-8674	182	35	solution	solution	NOUN
easat-8674	182	36	.	.	PUNCT
easat-8674	183	1	figure	figure	NOUN
easat-8674	183	2	6	6	NUM
easat-8674	183	3	.	.	PUNCT
easat-8674	184	1	response	response	NOUN
easat-8674	184	2	sheets	sheet	NOUN
easat-8674	184	3	of	of	ADP
easat-8674	184	4	s09	s09	NOUN
easat-8674	184	5	.	.	PUNCT
easat-8674	185	1	s10	s10	ADJ
easat-8674	185	2	response	response	NOUN
easat-8674	185	3	to	to	PART
easat-8674	185	4	question	question	VERB
easat-8674	185	5	number	number	NOUN
easat-8674	185	6	3	3	NUM
easat-8674	185	7	is	be	AUX
easat-8674	185	8	not	not	PART
easat-8674	185	9	fully	fully	ADV
easat-8674	185	10	complete	complete	ADJ
easat-8674	185	11	due	due	ADP
easat-8674	185	12	to	to	ADP
easat-8674	185	13	missing	miss	VERB
easat-8674	185	14	information	information	NOUN
easat-8674	185	15	.	.	PUNCT
easat-8674	186	1	s10	s10	PROPN
easat-8674	186	2	applied	apply	VERB
easat-8674	186	3	the	the	DET
easat-8674	186	4	substitution	substitution	NOUN
easat-8674	186	5	and	and	CCONJ
easat-8674	186	6	elimination	elimination	NOUN
easat-8674	186	7	methods	method	NOUN
easat-8674	186	8	to	to	PART
easat-8674	186	9	determine	determine	VERB
easat-8674	186	10	the	the	DET
easat-8674	186	11	height	height	NOUN
easat-8674	186	12	of	of	ADP
easat-8674	186	13	the	the	DET
easat-8674	186	14	third	third	ADJ
easat-8674	186	15	block	block	NOUN
easat-8674	186	16	.	.	PUNCT
easat-8674	187	1	the	the	DET
easat-8674	187	2	first	first	ADJ
easat-8674	187	3	equation	equation	NOUN
easat-8674	187	4	was	be	AUX
easat-8674	187	5	formed	form	VERB
easat-8674	187	6	from	from	ADP
easat-8674	187	7	three	three	NUM
easat-8674	187	8	cylinders	cylinder	NOUN
easat-8674	187	9	and	and	CCONJ
easat-8674	187	10	three	three	NUM
easat-8674	187	11	blocks	block	NOUN
easat-8674	187	12	,	,	PUNCT
easat-8674	187	13	and	and	CCONJ
easat-8674	187	14	the	the	DET
easat-8674	187	15	second	second	ADJ
easat-8674	187	16	equation	equation	NOUN
easat-8674	187	17	from	from	ADP
easat-8674	187	18	three	three	NUM
easat-8674	187	19	cylinders	cylinder	NOUN
easat-8674	187	20	and	and	CCONJ
easat-8674	187	21	two	two	NUM
easat-8674	187	22	blocks	block	NOUN
easat-8674	187	23	.	.	PUNCT
easat-8674	188	1	these	these	DET
easat-8674	188	2	two	two	NUM
easat-8674	188	3	equations	equation	NOUN
easat-8674	188	4	were	be	AUX
easat-8674	188	5	then	then	ADV
easat-8674	188	6	eliminated	eliminate	VERB
easat-8674	188	7	to	to	PART
easat-8674	188	8	find	find	VERB
easat-8674	188	9	the	the	DET
easat-8674	188	10	value	value	NOUN
easat-8674	188	11	of	of	ADP
easat-8674	188	12	𝑦	𝑦	NOUN
easat-8674	188	13	,	,	PUNCT
easat-8674	188	14	which	which	PRON
easat-8674	188	15	was	be	AUX
easat-8674	188	16	subsequently	subsequently	ADV
easat-8674	188	17	substituted	substitute	VERB
easat-8674	188	18	into	into	ADP
easat-8674	188	19	the	the	DET
easat-8674	188	20	third	third	ADJ
easat-8674	188	21	equation	equation	NOUN
easat-8674	188	22	involving	involve	VERB
easat-8674	188	23	one	one	NUM
easat-8674	188	24	cylinder	cylinder	NOUN
easat-8674	188	25	and	and	CCONJ
easat-8674	188	26	two	two	NUM
easat-8674	188	27	blocks	block	NOUN
easat-8674	188	28	.	.	PUNCT
easat-8674	189	1	through	through	ADP
easat-8674	189	2	this	this	DET
easat-8674	189	3	process	process	NOUN
easat-8674	189	4	,	,	PUNCT
easat-8674	189	5	s10	s10	PROPN
easat-8674	189	6	was	be	AUX
easat-8674	189	7	able	able	ADJ
easat-8674	189	8	to	to	PART
easat-8674	189	9	arrive	arrive	VERB
easat-8674	189	10	at	at	ADP
easat-8674	189	11	the	the	DET
easat-8674	189	12	correct	correct	ADJ
easat-8674	189	13	answer	answer	NOUN
easat-8674	189	14	and	and	CCONJ
easat-8674	189	15	draw	draw	VERB
easat-8674	189	16	an	an	DET
easat-8674	189	17	accurate	accurate	ADJ
easat-8674	189	18	conclusion	conclusion	NOUN
easat-8674	189	19	about	about	ADP
easat-8674	189	20	the	the	DET
easat-8674	189	21	height	height	NOUN
easat-8674	189	22	of	of	ADP
easat-8674	189	23	the	the	DET
easat-8674	189	24	third	third	ADJ
easat-8674	189	25	block	block	NOUN
easat-8674	189	26	.	.	PUNCT
easat-8674	190	1	figure	figure	NOUN
easat-8674	190	2	7	7	NUM
easat-8674	190	3	.	.	PUNCT
easat-8674	191	1	response	response	NOUN
easat-8674	191	2	sheets	sheet	NOUN
easat-8674	191	3	of	of	ADP
easat-8674	191	4	s10	s10	NOUN
easat-8674	191	5	.	.	PUNCT
easat-8674	192	1	590	590	NUM
easat-8674	192	2	edelweiss	edelweiss	PROPN
easat-8674	192	3	applied	apply	VERB
easat-8674	192	4	science	science	NOUN
easat-8674	192	5	and	and	CCONJ
easat-8674	192	6	technology	technology	NOUN
easat-8674	192	7	issn	issn	PROPN
easat-8674	192	8	:	:	PUNCT
easat-8674	192	9	2576	2576	NUM
easat-8674	192	10	-	-	SYM
easat-8674	192	11	8484	8484	NUM
easat-8674	192	12	vol	vol	NOUN
easat-8674	192	13	.	.	PROPN
easat-8674	193	1	9	9	NUM
easat-8674	193	2	,	,	PUNCT
easat-8674	193	3	no	no	INTJ
easat-8674	193	4	.	.	NOUN
easat-8674	194	1	7	7	NUM
easat-8674	194	2	:	:	SYM
easat-8674	194	3	580	580	NUM
easat-8674	194	4	-	-	SYM
easat-8674	194	5	594	594	NUM
easat-8674	194	6	,	,	PUNCT
easat-8674	194	7	2025	2025	NUM
easat-8674	194	8	doi	doi	NOUN
easat-8674	194	9	:	:	PUNCT
easat-8674	194	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	194	11	©	©	PROPN
easat-8674	194	12	2025	2025	NUM
easat-8674	194	13	by	by	ADP
easat-8674	194	14	the	the	DET
easat-8674	194	15	authors	author	NOUN
easat-8674	194	16	;	;	PUNCT
easat-8674	194	17	licensee	licensee	PROPN
easat-8674	194	18	learning	learning	NOUN
easat-8674	194	19	gate	gate	NOUN
easat-8674	194	20	based	base	VERB
easat-8674	194	21	on	on	ADP
easat-8674	194	22	figures	figure	NOUN
easat-8674	194	23	6	6	NUM
easat-8674	194	24	and	and	CCONJ
easat-8674	194	25	7	7	NUM
easat-8674	194	26	,	,	PUNCT
easat-8674	194	27	the	the	DET
easat-8674	194	28	answer	answer	NOUN
easat-8674	194	29	sheets	sheet	NOUN
easat-8674	194	30	of	of	ADP
easat-8674	194	31	s09	s09	NOUN
easat-8674	194	32	and	and	CCONJ
easat-8674	194	33	s10	s10	PROPN
easat-8674	194	34	reflect	reflect	VERB
easat-8674	194	35	their	their	PRON
easat-8674	194	36	content	content	NOUN
easat-8674	194	37	knowledge	knowledge	NOUN
easat-8674	194	38	in	in	ADP
easat-8674	194	39	solving	solve	VERB
easat-8674	194	40	the	the	DET
easat-8674	194	41	problem	problem	NOUN
easat-8674	194	42	.	.	PUNCT
easat-8674	195	1	however	however	ADV
easat-8674	195	2	,	,	PUNCT
easat-8674	195	3	to	to	PART
easat-8674	195	4	clarify	clarify	VERB
easat-8674	195	5	several	several	ADJ
easat-8674	195	6	aspects	aspect	NOUN
easat-8674	195	7	that	that	PRON
easat-8674	195	8	remained	remain	VERB
easat-8674	195	9	unclear	unclear	ADJ
easat-8674	195	10	such	such	ADJ
easat-8674	195	11	as	as	ADP
easat-8674	195	12	their	their	PRON
easat-8674	195	13	interpretation	interpretation	NOUN
easat-8674	195	14	of	of	ADP
easat-8674	195	15	the	the	DET
easat-8674	195	16	problem	problem	NOUN
easat-8674	195	17	statement	statement	NOUN
easat-8674	195	18	,	,	PUNCT
easat-8674	195	19	the	the	DET
easat-8674	195	20	structure	structure	NOUN
easat-8674	195	21	of	of	ADP
easat-8674	195	22	each	each	DET
easat-8674	195	23	block	block	NOUN
easat-8674	195	24	arrangement	arrangement	NOUN
easat-8674	195	25	,	,	PUNCT
easat-8674	195	26	the	the	DET
easat-8674	195	27	reasoning	reasoning	NOUN
easat-8674	195	28	behind	behind	ADP
easat-8674	195	29	their	their	PRON
easat-8674	195	30	answers	answer	NOUN
easat-8674	195	31	,	,	PUNCT
easat-8674	195	32	and	and	CCONJ
easat-8674	195	33	the	the	DET
easat-8674	195	34	justification	justification	NOUN
easat-8674	195	35	of	of	ADP
easat-8674	195	36	their	their	PRON
easat-8674	195	37	solutions	solution	NOUN
easat-8674	195	38	the	the	DET
easat-8674	195	39	researcher	researcher	NOUN
easat-8674	195	40	conducted	conduct	VERB
easat-8674	195	41	follow	follow	NOUN
easat-8674	195	42	-	-	PUNCT
easat-8674	195	43	up	up	ADP
easat-8674	195	44	interviews	interview	NOUN
easat-8674	195	45	with	with	ADP
easat-8674	195	46	both	both	DET
easat-8674	195	47	students	student	NOUN
easat-8674	195	48	.	.	PUNCT
easat-8674	196	1	the	the	DET
easat-8674	196	2	following	follow	VERB
easat-8674	196	3	are	be	AUX
easat-8674	196	4	excerpts	excerpt	NOUN
easat-8674	196	5	from	from	ADP
easat-8674	196	6	the	the	DET
easat-8674	196	7	interviews	interview	NOUN
easat-8674	196	8	with	with	ADP
easat-8674	196	9	s09	s09	NOUN
easat-8674	196	10	and	and	CCONJ
easat-8674	196	11	s10	s10	NOUN
easat-8674	196	12	regarding	regard	VERB
easat-8674	196	13	question	question	NOUN
easat-8674	196	14	number	number	NOUN
easat-8674	196	15	3	3	NUM
easat-8674	196	16	r	r	NOUN
easat-8674	197	1	how	how	SCONJ
easat-8674	197	2	did	do	AUX
easat-8674	197	3	you	you	PRON
easat-8674	197	4	solve	solve	VERB
easat-8674	197	5	this	this	DET
easat-8674	197	6	problem	problem	NOUN
easat-8674	197	7	?	?	PUNCT
easat-8674	198	1	s09	s09	VERB
easat-8674	198	2	the	the	DET
easat-8674	198	3	height	height	NOUN
easat-8674	198	4	of	of	ADP
easat-8674	198	5	the	the	DET
easat-8674	198	6	first	first	ADJ
easat-8674	198	7	stack	stack	NOUN
easat-8674	198	8	of	of	ADP
easat-8674	198	9	blocks	block	NOUN
easat-8674	198	10	(	(	PUNCT
easat-8674	198	11	squares	square	NOUN
easat-8674	198	12	)	)	PUNCT
easat-8674	198	13	is	be	AUX
easat-8674	198	14	21	21	NUM
easat-8674	198	15	cm	cm	NOUN
easat-8674	198	16	,	,	PUNCT
easat-8674	198	17	while	while	SCONJ
easat-8674	198	18	the	the	DET
easat-8674	198	19	second	second	ADJ
easat-8674	198	20	stack	stack	NOUN
easat-8674	198	21	(	(	PUNCT
easat-8674	198	22	cylinders	cylinder	NOUN
easat-8674	198	23	)	)	PUNCT
easat-8674	198	24	is	be	AUX
easat-8674	198	25	19	19	NUM
easat-8674	198	26	cm	cm	NOUN
easat-8674	198	27	.	.	PUNCT
easat-8674	199	1	since	since	SCONJ
easat-8674	199	2	the	the	DET
easat-8674	199	3	third	third	ADJ
easat-8674	199	4	stack	stack	NOUN
easat-8674	199	5	consists	consist	VERB
easat-8674	199	6	of	of	ADP
easat-8674	199	7	both	both	DET
easat-8674	199	8	shapes	shape	NOUN
easat-8674	199	9	,	,	PUNCT
easat-8674	199	10	i	i	PRON
easat-8674	199	11	subtracted	subtract	VERB
easat-8674	199	12	:	:	PUNCT
easat-8674	199	13	21	21	NUM
easat-8674	199	14	–	–	SYM
easat-8674	199	15	19	19	NUM
easat-8674	199	16	=	=	SYM
easat-8674	199	17	2	2	NUM
easat-8674	199	18	cm	cm	NOUN
easat-8674	199	19	r	r	NOUN
easat-8674	199	20	were	be	AUX
easat-8674	199	21	all	all	PRON
easat-8674	199	22	blocks	block	NOUN
easat-8674	199	23	in	in	ADP
easat-8674	199	24	the	the	DET
easat-8674	199	25	first	first	ADJ
easat-8674	199	26	stack	stack	NOUN
easat-8674	199	27	squares	square	NOUN
easat-8674	199	28	,	,	PUNCT
easat-8674	199	29	and	and	CCONJ
easat-8674	199	30	all	all	PRON
easat-8674	199	31	in	in	ADP
easat-8674	199	32	the	the	DET
easat-8674	199	33	second	second	ADJ
easat-8674	199	34	stack	stack	NOUN
easat-8674	199	35	cylinders	cylinder	NOUN
easat-8674	199	36	?	?	PUNCT
easat-8674	200	1	s09	s09	PROPN
easat-8674	200	2	no	no	INTJ
easat-8674	200	3	.	.	PUNCT
easat-8674	201	1	according	accord	VERB
easat-8674	201	2	to	to	ADP
easat-8674	201	3	the	the	DET
easat-8674	201	4	diagram	diagram	NOUN
easat-8674	201	5	,	,	PUNCT
easat-8674	201	6	the	the	DET
easat-8674	201	7	first	first	ADJ
easat-8674	201	8	stack	stack	NOUN
easat-8674	201	9	has	have	VERB
easat-8674	201	10	3	3	NUM
easat-8674	201	11	squares	square	NOUN
easat-8674	201	12	and	and	CCONJ
easat-8674	201	13	3	3	NUM
easat-8674	201	14	cylinders	cylinder	NOUN
easat-8674	201	15	,	,	PUNCT
easat-8674	201	16	while	while	SCONJ
easat-8674	201	17	the	the	DET
easat-8674	201	18	second	second	ADJ
easat-8674	201	19	stack	stack	NOUN
easat-8674	201	20	has	have	VERB
easat-8674	201	21	2	2	NUM
easat-8674	201	22	squares	square	NOUN
easat-8674	201	23	and	and	CCONJ
easat-8674	201	24	3	3	NUM
easat-8674	201	25	cylinders	cylinder	NOUN
easat-8674	201	26	r	r	NOUN
easat-8674	202	1	how	how	SCONJ
easat-8674	202	2	are	be	AUX
easat-8674	202	3	you	you	PRON
easat-8674	202	4	confident	confident	ADJ
easat-8674	202	5	that	that	SCONJ
easat-8674	202	6	your	your	PRON
easat-8674	202	7	answer	answer	NOUN
easat-8674	202	8	for	for	ADP
easat-8674	202	9	question	question	NOUN
easat-8674	202	10	3	3	NUM
easat-8674	202	11	is	be	AUX
easat-8674	202	12	correct	correct	ADJ
easat-8674	202	13	?	?	PUNCT
easat-8674	203	1	s10	s10	PROPN
easat-8674	203	2	i	i	PRON
easat-8674	203	3	represented	represent	VERB
easat-8674	203	4	the	the	DET
easat-8674	203	5	square	square	NOUN
easat-8674	203	6	as	as	ADP
easat-8674	203	7	x	x	PROPN
easat-8674	203	8	and	and	CCONJ
easat-8674	203	9	the	the	DET
easat-8674	203	10	cylinder	cylinder	NOUN
easat-8674	203	11	as	as	ADP
easat-8674	203	12	y.	y.	PROPN
easat-8674	203	13	since	since	SCONJ
easat-8674	203	14	the	the	DET
easat-8674	203	15	first	first	ADJ
easat-8674	203	16	stack	stack	NOUN
easat-8674	203	17	consists	consist	VERB
easat-8674	203	18	of	of	ADP
easat-8674	203	19	3	3	NUM
easat-8674	203	20	squares	square	NOUN
easat-8674	203	21	and	and	CCONJ
easat-8674	203	22	3	3	NUM
easat-8674	203	23	cylinders	cylinder	NOUN
easat-8674	203	24	,	,	PUNCT
easat-8674	203	25	i	i	PRON
easat-8674	203	26	wrote	write	VERB
easat-8674	203	27	3𝑥	3𝑥	NUM
easat-8674	203	28	+	+	CCONJ
easat-8674	203	29	3𝑦	3𝑦	NOUN
easat-8674	203	30	=	=	SYM
easat-8674	203	31	21	21	NUM
easat-8674	203	32	and	and	CCONJ
easat-8674	203	33	the	the	DET
easat-8674	203	34	second	second	ADJ
easat-8674	203	35	stack	stack	NOUN
easat-8674	203	36	as	as	ADP
easat-8674	203	37	2𝑥	2𝑥	NOUN
easat-8674	203	38	+	+	CCONJ
easat-8674	203	39	3𝑦	3𝑦	NOUN
easat-8674	203	40	=	=	SYM
easat-8674	203	41	19	19	NUM
easat-8674	203	42	.	.	PUNCT
easat-8674	204	1	i	i	PRON
easat-8674	204	2	used	use	VERB
easat-8674	204	3	the	the	DET
easat-8674	204	4	elimination	elimination	NOUN
easat-8674	204	5	method	method	NOUN
easat-8674	204	6	to	to	PART
easat-8674	204	7	find	find	VERB
easat-8674	204	8	x	x	PRON
easat-8674	204	9	,	,	PUNCT
easat-8674	204	10	and	and	CCONJ
easat-8674	204	11	substitution	substitution	NOUN
easat-8674	204	12	to	to	PART
easat-8674	204	13	find	find	VERB
easat-8674	204	14	y.	y.	PROPN
easat-8674	204	15	then	then	ADV
easat-8674	204	16	i	i	PRON
easat-8674	204	17	substituted	substitute	VERB
easat-8674	204	18	into	into	ADP
easat-8674	204	19	the	the	DET
easat-8674	204	20	target	target	NOUN
easat-8674	204	21	expression	expression	NOUN
easat-8674	204	22	2𝑥	2𝑥	NOUN
easat-8674	204	23	+	+	CCONJ
easat-8674	204	24	𝑦	𝑦	NOUN
easat-8674	204	25	=	=	SYM
easat-8674	204	26	2	2	NUM
easat-8674	204	27	(	(	PUNCT
easat-8674	204	28	2	2	NUM
easat-8674	204	29	)	)	PUNCT
easat-8674	204	30	+	+	CCONJ
easat-8674	204	31	5	5	NUM
easat-8674	204	32	=	=	SYM
easat-8674	204	33	9	9	NUM
easat-8674	204	34	.	.	PUNCT
easat-8674	205	1	so	so	ADV
easat-8674	205	2	,	,	PUNCT
easat-8674	205	3	the	the	DET
easat-8674	205	4	height	height	NOUN
easat-8674	205	5	of	of	ADP
easat-8674	205	6	the	the	DET
easat-8674	205	7	third	third	ADJ
easat-8674	205	8	stack	stack	NOUN
easat-8674	205	9	is	be	AUX
easat-8674	205	10	9	9	NUM
easat-8674	205	11	cm	cm	NOUN
easat-8674	205	12	.	.	PUNCT
easat-8674	206	1	r	r	NOUN
easat-8674	206	2	can	can	AUX
easat-8674	206	3	you	you	PRON
easat-8674	206	4	prove	prove	VERB
easat-8674	206	5	that	that	SCONJ
easat-8674	206	6	your	your	PRON
easat-8674	206	7	answer	answer	NOUN
easat-8674	206	8	is	be	AUX
easat-8674	206	9	correct	correct	ADJ
easat-8674	206	10	?	?	PUNCT
easat-8674	207	1	s10	s10	PROPN
easat-8674	207	2	yes	yes	INTJ
easat-8674	207	3	.	.	PUNCT
easat-8674	208	1	substituting	substitute	VERB
easat-8674	208	2	𝑥	𝑥	PROPN
easat-8674	208	3	=	=	SYM
easat-8674	208	4	2	2	NUM
easat-8674	208	5	and	and	CCONJ
easat-8674	208	6	𝑦	𝑦	NOUN
easat-8674	208	7	=	=	SYM
easat-8674	208	8	5	5	NUM
easat-8674	208	9	into	into	ADP
easat-8674	208	10	the	the	DET
easat-8674	208	11	first	first	ADJ
easat-8674	208	12	equation	equation	NOUN
easat-8674	208	13	gives	give	VERB
easat-8674	208	14	3(2	3(2	NUM
easat-8674	208	15	)	)	PUNCT
easat-8674	209	1	+	+	SYM
easat-8674	209	2	3(5	3(5	X
easat-8674	209	3	)	)	PUNCT
easat-8674	209	4	=	=	NOUN
easat-8674	209	5	6	6	NUM
easat-8674	209	6	+	+	NUM
easat-8674	209	7	15	15	NUM
easat-8674	209	8	=	=	SYM
easat-8674	209	9	21	21	NUM
easat-8674	209	10	,	,	PUNCT
easat-8674	209	11	which	which	PRON
easat-8674	209	12	matches	match	VERB
easat-8674	209	13	the	the	DET
easat-8674	209	14	total	total	ADJ
easat-8674	209	15	height	height	NOUN
easat-8674	209	16	.	.	PUNCT
easat-8674	210	1	therefore	therefore	ADV
easat-8674	210	2	,	,	PUNCT
easat-8674	210	3	the	the	DET
easat-8674	210	4	values	value	NOUN
easat-8674	210	5	are	be	AUX
easat-8674	210	6	correct	correct	ADJ
easat-8674	210	7	.	.	PUNCT
easat-8674	211	1	this	this	DET
easat-8674	211	2	problem	problem	NOUN
easat-8674	211	3	evaluated	evaluate	VERB
easat-8674	211	4	students	student	NOUN
easat-8674	211	5	'	'	PART
easat-8674	211	6	ability	ability	NOUN
easat-8674	211	7	to	to	PART
easat-8674	211	8	model	model	VERB
easat-8674	211	9	a	a	DET
easat-8674	211	10	concrete	concrete	ADJ
easat-8674	211	11	situation	situation	NOUN
easat-8674	211	12	into	into	ADP
easat-8674	211	13	a	a	DET
easat-8674	211	14	system	system	NOUN
easat-8674	211	15	of	of	ADP
easat-8674	211	16	linear	linear	ADJ
easat-8674	211	17	equations	equation	NOUN
easat-8674	211	18	and	and	CCONJ
easat-8674	211	19	to	to	PART
easat-8674	211	20	use	use	VERB
easat-8674	211	21	elimination	elimination	NOUN
easat-8674	211	22	and	and	CCONJ
easat-8674	211	23	substitution	substitution	NOUN
easat-8674	211	24	to	to	PART
easat-8674	211	25	solve	solve	VERB
easat-8674	211	26	it	it	PRON
easat-8674	211	27	.	.	PUNCT
easat-8674	212	1	the	the	DET
easat-8674	212	2	visual	visual	ADJ
easat-8674	212	3	context	context	NOUN
easat-8674	212	4	required	require	VERB
easat-8674	212	5	interpretation	interpretation	NOUN
easat-8674	212	6	and	and	CCONJ
easat-8674	212	7	algebraic	algebraic	ADJ
easat-8674	212	8	translation	translation	NOUN
easat-8674	212	9	.	.	PUNCT
easat-8674	213	1	s09	s09	PROPN
easat-8674	213	2	relied	rely	VERB
easat-8674	213	3	on	on	ADP
easat-8674	213	4	a	a	DET
easat-8674	213	5	direct	direct	ADJ
easat-8674	213	6	comparison	comparison	NOUN
easat-8674	213	7	of	of	ADP
easat-8674	213	8	total	total	ADJ
easat-8674	213	9	heights	height	NOUN
easat-8674	213	10	without	without	ADP
easat-8674	213	11	using	use	VERB
easat-8674	213	12	symbolic	symbolic	ADJ
easat-8674	213	13	representation	representation	NOUN
easat-8674	213	14	.	.	PUNCT
easat-8674	214	1	while	while	SCONJ
easat-8674	214	2	he	he	PRON
easat-8674	214	3	recognized	recognize	VERB
easat-8674	214	4	the	the	DET
easat-8674	214	5	composition	composition	NOUN
easat-8674	214	6	of	of	ADP
easat-8674	214	7	each	each	DET
easat-8674	214	8	stack	stack	NOUN
easat-8674	214	9	,	,	PUNCT
easat-8674	214	10	his	his	PRON
easat-8674	214	11	approach	approach	NOUN
easat-8674	214	12	remained	remain	VERB
easat-8674	214	13	intuitive	intuitive	ADJ
easat-8674	214	14	and	and	CCONJ
easat-8674	214	15	lacked	lack	VERB
easat-8674	214	16	systematic	systematic	ADJ
easat-8674	214	17	mathematical	mathematical	ADJ
easat-8674	214	18	formulation	formulation	NOUN
easat-8674	214	19	.	.	PUNCT
easat-8674	215	1	without	without	ADP
easat-8674	215	2	defining	define	VERB
easat-8674	215	3	variables	variable	NOUN
easat-8674	215	4	or	or	CCONJ
easat-8674	215	5	constructing	construct	VERB
easat-8674	215	6	equations	equation	NOUN
easat-8674	215	7	,	,	PUNCT
easat-8674	215	8	his	his	PRON
easat-8674	215	9	response	response	NOUN
easat-8674	215	10	can	can	AUX
easat-8674	215	11	not	not	PART
easat-8674	215	12	be	be	AUX
easat-8674	215	13	algebraically	algebraically	ADV
easat-8674	215	14	validated	validate	VERB
easat-8674	215	15	.	.	PUNCT
easat-8674	216	1	in	in	ADP
easat-8674	216	2	contrast	contrast	NOUN
easat-8674	216	3	,	,	PUNCT
easat-8674	216	4	s10	s10	PROPN
easat-8674	216	5	demonstrated	demonstrate	VERB
easat-8674	216	6	stronger	strong	ADJ
easat-8674	216	7	algebraic	algebraic	ADJ
easat-8674	216	8	reasoning	reasoning	NOUN
easat-8674	216	9	.	.	PUNCT
easat-8674	217	1	he	he	PRON
easat-8674	217	2	correctly	correctly	ADV
easat-8674	217	3	formulated	formulate	VERB
easat-8674	217	4	the	the	DET
easat-8674	217	5	system	system	NOUN
easat-8674	217	6	of	of	ADP
easat-8674	217	7	equations	equation	NOUN
easat-8674	217	8	,	,	PUNCT
easat-8674	217	9	applied	apply	VERB
easat-8674	217	10	algebraic	algebraic	ADJ
easat-8674	217	11	techniques	technique	NOUN
easat-8674	217	12	systematically	systematically	ADV
easat-8674	217	13	,	,	PUNCT
easat-8674	217	14	and	and	CCONJ
easat-8674	217	15	validated	validate	VERB
easat-8674	217	16	his	his	PRON
easat-8674	217	17	solution	solution	NOUN
easat-8674	217	18	by	by	ADP
easat-8674	217	19	substitution	substitution	NOUN
easat-8674	217	20	.	.	PUNCT
easat-8674	218	1	these	these	DET
easat-8674	218	2	steps	step	NOUN
easat-8674	218	3	illustrate	illustrate	VERB
easat-8674	218	4	a	a	DET
easat-8674	218	5	more	more	ADV
easat-8674	218	6	advanced	advanced	ADJ
easat-8674	218	7	level	level	NOUN
easat-8674	218	8	of	of	ADP
easat-8674	218	9	algebraic	algebraic	ADJ
easat-8674	218	10	literacy	literacy	NOUN
easat-8674	218	11	,	,	PUNCT
easat-8674	218	12	particularly	particularly	ADV
easat-8674	218	13	in	in	ADP
easat-8674	218	14	mathematical	mathematical	ADJ
easat-8674	218	15	modeling	modeling	NOUN
easat-8674	218	16	.	.	PUNCT
easat-8674	219	1	therefore	therefore	ADV
easat-8674	219	2	,	,	PUNCT
easat-8674	219	3	s10	s10	PROPN
easat-8674	219	4	is	be	AUX
easat-8674	219	5	categorized	categorize	VERB
easat-8674	219	6	as	as	ADP
easat-8674	219	7	mba	mba	NOUN
easat-8674	219	8	-	-	PUNCT
easat-8674	219	9	j	j	NOUN
easat-8674	219	10	,	,	PUNCT
easat-8674	219	11	while	while	SCONJ
easat-8674	219	12	s09	s09	NOUN
easat-8674	219	13	falls	fall	VERB
easat-8674	219	14	under	under	ADP
easat-8674	219	15	dta	dta	PROPN
easat-8674	219	16	-	-	PUNCT
easat-8674	219	17	np	np	NOUN
easat-8674	219	18	.	.	PROPN
easat-8674	219	19	5	5	NUM
easat-8674	219	20	.	.	X
easat-8674	219	21	discussion	discussion	NOUN
easat-8674	219	22	an	an	DET
easat-8674	219	23	analysis	analysis	NOUN
easat-8674	219	24	of	of	ADP
easat-8674	219	25	three	three	NUM
easat-8674	219	26	algebra	algebra	NOUN
easat-8674	219	27	cases	case	NOUN
easat-8674	219	28	revealed	reveal	VERB
easat-8674	219	29	significant	significant	ADJ
easat-8674	219	30	variations	variation	NOUN
easat-8674	219	31	in	in	ADP
easat-8674	219	32	the	the	DET
easat-8674	219	33	pre	pre	ADJ
easat-8674	219	34	-	-	ADJ
easat-8674	219	35	service	service	ADJ
easat-8674	219	36	teachers	teacher	NOUN
easat-8674	219	37	’	'	PUNCT
easat-8674	219	38	ability	ability	NOUN
easat-8674	219	39	to	to	PART
easat-8674	219	40	represent	represent	VERB
easat-8674	219	41	,	,	PUNCT
easat-8674	219	42	manipulate	manipulate	VERB
easat-8674	219	43	,	,	PUNCT
easat-8674	219	44	and	and	CCONJ
easat-8674	219	45	interpret	interpret	VERB
easat-8674	219	46	symbolic	symbolic	ADJ
easat-8674	219	47	information	information	NOUN
easat-8674	219	48	.	.	PUNCT
easat-8674	220	1	each	each	DET
easat-8674	220	2	problem	problem	NOUN
easat-8674	220	3	context	context	NOUN
easat-8674	220	4	required	require	VERB
easat-8674	220	5	students	student	NOUN
easat-8674	220	6	to	to	PART
easat-8674	220	7	accurately	accurately	ADV
easat-8674	220	8	connect	connect	VERB
easat-8674	220	9	contextual	contextual	ADJ
easat-8674	220	10	information	information	NOUN
easat-8674	220	11	with	with	ADP
easat-8674	220	12	algebraic	algebraic	ADJ
easat-8674	220	13	representations	representation	NOUN
easat-8674	220	14	.	.	PUNCT
easat-8674	221	1	however	however	ADV
easat-8674	221	2	,	,	PUNCT
easat-8674	221	3	there	there	PRON
easat-8674	221	4	were	be	VERB
easat-8674	221	5	fundamental	fundamental	ADJ
easat-8674	221	6	differences	difference	NOUN
easat-8674	221	7	in	in	ADP
easat-8674	221	8	students	student	NOUN
easat-8674	221	9	’	'	PUNCT
easat-8674	221	10	conceptual	conceptual	ADJ
easat-8674	221	11	approaches	approach	NOUN
easat-8674	221	12	and	and	CCONJ
easat-8674	221	13	problemsolving	problemsolve	VERB
easat-8674	221	14	strategies	strategy	NOUN
easat-8674	221	15	.	.	PUNCT
easat-8674	222	1	during	during	ADP
easat-8674	222	2	the	the	DET
easat-8674	222	3	problem	problem	NOUN
easat-8674	222	4	-	-	PUNCT
easat-8674	222	5	solving	solve	VERB
easat-8674	222	6	process	process	NOUN
easat-8674	222	7	,	,	PUNCT
easat-8674	222	8	students	student	NOUN
easat-8674	222	9	frequently	frequently	ADV
easat-8674	222	10	identified	identify	VERB
easat-8674	222	11	misconceptions	misconception	NOUN
easat-8674	222	12	related	relate	VERB
easat-8674	222	13	to	to	ADP
easat-8674	222	14	the	the	DET
easat-8674	222	15	mathematical	mathematical	ADJ
easat-8674	222	16	concepts	concept	NOUN
easat-8674	222	17	under	under	ADP
easat-8674	222	18	investigation	investigation	NOUN
easat-8674	222	19	[	[	X
easat-8674	222	20	26	26	NUM
easat-8674	222	21	]	]	PUNCT
easat-8674	222	22	.	.	PUNCT
easat-8674	223	1	these	these	DET
easat-8674	223	2	differences	difference	NOUN
easat-8674	223	3	reflect	reflect	VERB
easat-8674	223	4	a	a	DET
easat-8674	223	5	broad	broad	ADJ
easat-8674	223	6	range	range	NOUN
easat-8674	223	7	of	of	ADP
easat-8674	223	8	mastery	mastery	NOUN
easat-8674	223	9	in	in	ADP
easat-8674	223	10	content	content	NOUN
easat-8674	223	11	knowledge	knowledge	NOUN
easat-8674	223	12	(	(	PUNCT
easat-8674	223	13	ck	ck	NOUN
easat-8674	223	14	)	)	PUNCT
easat-8674	223	15	among	among	ADP
easat-8674	223	16	the	the	DET
easat-8674	223	17	participants	participant	NOUN
easat-8674	223	18	.	.	PUNCT
easat-8674	224	1	an	an	DET
easat-8674	224	2	analysis	analysis	NOUN
easat-8674	224	3	of	of	ADP
easat-8674	224	4	the	the	DET
easat-8674	224	5	three	three	NUM
easat-8674	224	6	algebra	algebra	NOUN
easat-8674	224	7	cases	case	NOUN
easat-8674	224	8	revealed	reveal	VERB
easat-8674	224	9	significant	significant	ADJ
easat-8674	224	10	variations	variation	NOUN
easat-8674	224	11	in	in	ADP
easat-8674	224	12	undergraduate	undergraduate	ADJ
easat-8674	224	13	students	student	NOUN
easat-8674	224	14	’	'	PUNCT
easat-8674	224	15	ability	ability	NOUN
easat-8674	224	16	to	to	PART
easat-8674	224	17	represent	represent	VERB
easat-8674	224	18	,	,	PUNCT
easat-8674	224	19	manipulate	manipulate	VERB
easat-8674	224	20	,	,	PUNCT
easat-8674	224	21	and	and	CCONJ
easat-8674	224	22	interpret	interpret	VERB
easat-8674	224	23	symbolic	symbolic	ADJ
easat-8674	224	24	information	information	NOUN
easat-8674	224	25	.	.	PUNCT
easat-8674	225	1	each	each	DET
easat-8674	225	2	problem	problem	NOUN
easat-8674	225	3	context	context	NOUN
easat-8674	225	4	required	require	VERB
easat-8674	225	5	students	student	NOUN
easat-8674	225	6	to	to	PART
easat-8674	225	7	accurately	accurately	ADV
easat-8674	225	8	connect	connect	VERB
easat-8674	225	9	contextual	contextual	ADJ
easat-8674	225	10	information	information	NOUN
easat-8674	225	11	with	with	ADP
easat-8674	225	12	algebraic	algebraic	ADJ
easat-8674	225	13	representations	representation	NOUN
easat-8674	225	14	.	.	PUNCT
easat-8674	226	1	however	however	ADV
easat-8674	226	2	,	,	PUNCT
easat-8674	226	3	fundamental	fundamental	ADJ
easat-8674	226	4	differences	difference	NOUN
easat-8674	226	5	were	be	AUX
easat-8674	226	6	observed	observe	VERB
easat-8674	226	7	in	in	ADP
easat-8674	226	8	their	their	PRON
easat-8674	226	9	conceptual	conceptual	ADJ
easat-8674	226	10	approaches	approach	NOUN
easat-8674	226	11	and	and	CCONJ
easat-8674	226	12	problemsolving	problemsolve	VERB
easat-8674	226	13	strategies	strategy	NOUN
easat-8674	226	14	.	.	PUNCT
easat-8674	227	1	during	during	ADP
easat-8674	227	2	the	the	DET
easat-8674	227	3	problem	problem	NOUN
easat-8674	227	4	-	-	PUNCT
easat-8674	227	5	solving	solve	VERB
easat-8674	227	6	process	process	NOUN
easat-8674	227	7	,	,	PUNCT
easat-8674	227	8	students	student	NOUN
easat-8674	227	9	frequently	frequently	ADV
easat-8674	227	10	demonstrated	demonstrate	VERB
easat-8674	227	11	misconceptions	misconception	NOUN
easat-8674	227	12	related	relate	VERB
easat-8674	227	13	to	to	ADP
easat-8674	227	14	the	the	DET
easat-8674	227	15	mathematical	mathematical	ADJ
easat-8674	227	16	concepts	concept	NOUN
easat-8674	227	17	being	be	AUX
easat-8674	227	18	assessed	assess	VERB
easat-8674	227	19	[	[	X
easat-8674	227	20	26	26	NUM
easat-8674	227	21	]	]	PUNCT
easat-8674	227	22	.	.	PUNCT
easat-8674	228	1	these	these	DET
easat-8674	228	2	differences	difference	NOUN
easat-8674	228	3	reflect	reflect	VERB
easat-8674	228	4	a	a	DET
easat-8674	228	5	wide	wide	ADJ
easat-8674	228	6	range	range	NOUN
easat-8674	228	7	of	of	ADP
easat-8674	228	8	content	content	ADJ
easat-8674	228	9	knowledge	knowledge	NOUN
easat-8674	228	10	(	(	PUNCT
easat-8674	228	11	ck	ck	NOUN
easat-8674	228	12	)	)	PUNCT
easat-8674	228	13	mastery	mastery	NOUN
easat-8674	228	14	among	among	ADP
easat-8674	228	15	the	the	DET
easat-8674	228	16	participants	participant	NOUN
easat-8674	228	17	.	.	PUNCT
easat-8674	229	1	strong	strong	ADJ
easat-8674	229	2	ck	ck	NOUN
easat-8674	229	3	enables	enable	VERB
easat-8674	229	4	undergraduate	undergraduate	VERB
easat-8674	229	5	students	student	NOUN
easat-8674	229	6	to	to	PART
easat-8674	229	7	present	present	VERB
easat-8674	229	8	content	content	NOUN
easat-8674	229	9	through	through	ADP
easat-8674	229	10	varied	varied	ADJ
easat-8674	229	11	representations	representation	NOUN
easat-8674	229	12	,	,	PUNCT
easat-8674	229	13	anticipate	anticipate	VERB
easat-8674	229	14	student	student	NOUN
easat-8674	229	15	errors	error	NOUN
easat-8674	229	16	,	,	PUNCT
easat-8674	229	17	and	and	CCONJ
easat-8674	229	18	offer	offer	VERB
easat-8674	229	19	meaningful	meaningful	ADJ
easat-8674	229	20	conceptual	conceptual	ADJ
easat-8674	229	21	explanations	explanation	NOUN
easat-8674	229	22	.	.	PUNCT
easat-8674	230	1	a	a	DET
easat-8674	230	2	recent	recent	ADJ
easat-8674	230	3	meta	meta	ADJ
easat-8674	230	4	-	-	PUNCT
easat-8674	230	5	analysis	analysis	NOUN
easat-8674	230	6	[	[	X
easat-8674	230	7	11	11	NUM
easat-8674	230	8	]	]	PUNCT
easat-8674	230	9	demonstrated	demonstrate	VERB
easat-8674	230	10	a	a	DET
easat-8674	230	11	significant	significant	ADJ
easat-8674	230	12	correlation	correlation	NOUN
easat-8674	230	13	between	between	ADP
easat-8674	230	14	high	high	ADJ
easat-8674	230	15	ck	ck	PROPN
easat-8674	230	16	levels	level	NOUN
easat-8674	230	17	and	and	CCONJ
easat-8674	230	18	improved	improved	ADJ
easat-8674	230	19	student	student	NOUN
easat-8674	230	20	591	591	NUM
easat-8674	230	21	edelweiss	edelweiss	PROPN
easat-8674	230	22	applied	apply	VERB
easat-8674	230	23	science	science	NOUN
easat-8674	230	24	and	and	CCONJ
easat-8674	230	25	technology	technology	NOUN
easat-8674	230	26	issn	issn	PROPN
easat-8674	230	27	:	:	PUNCT
easat-8674	230	28	2576	2576	NUM
easat-8674	230	29	-	-	SYM
easat-8674	230	30	8484	8484	NUM
easat-8674	230	31	vol	vol	NOUN
easat-8674	230	32	.	.	PROPN
easat-8674	231	1	9	9	NUM
easat-8674	231	2	,	,	PUNCT
easat-8674	231	3	no	no	INTJ
easat-8674	231	4	.	.	NOUN
easat-8674	232	1	7	7	NUM
easat-8674	232	2	:	:	SYM
easat-8674	232	3	580	580	NUM
easat-8674	232	4	-	-	SYM
easat-8674	232	5	594	594	NUM
easat-8674	232	6	,	,	PUNCT
easat-8674	232	7	2025	2025	NUM
easat-8674	232	8	doi	doi	NOUN
easat-8674	232	9	:	:	PUNCT
easat-8674	232	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	232	11	©	©	PROPN
easat-8674	232	12	2025	2025	NUM
easat-8674	232	13	by	by	ADP
easat-8674	232	14	the	the	DET
easat-8674	232	15	authors	author	NOUN
easat-8674	232	16	;	;	PUNCT
easat-8674	232	17	licensee	licensee	PROPN
easat-8674	232	18	learning	learn	VERB
easat-8674	232	19	gate	gate	NOUN
easat-8674	232	20	understanding	understanding	NOUN
easat-8674	232	21	in	in	ADP
easat-8674	232	22	mathematics	mathematic	NOUN
easat-8674	232	23	.	.	PUNCT
easat-8674	233	1	undergraduate	undergraduate	ADJ
easat-8674	233	2	students	student	NOUN
easat-8674	233	3	with	with	ADP
easat-8674	233	4	strong	strong	ADJ
easat-8674	233	5	ck	ck	NOUN
easat-8674	233	6	are	be	AUX
easat-8674	233	7	also	also	ADV
easat-8674	233	8	more	more	ADV
easat-8674	233	9	flexible	flexible	ADJ
easat-8674	233	10	in	in	ADP
easat-8674	233	11	employing	employ	VERB
easat-8674	233	12	pedagogical	pedagogical	ADJ
easat-8674	233	13	strategies	strategy	NOUN
easat-8674	233	14	tailored	tailor	VERB
easat-8674	233	15	to	to	ADP
easat-8674	233	16	students	student	NOUN
easat-8674	233	17	’	'	PUNCT
easat-8674	233	18	needs	need	NOUN
easat-8674	233	19	.	.	PUNCT
easat-8674	234	1	this	this	DET
easat-8674	234	2	finding	finding	NOUN
easat-8674	234	3	is	be	AUX
easat-8674	234	4	supported	support	VERB
easat-8674	234	5	by	by	ADP
easat-8674	234	6	the	the	DET
easat-8674	234	7	present	present	ADJ
easat-8674	234	8	study	study	NOUN
easat-8674	234	9	:	:	PUNCT
easat-8674	234	10	students	student	NOUN
easat-8674	234	11	with	with	ADP
easat-8674	234	12	a	a	DET
easat-8674	234	13	strong	strong	ADJ
easat-8674	234	14	conceptual	conceptual	ADJ
easat-8674	234	15	foundation	foundation	NOUN
easat-8674	234	16	(	(	PUNCT
easat-8674	234	17	such	such	ADJ
easat-8674	234	18	as	as	ADP
easat-8674	234	19	s01	s01	NOUN
easat-8674	234	20	and	and	CCONJ
easat-8674	234	21	s10	s10	NOUN
easat-8674	234	22	)	)	PUNCT
easat-8674	234	23	were	be	AUX
easat-8674	234	24	able	able	ADJ
easat-8674	234	25	to	to	PART
easat-8674	234	26	accurately	accurately	ADV
easat-8674	234	27	apply	apply	VERB
easat-8674	234	28	mathematical	mathematical	ADJ
easat-8674	234	29	concepts	concept	NOUN
easat-8674	234	30	in	in	ADP
easat-8674	234	31	tasks	task	NOUN
easat-8674	234	32	involving	involve	VERB
easat-8674	234	33	unit	unit	NOUN
easat-8674	234	34	conversion	conversion	NOUN
easat-8674	234	35	,	,	PUNCT
easat-8674	234	36	formula	formula	NOUN
easat-8674	234	37	application	application	NOUN
easat-8674	234	38	,	,	PUNCT
easat-8674	234	39	and	and	CCONJ
easat-8674	234	40	linear	linear	ADJ
easat-8674	234	41	system	system	NOUN
easat-8674	234	42	modeling	modeling	NOUN
easat-8674	234	43	.	.	PUNCT
easat-8674	235	1	for	for	ADP
easat-8674	235	2	instance	instance	NOUN
easat-8674	235	3	,	,	PUNCT
easat-8674	235	4	in	in	ADP
easat-8674	235	5	the	the	DET
easat-8674	235	6	context	context	NOUN
easat-8674	235	7	of	of	ADP
easat-8674	235	8	time	time	NOUN
easat-8674	235	9	conversion	conversion	NOUN
easat-8674	235	10	and	and	CCONJ
easat-8674	235	11	use	use	NOUN
easat-8674	235	12	of	of	ADP
easat-8674	235	13	the	the	DET
easat-8674	235	14	velocity	velocity	NOUN
easat-8674	235	15	formula	formula	NOUN
easat-8674	235	16	𝑠	𝑠	PROPN
easat-8674	235	17	=	=	SYM
easat-8674	235	18	𝑣	𝑣	PROPN
easat-8674	235	19	.	.	PUNCT
easat-8674	236	1	𝑡	𝑡	NOUN
easat-8674	236	2	,	,	PUNCT
easat-8674	236	3	s01	s01	PROPN
easat-8674	236	4	showed	show	VERB
easat-8674	236	5	a	a	DET
easat-8674	236	6	clear	clear	ADJ
easat-8674	236	7	understanding	understanding	NOUN
easat-8674	236	8	of	of	ADP
easat-8674	236	9	converting	convert	VERB
easat-8674	236	10	10	10	NUM
easat-8674	236	11	minutes	minute	NOUN
easat-8674	236	12	to	to	ADP
easat-8674	236	13	hours	hour	NOUN
easat-8674	236	14	and	and	CCONJ
easat-8674	236	15	the	the	DET
easat-8674	236	16	importance	importance	NOUN
easat-8674	236	17	of	of	ADP
easat-8674	236	18	consistent	consistent	ADJ
easat-8674	236	19	units	unit	NOUN
easat-8674	236	20	in	in	ADP
easat-8674	236	21	algebraic	algebraic	ADJ
easat-8674	236	22	operations	operation	NOUN
easat-8674	236	23	.	.	PUNCT
easat-8674	237	1	similarly	similarly	ADV
easat-8674	237	2	,	,	PUNCT
easat-8674	237	3	s10	s10	PROPN
easat-8674	237	4	demonstrated	demonstrate	VERB
easat-8674	237	5	proficiency	proficiency	NOUN
easat-8674	237	6	in	in	ADP
easat-8674	237	7	modeling	model	VERB
easat-8674	237	8	real	real	ADJ
easat-8674	237	9	-	-	PUNCT
easat-8674	237	10	world	world	NOUN
easat-8674	237	11	contexts	context	NOUN
easat-8674	237	12	through	through	ADP
easat-8674	237	13	systems	system	NOUN
easat-8674	237	14	of	of	ADP
easat-8674	237	15	linear	linear	PROPN
easat-8674	237	16	equations	equation	NOUN
easat-8674	237	17	,	,	PUNCT
easat-8674	237	18	using	use	VERB
easat-8674	237	19	elimination	elimination	NOUN
easat-8674	237	20	and	and	CCONJ
easat-8674	237	21	substitution	substitution	NOUN
easat-8674	237	22	to	to	PART
easat-8674	237	23	reach	reach	VERB
easat-8674	237	24	a	a	DET
easat-8674	237	25	validated	validate	VERB
easat-8674	237	26	solution	solution	NOUN
easat-8674	237	27	.	.	PUNCT
easat-8674	238	1	conversely	conversely	ADV
easat-8674	238	2	,	,	PUNCT
easat-8674	238	3	students	student	NOUN
easat-8674	238	4	with	with	ADP
easat-8674	238	5	a	a	DET
easat-8674	238	6	predominantly	predominantly	ADV
easat-8674	238	7	procedural	procedural	ADJ
easat-8674	238	8	understanding	understanding	NOUN
easat-8674	238	9	(	(	PUNCT
easat-8674	238	10	e.g.	e.g.	ADV
easat-8674	238	11	,	,	PUNCT
easat-8674	238	12	s02	s02	NOUN
easat-8674	238	13	and	and	CCONJ
easat-8674	238	14	s06	s06	NOUN
easat-8674	238	15	)	)	PUNCT
easat-8674	238	16	struggled	struggle	VERB
easat-8674	238	17	to	to	PART
easat-8674	238	18	relate	relate	VERB
easat-8674	238	19	mathematical	mathematical	ADJ
easat-8674	238	20	symbols	symbol	NOUN
easat-8674	238	21	to	to	ADP
easat-8674	238	22	contextual	contextual	ADJ
easat-8674	238	23	meaning	meaning	NOUN
easat-8674	238	24	,	,	PUNCT
easat-8674	238	25	indicating	indicate	VERB
easat-8674	238	26	weaker	weak	ADJ
easat-8674	238	27	ck	ck	NOUN
easat-8674	239	1	.	.	PUNCT
easat-8674	239	2	s02	s02	PROPN
easat-8674	239	3	,	,	PUNCT
easat-8674	239	4	for	for	ADP
easat-8674	239	5	example	example	NOUN
easat-8674	239	6	,	,	PUNCT
easat-8674	239	7	failed	fail	VERB
easat-8674	239	8	to	to	PART
easat-8674	239	9	convert	convert	VERB
easat-8674	239	10	time	time	NOUN
easat-8674	239	11	units	unit	NOUN
easat-8674	239	12	properly	properly	ADV
easat-8674	239	13	and	and	CCONJ
easat-8674	239	14	merely	merely	ADV
easat-8674	239	15	cited	cite	VERB
easat-8674	239	16	the	the	DET
easat-8674	239	17	formula	formula	NOUN
easat-8674	239	18	without	without	ADP
easat-8674	239	19	showing	show	VERB
easat-8674	239	20	conceptual	conceptual	ADJ
easat-8674	239	21	insight	insight	NOUN
easat-8674	239	22	.	.	PUNCT
easat-8674	240	1	this	this	PRON
easat-8674	240	2	illustrates	illustrate	VERB
easat-8674	240	3	a	a	DET
easat-8674	240	4	common	common	ADJ
easat-8674	240	5	issue	issue	NOUN
easat-8674	240	6	—	—	PUNCT
easat-8674	240	7	students	student	NOUN
easat-8674	240	8	being	be	AUX
easat-8674	240	9	able	able	ADJ
easat-8674	240	10	to	to	PART
easat-8674	240	11	perform	perform	VERB
easat-8674	240	12	procedures	procedure	NOUN
easat-8674	240	13	without	without	ADP
easat-8674	240	14	understanding	understand	VERB
easat-8674	240	15	their	their	PRON
easat-8674	240	16	underlying	underlie	VERB
easat-8674	240	17	logic	logic	NOUN
easat-8674	240	18	.	.	PUNCT
easat-8674	241	1	s06	s06	PROPN
easat-8674	241	2	also	also	ADV
easat-8674	241	3	misapplied	misapply	VERB
easat-8674	241	4	the	the	DET
easat-8674	241	5	difference	difference	NOUN
easat-8674	241	6	of	of	ADP
easat-8674	241	7	squares	square	NOUN
easat-8674	241	8	identity	identity	NOUN
easat-8674	241	9	,	,	PUNCT
easat-8674	241	10	confusing	confuse	VERB
easat-8674	241	11	it	it	PRON
easat-8674	241	12	with	with	ADP
easat-8674	241	13	the	the	DET
easat-8674	241	14	pythagorean	pythagorean	PROPN
easat-8674	241	15	theorem	theorem	PROPN
easat-8674	241	16	,	,	PUNCT
easat-8674	241	17	further	far	ADV
easat-8674	241	18	highlighting	highlight	VERB
easat-8674	241	19	the	the	DET
easat-8674	241	20	impact	impact	NOUN
easat-8674	241	21	of	of	ADP
easat-8674	241	22	rote	rote	ADJ
easat-8674	241	23	learning	learning	NOUN
easat-8674	241	24	and	and	CCONJ
easat-8674	241	25	a	a	DET
easat-8674	241	26	lack	lack	NOUN
easat-8674	241	27	of	of	ADP
easat-8674	241	28	deep	deep	ADJ
easat-8674	241	29	conceptual	conceptual	ADJ
easat-8674	241	30	engagement	engagement	NOUN
easat-8674	241	31	[	[	X
easat-8674	241	32	27	27	NUM
easat-8674	241	33	,	,	PUNCT
easat-8674	241	34	28	28	NUM
easat-8674	241	35	]	]	PUNCT
easat-8674	241	36	.	.	PUNCT
easat-8674	242	1	these	these	DET
easat-8674	242	2	findings	finding	NOUN
easat-8674	242	3	support	support	VERB
easat-8674	242	4	the	the	DET
easat-8674	242	5	argument	argument	NOUN
easat-8674	242	6	made	make	VERB
easat-8674	242	7	by	by	ADP
easat-8674	242	8	salazar	salazar	NOUN
easat-8674	242	9	and	and	CCONJ
easat-8674	242	10	yilmaz	yilmaz	NOUN
easat-8674	243	1	[	[	X
easat-8674	243	2	29	29	NUM
easat-8674	243	3	]	]	PUNCT
easat-8674	243	4	who	who	PRON
easat-8674	243	5	emphasized	emphasize	VERB
easat-8674	243	6	that	that	SCONJ
easat-8674	243	7	effective	effective	ADJ
easat-8674	243	8	ck	ck	NOUN
easat-8674	243	9	involves	involve	VERB
easat-8674	243	10	the	the	DET
easat-8674	243	11	ability	ability	NOUN
easat-8674	243	12	to	to	PART
easat-8674	243	13	translate	translate	VERB
easat-8674	243	14	between	between	ADP
easat-8674	243	15	symbols	symbol	NOUN
easat-8674	243	16	,	,	PUNCT
easat-8674	243	17	context	context	NOUN
easat-8674	243	18	,	,	PUNCT
easat-8674	243	19	and	and	CCONJ
easat-8674	243	20	meaning	mean	VERB
easat-8674	243	21	especially	especially	ADV
easat-8674	243	22	in	in	ADP
easat-8674	243	23	algebra	algebra	NOUN
easat-8674	243	24	and	and	CCONJ
easat-8674	243	25	geometry	geometry	NOUN
easat-8674	243	26	.	.	PUNCT
easat-8674	244	1	furthermore	furthermore	ADV
easat-8674	244	2	,	,	PUNCT
easat-8674	244	3	systematic	systematic	ADJ
easat-8674	244	4	reviews	review	NOUN
easat-8674	244	5	[	[	X
easat-8674	244	6	11	11	NUM
easat-8674	244	7	]	]	PUNCT
easat-8674	244	8	indicate	indicate	VERB
easat-8674	244	9	that	that	SCONJ
easat-8674	244	10	the	the	DET
easat-8674	244	11	development	development	NOUN
easat-8674	244	12	of	of	ADP
easat-8674	244	13	ck	ck	PROPN
easat-8674	244	14	in	in	ADP
easat-8674	244	15	teacher	teacher	NOUN
easat-8674	244	16	education	education	NOUN
easat-8674	244	17	remains	remain	VERB
easat-8674	244	18	uneven	uneven	ADJ
easat-8674	244	19	.	.	PUNCT
easat-8674	245	1	instructional	instructional	ADJ
easat-8674	245	2	designs	design	NOUN
easat-8674	245	3	that	that	PRON
easat-8674	245	4	overemphasize	overemphasize	VERB
easat-8674	245	5	procedural	procedural	ADJ
easat-8674	245	6	tasks	task	NOUN
easat-8674	245	7	often	often	ADV
easat-8674	245	8	fail	fail	VERB
easat-8674	245	9	to	to	PART
easat-8674	245	10	cultivate	cultivate	VERB
easat-8674	245	11	deeper	deep	ADJ
easat-8674	245	12	conceptual	conceptual	ADJ
easat-8674	245	13	understanding	understanding	NOUN
easat-8674	245	14	.	.	PUNCT
easat-8674	246	1	in	in	ADP
easat-8674	246	2	this	this	DET
easat-8674	246	3	study	study	NOUN
easat-8674	246	4	,	,	PUNCT
easat-8674	246	5	s09	s09	NOUN
easat-8674	246	6	relied	rely	VERB
easat-8674	246	7	on	on	ADP
easat-8674	246	8	direct	direct	ADJ
easat-8674	246	9	numerical	numerical	ADJ
easat-8674	246	10	comparisons	comparison	NOUN
easat-8674	246	11	without	without	ADP
easat-8674	246	12	developing	develop	VERB
easat-8674	246	13	an	an	DET
easat-8674	246	14	algebraic	algebraic	ADJ
easat-8674	246	15	model	model	NOUN
easat-8674	246	16	.	.	PUNCT
easat-8674	247	1	although	although	SCONJ
easat-8674	247	2	s09	s09	NOUN
easat-8674	247	3	recognized	recognize	VERB
easat-8674	247	4	the	the	DET
easat-8674	247	5	block	block	NOUN
easat-8674	247	6	arrangement	arrangement	NOUN
easat-8674	247	7	’s	’s	PART
easat-8674	247	8	components	component	NOUN
easat-8674	247	9	,	,	PUNCT
easat-8674	247	10	the	the	DET
easat-8674	247	11	solution	solution	NOUN
easat-8674	247	12	lacked	lack	VERB
easat-8674	247	13	formulaic	formulaic	ADJ
easat-8674	247	14	representation	representation	NOUN
easat-8674	247	15	and	and	CCONJ
easat-8674	247	16	systematic	systematic	ADJ
easat-8674	247	17	execution	execution	NOUN
easat-8674	247	18	,	,	PUNCT
easat-8674	247	19	reflecting	reflect	VERB
easat-8674	247	20	an	an	DET
easat-8674	247	21	intuitive	intuitive	ADJ
easat-8674	247	22	rather	rather	ADV
easat-8674	247	23	than	than	ADP
easat-8674	247	24	structured	structure	VERB
easat-8674	247	25	algebraic	algebraic	ADJ
easat-8674	247	26	approach	approach	NOUN
easat-8674	247	27	[	[	X
easat-8674	247	28	30	30	NUM
easat-8674	247	29	-	-	SYM
easat-8674	247	30	34	34	NUM
easat-8674	247	31	]	]	PUNCT
easat-8674	247	32	.	.	PUNCT
easat-8674	248	1	in	in	ADP
easat-8674	248	2	contrast	contrast	NOUN
easat-8674	248	3	,	,	PUNCT
easat-8674	248	4	s04	s04	INTJ
easat-8674	248	5	,	,	PUNCT
easat-8674	248	6	when	when	SCONJ
easat-8674	248	7	tasked	task	VERB
easat-8674	248	8	with	with	ADP
easat-8674	248	9	modeling	model	VERB
easat-8674	248	10	relationships	relationship	NOUN
easat-8674	248	11	using	use	VERB
easat-8674	248	12	the	the	DET
easat-8674	248	13	difference	difference	NOUN
easat-8674	248	14	of	of	ADP
easat-8674	248	15	squares	square	NOUN
easat-8674	248	16	identity	identity	NOUN
easat-8674	248	17	,	,	PUNCT
easat-8674	248	18	was	be	AUX
easat-8674	248	19	able	able	ADJ
easat-8674	248	20	to	to	PART
easat-8674	248	21	construct	construct	VERB
easat-8674	248	22	a	a	DET
easat-8674	248	23	symbolic	symbolic	ADJ
easat-8674	248	24	representation	representation	NOUN
easat-8674	248	25	from	from	ADP
easat-8674	248	26	verbal	verbal	ADJ
easat-8674	248	27	information	information	NOUN
easat-8674	248	28	.	.	PUNCT
easat-8674	249	1	this	this	PRON
easat-8674	249	2	showed	show	VERB
easat-8674	249	3	a	a	DET
easat-8674	249	4	clear	clear	ADJ
easat-8674	249	5	understanding	understanding	NOUN
easat-8674	249	6	of	of	ADP
easat-8674	249	7	variable	variable	ADJ
easat-8674	249	8	structure	structure	NOUN
easat-8674	249	9	and	and	CCONJ
easat-8674	249	10	algebraic	algebraic	ADJ
easat-8674	249	11	modeling	modeling	NOUN
easat-8674	249	12	,	,	PUNCT
easat-8674	249	13	even	even	ADV
easat-8674	249	14	if	if	SCONJ
easat-8674	249	15	a	a	DET
easat-8674	249	16	final	final	ADJ
easat-8674	249	17	conclusion	conclusion	NOUN
easat-8674	249	18	was	be	AUX
easat-8674	249	19	missing	missing	ADJ
easat-8674	249	20	.	.	PUNCT
easat-8674	250	1	these	these	DET
easat-8674	250	2	contrasting	contrast	VERB
easat-8674	250	3	cases	case	NOUN
easat-8674	250	4	underscore	underscore	VERB
easat-8674	250	5	a	a	DET
easat-8674	250	6	major	major	ADJ
easat-8674	250	7	challenge	challenge	NOUN
easat-8674	250	8	in	in	ADP
easat-8674	250	9	ck	ck	PROPN
easat-8674	250	10	development	development	NOUN
easat-8674	250	11	bridging	bridge	VERB
easat-8674	250	12	the	the	DET
easat-8674	250	13	gap	gap	NOUN
easat-8674	250	14	between	between	ADP
easat-8674	250	15	procedural	procedural	ADJ
easat-8674	250	16	fluency	fluency	NOUN
easat-8674	250	17	and	and	CCONJ
easat-8674	250	18	conceptual	conceptual	ADJ
easat-8674	250	19	application	application	NOUN
easat-8674	250	20	.	.	PUNCT
easat-8674	251	1	as	as	ADP
easat-8674	251	2	pincheira	pincheira	PROPN
easat-8674	251	3	and	and	CCONJ
easat-8674	251	4	alsina	alsina	NOUN
easat-8674	251	5	[	[	X
easat-8674	251	6	34	34	NUM
easat-8674	251	7	]	]	X
easat-8674	251	8	observed	observe	VERB
easat-8674	251	9	,	,	PUNCT
easat-8674	251	10	many	many	ADJ
easat-8674	251	11	pre	pre	ADJ
easat-8674	251	12	-	-	ADJ
easat-8674	251	13	service	service	ADJ
easat-8674	251	14	teachers	teacher	NOUN
easat-8674	251	15	can	can	AUX
easat-8674	251	16	perform	perform	VERB
easat-8674	251	17	algorithms	algorithm	NOUN
easat-8674	251	18	but	but	CCONJ
easat-8674	251	19	struggle	struggle	VERB
easat-8674	251	20	to	to	PART
easat-8674	251	21	explain	explain	VERB
easat-8674	251	22	the	the	DET
easat-8674	251	23	reasoning	reasoning	NOUN
easat-8674	251	24	behind	behind	ADP
easat-8674	251	25	their	their	PRON
easat-8674	251	26	steps	step	NOUN
easat-8674	251	27	.	.	PUNCT
easat-8674	252	1	this	this	DET
easat-8674	252	2	issue	issue	NOUN
easat-8674	252	3	was	be	AUX
easat-8674	252	4	mirrored	mirror	VERB
easat-8674	252	5	in	in	ADP
easat-8674	252	6	our	our	PRON
easat-8674	252	7	findings	finding	NOUN
easat-8674	252	8	,	,	PUNCT
easat-8674	252	9	where	where	SCONJ
easat-8674	252	10	some	some	DET
easat-8674	252	11	students	student	NOUN
easat-8674	252	12	could	could	AUX
easat-8674	252	13	recognize	recognize	VERB
easat-8674	252	14	numerical	numerical	ADJ
easat-8674	252	15	elements	element	NOUN
easat-8674	252	16	in	in	ADP
easat-8674	252	17	problems	problem	NOUN
easat-8674	252	18	but	but	CCONJ
easat-8674	252	19	failed	fail	VERB
easat-8674	252	20	to	to	PART
easat-8674	252	21	build	build	VERB
easat-8674	252	22	comprehensive	comprehensive	ADJ
easat-8674	252	23	mathematical	mathematical	ADJ
easat-8674	252	24	models	model	NOUN
easat-8674	252	25	.	.	PUNCT
easat-8674	253	1	this	this	DET
easat-8674	253	2	study	study	NOUN
easat-8674	253	3	contributes	contribute	VERB
easat-8674	253	4	new	new	ADJ
easat-8674	253	5	insight	insight	NOUN
easat-8674	253	6	by	by	ADP
easat-8674	253	7	applying	apply	VERB
easat-8674	253	8	refined	refined	ADJ
easat-8674	253	9	categories	category	NOUN
easat-8674	253	10	mba	mba	PROPN
easat-8674	253	11	-	-	PUNCT
easat-8674	253	12	j	j	PROPN
easat-8674	253	13	,	,	PUNCT
easat-8674	253	14	dta	dta	PROPN
easat-8674	253	15	-	-	PUNCT
easat-8674	253	16	lc	lc	NOUN
easat-8674	253	17	,	,	PUNCT
easat-8674	253	18	and	and	CCONJ
easat-8674	253	19	dtanp	dtanp	VERB
easat-8674	253	20	to	to	PART
easat-8674	253	21	characterize	characterize	VERB
easat-8674	253	22	undergraduate	undergraduate	ADJ
easat-8674	253	23	students	student	NOUN
easat-8674	253	24	thinking	think	VERB
easat-8674	253	25	in	in	ADP
easat-8674	253	26	solving	solve	VERB
easat-8674	253	27	contextual	contextual	ADJ
easat-8674	253	28	algebra	algebra	NOUN
easat-8674	253	29	problems	problem	NOUN
easat-8674	253	30	.	.	PUNCT
easat-8674	254	1	these	these	DET
easat-8674	254	2	categories	category	NOUN
easat-8674	254	3	provide	provide	VERB
easat-8674	254	4	a	a	DET
easat-8674	254	5	more	more	ADV
easat-8674	254	6	nuanced	nuanced	ADJ
easat-8674	254	7	classification	classification	NOUN
easat-8674	254	8	than	than	ADP
easat-8674	254	9	traditional	traditional	ADJ
easat-8674	254	10	dichotomies	dichotomy	NOUN
easat-8674	254	11	between	between	ADP
easat-8674	254	12	“	"	PUNCT
easat-8674	254	13	conceptual	conceptual	ADJ
easat-8674	254	14	”	"	PUNCT
easat-8674	254	15	and	and	CCONJ
easat-8674	254	16	“	"	PUNCT
easat-8674	254	17	procedural	procedural	ADJ
easat-8674	254	18	”	"	PUNCT
easat-8674	254	19	understanding	understanding	NOUN
easat-8674	254	20	.	.	PUNCT
easat-8674	255	1	few	few	ADJ
easat-8674	255	2	previous	previous	ADJ
easat-8674	255	3	studies	study	NOUN
easat-8674	255	4	have	have	AUX
easat-8674	255	5	examined	examine	VERB
easat-8674	255	6	all	all	DET
easat-8674	255	7	three	three	NUM
easat-8674	255	8	dimensions	dimension	NOUN
easat-8674	255	9	(	(	PUNCT
easat-8674	255	10	conceptual	conceptual	ADJ
easat-8674	255	11	,	,	PUNCT
easat-8674	255	12	procedural	procedural	ADJ
easat-8674	255	13	,	,	PUNCT
easat-8674	255	14	justificatory	justificatory	NOUN
easat-8674	255	15	)	)	PUNCT
easat-8674	255	16	simultaneously	simultaneously	ADV
easat-8674	255	17	within	within	ADP
easat-8674	255	18	the	the	DET
easat-8674	255	19	context	context	NOUN
easat-8674	255	20	of	of	ADP
easat-8674	255	21	algebra	algebra	NOUN
easat-8674	255	22	education	education	NOUN
easat-8674	255	23	.	.	PUNCT
easat-8674	256	1	our	our	PRON
easat-8674	256	2	study	study	NOUN
easat-8674	256	3	shows	show	VERB
easat-8674	256	4	that	that	SCONJ
easat-8674	256	5	the	the	DET
easat-8674	256	6	success	success	NOUN
easat-8674	256	7	or	or	CCONJ
easat-8674	256	8	failure	failure	NOUN
easat-8674	256	9	in	in	ADP
easat-8674	256	10	each	each	DET
easat-8674	256	11	dimension	dimension	NOUN
easat-8674	256	12	directly	directly	ADV
easat-8674	256	13	affects	affect	VERB
easat-8674	256	14	the	the	DET
easat-8674	256	15	coherence	coherence	NOUN
easat-8674	256	16	and	and	CCONJ
easat-8674	256	17	completeness	completeness	NOUN
easat-8674	256	18	of	of	ADP
easat-8674	256	19	students	student	NOUN
easat-8674	256	20	’	’	PART
easat-8674	256	21	problem	problem	NOUN
easat-8674	256	22	-	-	PUNCT
easat-8674	256	23	solving	solve	VERB
easat-8674	256	24	processes	process	NOUN
easat-8674	256	25	.	.	PUNCT
easat-8674	257	1	additionally	additionally	ADV
easat-8674	257	2	,	,	PUNCT
easat-8674	257	3	this	this	DET
easat-8674	257	4	study	study	NOUN
easat-8674	257	5	employed	employ	VERB
easat-8674	257	6	data	datum	NOUN
easat-8674	257	7	triangulation	triangulation	NOUN
easat-8674	257	8	through	through	ADP
easat-8674	257	9	written	write	VERB
easat-8674	257	10	responses	response	NOUN
easat-8674	257	11	and	and	CCONJ
easat-8674	257	12	interview	interview	NOUN
easat-8674	257	13	excerpts	excerpt	NOUN
easat-8674	257	14	,	,	PUNCT
easat-8674	257	15	providing	provide	VERB
easat-8674	257	16	deeper	deep	ADJ
easat-8674	257	17	insight	insight	NOUN
easat-8674	257	18	into	into	ADP
easat-8674	257	19	students	student	NOUN
easat-8674	257	20	’	'	PUNCT
easat-8674	257	21	reasoning	reasoning	NOUN
easat-8674	257	22	beyond	beyond	ADP
easat-8674	257	23	surface	surface	NOUN
easat-8674	257	24	-	-	PUNCT
easat-8674	257	25	level	level	NOUN
easat-8674	257	26	answers	answer	NOUN
easat-8674	257	27	.	.	PUNCT
easat-8674	258	1	this	this	DET
easat-8674	258	2	method	method	NOUN
easat-8674	258	3	offers	offer	VERB
easat-8674	258	4	a	a	DET
easat-8674	258	5	valuable	valuable	ADJ
easat-8674	258	6	contribution	contribution	NOUN
easat-8674	258	7	to	to	ADP
easat-8674	258	8	in	in	ADP
easat-8674	258	9	-	-	PUNCT
easat-8674	258	10	situ	situ	NOUN
easat-8674	258	11	analysis	analysis	NOUN
easat-8674	258	12	of	of	ADP
easat-8674	258	13	mathematical	mathematical	ADJ
easat-8674	258	14	thinking	thinking	NOUN
easat-8674	258	15	.	.	PUNCT
easat-8674	259	1	bruna	bruna	PROPN
easat-8674	260	1	[	[	X
easat-8674	260	2	35	35	NUM
easat-8674	260	3	]	]	PUNCT
easat-8674	260	4	in	in	ADP
easat-8674	260	5	a	a	DET
easat-8674	260	6	study	study	NOUN
easat-8674	260	7	on	on	ADP
easat-8674	260	8	teacher	teacher	NOUN
easat-8674	260	9	education	education	NOUN
easat-8674	260	10	programs	program	NOUN
easat-8674	260	11	at	at	ADP
easat-8674	260	12	pontificia	pontificia	PROPN
easat-8674	260	13	universidad	universidad	PROPN
easat-8674	260	14	católica	católica	PROPN
easat-8674	260	15	de	de	PROPN
easat-8674	260	16	chile	chile	PROPN
easat-8674	260	17	,	,	PUNCT
easat-8674	260	18	demonstrated	demonstrate	VERB
easat-8674	260	19	that	that	SCONJ
easat-8674	260	20	using	use	VERB
easat-8674	260	21	academic	academic	ADJ
easat-8674	260	22	portfolios	portfolio	NOUN
easat-8674	260	23	in	in	ADP
easat-8674	260	24	advanced	advanced	ADJ
easat-8674	260	25	mathematics	mathematic	NOUN
easat-8674	260	26	courses	course	NOUN
easat-8674	260	27	improved	improve	VERB
easat-8674	260	28	pre	pre	ADJ
easat-8674	260	29	-	-	ADJ
easat-8674	260	30	service	service	ADJ
easat-8674	260	31	teachers	teacher	NOUN
easat-8674	260	32	’	'	PUNCT
easat-8674	260	33	engagement	engagement	NOUN
easat-8674	260	34	and	and	CCONJ
easat-8674	260	35	conceptual	conceptual	ADJ
easat-8674	260	36	understanding	understanding	NOUN
easat-8674	260	37	.	.	PUNCT
easat-8674	261	1	the	the	DET
easat-8674	261	2	portfolio	portfolio	NOUN
easat-8674	261	3	process	process	NOUN
easat-8674	261	4	including	include	VERB
easat-8674	261	5	reflection	reflection	NOUN
easat-8674	261	6	,	,	PUNCT
easat-8674	261	7	documentation	documentation	NOUN
easat-8674	261	8	,	,	PUNCT
easat-8674	261	9	and	and	CCONJ
easat-8674	261	10	negotiated	negotiate	VERB
easat-8674	261	11	learning	learning	NOUN
easat-8674	261	12	contracts	contract	NOUN
easat-8674	261	13	was	be	AUX
easat-8674	261	14	shown	show	VERB
easat-8674	261	15	to	to	PART
easat-8674	261	16	strengthen	strengthen	VERB
easat-8674	261	17	mathematical	mathematical	ADJ
easat-8674	261	18	understanding	understanding	NOUN
easat-8674	261	19	and	and	CCONJ
easat-8674	261	20	better	well	ADJ
easat-8674	261	21	prepare	prepare	VERB
easat-8674	261	22	teachers	teacher	NOUN
easat-8674	261	23	for	for	ADP
easat-8674	261	24	classroom	classroom	NOUN
easat-8674	261	25	practice	practice	NOUN
easat-8674	261	26	.	.	PUNCT
easat-8674	262	1	these	these	DET
easat-8674	262	2	findings	finding	NOUN
easat-8674	262	3	support	support	VERB
easat-8674	262	4	the	the	DET
easat-8674	262	5	methodological	methodological	ADJ
easat-8674	262	6	design	design	NOUN
easat-8674	262	7	of	of	ADP
easat-8674	262	8	this	this	DET
easat-8674	262	9	study	study	NOUN
easat-8674	262	10	,	,	PUNCT
easat-8674	262	11	which	which	PRON
easat-8674	262	12	integrates	integrate	VERB
easat-8674	262	13	reflective	reflective	ADJ
easat-8674	262	14	written	write	VERB
easat-8674	262	15	and	and	CCONJ
easat-8674	262	16	verbal	verbal	ADJ
easat-8674	262	17	data	datum	NOUN
easat-8674	262	18	to	to	PART
easat-8674	262	19	explore	explore	VERB
easat-8674	262	20	students	student	NOUN
easat-8674	262	21	’	'	PUNCT
easat-8674	262	22	cognitive	cognitive	ADJ
easat-8674	262	23	processes	process	NOUN
easat-8674	262	24	in	in	ADP
easat-8674	262	25	greater	great	ADJ
easat-8674	262	26	depth	depth	NOUN
easat-8674	262	27	.	.	PUNCT
easat-8674	263	1	592	592	NUM
easat-8674	263	2	edelweiss	edelweiss	PROPN
easat-8674	263	3	applied	apply	VERB
easat-8674	263	4	science	science	NOUN
easat-8674	263	5	and	and	CCONJ
easat-8674	263	6	technology	technology	NOUN
easat-8674	263	7	issn	issn	PROPN
easat-8674	263	8	:	:	PUNCT
easat-8674	263	9	2576	2576	NUM
easat-8674	263	10	-	-	SYM
easat-8674	263	11	8484	8484	NUM
easat-8674	263	12	vol	vol	NOUN
easat-8674	263	13	.	.	PROPN
easat-8674	264	1	9	9	NUM
easat-8674	264	2	,	,	PUNCT
easat-8674	264	3	no	no	INTJ
easat-8674	264	4	.	.	NOUN
easat-8674	265	1	7	7	NUM
easat-8674	265	2	:	:	SYM
easat-8674	265	3	580	580	NUM
easat-8674	265	4	-	-	SYM
easat-8674	265	5	594	594	NUM
easat-8674	265	6	,	,	PUNCT
easat-8674	265	7	2025	2025	NUM
easat-8674	265	8	doi	doi	NOUN
easat-8674	265	9	:	:	PUNCT
easat-8674	265	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	265	11	©	©	PROPN
easat-8674	265	12	2025	2025	NUM
easat-8674	265	13	by	by	ADP
easat-8674	265	14	the	the	DET
easat-8674	265	15	authors	author	NOUN
easat-8674	265	16	;	;	PUNCT
easat-8674	265	17	licensee	licensee	PROPN
easat-8674	265	18	learning	learning	NOUN
easat-8674	265	19	gate	gate	PROPN
easat-8674	265	20	overall	overall	ADV
easat-8674	265	21	,	,	PUNCT
easat-8674	265	22	these	these	DET
easat-8674	265	23	results	result	NOUN
easat-8674	265	24	suggest	suggest	VERB
easat-8674	265	25	that	that	SCONJ
easat-8674	265	26	mathematics	mathematics	NOUN
easat-8674	265	27	teacher	teacher	NOUN
easat-8674	265	28	education	education	NOUN
easat-8674	265	29	should	should	AUX
easat-8674	265	30	place	place	VERB
easat-8674	265	31	greater	great	ADJ
easat-8674	265	32	emphasis	emphasis	NOUN
easat-8674	265	33	on	on	ADP
easat-8674	265	34	developing	develop	VERB
easat-8674	265	35	students	student	NOUN
easat-8674	265	36	’	'	PUNCT
easat-8674	265	37	abilities	ability	NOUN
easat-8674	265	38	in	in	ADP
easat-8674	265	39	contextual	contextual	ADJ
easat-8674	265	40	interpretation	interpretation	NOUN
easat-8674	265	41	,	,	PUNCT
easat-8674	265	42	symbolic	symbolic	ADJ
easat-8674	265	43	representation	representation	NOUN
easat-8674	265	44	,	,	PUNCT
easat-8674	265	45	and	and	CCONJ
easat-8674	265	46	solution	solution	NOUN
easat-8674	265	47	validation	validation	NOUN
easat-8674	265	48	.	.	PUNCT
easat-8674	266	1	this	this	PRON
easat-8674	266	2	provides	provide	VERB
easat-8674	266	3	a	a	DET
easat-8674	266	4	foundation	foundation	NOUN
easat-8674	266	5	for	for	ADP
easat-8674	266	6	designing	design	VERB
easat-8674	266	7	context	context	NOUN
easat-8674	266	8	-	-	PUNCT
easat-8674	266	9	based	base	VERB
easat-8674	266	10	modules	module	NOUN
easat-8674	266	11	that	that	PRON
easat-8674	266	12	foster	foster	VERB
easat-8674	266	13	reflective	reflective	ADJ
easat-8674	266	14	thinking	thinking	NOUN
easat-8674	266	15	and	and	CCONJ
easat-8674	266	16	mathematical	mathematical	ADJ
easat-8674	266	17	justification	justification	NOUN
easat-8674	266	18	skills	skill	NOUN
easat-8674	266	19	essential	essential	ADJ
easat-8674	266	20	for	for	ADP
easat-8674	266	21	future	future	ADJ
easat-8674	266	22	educators	educator	NOUN
easat-8674	266	23	.	.	PUNCT
easat-8674	267	1	6	6	X
easat-8674	267	2	.	.	X
easat-8674	267	3	conclusion	conclusion	VERB
easat-8674	267	4	the	the	DET
easat-8674	267	5	ability	ability	NOUN
easat-8674	267	6	to	to	PART
easat-8674	267	7	represent	represent	VERB
easat-8674	267	8	contextual	contextual	ADJ
easat-8674	267	9	information	information	NOUN
easat-8674	267	10	algebraically	algebraically	ADV
easat-8674	267	11	serves	serve	VERB
easat-8674	267	12	as	as	ADP
easat-8674	267	13	a	a	DET
easat-8674	267	14	key	key	ADJ
easat-8674	267	15	distinguishing	distinguish	VERB
easat-8674	267	16	factor	factor	NOUN
easat-8674	267	17	between	between	ADP
easat-8674	267	18	students	student	NOUN
easat-8674	267	19	categorized	categorize	VERB
easat-8674	267	20	under	under	ADP
easat-8674	267	21	the	the	DET
easat-8674	267	22	meaning	meaning	NOUN
easat-8674	267	23	-	-	PUNCT
easat-8674	267	24	based	base	VERB
easat-8674	267	25	approach	approach	NOUN
easat-8674	267	26	(	(	PUNCT
easat-8674	267	27	mba	mba	NOUN
easat-8674	267	28	)	)	PUNCT
easat-8674	267	29	and	and	CCONJ
easat-8674	267	30	those	those	PRON
easat-8674	267	31	under	under	ADP
easat-8674	267	32	the	the	DET
easat-8674	267	33	direct	direct	ADJ
easat-8674	267	34	translation	translation	NOUN
easat-8674	267	35	approach	approach	NOUN
easat-8674	267	36	(	(	PUNCT
easat-8674	267	37	dta	dta	PROPN
easat-8674	267	38	)	)	PUNCT
easat-8674	267	39	.	.	PUNCT
easat-8674	268	1	subjects	subject	NOUN
easat-8674	268	2	s01	s01	VERB
easat-8674	268	3	,	,	PUNCT
easat-8674	268	4	s04	s04	NOUN
easat-8674	268	5	,	,	PUNCT
easat-8674	268	6	and	and	CCONJ
easat-8674	268	7	s10	s10	PROPN
easat-8674	268	8	exhibited	exhibit	VERB
easat-8674	268	9	characteristics	characteristic	NOUN
easat-8674	268	10	of	of	ADP
easat-8674	268	11	students	student	NOUN
easat-8674	268	12	with	with	ADP
easat-8674	268	13	stronger	strong	ADJ
easat-8674	268	14	algebraic	algebraic	ADJ
easat-8674	268	15	understanding	understanding	NOUN
easat-8674	268	16	(	(	PUNCT
easat-8674	268	17	mba	mba	NOUN
easat-8674	268	18	)	)	PUNCT
easat-8674	268	19	.	.	PUNCT
easat-8674	269	1	this	this	PRON
easat-8674	269	2	was	be	AUX
easat-8674	269	3	demonstrated	demonstrate	VERB
easat-8674	269	4	through	through	ADP
easat-8674	269	5	their	their	PRON
easat-8674	269	6	ability	ability	NOUN
easat-8674	269	7	to	to	PART
easat-8674	269	8	identify	identify	VERB
easat-8674	269	9	variable	variable	ADJ
easat-8674	269	10	relationships	relationship	NOUN
easat-8674	269	11	,	,	PUNCT
easat-8674	269	12	construct	construct	VERB
easat-8674	269	13	symbolic	symbolic	ADJ
easat-8674	269	14	representations	representation	NOUN
easat-8674	269	15	,	,	PUNCT
easat-8674	269	16	apply	apply	VERB
easat-8674	269	17	appropriate	appropriate	ADJ
easat-8674	269	18	procedures	procedure	NOUN
easat-8674	269	19	,	,	PUNCT
easat-8674	269	20	and	and	CCONJ
easat-8674	269	21	validate	validate	VERB
easat-8674	269	22	their	their	PRON
easat-8674	269	23	results	result	NOUN
easat-8674	269	24	.	.	PUNCT
easat-8674	270	1	in	in	ADP
easat-8674	270	2	contrast	contrast	NOUN
easat-8674	270	3	,	,	PUNCT
easat-8674	270	4	subjects	subject	NOUN
easat-8674	270	5	s02	s02	PROPN
easat-8674	270	6	,	,	PUNCT
easat-8674	270	7	s06	s06	NOUN
easat-8674	270	8	,	,	PUNCT
easat-8674	270	9	and	and	CCONJ
easat-8674	270	10	s09	s09	VERB
easat-8674	270	11	although	although	SCONJ
easat-8674	270	12	capable	capable	ADJ
easat-8674	270	13	of	of	ADP
easat-8674	270	14	recognizing	recognize	VERB
easat-8674	270	15	important	important	ADJ
easat-8674	270	16	problem	problem	NOUN
easat-8674	270	17	elements	element	NOUN
easat-8674	270	18	struggled	struggle	VERB
easat-8674	270	19	to	to	PART
easat-8674	270	20	construct	construct	VERB
easat-8674	270	21	coherent	coherent	ADJ
easat-8674	270	22	algebraic	algebraic	ADJ
easat-8674	270	23	models	model	NOUN
easat-8674	270	24	and	and	CCONJ
easat-8674	270	25	apply	apply	VERB
easat-8674	270	26	them	they	PRON
easat-8674	270	27	consistently	consistently	ADV
easat-8674	270	28	.	.	PUNCT
easat-8674	271	1	their	their	PRON
easat-8674	271	2	problem	problem	NOUN
easat-8674	271	3	-	-	PUNCT
easat-8674	271	4	solving	solve	VERB
easat-8674	271	5	approaches	approach	NOUN
easat-8674	271	6	tended	tend	VERB
easat-8674	271	7	to	to	PART
easat-8674	271	8	rely	rely	VERB
easat-8674	271	9	on	on	ADP
easat-8674	271	10	procedural	procedural	ADJ
easat-8674	271	11	routines	routine	NOUN
easat-8674	271	12	or	or	CCONJ
easat-8674	271	13	intuitive	intuitive	ADJ
easat-8674	271	14	reasoning	reasoning	NOUN
easat-8674	271	15	,	,	PUNCT
easat-8674	271	16	often	often	ADV
easat-8674	271	17	lacking	lack	VERB
easat-8674	271	18	sufficient	sufficient	ADJ
easat-8674	271	19	validation	validation	NOUN
easat-8674	271	20	.	.	PUNCT
easat-8674	272	1	these	these	DET
easat-8674	272	2	contrasting	contrast	VERB
easat-8674	272	3	approaches	approach	NOUN
easat-8674	272	4	underscore	underscore	VERB
easat-8674	272	5	the	the	DET
easat-8674	272	6	need	need	NOUN
easat-8674	272	7	to	to	PART
easat-8674	272	8	emphasize	emphasize	VERB
easat-8674	272	9	the	the	DET
easat-8674	272	10	development	development	NOUN
easat-8674	272	11	of	of	ADP
easat-8674	272	12	conceptual	conceptual	ADJ
easat-8674	272	13	understanding	understanding	NOUN
easat-8674	272	14	in	in	ADP
easat-8674	272	15	algebra	algebra	NOUN
easat-8674	272	16	,	,	PUNCT
easat-8674	272	17	particularly	particularly	ADV
easat-8674	272	18	in	in	ADP
easat-8674	272	19	aspects	aspect	NOUN
easat-8674	272	20	such	such	ADJ
easat-8674	272	21	as	as	ADP
easat-8674	272	22	unit	unit	NOUN
easat-8674	272	23	conversion	conversion	NOUN
easat-8674	272	24	,	,	PUNCT
easat-8674	272	25	equation	equation	NOUN
easat-8674	272	26	structure	structure	NOUN
easat-8674	272	27	,	,	PUNCT
easat-8674	272	28	and	and	CCONJ
easat-8674	272	29	real	real	ADJ
easat-8674	272	30	-	-	PUNCT
easat-8674	272	31	world	world	NOUN
easat-8674	272	32	mathematical	mathematical	ADJ
easat-8674	272	33	modeling	modeling	NOUN
easat-8674	272	34	.	.	PUNCT
easat-8674	273	1	the	the	DET
easat-8674	273	2	study	study	NOUN
easat-8674	273	3	reveals	reveal	VERB
easat-8674	273	4	that	that	SCONJ
easat-8674	273	5	undergraduate	undergraduate	ADJ
easat-8674	273	6	students	student	NOUN
easat-8674	273	7	display	display	VERB
easat-8674	273	8	a	a	DET
easat-8674	273	9	wide	wide	ADJ
easat-8674	273	10	range	range	NOUN
easat-8674	273	11	of	of	ADP
easat-8674	273	12	understandings	understanding	NOUN
easat-8674	273	13	and	and	CCONJ
easat-8674	273	14	strategies	strategy	NOUN
easat-8674	273	15	when	when	SCONJ
easat-8674	273	16	solving	solve	VERB
easat-8674	273	17	contextual	contextual	ADJ
easat-8674	273	18	algebra	algebra	NOUN
easat-8674	273	19	problems	problem	NOUN
easat-8674	273	20	.	.	PUNCT
easat-8674	274	1	these	these	DET
easat-8674	274	2	variations	variation	NOUN
easat-8674	274	3	are	be	AUX
easat-8674	274	4	evident	evident	ADJ
easat-8674	274	5	in	in	ADP
easat-8674	274	6	three	three	NUM
easat-8674	274	7	key	key	ADJ
easat-8674	274	8	areas	area	NOUN
easat-8674	274	9	:	:	PUNCT
easat-8674	274	10	(	(	PUNCT
easat-8674	274	11	1	1	X
easat-8674	274	12	)	)	PUNCT
easat-8674	274	13	the	the	DET
easat-8674	274	14	ability	ability	NOUN
easat-8674	274	15	to	to	PART
easat-8674	274	16	convert	convert	VERB
easat-8674	274	17	units	unit	NOUN
easat-8674	274	18	and	and	CCONJ
easat-8674	274	19	maintain	maintain	VERB
easat-8674	274	20	consistency	consistency	NOUN
easat-8674	274	21	in	in	ADP
easat-8674	274	22	symbolic	symbolic	ADJ
easat-8674	274	23	representation	representation	NOUN
easat-8674	274	24	;	;	PUNCT
easat-8674	274	25	(	(	PUNCT
easat-8674	274	26	2	2	X
easat-8674	274	27	)	)	PUNCT
easat-8674	274	28	the	the	DET
easat-8674	274	29	ability	ability	NOUN
easat-8674	274	30	to	to	PART
easat-8674	274	31	construct	construct	VERB
easat-8674	274	32	algebraic	algebraic	ADJ
easat-8674	274	33	models	model	NOUN
easat-8674	274	34	from	from	ADP
easat-8674	274	35	verbal	verbal	ADJ
easat-8674	274	36	or	or	CCONJ
easat-8674	274	37	visual	visual	ADJ
easat-8674	274	38	contexts	context	NOUN
easat-8674	274	39	;	;	PUNCT
easat-8674	274	40	(	(	PUNCT
easat-8674	274	41	3	3	X
easat-8674	274	42	)	)	PUNCT
easat-8674	274	43	the	the	DET
easat-8674	274	44	ability	ability	NOUN
easat-8674	274	45	to	to	PART
easat-8674	274	46	validate	validate	VERB
easat-8674	274	47	and	and	CCONJ
easat-8674	274	48	justify	justify	VERB
easat-8674	274	49	mathematical	mathematical	ADJ
easat-8674	274	50	solutions	solution	NOUN
easat-8674	274	51	.	.	PUNCT
easat-8674	275	1	undergraduate	undergraduate	NOUN
easat-8674	275	2	students	student	NOUN
easat-8674	275	3	categorized	categorize	VERB
easat-8674	275	4	under	under	ADP
easat-8674	275	5	mba	mba	NOUN
easat-8674	275	6	-	-	PUNCT
easat-8674	275	7	j	j	PROPN
easat-8674	275	8	demonstrated	demonstrate	VERB
easat-8674	275	9	strong	strong	ADJ
easat-8674	275	10	conceptual	conceptual	ADJ
easat-8674	275	11	understanding	understanding	NOUN
easat-8674	275	12	,	,	PUNCT
easat-8674	275	13	accurately	accurately	ADV
easat-8674	275	14	built	build	VERB
easat-8674	275	15	systems	system	NOUN
easat-8674	275	16	of	of	ADP
easat-8674	275	17	equations	equation	NOUN
easat-8674	275	18	,	,	PUNCT
easat-8674	275	19	and	and	CCONJ
easat-8674	275	20	engaged	engage	VERB
easat-8674	275	21	in	in	ADP
easat-8674	275	22	solution	solution	NOUN
easat-8674	275	23	validation	validation	NOUN
easat-8674	275	24	.	.	PUNCT
easat-8674	276	1	in	in	ADP
easat-8674	276	2	contrast	contrast	NOUN
easat-8674	276	3	,	,	PUNCT
easat-8674	276	4	those	those	PRON
easat-8674	276	5	in	in	ADP
easat-8674	276	6	the	the	DET
easat-8674	276	7	dta	dta	PROPN
easat-8674	276	8	-	-	PUNCT
easat-8674	276	9	lc	lc	PROPN
easat-8674	276	10	and	and	CCONJ
easat-8674	276	11	dta	dta	PROPN
easat-8674	276	12	-	-	PUNCT
easat-8674	276	13	np	np	NOUN
easat-8674	276	14	categories	category	NOUN
easat-8674	276	15	predominantly	predominantly	ADV
easat-8674	276	16	relied	rely	VERB
easat-8674	276	17	on	on	ADP
easat-8674	276	18	procedural	procedural	ADJ
easat-8674	276	19	strategies	strategy	NOUN
easat-8674	276	20	with	with	ADP
easat-8674	276	21	limited	limited	ADJ
easat-8674	276	22	integration	integration	NOUN
easat-8674	276	23	of	of	ADP
easat-8674	276	24	contextual	contextual	ADJ
easat-8674	276	25	understanding	understanding	NOUN
easat-8674	276	26	or	or	CCONJ
easat-8674	276	27	justification	justification	NOUN
easat-8674	276	28	.	.	PUNCT
easat-8674	277	1	therefore	therefore	ADV
easat-8674	277	2	,	,	PUNCT
easat-8674	277	3	algebra	algebra	NOUN
easat-8674	277	4	instruction	instruction	NOUN
easat-8674	277	5	in	in	ADP
easat-8674	277	6	teacher	teacher	NOUN
easat-8674	277	7	education	education	NOUN
easat-8674	277	8	programs	program	NOUN
easat-8674	277	9	must	must	AUX
easat-8674	277	10	place	place	VERB
easat-8674	277	11	greater	great	ADJ
easat-8674	277	12	emphasis	emphasis	NOUN
easat-8674	277	13	on	on	ADP
easat-8674	277	14	developing	develop	VERB
easat-8674	277	15	meaningful	meaningful	ADJ
easat-8674	277	16	symbolic	symbolic	ADJ
easat-8674	277	17	representations	representation	NOUN
easat-8674	277	18	and	and	CCONJ
easat-8674	277	19	fostering	foster	VERB
easat-8674	277	20	reflective	reflective	ADJ
easat-8674	277	21	algebraic	algebraic	ADJ
easat-8674	277	22	thinking	thinking	NOUN
easat-8674	277	23	.	.	PUNCT
easat-8674	278	1	these	these	DET
easat-8674	278	2	findings	finding	NOUN
easat-8674	278	3	support	support	VERB
easat-8674	278	4	the	the	DET
easat-8674	278	5	theoretical	theoretical	ADJ
easat-8674	278	6	perspective	perspective	NOUN
easat-8674	278	7	that	that	SCONJ
easat-8674	278	8	robust	robust	ADJ
easat-8674	278	9	algebraic	algebraic	ADJ
easat-8674	278	10	competence	competence	NOUN
easat-8674	278	11	can	can	AUX
easat-8674	278	12	not	not	PART
easat-8674	278	13	be	be	AUX
easat-8674	278	14	cultivated	cultivate	VERB
easat-8674	278	15	without	without	ADP
easat-8674	278	16	integrating	integrate	VERB
easat-8674	278	17	context	context	NOUN
easat-8674	278	18	,	,	PUNCT
easat-8674	278	19	symbolism	symbolism	NOUN
easat-8674	278	20	,	,	PUNCT
easat-8674	278	21	and	and	CCONJ
easat-8674	278	22	justification	justification	NOUN
easat-8674	278	23	.	.	PUNCT
easat-8674	279	1	7	7	X
easat-8674	279	2	.	.	X
easat-8674	279	3	implications	implication	NOUN
easat-8674	279	4	contextual	contextual	ADJ
easat-8674	279	5	problem	problem	NOUN
easat-8674	279	6	-	-	PUNCT
easat-8674	279	7	based	base	VERB
easat-8674	279	8	learning	learning	NOUN
easat-8674	279	9	design	design	NOUN
easat-8674	279	10	:	:	PUNCT
easat-8674	279	11	algebra	algebra	NOUN
easat-8674	279	12	instruction	instruction	NOUN
easat-8674	279	13	for	for	ADP
easat-8674	279	14	prospective	prospective	ADJ
easat-8674	279	15	undergraduate	undergraduate	ADJ
easat-8674	279	16	students	student	NOUN
easat-8674	279	17	should	should	AUX
easat-8674	279	18	prioritize	prioritize	VERB
easat-8674	279	19	learning	learn	VERB
easat-8674	279	20	experiences	experience	NOUN
easat-8674	279	21	grounded	ground	VERB
easat-8674	279	22	in	in	ADP
easat-8674	279	23	real	real	ADJ
easat-8674	279	24	world	world	NOUN
easat-8674	279	25	problems	problem	NOUN
easat-8674	279	26	that	that	PRON
easat-8674	279	27	require	require	VERB
easat-8674	279	28	unit	unit	NOUN
easat-8674	279	29	conversion	conversion	NOUN
easat-8674	279	30	,	,	PUNCT
easat-8674	279	31	visual	visual	ADJ
easat-8674	279	32	interpretation	interpretation	NOUN
easat-8674	279	33	,	,	PUNCT
easat-8674	279	34	and	and	CCONJ
easat-8674	279	35	mathematical	mathematical	ADJ
easat-8674	279	36	modeling	modeling	NOUN
easat-8674	279	37	.	.	PUNCT
easat-8674	280	1	such	such	ADJ
easat-8674	280	2	approaches	approach	NOUN
easat-8674	280	3	enhance	enhance	VERB
easat-8674	280	4	students	student	NOUN
easat-8674	280	5	’	'	PUNCT
easat-8674	280	6	ability	ability	NOUN
easat-8674	280	7	to	to	PART
easat-8674	280	8	link	link	VERB
easat-8674	280	9	abstract	abstract	ADJ
easat-8674	280	10	concepts	concept	NOUN
easat-8674	280	11	to	to	ADP
easat-8674	280	12	practical	practical	ADJ
easat-8674	280	13	applications	application	NOUN
easat-8674	280	14	,	,	PUNCT
easat-8674	280	15	fostering	foster	VERB
easat-8674	280	16	deeper	deep	ADJ
easat-8674	280	17	and	and	CCONJ
easat-8674	280	18	more	more	ADV
easat-8674	280	19	meaningful	meaningful	ADJ
easat-8674	280	20	algebraic	algebraic	ADJ
easat-8674	280	21	understanding	understanding	NOUN
easat-8674	280	22	.	.	PUNCT
easat-8674	281	1	emphasis	emphasis	NOUN
easat-8674	281	2	on	on	ADP
easat-8674	281	3	justification	justification	NOUN
easat-8674	281	4	and	and	CCONJ
easat-8674	281	5	answer	answer	NOUN
easat-8674	281	6	validation	validation	NOUN
easat-8674	281	7	processes	process	NOUN
easat-8674	281	8	:	:	PUNCT
easat-8674	281	9	instructors	instructor	NOUN
easat-8674	281	10	must	must	AUX
easat-8674	281	11	guide	guide	VERB
easat-8674	281	12	students	student	NOUN
easat-8674	281	13	not	not	PART
easat-8674	281	14	only	only	ADV
easat-8674	281	15	toward	toward	ADP
easat-8674	281	16	correct	correct	ADJ
easat-8674	281	17	answers	answer	NOUN
easat-8674	281	18	but	but	CCONJ
easat-8674	281	19	also	also	ADV
easat-8674	281	20	through	through	ADP
easat-8674	281	21	rigorous	rigorous	ADJ
easat-8674	281	22	validation	validation	NOUN
easat-8674	281	23	techniques	technique	NOUN
easat-8674	281	24	,	,	PUNCT
easat-8674	281	25	such	such	ADJ
easat-8674	281	26	as	as	ADP
easat-8674	281	27	substitution	substitution	NOUN
easat-8674	281	28	,	,	PUNCT
easat-8674	281	29	logical	logical	ADJ
easat-8674	281	30	proof	proof	NOUN
easat-8674	281	31	,	,	PUNCT
easat-8674	281	32	and	and	CCONJ
easat-8674	281	33	reflective	reflective	ADJ
easat-8674	281	34	evaluation	evaluation	NOUN
easat-8674	281	35	.	.	PUNCT
easat-8674	282	1	these	these	DET
easat-8674	282	2	processes	process	NOUN
easat-8674	282	3	are	be	AUX
easat-8674	282	4	critical	critical	ADJ
easat-8674	282	5	in	in	ADP
easat-8674	282	6	training	train	VERB
easat-8674	282	7	future	future	ADJ
easat-8674	282	8	undergraduate	undergraduate	ADJ
easat-8674	282	9	students	student	NOUN
easat-8674	282	10	to	to	PART
easat-8674	282	11	foster	foster	VERB
easat-8674	282	12	mathematical	mathematical	ADJ
easat-8674	282	13	reasoning	reasoning	NOUN
easat-8674	282	14	and	and	CCONJ
easat-8674	282	15	critical	critical	ADJ
easat-8674	282	16	thinking	thinking	NOUN
easat-8674	282	17	among	among	ADP
easat-8674	282	18	their	their	PRON
easat-8674	282	19	students	student	NOUN
easat-8674	282	20	.	.	PUNCT
easat-8674	283	1	development	development	NOUN
easat-8674	283	2	of	of	ADP
easat-8674	283	3	algebraic	algebraic	PROPN
easat-8674	283	4	modeling	model	VERB
easat-8674	283	5	support	support	NOUN
easat-8674	283	6	programs	program	NOUN
easat-8674	283	7	:	:	PUNCT
easat-8674	283	8	there	there	PRON
easat-8674	283	9	is	be	VERB
easat-8674	283	10	a	a	DET
easat-8674	283	11	need	need	NOUN
easat-8674	283	12	to	to	PART
easat-8674	283	13	design	design	VERB
easat-8674	283	14	dedicated	dedicated	ADJ
easat-8674	283	15	modules	module	NOUN
easat-8674	283	16	or	or	CCONJ
easat-8674	283	17	supplementary	supplementary	ADJ
easat-8674	283	18	programs	program	NOUN
easat-8674	283	19	that	that	PRON
easat-8674	283	20	explicitly	explicitly	ADV
easat-8674	283	21	train	train	VERB
easat-8674	283	22	students	student	NOUN
easat-8674	283	23	in	in	ADP
easat-8674	283	24	formulating	formulate	VERB
easat-8674	283	25	algebraic	algebraic	ADJ
easat-8674	283	26	equations	equation	NOUN
easat-8674	283	27	from	from	ADP
easat-8674	283	28	verbal	verbal	ADJ
easat-8674	283	29	and	and	CCONJ
easat-8674	283	30	visual	visual	ADJ
easat-8674	283	31	contexts	contexts	NOUN
easat-8674	283	32	.	.	PUNCT
easat-8674	284	1	these	these	PRON
easat-8674	284	2	should	should	AUX
easat-8674	284	3	include	include	VERB
easat-8674	284	4	targeted	targeted	ADJ
easat-8674	284	5	practice	practice	NOUN
easat-8674	284	6	in	in	ADP
easat-8674	284	7	translating	translate	VERB
easat-8674	284	8	real	real	ADJ
easat-8674	284	9	-	-	PUNCT
easat-8674	284	10	world	world	NOUN
easat-8674	284	11	situations	situation	NOUN
easat-8674	284	12	into	into	ADP
easat-8674	284	13	mathematical	mathematical	ADJ
easat-8674	284	14	models	model	NOUN
easat-8674	284	15	,	,	PUNCT
easat-8674	284	16	thereby	thereby	ADV
easat-8674	284	17	strengthening	strengthen	VERB
easat-8674	284	18	students	student	NOUN
easat-8674	284	19	’	’	PART
easat-8674	284	20	modeling	modeling	NOUN
easat-8674	284	21	competencies	competency	NOUN
easat-8674	284	22	.	.	PUNCT
easat-8674	285	1	diagnostic	diagnostic	ADJ
easat-8674	285	2	assessment	assessment	NOUN
easat-8674	285	3	based	base	VERB
easat-8674	285	4	on	on	ADP
easat-8674	285	5	understanding	understand	VERB
easat-8674	285	6	categories	category	NOUN
easat-8674	285	7	:	:	PUNCT
easat-8674	285	8	the	the	DET
easat-8674	285	9	categories	category	NOUN
easat-8674	285	10	mba	mba	PROPN
easat-8674	285	11	-	-	PUNCT
easat-8674	285	12	j	j	PROPN
easat-8674	285	13	,	,	PUNCT
easat-8674	285	14	dta	dta	PROPN
easat-8674	285	15	-	-	PUNCT
easat-8674	285	16	lc	lc	NOUN
easat-8674	285	17	,	,	PUNCT
easat-8674	285	18	and	and	CCONJ
easat-8674	285	19	dta	dta	PROPN
easat-8674	285	20	-	-	PUNCT
easat-8674	285	21	np	np	NOUN
easat-8674	285	22	offer	offer	VERB
easat-8674	285	23	a	a	DET
easat-8674	285	24	useful	useful	ADJ
easat-8674	285	25	framework	framework	NOUN
easat-8674	285	26	for	for	ADP
easat-8674	285	27	diagnostic	diagnostic	ADJ
easat-8674	285	28	assessments	assessment	NOUN
easat-8674	285	29	that	that	PRON
easat-8674	285	30	can	can	AUX
easat-8674	285	31	help	help	AUX
easat-8674	285	32	identify	identify	VERB
easat-8674	285	33	students	student	NOUN
easat-8674	285	34	’	'	PUNCT
easat-8674	285	35	dominant	dominant	ADJ
easat-8674	285	36	modes	mode	NOUN
easat-8674	285	37	of	of	ADP
easat-8674	285	38	thinking	thinking	NOUN
easat-8674	285	39	.	.	PUNCT
easat-8674	286	1	these	these	DET
easat-8674	286	2	assessments	assessment	NOUN
easat-8674	286	3	will	will	AUX
easat-8674	286	4	allow	allow	VERB
easat-8674	286	5	teacher	teacher	NOUN
easat-8674	286	6	educators	educator	NOUN
easat-8674	286	7	to	to	PART
easat-8674	286	8	tailor	tailor	VERB
easat-8674	286	9	instructional	instructional	ADJ
easat-8674	286	10	interventions	intervention	NOUN
easat-8674	286	11	that	that	PRON
easat-8674	286	12	address	address	VERB
easat-8674	286	13	specific	specific	ADJ
easat-8674	286	14	conceptual	conceptual	ADJ
easat-8674	286	15	or	or	CCONJ
easat-8674	286	16	procedural	procedural	ADJ
easat-8674	286	17	weaknesses	weakness	NOUN
easat-8674	286	18	in	in	ADP
easat-8674	286	19	algebraic	algebraic	ADJ
easat-8674	286	20	reasoning	reasoning	NOUN
easat-8674	286	21	.	.	PUNCT
easat-8674	287	1	593	593	NUM
easat-8674	287	2	edelweiss	edelweiss	PROPN
easat-8674	287	3	applied	apply	VERB
easat-8674	287	4	science	science	NOUN
easat-8674	287	5	and	and	CCONJ
easat-8674	287	6	technology	technology	NOUN
easat-8674	287	7	issn	issn	PROPN
easat-8674	287	8	:	:	PUNCT
easat-8674	287	9	2576	2576	NUM
easat-8674	287	10	-	-	SYM
easat-8674	287	11	8484	8484	NUM
easat-8674	287	12	vol	vol	NOUN
easat-8674	287	13	.	.	PROPN
easat-8674	288	1	9	9	NUM
easat-8674	288	2	,	,	PUNCT
easat-8674	288	3	no	no	INTJ
easat-8674	288	4	.	.	NOUN
easat-8674	289	1	7	7	NUM
easat-8674	289	2	:	:	SYM
easat-8674	289	3	580	580	NUM
easat-8674	289	4	-	-	SYM
easat-8674	289	5	594	594	NUM
easat-8674	289	6	,	,	PUNCT
easat-8674	289	7	2025	2025	NUM
easat-8674	289	8	doi	doi	NOUN
easat-8674	289	9	:	:	PUNCT
easat-8674	289	10	10.55214/25768484.v9i7.8674	10.55214/25768484.v9i7.8674	NUM
easat-8674	289	11	©	©	PROPN
easat-8674	289	12	2025	2025	NUM
easat-8674	289	13	by	by	ADP
easat-8674	289	14	the	the	DET
easat-8674	289	15	authors	author	NOUN
easat-8674	289	16	;	;	PUNCT
easat-8674	289	17	licensee	licensee	PROPN
easat-8674	289	18	learning	learn	VERB
easat-8674	289	19	gate	gate	PROPN
easat-8674	289	20	institutional	institutional	PROPN
easat-8674	289	21	review	review	PROPN
easat-8674	289	22	board	board	NOUN
easat-8674	289	23	statement	statement	NOUN
easat-8674	289	24	:	:	PUNCT
easat-8674	289	25	this	this	DET
easat-8674	289	26	study	study	NOUN
easat-8674	289	27	was	be	AUX
easat-8674	289	28	reviewed	review	VERB
easat-8674	289	29	and	and	CCONJ
easat-8674	289	30	approved	approve	VERB
easat-8674	289	31	by	by	ADP
easat-8674	289	32	the	the	DET
easat-8674	289	33	promoter	promoter	NOUN
easat-8674	289	34	and	and	CCONJ
easat-8674	289	35	co	co	NOUN
easat-8674	289	36	-	-	NOUN
easat-8674	289	37	promoter	promoter	NOUN
easat-8674	289	38	of	of	ADP
easat-8674	289	39	universitas	universitas	PROPN
easat-8674	289	40	negeri	negeri	PROPN
easat-8674	289	41	surabaya	surabaya	PROPN
easat-8674	289	42	,	,	PUNCT
easat-8674	289	43	indonesia	indonesia	PROPN
easat-8674	289	44	(	(	PUNCT
easat-8674	289	45	letter	letter	NOUN
easat-8674	289	46	no	no	INTJ
easat-8674	289	47	.	.	PUNCT
easat-8674	290	1	b/4065	b/4065	NOUN
easat-8674	290	2	/	/	SYM
easat-8674	290	3	un38.3	un38.3	ADJ
easat-8674	290	4	/	/	SYM
easat-8674	290	5	lt.02.02/2023	lt.02.02/2023	PROPN
easat-8674	290	6	)	)	PUNCT
easat-8674	290	7	.	.	PUNCT
easat-8674	291	1	all	all	DET
easat-8674	291	2	participants	participant	NOUN
easat-8674	291	3	provided	provide	VERB
easat-8674	291	4	written	write	VERB
easat-8674	291	5	informed	inform	VERB
easat-8674	291	6	consent	consent	NOUN
easat-8674	291	7	prior	prior	ADV
easat-8674	291	8	to	to	ADP
easat-8674	291	9	their	their	PRON
easat-8674	291	10	participation	participation	NOUN
easat-8674	291	11	,	,	PUNCT
easat-8674	291	12	in	in	ADP
easat-8674	291	13	accordance	accordance	NOUN
easat-8674	291	14	with	with	ADP
easat-8674	291	15	the	the	DET
easat-8674	291	16	ethical	ethical	ADJ
easat-8674	291	17	standards	standard	NOUN
easat-8674	291	18	set	set	VERB
easat-8674	291	19	by	by	ADP
easat-8674	291	20	institutional	institutional	ADJ
easat-8674	291	21	and	and	CCONJ
easat-8674	291	22	national	national	ADJ
easat-8674	291	23	research	research	NOUN
easat-8674	291	24	committees	committee	NOUN
easat-8674	291	25	.	.	PUNCT
easat-8674	292	1	transparency	transparency	NOUN
easat-8674	292	2	:	:	PUNCT
easat-8674	292	3	the	the	DET
easat-8674	292	4	authors	author	NOUN
easat-8674	292	5	confirm	confirm	VERB
easat-8674	292	6	that	that	SCONJ
easat-8674	292	7	the	the	DET
easat-8674	292	8	manuscript	manuscript	NOUN
easat-8674	292	9	is	be	AUX
easat-8674	292	10	an	an	DET
easat-8674	292	11	honest	honest	ADJ
easat-8674	292	12	,	,	PUNCT
easat-8674	292	13	accurate	accurate	ADJ
easat-8674	292	14	,	,	PUNCT
easat-8674	292	15	and	and	CCONJ
easat-8674	292	16	transparent	transparent	ADJ
easat-8674	292	17	account	account	NOUN
easat-8674	292	18	of	of	ADP
easat-8674	292	19	the	the	DET
easat-8674	292	20	study	study	NOUN
easat-8674	292	21	;	;	PUNCT
easat-8674	292	22	that	that	SCONJ
easat-8674	292	23	no	no	DET
easat-8674	292	24	vital	vital	ADJ
easat-8674	292	25	features	feature	NOUN
easat-8674	292	26	of	of	ADP
easat-8674	292	27	the	the	DET
easat-8674	292	28	study	study	NOUN
easat-8674	292	29	have	have	AUX
easat-8674	292	30	been	be	AUX
easat-8674	292	31	omitted	omit	VERB
easat-8674	292	32	;	;	PUNCT
easat-8674	292	33	and	and	CCONJ
easat-8674	292	34	that	that	SCONJ
easat-8674	292	35	any	any	DET
easat-8674	292	36	discrepancies	discrepancy	NOUN
easat-8674	292	37	from	from	ADP
easat-8674	292	38	the	the	DET
easat-8674	292	39	study	study	NOUN
easat-8674	292	40	as	as	SCONJ
easat-8674	292	41	planned	plan	VERB
easat-8674	292	42	have	have	AUX
easat-8674	292	43	been	be	AUX
easat-8674	292	44	explained	explain	VERB
easat-8674	292	45	.	.	PUNCT
easat-8674	293	1	this	this	DET
easat-8674	293	2	study	study	NOUN
easat-8674	293	3	followed	follow	VERB
easat-8674	293	4	all	all	DET
easat-8674	293	5	ethical	ethical	ADJ
easat-8674	293	6	practices	practice	NOUN
easat-8674	293	7	during	during	ADP
easat-8674	293	8	writing	writing	NOUN
easat-8674	293	9	.	.	PUNCT
easat-8674	294	1	acknowledgement	acknowledgement	NOUN
easat-8674	294	2	:	:	PUNCT
easat-8674	294	3	the	the	DET
easat-8674	294	4	authors	author	NOUN
easat-8674	294	5	would	would	AUX
easat-8674	294	6	like	like	VERB
easat-8674	294	7	to	to	PART
easat-8674	294	8	thank	thank	VERB
easat-8674	294	9	the	the	DET
easat-8674	294	10	center	center	NOUN
easat-8674	294	11	for	for	ADP
easat-8674	294	12	higher	high	ADJ
easat-8674	294	13	education	education	NOUN
easat-8674	294	14	funding	funding	NOUN
easat-8674	294	15	(	(	PUNCT
easat-8674	294	16	balai	balai	PROPN
easat-8674	294	17	pembiayaan	pembiayaan	PROPN
easat-8674	294	18	pendidikan	pendidikan	PROPN
easat-8674	294	19	tinggi	tinggi	PROPN
easat-8674	294	20	)	)	PUNCT
easat-8674	294	21	and	and	CCONJ
easat-8674	294	22	the	the	DET
easat-8674	294	23	indonesia	indonesia	PROPN
easat-8674	294	24	endowment	endowment	PROPN
easat-8674	294	25	funds	fund	NOUN
easat-8674	294	26	for	for	ADP
easat-8674	294	27	education	education	NOUN
easat-8674	294	28	(	(	PUNCT
easat-8674	294	29	lembaga	lembaga	PROPN
easat-8674	294	30	pengelola	pengelola	PROPN
easat-8674	294	31	dana	dana	PROPN
easat-8674	294	32	pendidikan	pendidikan	PROPN
easat-8674	294	33	)	)	PUNCT
easat-8674	294	34	for	for	ADP
easat-8674	294	35	providing	provide	VERB
easat-8674	294	36	scholarships	scholarship	NOUN
easat-8674	294	37	from	from	ADP
easat-8674	294	38	the	the	DET
easat-8674	294	39	indonesian	indonesian	PROPN
easat-8674	294	40	ministry	ministry	PROPN
easat-8674	294	41	of	of	ADP
easat-8674	294	42	education	education	PROPN
easat-8674	294	43	,	,	PUNCT
easat-8674	294	44	culture	culture	NOUN
easat-8674	294	45	,	,	PUNCT
easat-8674	294	46	research	research	NOUN
easat-8674	294	47	and	and	CCONJ
easat-8674	294	48	technology	technology	NOUN
easat-8674	294	49	,	,	PUNCT
easat-8674	294	50	and	and	CCONJ
easat-8674	294	51	we	we	PRON
easat-8674	294	52	would	would	AUX
easat-8674	294	53	like	like	VERB
easat-8674	294	54	to	to	PART
easat-8674	294	55	thank	thank	VERB
easat-8674	294	56	our	our	PRON
easat-8674	294	57	team	team	NOUN
easat-8674	294	58	from	from	ADP
easat-8674	294	59	the	the	DET
easat-8674	294	60	department	department	NOUN
easat-8674	294	61	of	of	ADP
easat-8674	294	62	mathematics	mathematics	PROPN
easat-8674	294	63	education	education	NOUN
easat-8674	294	64	,	,	PUNCT
easat-8674	294	65	faculty	faculty	NOUN
easat-8674	294	66	of	of	ADP
easat-8674	294	67	mathematics	mathematic	NOUN
easat-8674	294	68	and	and	CCONJ
easat-8674	294	69	natural	natural	ADJ
easat-8674	294	70	sciences	science	NOUN
easat-8674	294	71	,	,	PUNCT
easat-8674	294	72	universitas	universitas	PROPN
easat-8674	294	73	negeri	negeri	PROPN
easat-8674	294	74	surabaya	surabaya	PROPN
easat-8674	294	75	,	,	PUNCT
easat-8674	294	76	surabaya	surabaya	PROPN
easat-8674	294	77	,	,	PUNCT
easat-8674	294	78	indonesia	indonesia	PROPN
easat-8674	294	79	.	.	PUNCT
easat-8674	295	1	copyright	copyright	NOUN
easat-8674	295	2	:	:	PUNCT
easat-8674	295	3	©	©	PROPN
easat-8674	295	4	2025	2025	NUM
easat-8674	295	5	by	by	ADP
easat-8674	295	6	the	the	DET
easat-8674	295	7	authors	author	NOUN
easat-8674	295	8	.	.	PUNCT
easat-8674	296	1	this	this	DET
easat-8674	296	2	open	open	ADJ
easat-8674	296	3	-	-	PUNCT
easat-8674	296	4	access	access	NOUN
easat-8674	296	5	article	article	NOUN
easat-8674	296	6	is	be	AUX
easat-8674	296	7	distributed	distribute	VERB
easat-8674	296	8	under	under	ADP
easat-8674	296	9	the	the	DET
easat-8674	296	10	terms	term	NOUN
easat-8674	296	11	and	and	CCONJ
easat-8674	296	12	conditions	condition	NOUN
easat-8674	296	13	of	of	ADP
easat-8674	296	14	the	the	DET
easat-8674	296	15	creative	creative	ADJ
easat-8674	296	16	commons	common	NOUN
easat-8674	296	17	attribution	attribution	NOUN
easat-8674	296	18	(	(	PUNCT
easat-8674	296	19	cc	cc	NOUN
easat-8674	296	20	by	by	ADP
easat-8674	296	21	)	)	PUNCT
easat-8674	296	22	license	license	NOUN
easat-8674	296	23	(	(	PUNCT
easat-8674	296	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-8674	296	25	)	)	PUNCT
easat-8674	296	26	.	.	PUNCT
easat-8674	297	1	references	reference	NOUN
easat-8674	297	2	[	[	X
easat-8674	297	3	1	1	NUM
easat-8674	297	4	]	]	PUNCT
easat-8674	297	5	r.	r.	PROPN
easat-8674	297	6	ekawati	ekawati	PROPN
easat-8674	297	7	,	,	PUNCT
easat-8674	297	8	a.	a.	PROPN
easat-8674	297	9	h.	h.	PROPN
easat-8674	297	10	rosyidi	rosyidi	PROPN
easat-8674	297	11	,	,	PUNCT
easat-8674	297	12	b.	b.	PROPN
easat-8674	297	13	p.	p.	PROPN
easat-8674	297	14	prawoto	prawoto	PROPN
easat-8674	297	15	,	,	PUNCT
easat-8674	297	16	r.	r.	PROPN
easat-8674	297	17	c.	c.	PROPN
easat-8674	297	18	i.	i.	PROPN
easat-8674	297	19	prahmana	prahmana	PROPN
easat-8674	297	20	,	,	PUNCT
easat-8674	297	21	and	and	CCONJ
easat-8674	297	22	f.-l	f.-l	PROPN
easat-8674	297	23	.	.	PUNCT
easat-8674	298	1	lin	lin	PROPN
easat-8674	298	2	,	,	PUNCT
easat-8674	298	3	"	"	PUNCT
easat-8674	298	4	developing	develop	VERB
easat-8674	298	5	a	a	DET
easat-8674	298	6	constructive	constructive	ADJ
easat-8674	298	7	conceptual	conceptual	ADJ
easat-8674	298	8	framework	framework	NOUN
easat-8674	298	9	of	of	ADP
easat-8674	298	10	a	a	DET
easat-8674	298	11	pre	pre	ADJ
easat-8674	298	12	-	-	ADJ
easat-8674	298	13	service	service	ADJ
easat-8674	298	14	mathematics	mathematic	NOUN
easat-8674	298	15	teachers	teacher	NOUN
easat-8674	298	16	’	'	PUNCT
easat-8674	298	17	content	content	NOUN
easat-8674	298	18	knowledge	knowledge	NOUN
easat-8674	298	19	instrument	instrument	NOUN
easat-8674	298	20	on	on	ADP
easat-8674	298	21	space	space	NOUN
easat-8674	298	22	and	and	CCONJ
easat-8674	298	23	shape	shape	NOUN
easat-8674	298	24	,	,	PUNCT
easat-8674	298	25	"	"	PUNCT
easat-8674	298	26	mathematics	mathematic	NOUN
easat-8674	298	27	,	,	PUNCT
easat-8674	298	28	vol	vol	NOUN
easat-8674	298	29	.	.	PROPN
easat-8674	298	30	10	10	NUM
easat-8674	298	31	,	,	PUNCT
easat-8674	298	32	no	no	INTJ
easat-8674	298	33	.	.	NOUN
easat-8674	298	34	1	1	NUM
easat-8674	298	35	,	,	PUNCT
easat-8674	298	36	p.	p.	NOUN
easat-8674	298	37	137	137	NUM
easat-8674	298	38	,	,	PUNCT
easat-8674	298	39	2022	2022	NUM
easat-8674	298	40	.	.	PUNCT
easat-8674	299	1	https://doi.org/10.3390/math10010137	https://doi.org/10.3390/math10010137	NOUN
easat-8674	299	2	[	[	X
easat-8674	299	3	2	2	X
easat-8674	299	4	]	]	PUNCT
easat-8674	299	5	w.	w.	PROPN
easat-8674	299	6	osei	osei	PROPN
easat-8674	299	7	and	and	CCONJ
easat-8674	299	8	d.	d.	PROPN
easat-8674	299	9	d.	d.	PROPN
easat-8674	299	10	agyei	agyei	PROPN
easat-8674	299	11	,	,	PUNCT
easat-8674	299	12	"	"	PUNCT
easat-8674	299	13	teaching	teach	VERB
easat-8674	299	14	knowledge	knowledge	NOUN
easat-8674	299	15	and	and	CCONJ
easat-8674	299	16	difficulties	difficulty	NOUN
easat-8674	299	17	of	of	ADP
easat-8674	299	18	in	in	ADP
easat-8674	299	19	-	-	PUNCT
easat-8674	299	20	field	field	NOUN
easat-8674	299	21	and	and	CCONJ
easat-8674	299	22	out	out	ADP
easat-8674	299	23	-	-	PUNCT
easat-8674	299	24	of	of	ADP
easat-8674	299	25	-	-	PUNCT
easat-8674	299	26	field	field	NOUN
easat-8674	299	27	junior	junior	ADJ
easat-8674	299	28	high	high	ADJ
easat-8674	299	29	school	school	NOUN
easat-8674	299	30	mathematics	mathematic	NOUN
easat-8674	299	31	teachers	teacher	NOUN
easat-8674	299	32	in	in	ADP
easat-8674	299	33	algebra	algebra	NOUN
easat-8674	299	34	,	,	PUNCT
easat-8674	299	35	"	"	PUNCT
easat-8674	299	36	cogent	cogent	ADJ
easat-8674	299	37	education	education	NOUN
easat-8674	299	38	,	,	PUNCT
easat-8674	299	39	vol	vol	NOUN
easat-8674	299	40	.	.	PROPN
easat-8674	300	1	10	10	NUM
easat-8674	300	2	,	,	PUNCT
easat-8674	300	3	no	no	INTJ
easat-8674	300	4	.	.	NOUN
easat-8674	300	5	2	2	NUM
easat-8674	300	6	,	,	PUNCT
easat-8674	300	7	p.	p.	NOUN
easat-8674	300	8	2232240	2232240	NUM
easat-8674	300	9	,	,	PUNCT
easat-8674	300	10	2023	2023	NUM
easat-8674	300	11	.	.	PUNCT
easat-8674	301	1	https://doi.org/10.1080/2331186x.2023.2232240	https://doi.org/10.1080/2331186x.2023.2232240	X
easat-8674	301	2	[	[	X
easat-8674	301	3	3	3	NUM
easat-8674	301	4	]	]	PUNCT
easat-8674	301	5	m.	m.	NOUN
easat-8674	301	6	guler	guler	NOUN
easat-8674	301	7	and	and	CCONJ
easat-8674	301	8	d.	d.	PROPN
easat-8674	301	9	celik	celik	PROPN
easat-8674	301	10	,	,	PUNCT
easat-8674	301	11	"	"	PUNCT
easat-8674	301	12	the	the	DET
easat-8674	301	13	effect	effect	NOUN
easat-8674	301	14	of	of	ADP
easat-8674	301	15	an	an	DET
easat-8674	301	16	elective	elective	ADJ
easat-8674	301	17	algebra	algebra	NOUN
easat-8674	301	18	teaching	teach	VERB
easat-8674	301	19	course	course	NOUN
easat-8674	301	20	on	on	ADP
easat-8674	301	21	prospective	prospective	ADJ
easat-8674	301	22	mathematics	mathematic	NOUN
easat-8674	301	23	teachers	teacher	NOUN
easat-8674	301	24	’	'	PUNCT
easat-8674	301	25	pedagogical	pedagogical	ADJ
easat-8674	301	26	content	content	NOUN
easat-8674	301	27	knowledge	knowledge	NOUN
easat-8674	301	28	,	,	PUNCT
easat-8674	301	29	"	"	PUNCT
easat-8674	301	30	international	international	ADJ
easat-8674	301	31	electronic	electronic	ADJ
easat-8674	301	32	journal	journal	NOUN
easat-8674	301	33	of	of	ADP
easat-8674	301	34	mathematics	mathematics	PROPN
easat-8674	301	35	education	education	NOUN
easat-8674	301	36	,	,	PUNCT
easat-8674	301	37	vol	vol	NOUN
easat-8674	301	38	.	.	PROPN
easat-8674	302	1	16	16	NUM
easat-8674	302	2	,	,	PUNCT
easat-8674	302	3	no	no	INTJ
easat-8674	302	4	.	.	NOUN
easat-8674	302	5	2	2	NUM
easat-8674	302	6	,	,	PUNCT
easat-8674	302	7	p.	p.	NOUN
easat-8674	302	8	em0636	em0636	PROPN
easat-8674	302	9	,	,	PUNCT
easat-8674	302	10	2021	2021	NUM
easat-8674	302	11	.	.	PUNCT
easat-8674	303	1	https://doi.org/10.29333/iejme/10902	https://doi.org/10.29333/iejme/10902	PUNCT
easat-8674	304	1	[	[	X
easat-8674	304	2	4	4	X
easat-8674	304	3	]	]	X
easat-8674	304	4	l.	l.	PROPN
easat-8674	304	5	sahidin	sahidin	PROPN
easat-8674	304	6	,	,	PUNCT
easat-8674	304	7	m.	m.	NOUN
easat-8674	304	8	t.	t.	PROPN
easat-8674	304	9	budiarto	budiarto	PROPN
easat-8674	304	10	,	,	PUNCT
easat-8674	304	11	and	and	CCONJ
easat-8674	304	12	y.	y.	PROPN
easat-8674	304	13	fuad	fuad	PROPN
easat-8674	304	14	,	,	PUNCT
easat-8674	304	15	"	"	PUNCT
easat-8674	304	16	what	what	PRON
easat-8674	304	17	construct	construct	NOUN
easat-8674	304	18	of	of	ADP
easat-8674	304	19	mathematical	mathematical	ADJ
easat-8674	304	20	knowledge	knowledge	NOUN
easat-8674	304	21	for	for	ADP
easat-8674	304	22	teaching	teaching	NOUN
easat-8674	304	23	do	do	VERB
easat-8674	304	24	mathematics	mathematics	NOUN
easat-8674	304	25	teachers	teacher	NOUN
easat-8674	304	26	need?(a	need?(a	ADJ
easat-8674	304	27	theoretical	theoretical	ADJ
easat-8674	304	28	framework	framework	NOUN
easat-8674	304	29	and	and	CCONJ
easat-8674	304	30	conceptualization	conceptualization	NOUN
easat-8674	304	31	in	in	ADP
easat-8674	304	32	geometry	geometry	NOUN
easat-8674	304	33	)	)	PUNCT
easat-8674	304	34	,	,	PUNCT
easat-8674	304	35	"	"	PUNCT
easat-8674	304	36	presented	present	VERB
easat-8674	304	37	at	at	ADP
easat-8674	304	38	the	the	DET
easat-8674	304	39	1st	1st	ADJ
easat-8674	304	40	international	international	ADJ
easat-8674	304	41	conference	conference	NOUN
easat-8674	304	42	on	on	ADP
easat-8674	304	43	advanced	advanced	ADJ
easat-8674	304	44	multidisciplinary	multidisciplinary	ADJ
easat-8674	304	45	research	research	NOUN
easat-8674	304	46	(	(	PUNCT
easat-8674	304	47	icamr	icamr	PROPN
easat-8674	304	48	2018	2018	NUM
easat-8674	304	49	)	)	PUNCT
easat-8674	304	50	,	,	PUNCT
easat-8674	304	51	2019	2019	NUM
easat-8674	304	52	.	.	PUNCT
easat-8674	305	1	[	[	X
easat-8674	305	2	5	5	X
easat-8674	305	3	]	]	PUNCT
easat-8674	305	4	h.	h.	PROPN
easat-8674	305	5	c.	c.	PROPN
easat-8674	305	6	hill	hill	PROPN
easat-8674	305	7	,	,	PUNCT
easat-8674	305	8	d.	d.	PROPN
easat-8674	305	9	l.	l.	PROPN
easat-8674	305	10	ball	ball	PROPN
easat-8674	305	11	,	,	PUNCT
easat-8674	305	12	and	and	CCONJ
easat-8674	305	13	s.	s.	PROPN
easat-8674	305	14	g.	g.	PROPN
easat-8674	305	15	schilling	schilling	PROPN
easat-8674	305	16	,	,	PUNCT
easat-8674	305	17	"	"	PUNCT
easat-8674	305	18	unpacking	unpack	VERB
easat-8674	305	19	pedagogical	pedagogical	ADJ
easat-8674	305	20	content	content	NOUN
easat-8674	305	21	knowledge	knowledge	NOUN
easat-8674	305	22	:	:	PUNCT
easat-8674	305	23	conceptualizing	conceptualize	VERB
easat-8674	305	24	and	and	CCONJ
easat-8674	305	25	measuring	measure	VERB
easat-8674	305	26	teachers	teacher	NOUN
easat-8674	305	27	'	'	PART
easat-8674	305	28	topic	topic	NOUN
easat-8674	305	29	-	-	PUNCT
easat-8674	305	30	specific	specific	ADJ
easat-8674	305	31	knowledge	knowledge	NOUN
easat-8674	305	32	of	of	ADP
easat-8674	305	33	students	student	NOUN
easat-8674	305	34	,	,	PUNCT
easat-8674	305	35	"	"	PUNCT
easat-8674	305	36	journal	journal	NOUN
easat-8674	305	37	for	for	ADP
easat-8674	305	38	research	research	NOUN
easat-8674	305	39	in	in	ADP
easat-8674	305	40	mathematics	mathematics	PROPN
easat-8674	305	41	education	education	NOUN
easat-8674	305	42	,	,	PUNCT
easat-8674	305	43	vol	vol	NOUN
easat-8674	305	44	.	.	PROPN
easat-8674	305	45	39	39	NUM
easat-8674	305	46	,	,	PUNCT
easat-8674	305	47	no	no	INTJ
easat-8674	305	48	.	.	NOUN
easat-8674	305	49	4	4	NUM
easat-8674	305	50	,	,	PUNCT
easat-8674	305	51	pp	pp	ADJ
easat-8674	305	52	.	.	PUNCT
easat-8674	306	1	372	372	NUM
easat-8674	306	2	-	-	SYM
easat-8674	306	3	400	400	NUM
easat-8674	306	4	,	,	PUNCT
easat-8674	306	5	2008	2008	NUM
easat-8674	306	6	.	.	PUNCT
easat-8674	307	1	https://doi.org/10.5951/jresematheduc.39.4.0372	https://doi.org/10.5951/jresematheduc.39.4.0372	ADJ
easat-8674	308	1	[	[	X
easat-8674	308	2	6	6	NUM
easat-8674	308	3	]	]	PUNCT
easat-8674	308	4	j.	j.	PROPN
easat-8674	308	5	hattie	hattie	PROPN
easat-8674	308	6	,	,	PUNCT
easat-8674	308	7	visible	visible	ADJ
easat-8674	308	8	learning	learning	NOUN
easat-8674	308	9	:	:	PUNCT
easat-8674	308	10	a	a	DET
easat-8674	308	11	synthesis	synthesis	NOUN
easat-8674	308	12	of	of	ADP
easat-8674	308	13	over	over	ADP
easat-8674	308	14	800	800	NUM
easat-8674	308	15	meta	meta	ADJ
easat-8674	308	16	-	-	PUNCT
easat-8674	308	17	analyses	analysis	NOUN
easat-8674	308	18	relating	relate	VERB
easat-8674	308	19	to	to	ADP
easat-8674	308	20	achievement	achievement	NOUN
easat-8674	308	21	.	.	PUNCT
easat-8674	309	1	london	london	PROPN
easat-8674	309	2	:	:	PUNCT
easat-8674	309	3	routledge	routledge	PROPN
easat-8674	309	4	,	,	PUNCT
easat-8674	309	5	2008	2008	NUM
easat-8674	309	6	.	.	PUNCT
easat-8674	310	1	[	[	X
easat-8674	310	2	7	7	X
easat-8674	310	3	]	]	X
easat-8674	310	4	l.	l.	PROPN
easat-8674	310	5	s.	s.	PROPN
easat-8674	310	6	shulman	shulman	PROPN
easat-8674	310	7	,	,	PUNCT
easat-8674	310	8	"	"	PUNCT
easat-8674	310	9	those	those	PRON
easat-8674	310	10	who	who	PRON
easat-8674	310	11	understand	understand	VERB
easat-8674	310	12	:	:	PUNCT
easat-8674	310	13	knowledge	knowledge	NOUN
easat-8674	310	14	growth	growth	NOUN
easat-8674	310	15	in	in	ADP
easat-8674	310	16	teaching	teaching	NOUN
easat-8674	310	17	,	,	PUNCT
easat-8674	310	18	"	"	PUNCT
easat-8674	310	19	educational	educational	ADJ
easat-8674	310	20	researcher	researcher	NOUN
easat-8674	310	21	,	,	PUNCT
easat-8674	310	22	vol	vol	NOUN
easat-8674	310	23	.	.	PROPN
easat-8674	310	24	15	15	NUM
easat-8674	310	25	,	,	PUNCT
easat-8674	310	26	no	no	INTJ
easat-8674	310	27	.	.	NOUN
easat-8674	310	28	2	2	NUM
easat-8674	310	29	,	,	PUNCT
easat-8674	310	30	pp	pp	ADJ
easat-8674	310	31	.	.	PUNCT
easat-8674	311	1	414	414	NUM
easat-8674	311	2	,	,	PUNCT
easat-8674	311	3	1986	1986	NUM
easat-8674	311	4	.	.	PUNCT
easat-8674	312	1	https://doi.org/10.3102/0013189x015002004	https://doi.org/10.3102/0013189x015002004	X
easat-8674	313	1	[	[	X
easat-8674	313	2	8	8	X
easat-8674	313	3	]	]	X
easat-8674	313	4	c.	c.	PROPN
easat-8674	313	5	a.	a.	PROPN
easat-8674	313	6	vitantri	vitantri	PROPN
easat-8674	313	7	,	,	PUNCT
easat-8674	313	8	"	"	PUNCT
easat-8674	313	9	an	an	DET
easat-8674	313	10	analysis	analysis	NOUN
easat-8674	313	11	of	of	ADP
easat-8674	313	12	novice	novice	NOUN
easat-8674	313	13	students	student	NOUN
easat-8674	313	14	'	'	PART
easat-8674	313	15	errors	error	NOUN
easat-8674	313	16	in	in	ADP
easat-8674	313	17	solving	solve	VERB
easat-8674	313	18	algebra	algebra	NOUN
easat-8674	313	19	problems	problem	NOUN
easat-8674	313	20	,	,	PUNCT
easat-8674	313	21	"	"	PUNCT
easat-8674	313	22	jpmi	jpmi	ADJ
easat-8674	313	23	(	(	PUNCT
easat-8674	313	24	jurnal	jurnal	ADJ
easat-8674	313	25	pembelajaran	pembelajaran	PROPN
easat-8674	313	26	matematika	matematika	PROPN
easat-8674	313	27	inovatif	inovatif	PROPN
easat-8674	313	28	)	)	PUNCT
easat-8674	313	29	,	,	PUNCT
easat-8674	313	30	vol	vol	NOUN
easat-8674	313	31	.	.	PROPN
easat-8674	313	32	4	4	NUM
easat-8674	313	33	,	,	PUNCT
easat-8674	313	34	no	no	INTJ
easat-8674	313	35	.	.	NOUN
easat-8674	313	36	2	2	NUM
easat-8674	313	37	,	,	PUNCT
easat-8674	313	38	pp	pp	ADJ
easat-8674	313	39	.	.	PUNCT
easat-8674	314	1	295	295	NUM
easat-8674	314	2	-	-	SYM
easat-8674	314	3	306	306	NUM
easat-8674	314	4	,	,	PUNCT
easat-8674	314	5	2021	2021	NUM
easat-8674	314	6	.	.	PUNCT
easat-8674	315	1	https://doi.org/10.22460/jpmi.v4i2.p%25p	https://doi.org/10.22460/jpmi.v4i2.p%25p	PRON
easat-8674	316	1	[	[	X
easat-8674	316	2	9	9	X
easat-8674	316	3	]	]	PUNCT
easat-8674	316	4	t.	t.	NOUN
easat-8674	316	5	grigaliūnienė	grigaliūnienė	PROPN
easat-8674	316	6	,	,	PUNCT
easat-8674	316	7	v.	v.	CCONJ
easat-8674	316	8	dagienė	dagienė	NOUN
easat-8674	316	9	,	,	PUNCT
easat-8674	316	10	and	and	CCONJ
easat-8674	316	11	r.	r.	PROPN
easat-8674	316	12	žagunis	žagunis	PROPN
easat-8674	316	13	,	,	PUNCT
easat-8674	316	14	"	"	PUNCT
easat-8674	316	15	pedagogical	pedagogical	ADJ
easat-8674	316	16	content	content	NOUN
easat-8674	316	17	knowledge	knowledge	NOUN
easat-8674	316	18	in	in	ADP
easat-8674	316	19	mathematics	mathematic	NOUN
easat-8674	316	20	:	:	PUNCT
easat-8674	316	21	a	a	DET
easat-8674	316	22	systematic	systematic	ADJ
easat-8674	316	23	literature	literature	NOUN
easat-8674	316	24	review	review	NOUN
easat-8674	316	25	,	,	PUNCT
easat-8674	316	26	"	"	PUNCT
easat-8674	316	27	education	education	NOUN
easat-8674	316	28	sciences	science	NOUN
easat-8674	316	29	,	,	PUNCT
easat-8674	316	30	vol	vol	NOUN
easat-8674	316	31	.	.	PROPN
easat-8674	316	32	15	15	NUM
easat-8674	316	33	,	,	PUNCT
easat-8674	316	34	no	no	INTJ
easat-8674	316	35	.	.	NOUN
easat-8674	316	36	3	3	NUM
easat-8674	316	37	,	,	PUNCT
easat-8674	316	38	pp	pp	PROPN
easat-8674	316	39	.	.	PUNCT
easat-8674	317	1	1–23	1–23	NOUN
easat-8674	317	2	,	,	PUNCT
easat-8674	317	3	2025	2025	NUM
easat-8674	317	4	.	.	PUNCT
easat-8674	318	1	[	[	X
easat-8674	318	2	10	10	NUM
easat-8674	318	3	]	]	X
easat-8674	318	4	w.	w.	NOUN
easat-8674	318	5	rupasinghe	rupasinghe	NOUN
easat-8674	318	6	,	,	PUNCT
easat-8674	318	7	"	"	PUNCT
easat-8674	318	8	exploring	explore	VERB
easat-8674	318	9	pedagogical	pedagogical	ADJ
easat-8674	318	10	content	content	NOUN
easat-8674	318	11	knowledge	knowledge	NOUN
easat-8674	318	12	of	of	ADP
easat-8674	318	13	middle	middle	ADJ
easat-8674	318	14	school	school	NOUN
easat-8674	318	15	mathematics	mathematic	NOUN
easat-8674	318	16	teachers	teacher	NOUN
easat-8674	318	17	in	in	ADP
easat-8674	318	18	teaching	teach	VERB
easat-8674	318	19	algebraic	algebraic	ADJ
easat-8674	318	20	symbols	symbol	NOUN
easat-8674	318	21	,	,	PUNCT
easat-8674	318	22	"	"	PUNCT
easat-8674	318	23	international	international	ADJ
easat-8674	318	24	journal	journal	NOUN
easat-8674	318	25	of	of	ADP
easat-8674	318	26	educational	educational	ADJ
easat-8674	318	27	research	research	NOUN
easat-8674	318	28	open	open	ADJ
easat-8674	318	29	,	,	PUNCT
easat-8674	318	30	vol	vol	NOUN
easat-8674	318	31	.	.	PROPN
easat-8674	318	32	6	6	NUM
easat-8674	318	33	,	,	PUNCT
easat-8674	318	34	pp	pp	ADJ
easat-8674	318	35	.	.	PUNCT
easat-8674	319	1	1–9	1–9	NOUN
easat-8674	319	2	,	,	PUNCT
easat-8674	319	3	2023	2023	NUM
easat-8674	319	4	.	.	PUNCT
easat-8674	320	1	[	[	X
easat-8674	320	2	11	11	NUM
easat-8674	320	3	]	]	PUNCT
easat-8674	320	4	t.	t.	PROPN
easat-8674	320	5	fukaya	fukaya	PROPN
easat-8674	320	6	,	,	PUNCT
easat-8674	320	7	d.	d.	PROPN
easat-8674	320	8	nakamura	nakamura	PROPN
easat-8674	320	9	,	,	PUNCT
easat-8674	320	10	y.	y.	PROPN
easat-8674	320	11	kitayama	kitayama	PROPN
easat-8674	320	12	,	,	PUNCT
easat-8674	320	13	and	and	CCONJ
easat-8674	320	14	t.	t.	PROPN
easat-8674	320	15	nakagoshi	nakagoshi	PROPN
easat-8674	320	16	,	,	PUNCT
easat-8674	320	17	"	"	PUNCT
easat-8674	320	18	a	a	DET
easat-8674	320	19	systematic	systematic	ADJ
easat-8674	320	20	review	review	NOUN
easat-8674	320	21	and	and	CCONJ
easat-8674	320	22	meta	meta	ADJ
easat-8674	320	23	-	-	PUNCT
easat-8674	320	24	analysis	analysis	NOUN
easat-8674	320	25	of	of	ADP
easat-8674	320	26	research	research	NOUN
easat-8674	320	27	on	on	ADP
easat-8674	320	28	mathematics	mathematic	NOUN
easat-8674	320	29	and	and	CCONJ
easat-8674	320	30	science	science	NOUN
easat-8674	320	31	pedagogical	pedagogical	ADJ
easat-8674	320	32	content	content	NOUN
easat-8674	320	33	knowledge	knowledge	NOUN
easat-8674	320	34	:	:	PUNCT
easat-8674	320	35	exploring	explore	VERB
easat-8674	320	36	its	its	PRON
easat-8674	320	37	associations	association	NOUN
easat-8674	320	38	with	with	ADP
easat-8674	320	39	teacher	teacher	NOUN
easat-8674	320	40	and	and	CCONJ
easat-8674	320	41	student	student	NOUN
easat-8674	320	42	variables	variable	NOUN
easat-8674	320	43	,	,	PUNCT
easat-8674	320	44	"	"	PUNCT
easat-8674	320	45	teaching	teaching	NOUN
easat-8674	320	46	and	and	CCONJ
easat-8674	320	47	teacher	teacher	NOUN
easat-8674	320	48	education	education	NOUN
easat-8674	320	49	,	,	PUNCT
easat-8674	320	50	vol	vol	NOUN
easat-8674	320	51	.	.	PROPN
easat-8674	320	52	155	155	NUM
easat-8674	320	53	,	,	PUNCT
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easat-8674	320	55	104881	104881	NUM
easat-8674	320	56	,	,	PUNCT
easat-8674	320	57	2025	2025	NUM
easat-8674	320	58	.	.	PUNCT
easat-8674	321	1	https://doi.org/10.1016/j.tate.2024.104881	https://doi.org/10.1016/j.tate.2024.104881	NOUN
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easat-8674	321	3	12	12	NUM
easat-8674	321	4	]	]	PUNCT
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easat-8674	321	6	rieu	rieu	PROPN
easat-8674	321	7	,	,	PUNCT
easat-8674	321	8	t.	t.	PROPN
easat-8674	321	9	leuders	leuder	NOUN
easat-8674	321	10	,	,	PUNCT
easat-8674	321	11	and	and	CCONJ
easat-8674	321	12	k.	k.	PROPN
easat-8674	321	13	loibl	loibl	PROPN
easat-8674	321	14	,	,	PUNCT
easat-8674	321	15	"	"	PUNCT
easat-8674	321	16	teachers	teacher	NOUN
easat-8674	321	17	’	'	PUNCT
easat-8674	321	18	diagnostic	diagnostic	ADJ
easat-8674	321	19	judgments	judgment	NOUN
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easat-8674	321	21	tasks	task	NOUN
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easat-8674	321	24	processing	processing	NOUN
easat-8674	321	25	–	–	PUNCT
easat-8674	321	26	the	the	DET
easat-8674	321	27	role	role	NOUN
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easat-8674	321	30	content	content	NOUN
easat-8674	321	31	knowledge	knowledge	NOUN
easat-8674	321	32	for	for	ADP
easat-8674	321	33	task	task	NOUN
easat-8674	321	34	diagnosis	diagnosis	NOUN
easat-8674	321	35	,	,	PUNCT
easat-8674	321	36	"	"	PUNCT
easat-8674	321	37	teaching	teaching	NOUN
easat-8674	321	38	and	and	CCONJ
easat-8674	321	39	teacher	teacher	NOUN
easat-8674	321	40	education	education	NOUN
easat-8674	321	41	,	,	PUNCT
easat-8674	321	42	vol	vol	NOUN
easat-8674	321	43	.	.	NOUN
easat-8674	321	44	111	111	NUM
easat-8674	321	45	,	,	PUNCT
easat-8674	321	46	p.	p.	NOUN
easat-8674	321	47	103621	103621	NUM
easat-8674	321	48	,	,	PUNCT
easat-8674	321	49	2022	2022	NUM
easat-8674	321	50	.	.	PUNCT
easat-8674	322	1	https://doi.org/10.1016/j.tate.2021.103621	https://doi.org/10.1016/j.tate.2021.103621	PROPN
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easat-8674	323	1	https://doi.org/10.22460/jpmi.v4i2.p%25p	https://doi.org/10.22460/jpmi.v4i2.p%25p	PRON
easat-8674	323	2	https://doi.org/10.1016/j.tate.2024.104881	https://doi.org/10.1016/j.tate.2024.104881	ADJ
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easat-8674	323	4	594	594	NUM
easat-8674	323	5	edelweiss	edelweiss	PROPN
easat-8674	323	6	applied	apply	VERB
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easat-8674	323	8	and	and	CCONJ
easat-8674	323	9	technology	technology	NOUN
easat-8674	323	10	issn	issn	PROPN
easat-8674	323	11	:	:	PUNCT
easat-8674	323	12	2576	2576	NUM
easat-8674	323	13	-	-	SYM
easat-8674	323	14	8484	8484	NUM
easat-8674	323	15	vol	vol	NOUN
easat-8674	323	16	.	.	PROPN
easat-8674	323	17	9	9	NUM
easat-8674	323	18	,	,	PUNCT
easat-8674	323	19	no	no	INTJ
easat-8674	323	20	.	.	NOUN
easat-8674	323	21	7	7	NUM
easat-8674	323	22	:	:	SYM
easat-8674	323	23	580	580	NUM
easat-8674	323	24	-	-	SYM
easat-8674	323	25	594	594	NUM
easat-8674	323	26	,	,	PUNCT
easat-8674	323	27	2025	2025	NUM
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easat-8674	323	29	:	:	PUNCT
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easat-8674	323	39	gate	gate	NOUN
easat-8674	323	40	[	[	X
easat-8674	323	41	13	13	NUM
easat-8674	323	42	]	]	X
easat-8674	323	43	y.	y.	PROPN
easat-8674	323	44	ergen	ergen	PROPN
easat-8674	323	45	,	,	PUNCT
easat-8674	323	46	"	"	PUNCT
easat-8674	323	47	'	'	PUNCT
easat-8674	323	48	does	do	AUX
easat-8674	323	49	mathematics	mathematic	NOUN
easat-8674	323	50	fool	fool	VERB
easat-8674	323	51	us?:'a	us?:'a	PROPN
easat-8674	323	52	study	study	NOUN
easat-8674	323	53	on	on	ADP
easat-8674	323	54	fourth	fourth	ADJ
easat-8674	323	55	grade	grade	NOUN
easat-8674	323	56	students	student	NOUN
easat-8674	323	57	'	'	PART
easat-8674	323	58	non	non	ADJ
easat-8674	323	59	-	-	ADJ
easat-8674	323	60	routine	routine	ADJ
easat-8674	323	61	maths	math	NOUN
easat-8674	323	62	problem	problem	NOUN
easat-8674	323	63	solving	solving	NOUN
easat-8674	323	64	skills	skill	NOUN
easat-8674	323	65	,	,	PUNCT
easat-8674	323	66	"	"	PUNCT
easat-8674	323	67	issues	issue	NOUN
easat-8674	323	68	in	in	ADP
easat-8674	323	69	educational	educational	ADJ
easat-8674	323	70	research	research	NOUN
easat-8674	323	71	,	,	PUNCT
easat-8674	323	72	vol	vol	NOUN
easat-8674	323	73	.	.	PROPN
easat-8674	323	74	30	30	NUM
easat-8674	323	75	,	,	PUNCT
easat-8674	323	76	no	no	INTJ
easat-8674	323	77	.	.	NOUN
easat-8674	323	78	3	3	NUM
easat-8674	323	79	,	,	PUNCT
easat-8674	323	80	pp	pp	ADJ
easat-8674	323	81	.	.	PUNCT
easat-8674	323	82	845	845	NUM
easat-8674	323	83	-	-	SYM
easat-8674	323	84	865	865	NUM
easat-8674	323	85	,	,	PUNCT
easat-8674	323	86	2020	2020	NUM
easat-8674	323	87	.	.	PUNCT
easat-8674	324	1	[	[	X
easat-8674	324	2	14	14	NUM
easat-8674	324	3	]	]	PUNCT
easat-8674	324	4	s.	s.	PROPN
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easat-8674	324	6	pape	pape	PROPN
easat-8674	324	7	,	,	PUNCT
easat-8674	324	8	"	"	PUNCT
easat-8674	324	9	middle	middle	ADJ
easat-8674	324	10	school	school	NOUN
easat-8674	324	11	children	child	NOUN
easat-8674	324	12	's	's	PART
easat-8674	324	13	problem	problem	NOUN
easat-8674	324	14	-	-	PUNCT
easat-8674	324	15	solving	solve	VERB
easat-8674	324	16	behavior	behavior	NOUN
easat-8674	324	17	:	:	PUNCT
easat-8674	324	18	a	a	DET
easat-8674	324	19	cognitive	cognitive	ADJ
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easat-8674	324	21	from	from	ADP
easat-8674	324	22	a	a	DET
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easat-8674	324	25	perspective	perspective	NOUN
easat-8674	324	26	,	,	PUNCT
easat-8674	324	27	"	"	PUNCT
easat-8674	324	28	journal	journal	NOUN
easat-8674	324	29	for	for	ADP
easat-8674	324	30	research	research	NOUN
easat-8674	324	31	in	in	ADP
easat-8674	324	32	mathematics	mathematics	PROPN
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easat-8674	324	34	,	,	PUNCT
easat-8674	324	35	vol	vol	NOUN
easat-8674	324	36	.	.	PROPN
easat-8674	324	37	35	35	NUM
easat-8674	324	38	,	,	PUNCT
easat-8674	324	39	no	no	INTJ
easat-8674	324	40	.	.	NOUN
easat-8674	324	41	3	3	NUM
easat-8674	324	42	,	,	PUNCT
easat-8674	324	43	pp	pp	ADJ
easat-8674	324	44	.	.	PUNCT
easat-8674	325	1	187	187	NUM
easat-8674	325	2	-	-	SYM
easat-8674	325	3	219	219	NUM
easat-8674	325	4	,	,	PUNCT
easat-8674	325	5	2004	2004	NUM
easat-8674	325	6	.	.	PUNCT
easat-8674	326	1	https://doi.org/10.2307/30034912	https://doi.org/10.2307/30034912	X
easat-8674	327	1	[	[	X
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easat-8674	327	3	]	]	X
easat-8674	327	4	s.	s.	PROPN
easat-8674	327	5	k.	k.	PROPN
easat-8674	327	6	ünver	ünver	PROPN
easat-8674	327	7	,	,	PUNCT
easat-8674	327	8	z.	z.	PROPN
easat-8674	327	9	özgür	özgür	PROPN
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easat-8674	327	11	and	and	CCONJ
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easat-8674	327	15	,	,	PUNCT
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easat-8674	327	17	investigating	investigate	VERB
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easat-8674	327	35	,	,	PUNCT
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easat-8674	327	37	.	.	PROPN
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easat-8674	327	39	,	,	PUNCT
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easat-8674	327	41	.	.	NOUN
easat-8674	327	42	1	1	NUM
easat-8674	327	43	,	,	PUNCT
easat-8674	327	44	pp	pp	ADJ
easat-8674	327	45	.	.	PUNCT
easat-8674	328	1	62	62	NUM
easat-8674	328	2	-	-	SYM
easat-8674	328	3	87	87	NUM
easat-8674	328	4	,	,	PUNCT
easat-8674	328	5	2020	2020	NUM
easat-8674	328	6	.	.	PUNCT
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easat-8674	330	29	"	"	PUNCT
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easat-8674	330	33	journal	journal	PROPN
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easat-8674	330	35	vol	vol	NOUN
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easat-8674	330	38	,	,	PUNCT
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easat-8674	330	40	.	.	NOUN
easat-8674	330	41	2	2	NUM
easat-8674	330	42	,	,	PUNCT
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easat-8674	330	44	.	.	PUNCT
easat-8674	330	45	371	371	NUM
easat-8674	330	46	-	-	SYM
easat-8674	330	47	406	406	NUM
easat-8674	330	48	,	,	PUNCT
easat-8674	330	49	2005	2005	NUM
easat-8674	330	50	.	.	PUNCT
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easat-8674	331	3	]	]	PUNCT
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easat-8674	331	14	procedia	procedia	NOUN
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easat-8674	331	22	.	.	PROPN
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easat-8674	331	24	,	,	PUNCT
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easat-8674	332	1	2798	2798	NUM
easat-8674	332	2	-	-	SYM
easat-8674	332	3	2805	2805	NUM
easat-8674	332	4	,	,	PUNCT
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easat-8674	333	1	https://doi.org/10.1016/j.sbspro.2015.01.970	https://doi.org/10.1016/j.sbspro.2015.01.970	PROPN
easat-8674	333	2	[	[	X
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easat-8674	333	10	,	,	PUNCT
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easat-8674	333	12	defining	define	VERB
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easat-8674	333	37	26	26	NUM
easat-8674	333	38	,	,	PUNCT
easat-8674	333	39	pp	pp	ADJ
easat-8674	333	40	.	.	PUNCT
easat-8674	334	1	279	279	NUM
easat-8674	334	2	-	-	SYM
easat-8674	334	3	299	299	NUM
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easat-8674	336	9	,	,	PUNCT
easat-8674	336	10	"	"	PUNCT
easat-8674	336	11	evolution	evolution	NOUN
easat-8674	336	12	of	of	ADP
easat-8674	336	13	a	a	DET
easat-8674	336	14	teaching	teaching	NOUN
easat-8674	336	15	approach	approach	NOUN
easat-8674	336	16	for	for	ADP
easat-8674	336	17	beginning	begin	VERB
easat-8674	336	18	algebra	algebra	NOUN
easat-8674	336	19	,	,	PUNCT
easat-8674	336	20	"	"	PUNCT
easat-8674	336	21	educational	educational	ADJ
easat-8674	336	22	studies	study	NOUN
easat-8674	336	23	in	in	ADP
easat-8674	336	24	mathematics	mathematic	NOUN
easat-8674	336	25	,	,	PUNCT
easat-8674	336	26	vol	vol	NOUN
easat-8674	336	27	.	.	PROPN
easat-8674	336	28	80	80	NUM
easat-8674	336	29	,	,	PUNCT
easat-8674	336	30	pp	pp	ADJ
easat-8674	336	31	.	.	PUNCT
easat-8674	336	32	351	351	NUM
easat-8674	336	33	-	-	SYM
easat-8674	336	34	367	367	NUM
easat-8674	336	35	,	,	PUNCT
easat-8674	336	36	2012	2012	NUM
easat-8674	336	37	.	.	PUNCT
easat-8674	337	1	https://doi.org/10.1007/s10649-011-9353-y	https://doi.org/10.1007/s10649-011-9353-y	PROPN
easat-8674	337	2	[	[	X
easat-8674	337	3	20	20	NUM
easat-8674	337	4	]	]	PUNCT
easat-8674	337	5	z.	z.	PROPN
easat-8674	337	6	usiskin	usiskin	PROPN
easat-8674	337	7	,	,	PUNCT
easat-8674	337	8	"	"	PUNCT
easat-8674	337	9	conceptions	conception	NOUN
easat-8674	337	10	of	of	ADP
easat-8674	337	11	school	school	NOUN
easat-8674	337	12	algebra	algebra	NOUN
easat-8674	337	13	and	and	CCONJ
easat-8674	337	14	uses	use	NOUN
easat-8674	337	15	of	of	ADP
easat-8674	337	16	variables	variable	NOUN
easat-8674	337	17	,	,	PUNCT
easat-8674	337	18	"	"	PUNCT
easat-8674	337	19	the	the	DET
easat-8674	337	20	ideas	idea	NOUN
easat-8674	337	21	of	of	ADP
easat-8674	337	22	algebra	algebra	NOUN
easat-8674	337	23	,	,	PUNCT
easat-8674	337	24	k-12	k-12	PROPN
easat-8674	337	25	,	,	PUNCT
easat-8674	337	26	vol	vol	NOUN
easat-8674	337	27	.	.	PROPN
easat-8674	337	28	8	8	NUM
easat-8674	337	29	,	,	PUNCT
easat-8674	337	30	no	no	INTJ
easat-8674	337	31	.	.	NOUN
easat-8674	337	32	1	1	NUM
easat-8674	337	33	,	,	PUNCT
easat-8674	337	34	pp	pp	ADJ
easat-8674	337	35	.	.	PUNCT
easat-8674	338	1	1	1	NUM
easat-8674	338	2	-	-	SYM
easat-8674	338	3	7	7	NUM
easat-8674	338	4	,	,	PUNCT
easat-8674	338	5	1988	1988	NUM
easat-8674	338	6	.	.	PUNCT
easat-8674	339	1	[	[	X
easat-8674	339	2	21	21	NUM
easat-8674	339	3	]	]	X
easat-8674	339	4	c.	c.	PROPN
easat-8674	339	5	kieran	kieran	PROPN
easat-8674	339	6	,	,	PUNCT
easat-8674	339	7	a.	a.	PROPN
easat-8674	339	8	boileau	boileau	PROPN
easat-8674	339	9	,	,	PUNCT
easat-8674	339	10	and	and	CCONJ
easat-8674	339	11	m.	m.	NOUN
easat-8674	339	12	garançon	garançon	NOUN
easat-8674	339	13	,	,	PUNCT
easat-8674	339	14	introducing	introduce	VERB
easat-8674	339	15	algebra	algebra	NOUN
easat-8674	339	16	by	by	ADP
easat-8674	339	17	means	mean	NOUN
easat-8674	339	18	of	of	ADP
easat-8674	339	19	a	a	DET
easat-8674	339	20	technology	technology	NOUN
easat-8674	339	21	-	-	PUNCT
easat-8674	339	22	supported	support	VERB
easat-8674	339	23	,	,	PUNCT
easat-8674	339	24	functional	functional	ADJ
easat-8674	339	25	approach	approach	NOUN
easat-8674	339	26	.	.	PUNCT
easat-8674	340	1	in	in	ADP
easat-8674	340	2	approaches	approach	NOUN
easat-8674	340	3	to	to	ADP
easat-8674	340	4	algebra	algebra	NOUN
easat-8674	340	5	:	:	PUNCT
easat-8674	340	6	perspectives	perspective	NOUN
easat-8674	340	7	for	for	ADP
easat-8674	340	8	research	research	NOUN
easat-8674	340	9	and	and	CCONJ
easat-8674	340	10	teaching	teaching	NOUN
easat-8674	340	11	.	.	PUNCT
easat-8674	341	1	dordrecht	dordrecht	PROPN
easat-8674	341	2	:	:	PUNCT
easat-8674	341	3	springer	springer	PROPN
easat-8674	341	4	netherlands	netherlands	PROPN
easat-8674	341	5	,	,	PUNCT
easat-8674	341	6	1996	1996	NUM
easat-8674	341	7	.	.	PUNCT
easat-8674	342	1	[	[	X
easat-8674	342	2	22	22	NUM
easat-8674	342	3	]	]	PUNCT
easat-8674	342	4	j.	j.	PROPN
easat-8674	342	5	l.	l.	PROPN
easat-8674	342	6	booth	booth	PROPN
easat-8674	342	7	,	,	PUNCT
easat-8674	342	8	c.	c.	PROPN
easat-8674	342	9	barbieri	barbieri	PROPN
easat-8674	342	10	,	,	PUNCT
easat-8674	342	11	f.	f.	PROPN
easat-8674	342	12	eyer	eyer	PROPN
easat-8674	342	13	,	,	PUNCT
easat-8674	342	14	and	and	CCONJ
easat-8674	342	15	e.	e.	PROPN
easat-8674	342	16	j.	j.	PROPN
easat-8674	342	17	paré	paré	PROPN
easat-8674	342	18	-	-	PUNCT
easat-8674	342	19	blagoev	blagoev	NOUN
easat-8674	342	20	,	,	PUNCT
easat-8674	342	21	"	"	PUNCT
easat-8674	342	22	persistent	persistent	ADJ
easat-8674	342	23	misconceptions	misconception	NOUN
easat-8674	342	24	in	in	ADP
easat-8674	342	25	algebraic	algebraic	ADJ
easat-8674	342	26	problem	problem	NOUN
easat-8674	342	27	solving	solve	VERB
easat-8674	342	28	:	:	PUNCT
easat-8674	342	29	contributions	contribution	NOUN
easat-8674	342	30	of	of	ADP
easat-8674	342	31	knowledge	knowledge	NOUN
easat-8674	342	32	,	,	PUNCT
easat-8674	342	33	executive	executive	NOUN
easat-8674	342	34	functions	function	NOUN
easat-8674	342	35	,	,	PUNCT
easat-8674	342	36	and	and	CCONJ
easat-8674	342	37	affect	affect	VERB
easat-8674	342	38	,	,	PUNCT
easat-8674	342	39	"	"	PUNCT
easat-8674	342	40	learning	learning	NOUN
easat-8674	342	41	and	and	CCONJ
easat-8674	342	42	individual	individual	ADJ
easat-8674	342	43	differences	difference	NOUN
easat-8674	342	44	,	,	PUNCT
easat-8674	342	45	vol	vol	NOUN
easat-8674	342	46	.	.	PROPN
easat-8674	342	47	31	31	NUM
easat-8674	342	48	,	,	PUNCT
easat-8674	342	49	pp	pp	ADJ
easat-8674	342	50	.	.	PUNCT
easat-8674	342	51	10–20	10–20	NUM
easat-8674	342	52	,	,	PUNCT
easat-8674	342	53	2014	2014	NUM
easat-8674	342	54	.	.	PUNCT
easat-8674	343	1	[	[	X
easat-8674	343	2	23	23	NUM
easat-8674	343	3	]	]	X
easat-8674	343	4	r.	r.	PROPN
easat-8674	343	5	zazkis	zazkis	PROPN
easat-8674	343	6	and	and	CCONJ
easat-8674	343	7	r.	r.	PROPN
easat-8674	343	8	leikin	leikin	NOUN
easat-8674	343	9	,	,	PUNCT
easat-8674	343	10	"	"	PUNCT
easat-8674	343	11	advanced	advanced	ADJ
easat-8674	343	12	mathematical	mathematical	ADJ
easat-8674	343	13	knowledge	knowledge	NOUN
easat-8674	343	14	in	in	ADP
easat-8674	343	15	teaching	teach	VERB
easat-8674	343	16	practice	practice	NOUN
easat-8674	343	17	:	:	PUNCT
easat-8674	343	18	perceptions	perception	NOUN
easat-8674	343	19	of	of	ADP
easat-8674	343	20	secondary	secondary	ADJ
easat-8674	343	21	mathematics	mathematic	NOUN
easat-8674	343	22	teachers	teacher	NOUN
easat-8674	343	23	,	,	PUNCT
easat-8674	343	24	"	"	PUNCT
easat-8674	343	25	mathematical	mathematical	ADJ
easat-8674	343	26	thinking	thinking	NOUN
easat-8674	343	27	and	and	CCONJ
easat-8674	343	28	learning	learning	NOUN
easat-8674	343	29	,	,	PUNCT
easat-8674	343	30	vol	vol	NOUN
easat-8674	343	31	.	.	PROPN
easat-8674	344	1	12	12	NUM
easat-8674	344	2	,	,	PUNCT
easat-8674	344	3	no	no	INTJ
easat-8674	344	4	.	.	NOUN
easat-8674	344	5	4	4	NUM
easat-8674	344	6	,	,	PUNCT
easat-8674	344	7	pp	pp	ADJ
easat-8674	344	8	.	.	PUNCT
easat-8674	345	1	263	263	NUM
easat-8674	345	2	-	-	SYM
easat-8674	345	3	281	281	NUM
easat-8674	345	4	,	,	PUNCT
easat-8674	345	5	2010	2010	NUM
easat-8674	345	6	.	.	PUNCT
easat-8674	346	1	https://doi.org/10.1080/10986061003786349	https://doi.org/10.1080/10986061003786349	X
easat-8674	347	1	[	[	X
easat-8674	347	2	24	24	NUM
easat-8674	347	3	]	]	PUNCT
easat-8674	347	4	a.	a.	NOUN
easat-8674	347	5	c.	c.	PROPN
easat-8674	347	6	stephens	stephens	PROPN
easat-8674	347	7	,	,	PUNCT
easat-8674	347	8	b.	b.	PROPN
easat-8674	347	9	j.	j.	PROPN
easat-8674	347	10	dougherty	dougherty	PROPN
easat-8674	347	11	,	,	PUNCT
easat-8674	347	12	and	and	CCONJ
easat-8674	347	13	p.	p.	NOUN
easat-8674	347	14	a.	a.	NOUN
easat-8674	347	15	gunter	gunter	PROPN
easat-8674	347	16	,	,	PUNCT
easat-8674	347	17	algebra	algebra	NOUN
easat-8674	347	18	thinking	thinking	NOUN
easat-8674	347	19	in	in	ADP
easat-8674	347	20	the	the	DET
easat-8674	347	21	elementary	elementary	ADJ
easat-8674	347	22	and	and	CCONJ
easat-8674	347	23	middle	middle	ADJ
easat-8674	347	24	grades	grade	NOUN
easat-8674	347	25	.	.	PUNCT
easat-8674	348	1	in	in	ADP
easat-8674	348	2	d.	d.	PROPN
easat-8674	348	3	t.	t.	PROPN
easat-8674	348	4	owens	owens	PROPN
easat-8674	348	5	,	,	PUNCT
easat-8674	348	6	g.	g.	PROPN
easat-8674	348	7	m.	m.	PROPN
easat-8674	348	8	hackett	hackett	PROPN
easat-8674	348	9	,	,	PUNCT
easat-8674	348	10	&	&	CCONJ
easat-8674	348	11	l.	l.	PROPN
easat-8674	348	12	m.	m.	PROPN
easat-8674	348	13	lovin	lovin	PROPN
easat-8674	348	14	(	(	PUNCT
easat-8674	348	15	eds	eds	PROPN
easat-8674	348	16	.	.	PUNCT
easat-8674	348	17	)	)	PUNCT
easat-8674	348	18	,	,	PUNCT
easat-8674	348	19	curriculum	curriculum	NOUN
easat-8674	348	20	and	and	CCONJ
easat-8674	348	21	research	research	NOUN
easat-8674	348	22	framework	framework	NOUN
easat-8674	348	23	for	for	ADP
easat-8674	348	24	algebra	algebra	NOUN
easat-8674	348	25	in	in	ADP
easat-8674	348	26	the	the	DET
easat-8674	348	27	elementary	elementary	ADJ
easat-8674	348	28	and	and	CCONJ
easat-8674	348	29	middle	middle	ADJ
easat-8674	348	30	grades	grade	NOUN
easat-8674	348	31	.	.	PUNCT
easat-8674	349	1	reston	reston	PROPN
easat-8674	349	2	,	,	PUNCT
easat-8674	349	3	va	va	PROPN
easat-8674	349	4	:	:	PUNCT
easat-8674	349	5	national	national	ADJ
easat-8674	349	6	council	council	PROPN
easat-8674	349	7	of	of	ADP
easat-8674	349	8	teachers	teacher	NOUN
easat-8674	349	9	of	of	ADP
easat-8674	349	10	mathematics	mathematic	NOUN
easat-8674	349	11	,	,	PUNCT
easat-8674	349	12	2019	2019	NUM
easat-8674	349	13	.	.	PUNCT
easat-8674	350	1	[	[	X
easat-8674	350	2	25	25	NUM
easat-8674	350	3	]	]	PUNCT
easat-8674	350	4	j.	j.	PROPN
easat-8674	350	5	w.	w.	PROPN
easat-8674	350	6	creswell	creswell	PROPN
easat-8674	350	7	,	,	PUNCT
easat-8674	350	8	qualitative	qualitative	ADJ
easat-8674	350	9	research	research	NOUN
easat-8674	350	10	and	and	CCONJ
easat-8674	350	11	research	research	NOUN
easat-8674	350	12	design	design	NOUN
easat-8674	350	13	:	:	PUNCT
easat-8674	350	14	choosing	choose	VERB
easat-8674	350	15	among	among	ADP
easat-8674	350	16	five	five	NUM
easat-8674	350	17	approaches	approach	NOUN
easat-8674	350	18	.	.	PUNCT
easat-8674	351	1	yogyakarta	yogyakarta	PROPN
easat-8674	351	2	:	:	PUNCT
easat-8674	351	3	pustaka	pustaka	ADJ
easat-8674	351	4	pelajar	pelajar	NOUN
easat-8674	351	5	,	,	PUNCT
easat-8674	351	6	2015	2015	NUM
easat-8674	351	7	.	.	PUNCT
easat-8674	352	1	[	[	X
easat-8674	352	2	26	26	NUM
easat-8674	352	3	]	]	PUNCT
easat-8674	352	4	a.	a.	NOUN
easat-8674	352	5	appova	appova	PROPN
easat-8674	352	6	and	and	CCONJ
easat-8674	352	7	c.	c.	PROPN
easat-8674	352	8	e.	e.	PROPN
easat-8674	352	9	taylor	taylor	PROPN
easat-8674	352	10	,	,	PUNCT
easat-8674	352	11	"	"	PUNCT
easat-8674	352	12	expert	expert	ADJ
easat-8674	352	13	mathematics	mathematics	NOUN
easat-8674	352	14	teacher	teacher	NOUN
easat-8674	352	15	educators	educator	NOUN
easat-8674	352	16	’	’	PART
easat-8674	352	17	purposes	purpose	NOUN
easat-8674	352	18	and	and	CCONJ
easat-8674	352	19	practices	practice	NOUN
easat-8674	352	20	for	for	ADP
easat-8674	352	21	providing	provide	VERB
easat-8674	352	22	prospective	prospective	ADJ
easat-8674	352	23	teachers	teacher	NOUN
easat-8674	352	24	with	with	ADP
easat-8674	352	25	opportunities	opportunity	NOUN
easat-8674	352	26	to	to	PART
easat-8674	352	27	develop	develop	VERB
easat-8674	352	28	pedagogical	pedagogical	ADJ
easat-8674	352	29	content	content	NOUN
easat-8674	352	30	knowledge	knowledge	NOUN
easat-8674	352	31	in	in	ADP
easat-8674	352	32	content	content	NOUN
easat-8674	352	33	courses	course	NOUN
easat-8674	352	34	,	,	PUNCT
easat-8674	352	35	"	"	PUNCT
easat-8674	352	36	journal	journal	NOUN
easat-8674	352	37	of	of	ADP
easat-8674	352	38	mathematics	mathematics	PROPN
easat-8674	352	39	teacher	teacher	NOUN
easat-8674	352	40	education	education	NOUN
easat-8674	352	41	,	,	PUNCT
easat-8674	352	42	vol	vol	NOUN
easat-8674	352	43	.	.	PROPN
easat-8674	352	44	22	22	NUM
easat-8674	352	45	,	,	PUNCT
easat-8674	352	46	pp	pp	ADJ
easat-8674	352	47	.	.	PUNCT
easat-8674	353	1	179	179	NUM
easat-8674	353	2	-	-	SYM
easat-8674	353	3	204	204	NUM
easat-8674	353	4	,	,	PUNCT
easat-8674	353	5	2019	2019	NUM
easat-8674	353	6	.	.	PUNCT
easat-8674	354	1	https://doi.org/10.1007/s10857-017-9385-z	https://doi.org/10.1007/s10857-017-9385-z	PROPN
easat-8674	355	1	[	[	X
easat-8674	355	2	27	27	NUM
easat-8674	355	3	]	]	PUNCT
easat-8674	355	4	s.	s.	PROPN
easat-8674	355	5	b.	b.	PROPN
easat-8674	355	6	bush	bush	PROPN
easat-8674	355	7	and	and	CCONJ
easat-8674	355	8	k.	k.	PROPN
easat-8674	355	9	s.	s.	PROPN
easat-8674	355	10	karp	karp	PROPN
easat-8674	355	11	,	,	PUNCT
easat-8674	355	12	"	"	PUNCT
easat-8674	355	13	prerequisite	prerequisite	ADJ
easat-8674	355	14	algebra	algebra	NOUN
easat-8674	355	15	skills	skill	NOUN
easat-8674	355	16	and	and	CCONJ
easat-8674	355	17	associated	associated	ADJ
easat-8674	355	18	misconceptions	misconception	NOUN
easat-8674	355	19	of	of	ADP
easat-8674	355	20	middle	middle	ADJ
easat-8674	355	21	grade	grade	NOUN
easat-8674	355	22	students	student	NOUN
easat-8674	355	23	:	:	PUNCT
easat-8674	355	24	a	a	DET
easat-8674	355	25	review	review	NOUN
easat-8674	355	26	,	,	PUNCT
easat-8674	355	27	"	"	PUNCT
easat-8674	355	28	the	the	DET
easat-8674	355	29	journal	journal	NOUN
easat-8674	355	30	of	of	ADP
easat-8674	355	31	mathematical	mathematical	ADJ
easat-8674	355	32	behavior	behavior	NOUN
easat-8674	355	33	,	,	PUNCT
easat-8674	355	34	vol	vol	NOUN
easat-8674	355	35	.	.	PROPN
easat-8674	355	36	32	32	NUM
easat-8674	355	37	,	,	PUNCT
easat-8674	355	38	no	no	INTJ
easat-8674	355	39	.	.	NOUN
easat-8674	355	40	3	3	NUM
easat-8674	355	41	,	,	PUNCT
easat-8674	355	42	pp	pp	ADJ
easat-8674	355	43	.	.	PUNCT
easat-8674	356	1	613	613	NUM
easat-8674	356	2	-	-	SYM
easat-8674	356	3	632	632	NUM
easat-8674	356	4	,	,	PUNCT
easat-8674	356	5	2013	2013	NUM
easat-8674	356	6	.	.	PUNCT
easat-8674	357	1	https://doi.org/10.1016/j.jmathb.2013.07.002	https://doi.org/10.1016/j.jmathb.2013.07.002	NOUN
easat-8674	357	2	[	[	X
easat-8674	357	3	28	28	NUM
easat-8674	357	4	]	]	X
easat-8674	357	5	m.	m.	NOUN
easat-8674	357	6	josefsson	josefsson	PROPN
easat-8674	357	7	,	,	PUNCT
easat-8674	357	8	"	"	PUNCT
easat-8674	357	9	characterizations	characterization	NOUN
easat-8674	357	10	of	of	ADP
easat-8674	357	11	trapezoids	trapezoid	NOUN
easat-8674	357	12	,	,	PUNCT
easat-8674	357	13	"	"	PUNCT
easat-8674	357	14	forum	forum	NOUN
easat-8674	357	15	geom	geom	PROPN
easat-8674	357	16	,	,	PUNCT
easat-8674	357	17	vol	vol	NOUN
easat-8674	357	18	.	.	PROPN
easat-8674	357	19	13	13	NUM
easat-8674	357	20	,	,	PUNCT
easat-8674	357	21	pp	pp	ADJ
easat-8674	357	22	.	.	PUNCT
easat-8674	358	1	23	23	NUM
easat-8674	358	2	-	-	SYM
easat-8674	358	3	35	35	NUM
easat-8674	358	4	,	,	PUNCT
easat-8674	358	5	2013	2013	NUM
easat-8674	358	6	.	.	PUNCT
easat-8674	359	1	[	[	X
easat-8674	359	2	29	29	NUM
easat-8674	359	3	]	]	X
easat-8674	359	4	r.	r.	PROPN
easat-8674	359	5	salazar	salazar	PROPN
easat-8674	359	6	and	and	CCONJ
easat-8674	359	7	a.	a.	NOUN
easat-8674	359	8	yilmaz	yilmaz	PROPN
easat-8674	359	9	,	,	PUNCT
easat-8674	359	10	"	"	PUNCT
easat-8674	359	11	contextual	contextual	ADJ
easat-8674	359	12	applications	application	NOUN
easat-8674	359	13	of	of	ADP
easat-8674	359	14	ck	ck	PROPN
easat-8674	359	15	in	in	ADP
easat-8674	359	16	algebra	algebra	NOUN
easat-8674	359	17	,	,	PUNCT
easat-8674	359	18	"	"	PUNCT
easat-8674	359	19	frontiers	frontier	NOUN
easat-8674	359	20	in	in	ADP
easat-8674	359	21	education	education	NOUN
easat-8674	359	22	,	,	PUNCT
easat-8674	359	23	vol	vol	NOUN
easat-8674	359	24	.	.	PROPN
easat-8674	359	25	9	9	NUM
easat-8674	359	26	,	,	PUNCT
easat-8674	359	27	2014	2014	NUM
easat-8674	359	28	.	.	PUNCT
easat-8674	360	1	[	[	X
easat-8674	360	2	30	30	NUM
easat-8674	360	3	]	]	PUNCT
easat-8674	360	4	m.	m.	NOUN
easat-8674	360	5	chinnappan	chinnappan	NOUN
easat-8674	360	6	,	,	PUNCT
easat-8674	360	7	"	"	PUNCT
easat-8674	360	8	cognitive	cognitive	ADJ
easat-8674	360	9	load	load	NOUN
easat-8674	360	10	and	and	CCONJ
easat-8674	360	11	modelling	modelling	NOUN
easat-8674	360	12	of	of	ADP
easat-8674	360	13	an	an	DET
easat-8674	360	14	algebra	algebra	NOUN
easat-8674	360	15	problem	problem	NOUN
easat-8674	360	16	,	,	PUNCT
easat-8674	360	17	"	"	PUNCT
easat-8674	360	18	mathematics	mathematics	PROPN
easat-8674	360	19	education	education	NOUN
easat-8674	360	20	research	research	NOUN
easat-8674	360	21	journal	journal	NOUN
easat-8674	360	22	,	,	PUNCT
easat-8674	360	23	vol	vol	NOUN
easat-8674	360	24	.	.	PROPN
easat-8674	360	25	22	22	NUM
easat-8674	360	26	,	,	PUNCT
easat-8674	360	27	no	no	INTJ
easat-8674	360	28	.	.	NOUN
easat-8674	360	29	2	2	NUM
easat-8674	360	30	,	,	PUNCT
easat-8674	360	31	pp	pp	ADJ
easat-8674	360	32	.	.	PUNCT
easat-8674	360	33	8	8	NUM
easat-8674	360	34	-	-	SYM
easat-8674	360	35	23	23	NUM
easat-8674	360	36	,	,	PUNCT
easat-8674	360	37	2010	2010	NUM
easat-8674	360	38	.	.	PUNCT
easat-8674	360	39	https://doi.org/10.1007/bf03217563	https://doi.org/10.1007/bf03217563	VERB
easat-8674	361	1	[	[	X
easat-8674	361	2	31	31	NUM
easat-8674	361	3	]	]	PUNCT
easat-8674	361	4	s.	s.	PROPN
easat-8674	361	5	l.	l.	PROPN
easat-8674	361	6	bair	bair	PROPN
easat-8674	361	7	and	and	CCONJ
easat-8674	361	8	b.	b.	PROPN
easat-8674	361	9	s.	s.	PROPN
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easat-8674	361	11	,	,	PUNCT
easat-8674	361	12	"	"	PUNCT
easat-8674	361	13	characterizing	characterize	VERB
easat-8674	361	14	the	the	DET
easat-8674	361	15	development	development	NOUN
easat-8674	361	16	of	of	ADP
easat-8674	361	17	specialized	specialized	ADJ
easat-8674	361	18	mathematical	mathematical	ADJ
easat-8674	361	19	content	content	NOUN
easat-8674	361	20	knowledge	knowledge	NOUN
easat-8674	361	21	for	for	ADP
easat-8674	361	22	teaching	teach	VERB
easat-8674	361	23	in	in	ADP
easat-8674	361	24	algebraic	algebraic	ADJ
easat-8674	361	25	reasoning	reasoning	NOUN
easat-8674	361	26	and	and	CCONJ
easat-8674	361	27	number	number	NOUN
easat-8674	361	28	theory	theory	NOUN
easat-8674	361	29	,	,	PUNCT
easat-8674	361	30	"	"	PUNCT
easat-8674	361	31	mathematical	mathematical	ADJ
easat-8674	361	32	thinking	thinking	NOUN
easat-8674	361	33	and	and	CCONJ
easat-8674	361	34	learning	learning	NOUN
easat-8674	361	35	,	,	PUNCT
easat-8674	361	36	vol	vol	NOUN
easat-8674	361	37	.	.	PROPN
easat-8674	361	38	13	13	NUM
easat-8674	361	39	,	,	PUNCT
easat-8674	361	40	no	no	INTJ
easat-8674	361	41	.	.	NOUN
easat-8674	361	42	4	4	NUM
easat-8674	361	43	,	,	PUNCT
easat-8674	361	44	pp	pp	ADJ
easat-8674	361	45	.	.	PUNCT
easat-8674	362	1	292	292	NUM
easat-8674	362	2	-	-	SYM
easat-8674	362	3	321	321	NUM
easat-8674	362	4	,	,	PUNCT
easat-8674	362	5	2011	2011	NUM
easat-8674	362	6	.	.	PUNCT
easat-8674	362	7	https://doi.org/10.1080/10986065.2011.608345	https://doi.org/10.1080/10986065.2011.608345	PUNCT
easat-8674	363	1	[	[	X
easat-8674	363	2	32	32	NUM
easat-8674	363	3	]	]	PUNCT
easat-8674	363	4	f.	f.	PROPN
easat-8674	363	5	depaepe	depaepe	PROPN
easat-8674	363	6	et	et	PROPN
easat-8674	363	7	al	al	PROPN
easat-8674	363	8	.	.	PROPN
easat-8674	363	9	,	,	PUNCT
easat-8674	363	10	"	"	PUNCT
easat-8674	363	11	teachers	teacher	NOUN
easat-8674	363	12	'	'	PART
easat-8674	363	13	content	content	NOUN
easat-8674	363	14	and	and	CCONJ
easat-8674	363	15	pedagogical	pedagogical	ADJ
easat-8674	363	16	content	content	NOUN
easat-8674	363	17	knowledge	knowledge	NOUN
easat-8674	363	18	on	on	ADP
easat-8674	363	19	rational	rational	ADJ
easat-8674	363	20	numbers	number	NOUN
easat-8674	363	21	:	:	PUNCT
easat-8674	363	22	a	a	DET
easat-8674	363	23	comparison	comparison	NOUN
easat-8674	363	24	of	of	ADP
easat-8674	363	25	prospective	prospective	ADJ
easat-8674	363	26	elementary	elementary	NOUN
easat-8674	363	27	and	and	CCONJ
easat-8674	363	28	lower	low	ADJ
easat-8674	363	29	secondary	secondary	ADJ
easat-8674	363	30	school	school	NOUN
easat-8674	363	31	teachers	teacher	NOUN
easat-8674	363	32	,	,	PUNCT
easat-8674	363	33	"	"	PUNCT
easat-8674	363	34	teaching	teaching	NOUN
easat-8674	363	35	and	and	CCONJ
easat-8674	363	36	teacher	teacher	NOUN
easat-8674	363	37	education	education	NOUN
easat-8674	363	38	,	,	PUNCT
easat-8674	363	39	vol	vol	NOUN
easat-8674	363	40	.	.	PROPN
easat-8674	364	1	47	47	NUM
easat-8674	364	2	,	,	PUNCT
easat-8674	365	1	pp	pp	ADJ
easat-8674	365	2	.	.	PUNCT
easat-8674	366	1	82	82	NUM
easat-8674	366	2	-	-	SYM
easat-8674	366	3	92	92	NUM
easat-8674	366	4	,	,	PUNCT
easat-8674	366	5	2015	2015	NUM
easat-8674	366	6	.	.	PUNCT
easat-8674	367	1	https://doi.org/10.1016/j.tate.2014.12.009	https://doi.org/10.1016/j.tate.2014.12.009	PROPN
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easat-8674	367	4	]	]	PUNCT
easat-8674	367	5	s.	s.	PROPN
easat-8674	367	6	d.	d.	PROPN
easat-8674	367	7	kılıç	kılıç	PROPN
easat-8674	367	8	,	,	PUNCT
easat-8674	367	9	"	"	PUNCT
easat-8674	367	10	pre	pre	ADJ
easat-8674	367	11	-	-	ADJ
easat-8674	367	12	service	service	ADJ
easat-8674	367	13	teachers	teacher	NOUN
easat-8674	367	14	’	'	PUNCT
easat-8674	367	15	noticing	notice	VERB
easat-8674	367	16	of	of	ADP
easat-8674	367	17	7th	7th	ADJ
easat-8674	367	18	grade	grade	NOUN
easat-8674	367	19	students	student	NOUN
easat-8674	367	20	’	’	PART
easat-8674	367	21	errors	error	NOUN
easat-8674	367	22	and	and	CCONJ
easat-8674	367	23	misconceptions	misconception	NOUN
easat-8674	367	24	about	about	ADP
easat-8674	367	25	the	the	DET
easat-8674	367	26	subject	subject	NOUN
easat-8674	367	27	of	of	ADP
easat-8674	367	28	equations	equation	NOUN
easat-8674	367	29	,	,	PUNCT
easat-8674	367	30	"	"	PUNCT
easat-8674	367	31	sakarya	sakarya	NOUN
easat-8674	367	32	university	university	NOUN
easat-8674	367	33	journal	journal	NOUN
easat-8674	367	34	of	of	ADP
easat-8674	367	35	education	education	NOUN
easat-8674	367	36	,	,	PUNCT
easat-8674	367	37	vol	vol	NOUN
easat-8674	367	38	.	.	PROPN
easat-8674	367	39	9	9	NUM
easat-8674	367	40	,	,	PUNCT
easat-8674	367	41	no	no	INTJ
easat-8674	367	42	.	.	NOUN
easat-8674	367	43	1	1	NUM
easat-8674	367	44	,	,	PUNCT
easat-8674	367	45	pp	pp	ADJ
easat-8674	367	46	.	.	PUNCT
easat-8674	368	1	184	184	NUM
easat-8674	368	2	-	-	SYM
easat-8674	368	3	207	207	NUM
easat-8674	368	4	,	,	PUNCT
easat-8674	368	5	2019	2019	NUM
easat-8674	368	6	.	.	PUNCT
easat-8674	369	1	https://doi.org/10.19126/suje.535565	https://doi.org/10.19126/suje.535565	NOUN
easat-8674	370	1	[	[	X
easat-8674	370	2	34	34	NUM
easat-8674	370	3	]	]	X
easat-8674	370	4	n.	n.	NOUN
easat-8674	370	5	pincheira	pincheira	PROPN
easat-8674	370	6	and	and	CCONJ
easat-8674	370	7	á	á	PROPN
easat-8674	370	8	.	.	PUNCT
easat-8674	370	9	alsina	alsina	PROPN
easat-8674	370	10	,	,	PUNCT
easat-8674	370	11	"	"	PUNCT
easat-8674	370	12	teachers	teacher	NOUN
easat-8674	370	13	’	'	PUNCT
easat-8674	370	14	mathematics	mathematic	NOUN
easat-8674	370	15	knowledge	knowledge	NOUN
easat-8674	370	16	for	for	ADP
easat-8674	370	17	teaching	teach	VERB
easat-8674	370	18	early	early	ADJ
easat-8674	370	19	algebra	algebra	NOUN
easat-8674	370	20	:	:	PUNCT
easat-8674	370	21	a	a	DET
easat-8674	370	22	systematic	systematic	ADJ
easat-8674	370	23	review	review	NOUN
easat-8674	370	24	from	from	ADP
easat-8674	370	25	the	the	DET
easat-8674	370	26	mkt	mkt	PROPN
easat-8674	370	27	perspective	perspective	NOUN
easat-8674	370	28	,	,	PUNCT
easat-8674	370	29	"	"	PUNCT
easat-8674	370	30	mathematics	mathematic	NOUN
easat-8674	370	31	,	,	PUNCT
easat-8674	370	32	vol	vol	NOUN
easat-8674	370	33	.	.	PROPN
easat-8674	370	34	9	9	NUM
easat-8674	370	35	,	,	PUNCT
easat-8674	370	36	no	no	INTJ
easat-8674	370	37	.	.	NOUN
easat-8674	370	38	20	20	NUM
easat-8674	370	39	,	,	PUNCT
easat-8674	370	40	p.	p.	NOUN
easat-8674	370	41	2590	2590	NUM
easat-8674	370	42	,	,	PUNCT
easat-8674	370	43	2021	2021	NUM
easat-8674	370	44	.	.	PUNCT
easat-8674	371	1	https://doi.org/10.3390/math9202590	https://doi.org/10.3390/math9202590	PROPN
easat-8674	371	2	[	[	X
easat-8674	371	3	35	35	NUM
easat-8674	371	4	]	]	X
easat-8674	371	5	c.	c.	PROPN
easat-8674	371	6	r.	r.	PROPN
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easat-8674	371	8	,	,	PUNCT
easat-8674	371	9	"	"	PUNCT
easat-8674	371	10	enhancing	enhance	VERB
easat-8674	371	11	primary	primary	ADJ
easat-8674	371	12	teacher	teacher	NOUN
easat-8674	371	13	training	train	VERB
easat-8674	371	14	through	through	ADP
easat-8674	371	15	academic	academic	ADJ
easat-8674	371	16	portfolios	portfolio	NOUN
easat-8674	371	17	in	in	ADP
easat-8674	371	18	advanced	advanced	ADJ
easat-8674	371	19	mathematics	mathematic	NOUN
easat-8674	371	20	courses	course	NOUN
easat-8674	371	21	,	,	PUNCT
easat-8674	371	22	"	"	PUNCT
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easat-8674	371	26	,	,	PUNCT
easat-8674	371	27	2025	2025	NUM
easat-8674	371	28	.	.	PUNCT
easat-8674	372	1	https://doi.org/10.48550/arxiv.2504.06159	https://doi.org/10.48550/arxiv.2504.06159	PROPN
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easat-8674	373	1	https://doi.org/10.1007/s10857-017-9385-z	https://doi.org/10.1007/s10857-017-9385-z	PROPN
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easat-8674	373	8	https://doi.org/10.48550/arxiv.2504.06159	https://doi.org/10.48550/arxiv.2504.06159	PROPN