id	sid	tid	token	lemma	pos
easat-8773	1	1	edelweiss	edelweiss	PROPN
easat-8773	1	2	applied	apply	VERB
easat-8773	1	3	science	science	NOUN
easat-8773	1	4	and	and	CCONJ
easat-8773	1	5	technology	technology	NOUN
easat-8773	1	6	issn	issn	PROPN
easat-8773	1	7	:	:	PUNCT
easat-8773	1	8	2576	2576	NUM
easat-8773	1	9	-	-	SYM
easat-8773	1	10	8484	8484	NUM
easat-8773	1	11	vol	vol	NOUN
easat-8773	1	12	.	.	PROPN
easat-8773	2	1	9	9	NUM
easat-8773	2	2	,	,	PUNCT
easat-8773	2	3	no	no	INTJ
easat-8773	2	4	.	.	NOUN
easat-8773	2	5	7	7	NUM
easat-8773	2	6	,	,	PUNCT
easat-8773	2	7	947	947	NUM
easat-8773	2	8	-	-	SYM
easat-8773	2	9	959	959	NUM
easat-8773	2	10	2025	2025	NUM
easat-8773	2	11	publisher	publisher	NOUN
easat-8773	2	12	:	:	PUNCT
easat-8773	2	13	learning	learn	VERB
easat-8773	2	14	gate	gate	NOUN
easat-8773	2	15	doi	doi	PROPN
easat-8773	2	16	:	:	PUNCT
easat-8773	2	17	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	2	18	©	©	PROPN
easat-8773	2	19	2025	2025	NUM
easat-8773	2	20	by	by	ADP
easat-8773	2	21	the	the	DET
easat-8773	2	22	authors	author	NOUN
easat-8773	2	23	;	;	PUNCT
easat-8773	2	24	licensee	licensee	PROPN
easat-8773	2	25	learning	learning	NOUN
easat-8773	2	26	gate	gate	NOUN
easat-8773	3	1	©	©	PROPN
easat-8773	3	2	2025	2025	NUM
easat-8773	3	3	by	by	ADP
easat-8773	3	4	the	the	DET
easat-8773	3	5	authors	author	NOUN
easat-8773	3	6	;	;	PUNCT
easat-8773	3	7	licensee	licensee	PROPN
easat-8773	3	8	learning	learning	NOUN
easat-8773	3	9	gate	gate	NOUN
easat-8773	3	10	history	history	NOUN
easat-8773	3	11	:	:	PUNCT
easat-8773	3	12	received	receive	VERB
easat-8773	3	13	:	:	PUNCT
easat-8773	3	14	30	30	NUM
easat-8773	3	15	april	april	PROPN
easat-8773	3	16	2025	2025	NUM
easat-8773	3	17	;	;	PUNCT
easat-8773	3	18	revised	revise	VERB
easat-8773	3	19	:	:	PUNCT
easat-8773	3	20	11	11	NUM
easat-8773	3	21	june	june	PROPN
easat-8773	3	22	2025	2025	NUM
easat-8773	3	23	;	;	PUNCT
easat-8773	3	24	accepted	accept	VERB
easat-8773	3	25	:	:	PUNCT
easat-8773	3	26	16	16	NUM
easat-8773	3	27	june	june	PROPN
easat-8773	3	28	2025	2025	NUM
easat-8773	3	29	;	;	PUNCT
easat-8773	3	30	published	publish	VERB
easat-8773	3	31	:	:	PUNCT
easat-8773	4	1	11	11	NUM
easat-8773	4	2	july	july	PROPN
easat-8773	4	3	2025	2025	NUM
easat-8773	4	4	*	*	PUNCT
easat-8773	4	5	correspondence	correspondence	NOUN
easat-8773	4	6	:	:	PUNCT
easat-8773	5	1	yusuffuad@unesa.ac.id	yusuffuad@unesa.ac.id	VERB
easat-8773	5	2	analysis	analysis	NOUN
easat-8773	5	3	of	of	ADP
easat-8773	5	4	error	error	NOUN
easat-8773	5	5	in	in	ADP
easat-8773	5	6	mathematical	mathematical	ADJ
easat-8773	5	7	modeling	modeling	NOUN
easat-8773	5	8	problems	problem	NOUN
easat-8773	5	9	:	:	PUNCT
easat-8773	5	10	an	an	DET
easat-8773	5	11	exploratory	exploratory	ADJ
easat-8773	5	12	study	study	NOUN
easat-8773	5	13	of	of	ADP
easat-8773	5	14	middle	middle	ADJ
easat-8773	5	15	school	school	NOUN
easat-8773	5	16	students	student	NOUN
easat-8773	5	17	jeliana	jeliana	PROPN
easat-8773	5	18	intan	intan	PROPN
easat-8773	5	19	permata1	permata1	PROPN
easat-8773	5	20	,	,	PUNCT
easat-8773	5	21	mega	mega	ADJ
easat-8773	5	22	teguh	teguh	NOUN
easat-8773	5	23	budiarto2	budiarto2	PROPN
easat-8773	5	24	,	,	PUNCT
easat-8773	5	25	yusuf	yusuf	PROPN
easat-8773	5	26	fuad3	fuad3	PROPN
easat-8773	5	27	*	*	SYM
easat-8773	5	28	1doctoral	1doctoral	NUM
easat-8773	5	29	program	program	NOUN
easat-8773	5	30	of	of	ADP
easat-8773	5	31	mathematics	mathematic	NOUN
easat-8773	5	32	education	education	NOUN
easat-8773	5	33	,	,	PUNCT
easat-8773	5	34	universitas	universitas	PROPN
easat-8773	5	35	negeri	negeri	PROPN
easat-8773	5	36	surabaya	surabaya	PROPN
easat-8773	5	37	,	,	PUNCT
easat-8773	5	38	surabaya	surabaya	PROPN
easat-8773	5	39	,	,	PUNCT
easat-8773	5	40	indonesia	indonesia	PROPN
easat-8773	5	41	;	;	PUNCT
easat-8773	5	42	jeliana.20007@mhs.unesa.ac.id	jeliana.20007@mhs.unesa.ac.id	PROPN
easat-8773	5	43	(	(	PUNCT
easat-8773	5	44	j.i.p	j.i.p	PROPN
easat-8773	5	45	)	)	PUNCT
easat-8773	5	46	.	.	PUNCT
easat-8773	6	1	2,3department	2,3department	NUM
easat-8773	6	2	of	of	ADP
easat-8773	6	3	mathematics	mathematic	NOUN
easat-8773	6	4	education	education	NOUN
easat-8773	6	5	,	,	PUNCT
easat-8773	6	6	universitas	universitas	PROPN
easat-8773	6	7	negeri	negeri	PROPN
easat-8773	6	8	surabaya	surabaya	PROPN
easat-8773	6	9	,	,	PUNCT
easat-8773	6	10	surabaya	surabaya	PROPN
easat-8773	6	11	,	,	PUNCT
easat-8773	6	12	indonesia	indonesia	PROPN
easat-8773	6	13	;	;	PUNCT
easat-8773	6	14	megatbudiarto@unesa.ac.id	megatbudiarto@unesa.ac.id	NOUN
easat-8773	6	15	(	(	PUNCT
easat-8773	6	16	m.t.b	m.t.b	NOUN
easat-8773	6	17	.	.	PUNCT
easat-8773	6	18	)	)	PUNCT
easat-8773	7	1	yusuffuad@unesa.ac.id	yusuffuad@unesa.ac.id	PROPN
easat-8773	7	2	(	(	PUNCT
easat-8773	7	3	y.f	y.f	PROPN
easat-8773	7	4	)	)	PUNCT
easat-8773	7	5	.	.	PUNCT
easat-8773	8	1	abstract	abstract	ADJ
easat-8773	8	2	:	:	PUNCT
easat-8773	8	3	this	this	DET
easat-8773	8	4	study	study	NOUN
easat-8773	8	5	analyzes	analyze	VERB
easat-8773	8	6	students	student	NOUN
easat-8773	8	7	'	'	PART
easat-8773	8	8	errors	error	NOUN
easat-8773	8	9	in	in	ADP
easat-8773	8	10	solving	solve	VERB
easat-8773	8	11	mathematical	mathematical	ADJ
easat-8773	8	12	modeling	modeling	NOUN
easat-8773	8	13	problems	problem	NOUN
easat-8773	8	14	based	base	VERB
easat-8773	8	15	on	on	ADP
easat-8773	8	16	their	their	PRON
easat-8773	8	17	mathematical	mathematical	ADJ
easat-8773	8	18	ability	ability	NOUN
easat-8773	8	19	levels	level	NOUN
easat-8773	8	20	through	through	ADP
easat-8773	8	21	a	a	DET
easat-8773	8	22	quantitative	quantitative	ADJ
easat-8773	8	23	,	,	PUNCT
easat-8773	8	24	descriptive	descriptive	ADJ
easat-8773	8	25	,	,	PUNCT
easat-8773	8	26	and	and	CCONJ
easat-8773	8	27	exploratory	exploratory	ADJ
easat-8773	8	28	approach	approach	NOUN
easat-8773	8	29	.	.	PUNCT
easat-8773	9	1	it	it	PRON
easat-8773	9	2	involves	involve	VERB
easat-8773	9	3	72	72	NUM
easat-8773	9	4	eighth	eighth	ADJ
easat-8773	9	5	-	-	PUNCT
easat-8773	9	6	grade	grade	NOUN
easat-8773	9	7	students	student	NOUN
easat-8773	9	8	at	at	ADP
easat-8773	9	9	a	a	DET
easat-8773	9	10	private	private	ADJ
easat-8773	9	11	school	school	NOUN
easat-8773	9	12	,	,	PUNCT
easat-8773	9	13	smp	smp	PROPN
easat-8773	9	14	st	st	PROPN
easat-8773	9	15	.	.	PROPN
easat-8773	9	16	benediktus	benediktus	PROPN
easat-8773	9	17	.	.	PUNCT
easat-8773	10	1	the	the	DET
easat-8773	10	2	instruments	instrument	NOUN
easat-8773	10	3	used	use	VERB
easat-8773	10	4	are	be	AUX
easat-8773	10	5	the	the	DET
easat-8773	10	6	mathematical	mathematical	ADJ
easat-8773	10	7	competence	competence	NOUN
easat-8773	10	8	test	test	NOUN
easat-8773	10	9	(	(	PUNCT
easat-8773	10	10	mct	mct	PROPN
easat-8773	10	11	)	)	PUNCT
easat-8773	10	12	and	and	CCONJ
easat-8773	10	13	the	the	DET
easat-8773	10	14	mathematical	mathematical	ADJ
easat-8773	10	15	modeling	modeling	NOUN
easat-8773	10	16	test	test	NOUN
easat-8773	10	17	(	(	PUNCT
easat-8773	10	18	mmt	mmt	NOUN
easat-8773	10	19	)	)	PUNCT
easat-8773	10	20	.	.	PUNCT
easat-8773	11	1	both	both	DET
easat-8773	11	2	instruments	instrument	NOUN
easat-8773	11	3	were	be	AUX
easat-8773	11	4	validated	validate	VERB
easat-8773	11	5	by	by	ADP
easat-8773	11	6	three	three	NUM
easat-8773	11	7	associate	associate	ADJ
easat-8773	11	8	professors	professor	NOUN
easat-8773	11	9	and	and	CCONJ
easat-8773	11	10	one	one	NUM
easat-8773	11	11	mathematics	mathematic	NOUN
easat-8773	11	12	teacher	teacher	NOUN
easat-8773	11	13	,	,	PUNCT
easat-8773	11	14	with	with	ADP
easat-8773	11	15	validity	validity	NOUN
easat-8773	11	16	confirmed	confirm	VERB
easat-8773	11	17	by	by	ADP
easat-8773	11	18	v	v	PROPN
easat-8773	11	19	aiken	aiken	PROPN
easat-8773	11	20	’s	’s	PART
easat-8773	11	21	coefficient	coefficient	NOUN
easat-8773	11	22	of	of	ADP
easat-8773	11	23	0.83	0.83	NUM
easat-8773	11	24	,	,	PUNCT
easat-8773	11	25	exceeding	exceed	VERB
easat-8773	11	26	the	the	DET
easat-8773	11	27	threshold	threshold	NOUN
easat-8773	11	28	of	of	ADP
easat-8773	11	29	0.4	0.4	NUM
easat-8773	11	30	.	.	PUNCT
easat-8773	12	1	students	student	NOUN
easat-8773	12	2	completed	complete	VERB
easat-8773	12	3	the	the	DET
easat-8773	12	4	mct	mct	PROPN
easat-8773	12	5	and	and	CCONJ
easat-8773	12	6	mmt	mmt	PROPN
easat-8773	12	7	on	on	ADP
easat-8773	12	8	separate	separate	ADJ
easat-8773	12	9	days	day	NOUN
easat-8773	12	10	.	.	PUNCT
easat-8773	13	1	based	base	VERB
easat-8773	13	2	on	on	ADP
easat-8773	13	3	the	the	DET
easat-8773	13	4	results	result	NOUN
easat-8773	13	5	,	,	PUNCT
easat-8773	13	6	students	student	NOUN
easat-8773	13	7	were	be	AUX
easat-8773	13	8	classified	classify	VERB
easat-8773	13	9	as	as	ADP
easat-8773	13	10	high	high	ADJ
easat-8773	13	11	(	(	PUNCT
easat-8773	13	12	20	20	NUM
easat-8773	13	13	)	)	PUNCT
easat-8773	13	14	,	,	PUNCT
easat-8773	13	15	medium	medium	NOUN
easat-8773	13	16	(	(	PUNCT
easat-8773	13	17	19	19	NUM
easat-8773	13	18	)	)	PUNCT
easat-8773	13	19	,	,	PUNCT
easat-8773	13	20	and	and	CCONJ
easat-8773	13	21	low	low	ADJ
easat-8773	13	22	ability	ability	NOUN
easat-8773	13	23	(	(	PUNCT
easat-8773	13	24	33	33	NUM
easat-8773	13	25	)	)	PUNCT
easat-8773	13	26	.	.	PUNCT
easat-8773	14	1	mmt	mmt	PROPN
easat-8773	14	2	responses	response	NOUN
easat-8773	14	3	were	be	AUX
easat-8773	14	4	analyzed	analyze	VERB
easat-8773	14	5	using	use	VERB
easat-8773	14	6	newman	newman	PROPN
easat-8773	14	7	error	error	NOUN
easat-8773	14	8	analysis	analysis	NOUN
easat-8773	14	9	and	and	CCONJ
easat-8773	14	10	the	the	DET
easat-8773	14	11	six	six	NUM
easat-8773	14	12	modeling	modeling	NOUN
easat-8773	14	13	processes	process	NOUN
easat-8773	14	14	from	from	ADP
easat-8773	14	15	the	the	DET
easat-8773	14	16	blum	blum	ADJ
easat-8773	14	17	and	and	CCONJ
easat-8773	14	18	leiß	leiß	NOUN
easat-8773	14	19	framework	framework	NOUN
easat-8773	14	20	.	.	PUNCT
easat-8773	15	1	the	the	DET
easat-8773	15	2	results	result	NOUN
easat-8773	15	3	show	show	VERB
easat-8773	15	4	that	that	SCONJ
easat-8773	15	5	67	67	NUM
easat-8773	15	6	students	student	NOUN
easat-8773	15	7	made	make	VERB
easat-8773	15	8	errors	error	NOUN
easat-8773	15	9	across	across	ADP
easat-8773	15	10	various	various	ADJ
easat-8773	15	11	stages	stage	NOUN
easat-8773	15	12	,	,	PUNCT
easat-8773	15	13	mainly	mainly	ADV
easat-8773	15	14	in	in	ADP
easat-8773	15	15	validating	validate	VERB
easat-8773	15	16	(	(	PUNCT
easat-8773	15	17	47.56	47.56	NUM
easat-8773	15	18	%	%	NOUN
easat-8773	15	19	)	)	PUNCT
easat-8773	15	20	and	and	CCONJ
easat-8773	15	21	understanding	understanding	NOUN
easat-8773	15	22	(	(	PUNCT
easat-8773	15	23	31.59	31.59	NUM
easat-8773	15	24	%	%	NOUN
easat-8773	15	25	)	)	PUNCT
easat-8773	15	26	,	,	PUNCT
easat-8773	15	27	simplifying	simplify	VERB
easat-8773	15	28	(	(	PUNCT
easat-8773	15	29	37.84	37.84	NUM
easat-8773	15	30	%	%	NOUN
easat-8773	15	31	)	)	PUNCT
easat-8773	15	32	,	,	PUNCT
easat-8773	15	33	and	and	CCONJ
easat-8773	15	34	mathematizing	mathematize	VERB
easat-8773	15	35	(	(	PUNCT
easat-8773	15	36	39.58	39.58	NUM
easat-8773	15	37	%	%	NOUN
easat-8773	15	38	)	)	PUNCT
easat-8773	15	39	.	.	PUNCT
easat-8773	16	1	high	high	ADJ
easat-8773	16	2	-	-	PUNCT
easat-8773	16	3	ability	ability	NOUN
easat-8773	16	4	students	student	NOUN
easat-8773	16	5	often	often	ADV
easat-8773	16	6	made	make	VERB
easat-8773	16	7	errors	error	NOUN
easat-8773	16	8	in	in	ADP
easat-8773	16	9	interpreting	interpret	VERB
easat-8773	16	10	(	(	PUNCT
easat-8773	16	11	18	18	NUM
easat-8773	16	12	%	%	NOUN
easat-8773	16	13	)	)	PUNCT
easat-8773	16	14	and	and	CCONJ
easat-8773	16	15	validating	validate	VERB
easat-8773	16	16	(	(	PUNCT
easat-8773	16	17	25	25	NUM
easat-8773	16	18	%	%	NOUN
easat-8773	16	19	)	)	PUNCT
easat-8773	16	20	processes	process	NOUN
easat-8773	16	21	,	,	PUNCT
easat-8773	16	22	medium	medium	ADJ
easat-8773	16	23	-	-	PUNCT
easat-8773	16	24	ability	ability	NOUN
easat-8773	16	25	students	student	NOUN
easat-8773	16	26	in	in	ADP
easat-8773	16	27	working	work	VERB
easat-8773	16	28	mathematically	mathematically	ADV
easat-8773	16	29	(	(	PUNCT
easat-8773	16	30	25	25	NUM
easat-8773	16	31	%	%	NOUN
easat-8773	16	32	)	)	PUNCT
easat-8773	16	33	,	,	PUNCT
easat-8773	16	34	and	and	CCONJ
easat-8773	16	35	low	low	ADJ
easat-8773	16	36	-	-	PUNCT
easat-8773	16	37	ability	ability	NOUN
easat-8773	16	38	students	student	NOUN
easat-8773	16	39	in	in	ADP
easat-8773	16	40	understanding	understanding	NOUN
easat-8773	16	41	(	(	PUNCT
easat-8773	16	42	38.75	38.75	NUM
easat-8773	16	43	%	%	NOUN
easat-8773	16	44	)	)	PUNCT
easat-8773	16	45	.	.	PUNCT
easat-8773	17	1	these	these	DET
easat-8773	17	2	results	result	NOUN
easat-8773	17	3	suggest	suggest	VERB
easat-8773	17	4	that	that	SCONJ
easat-8773	17	5	error	error	NOUN
easat-8773	17	6	types	type	NOUN
easat-8773	17	7	are	be	AUX
easat-8773	17	8	closely	closely	ADV
easat-8773	17	9	related	relate	VERB
easat-8773	17	10	to	to	ADP
easat-8773	17	11	students	student	NOUN
easat-8773	17	12	'	'	PART
easat-8773	17	13	mathematical	mathematical	ADJ
easat-8773	17	14	abilities	ability	NOUN
easat-8773	17	15	.	.	PUNCT
easat-8773	18	1	further	further	ADJ
easat-8773	18	2	research	research	NOUN
easat-8773	18	3	should	should	AUX
easat-8773	18	4	focus	focus	VERB
easat-8773	18	5	on	on	ADP
easat-8773	18	6	aligning	align	VERB
easat-8773	18	7	instruction	instruction	NOUN
easat-8773	18	8	with	with	ADP
easat-8773	18	9	student	student	NOUN
easat-8773	18	10	abilities	ability	NOUN
easat-8773	18	11	,	,	PUNCT
easat-8773	18	12	supporting	support	VERB
easat-8773	18	13	adaptive	adaptive	ADJ
easat-8773	18	14	learning	learning	NOUN
easat-8773	18	15	,	,	PUNCT
easat-8773	18	16	and	and	CCONJ
easat-8773	18	17	exploring	explore	VERB
easat-8773	18	18	targeted	target	VERB
easat-8773	18	19	interventions	intervention	NOUN
easat-8773	18	20	to	to	PART
easat-8773	18	21	address	address	VERB
easat-8773	18	22	specific	specific	ADJ
easat-8773	18	23	errors	error	NOUN
easat-8773	18	24	in	in	ADP
easat-8773	18	25	the	the	DET
easat-8773	18	26	modeling	modeling	NOUN
easat-8773	18	27	process	process	NOUN
easat-8773	18	28	.	.	PUNCT
easat-8773	19	1	keywords	keyword	NOUN
easat-8773	19	2	:	:	PUNCT
easat-8773	19	3	error	error	NOUN
easat-8773	19	4	analysis	analysis	NOUN
easat-8773	19	5	,	,	PUNCT
easat-8773	19	6	mathematical	mathematical	ADJ
easat-8773	19	7	modeling	modeling	NOUN
easat-8773	19	8	ability	ability	NOUN
easat-8773	19	9	,	,	PUNCT
easat-8773	19	10	modeling	modeling	NOUN
easat-8773	19	11	process	process	NOUN
easat-8773	19	12	.	.	PUNCT
easat-8773	20	1	1	1	X
easat-8773	20	2	.	.	X
easat-8773	20	3	introduction	introduction	NOUN
easat-8773	20	4	mathematical	mathematical	ADJ
easat-8773	20	5	modeling	modeling	NOUN
easat-8773	20	6	plays	play	VERB
easat-8773	20	7	a	a	DET
easat-8773	20	8	vital	vital	ADJ
easat-8773	20	9	role	role	NOUN
easat-8773	20	10	in	in	ADP
easat-8773	20	11	developing	develop	VERB
easat-8773	20	12	students	student	NOUN
easat-8773	20	13	’	'	PUNCT
easat-8773	20	14	competence	competence	NOUN
easat-8773	20	15	to	to	PART
easat-8773	20	16	solve	solve	VERB
easat-8773	20	17	real	real	ADJ
easat-8773	20	18	-	-	PUNCT
easat-8773	20	19	world	world	NOUN
easat-8773	20	20	problem	problem	NOUN
easat-8773	20	21	in	in	ADP
easat-8773	20	22	mathematics	mathematic	NOUN
easat-8773	20	23	education	education	NOUN
easat-8773	20	24	.	.	PUNCT
easat-8773	21	1	with	with	ADP
easat-8773	21	2	the	the	DET
easat-8773	21	3	rapid	rapid	ADJ
easat-8773	21	4	advancement	advancement	NOUN
easat-8773	21	5	of	of	ADP
easat-8773	21	6	technology	technology	NOUN
easat-8773	21	7	and	and	CCONJ
easat-8773	21	8	science	science	NOUN
easat-8773	21	9	,	,	PUNCT
easat-8773	21	10	modeling	modeling	NOUN
easat-8773	21	11	is	be	AUX
easat-8773	21	12	increasingly	increasingly	ADV
easat-8773	21	13	recognized	recognize	VERB
easat-8773	21	14	as	as	ADP
easat-8773	21	15	a	a	DET
easat-8773	21	16	key	key	ADJ
easat-8773	21	17	competence	competence	NOUN
easat-8773	21	18	for	for	ADP
easat-8773	21	19	the	the	DET
easat-8773	21	20	future	future	NOUN
easat-8773	21	21	,	,	PUNCT
easat-8773	21	22	not	not	PART
easat-8773	21	23	only	only	ADV
easat-8773	21	24	fostering	foster	VERB
easat-8773	21	25	mathematical	mathematical	ADJ
easat-8773	21	26	literacy	literacy	NOUN
easat-8773	21	27	but	but	CCONJ
easat-8773	21	28	also	also	ADV
easat-8773	21	29	enhancing	enhance	VERB
easat-8773	21	30	society	society	NOUN
easat-8773	21	31	’s	’s	PART
easat-8773	21	32	ability	ability	NOUN
easat-8773	21	33	to	to	PART
easat-8773	21	34	adapt	adapt	VERB
easat-8773	21	35	to	to	ADP
easat-8773	21	36	shifting	shift	VERB
easat-8773	21	37	conditions	condition	NOUN
easat-8773	22	1	[	[	X
easat-8773	22	2	1	1	NUM
easat-8773	22	3	]	]	PUNCT
easat-8773	22	4	.	.	PUNCT
easat-8773	23	1	as	as	SCONJ
easat-8773	23	2	such	such	ADJ
easat-8773	23	3	modeling	modeling	NOUN
easat-8773	23	4	serves	serve	VERB
easat-8773	23	5	a	a	DET
easat-8773	23	6	critical	critical	ADJ
easat-8773	23	7	bridge	bridge	NOUN
easat-8773	23	8	between	between	ADP
easat-8773	23	9	real	real	ADJ
easat-8773	23	10	-	-	PUNCT
easat-8773	23	11	life	life	NOUN
easat-8773	23	12	scenarios	scenario	NOUN
easat-8773	23	13	and	and	CCONJ
easat-8773	23	14	abstract	abstract	ADJ
easat-8773	23	15	mathematical	mathematical	ADJ
easat-8773	23	16	representations	representation	NOUN
easat-8773	23	17	,	,	PUNCT
easat-8773	23	18	providing	provide	VERB
easat-8773	23	19	students	student	NOUN
easat-8773	23	20	with	with	ADP
easat-8773	23	21	the	the	DET
easat-8773	23	22	opportunity	opportunity	NOUN
easat-8773	23	23	to	to	PART
easat-8773	23	24	apply	apply	VERB
easat-8773	23	25	mathematical	mathematical	ADJ
easat-8773	23	26	tools	tool	NOUN
easat-8773	23	27	to	to	PART
easat-8773	23	28	problem	problem	NOUN
easat-8773	23	29	encountered	encounter	VERB
easat-8773	23	30	in	in	ADP
easat-8773	23	31	daily	daily	ADJ
easat-8773	23	32	life	life	NOUN
easat-8773	23	33	,	,	PUNCT
easat-8773	23	34	community	community	NOUN
easat-8773	23	35	settings	setting	NOUN
easat-8773	23	36	,	,	PUNCT
easat-8773	23	37	and	and	CCONJ
easat-8773	23	38	professional	professional	ADJ
easat-8773	23	39	contexts	context	NOUN
easat-8773	23	40	[	[	X
easat-8773	23	41	2	2	NUM
easat-8773	23	42	]	]	PUNCT
easat-8773	23	43	.	.	PUNCT
easat-8773	24	1	in	in	ADP
easat-8773	24	2	instructional	instructional	ADJ
easat-8773	24	3	practice	practice	NOUN
easat-8773	24	4	,	,	PUNCT
easat-8773	24	5	mathematical	mathematical	ADJ
easat-8773	24	6	modeling	modeling	NOUN
easat-8773	24	7	supports	support	VERB
easat-8773	24	8	the	the	DET
easat-8773	24	9	development	development	NOUN
easat-8773	24	10	of	of	ADP
easat-8773	24	11	abstract	abstract	ADJ
easat-8773	24	12	thinking	thinking	NOUN
easat-8773	24	13	through	through	ADP
easat-8773	24	14	contextual	contextual	ADJ
easat-8773	24	15	and	and	CCONJ
easat-8773	24	16	applicable	applicable	ADJ
easat-8773	24	17	approaches	approach	NOUN
easat-8773	24	18	[	[	X
easat-8773	24	19	3	3	NUM
easat-8773	24	20	]	]	PUNCT
easat-8773	24	21	.	.	PUNCT
easat-8773	25	1	this	this	DET
easat-8773	25	2	multifaceted	multifaceted	ADJ
easat-8773	25	3	process	process	NOUN
easat-8773	25	4	includes	include	VERB
easat-8773	25	5	identifying	identify	VERB
easat-8773	25	6	the	the	DET
easat-8773	25	7	real	real	ADJ
easat-8773	25	8	-	-	PUNCT
easat-8773	25	9	world	world	NOUN
easat-8773	25	10	problem	problem	NOUN
easat-8773	25	11	,	,	PUNCT
easat-8773	25	12	selecting	select	VERB
easat-8773	25	13	relevant	relevant	ADJ
easat-8773	25	14	variables	variable	NOUN
easat-8773	25	15	and	and	CCONJ
easat-8773	25	16	parameters	parameter	NOUN
easat-8773	25	17	,	,	PUNCT
easat-8773	25	18	mathematizing	mathematizing	NOUN
easat-8773	25	19	situations	situation	NOUN
easat-8773	25	20	,	,	PUNCT
easat-8773	25	21	and	and	CCONJ
easat-8773	25	22	validating	validate	VERB
easat-8773	25	23	the	the	DET
easat-8773	25	24	resulting	result	VERB
easat-8773	25	25	models	model	NOUN
easat-8773	25	26	[	[	X
easat-8773	25	27	4	4	NUM
easat-8773	25	28	]	]	PUNCT
easat-8773	25	29	.	.	PUNCT
easat-8773	26	1	however	however	ADV
easat-8773	26	2	,	,	PUNCT
easat-8773	26	3	each	each	PRON
easat-8773	26	4	of	of	ADP
easat-8773	26	5	these	these	DET
easat-8773	26	6	stages	stage	NOUN
easat-8773	26	7	presents	present	VERB
easat-8773	26	8	potential	potential	ADJ
easat-8773	26	9	cognitive	cognitive	ADJ
easat-8773	26	10	demands	demand	NOUN
easat-8773	26	11	,	,	PUNCT
easat-8773	26	12	especially	especially	ADV
easat-8773	26	13	as	as	SCONJ
easat-8773	26	14	students	student	NOUN
easat-8773	26	15	must	must	AUX
easat-8773	26	16	not	not	PART
easat-8773	26	17	only	only	ADV
easat-8773	26	18	master	master	VERB
easat-8773	26	19	mathematical	mathematical	ADJ
easat-8773	26	20	concepts	concept	NOUN
easat-8773	26	21	but	but	CCONJ
easat-8773	26	22	also	also	ADV
easat-8773	26	23	transfer	transfer	VERB
easat-8773	26	24	them	they	PRON
easat-8773	26	25	across	across	ADP
easat-8773	26	26	representations	representation	NOUN
easat-8773	26	27	and	and	CCONJ
easat-8773	26	28	contextual	contextual	ADJ
easat-8773	26	29	boundaries	boundary	NOUN
easat-8773	26	30	[	[	X
easat-8773	26	31	5	5	NUM
easat-8773	26	32	,	,	PUNCT
easat-8773	26	33	6	6	NUM
easat-8773	26	34	]	]	PUNCT
easat-8773	26	35	.	.	PUNCT
easat-8773	27	1	students	student	NOUN
easat-8773	27	2	’	'	PUNCT
easat-8773	27	3	ability	ability	NOUN
easat-8773	27	4	to	to	PART
easat-8773	27	5	carry	carry	VERB
easat-8773	27	6	out	out	ADP
easat-8773	27	7	the	the	DET
easat-8773	27	8	modeling	modeling	NOUN
easat-8773	27	9	process	process	NOUN
easat-8773	27	10	is	be	AUX
easat-8773	27	11	influenced	influence	VERB
easat-8773	27	12	by	by	ADP
easat-8773	27	13	their	their	PRON
easat-8773	27	14	level	level	NOUN
easat-8773	27	15	of	of	ADP
easat-8773	27	16	mathematical	mathematical	ADJ
easat-8773	27	17	competence	competence	NOUN
easat-8773	27	18	,	,	PUNCT
easat-8773	27	19	which	which	PRON
easat-8773	27	20	determines	determine	VERB
easat-8773	27	21	how	how	SCONJ
easat-8773	27	22	effectively	effectively	ADV
easat-8773	27	23	they	they	PRON
easat-8773	27	24	can	can	AUX
easat-8773	27	25	navigate	navigate	VERB
easat-8773	27	26	each	each	DET
easat-8773	27	27	stage	stage	NOUN
easat-8773	27	28	from	from	ADP
easat-8773	27	29	understanding	understand	VERB
easat-8773	27	30	the	the	DET
easat-8773	27	31	https://orcid.org/0009-0000-2878-1265	https://orcid.org/0009-0000-2878-1265	PROPN
easat-8773	27	32	https://orcid.org/0000-0002-9052-3141	https://orcid.org/0000-0002-9052-3141	NOUN
easat-8773	27	33	https://orcid.org/0000-0002-9589-7839	https://orcid.org/0000-0002-9589-7839	PROPN
easat-8773	27	34	948	948	NUM
easat-8773	27	35	edelweiss	edelweiss	PROPN
easat-8773	27	36	applied	apply	VERB
easat-8773	27	37	science	science	NOUN
easat-8773	27	38	and	and	CCONJ
easat-8773	27	39	technology	technology	NOUN
easat-8773	27	40	issn	issn	PROPN
easat-8773	27	41	:	:	PUNCT
easat-8773	27	42	2576	2576	NUM
easat-8773	27	43	-	-	SYM
easat-8773	27	44	8484	8484	NUM
easat-8773	27	45	vol	vol	NOUN
easat-8773	27	46	.	.	PROPN
easat-8773	28	1	9	9	NUM
easat-8773	28	2	,	,	PUNCT
easat-8773	28	3	no	no	INTJ
easat-8773	28	4	.	.	NOUN
easat-8773	29	1	7	7	NUM
easat-8773	29	2	:	:	SYM
easat-8773	29	3	947	947	NUM
easat-8773	29	4	-	-	SYM
easat-8773	29	5	959	959	NUM
easat-8773	29	6	,	,	PUNCT
easat-8773	29	7	2025	2025	NUM
easat-8773	29	8	doi	doi	NOUN
easat-8773	29	9	:	:	PUNCT
easat-8773	29	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	29	11	©	©	PROPN
easat-8773	29	12	2025	2025	NUM
easat-8773	29	13	by	by	ADP
easat-8773	29	14	the	the	DET
easat-8773	29	15	authors	author	NOUN
easat-8773	29	16	;	;	PUNCT
easat-8773	29	17	licensee	licensee	PROPN
easat-8773	29	18	learning	learn	VERB
easat-8773	29	19	gate	gate	PROPN
easat-8773	29	20	problem	problem	NOUN
easat-8773	29	21	to	to	ADP
easat-8773	29	22	validating	validate	VERB
easat-8773	29	23	the	the	DET
easat-8773	29	24	solution	solution	NOUN
easat-8773	29	25	[	[	X
easat-8773	29	26	7	7	NUM
easat-8773	29	27	,	,	PUNCT
easat-8773	29	28	8	8	NUM
easat-8773	29	29	]	]	PUNCT
easat-8773	29	30	.	.	PUNCT
easat-8773	30	1	prior	prior	ADJ
easat-8773	30	2	studies	study	NOUN
easat-8773	30	3	have	have	AUX
easat-8773	30	4	shown	show	VERB
easat-8773	30	5	that	that	SCONJ
easat-8773	30	6	modeling	modeling	NOUN
easat-8773	30	7	tasks	task	NOUN
easat-8773	30	8	often	often	ADV
easat-8773	30	9	require	require	VERB
easat-8773	30	10	a	a	DET
easat-8773	30	11	high	high	ADJ
easat-8773	30	12	degree	degree	NOUN
easat-8773	30	13	of	of	ADP
easat-8773	30	14	metacognition	metacognition	NOUN
easat-8773	30	15	and	and	CCONJ
easat-8773	30	16	situational	situational	ADJ
easat-8773	30	17	understanding	understanding	NOUN
easat-8773	30	18	[	[	X
easat-8773	30	19	9	9	NUM
easat-8773	30	20	]	]	PUNCT
easat-8773	30	21	and	and	CCONJ
easat-8773	30	22	students	student	NOUN
easat-8773	30	23	commonly	commonly	ADV
easat-8773	30	24	experience	experience	VERB
easat-8773	30	25	or	or	CCONJ
easat-8773	30	26	reading	reading	NOUN
easat-8773	30	27	comprehension	comprehension	NOUN
easat-8773	30	28	skills	skill	NOUN
easat-8773	30	29	[	[	X
easat-8773	30	30	10	10	NUM
easat-8773	30	31	,	,	PUNCT
easat-8773	30	32	11	11	NUM
easat-8773	30	33	]	]	PUNCT
easat-8773	30	34	.	.	PUNCT
easat-8773	31	1	building	build	VERB
easat-8773	31	2	on	on	ADP
easat-8773	31	3	this	this	DET
easat-8773	31	4	foundation	foundation	NOUN
easat-8773	31	5	,	,	PUNCT
easat-8773	31	6	the	the	DET
easat-8773	31	7	present	present	ADJ
easat-8773	31	8	study	study	NOUN
easat-8773	31	9	aims	aim	VERB
easat-8773	31	10	to	to	PART
easat-8773	31	11	analyze	analyze	VERB
easat-8773	31	12	the	the	DET
easat-8773	31	13	types	type	NOUN
easat-8773	31	14	and	and	CCONJ
easat-8773	31	15	tendencies	tendency	NOUN
easat-8773	31	16	of	of	ADP
easat-8773	31	17	student	student	NOUN
easat-8773	31	18	errors	error	NOUN
easat-8773	31	19	across	across	ADP
easat-8773	31	20	each	each	DET
easat-8773	31	21	stage	stage	NOUN
easat-8773	31	22	of	of	ADP
easat-8773	31	23	modeling	model	VERB
easat-8773	31	24	cycle	cycle	NOUN
easat-8773	31	25	,	,	PUNCT
easat-8773	31	26	while	while	SCONJ
easat-8773	31	27	also	also	ADV
easat-8773	31	28	investigating	investigate	VERB
easat-8773	31	29	how	how	SCONJ
easat-8773	31	30	these	these	DET
easat-8773	31	31	errors	error	NOUN
easat-8773	31	32	vary	vary	VERB
easat-8773	31	33	by	by	ADP
easat-8773	31	34	students	student	NOUN
easat-8773	31	35	’	'	PUNCT
easat-8773	31	36	mathematical	mathematical	ADJ
easat-8773	31	37	ability	ability	NOUN
easat-8773	31	38	levels	level	NOUN
easat-8773	31	39	.	.	PUNCT
easat-8773	32	1	understanding	understand	VERB
easat-8773	32	2	these	these	DET
easat-8773	32	3	patterns	pattern	NOUN
easat-8773	32	4	is	be	AUX
easat-8773	32	5	essential	essential	ADJ
easat-8773	32	6	for	for	ADP
easat-8773	32	7	designing	design	VERB
easat-8773	32	8	instructional	instructional	ADJ
easat-8773	32	9	support	support	NOUN
easat-8773	32	10	that	that	PRON
easat-8773	32	11	targets	target	VERB
easat-8773	32	12	cognitive	cognitive	ADJ
easat-8773	32	13	barriers	barrier	NOUN
easat-8773	32	14	at	at	ADP
easat-8773	32	15	each	each	DET
easat-8773	32	16	stage	stage	NOUN
easat-8773	32	17	of	of	ADP
easat-8773	32	18	the	the	DET
easat-8773	32	19	modeling	modeling	NOUN
easat-8773	32	20	process	process	NOUN
easat-8773	32	21	.	.	PUNCT
easat-8773	33	1	2	2	X
easat-8773	33	2	.	.	X
easat-8773	33	3	literature	literature	NOUN
easat-8773	33	4	review	review	VERB
easat-8773	33	5	2.1	2.1	NUM
easat-8773	33	6	.	.	PUNCT
easat-8773	34	1	mathematical	mathematical	ADJ
easat-8773	34	2	modeling	modeling	NOUN
easat-8773	34	3	models	model	NOUN
easat-8773	34	4	in	in	ADP
easat-8773	34	5	a	a	DET
easat-8773	34	6	problem	problem	NOUN
easat-8773	34	7	are	be	AUX
easat-8773	34	8	created	create	VERB
easat-8773	34	9	after	after	SCONJ
easat-8773	34	10	the	the	DET
easat-8773	34	11	problem	problem	NOUN
easat-8773	34	12	is	be	AUX
easat-8773	34	13	studied	study	VERB
easat-8773	34	14	to	to	PART
easat-8773	34	15	represent	represent	VERB
easat-8773	34	16	the	the	DET
easat-8773	34	17	problem	problem	NOUN
easat-8773	34	18	.	.	PUNCT
easat-8773	35	1	mathematical	mathematical	ADJ
easat-8773	35	2	models	model	NOUN
easat-8773	35	3	are	be	AUX
easat-8773	35	4	built	build	VERB
easat-8773	35	5	through	through	ADP
easat-8773	35	6	adjustment	adjustment	NOUN
easat-8773	35	7	,	,	PUNCT
easat-8773	35	8	determination	determination	NOUN
easat-8773	35	9	and	and	CCONJ
easat-8773	35	10	mathematization	mathematization	NOUN
easat-8773	35	11	of	of	ADP
easat-8773	35	12	the	the	DET
easat-8773	35	13	real	real	ADJ
easat-8773	35	14	situation	situation	NOUN
easat-8773	35	15	of	of	ADP
easat-8773	35	16	a	a	DET
easat-8773	35	17	problem	problem	NOUN
easat-8773	35	18	[	[	X
easat-8773	35	19	4	4	NUM
easat-8773	35	20	]	]	PUNCT
easat-8773	35	21	.	.	PUNCT
easat-8773	36	1	in	in	ADP
easat-8773	36	2	modeling	modeling	NOUN
easat-8773	36	3	,	,	PUNCT
easat-8773	36	4	it	it	PRON
easat-8773	36	5	is	be	AUX
easat-8773	36	6	necessary	necessary	ADJ
easat-8773	36	7	to	to	PART
easat-8773	36	8	be	be	AUX
easat-8773	36	9	precise	precise	ADJ
easat-8773	36	10	in	in	ADP
easat-8773	36	11	choosing	choose	VERB
easat-8773	36	12	things	thing	NOUN
easat-8773	36	13	that	that	PRON
easat-8773	36	14	are	be	AUX
easat-8773	36	15	set	set	VERB
easat-8773	36	16	aside	aside	ADV
easat-8773	36	17	and	and	CCONJ
easat-8773	36	18	things	thing	NOUN
easat-8773	36	19	that	that	PRON
easat-8773	36	20	need	need	VERB
easat-8773	36	21	to	to	PART
easat-8773	36	22	be	be	AUX
easat-8773	36	23	included	include	VERB
easat-8773	36	24	in	in	ADP
easat-8773	36	25	the	the	DET
easat-8773	36	26	mathematical	mathematical	ADJ
easat-8773	36	27	model	model	NOUN
easat-8773	36	28	.	.	PUNCT
easat-8773	37	1	the	the	DET
easat-8773	37	2	important	important	ADJ
easat-8773	37	3	components	component	NOUN
easat-8773	37	4	of	of	ADP
easat-8773	37	5	mathematics	mathematic	NOUN
easat-8773	37	6	are	be	AUX
easat-8773	37	7	mathematical	mathematical	ADJ
easat-8773	37	8	modeling	modeling	NOUN
easat-8773	37	9	and	and	CCONJ
easat-8773	37	10	its	its	PRON
easat-8773	37	11	applications	application	NOUN
easat-8773	37	12	that	that	PRON
easat-8773	37	13	can	can	AUX
easat-8773	37	14	encourage	encourage	VERB
easat-8773	37	15	students	student	NOUN
easat-8773	37	16	'	'	PART
easat-8773	37	17	competence	competence	NOUN
easat-8773	37	18	in	in	ADP
easat-8773	37	19	solving	solve	VERB
easat-8773	37	20	real	real	ADJ
easat-8773	37	21	problems	problem	NOUN
easat-8773	37	22	in	in	ADP
easat-8773	37	23	mathematics	mathematics	NOUN
easat-8773	37	24	education	education	NOUN
easat-8773	37	25	[	[	X
easat-8773	37	26	11	11	NUM
easat-8773	37	27	,	,	PUNCT
easat-8773	37	28	12	12	NUM
easat-8773	37	29	]	]	PUNCT
easat-8773	37	30	.	.	PUNCT
easat-8773	38	1	this	this	DET
easat-8773	38	2	activity	activity	NOUN
easat-8773	38	3	requires	require	VERB
easat-8773	38	4	not	not	PART
easat-8773	38	5	only	only	ADV
easat-8773	38	6	mastery	mastery	NOUN
easat-8773	38	7	of	of	ADP
easat-8773	38	8	mathematical	mathematical	ADJ
easat-8773	38	9	concepts	concept	NOUN
easat-8773	38	10	and	and	CCONJ
easat-8773	38	11	procedures	procedure	NOUN
easat-8773	38	12	,	,	PUNCT
easat-8773	38	13	but	but	CCONJ
easat-8773	38	14	also	also	ADV
easat-8773	38	15	skills	skill	VERB
easat-8773	38	16	in	in	ADP
easat-8773	38	17	critical	critical	ADJ
easat-8773	38	18	thinking	thinking	NOUN
easat-8773	38	19	,	,	PUNCT
easat-8773	38	20	choosing	choose	VERB
easat-8773	38	21	appropriate	appropriate	ADJ
easat-8773	38	22	representations	representation	NOUN
easat-8773	38	23	,	,	PUNCT
easat-8773	38	24	and	and	CCONJ
easat-8773	38	25	evaluating	evaluate	VERB
easat-8773	38	26	solutions	solution	NOUN
easat-8773	38	27	reflectively	reflectively	ADV
easat-8773	38	28	[	[	X
easat-8773	38	29	13	13	NUM
easat-8773	38	30	,	,	PUNCT
easat-8773	38	31	14	14	NUM
easat-8773	38	32	]	]	PUNCT
easat-8773	38	33	.	.	PUNCT
easat-8773	39	1	mathematical	mathematical	ADJ
easat-8773	39	2	modeling	modeling	NOUN
easat-8773	39	3	is	be	AUX
easat-8773	39	4	defined	define	VERB
easat-8773	39	5	as	as	ADP
easat-8773	39	6	the	the	DET
easat-8773	39	7	process	process	NOUN
easat-8773	39	8	of	of	ADP
easat-8773	39	9	translating	translate	VERB
easat-8773	39	10	real	real	ADJ
easat-8773	39	11	-	-	PUNCT
easat-8773	39	12	world	world	NOUN
easat-8773	39	13	problems	problem	NOUN
easat-8773	39	14	into	into	ADP
easat-8773	39	15	mathematical	mathematical	ADJ
easat-8773	39	16	terms	term	NOUN
easat-8773	39	17	and	and	CCONJ
easat-8773	39	18	developing	develop	VERB
easat-8773	39	19	appropriate	appropriate	ADJ
easat-8773	39	20	mathematical	mathematical	ADJ
easat-8773	39	21	strategies	strategy	NOUN
easat-8773	39	22	to	to	PART
easat-8773	39	23	solve	solve	VERB
easat-8773	39	24	the	the	DET
easat-8773	39	25	problem	problem	NOUN
easat-8773	39	26	[	[	X
easat-8773	39	27	5	5	NUM
easat-8773	39	28	,	,	PUNCT
easat-8773	39	29	15	15	NUM
easat-8773	39	30	]	]	PUNCT
easat-8773	39	31	.	.	PUNCT
easat-8773	40	1	as	as	ADP
easat-8773	40	2	an	an	DET
easat-8773	40	3	essential	essential	ADJ
easat-8773	40	4	component	component	NOUN
easat-8773	40	5	of	of	ADP
easat-8773	40	6	mathematics	mathematic	NOUN
easat-8773	40	7	education	education	NOUN
easat-8773	40	8	,	,	PUNCT
easat-8773	40	9	modeling	modeling	NOUN
easat-8773	40	10	allows	allow	VERB
easat-8773	40	11	students	student	NOUN
easat-8773	40	12	to	to	PART
easat-8773	40	13	apply	apply	VERB
easat-8773	40	14	their	their	PRON
easat-8773	40	15	mathematical	mathematical	ADJ
easat-8773	40	16	knowledge	knowledge	NOUN
easat-8773	40	17	to	to	ADP
easat-8773	40	18	realistic	realistic	ADJ
easat-8773	40	19	and	and	CCONJ
easat-8773	40	20	complex	complex	ADJ
easat-8773	40	21	contexts	context	NOUN
easat-8773	40	22	,	,	PUNCT
easat-8773	40	23	whether	whether	SCONJ
easat-8773	40	24	from	from	ADP
easat-8773	40	25	daily	daily	ADJ
easat-8773	40	26	life	life	NOUN
easat-8773	40	27	,	,	PUNCT
easat-8773	40	28	social	social	ADJ
easat-8773	40	29	issues	issue	NOUN
easat-8773	40	30	,	,	PUNCT
easat-8773	40	31	or	or	CCONJ
easat-8773	40	32	the	the	DET
easat-8773	40	33	workplace	workplace	NOUN
easat-8773	40	34	[	[	X
easat-8773	40	35	2	2	NUM
easat-8773	40	36	,	,	PUNCT
easat-8773	40	37	16	16	NUM
easat-8773	40	38	]	]	PUNCT
easat-8773	40	39	.	.	PUNCT
easat-8773	41	1	this	this	DET
easat-8773	41	2	process	process	NOUN
easat-8773	41	3	demands	demand	VERB
easat-8773	41	4	not	not	PART
easat-8773	41	5	only	only	ADV
easat-8773	41	6	conceptual	conceptual	ADJ
easat-8773	41	7	and	and	CCONJ
easat-8773	41	8	procedural	procedural	ADJ
easat-8773	41	9	knowledge	knowledge	NOUN
easat-8773	41	10	,	,	PUNCT
easat-8773	41	11	but	but	CCONJ
easat-8773	41	12	also	also	ADV
easat-8773	41	13	metacognitive	metacognitive	ADJ
easat-8773	41	14	and	and	CCONJ
easat-8773	41	15	contextual	contextual	ADJ
easat-8773	41	16	awareness	awareness	NOUN
easat-8773	41	17	,	,	PUNCT
easat-8773	41	18	especially	especially	ADV
easat-8773	41	19	when	when	SCONJ
easat-8773	41	20	transitioning	transition	VERB
easat-8773	41	21	between	between	ADP
easat-8773	41	22	real	real	ADJ
easat-8773	41	23	contexts	context	NOUN
easat-8773	41	24	and	and	CCONJ
easat-8773	41	25	mathematical	mathematical	ADJ
easat-8773	41	26	abstraction	abstraction	NOUN
easat-8773	41	27	[	[	X
easat-8773	41	28	6	6	NUM
easat-8773	41	29	,	,	PUNCT
easat-8773	41	30	17	17	NUM
easat-8773	41	31	]	]	PUNCT
easat-8773	41	32	.	.	PUNCT
easat-8773	42	1	study	study	NOUN
easat-8773	42	2	has	have	AUX
easat-8773	42	3	highlighted	highlight	VERB
easat-8773	42	4	that	that	SCONJ
easat-8773	42	5	each	each	DET
easat-8773	42	6	stage	stage	NOUN
easat-8773	42	7	in	in	ADP
easat-8773	42	8	modeling	model	VERB
easat-8773	42	9	process	process	NOUN
easat-8773	42	10	presents	present	VERB
easat-8773	42	11	unique	unique	ADJ
easat-8773	42	12	cognitive	cognitive	ADJ
easat-8773	42	13	challenges	challenge	NOUN
easat-8773	42	14	,	,	PUNCT
easat-8773	42	15	which	which	PRON
easat-8773	42	16	can	can	AUX
easat-8773	42	17	result	result	VERB
easat-8773	42	18	in	in	ADP
easat-8773	42	19	a	a	DET
easat-8773	42	20	variety	variety	NOUN
easat-8773	42	21	of	of	ADP
easat-8773	42	22	student	student	NOUN
easat-8773	42	23	errors	error	NOUN
easat-8773	42	24	depending	depend	VERB
easat-8773	42	25	on	on	ADP
easat-8773	42	26	their	their	PRON
easat-8773	42	27	level	level	NOUN
easat-8773	42	28	of	of	ADP
easat-8773	42	29	mathematical	mathematical	ADJ
easat-8773	42	30	competence	competence	NOUN
easat-8773	42	31	[	[	X
easat-8773	42	32	7	7	NUM
easat-8773	42	33	,	,	PUNCT
easat-8773	42	34	8	8	NUM
easat-8773	42	35	]	]	PUNCT
easat-8773	42	36	.	.	PUNCT
easat-8773	43	1	unlike	unlike	ADP
easat-8773	43	2	traditional	traditional	ADJ
easat-8773	43	3	problem	problem	NOUN
easat-8773	43	4	solving	solving	NOUN
easat-8773	43	5	,	,	PUNCT
easat-8773	43	6	modeling	modeling	NOUN
easat-8773	43	7	requires	require	VERB
easat-8773	43	8	students	student	NOUN
easat-8773	43	9	to	to	PART
easat-8773	43	10	navigate	navigate	VERB
easat-8773	43	11	a	a	DET
easat-8773	43	12	cycle	cycle	NOUN
easat-8773	43	13	of	of	ADP
easat-8773	43	14	steps	step	NOUN
easat-8773	43	15	involving	involve	VERB
easat-8773	43	16	understanding	understand	VERB
easat-8773	43	17	the	the	DET
easat-8773	43	18	situation	situation	NOUN
easat-8773	43	19	,	,	PUNCT
easat-8773	43	20	simplifying	simplify	VERB
easat-8773	43	21	the	the	DET
easat-8773	43	22	problem	problem	NOUN
easat-8773	43	23	,	,	PUNCT
easat-8773	43	24	mathematizing	mathematize	VERB
easat-8773	43	25	,	,	PUNCT
easat-8773	43	26	working	work	VERB
easat-8773	43	27	mathematically	mathematically	ADV
easat-8773	43	28	,	,	PUNCT
easat-8773	43	29	interpreting	interpret	VERB
easat-8773	43	30	results	result	NOUN
easat-8773	43	31	,	,	PUNCT
easat-8773	43	32	and	and	CCONJ
easat-8773	43	33	validating	validate	VERB
easat-8773	43	34	the	the	DET
easat-8773	43	35	solution	solution	NOUN
easat-8773	43	36	,	,	PUNCT
easat-8773	43	37	the	the	DET
easat-8773	43	38	ability	ability	NOUN
easat-8773	43	39	to	to	PART
easat-8773	43	40	mathematize	mathematize	VERB
easat-8773	43	41	real	real	ADJ
easat-8773	43	42	situations	situation	NOUN
easat-8773	43	43	,	,	PUNCT
easat-8773	43	44	in	in	ADP
easat-8773	43	45	particular	particular	ADJ
easat-8773	43	46	,	,	PUNCT
easat-8773	43	47	is	be	AUX
easat-8773	43	48	noted	note	VERB
easat-8773	43	49	as	as	ADP
easat-8773	43	50	one	one	NUM
easat-8773	43	51	of	of	ADP
easat-8773	43	52	the	the	DET
easat-8773	43	53	most	most	ADV
easat-8773	43	54	demanding	demanding	ADJ
easat-8773	43	55	and	and	CCONJ
easat-8773	43	56	error	error	NOUN
easat-8773	43	57	-	-	PUNCT
easat-8773	43	58	prone	prone	ADJ
easat-8773	43	59	stages	stage	NOUN
easat-8773	43	60	[	[	X
easat-8773	43	61	14	14	NUM
easat-8773	43	62	]	]	PUNCT
easat-8773	43	63	.	.	PUNCT
easat-8773	44	1	therefore	therefore	ADV
easat-8773	44	2	,	,	PUNCT
easat-8773	44	3	understanding	understand	VERB
easat-8773	44	4	the	the	DET
easat-8773	44	5	type	type	NOUN
easat-8773	44	6	and	and	CCONJ
easat-8773	44	7	frequency	frequency	NOUN
easat-8773	44	8	errors	error	NOUN
easat-8773	44	9	across	across	ADP
easat-8773	44	10	stages	stage	NOUN
easat-8773	44	11	and	and	CCONJ
easat-8773	44	12	among	among	ADP
easat-8773	44	13	students	student	NOUN
easat-8773	44	14	of	of	ADP
easat-8773	44	15	differing	differ	VERB
easat-8773	44	16	ability	ability	NOUN
easat-8773	44	17	levels	level	NOUN
easat-8773	44	18	is	be	AUX
easat-8773	44	19	critical	critical	ADJ
easat-8773	44	20	for	for	ADP
easat-8773	44	21	designing	design	VERB
easat-8773	44	22	effective	effective	ADJ
easat-8773	44	23	interventions	intervention	NOUN
easat-8773	44	24	and	and	CCONJ
easat-8773	44	25	instructional	instructional	ADJ
easat-8773	44	26	scaffolds	scaffold	NOUN
easat-8773	44	27	.	.	PUNCT
easat-8773	45	1	2.2	2.2	NUM
easat-8773	45	2	.	.	PUNCT
easat-8773	45	3	modelling	model	VERB
easat-8773	45	4	competence	competence	NOUN
easat-8773	45	5	and	and	CCONJ
easat-8773	45	6	modeling	model	VERB
easat-8773	45	7	cycle	cycle	NOUN
easat-8773	45	8	modeling	modeling	NOUN
easat-8773	45	9	ability	ability	NOUN
easat-8773	45	10	includes	include	VERB
easat-8773	45	11	aspects	aspect	NOUN
easat-8773	45	12	of	of	ADP
easat-8773	45	13	mathematical	mathematical	ADJ
easat-8773	45	14	knowledge	knowledge	NOUN
easat-8773	45	15	and	and	CCONJ
easat-8773	45	16	skills	skill	NOUN
easat-8773	45	17	,	,	PUNCT
easat-8773	45	18	as	as	ADV
easat-8773	45	19	well	well	ADV
easat-8773	45	20	as	as	ADP
easat-8773	45	21	the	the	DET
easat-8773	45	22	willingness	willingness	NOUN
easat-8773	45	23	to	to	PART
easat-8773	45	24	carry	carry	VERB
easat-8773	45	25	out	out	ADP
easat-8773	45	26	the	the	DET
easat-8773	45	27	modeling	modeling	NOUN
easat-8773	45	28	process	process	NOUN
easat-8773	45	29	appropriately	appropriately	ADV
easat-8773	45	30	and	and	CCONJ
easat-8773	45	31	goal	goal	NOUN
easat-8773	45	32	-	-	PUNCT
easat-8773	45	33	oriented	orient	VERB
easat-8773	45	34	and	and	CCONJ
easat-8773	45	35	the	the	DET
easat-8773	45	36	willingness	willingness	NOUN
easat-8773	45	37	to	to	PART
easat-8773	45	38	apply	apply	VERB
easat-8773	45	39	it	it	PRON
easat-8773	45	40	[	[	X
easat-8773	45	41	18	18	NUM
easat-8773	45	42	]	]	PUNCT
easat-8773	45	43	.	.	PUNCT
easat-8773	46	1	this	this	DET
easat-8773	46	2	process	process	NOUN
easat-8773	46	3	also	also	ADV
easat-8773	46	4	requires	require	VERB
easat-8773	46	5	the	the	DET
easat-8773	46	6	integration	integration	NOUN
easat-8773	46	7	of	of	ADP
easat-8773	46	8	a	a	DET
easat-8773	46	9	number	number	NOUN
easat-8773	46	10	of	of	ADP
easat-8773	46	11	competencies	competency	NOUN
easat-8773	46	12	such	such	ADJ
easat-8773	46	13	as	as	ADP
easat-8773	46	14	reading	read	VERB
easat-8773	46	15	the	the	DET
easat-8773	46	16	context	context	NOUN
easat-8773	46	17	of	of	ADP
easat-8773	46	18	the	the	DET
easat-8773	46	19	problem	problem	NOUN
easat-8773	46	20	,	,	PUNCT
easat-8773	46	21	developing	develop	VERB
easat-8773	46	22	a	a	DET
easat-8773	46	23	solution	solution	NOUN
easat-8773	46	24	strategy	strategy	NOUN
easat-8773	46	25	,	,	PUNCT
easat-8773	46	26	building	build	VERB
easat-8773	46	27	a	a	DET
easat-8773	46	28	mathematical	mathematical	ADJ
easat-8773	46	29	model	model	NOUN
easat-8773	46	30	,	,	PUNCT
easat-8773	46	31	and	and	CCONJ
easat-8773	46	32	interpreting	interpret	VERB
easat-8773	46	33	and	and	CCONJ
easat-8773	46	34	validating	validate	VERB
easat-8773	46	35	the	the	DET
easat-8773	46	36	results	result	NOUN
easat-8773	46	37	[	[	X
easat-8773	46	38	15	15	NUM
easat-8773	46	39	]	]	PUNCT
easat-8773	46	40	.	.	PUNCT
easat-8773	47	1	the	the	DET
easat-8773	47	2	phases	phase	NOUN
easat-8773	47	3	of	of	ADP
easat-8773	47	4	the	the	DET
easat-8773	47	5	mathematical	mathematical	ADJ
easat-8773	47	6	modeling	modeling	NOUN
easat-8773	47	7	cycle	cycle	NOUN
easat-8773	47	8	process	process	NOUN
easat-8773	47	9	are	be	AUX
easat-8773	47	10	understanding	understand	VERB
easat-8773	47	11	the	the	DET
easat-8773	47	12	real	real	ADJ
easat-8773	47	13	-	-	PUNCT
easat-8773	47	14	world	world	NOUN
easat-8773	47	15	situation	situation	NOUN
easat-8773	47	16	;	;	PUNCT
easat-8773	47	17	simplifying	simplify	VERB
easat-8773	47	18	/	/	SYM
easat-8773	47	19	idealizing	idealize	VERB
easat-8773	47	20	the	the	DET
easat-8773	47	21	real	real	ADJ
easat-8773	47	22	-	-	PUNCT
easat-8773	47	23	world	world	NOUN
easat-8773	47	24	situation	situation	NOUN
easat-8773	47	25	to	to	PART
easat-8773	47	26	obtain	obtain	VERB
easat-8773	47	27	a	a	DET
easat-8773	47	28	model	model	NOUN
easat-8773	47	29	of	of	ADP
easat-8773	47	30	the	the	DET
easat-8773	47	31	real	real	ADJ
easat-8773	47	32	world	world	NOUN
easat-8773	47	33	;	;	PUNCT
easat-8773	47	34	mathematizing	mathematize	VERB
easat-8773	47	35	the	the	DET
easat-8773	47	36	real	real	ADJ
easat-8773	47	37	-	-	PUNCT
easat-8773	47	38	world	world	NOUN
easat-8773	47	39	model	model	NOUN
easat-8773	47	40	,	,	PUNCT
easat-8773	47	41	which	which	PRON
easat-8773	47	42	is	be	AUX
easat-8773	47	43	designing	design	VERB
easat-8773	47	44	a	a	DET
easat-8773	47	45	plan	plan	NOUN
easat-8773	47	46	to	to	PART
easat-8773	47	47	solve	solve	VERB
easat-8773	47	48	the	the	DET
easat-8773	47	49	problem	problem	NOUN
easat-8773	47	50	by	by	ADP
easat-8773	47	51	translating	translate	VERB
easat-8773	47	52	the	the	DET
easat-8773	47	53	real	real	ADJ
easat-8773	47	54	-	-	PUNCT
easat-8773	47	55	world	world	NOUN
easat-8773	47	56	model	model	NOUN
easat-8773	47	57	into	into	ADP
easat-8773	47	58	a	a	DET
easat-8773	47	59	mathematical	mathematical	ADJ
easat-8773	47	60	model	model	NOUN
easat-8773	47	61	;	;	PUNCT
easat-8773	47	62	applying	apply	VERB
easat-8773	47	63	mathematical	mathematical	ADJ
easat-8773	47	64	routines	routine	NOUN
easat-8773	47	65	and	and	CCONJ
easat-8773	47	66	processes	process	NOUN
easat-8773	47	67	;	;	PUNCT
easat-8773	47	68	interpreting	interpret	VERB
easat-8773	47	69	the	the	DET
easat-8773	47	70	mathematical	mathematical	ADJ
easat-8773	47	71	solution	solution	NOUN
easat-8773	47	72	by	by	ADP
easat-8773	47	73	verifying	verify	VERB
easat-8773	47	74	that	that	SCONJ
easat-8773	47	75	the	the	DET
easat-8773	47	76	problem	problem	NOUN
easat-8773	47	77	corresponds	correspond	VERB
easat-8773	47	78	to	to	ADP
easat-8773	47	79	reality	reality	NOUN
easat-8773	47	80	;	;	PUNCT
easat-8773	47	81	validating	validate	VERB
easat-8773	47	82	the	the	DET
easat-8773	47	83	results	result	NOUN
easat-8773	47	84	of	of	ADP
easat-8773	47	85	the	the	DET
easat-8773	47	86	previous	previous	ADJ
easat-8773	47	87	stage	stage	NOUN
easat-8773	47	88	by	by	ADP
easat-8773	47	89	checking	check	VERB
easat-8773	47	90	the	the	DET
easat-8773	47	91	adequacy	adequacy	NOUN
easat-8773	47	92	of	of	ADP
easat-8773	47	93	the	the	DET
easat-8773	47	94	results	result	NOUN
easat-8773	47	95	and	and	CCONJ
easat-8773	47	96	if	if	SCONJ
easat-8773	47	97	necessary	necessary	ADJ
easat-8773	47	98	repeating	repeat	VERB
easat-8773	47	99	certain	certain	ADJ
easat-8773	47	100	stages	stage	NOUN
easat-8773	47	101	or	or	CCONJ
easat-8773	47	102	even	even	ADV
easat-8773	47	103	the	the	DET
easat-8773	47	104	entire	entire	ADJ
easat-8773	47	105	modeling	modeling	NOUN
easat-8773	47	106	process	process	NOUN
easat-8773	47	107	;	;	PUNCT
easat-8773	47	108	and	and	CCONJ
easat-8773	47	109	presenting	present	VERB
easat-8773	47	110	the	the	DET
easat-8773	47	111	final	final	ADJ
easat-8773	47	112	results	result	NOUN
easat-8773	47	113	of	of	ADP
easat-8773	47	114	the	the	DET
easat-8773	47	115	modeling	modeling	NOUN
easat-8773	47	116	cycle	cycle	NOUN
easat-8773	47	117	[	[	X
easat-8773	47	118	19	19	NUM
easat-8773	47	119	]	]	PUNCT
easat-8773	47	120	.	.	PUNCT
easat-8773	48	1	the	the	DET
easat-8773	48	2	model	model	NOUN
easat-8773	48	3	proposed	propose	VERB
easat-8773	48	4	by	by	ADP
easat-8773	48	5	blum	blum	NOUN
easat-8773	48	6	and	and	CCONJ
easat-8773	48	7	leiß	leiß	NOUN
easat-8773	48	8	[	[	X
easat-8773	48	9	14	14	NUM
easat-8773	48	10	]	]	PUNCT
easat-8773	48	11	offers	offer	VERB
easat-8773	48	12	a	a	DET
easat-8773	48	13	structured	structured	ADJ
easat-8773	48	14	representation	representation	NOUN
easat-8773	48	15	of	of	ADP
easat-8773	48	16	modeling	modeling	NOUN
easat-8773	48	17	process	process	NOUN
easat-8773	48	18	commonly	commonly	ADV
easat-8773	48	19	referred	refer	VERB
easat-8773	48	20	to	to	ADP
easat-8773	48	21	as	as	ADP
easat-8773	48	22	the	the	DET
easat-8773	48	23	modeling	modeling	NOUN
easat-8773	48	24	cycle	cycle	NOUN
easat-8773	48	25	which	which	PRON
easat-8773	48	26	begin	begin	VERB
easat-8773	48	27	with	with	ADP
easat-8773	48	28	contextual	contextual	ADJ
easat-8773	48	29	understanding	understanding	NOUN
easat-8773	48	30	and	and	CCONJ
easat-8773	48	31	culminates	culminate	NOUN
easat-8773	48	32	in	in	ADP
easat-8773	48	33	validating	validate	VERB
easat-8773	48	34	mathematical	mathematical	ADJ
easat-8773	48	35	results	result	NOUN
easat-8773	48	36	.	.	PUNCT
easat-8773	49	1	this	this	DET
easat-8773	49	2	framework	framework	NOUN
easat-8773	49	3	provides	provide	VERB
easat-8773	49	4	a	a	DET
easat-8773	49	5	lens	lens	NOUN
easat-8773	49	6	through	through	ADP
easat-8773	49	7	which	which	PRON
easat-8773	49	8	student	student	NOUN
easat-8773	49	9	responses	response	NOUN
easat-8773	49	10	can	can	AUX
easat-8773	49	11	be	be	AUX
easat-8773	49	12	categorized	categorize	VERB
easat-8773	49	13	and	and	CCONJ
easat-8773	49	14	analyzed	analyze	VERB
easat-8773	49	15	,	,	PUNCT
easat-8773	49	16	especially	especially	ADV
easat-8773	49	17	when	when	SCONJ
easat-8773	49	18	identifying	identify	VERB
easat-8773	49	19	where	where	SCONJ
easat-8773	49	20	errors	error	NOUN
easat-8773	49	21	or	or	CCONJ
easat-8773	49	22	misconceptions	misconception	NOUN
easat-8773	49	23	949	949	NUM
easat-8773	49	24	edelweiss	edelweiss	PROPN
easat-8773	49	25	applied	apply	VERB
easat-8773	49	26	science	science	NOUN
easat-8773	49	27	and	and	CCONJ
easat-8773	49	28	technology	technology	NOUN
easat-8773	49	29	issn	issn	PROPN
easat-8773	49	30	:	:	PUNCT
easat-8773	49	31	2576	2576	NUM
easat-8773	49	32	-	-	SYM
easat-8773	49	33	8484	8484	NUM
easat-8773	49	34	vol	vol	NOUN
easat-8773	49	35	.	.	PROPN
easat-8773	50	1	9	9	NUM
easat-8773	50	2	,	,	PUNCT
easat-8773	50	3	no	no	INTJ
easat-8773	50	4	.	.	NOUN
easat-8773	51	1	7	7	NUM
easat-8773	51	2	:	:	SYM
easat-8773	51	3	947	947	NUM
easat-8773	51	4	-	-	SYM
easat-8773	51	5	959	959	NUM
easat-8773	51	6	,	,	PUNCT
easat-8773	51	7	2025	2025	NUM
easat-8773	51	8	doi	doi	NOUN
easat-8773	51	9	:	:	PUNCT
easat-8773	51	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	51	11	©	©	PROPN
easat-8773	51	12	2025	2025	NUM
easat-8773	51	13	by	by	ADP
easat-8773	51	14	the	the	DET
easat-8773	51	15	authors	author	NOUN
easat-8773	51	16	;	;	PUNCT
easat-8773	51	17	licensee	licensee	PROPN
easat-8773	51	18	learning	learn	VERB
easat-8773	51	19	gate	gate	NOUN
easat-8773	51	20	occur	occur	VERB
easat-8773	51	21	.	.	PUNCT
easat-8773	52	1	the	the	DET
easat-8773	52	2	descriptive	descriptive	ADJ
easat-8773	52	3	model	model	NOUN
easat-8773	52	4	of	of	ADP
easat-8773	52	5	a	a	DET
easat-8773	52	6	modeling	modeling	NOUN
easat-8773	52	7	process	process	NOUN
easat-8773	52	8	,	,	PUNCT
easat-8773	52	9	as	as	SCONJ
easat-8773	52	10	seen	see	VERB
easat-8773	52	11	in	in	ADP
easat-8773	52	12	figure	figure	NOUN
easat-8773	52	13	1	1	NUM
easat-8773	52	14	,	,	PUNCT
easat-8773	52	15	can	can	AUX
easat-8773	52	16	be	be	AUX
easat-8773	52	17	used	use	VERB
easat-8773	52	18	as	as	ADP
easat-8773	52	19	a	a	DET
easat-8773	52	20	basis	basis	NOUN
easat-8773	52	21	for	for	ADP
easat-8773	52	22	characterizing	characterize	VERB
easat-8773	52	23	students	student	NOUN
easat-8773	52	24	’	'	PUNCT
easat-8773	52	25	processes	process	NOUN
easat-8773	52	26	in	in	ADP
easat-8773	52	27	modelling	modelling	NOUN
easat-8773	52	28	.	.	PUNCT
easat-8773	53	1	figure	figure	NOUN
easat-8773	53	2	1	1	NUM
easat-8773	53	3	.	.	PUNCT
easat-8773	54	1	modeling	modeling	NOUN
easat-8773	54	2	cycle	cycle	NOUN
easat-8773	54	3	followed	follow	VERB
easat-8773	54	4	blum	blum	PROPN
easat-8773	54	5	&	&	CCONJ
easat-8773	54	6	leiß	leiß	PROPN
easat-8773	54	7	the	the	DET
easat-8773	54	8	modeling	modeling	NOUN
easat-8773	54	9	process	process	NOUN
easat-8773	54	10	begins	begin	VERB
easat-8773	54	11	with	with	ADP
easat-8773	54	12	the	the	DET
easat-8773	54	13	real	real	ADJ
easat-8773	54	14	situation	situation	NOUN
easat-8773	54	15	.	.	PUNCT
easat-8773	55	1	by	by	ADP
easat-8773	55	2	simplifying	simplify	VERB
easat-8773	55	3	,	,	PUNCT
easat-8773	55	4	structuring	structuring	NOUN
easat-8773	55	5	,	,	PUNCT
easat-8773	55	6	and	and	CCONJ
easat-8773	55	7	idealizing	idealize	VERB
easat-8773	55	8	this	this	DET
easat-8773	55	9	problem	problem	NOUN
easat-8773	55	10	,	,	PUNCT
easat-8773	55	11	a	a	DET
easat-8773	55	12	real	real	ADJ
easat-8773	55	13	model	model	NOUN
easat-8773	55	14	can	can	AUX
easat-8773	55	15	be	be	AUX
easat-8773	55	16	identified	identify	VERB
easat-8773	55	17	.	.	PUNCT
easat-8773	56	1	the	the	DET
easat-8773	56	2	mathematizing	mathematizing	NOUN
easat-8773	56	3	of	of	ADP
easat-8773	56	4	the	the	DET
easat-8773	56	5	real	real	ADJ
easat-8773	56	6	model	model	NOUN
easat-8773	56	7	leads	lead	VERB
easat-8773	56	8	to	to	ADP
easat-8773	56	9	a	a	DET
easat-8773	56	10	mathematical	mathematical	ADJ
easat-8773	56	11	model	model	NOUN
easat-8773	56	12	.	.	PUNCT
easat-8773	57	1	additionally	additionally	ADV
easat-8773	57	2	,	,	PUNCT
easat-8773	57	3	mathematical	mathematical	ADJ
easat-8773	57	4	solutions	solution	NOUN
easat-8773	57	5	can	can	AUX
easat-8773	57	6	be	be	AUX
easat-8773	57	7	found	find	VERB
easat-8773	57	8	by	by	ADP
easat-8773	57	9	working	work	VERB
easat-8773	57	10	mathematically	mathematically	ADV
easat-8773	57	11	.	.	PUNCT
easat-8773	58	1	this	this	DET
easat-8773	58	2	solution	solution	NOUN
easat-8773	58	3	has	have	VERB
easat-8773	58	4	to	to	PART
easat-8773	58	5	be	be	AUX
easat-8773	58	6	interpreted	interpret	VERB
easat-8773	58	7	first	first	ADV
easat-8773	58	8	and	and	CCONJ
easat-8773	58	9	then	then	ADV
easat-8773	58	10	validated	validate	VERB
easat-8773	58	11	.	.	PUNCT
easat-8773	59	1	if	if	SCONJ
easat-8773	59	2	the	the	DET
easat-8773	59	3	solution	solution	NOUN
easat-8773	59	4	or	or	CCONJ
easat-8773	59	5	the	the	DET
easat-8773	59	6	chosen	choose	VERB
easat-8773	59	7	process	process	NOUN
easat-8773	59	8	does	do	AUX
easat-8773	59	9	not	not	PART
easat-8773	59	10	prove	prove	VERB
easat-8773	59	11	to	to	PART
easat-8773	59	12	be	be	AUX
easat-8773	59	13	appropriate	appropriate	ADJ
easat-8773	59	14	to	to	ADP
easat-8773	59	15	reality	reality	NOUN
easat-8773	59	16	,	,	PUNCT
easat-8773	59	17	particular	particular	ADJ
easat-8773	59	18	steps	step	NOUN
easat-8773	59	19	or	or	CCONJ
easat-8773	59	20	maybe	maybe	ADV
easat-8773	59	21	even	even	ADV
easat-8773	59	22	the	the	DET
easat-8773	59	23	entire	entire	ADJ
easat-8773	59	24	modeling	modeling	NOUN
easat-8773	59	25	process	process	NOUN
easat-8773	59	26	needs	need	VERB
easat-8773	59	27	to	to	PART
easat-8773	59	28	be	be	AUX
easat-8773	59	29	worked	work	VERB
easat-8773	59	30	through	through	ADP
easat-8773	59	31	again	again	ADV
easat-8773	59	32	.	.	PUNCT
easat-8773	60	1	2.3	2.3	NUM
easat-8773	60	2	.	.	PUNCT
easat-8773	61	1	newman	newman	NOUN
easat-8773	61	2	error	error	NOUN
easat-8773	61	3	analysis	analysis	NOUN
easat-8773	61	4	(	(	PUNCT
easat-8773	61	5	nea	nea	NOUN
easat-8773	61	6	)	)	PUNCT
easat-8773	61	7	and	and	CCONJ
easat-8773	61	8	its	its	PRON
easat-8773	61	9	relevance	relevance	NOUN
easat-8773	61	10	to	to	ADP
easat-8773	61	11	modeling	modeling	NOUN
easat-8773	61	12	to	to	PART
easat-8773	61	13	further	further	ADJ
easat-8773	61	14	diagnose	diagnose	NOUN
easat-8773	61	15	students	student	NOUN
easat-8773	61	16	’	'	PUNCT
easat-8773	61	17	error	error	NOUN
easat-8773	61	18	,	,	PUNCT
easat-8773	61	19	this	this	DET
easat-8773	61	20	study	study	NOUN
easat-8773	61	21	also	also	ADV
easat-8773	61	22	incorporates	incorporate	VERB
easat-8773	61	23	nea	nea	PROPN
easat-8773	61	24	as	as	ADP
easat-8773	61	25	a	a	DET
easat-8773	61	26	complementary	complementary	ADJ
easat-8773	61	27	tool	tool	NOUN
easat-8773	61	28	.	.	PUNCT
easat-8773	62	1	nea	nea	PROPN
easat-8773	62	2	categorizes	categorize	VERB
easat-8773	62	3	five	five	NUM
easat-8773	62	4	key	key	ADJ
easat-8773	62	5	types	type	NOUN
easat-8773	62	6	of	of	ADP
easat-8773	62	7	student	student	NOUN
easat-8773	62	8	errors	error	NOUN
easat-8773	62	9	including	include	VERB
easat-8773	62	10	reading	reading	NOUN
easat-8773	62	11	,	,	PUNCT
easat-8773	62	12	comprehension	comprehension	NOUN
easat-8773	62	13	,	,	PUNCT
easat-8773	62	14	transformation	transformation	NOUN
easat-8773	62	15	,	,	PUNCT
easat-8773	62	16	process	process	NOUN
easat-8773	62	17	skills	skill	NOUN
easat-8773	62	18	,	,	PUNCT
easat-8773	62	19	and	and	CCONJ
easat-8773	62	20	encoding	encode	VERB
easat-8773	62	21	when	when	SCONJ
easat-8773	62	22	solving	solve	VERB
easat-8773	62	23	mathematical	mathematical	ADJ
easat-8773	62	24	world	world	NOUN
easat-8773	62	25	problems	problem	NOUN
easat-8773	62	26	[	[	X
easat-8773	62	27	20	20	NUM
easat-8773	62	28	]	]	PUNCT
easat-8773	62	29	.	.	PUNCT
easat-8773	63	1	previous	previous	ADJ
easat-8773	63	2	studies	study	NOUN
easat-8773	63	3	have	have	AUX
easat-8773	63	4	found	find	VERB
easat-8773	63	5	strong	strong	ADJ
easat-8773	63	6	parallels	parallel	NOUN
easat-8773	63	7	between	between	ADP
easat-8773	63	8	newman	newman	PROPN
easat-8773	63	9	’s	’s	PART
easat-8773	63	10	framework	framework	NOUN
easat-8773	63	11	and	and	CCONJ
easat-8773	63	12	the	the	DET
easat-8773	63	13	stages	stage	NOUN
easat-8773	63	14	of	of	ADP
easat-8773	63	15	the	the	DET
easat-8773	63	16	modeling	modeling	NOUN
easat-8773	63	17	cycle	cycle	NOUN
easat-8773	63	18	wijaya	wijaya	PROPN
easat-8773	63	19	,	,	PUNCT
easat-8773	63	20	et	et	PROPN
easat-8773	63	21	al	al	PROPN
easat-8773	63	22	.	.	PUNCT
easat-8773	64	1	[	[	X
easat-8773	64	2	21	21	NUM
easat-8773	64	3	]	]	PUNCT
easat-8773	64	4	making	make	VERB
easat-8773	64	5	it	it	PRON
easat-8773	64	6	valuable	valuable	ADJ
easat-8773	64	7	method	method	NOUN
easat-8773	64	8	to	to	PART
easat-8773	64	9	map	map	VERB
easat-8773	64	10	observed	observed	ADJ
easat-8773	64	11	errors	error	NOUN
easat-8773	64	12	during	during	ADP
easat-8773	64	13	the	the	DET
easat-8773	64	14	modeling	modeling	NOUN
easat-8773	64	15	process	process	NOUN
easat-8773	64	16	.	.	PUNCT
easat-8773	65	1	the	the	DET
easat-8773	65	2	integration	integration	NOUN
easat-8773	65	3	of	of	ADP
easat-8773	65	4	nea	nea	PROPN
easat-8773	65	5	with	with	ADP
easat-8773	65	6	the	the	DET
easat-8773	65	7	modeling	modeling	NOUN
easat-8773	65	8	cycle	cycle	NOUN
easat-8773	65	9	enables	enable	VERB
easat-8773	65	10	a	a	DET
easat-8773	65	11	nuanced	nuanced	ADJ
easat-8773	65	12	analysis	analysis	NOUN
easat-8773	65	13	of	of	ADP
easat-8773	65	14	students	student	NOUN
easat-8773	65	15	’	’	PART
easat-8773	65	16	errors	error	NOUN
easat-8773	65	17	,	,	PUNCT
easat-8773	65	18	especially	especially	ADV
easat-8773	65	19	when	when	SCONJ
easat-8773	65	20	combined	combine	VERB
easat-8773	65	21	with	with	ADP
easat-8773	65	22	data	datum	NOUN
easat-8773	65	23	such	such	ADJ
easat-8773	65	24	as	as	ADP
easat-8773	65	25	written	write	VERB
easat-8773	65	26	responses	response	NOUN
easat-8773	65	27	and	and	CCONJ
easat-8773	65	28	interviews	interview	NOUN
easat-8773	65	29	.	.	PUNCT
easat-8773	66	1	table	table	NOUN
easat-8773	66	2	1	1	NUM
easat-8773	66	3	illustrates	illustrate	VERB
easat-8773	66	4	how	how	SCONJ
easat-8773	66	5	each	each	DET
easat-8773	66	6	error	error	NOUN
easat-8773	66	7	category	category	NOUN
easat-8773	66	8	aligns	align	VERB
easat-8773	66	9	with	with	ADP
easat-8773	66	10	specific	specific	ADJ
easat-8773	66	11	stages	stage	NOUN
easat-8773	66	12	in	in	ADP
easat-8773	66	13	modeling	modeling	NOUN
easat-8773	66	14	process	process	NOUN
easat-8773	66	15	,	,	PUNCT
easat-8773	66	16	providing	provide	VERB
easat-8773	66	17	a	a	DET
easat-8773	66	18	clear	clear	ADJ
easat-8773	66	19	structure	structure	NOUN
easat-8773	66	20	for	for	ADP
easat-8773	66	21	evaluating	evaluate	VERB
easat-8773	66	22	student	student	NOUN
easat-8773	66	23	performance	performance	NOUN
easat-8773	66	24	and	and	CCONJ
easat-8773	66	25	identifying	identify	VERB
easat-8773	66	26	common	common	ADJ
easat-8773	66	27	patterns	pattern	NOUN
easat-8773	66	28	of	of	ADP
easat-8773	66	29	errors	error	NOUN
easat-8773	66	30	[	[	X
easat-8773	66	31	21	21	NUM
easat-8773	66	32	]	]	PUNCT
easat-8773	66	33	.	.	PUNCT
easat-8773	67	1	950	950	NUM
easat-8773	67	2	edelweiss	edelweiss	PROPN
easat-8773	67	3	applied	apply	VERB
easat-8773	67	4	science	science	NOUN
easat-8773	67	5	and	and	CCONJ
easat-8773	67	6	technology	technology	NOUN
easat-8773	67	7	issn	issn	PROPN
easat-8773	67	8	:	:	PUNCT
easat-8773	67	9	2576	2576	NUM
easat-8773	67	10	-	-	SYM
easat-8773	67	11	8484	8484	NUM
easat-8773	67	12	vol	vol	NOUN
easat-8773	67	13	.	.	PROPN
easat-8773	68	1	9	9	NUM
easat-8773	68	2	,	,	PUNCT
easat-8773	68	3	no	no	INTJ
easat-8773	68	4	.	.	NOUN
easat-8773	69	1	7	7	NUM
easat-8773	69	2	:	:	SYM
easat-8773	69	3	947	947	NUM
easat-8773	69	4	-	-	SYM
easat-8773	69	5	959	959	NUM
easat-8773	69	6	,	,	PUNCT
easat-8773	69	7	2025	2025	NUM
easat-8773	69	8	doi	doi	NOUN
easat-8773	69	9	:	:	PUNCT
easat-8773	69	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	69	11	©	©	PROPN
easat-8773	69	12	2025	2025	NUM
easat-8773	69	13	by	by	ADP
easat-8773	69	14	the	the	DET
easat-8773	69	15	authors	author	NOUN
easat-8773	69	16	;	;	PUNCT
easat-8773	69	17	licensee	licensee	PROPN
easat-8773	69	18	learning	learn	VERB
easat-8773	69	19	gate	gate	NOUN
easat-8773	69	20	table	table	NOUN
easat-8773	69	21	1	1	NUM
easat-8773	69	22	.	.	PUNCT
easat-8773	70	1	newman	newman	PROPN
easat-8773	70	2	's	's	PART
easat-8773	70	3	error	error	NOUN
easat-8773	70	4	categories	category	NOUN
easat-8773	70	5	and	and	CCONJ
easat-8773	70	6	modeling	modeling	NOUN
easat-8773	70	7	process	process	NOUN
easat-8773	70	8	following	follow	VERB
easat-8773	70	9	blum	blum	NOUN
easat-8773	70	10	and	and	CCONJ
easat-8773	70	11	leiß	leiß	NOUN
easat-8773	70	12	.	.	PUNCT
easat-8773	71	1	3	3	X
easat-8773	71	2	.	.	X
easat-8773	71	3	methodology	methodology	NOUN
easat-8773	71	4	this	this	DET
easat-8773	71	5	study	study	NOUN
easat-8773	71	6	employs	employ	VERB
easat-8773	71	7	a	a	DET
easat-8773	71	8	quantitative	quantitative	ADJ
easat-8773	71	9	descriptive	descriptive	ADJ
easat-8773	71	10	and	and	CCONJ
easat-8773	71	11	exploratory	exploratory	ADJ
easat-8773	71	12	approach	approach	NOUN
easat-8773	71	13	to	to	PART
easat-8773	71	14	examine	examine	VERB
easat-8773	71	15	errors	error	NOUN
easat-8773	71	16	in	in	ADP
easat-8773	71	17	the	the	DET
easat-8773	71	18	mathematical	mathematical	ADJ
easat-8773	71	19	modeling	modeling	NOUN
easat-8773	71	20	process	process	NOUN
easat-8773	71	21	and	and	CCONJ
easat-8773	71	22	explore	explore	VERB
easat-8773	71	23	their	their	PRON
easat-8773	71	24	relationship	relationship	NOUN
easat-8773	71	25	with	with	ADP
easat-8773	71	26	students	student	NOUN
easat-8773	71	27	’	'	PUNCT
easat-8773	71	28	mathematical	mathematical	ADJ
easat-8773	71	29	ability	ability	NOUN
easat-8773	71	30	levels	level	NOUN
easat-8773	71	31	.	.	PUNCT
easat-8773	72	1	this	this	DET
easat-8773	72	2	study	study	NOUN
easat-8773	72	3	involves	involve	VERB
easat-8773	72	4	72	72	NUM
easat-8773	72	5	eighth	eighth	ADJ
easat-8773	72	6	-	-	PUNCT
easat-8773	72	7	grade	grade	NOUN
easat-8773	72	8	students	student	NOUN
easat-8773	72	9	at	at	ADP
easat-8773	72	10	a	a	DET
easat-8773	72	11	private	private	ADJ
easat-8773	72	12	school	school	NOUN
easat-8773	72	13	namely	namely	ADV
easat-8773	72	14	smp	smp	PROPN
easat-8773	72	15	st	st	PROPN
easat-8773	72	16	.	.	PROPN
easat-8773	72	17	benediktus	benediktus	PROPN
easat-8773	72	18	,	,	PUNCT
easat-8773	72	19	two	two	NUM
easat-8773	72	20	classes	class	NOUN
easat-8773	72	21	viiia	viiia	VERB
easat-8773	72	22	(	(	PUNCT
easat-8773	72	23	24	24	NUM
easat-8773	72	24	girls	girl	NOUN
easat-8773	72	25	and	and	CCONJ
easat-8773	72	26	13	13	NUM
easat-8773	72	27	boys	boy	NOUN
easat-8773	72	28	)	)	PUNCT
easat-8773	72	29	and	and	CCONJ
easat-8773	72	30	viiib	viiib	NOUN
easat-8773	72	31	(	(	PUNCT
easat-8773	72	32	20	20	NUM
easat-8773	72	33	girls	girl	NOUN
easat-8773	72	34	and	and	CCONJ
easat-8773	72	35	15	15	NUM
easat-8773	72	36	boys	boy	NOUN
easat-8773	72	37	)	)	PUNCT
easat-8773	72	38	are	be	AUX
easat-8773	72	39	randomly	randomly	ADV
easat-8773	72	40	chosen	choose	VERB
easat-8773	72	41	form	form	NOUN
easat-8773	72	42	three	three	NUM
easat-8773	72	43	classes	class	NOUN
easat-8773	72	44	.	.	PUNCT
easat-8773	73	1	this	this	DET
easat-8773	73	2	study	study	NOUN
easat-8773	73	3	utilized	utilize	VERB
easat-8773	73	4	two	two	NUM
easat-8773	73	5	instruments	instrument	NOUN
easat-8773	73	6	are	be	AUX
easat-8773	73	7	math	math	NOUN
easat-8773	73	8	competence	competence	NOUN
easat-8773	73	9	test	test	NOUN
easat-8773	73	10	(	(	PUNCT
easat-8773	73	11	mct	mct	PROPN
easat-8773	73	12	)	)	PUNCT
easat-8773	73	13	,	,	PUNCT
easat-8773	73	14	comprising	comprise	VERB
easat-8773	73	15	5	5	NUM
easat-8773	73	16	essay	essay	ADJ
easat-8773	73	17	questions	question	NOUN
easat-8773	73	18	covering	cover	VERB
easat-8773	73	19	topics	topic	NOUN
easat-8773	73	20	such	such	ADJ
easat-8773	73	21	as	as	ADP
easat-8773	73	22	numbers	number	NOUN
easat-8773	73	23	,	,	PUNCT
easat-8773	73	24	comparison	comparison	NOUN
easat-8773	73	25	,	,	PUNCT
easat-8773	73	26	arithmetic	arithmetic	ADJ
easat-8773	73	27	,	,	PUNCT
easat-8773	73	28	and	and	CCONJ
easat-8773	73	29	geometry	geometry	NOUN
easat-8773	73	30	;	;	PUNCT
easat-8773	73	31	and	and	CCONJ
easat-8773	73	32	mathematical	mathematical	ADJ
easat-8773	73	33	modeling	modeling	NOUN
easat-8773	73	34	test	test	NOUN
easat-8773	73	35	(	(	PUNCT
easat-8773	73	36	mmt	mmt	NOUN
easat-8773	73	37	)	)	PUNCT
easat-8773	73	38	,	,	PUNCT
easat-8773	73	39	which	which	PRON
easat-8773	73	40	included	include	VERB
easat-8773	73	41	4	4	NUM
easat-8773	73	42	essay	essay	ADJ
easat-8773	73	43	questions	question	NOUN
easat-8773	73	44	on	on	ADP
easat-8773	73	45	social	social	ADJ
easat-8773	73	46	arithmetic	arithmetic	ADJ
easat-8773	73	47	,	,	PUNCT
easat-8773	73	48	numbers	number	NOUN
easat-8773	73	49	,	,	PUNCT
easat-8773	73	50	and	and	CCONJ
easat-8773	73	51	geometry	geometry	NOUN
easat-8773	73	52	.	.	PUNCT
easat-8773	74	1	instrument	instrument	NOUN
easat-8773	74	2	validation	validation	NOUN
easat-8773	74	3	was	be	AUX
easat-8773	74	4	conducted	conduct	VERB
easat-8773	74	5	by	by	ADP
easat-8773	74	6	three	three	NUM
easat-8773	74	7	associate	associate	ADJ
easat-8773	74	8	professors	professor	NOUN
easat-8773	74	9	and	and	CCONJ
easat-8773	74	10	one	one	NUM
easat-8773	74	11	mathematics	mathematic	NOUN
easat-8773	74	12	teacher	teacher	NOUN
easat-8773	74	13	with	with	ADP
easat-8773	74	14	a	a	DET
easat-8773	74	15	master	master	NOUN
easat-8773	74	16	’s	’s	PART
easat-8773	74	17	degree	degree	NOUN
easat-8773	74	18	,	,	PUNCT
easat-8773	74	19	using	use	VERB
easat-8773	74	20	a	a	DET
easat-8773	74	21	4	4	NUM
easat-8773	74	22	-	-	PUNCT
easat-8773	74	23	point	point	NOUN
easat-8773	74	24	likert	likert	ADJ
easat-8773	74	25	scale	scale	NOUN
easat-8773	74	26	,	,	PUNCT
easat-8773	74	27	with	with	ADP
easat-8773	74	28	an	an	DET
easat-8773	74	29	aiken	aiken	PROPN
easat-8773	74	30	index	index	NOUN
easat-8773	74	31	threshold	threshold	NOUN
easat-8773	74	32	of	of	ADP
easat-8773	74	33	𝑉	𝑉	PROPN
easat-8773	74	34	≥	≥	NUM
easat-8773	74	35	0.4	0.4	NUM
easat-8773	74	36	.	.	PUNCT
easat-8773	75	1	the	the	DET
easat-8773	75	2	validity	validity	NOUN
easat-8773	75	3	value	value	NOUN
easat-8773	75	4	exceeded	exceed	VERB
easat-8773	75	5	0.83	0.83	NUM
easat-8773	75	6	,	,	PUNCT
easat-8773	75	7	indicating	indicate	VERB
easat-8773	75	8	strong	strong	ADJ
easat-8773	75	9	content	content	NOUN
easat-8773	75	10	validity	validity	NOUN
easat-8773	75	11	.	.	PUNCT
easat-8773	76	1	data	datum	NOUN
easat-8773	76	2	collection	collection	NOUN
easat-8773	76	3	occurred	occur	VERB
easat-8773	76	4	over	over	ADP
easat-8773	76	5	two	two	NUM
easat-8773	76	6	separate	separate	ADJ
easat-8773	76	7	days	day	NOUN
easat-8773	76	8	,	,	PUNCT
easat-8773	76	9	where	where	SCONJ
easat-8773	76	10	students	student	NOUN
easat-8773	76	11	completed	complete	VERB
easat-8773	76	12	the	the	DET
easat-8773	76	13	mct	mct	PROPN
easat-8773	76	14	and	and	CCONJ
easat-8773	76	15	mmt	mmt	NOUN
easat-8773	76	16	within	within	ADP
easat-8773	76	17	90	90	NUM
easat-8773	76	18	-	-	PUNCT
easat-8773	76	19	minute	minute	NOUN
easat-8773	76	20	sessions	session	NOUN
easat-8773	76	21	,	,	PUNCT
easat-8773	76	22	under	under	ADP
easat-8773	76	23	direct	direct	ADJ
easat-8773	76	24	observation	observation	NOUN
easat-8773	76	25	by	by	ADP
easat-8773	76	26	researchers	researcher	NOUN
easat-8773	76	27	.	.	PUNCT
easat-8773	77	1	students	student	NOUN
easat-8773	77	2	’	'	PUNCT
easat-8773	77	3	mathematical	mathematical	ADJ
easat-8773	77	4	ability	ability	NOUN
easat-8773	77	5	levels	level	NOUN
easat-8773	77	6	were	be	AUX
easat-8773	77	7	categorized	categorize	VERB
easat-8773	77	8	as	as	ADP
easat-8773	77	9	high	high	ADJ
easat-8773	77	10	ability	ability	NOUN
easat-8773	77	11	(	(	PUNCT
easat-8773	77	12	skor	skor	X
easat-8773	77	13	≥	≥	NUM
easat-8773	77	14	80	80	NUM
easat-8773	77	15	)	)	PUNCT
easat-8773	77	16	,	,	PUNCT
easat-8773	77	17	medium	medium	NOUN
easat-8773	77	18	ability	ability	NOUN
easat-8773	77	19	(	(	PUNCT
easat-8773	77	20	65	65	NUM
easat-8773	77	21	≤	≤	NUM
easat-8773	77	22	skor	skor	NOUN
easat-8773	77	23	<	<	X
easat-8773	77	24	80	80	NUM
easat-8773	77	25	)	)	PUNCT
easat-8773	77	26	,	,	PUNCT
easat-8773	77	27	and	and	CCONJ
easat-8773	77	28	low	low	ADJ
easat-8773	77	29	ability	ability	NOUN
easat-8773	77	30	(	(	PUNCT
easat-8773	77	31	skor	skor	VERB
easat-8773	77	32	<	<	X
easat-8773	77	33	65	65	NUM
easat-8773	77	34	)	)	PUNCT
easat-8773	77	35	based	base	VERB
easat-8773	77	36	on	on	ADP
easat-8773	77	37	results	result	NOUN
easat-8773	77	38	mct	mct	PROPN
easat-8773	77	39	.	.	PROPN
easat-8773	78	1	based	base	VERB
easat-8773	78	2	on	on	ADP
easat-8773	78	3	mmt	mmt	PROPN
easat-8773	78	4	responses	response	NOUN
easat-8773	78	5	students	student	NOUN
easat-8773	78	6	were	be	AUX
easat-8773	78	7	scored	score	VERB
easat-8773	78	8	as	as	ADP
easat-8773	78	9	1	1	NUM
easat-8773	78	10	(	(	PUNCT
easat-8773	78	11	correct	correct	ADJ
easat-8773	78	12	)	)	PUNCT
easat-8773	78	13	and	and	CCONJ
easat-8773	78	14	0	0	NUM
easat-8773	78	15	(	(	PUNCT
easat-8773	78	16	incorrect	incorrect	ADJ
easat-8773	78	17	)	)	PUNCT
easat-8773	78	18	,	,	PUNCT
easat-8773	78	19	and	and	CCONJ
easat-8773	78	20	errors	error	NOUN
easat-8773	78	21	analyzing	analyze	VERB
easat-8773	78	22	using	use	VERB
easat-8773	78	23	the	the	DET
easat-8773	78	24	nea	nea	PROPN
easat-8773	78	25	framework	framework	NOUN
easat-8773	78	26	integrated	integrate	VERB
easat-8773	78	27	with	with	ADP
easat-8773	78	28	six	six	NUM
easat-8773	78	29	modelling	modelling	NOUN
easat-8773	78	30	processes	process	NOUN
easat-8773	78	31	as	as	ADV
easat-8773	78	32	defined	define	VERB
easat-8773	78	33	by	by	ADP
easat-8773	78	34	blum	blum	NOUN
easat-8773	78	35	and	and	CCONJ
easat-8773	78	36	leiß	leiß	NOUN
easat-8773	78	37	and	and	CCONJ
easat-8773	78	38	explore	explore	VERB
easat-8773	78	39	analyzing	analyzing	NOUN
easat-8773	78	40	based	base	VERB
easat-8773	78	41	on	on	ADP
easat-8773	78	42	mathematical	mathematical	ADJ
easat-8773	78	43	ability	ability	NOUN
easat-8773	78	44	levels	level	NOUN
easat-8773	78	45	.	.	PUNCT
easat-8773	79	1	4	4	X
easat-8773	79	2	.	.	NOUN
easat-8773	79	3	results	result	VERB
easat-8773	79	4	the	the	DET
easat-8773	79	5	result	result	NOUN
easat-8773	79	6	of	of	ADP
easat-8773	79	7	the	the	DET
easat-8773	79	8	analysis	analysis	NOUN
easat-8773	79	9	was	be	AUX
easat-8773	79	10	conducted	conduct	VERB
easat-8773	79	11	on	on	ADP
easat-8773	79	12	the	the	DET
easat-8773	79	13	mathematical	mathematical	ADJ
easat-8773	79	14	competency	competency	NOUN
easat-8773	79	15	test	test	NOUN
easat-8773	79	16	(	(	PUNCT
easat-8773	79	17	mct	mct	PROPN
easat-8773	79	18	)	)	PUNCT
easat-8773	79	19	and	and	CCONJ
easat-8773	79	20	mathematical	mathematical	ADJ
easat-8773	79	21	modeling	modeling	NOUN
easat-8773	79	22	test	test	NOUN
easat-8773	79	23	(	(	PUNCT
easat-8773	79	24	mmt	mmt	NOUN
easat-8773	79	25	)	)	PUNCT
easat-8773	79	26	scores	score	NOUN
easat-8773	79	27	is	be	AUX
easat-8773	79	28	as	as	SCONJ
easat-8773	79	29	follows	follow	VERB
easat-8773	79	30	:	:	PUNCT
easat-8773	79	31	newman	newman	PROPN
easat-8773	79	32	's	's	PART
easat-8773	79	33	error	error	NOUN
easat-8773	79	34	categories	category	NOUN
easat-8773	79	35	modeling	modeling	NOUN
easat-8773	79	36	process	process	NOUN
easat-8773	79	37	description	description	NOUN
easat-8773	79	38	comprehension	comprehension	NOUN
easat-8773	79	39	:	:	PUNCT
easat-8773	79	40	errors	error	NOUN
easat-8773	79	41	in	in	ADP
easat-8773	79	42	understanding	understand	VERB
easat-8773	79	43	the	the	DET
easat-8773	79	44	meaning	meaning	NOUN
easat-8773	79	45	of	of	ADP
easat-8773	79	46	the	the	DET
easat-8773	79	47	problem	problem	NOUN
easat-8773	79	48	.	.	PUNCT
easat-8773	80	1	understanding	understand	VERB
easat-8773	80	2	problems	problem	NOUN
easat-8773	80	3	by	by	ADP
easat-8773	80	4	establishing	establish	VERB
easat-8773	80	5	situational	situational	ADJ
easat-8773	80	6	models	model	NOUN
easat-8773	80	7	.	.	PUNCT
easat-8773	81	1	▪	▪	ADJ
easat-8773	81	2	errors	error	NOUN
easat-8773	81	3	were	be	AUX
easat-8773	81	4	made	make	VERB
easat-8773	81	5	by	by	ADP
easat-8773	81	6	students	student	NOUN
easat-8773	81	7	who	who	PRON
easat-8773	81	8	could	could	AUX
easat-8773	81	9	not	not	PART
easat-8773	81	10	understand	understand	VERB
easat-8773	81	11	the	the	DET
easat-8773	81	12	test	test	NOUN
easat-8773	81	13	.	.	PUNCT
easat-8773	82	1	▪	▪	NOUN
easat-8773	82	2	a	a	DET
easat-8773	82	3	student	student	NOUN
easat-8773	82	4	misunderstood	misunderstood	VERB
easat-8773	82	5	a	a	DET
easat-8773	82	6	keyword	keyword	NOUN
easat-8773	82	7	,	,	PUNCT
easat-8773	82	8	which	which	PRON
easat-8773	82	9	was	be	AUX
easat-8773	82	10	usually	usually	ADV
easat-8773	82	11	a	a	DET
easat-8773	82	12	mathematical	mathematical	ADJ
easat-8773	82	13	term	term	NOUN
easat-8773	82	14	.	.	PUNCT
easat-8773	83	1	establishing	establish	VERB
easat-8773	83	2	real	real	ADJ
easat-8773	83	3	models	model	NOUN
easat-8773	83	4	by	by	ADP
easat-8773	83	5	simplifying	simplify	VERB
easat-8773	83	6	situational	situational	ADJ
easat-8773	83	7	models	model	NOUN
easat-8773	83	8	.	.	PUNCT
easat-8773	84	1	▪	▪	ADJ
easat-8773	84	2	errors	error	NOUN
easat-8773	84	3	in	in	ADP
easat-8773	84	4	making	make	VERB
easat-8773	84	5	assumptions	assumption	NOUN
easat-8773	84	6	about	about	ADP
easat-8773	84	7	the	the	DET
easat-8773	84	8	problem	problem	NOUN
easat-8773	84	9	and	and	CCONJ
easat-8773	84	10	simplifying	simplify	VERB
easat-8773	84	11	the	the	DET
easat-8773	84	12	situation	situation	NOUN
easat-8773	84	13	.	.	PUNCT
easat-8773	85	1	▪	▪	ADJ
easat-8773	85	2	errors	error	NOUN
easat-8773	85	3	in	in	ADP
easat-8773	85	4	recognizing	recognize	VERB
easat-8773	85	5	the	the	DET
easat-8773	85	6	quantities	quantity	NOUN
easat-8773	85	7	that	that	PRON
easat-8773	85	8	affect	affect	VERB
easat-8773	85	9	the	the	DET
easat-8773	85	10	situation	situation	NOUN
easat-8773	85	11	.	.	PUNCT
easat-8773	86	1	▪	▪	ADJ
easat-8773	86	2	errors	error	NOUN
easat-8773	86	3	in	in	ADP
easat-8773	86	4	naming	name	VERB
easat-8773	86	5	and	and	CCONJ
easat-8773	86	6	identifying	identify	VERB
easat-8773	86	7	key	key	ADJ
easat-8773	86	8	variables	variable	NOUN
easat-8773	86	9	.	.	PUNCT
easat-8773	87	1	transformation	transformation	NOUN
easat-8773	87	2	:	:	PUNCT
easat-8773	87	3	errors	error	NOUN
easat-8773	87	4	in	in	ADP
easat-8773	87	5	transforming	transform	VERB
easat-8773	87	6	a	a	DET
easat-8773	87	7	word	word	NOUN
easat-8773	87	8	problem	problem	NOUN
easat-8773	87	9	into	into	ADP
easat-8773	87	10	an	an	DET
easat-8773	87	11	appropriate	appropriate	ADJ
easat-8773	87	12	mathematical	mathematical	ADJ
easat-8773	87	13	problem	problem	NOUN
easat-8773	87	14	.	.	PUNCT
easat-8773	88	1	constructing	construct	VERB
easat-8773	88	2	a	a	DET
easat-8773	88	3	mathematical	mathematical	ADJ
easat-8773	88	4	model	model	NOUN
easat-8773	88	5	by	by	ADP
easat-8773	88	6	mathematizing	mathematize	VERB
easat-8773	88	7	real	real	ADJ
easat-8773	88	8	model	model	NOUN
easat-8773	88	9	.	.	PUNCT
easat-8773	89	1	errors	error	NOUN
easat-8773	89	2	in	in	ADP
easat-8773	89	3	creating	create	VERB
easat-8773	89	4	a	a	DET
easat-8773	89	5	mathematical	mathematical	ADJ
easat-8773	89	6	model	model	NOUN
easat-8773	89	7	.	.	PUNCT
easat-8773	90	1	process	process	NOUN
easat-8773	90	2	skill	skill	NOUN
easat-8773	90	3	:	:	PUNCT
easat-8773	90	4	errors	error	NOUN
easat-8773	90	5	in	in	ADP
easat-8773	90	6	performing	perform	VERB
easat-8773	90	7	mathematical	mathematical	ADJ
easat-8773	90	8	procedures	procedure	NOUN
easat-8773	90	9	.	.	PUNCT
easat-8773	91	1	working	work	VERB
easat-8773	91	2	mathematically	mathematically	ADV
easat-8773	91	3	to	to	PART
easat-8773	91	4	get	get	VERB
easat-8773	91	5	mathematical	mathematical	ADJ
easat-8773	91	6	solutions	solution	NOUN
easat-8773	91	7	.	.	PUNCT
easat-8773	92	1	errors	error	NOUN
easat-8773	92	2	in	in	ADP
easat-8773	92	3	applying	apply	VERB
easat-8773	92	4	mathematical	mathematical	ADJ
easat-8773	92	5	knowledge	knowledge	NOUN
easat-8773	92	6	to	to	PART
easat-8773	92	7	solve	solve	VERB
easat-8773	92	8	problems	problem	NOUN
easat-8773	92	9	,	,	PUNCT
easat-8773	92	10	such	such	ADJ
easat-8773	92	11	as	as	ADP
easat-8773	92	12	calculation	calculation	NOUN
easat-8773	92	13	errors	error	NOUN
easat-8773	92	14	.	.	PUNCT
easat-8773	93	1	encoding	encode	VERB
easat-8773	93	2	:	:	PUNCT
easat-8773	93	3	errors	error	NOUN
easat-8773	93	4	in	in	ADP
easat-8773	93	5	representing	represent	VERB
easat-8773	93	6	the	the	DET
easat-8773	93	7	mathematical	mathematical	ADJ
easat-8773	93	8	solution	solution	NOUN
easat-8773	93	9	into	into	ADP
easat-8773	93	10	an	an	DET
easat-8773	93	11	acceptable	acceptable	ADJ
easat-8773	93	12	written	write	VERB
easat-8773	93	13	form	form	NOUN
easat-8773	93	14	.	.	PUNCT
easat-8773	94	1	interpreting	interpret	VERB
easat-8773	94	2	mathematical	mathematical	ADJ
easat-8773	94	3	solutions	solution	NOUN
easat-8773	94	4	in	in	ADP
easat-8773	94	5	relation	relation	NOUN
easat-8773	94	6	to	to	ADP
easat-8773	94	7	the	the	DET
easat-8773	94	8	original	original	ADJ
easat-8773	94	9	problem	problem	NOUN
easat-8773	94	10	situations	situation	NOUN
easat-8773	94	11	.	.	PUNCT
easat-8773	95	1	errors	error	NOUN
easat-8773	95	2	in	in	ADP
easat-8773	95	3	connecting	connect	VERB
easat-8773	95	4	the	the	DET
easat-8773	95	5	results	result	NOUN
easat-8773	95	6	of	of	ADP
easat-8773	95	7	calculations	calculation	NOUN
easat-8773	95	8	carried	carry	VERB
easat-8773	95	9	out	out	ADP
easat-8773	95	10	with	with	ADP
easat-8773	95	11	the	the	DET
easat-8773	95	12	context	context	NOUN
easat-8773	95	13	of	of	ADP
easat-8773	95	14	the	the	DET
easat-8773	95	15	problem	problem	NOUN
easat-8773	95	16	.	.	PUNCT
easat-8773	96	1	validating	validate	VERB
easat-8773	96	2	the	the	DET
easat-8773	96	3	interpreted	interpret	VERB
easat-8773	96	4	mathematical	mathematical	ADJ
easat-8773	96	5	solution	solution	NOUN
easat-8773	96	6	by	by	ADP
easat-8773	96	7	checking	check	VERB
easat-8773	96	8	if	if	SCONJ
easat-8773	96	9	it	it	PRON
easat-8773	96	10	is	be	AUX
easat-8773	96	11	appropriate	appropriate	ADJ
easat-8773	96	12	and	and	CCONJ
easat-8773	96	13	reasonable	reasonable	ADJ
easat-8773	96	14	for	for	ADP
easat-8773	96	15	its	its	PRON
easat-8773	96	16	purpose	purpose	NOUN
easat-8773	96	17	.	.	PUNCT
easat-8773	97	1	▪	▪	ADJ
easat-8773	97	2	errors	error	NOUN
easat-8773	97	3	in	in	ADP
easat-8773	97	4	critically	critically	ADV
easat-8773	97	5	examining	examine	VERB
easat-8773	97	6	and	and	CCONJ
easat-8773	97	7	reflecting	reflect	VERB
easat-8773	97	8	on	on	ADP
easat-8773	97	9	the	the	DET
easat-8773	97	10	found	find	VERB
easat-8773	97	11	solution	solution	NOUN
easat-8773	97	12	.	.	PUNCT
easat-8773	98	1	▪	▪	ADJ
easat-8773	98	2	errors	error	NOUN
easat-8773	98	3	in	in	ADP
easat-8773	98	4	evaluating	evaluate	VERB
easat-8773	98	5	some	some	DET
easat-8773	98	6	parts	part	NOUN
easat-8773	98	7	of	of	ADP
easat-8773	98	8	the	the	DET
easat-8773	98	9	model	model	NOUN
easat-8773	98	10	or	or	CCONJ
easat-8773	98	11	in	in	ADP
easat-8773	98	12	repeating	repeat	VERB
easat-8773	98	13	the	the	DET
easat-8773	98	14	modeling	modeling	NOUN
easat-8773	98	15	process	process	NOUN
easat-8773	98	16	.	.	PUNCT
easat-8773	99	1	951	951	NUM
easat-8773	99	2	edelweiss	edelweiss	PROPN
easat-8773	99	3	applied	apply	VERB
easat-8773	99	4	science	science	NOUN
easat-8773	99	5	and	and	CCONJ
easat-8773	99	6	technology	technology	NOUN
easat-8773	99	7	issn	issn	PROPN
easat-8773	99	8	:	:	PUNCT
easat-8773	99	9	2576	2576	NUM
easat-8773	99	10	-	-	SYM
easat-8773	99	11	8484	8484	NUM
easat-8773	99	12	vol	vol	NOUN
easat-8773	99	13	.	.	PROPN
easat-8773	100	1	9	9	NUM
easat-8773	100	2	,	,	PUNCT
easat-8773	100	3	no	no	INTJ
easat-8773	100	4	.	.	NOUN
easat-8773	101	1	7	7	NUM
easat-8773	101	2	:	:	SYM
easat-8773	101	3	947	947	NUM
easat-8773	101	4	-	-	SYM
easat-8773	101	5	959	959	NUM
easat-8773	101	6	,	,	PUNCT
easat-8773	101	7	2025	2025	NUM
easat-8773	101	8	doi	doi	NOUN
easat-8773	101	9	:	:	PUNCT
easat-8773	101	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	101	11	©	©	PROPN
easat-8773	101	12	2025	2025	NUM
easat-8773	101	13	by	by	ADP
easat-8773	101	14	the	the	DET
easat-8773	101	15	authors	author	NOUN
easat-8773	101	16	;	;	PUNCT
easat-8773	101	17	licensee	licensee	PROPN
easat-8773	101	18	learning	learn	VERB
easat-8773	101	19	gate	gate	NOUN
easat-8773	101	20	table	table	NOUN
easat-8773	101	21	2	2	NUM
easat-8773	101	22	.	.	PUNCT
easat-8773	101	23	score	score	PROPN
easat-8773	101	24	mct	mct	PROPN
easat-8773	101	25	and	and	CCONJ
easat-8773	101	26	mmt	mmt	PROPN
easat-8773	101	27	.	.	PUNCT
easat-8773	102	1	statistical	statistical	ADJ
easat-8773	102	2	results	result	NOUN
easat-8773	102	3	mct	mct	PROPN
easat-8773	102	4	mmt	mmt	PROPN
easat-8773	102	5	n	n	PROPN
easat-8773	102	6	72	72	NUM
easat-8773	102	7	72	72	NUM
easat-8773	102	8	mean	mean	NOUN
easat-8773	102	9	61.77	61.77	NUM
easat-8773	102	10	66	66	NUM
easat-8773	102	11	std	std	NOUN
easat-8773	102	12	.	.	PUNCT
easat-8773	103	1	deviation	deviation	NOUN
easat-8773	103	2	19.40	19.40	NUM
easat-8773	103	3	19.68	19.68	NUM
easat-8773	103	4	highest	high	ADJ
easat-8773	103	5	student	student	NOUN
easat-8773	103	6	score	score	NOUN
easat-8773	103	7	100	100	NUM
easat-8773	103	8	100	100	NUM
easat-8773	103	9	lowest	low	ADJ
easat-8773	103	10	student	student	NOUN
easat-8773	103	11	score	score	NOUN
easat-8773	103	12	60	60	NUM
easat-8773	103	13	30	30	NUM
easat-8773	103	14	high	high	ADJ
easat-8773	103	15	level	level	NOUN
easat-8773	103	16	(	(	PUNCT
easat-8773	103	17	score	score	NOUN
easat-8773	103	18	≥	≥	NOUN
easat-8773	103	19	80	80	NUM
easat-8773	103	20	)	)	PUNCT
easat-8773	103	21	20	20	NUM
easat-8773	103	22	22	22	NUM
easat-8773	103	23	medium	medium	ADJ
easat-8773	103	24	level	level	NOUN
easat-8773	103	25	(	(	PUNCT
easat-8773	103	26	65	65	NUM
easat-8773	103	27	≤	≤	NUM
easat-8773	103	28	score	score	NOUN
easat-8773	103	29	<	<	X
easat-8773	103	30	80	80	NUM
easat-8773	103	31	)	)	PUNCT
easat-8773	103	32	19	19	NUM
easat-8773	103	33	15	15	NUM
easat-8773	103	34	low	low	ADJ
easat-8773	103	35	level	level	NOUN
easat-8773	103	36	(	(	PUNCT
easat-8773	103	37	score	score	NOUN
easat-8773	103	38	<	<	X
easat-8773	103	39	65	65	NUM
easat-8773	103	40	)	)	PUNCT
easat-8773	103	41	33	33	NUM
easat-8773	103	42	35	35	NUM
easat-8773	103	43	based	base	VERB
easat-8773	103	44	on	on	ADP
easat-8773	103	45	table	table	NOUN
easat-8773	103	46	2	2	NUM
easat-8773	103	47	,	,	PUNCT
easat-8773	103	48	these	these	DET
easat-8773	103	49	statistics	statistic	NOUN
easat-8773	103	50	provide	provide	VERB
easat-8773	103	51	insights	insight	NOUN
easat-8773	103	52	into	into	ADP
easat-8773	103	53	the	the	DET
easat-8773	103	54	overall	overall	ADJ
easat-8773	103	55	performance	performance	NOUN
easat-8773	103	56	distribution	distribution	NOUN
easat-8773	103	57	and	and	CCONJ
easat-8773	103	58	variability	variability	NOUN
easat-8773	103	59	among	among	ADP
easat-8773	103	60	students	student	NOUN
easat-8773	103	61	in	in	ADP
easat-8773	103	62	both	both	DET
easat-8773	103	63	assessments	assessment	NOUN
easat-8773	103	64	.	.	PUNCT
easat-8773	104	1	the	the	DET
easat-8773	104	2	mmt	mmt	PROPN
easat-8773	104	3	mean	mean	NOUN
easat-8773	104	4	score	score	NOUN
easat-8773	104	5	(	(	PUNCT
easat-8773	104	6	66.60	66.60	NUM
easat-8773	104	7	)	)	PUNCT
easat-8773	104	8	is	be	AUX
easat-8773	104	9	slightly	slightly	ADV
easat-8773	104	10	higher	high	ADJ
easat-8773	104	11	than	than	ADP
easat-8773	104	12	the	the	DET
easat-8773	104	13	mct	mct	PROPN
easat-8773	104	14	mean	mean	NOUN
easat-8773	104	15	score	score	NOUN
easat-8773	104	16	(	(	PUNCT
easat-8773	104	17	61.77	61.77	NUM
easat-8773	104	18	)	)	PUNCT
easat-8773	104	19	,	,	PUNCT
easat-8773	104	20	indicating	indicate	VERB
easat-8773	104	21	differences	difference	NOUN
easat-8773	104	22	in	in	ADP
easat-8773	104	23	students	student	NOUN
easat-8773	104	24	’	'	PUNCT
easat-8773	104	25	competencies	competency	NOUN
easat-8773	104	26	across	across	ADP
easat-8773	104	27	the	the	DET
easat-8773	104	28	two	two	NUM
easat-8773	104	29	domains	domain	NOUN
easat-8773	104	30	.	.	PUNCT
easat-8773	105	1	the	the	DET
easat-8773	105	2	fairly	fairly	ADV
easat-8773	105	3	high	high	ADJ
easat-8773	105	4	variation	variation	NOUN
easat-8773	105	5	in	in	ADP
easat-8773	105	6	scores	score	NOUN
easat-8773	105	7	(	(	PUNCT
easat-8773	105	8	as	as	SCONJ
easat-8773	105	9	indicated	indicate	VERB
easat-8773	105	10	by	by	ADP
easat-8773	105	11	the	the	DET
easat-8773	105	12	standard	standard	ADJ
easat-8773	105	13	deviation	deviation	NOUN
easat-8773	105	14	)	)	PUNCT
easat-8773	105	15	suggests	suggest	VERB
easat-8773	105	16	a	a	DET
easat-8773	105	17	significant	significant	ADJ
easat-8773	105	18	difference	difference	NOUN
easat-8773	105	19	in	in	ADP
easat-8773	105	20	frequency	frequency	NOUN
easat-8773	105	21	or	or	CCONJ
easat-8773	105	22	types	type	NOUN
easat-8773	105	23	of	of	ADP
easat-8773	105	24	errors	error	NOUN
easat-8773	105	25	between	between	ADP
easat-8773	105	26	more	more	ADV
easat-8773	105	27	proficient	proficient	ADJ
easat-8773	105	28	students	student	NOUN
easat-8773	105	29	and	and	CCONJ
easat-8773	105	30	those	those	PRON
easat-8773	105	31	who	who	PRON
easat-8773	105	32	tend	tend	VERB
easat-8773	105	33	to	to	PART
easat-8773	105	34	make	make	VERB
easat-8773	105	35	more	more	ADJ
easat-8773	105	36	errors	error	NOUN
easat-8773	105	37	.	.	PUNCT
easat-8773	106	1	more	more	ADJ
easat-8773	106	2	than	than	ADP
easat-8773	106	3	50	50	NUM
easat-8773	106	4	%	%	NOUN
easat-8773	106	5	of	of	ADP
easat-8773	106	6	students	student	NOUN
easat-8773	106	7	are	be	AUX
easat-8773	106	8	in	in	ADP
easat-8773	106	9	the	the	DET
easat-8773	106	10	medium	medium	ADJ
easat-8773	106	11	and	and	CCONJ
easat-8773	106	12	low	low	ADJ
easat-8773	106	13	mathematical	mathematical	ADJ
easat-8773	106	14	modeling	modeling	NOUN
easat-8773	106	15	ability	ability	NOUN
easat-8773	106	16	level	level	NOUN
easat-8773	106	17	,	,	PUNCT
easat-8773	106	18	this	this	PRON
easat-8773	106	19	indicates	indicate	VERB
easat-8773	106	20	that	that	SCONJ
easat-8773	106	21	many	many	ADJ
easat-8773	106	22	students	student	NOUN
easat-8773	106	23	make	make	VERB
easat-8773	106	24	errors	error	NOUN
easat-8773	106	25	in	in	ADP
easat-8773	106	26	solving	solve	VERB
easat-8773	106	27	mathematical	mathematical	ADJ
easat-8773	106	28	modeling	modeling	NOUN
easat-8773	106	29	problems	problem	NOUN
easat-8773	106	30	.	.	PUNCT
easat-8773	107	1	the	the	DET
easat-8773	107	2	analysis	analysis	NOUN
easat-8773	107	3	of	of	ADP
easat-8773	107	4	students	student	NOUN
easat-8773	107	5	’	'	PUNCT
easat-8773	107	6	responses	response	NOUN
easat-8773	107	7	reveals	reveal	VERB
easat-8773	107	8	that	that	SCONJ
easat-8773	107	9	67	67	NUM
easat-8773	107	10	students	student	NOUN
easat-8773	107	11	made	make	VERB
easat-8773	107	12	errors	error	NOUN
easat-8773	107	13	in	in	ADP
easat-8773	107	14	the	the	DET
easat-8773	107	15	mathematical	mathematical	ADJ
easat-8773	107	16	modeling	modeling	NOUN
easat-8773	107	17	process	process	NOUN
easat-8773	107	18	,	,	PUNCT
easat-8773	107	19	while	while	SCONJ
easat-8773	107	20	5	5	NUM
easat-8773	107	21	students	student	NOUN
easat-8773	107	22	managed	manage	VERB
easat-8773	107	23	to	to	PART
easat-8773	107	24	complete	complete	VERB
easat-8773	107	25	the	the	DET
easat-8773	107	26	entire	entire	ADJ
easat-8773	107	27	mathematical	mathematical	ADJ
easat-8773	107	28	modeling	modeling	NOUN
easat-8773	107	29	process	process	NOUN
easat-8773	107	30	,	,	PUNCT
easat-8773	107	31	see	see	VERB
easat-8773	107	32	table	table	NOUN
easat-8773	107	33	3	3	NUM
easat-8773	107	34	.	.	PUNCT
easat-8773	107	35	table	table	NOUN
easat-8773	107	36	3	3	NUM
easat-8773	107	37	.	.	PUNCT
easat-8773	107	38	frequencies	frequency	NOUN
easat-8773	107	39	students	student	NOUN
easat-8773	107	40	made	make	VERB
easat-8773	107	41	errors	error	NOUN
easat-8773	107	42	in	in	ADP
easat-8773	107	43	modelling	model	VERB
easat-8773	107	44	process	process	NOUN
easat-8773	107	45	.	.	PUNCT
easat-8773	108	1	items	item	NOUN
easat-8773	108	2	understanding	understand	VERB
easat-8773	108	3	simplifying	simplify	VERB
easat-8773	108	4	mathematizing	mathematize	VERB
easat-8773	108	5	working	work	VERB
easat-8773	108	6	within	within	ADP
easat-8773	108	7	mathematics	mathematics	NOUN
easat-8773	108	8	interpreting	interpret	VERB
easat-8773	108	9	validating	validate	VERB
easat-8773	108	10	1	1	NUM
easat-8773	108	11	14	14	NUM
easat-8773	108	12	22	22	NUM
easat-8773	108	13	24	24	NUM
easat-8773	108	14	25	25	NUM
easat-8773	108	15	25	25	NUM
easat-8773	108	16	25	25	NUM
easat-8773	108	17	2	2	NUM
easat-8773	108	18	28	28	NUM
easat-8773	108	19	33	33	NUM
easat-8773	108	20	34	34	NUM
easat-8773	108	21	38	38	NUM
easat-8773	108	22	40	40	NUM
easat-8773	108	23	40	40	NUM
easat-8773	108	24	3	3	NUM
easat-8773	108	25	19	19	NUM
easat-8773	108	26	20	20	NUM
easat-8773	108	27	21	21	NUM
easat-8773	108	28	24	24	NUM
easat-8773	108	29	24	24	NUM
easat-8773	108	30	27	27	NUM
easat-8773	108	31	4	4	NUM
easat-8773	108	32	30	30	NUM
easat-8773	108	33	34	34	NUM
easat-8773	108	34	35	35	NUM
easat-8773	108	35	39	39	NUM
easat-8773	108	36	42	42	NUM
easat-8773	108	37	45	45	NUM
easat-8773	108	38	based	base	VERB
easat-8773	108	39	on	on	ADP
easat-8773	108	40	table	table	NOUN
easat-8773	108	41	3	3	NUM
easat-8773	108	42	,	,	PUNCT
easat-8773	108	43	there	there	PRON
easat-8773	108	44	is	be	VERB
easat-8773	108	45	an	an	DET
easat-8773	108	46	increasing	increase	VERB
easat-8773	108	47	trend	trend	NOUN
easat-8773	108	48	of	of	ADP
easat-8773	108	49	errors	error	NOUN
easat-8773	108	50	from	from	ADP
easat-8773	108	51	item	item	NOUN
easat-8773	108	52	1	1	NUM
easat-8773	108	53	to	to	PART
easat-8773	108	54	item	item	VERB
easat-8773	108	55	4	4	NUM
easat-8773	108	56	at	at	ADP
easat-8773	108	57	all	all	DET
easat-8773	108	58	stages	stage	NOUN
easat-8773	108	59	.	.	PUNCT
easat-8773	109	1	this	this	PRON
easat-8773	109	2	shows	show	VERB
easat-8773	109	3	that	that	SCONJ
easat-8773	109	4	the	the	DET
easat-8773	109	5	more	more	ADV
easat-8773	109	6	complex	complex	ADJ
easat-8773	109	7	the	the	DET
easat-8773	109	8	problem	problem	NOUN
easat-8773	109	9	given	give	VERB
easat-8773	109	10	,	,	PUNCT
easat-8773	109	11	the	the	DET
easat-8773	109	12	more	more	ADV
easat-8773	109	13	likely	likely	ADJ
easat-8773	109	14	students	student	NOUN
easat-8773	109	15	are	be	AUX
easat-8773	109	16	to	to	PART
easat-8773	109	17	make	make	VERB
easat-8773	109	18	errors	error	NOUN
easat-8773	109	19	in	in	ADP
easat-8773	109	20	all	all	DET
easat-8773	109	21	aspects	aspect	NOUN
easat-8773	109	22	of	of	ADP
easat-8773	109	23	the	the	DET
easat-8773	109	24	modeling	modeling	NOUN
easat-8773	109	25	process	process	NOUN
easat-8773	109	26	.	.	PUNCT
easat-8773	110	1	the	the	DET
easat-8773	110	2	highest	high	ADJ
easat-8773	110	3	errors	error	NOUN
easat-8773	110	4	are	be	AUX
easat-8773	110	5	consistently	consistently	ADV
easat-8773	110	6	found	find	VERB
easat-8773	110	7	at	at	ADP
easat-8773	110	8	the	the	DET
easat-8773	110	9	validating	validate	VERB
easat-8773	110	10	(	(	PUNCT
easat-8773	110	11	the	the	DET
easat-8773	110	12	highest	high	ADJ
easat-8773	110	13	at	at	ADP
easat-8773	110	14	item	item	NOUN
easat-8773	110	15	4	4	NUM
easat-8773	110	16	=	=	SYM
easat-8773	110	17	45	45	NUM
easat-8773	110	18	errors	error	NOUN
easat-8773	110	19	)	)	PUNCT
easat-8773	110	20	and	and	CCONJ
easat-8773	110	21	interpreting	interpreting	NOUN
easat-8773	110	22	(	(	PUNCT
easat-8773	110	23	item	item	NOUN
easat-8773	110	24	4	4	NUM
easat-8773	110	25	=	=	SYM
easat-8773	110	26	42	42	NUM
easat-8773	110	27	errors	error	NOUN
easat-8773	110	28	)	)	PUNCT
easat-8773	110	29	process	process	NOUN
easat-8773	110	30	.	.	PUNCT
easat-8773	111	1	this	this	PRON
easat-8773	111	2	reflects	reflect	VERB
easat-8773	111	3	students	student	NOUN
easat-8773	111	4	are	be	AUX
easat-8773	111	5	not	not	PART
easat-8773	111	6	yet	yet	ADV
easat-8773	111	7	accustomed	accustomed	ADJ
easat-8773	111	8	to	to	ADP
easat-8773	111	9	reflecting	reflect	VERB
easat-8773	111	10	or	or	CCONJ
easat-8773	111	11	re	re	VERB
easat-8773	111	12	-	-	VERB
easat-8773	111	13	checking	check	VERB
easat-8773	111	14	their	their	PRON
easat-8773	111	15	modeling	modeling	NOUN
easat-8773	111	16	results	result	NOUN
easat-8773	111	17	against	against	ADP
easat-8773	111	18	the	the	DET
easat-8773	111	19	context	context	NOUN
easat-8773	111	20	of	of	ADP
easat-8773	111	21	the	the	DET
easat-8773	111	22	problem	problem	NOUN
easat-8773	111	23	.	.	PUNCT
easat-8773	112	1	although	although	SCONJ
easat-8773	112	2	still	still	ADV
easat-8773	112	3	significant	significant	ADJ
easat-8773	112	4	,	,	PUNCT
easat-8773	112	5	the	the	DET
easat-8773	112	6	understanding	understanding	NOUN
easat-8773	112	7	process	process	NOUN
easat-8773	112	8	shows	show	VERB
easat-8773	112	9	a	a	DET
easat-8773	112	10	lower	low	ADJ
easat-8773	112	11	frequency	frequency	NOUN
easat-8773	112	12	of	of	ADP
easat-8773	112	13	errors	error	NOUN
easat-8773	112	14	relative	relative	ADJ
easat-8773	112	15	to	to	ADP
easat-8773	112	16	other	other	ADJ
easat-8773	112	17	.	.	PUNCT
easat-8773	113	1	this	this	PRON
easat-8773	113	2	shows	show	VERB
easat-8773	113	3	that	that	SCONJ
easat-8773	113	4	understanding	understand	VERB
easat-8773	113	5	the	the	DET
easat-8773	113	6	initial	initial	ADJ
easat-8773	113	7	context	context	NOUN
easat-8773	113	8	of	of	ADP
easat-8773	113	9	the	the	DET
easat-8773	113	10	problem	problem	NOUN
easat-8773	113	11	is	be	AUX
easat-8773	113	12	easier	easy	ADJ
easat-8773	113	13	for	for	SCONJ
easat-8773	113	14	most	most	ADJ
easat-8773	113	15	students	student	NOUN
easat-8773	113	16	to	to	PART
easat-8773	113	17	achieve	achieve	VERB
easat-8773	113	18	than	than	ADP
easat-8773	113	19	the	the	DET
easat-8773	113	20	mathematization	mathematization	NOUN
easat-8773	113	21	and	and	CCONJ
easat-8773	113	22	evaluation	evaluation	NOUN
easat-8773	113	23	processes	process	NOUN
easat-8773	113	24	of	of	ADP
easat-8773	113	25	the	the	DET
easat-8773	113	26	model	model	NOUN
easat-8773	113	27	.	.	PUNCT
easat-8773	114	1	the	the	DET
easat-8773	114	2	mathematization	mathematization	NOUN
easat-8773	114	3	process	process	NOUN
easat-8773	114	4	(	(	PUNCT
easat-8773	114	5	changing	change	VERB
easat-8773	114	6	real	real	ADJ
easat-8773	114	7	problems	problem	NOUN
easat-8773	114	8	into	into	ADP
easat-8773	114	9	mathematical	mathematical	ADJ
easat-8773	114	10	representations	representation	NOUN
easat-8773	114	11	)	)	PUNCT
easat-8773	114	12	and	and	CCONJ
easat-8773	114	13	working	work	VERB
easat-8773	114	14	within	within	ADP
easat-8773	114	15	mathematics	mathematic	NOUN
easat-8773	114	16	(	(	PUNCT
easat-8773	114	17	solving	solving	NOUN
easat-8773	114	18	models	model	NOUN
easat-8773	114	19	)	)	PUNCT
easat-8773	114	20	also	also	ADV
easat-8773	114	21	show	show	VERB
easat-8773	114	22	a	a	DET
easat-8773	114	23	high	high	ADJ
easat-8773	114	24	frequency	frequency	NOUN
easat-8773	114	25	of	of	ADP
easat-8773	114	26	errors	error	NOUN
easat-8773	114	27	,	,	PUNCT
easat-8773	114	28	indicating	indicate	VERB
easat-8773	114	29	that	that	SCONJ
easat-8773	114	30	students	student	NOUN
easat-8773	114	31	face	face	VERB
easat-8773	114	32	not	not	PART
easat-8773	114	33	only	only	ADV
easat-8773	114	34	conceptual	conceptual	ADJ
easat-8773	114	35	but	but	CCONJ
easat-8773	114	36	also	also	ADV
easat-8773	114	37	procedural	procedural	ADJ
easat-8773	114	38	challenges	challenge	NOUN
easat-8773	114	39	in	in	ADP
easat-8773	114	40	solving	solve	VERB
easat-8773	114	41	mathematical	mathematical	ADJ
easat-8773	114	42	problems	problem	NOUN
easat-8773	114	43	.	.	PUNCT
easat-8773	115	1	these	these	DET
easat-8773	115	2	results	result	NOUN
easat-8773	115	3	indicate	indicate	VERB
easat-8773	115	4	that	that	SCONJ
easat-8773	115	5	students	student	NOUN
easat-8773	115	6	'	'	PART
easat-8773	115	7	mathematical	mathematical	ADJ
easat-8773	115	8	modeling	modeling	NOUN
easat-8773	115	9	abilities	ability	NOUN
easat-8773	115	10	are	be	AUX
easat-8773	115	11	multilevel	multilevel	ADJ
easat-8773	115	12	and	and	CCONJ
easat-8773	115	13	interrelated	interrelated	ADJ
easat-8773	115	14	.	.	PUNCT
easat-8773	116	1	students	student	NOUN
easat-8773	116	2	who	who	PRON
easat-8773	116	3	do	do	AUX
easat-8773	116	4	not	not	PART
easat-8773	116	5	understand	understand	VERB
easat-8773	116	6	the	the	DET
easat-8773	116	7	problem	problem	NOUN
easat-8773	116	8	well	well	ADV
easat-8773	116	9	will	will	AUX
easat-8773	116	10	have	have	VERB
easat-8773	116	11	errors	error	NOUN
easat-8773	116	12	in	in	ADP
easat-8773	116	13	simplifying	simplifying	NOUN
easat-8773	116	14	,	,	PUNCT
easat-8773	116	15	modeling	modeling	NOUN
easat-8773	116	16	,	,	PUNCT
easat-8773	116	17	solving	solving	NOUN
easat-8773	116	18	,	,	PUNCT
easat-8773	116	19	and	and	CCONJ
easat-8773	116	20	interpreting	interpret	VERB
easat-8773	116	21	and	and	CCONJ
easat-8773	116	22	validating	validate	VERB
easat-8773	116	23	solutions	solution	NOUN
easat-8773	116	24	.	.	PUNCT
easat-8773	117	1	therefore	therefore	ADV
easat-8773	117	2	,	,	PUNCT
easat-8773	117	3	learning	learn	VERB
easat-8773	117	4	needs	need	VERB
easat-8773	117	5	to	to	PART
easat-8773	117	6	focus	focus	VERB
easat-8773	117	7	more	more	ADJ
easat-8773	117	8	attention	attention	NOUN
easat-8773	117	9	on	on	ADP
easat-8773	117	10	the	the	DET
easat-8773	117	11	stages	stage	NOUN
easat-8773	117	12	of	of	ADP
easat-8773	117	13	interpretation	interpretation	NOUN
easat-8773	117	14	and	and	CCONJ
easat-8773	117	15	validation	validation	NOUN
easat-8773	117	16	,	,	PUNCT
easat-8773	117	17	develop	develop	VERB
easat-8773	117	18	students	student	NOUN
easat-8773	117	19	'	'	PART
easat-8773	117	20	reflective	reflective	ADJ
easat-8773	117	21	and	and	CCONJ
easat-8773	117	22	critical	critical	ADJ
easat-8773	117	23	thinking	thinking	NOUN
easat-8773	117	24	skills	skill	NOUN
easat-8773	117	25	,	,	PUNCT
easat-8773	117	26	and	and	CCONJ
easat-8773	117	27	increase	increase	VERB
easat-8773	117	28	problem	problem	NOUN
easat-8773	117	29	-	-	PUNCT
easat-8773	117	30	solving	solve	VERB
easat-8773	117	31	exercises	exercise	NOUN
easat-8773	117	32	that	that	PRON
easat-8773	117	33	require	require	VERB
easat-8773	117	34	more	more	ADJ
easat-8773	117	35	than	than	ADP
easat-8773	117	36	just	just	ADV
easat-8773	117	37	procedural	procedural	ADJ
easat-8773	117	38	skills	skill	NOUN
easat-8773	117	39	.	.	PUNCT
easat-8773	118	1	the	the	DET
easat-8773	118	2	percentages	percentage	NOUN
easat-8773	118	3	of	of	ADP
easat-8773	118	4	errors	error	NOUN
easat-8773	118	5	in	in	ADP
easat-8773	118	6	each	each	DET
easat-8773	118	7	mathematical	mathematical	ADJ
easat-8773	118	8	modeling	modeling	NOUN
easat-8773	118	9	process	process	NOUN
easat-8773	118	10	are	be	AUX
easat-8773	118	11	illustrated	illustrate	VERB
easat-8773	118	12	in	in	ADP
easat-8773	118	13	figure	figure	NOUN
easat-8773	118	14	2	2	NUM
easat-8773	118	15	.	.	NOUN
easat-8773	118	16	952	952	NUM
easat-8773	118	17	edelweiss	edelweiss	PROPN
easat-8773	118	18	applied	apply	VERB
easat-8773	118	19	science	science	NOUN
easat-8773	118	20	and	and	CCONJ
easat-8773	118	21	technology	technology	NOUN
easat-8773	118	22	issn	issn	PROPN
easat-8773	118	23	:	:	PUNCT
easat-8773	118	24	2576	2576	NUM
easat-8773	118	25	-	-	SYM
easat-8773	118	26	8484	8484	NUM
easat-8773	118	27	vol	vol	NOUN
easat-8773	118	28	.	.	PROPN
easat-8773	119	1	9	9	NUM
easat-8773	119	2	,	,	PUNCT
easat-8773	119	3	no	no	INTJ
easat-8773	119	4	.	.	NOUN
easat-8773	120	1	7	7	NUM
easat-8773	120	2	:	:	SYM
easat-8773	120	3	947	947	NUM
easat-8773	120	4	-	-	SYM
easat-8773	120	5	959	959	NUM
easat-8773	120	6	,	,	PUNCT
easat-8773	120	7	2025	2025	NUM
easat-8773	120	8	doi	doi	NOUN
easat-8773	120	9	:	:	PUNCT
easat-8773	120	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	120	11	©	©	PROPN
easat-8773	120	12	2025	2025	NUM
easat-8773	120	13	by	by	ADP
easat-8773	120	14	the	the	DET
easat-8773	120	15	authors	author	NOUN
easat-8773	120	16	;	;	PUNCT
easat-8773	120	17	licensee	licensee	PROPN
easat-8773	120	18	learning	learn	VERB
easat-8773	120	19	gate	gate	NOUN
easat-8773	120	20	figure	figure	NOUN
easat-8773	120	21	2	2	NUM
easat-8773	120	22	.	.	NOUN
easat-8773	120	23	percentage	percentage	NOUN
easat-8773	120	24	of	of	ADP
easat-8773	120	25	errors	error	NOUN
easat-8773	120	26	in	in	ADP
easat-8773	120	27	the	the	DET
easat-8773	120	28	modeling	modeling	NOUN
easat-8773	120	29	process	process	NOUN
easat-8773	120	30	.	.	PUNCT
easat-8773	121	1	from	from	ADP
easat-8773	121	2	the	the	DET
easat-8773	121	3	diagram	diagram	NOUN
easat-8773	121	4	in	in	ADP
easat-8773	121	5	figure	figure	NOUN
easat-8773	121	6	2	2	NUM
easat-8773	121	7	,	,	PUNCT
easat-8773	121	8	validating	validate	VERB
easat-8773	121	9	(	(	PUNCT
easat-8773	121	10	47.56	47.56	NUM
easat-8773	121	11	%	%	NOUN
easat-8773	121	12	)	)	PUNCT
easat-8773	121	13	showed	show	VERB
easat-8773	121	14	the	the	DET
easat-8773	121	15	highest	high	ADJ
easat-8773	121	16	error	error	NOUN
easat-8773	121	17	rate	rate	NOUN
easat-8773	121	18	.	.	PUNCT
easat-8773	122	1	this	this	PRON
easat-8773	122	2	indicates	indicate	VERB
easat-8773	122	3	that	that	SCONJ
easat-8773	122	4	many	many	ADJ
easat-8773	122	5	students	student	NOUN
easat-8773	122	6	have	have	VERB
easat-8773	122	7	errors	error	NOUN
easat-8773	122	8	in	in	ADP
easat-8773	122	9	checking	check	VERB
easat-8773	122	10	their	their	PRON
easat-8773	122	11	solutions	solution	NOUN
easat-8773	122	12	against	against	ADP
easat-8773	122	13	the	the	DET
easat-8773	122	14	context	context	NOUN
easat-8773	122	15	of	of	ADP
easat-8773	122	16	the	the	DET
easat-8773	122	17	problem	problem	NOUN
easat-8773	122	18	.	.	PUNCT
easat-8773	123	1	validating	validate	VERB
easat-8773	123	2	requires	require	VERB
easat-8773	123	3	a	a	DET
easat-8773	123	4	deep	deep	ADJ
easat-8773	123	5	understanding	understanding	NOUN
easat-8773	123	6	of	of	ADP
easat-8773	123	7	the	the	DET
easat-8773	123	8	relationship	relationship	NOUN
easat-8773	123	9	between	between	ADP
easat-8773	123	10	mathematical	mathematical	ADJ
easat-8773	123	11	results	result	NOUN
easat-8773	123	12	and	and	CCONJ
easat-8773	123	13	real	real	ADJ
easat-8773	123	14	situations	situation	NOUN
easat-8773	123	15	,	,	PUNCT
easat-8773	123	16	which	which	PRON
easat-8773	123	17	is	be	AUX
easat-8773	123	18	often	often	ADV
easat-8773	123	19	overlooked	overlook	VERB
easat-8773	123	20	.	.	PUNCT
easat-8773	124	1	interpreting	interpret	VERB
easat-8773	124	2	(	(	PUNCT
easat-8773	124	3	45.48	45.48	NUM
easat-8773	124	4	%	%	NOUN
easat-8773	124	5	)	)	PUNCT
easat-8773	124	6	also	also	ADV
easat-8773	124	7	showed	show	VERB
easat-8773	124	8	high	high	ADJ
easat-8773	124	9	errors	error	NOUN
easat-8773	124	10	.	.	PUNCT
easat-8773	125	1	this	this	PRON
easat-8773	125	2	reflects	reflect	VERB
easat-8773	125	3	the	the	DET
easat-8773	125	4	challenge	challenge	NOUN
easat-8773	125	5	in	in	ADP
easat-8773	125	6	presenting	present	VERB
easat-8773	125	7	calculation	calculation	NOUN
easat-8773	125	8	results	result	NOUN
easat-8773	125	9	with	with	ADP
easat-8773	125	10	contextual	contextual	ADJ
easat-8773	125	11	meaning	meaning	NOUN
easat-8773	125	12	.	.	PUNCT
easat-8773	126	1	students	student	NOUN
easat-8773	126	2	may	may	AUX
easat-8773	126	3	not	not	PART
easat-8773	126	4	be	be	AUX
easat-8773	126	5	able	able	ADJ
easat-8773	126	6	to	to	PART
easat-8773	126	7	solve	solve	VERB
easat-8773	126	8	the	the	DET
easat-8773	126	9	model	model	NOUN
easat-8773	126	10	,	,	PUNCT
easat-8773	126	11	but	but	CCONJ
easat-8773	126	12	fail	fail	VERB
easat-8773	126	13	to	to	PART
easat-8773	126	14	interpret	interpret	VERB
easat-8773	126	15	the	the	DET
easat-8773	126	16	results	result	NOUN
easat-8773	126	17	meaningfully	meaningfully	ADV
easat-8773	126	18	.	.	PUNCT
easat-8773	127	1	working	work	VERB
easat-8773	127	2	mathematically	mathematically	ADV
easat-8773	127	3	(	(	PUNCT
easat-8773	127	4	43.75	43.75	NUM
easat-8773	127	5	%	%	NOUN
easat-8773	127	6	)	)	PUNCT
easat-8773	127	7	refers	refer	VERB
easat-8773	127	8	to	to	ADP
easat-8773	127	9	the	the	DET
easat-8773	127	10	process	process	NOUN
easat-8773	127	11	of	of	ADP
easat-8773	127	12	mathematical	mathematical	ADJ
easat-8773	127	13	manipulation	manipulation	NOUN
easat-8773	127	14	.	.	PUNCT
easat-8773	128	1	errors	error	NOUN
easat-8773	128	2	at	at	ADP
easat-8773	128	3	this	this	DET
easat-8773	128	4	stage	stage	NOUN
easat-8773	128	5	can	can	AUX
easat-8773	128	6	come	come	VERB
easat-8773	128	7	from	from	ADP
easat-8773	128	8	incorrect	incorrect	ADJ
easat-8773	128	9	algebraic	algebraic	ADJ
easat-8773	128	10	procedures	procedure	NOUN
easat-8773	128	11	,	,	PUNCT
easat-8773	128	12	calculation	calculation	NOUN
easat-8773	128	13	errors	error	NOUN
easat-8773	128	14	,	,	PUNCT
easat-8773	128	15	or	or	CCONJ
easat-8773	128	16	inappropriate	inappropriate	ADJ
easat-8773	128	17	application	application	NOUN
easat-8773	128	18	formulations	formulation	NOUN
easat-8773	128	19	.	.	PUNCT
easat-8773	129	1	mathematizing	mathematize	VERB
easat-8773	129	2	(	(	PUNCT
easat-8773	129	3	39.58	39.58	NUM
easat-8773	129	4	%	%	NOUN
easat-8773	129	5	)	)	PUNCT
easat-8773	129	6	shows	show	VERB
easat-8773	129	7	that	that	SCONJ
easat-8773	129	8	students	student	NOUN
easat-8773	129	9	still	still	ADV
easat-8773	129	10	have	have	VERB
easat-8773	129	11	errors	error	NOUN
easat-8773	129	12	in	in	ADP
easat-8773	129	13	converting	convert	VERB
easat-8773	129	14	real	real	ADJ
easat-8773	129	15	-	-	PUNCT
easat-8773	129	16	world	world	NOUN
easat-8773	129	17	situations	situation	NOUN
easat-8773	129	18	into	into	ADP
easat-8773	129	19	mathematical	mathematical	ADJ
easat-8773	129	20	representations	representation	NOUN
easat-8773	129	21	.	.	PUNCT
easat-8773	130	1	this	this	PRON
easat-8773	130	2	can	can	AUX
easat-8773	130	3	be	be	AUX
easat-8773	130	4	caused	cause	VERB
easat-8773	130	5	by	by	ADP
easat-8773	130	6	misconceptions	misconception	NOUN
easat-8773	130	7	or	or	CCONJ
easat-8773	130	8	lack	lack	NOUN
easat-8773	130	9	of	of	ADP
easat-8773	130	10	experience	experience	NOUN
easat-8773	130	11	in	in	ADP
easat-8773	130	12	building	building	NOUN
easat-8773	130	13	models	model	NOUN
easat-8773	130	14	.	.	PUNCT
easat-8773	131	1	simplifying	simplify	VERB
easat-8773	131	2	(	(	PUNCT
easat-8773	131	3	37.84	37.84	NUM
easat-8773	131	4	%	%	NOUN
easat-8773	131	5	)	)	PUNCT
easat-8773	131	6	indicates	indicate	VERB
easat-8773	131	7	that	that	SCONJ
easat-8773	131	8	the	the	DET
easat-8773	131	9	process	process	NOUN
easat-8773	131	10	of	of	ADP
easat-8773	131	11	harmonizing	harmonize	VERB
easat-8773	131	12	information	information	NOUN
easat-8773	131	13	from	from	ADP
easat-8773	131	14	context	context	NOUN
easat-8773	131	15	to	to	ADP
easat-8773	131	16	a	a	DET
easat-8773	131	17	form	form	NOUN
easat-8773	131	18	that	that	PRON
easat-8773	131	19	can	can	AUX
easat-8773	131	20	be	be	AUX
easat-8773	131	21	modeled	model	VERB
easat-8773	131	22	is	be	AUX
easat-8773	131	23	also	also	ADV
easat-8773	131	24	a	a	DET
easat-8773	131	25	challenge	challenge	NOUN
easat-8773	131	26	.	.	PUNCT
easat-8773	132	1	students	student	NOUN
easat-8773	132	2	may	may	AUX
easat-8773	132	3	be	be	AUX
easat-8773	132	4	unable	unable	ADJ
easat-8773	132	5	to	to	PART
easat-8773	132	6	identify	identify	VERB
easat-8773	132	7	important	important	ADJ
easat-8773	132	8	information	information	NOUN
easat-8773	132	9	and	and	CCONJ
easat-8773	132	10	distinguish	distinguish	VERB
easat-8773	132	11	it	it	PRON
easat-8773	132	12	from	from	ADP
easat-8773	132	13	irrelevant	irrelevant	ADJ
easat-8773	132	14	information	information	NOUN
easat-8773	132	15	.	.	PUNCT
easat-8773	133	1	understanding	understanding	NOUN
easat-8773	133	2	(	(	PUNCT
easat-8773	133	3	31.59	31.59	NUM
easat-8773	133	4	%	%	NOUN
easat-8773	133	5	)	)	PUNCT
easat-8773	133	6	has	have	VERB
easat-8773	133	7	the	the	DET
easat-8773	133	8	lowest	low	ADJ
easat-8773	133	9	percentage	percentage	NOUN
easat-8773	133	10	of	of	ADP
easat-8773	133	11	errors	error	NOUN
easat-8773	133	12	,	,	PUNCT
easat-8773	133	13	but	but	CCONJ
easat-8773	133	14	is	be	AUX
easat-8773	133	15	still	still	ADV
easat-8773	133	16	significant	significant	ADJ
easat-8773	133	17	.	.	PUNCT
easat-8773	134	1	this	this	PRON
easat-8773	134	2	shows	show	VERB
easat-8773	134	3	that	that	SCONJ
easat-8773	134	4	although	although	SCONJ
easat-8773	134	5	most	most	ADJ
easat-8773	134	6	students	student	NOUN
easat-8773	134	7	can	can	AUX
easat-8773	134	8	understand	understand	VERB
easat-8773	134	9	the	the	DET
easat-8773	134	10	context	context	NOUN
easat-8773	134	11	of	of	ADP
easat-8773	134	12	the	the	DET
easat-8773	134	13	problem	problem	NOUN
easat-8773	134	14	,	,	PUNCT
easat-8773	134	15	there	there	PRON
easat-8773	134	16	are	be	VERB
easat-8773	134	17	still	still	ADV
easat-8773	134	18	some	some	PRON
easat-8773	134	19	who	who	PRON
easat-8773	134	20	have	have	VERB
easat-8773	134	21	errors	error	NOUN
easat-8773	134	22	in	in	ADP
easat-8773	134	23	understanding	understand	VERB
easat-8773	134	24	the	the	DET
easat-8773	134	25	initial	initial	ADJ
easat-8773	134	26	information	information	NOUN
easat-8773	134	27	as	as	ADP
easat-8773	134	28	a	a	DET
easat-8773	134	29	whole	whole	NOUN
easat-8773	134	30	.	.	PUNCT
easat-8773	135	1	based	base	VERB
easat-8773	135	2	on	on	ADP
easat-8773	135	3	the	the	DET
easat-8773	135	4	distribution	distribution	NOUN
easat-8773	135	5	of	of	ADP
easat-8773	135	6	error	error	NOUN
easat-8773	135	7	percentages	percentage	NOUN
easat-8773	135	8	,	,	PUNCT
easat-8773	135	9	it	it	PRON
easat-8773	135	10	can	can	AUX
easat-8773	135	11	be	be	AUX
easat-8773	135	12	seen	see	VERB
easat-8773	135	13	that	that	SCONJ
easat-8773	135	14	students	student	NOUN
easat-8773	135	15	experience	experience	VERB
easat-8773	135	16	increasing	increase	VERB
easat-8773	135	17	errors	error	NOUN
easat-8773	135	18	along	along	ADP
easat-8773	135	19	with	with	ADP
easat-8773	135	20	the	the	DET
easat-8773	135	21	complexity	complexity	NOUN
easat-8773	135	22	of	of	ADP
easat-8773	135	23	the	the	DET
easat-8773	135	24	mathematical	mathematical	ADJ
easat-8773	135	25	modeling	modeling	NOUN
easat-8773	135	26	process	process	NOUN
easat-8773	135	27	.	.	PUNCT
easat-8773	136	1	the	the	DET
easat-8773	136	2	lowest	low	ADJ
easat-8773	136	3	errors	error	NOUN
easat-8773	136	4	occurred	occur	VERB
easat-8773	136	5	at	at	ADP
easat-8773	136	6	the	the	DET
easat-8773	136	7	understanding	understanding	NOUN
easat-8773	136	8	process	process	NOUN
easat-8773	136	9	(	(	PUNCT
easat-8773	136	10	31.59	31.59	NUM
easat-8773	136	11	%	%	NOUN
easat-8773	136	12	)	)	PUNCT
easat-8773	136	13	,	,	PUNCT
easat-8773	136	14	indicating	indicate	VERB
easat-8773	136	15	that	that	SCONJ
easat-8773	136	16	most	most	ADJ
easat-8773	136	17	students	student	NOUN
easat-8773	136	18	were	be	AUX
easat-8773	136	19	able	able	ADJ
easat-8773	136	20	to	to	PART
easat-8773	136	21	understand	understand	VERB
easat-8773	136	22	the	the	DET
easat-8773	136	23	problem	problem	NOUN
easat-8773	136	24	situation	situation	NOUN
easat-8773	136	25	initially	initially	ADV
easat-8773	136	26	.	.	PUNCT
easat-8773	137	1	however	however	ADV
easat-8773	137	2	,	,	PUNCT
easat-8773	137	3	as	as	SCONJ
easat-8773	137	4	the	the	DET
easat-8773	137	5	process	process	NOUN
easat-8773	137	6	progressed	progress	VERB
easat-8773	137	7	,	,	PUNCT
easat-8773	137	8	errors	error	NOUN
easat-8773	137	9	increased	increase	VERB
easat-8773	137	10	gradually	gradually	ADV
easat-8773	137	11	,	,	PUNCT
easat-8773	137	12	reflecting	reflect	VERB
easat-8773	137	13	conceptual	conceptual	ADJ
easat-8773	137	14	and	and	CCONJ
easat-8773	137	15	procedural	procedural	ADJ
easat-8773	137	16	difficulties	difficulty	NOUN
easat-8773	137	17	.	.	PUNCT
easat-8773	138	1	the	the	DET
easat-8773	138	2	final	final	ADJ
easat-8773	138	3	process	process	NOUN
easat-8773	138	4	such	such	ADJ
easat-8773	138	5	as	as	ADP
easat-8773	138	6	interpreting	interpret	VERB
easat-8773	138	7	(	(	PUNCT
easat-8773	138	8	45.48	45.48	NUM
easat-8773	138	9	%	%	NOUN
easat-8773	138	10	)	)	PUNCT
easat-8773	138	11	and	and	CCONJ
easat-8773	138	12	validating	validate	VERB
easat-8773	138	13	(	(	PUNCT
easat-8773	138	14	47.56	47.56	NUM
easat-8773	138	15	%	%	NOUN
easat-8773	138	16	)	)	PUNCT
easat-8773	138	17	had	have	VERB
easat-8773	138	18	the	the	DET
easat-8773	138	19	highest	high	ADJ
easat-8773	138	20	error	error	NOUN
easat-8773	138	21	rates	rate	NOUN
easat-8773	138	22	,	,	PUNCT
easat-8773	138	23	indicating	indicate	VERB
easat-8773	138	24	students	student	NOUN
easat-8773	138	25	'	'	PART
easat-8773	138	26	weak	weak	ADJ
easat-8773	138	27	ability	ability	NOUN
easat-8773	138	28	to	to	PART
easat-8773	138	29	connect	connect	VERB
easat-8773	138	30	mathematical	mathematical	ADJ
easat-8773	138	31	results	result	NOUN
easat-8773	138	32	with	with	ADP
easat-8773	138	33	realworld	realworld	PROPN
easat-8773	138	34	contexts	contexts	PROPN
easat-8773	138	35	and	and	CCONJ
easat-8773	138	36	to	to	PART
easat-8773	138	37	verify	verify	VERB
easat-8773	138	38	the	the	DET
easat-8773	138	39	solutions	solution	NOUN
easat-8773	138	40	obtained	obtain	VERB
easat-8773	138	41	.	.	PUNCT
easat-8773	139	1	this	this	PRON
easat-8773	139	2	indicates	indicate	VERB
easat-8773	139	3	that	that	SCONJ
easat-8773	139	4	critical	critical	ADJ
easat-8773	139	5	reflection	reflection	NOUN
easat-8773	139	6	on	on	ADP
easat-8773	139	7	results	result	NOUN
easat-8773	139	8	and	and	CCONJ
easat-8773	139	9	contextual	contextual	ADJ
easat-8773	139	10	understanding	understanding	NOUN
easat-8773	139	11	are	be	AUX
easat-8773	139	12	still	still	ADV
easat-8773	139	13	major	major	ADJ
easat-8773	139	14	challenges	challenge	NOUN
easat-8773	139	15	in	in	ADP
easat-8773	139	16	the	the	DET
easat-8773	139	17	modeling	modeling	NOUN
easat-8773	139	18	process	process	NOUN
easat-8773	139	19	.	.	PUNCT
easat-8773	140	1	the	the	DET
easat-8773	140	2	results	result	VERB
easat-8773	140	3	analysis	analysis	NOUN
easat-8773	140	4	errors	error	NOUN
easat-8773	140	5	in	in	ADP
easat-8773	140	6	the	the	DET
easat-8773	140	7	mathematical	mathematical	ADJ
easat-8773	140	8	modeling	modeling	NOUN
easat-8773	140	9	process	process	NOUN
easat-8773	140	10	made	make	VERB
easat-8773	140	11	by	by	ADP
easat-8773	140	12	students	student	NOUN
easat-8773	140	13	in	in	ADP
easat-8773	140	14	the	the	DET
easat-8773	140	15	high	high	ADJ
easat-8773	140	16	,	,	PUNCT
easat-8773	140	17	medium	medium	ADJ
easat-8773	140	18	,	,	PUNCT
easat-8773	140	19	and	and	CCONJ
easat-8773	140	20	low	low	ADJ
easat-8773	140	21	mathematical	mathematical	ADJ
easat-8773	140	22	ability	ability	NOUN
easat-8773	140	23	levels	level	NOUN
easat-8773	140	24	are	be	AUX
easat-8773	140	25	presented	present	VERB
easat-8773	140	26	.	.	PUNCT
easat-8773	141	1	31.59	31.59	NUM
easat-8773	141	2	%	%	NOUN
easat-8773	141	3	37.84	37.84	NUM
easat-8773	141	4	%	%	NOUN
easat-8773	141	5	39.58	39.58	NUM
easat-8773	141	6	%	%	NOUN
easat-8773	141	7	43.75	43.75	NUM
easat-8773	141	8	%	%	NOUN
easat-8773	141	9	45.48	45.48	NUM
easat-8773	141	10	%	%	NOUN
easat-8773	141	11	47.56	47.56	NUM
easat-8773	141	12	%	%	NOUN
easat-8773	141	13	u	u	NOUN
easat-8773	141	14	n	n	NOUN
easat-8773	141	15	d	d	NOUN
easat-8773	141	16	e	e	NOUN
easat-8773	141	17	r	r	NOUN
easat-8773	141	18	s	s	PROPN
easat-8773	141	19	t	t	NOUN
easat-8773	141	20	a	a	DET
easat-8773	141	21	n	n	NOUN
easat-8773	141	22	d	d	NOUN
easat-8773	141	23	in	in	ADP
easat-8773	141	24	g	g	PROPN
easat-8773	141	25	s	s	PROPN
easat-8773	141	26	i	i	NOUN
easat-8773	141	27	m	m	VERB
easat-8773	141	28	p	p	NOUN
easat-8773	142	1	l	l	NOUN
easat-8773	143	1	i	i	PRON
easat-8773	143	2	f	f	NOUN
easat-8773	144	1	y	y	VERB
easat-8773	144	2	i	i	PRON
easat-8773	145	1	n	n	CCONJ
easat-8773	146	1	g	g	PROPN
easat-8773	146	2	m	m	PROPN
easat-8773	146	3	a	a	DET
easat-8773	146	4	t	t	NOUN
easat-8773	146	5	h	h	NOUN
easat-8773	147	1	e	e	NOUN
easat-8773	147	2	m	m	VERB
easat-8773	147	3	a	a	DET
easat-8773	147	4	t	t	X
easat-8773	148	1	iz	iz	INTJ
easat-8773	148	2	i	i	PRON
easat-8773	149	1	n	n	ADV
easat-8773	150	1	g	g	NOUN
easat-8773	150	2	w	w	NOUN
easat-8773	150	3	o	o	NOUN
easat-8773	150	4	r	r	NOUN
easat-8773	150	5	k	k	NOUN
easat-8773	150	6	in	in	ADP
easat-8773	150	7	g	g	PROPN
easat-8773	150	8	in	in	ADP
easat-8773	150	9	t	t	PROPN
easat-8773	150	10	e	e	NOUN
easat-8773	150	11	r	r	NOUN
easat-8773	150	12	p	p	NOUN
easat-8773	150	13	r	r	NOUN
easat-8773	150	14	e	e	NOUN
easat-8773	150	15	t	t	NOUN
easat-8773	150	16	in	in	ADP
easat-8773	150	17	g	g	PROPN
easat-8773	150	18	v	v	ADP
easat-8773	150	19	a	a	DET
easat-8773	150	20	lid	lid	NOUN
easat-8773	151	1	a	a	DET
easat-8773	151	2	t	t	NOUN
easat-8773	152	1	i	i	PRON
easat-8773	153	1	n	n	ADV
easat-8773	154	1	g	g	NOUN
easat-8773	154	2	pe	pe	INTJ
easat-8773	154	3	r	r	NOUN
easat-8773	154	4	c	c	NOUN
easat-8773	154	5	e	e	NOUN
easat-8773	154	6	nt	not	PART
easat-8773	154	7	age	age	VERB
easat-8773	155	1	o	o	NOUN
easat-8773	155	2	f	f	X
easat-8773	155	3	er	er	INTJ
easat-8773	155	4	r	r	NOUN
easat-8773	155	5	or	or	CCONJ
easat-8773	155	6	s	s	PROPN
easat-8773	155	7	953	953	NUM
easat-8773	155	8	edelweiss	edelweiss	PROPN
easat-8773	155	9	applied	apply	VERB
easat-8773	155	10	science	science	NOUN
easat-8773	155	11	and	and	CCONJ
easat-8773	155	12	technology	technology	NOUN
easat-8773	155	13	issn	issn	PROPN
easat-8773	155	14	:	:	PUNCT
easat-8773	155	15	2576	2576	NUM
easat-8773	155	16	-	-	SYM
easat-8773	155	17	8484	8484	NUM
easat-8773	155	18	vol	vol	NOUN
easat-8773	155	19	.	.	PROPN
easat-8773	156	1	9	9	NUM
easat-8773	156	2	,	,	PUNCT
easat-8773	156	3	no	no	INTJ
easat-8773	156	4	.	.	NOUN
easat-8773	157	1	7	7	NUM
easat-8773	157	2	:	:	SYM
easat-8773	157	3	947	947	NUM
easat-8773	157	4	-	-	SYM
easat-8773	157	5	959	959	NUM
easat-8773	157	6	,	,	PUNCT
easat-8773	157	7	2025	2025	NUM
easat-8773	157	8	doi	doi	NOUN
easat-8773	157	9	:	:	PUNCT
easat-8773	157	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	157	11	©	©	PROPN
easat-8773	157	12	2025	2025	NUM
easat-8773	157	13	by	by	ADP
easat-8773	157	14	the	the	DET
easat-8773	157	15	authors	author	NOUN
easat-8773	157	16	;	;	PUNCT
easat-8773	157	17	licensee	licensee	PROPN
easat-8773	157	18	learning	learn	VERB
easat-8773	157	19	gate	gate	NOUN
easat-8773	157	20	table	table	NOUN
easat-8773	157	21	4	4	NUM
easat-8773	157	22	.	.	PUNCT
easat-8773	157	23	student	student	NOUN
easat-8773	157	24	errors	error	NOUN
easat-8773	157	25	based	base	VERB
easat-8773	157	26	on	on	ADP
easat-8773	157	27	the	the	DET
easat-8773	157	28	level	level	NOUN
easat-8773	157	29	of	of	ADP
easat-8773	157	30	mathematical	mathematical	ADJ
easat-8773	157	31	ability	ability	NOUN
easat-8773	157	32	.	.	PUNCT
easat-8773	158	1	groups	group	NOUN
easat-8773	158	2	understanding	understand	VERB
easat-8773	158	3	simplifying	simplify	VERB
easat-8773	158	4	mathematizing	mathematize	VERB
easat-8773	158	5	working	work	VERB
easat-8773	158	6	mathematically	mathematically	ADV
easat-8773	158	7	interpreting	interpret	VERB
easat-8773	158	8	validating	validate	VERB
easat-8773	158	9	high	high	ADJ
easat-8773	158	10	0	0	NUM
easat-8773	158	11	%	%	NOUN
easat-8773	158	12	0	0	NUM
easat-8773	158	13	%	%	NOUN
easat-8773	158	14	0	0	NUM
easat-8773	158	15	%	%	NOUN
easat-8773	158	16	2.08	2.08	NUM
easat-8773	158	17	%	%	NOUN
easat-8773	158	18	18	18	NUM
easat-8773	158	19	%	%	NOUN
easat-8773	158	20	25	25	NUM
easat-8773	158	21	%	%	NOUN
easat-8773	158	22	medium	medium	ADJ
easat-8773	158	23	5	5	NUM
easat-8773	158	24	%	%	NOUN
easat-8773	158	25	12.5	12.5	NUM
easat-8773	158	26	%	%	NOUN
easat-8773	158	27	15	15	NUM
easat-8773	158	28	%	%	NOUN
easat-8773	158	29	25	25	NUM
easat-8773	158	30	%	%	NOUN
easat-8773	158	31	35	35	NUM
easat-8773	158	32	%	%	NOUN
easat-8773	158	33	37.5	37.5	NUM
easat-8773	158	34	%	%	NOUN
easat-8773	158	35	low	low	ADJ
easat-8773	158	36	38.75	38.75	NUM
easat-8773	158	37	%	%	NOUN
easat-8773	158	38	48.75	48.75	NUM
easat-8773	158	39	%	%	NOUN
easat-8773	158	40	52.5	52.5	NUM
easat-8773	158	41	%	%	NOUN
easat-8773	158	42	58.75	58.75	NUM
easat-8773	158	43	%	%	NOUN
easat-8773	158	44	62.5	62.5	NUM
easat-8773	158	45	%	%	NOUN
easat-8773	158	46	66.25	66.25	NUM
easat-8773	158	47	%	%	NOUN
easat-8773	158	48	based	base	VERB
easat-8773	158	49	on	on	ADP
easat-8773	158	50	table	table	NOUN
easat-8773	158	51	4	4	NUM
easat-8773	158	52	,	,	PUNCT
easat-8773	158	53	show	show	VERB
easat-8773	158	54	the	the	DET
easat-8773	158	55	lowest	low	ADJ
easat-8773	158	56	error	error	NOUN
easat-8773	158	57	in	in	ADP
easat-8773	158	58	the	the	DET
easat-8773	158	59	understanding	understanding	NOUN
easat-8773	158	60	process	process	NOUN
easat-8773	158	61	indicates	indicate	VERB
easat-8773	158	62	that	that	SCONJ
easat-8773	158	63	students	student	NOUN
easat-8773	158	64	are	be	AUX
easat-8773	158	65	generally	generally	ADV
easat-8773	158	66	able	able	ADJ
easat-8773	158	67	to	to	PART
easat-8773	158	68	understand	understand	VERB
easat-8773	158	69	the	the	DET
easat-8773	158	70	initial	initial	ADJ
easat-8773	158	71	context	context	NOUN
easat-8773	158	72	.	.	PUNCT
easat-8773	159	1	errors	error	NOUN
easat-8773	159	2	in	in	ADP
easat-8773	159	3	the	the	DET
easat-8773	159	4	validating	validate	VERB
easat-8773	159	5	process	process	NOUN
easat-8773	159	6	are	be	AUX
easat-8773	159	7	consistent	consistent	ADJ
easat-8773	159	8	with	with	ADP
easat-8773	159	9	the	the	DET
easat-8773	159	10	highest	high	ADJ
easat-8773	159	11	number	number	NOUN
easat-8773	159	12	of	of	ADP
easat-8773	159	13	errors	error	NOUN
easat-8773	159	14	,	,	PUNCT
easat-8773	159	15	indicating	indicate	VERB
easat-8773	159	16	weak	weak	ADJ
easat-8773	159	17	student	student	NOUN
easat-8773	159	18	metacognition	metacognition	NOUN
easat-8773	159	19	in	in	ADP
easat-8773	159	20	evaluating	evaluate	VERB
easat-8773	159	21	model	model	NOUN
easat-8773	159	22	suitability	suitability	NOUN
easat-8773	159	23	.	.	PUNCT
easat-8773	160	1	in	in	ADP
easat-8773	160	2	understanding	understanding	NOUN
easat-8773	160	3	and	and	CCONJ
easat-8773	160	4	simplifying	simplifying	NOUN
easat-8773	160	5	process	process	NOUN
easat-8773	160	6	,	,	PUNCT
easat-8773	160	7	there	there	PRON
easat-8773	160	8	were	be	VERB
easat-8773	160	9	no	no	DET
easat-8773	160	10	errors	error	NOUN
easat-8773	160	11	(	(	PUNCT
easat-8773	160	12	0	0	NUM
easat-8773	160	13	%	%	NOUN
easat-8773	160	14	)	)	PUNCT
easat-8773	160	15	made	make	VERB
easat-8773	160	16	by	by	ADP
easat-8773	160	17	high	high	ADJ
easat-8773	160	18	level	level	NOUN
easat-8773	160	19	students	student	NOUN
easat-8773	160	20	indicating	indicate	VERB
easat-8773	160	21	are	be	AUX
easat-8773	160	22	able	able	ADJ
easat-8773	160	23	to	to	PART
easat-8773	160	24	understanding	understanding	NOUN
easat-8773	160	25	of	of	ADP
easat-8773	160	26	the	the	DET
easat-8773	160	27	problem	problem	NOUN
easat-8773	160	28	context	context	NOUN
easat-8773	160	29	and	and	CCONJ
easat-8773	160	30	simplification	simplification	NOUN
easat-8773	160	31	of	of	ADP
easat-8773	160	32	information	information	NOUN
easat-8773	160	33	.	.	PUNCT
easat-8773	161	1	the	the	DET
easat-8773	161	2	emergence	emergence	NOUN
easat-8773	161	3	of	of	ADP
easat-8773	161	4	initial	initial	ADJ
easat-8773	161	5	errors	error	NOUN
easat-8773	161	6	(	(	PUNCT
easat-8773	161	7	5	5	NUM
easat-8773	161	8	%	%	NOUN
easat-8773	161	9	and	and	CCONJ
easat-8773	161	10	12.5	12.5	NUM
easat-8773	161	11	%	%	NOUN
easat-8773	161	12	)	)	PUNCT
easat-8773	161	13	in	in	ADP
easat-8773	161	14	medium	medium	ADJ
easat-8773	161	15	level	level	NOUN
easat-8773	161	16	students	student	NOUN
easat-8773	161	17	indicates	indicate	VERB
easat-8773	161	18	that	that	SCONJ
easat-8773	161	19	some	some	DET
easat-8773	161	20	students	student	NOUN
easat-8773	161	21	are	be	AUX
easat-8773	161	22	still	still	ADV
easat-8773	161	23	not	not	PART
easat-8773	161	24	consistently	consistently	ADV
easat-8773	161	25	able	able	ADJ
easat-8773	161	26	to	to	PART
easat-8773	161	27	understand	understand	VERB
easat-8773	161	28	the	the	DET
easat-8773	161	29	problem	problem	NOUN
easat-8773	161	30	completely	completely	ADV
easat-8773	161	31	.	.	PUNCT
easat-8773	162	1	the	the	DET
easat-8773	162	2	substantial	substantial	ADJ
easat-8773	162	3	proportion	proportion	NOUN
easat-8773	162	4	of	of	ADP
easat-8773	162	5	errors	error	NOUN
easat-8773	162	6	(	(	PUNCT
easat-8773	162	7	38.75	38.75	NUM
easat-8773	162	8	%	%	NOUN
easat-8773	162	9	and	and	CCONJ
easat-8773	162	10	48.75	48.75	NUM
easat-8773	162	11	%	%	NOUN
easat-8773	162	12	)	)	PUNCT
easat-8773	162	13	in	in	ADP
easat-8773	162	14	low	low	ADJ
easat-8773	162	15	level	level	NOUN
easat-8773	162	16	students	student	NOUN
easat-8773	162	17	indicates	indicate	VERB
easat-8773	162	18	that	that	SCONJ
easat-8773	162	19	errors	error	NOUN
easat-8773	162	20	have	have	AUX
easat-8773	162	21	arisen	arise	VERB
easat-8773	162	22	since	since	SCONJ
easat-8773	162	23	the	the	DET
easat-8773	162	24	initial	initial	ADJ
easat-8773	162	25	interpretation	interpretation	NOUN
easat-8773	162	26	stage	stage	NOUN
easat-8773	162	27	of	of	ADP
easat-8773	162	28	the	the	DET
easat-8773	162	29	question	question	NOUN
easat-8773	162	30	.	.	PUNCT
easat-8773	163	1	in	in	ADP
easat-8773	163	2	mathematizing	mathematize	VERB
easat-8773	163	3	and	and	CCONJ
easat-8773	163	4	working	work	VERB
easat-8773	163	5	mathematically	mathematically	ADV
easat-8773	163	6	process	process	NOUN
easat-8773	163	7	,	,	PUNCT
easat-8773	163	8	high	high	ADJ
easat-8773	163	9	level	level	NOUN
easat-8773	163	10	ability	ability	NOUN
easat-8773	163	11	students	student	NOUN
easat-8773	163	12	still	still	ADV
easat-8773	163	13	showed	show	VERB
easat-8773	163	14	good	good	ADJ
easat-8773	163	15	performance	performance	NOUN
easat-8773	163	16	,	,	PUNCT
easat-8773	163	17	with	with	ADP
easat-8773	163	18	very	very	ADV
easat-8773	163	19	low	low	ADJ
easat-8773	163	20	errors	error	NOUN
easat-8773	163	21	(	(	PUNCT
easat-8773	163	22	0	0	NUM
easat-8773	163	23	%	%	NOUN
easat-8773	163	24	and	and	CCONJ
easat-8773	163	25	2.08	2.08	NUM
easat-8773	163	26	%	%	NOUN
easat-8773	163	27	)	)	PUNCT
easat-8773	163	28	.	.	PUNCT
easat-8773	164	1	there	there	PRON
easat-8773	164	2	was	be	VERB
easat-8773	164	3	an	an	DET
easat-8773	164	4	increase	increase	NOUN
easat-8773	164	5	in	in	ADP
easat-8773	164	6	moderate	moderate	ADJ
easat-8773	164	7	errors	error	NOUN
easat-8773	164	8	(	(	PUNCT
easat-8773	164	9	15	15	NUM
easat-8773	164	10	%	%	NOUN
easat-8773	164	11	and	and	CCONJ
easat-8773	164	12	25	25	NUM
easat-8773	164	13	%	%	NOUN
easat-8773	164	14	)	)	PUNCT
easat-8773	164	15	indicating	indicate	VERB
easat-8773	164	16	challenges	challenge	NOUN
easat-8773	164	17	in	in	ADP
easat-8773	164	18	transforming	transform	VERB
easat-8773	164	19	real	real	ADJ
easat-8773	164	20	-	-	PUNCT
easat-8773	164	21	world	world	NOUN
easat-8773	164	22	situations	situation	NOUN
easat-8773	164	23	into	into	ADP
easat-8773	164	24	formal	formal	ADJ
easat-8773	164	25	representations	representation	NOUN
easat-8773	164	26	.	.	PUNCT
easat-8773	165	1	errors	error	NOUN
easat-8773	165	2	continued	continue	VERB
easat-8773	165	3	to	to	PART
easat-8773	165	4	increase	increase	VERB
easat-8773	165	5	(	(	PUNCT
easat-8773	165	6	52.5	52.5	NUM
easat-8773	165	7	%	%	NOUN
easat-8773	165	8	and	and	CCONJ
easat-8773	165	9	58.75	58.75	NUM
easat-8773	165	10	%	%	NOUN
easat-8773	165	11	)	)	PUNCT
easat-8773	165	12	in	in	ADP
easat-8773	165	13	low	low	ADJ
easat-8773	165	14	level	level	NOUN
easat-8773	165	15	ability	ability	NOUN
easat-8773	165	16	students	student	NOUN
easat-8773	165	17	,	,	PUNCT
easat-8773	165	18	indicating	indicate	VERB
easat-8773	165	19	weaknesses	weakness	NOUN
easat-8773	165	20	in	in	ADP
easat-8773	165	21	abstraction	abstraction	NOUN
easat-8773	165	22	and	and	CCONJ
easat-8773	165	23	mathematization	mathematization	NOUN
easat-8773	165	24	process	process	NOUN
easat-8773	165	25	.	.	PUNCT
easat-8773	166	1	in	in	ADP
easat-8773	166	2	interpreting	interpret	VERB
easat-8773	166	3	-	-	PUNCT
easat-8773	166	4	validating	validate	VERB
easat-8773	166	5	process	process	NOUN
easat-8773	166	6	,	,	PUNCT
easat-8773	166	7	errors	error	NOUN
easat-8773	166	8	began	begin	VERB
easat-8773	166	9	to	to	PART
easat-8773	166	10	dominate	dominate	VERB
easat-8773	166	11	(	(	PUNCT
easat-8773	166	12	18	18	NUM
easat-8773	166	13	%	%	NOUN
easat-8773	166	14	and	and	CCONJ
easat-8773	166	15	25	25	NUM
easat-8773	166	16	%	%	NOUN
easat-8773	166	17	)	)	PUNCT
easat-8773	166	18	in	in	ADP
easat-8773	166	19	high	high	ADJ
easat-8773	166	20	level	level	NOUN
easat-8773	166	21	students	student	NOUN
easat-8773	166	22	,	,	PUNCT
easat-8773	166	23	indicating	indicate	VERB
easat-8773	166	24	that	that	SCONJ
easat-8773	166	25	even	even	ADV
easat-8773	166	26	high	high	ADJ
easat-8773	166	27	ability	ability	NOUN
easat-8773	166	28	students	student	NOUN
easat-8773	166	29	still	still	ADV
easat-8773	166	30	need	need	VERB
easat-8773	166	31	guidance	guidance	NOUN
easat-8773	166	32	to	to	PART
easat-8773	166	33	improve	improve	VERB
easat-8773	166	34	the	the	DET
easat-8773	166	35	accuracy	accuracy	NOUN
easat-8773	166	36	of	of	ADP
easat-8773	166	37	interpretation	interpretation	NOUN
easat-8773	166	38	and	and	CCONJ
easat-8773	166	39	model	model	NOUN
easat-8773	166	40	evaluation	evaluation	NOUN
easat-8773	166	41	.	.	PUNCT
easat-8773	167	1	the	the	DET
easat-8773	167	2	highest	high	ADJ
easat-8773	167	3	errors	error	NOUN
easat-8773	167	4	(	(	PUNCT
easat-8773	167	5	35	35	NUM
easat-8773	167	6	%	%	NOUN
easat-8773	167	7	−	−	PROPN
easat-8773	167	8	66.25	66.25	NUM
easat-8773	167	9	%	%	NOUN
easat-8773	167	10	)	)	PUNCT
easat-8773	167	11	in	in	ADP
easat-8773	167	12	medium	medium	ADJ
easat-8773	167	13	and	and	CCONJ
easat-8773	167	14	low	low	ADJ
easat-8773	167	15	-	-	PUNCT
easat-8773	167	16	level	level	NOUN
easat-8773	167	17	students	student	NOUN
easat-8773	167	18	,	,	PUNCT
easat-8773	167	19	indicating	indicate	VERB
easat-8773	167	20	weak	weak	ADJ
easat-8773	167	21	reflective	reflective	ADJ
easat-8773	167	22	and	and	CCONJ
easat-8773	167	23	metacognitive	metacognitive	ADJ
easat-8773	167	24	skills	skill	NOUN
easat-8773	167	25	in	in	ADP
easat-8773	167	26	interpreting	interpret	VERB
easat-8773	167	27	results	result	NOUN
easat-8773	167	28	and	and	CCONJ
easat-8773	167	29	assessing	assess	VERB
easat-8773	167	30	model	model	NOUN
easat-8773	167	31	accuracy	accuracy	NOUN
easat-8773	167	32	.	.	PUNCT
easat-8773	168	1	the	the	DET
easat-8773	168	2	pattern	pattern	NOUN
easat-8773	168	3	of	of	ADP
easat-8773	168	4	errors	error	NOUN
easat-8773	168	5	is	be	AUX
easat-8773	168	6	progressive	progressive	ADJ
easat-8773	168	7	according	accord	VERB
easat-8773	168	8	to	to	ADP
easat-8773	168	9	the	the	DET
easat-8773	168	10	level	level	NOUN
easat-8773	168	11	of	of	ADP
easat-8773	168	12	student	student	NOUN
easat-8773	168	13	ability	ability	NOUN
easat-8773	168	14	,	,	PUNCT
easat-8773	168	15	where	where	SCONJ
easat-8773	168	16	students	student	NOUN
easat-8773	168	17	with	with	ADP
easat-8773	168	18	lower	low	ADJ
easat-8773	168	19	abilities	ability	NOUN
easat-8773	168	20	tend	tend	VERB
easat-8773	168	21	to	to	PART
easat-8773	168	22	make	make	VERB
easat-8773	168	23	errors	error	NOUN
easat-8773	168	24	at	at	ADP
easat-8773	168	25	the	the	DET
easat-8773	168	26	initial	initial	ADJ
easat-8773	168	27	stage	stage	NOUN
easat-8773	168	28	,	,	PUNCT
easat-8773	168	29	such	such	ADJ
easat-8773	168	30	as	as	ADP
easat-8773	168	31	understanding	understand	VERB
easat-8773	168	32	the	the	DET
easat-8773	168	33	context	context	NOUN
easat-8773	168	34	of	of	ADP
easat-8773	168	35	the	the	DET
easat-8773	168	36	problem	problem	NOUN
easat-8773	168	37	(	(	PUNCT
easat-8773	168	38	understanding	understanding	NOUN
easat-8773	168	39	)	)	PUNCT
easat-8773	168	40	and	and	CCONJ
easat-8773	168	41	the	the	DET
easat-8773	168	42	relationship	relationship	NOUN
easat-8773	168	43	of	of	ADP
easat-8773	168	44	information	information	NOUN
easat-8773	168	45	(	(	PUNCT
easat-8773	168	46	simplifying	simplifying	NOUN
easat-8773	168	47	)	)	PUNCT
easat-8773	168	48	.	.	PUNCT
easat-8773	169	1	this	this	PRON
easat-8773	169	2	indicates	indicate	VERB
easat-8773	169	3	limitations	limitation	NOUN
easat-8773	169	4	in	in	ADP
easat-8773	169	5	interpreting	interpret	VERB
easat-8773	169	6	important	important	ADJ
easat-8773	169	7	elements	element	NOUN
easat-8773	169	8	of	of	ADP
easat-8773	169	9	the	the	DET
easat-8773	169	10	real	real	ADJ
easat-8773	169	11	-	-	PUNCT
easat-8773	169	12	world	world	NOUN
easat-8773	169	13	situation	situation	NOUN
easat-8773	169	14	that	that	PRON
easat-8773	169	15	are	be	AUX
easat-8773	169	16	the	the	DET
easat-8773	169	17	opening	opening	NOUN
easat-8773	169	18	for	for	ADP
easat-8773	169	19	the	the	DET
easat-8773	169	20	subsequent	subsequent	ADJ
easat-8773	169	21	modeling	modeling	NOUN
easat-8773	169	22	process	process	NOUN
easat-8773	169	23	.	.	PUNCT
easat-8773	170	1	in	in	ADP
easat-8773	170	2	contrast	contrast	NOUN
easat-8773	170	3	,	,	PUNCT
easat-8773	170	4	students	student	NOUN
easat-8773	170	5	with	with	ADP
easat-8773	170	6	higher	high	ADJ
easat-8773	170	7	abilities	ability	NOUN
easat-8773	170	8	tend	tend	VERB
easat-8773	170	9	to	to	PART
easat-8773	170	10	pass	pass	VERB
easat-8773	170	11	the	the	DET
easat-8773	170	12	initial	initial	ADJ
easat-8773	170	13	stage	stage	NOUN
easat-8773	170	14	well	well	ADV
easat-8773	170	15	,	,	PUNCT
easat-8773	170	16	but	but	CCONJ
easat-8773	170	17	still	still	ADV
easat-8773	170	18	make	make	VERB
easat-8773	170	19	errors	error	NOUN
easat-8773	170	20	at	at	ADP
easat-8773	170	21	the	the	DET
easat-8773	170	22	advanced	advanced	ADJ
easat-8773	170	23	stages	stage	NOUN
easat-8773	170	24	such	such	ADJ
easat-8773	170	25	as	as	ADP
easat-8773	170	26	mathematization	mathematization	NOUN
easat-8773	170	27	,	,	PUNCT
easat-8773	170	28	solving	solve	VERB
easat-8773	170	29	the	the	DET
easat-8773	170	30	model	model	NOUN
easat-8773	170	31	(	(	PUNCT
easat-8773	170	32	working	work	VERB
easat-8773	170	33	mathematically	mathematically	ADV
easat-8773	170	34	)	)	PUNCT
easat-8773	170	35	,	,	PUNCT
easat-8773	170	36	interpretation	interpretation	NOUN
easat-8773	170	37	,	,	PUNCT
easat-8773	170	38	and	and	CCONJ
easat-8773	170	39	validation	validation	NOUN
easat-8773	170	40	.	.	PUNCT
easat-8773	171	1	this	this	PRON
easat-8773	171	2	shows	show	VERB
easat-8773	171	3	that	that	SCONJ
easat-8773	171	4	even	even	ADV
easat-8773	171	5	though	though	SCONJ
easat-8773	171	6	they	they	PRON
easat-8773	171	7	have	have	VERB
easat-8773	171	8	better	well	ADJ
easat-8773	171	9	initial	initial	ADJ
easat-8773	171	10	understanding	understanding	NOUN
easat-8773	171	11	capacity	capacity	NOUN
easat-8773	171	12	,	,	PUNCT
easat-8773	171	13	difficulties	difficulty	NOUN
easat-8773	171	14	still	still	ADV
easat-8773	171	15	arise	arise	VERB
easat-8773	171	16	when	when	SCONJ
easat-8773	171	17	they	they	PRON
easat-8773	171	18	have	have	VERB
easat-8773	171	19	to	to	PART
easat-8773	171	20	transform	transform	VERB
easat-8773	171	21	the	the	DET
easat-8773	171	22	context	context	NOUN
easat-8773	171	23	into	into	ADP
easat-8773	171	24	a	a	DET
easat-8773	171	25	mathematical	mathematical	ADJ
easat-8773	171	26	model	model	NOUN
easat-8773	171	27	and	and	CCONJ
easat-8773	171	28	ensure	ensure	VERB
easat-8773	171	29	that	that	SCONJ
easat-8773	171	30	the	the	DET
easat-8773	171	31	resulting	result	VERB
easat-8773	171	32	solution	solution	NOUN
easat-8773	171	33	is	be	AUX
easat-8773	171	34	contextually	contextually	ADV
easat-8773	171	35	relevant	relevant	ADJ
easat-8773	171	36	and	and	CCONJ
easat-8773	171	37	accurate	accurate	ADJ
easat-8773	171	38	.	.	PUNCT
easat-8773	172	1	the	the	DET
easat-8773	172	2	results	result	NOUN
easat-8773	172	3	show	show	VERB
easat-8773	172	4	that	that	SCONJ
easat-8773	172	5	the	the	DET
easat-8773	172	6	mathematical	mathematical	ADJ
easat-8773	172	7	modeling	modeling	NOUN
easat-8773	172	8	process	process	NOUN
easat-8773	172	9	requires	require	VERB
easat-8773	172	10	not	not	PART
easat-8773	172	11	only	only	ADV
easat-8773	172	12	procedural	procedural	ADJ
easat-8773	172	13	competence	competence	NOUN
easat-8773	172	14	,	,	PUNCT
easat-8773	172	15	but	but	CCONJ
easat-8773	172	16	also	also	ADV
easat-8773	172	17	deep	deep	ADV
easat-8773	172	18	reflective	reflective	ADJ
easat-8773	172	19	and	and	CCONJ
easat-8773	172	20	contextual	contextual	ADJ
easat-8773	172	21	abilities	ability	NOUN
easat-8773	172	22	.	.	PUNCT
easat-8773	173	1	therefore	therefore	ADV
easat-8773	173	2	,	,	PUNCT
easat-8773	173	3	an	an	DET
easat-8773	173	4	adaptive	adaptive	ADJ
easat-8773	173	5	pedagogical	pedagogical	ADJ
easat-8773	173	6	approach	approach	NOUN
easat-8773	173	7	-	-	PUNCT
easat-8773	173	8	one	one	NOUN
easat-8773	173	9	that	that	PRON
easat-8773	173	10	focuses	focus	VERB
easat-8773	173	11	not	not	PART
easat-8773	173	12	only	only	ADV
easat-8773	173	13	on	on	ADP
easat-8773	173	14	technical	technical	ADJ
easat-8773	173	15	skills	skill	NOUN
easat-8773	173	16	,	,	PUNCT
easat-8773	173	17	but	but	CCONJ
easat-8773	173	18	also	also	ADV
easat-8773	173	19	on	on	ADP
easat-8773	173	20	strengthening	strengthen	VERB
easat-8773	173	21	conceptual	conceptual	ADJ
easat-8773	173	22	understanding	understanding	NOUN
easat-8773	173	23	and	and	CCONJ
easat-8773	173	24	higherorder	higherorder	NOUN
easat-8773	173	25	thinking	thinking	NOUN
easat-8773	173	26	skills	skill	NOUN
easat-8773	173	27	is	be	AUX
easat-8773	173	28	needed	need	VERB
easat-8773	173	29	to	to	PART
easat-8773	173	30	support	support	VERB
easat-8773	173	31	students	student	NOUN
easat-8773	173	32	at	at	ADP
easat-8773	173	33	all	all	DET
easat-8773	173	34	ability	ability	NOUN
easat-8773	173	35	levels	level	NOUN
easat-8773	173	36	.	.	PUNCT
easat-8773	174	1	in	in	ADP
easat-8773	174	2	this	this	DET
easat-8773	174	3	section	section	NOUN
easat-8773	174	4	,	,	PUNCT
easat-8773	174	5	an	an	DET
easat-8773	174	6	example	example	NOUN
easat-8773	174	7	of	of	ADP
easat-8773	174	8	errors	error	NOUN
easat-8773	174	9	made	make	VERB
easat-8773	174	10	by	by	ADP
easat-8773	174	11	students	student	NOUN
easat-8773	174	12	in	in	ADP
easat-8773	174	13	the	the	DET
easat-8773	174	14	mathematical	mathematical	ADJ
easat-8773	174	15	modeling	modeling	NOUN
easat-8773	174	16	process	process	NOUN
easat-8773	174	17	.	.	PUNCT
easat-8773	175	1	example	example	NOUN
easat-8773	175	2	error	error	NOUN
easat-8773	175	3	made	make	VERB
easat-8773	175	4	by	by	ADP
easat-8773	175	5	student	student	NOUN
easat-8773	175	6	with	with	ADP
easat-8773	175	7	low	low	ADJ
easat-8773	175	8	level	level	NOUN
easat-8773	175	9	mathematical	mathematical	ADJ
easat-8773	175	10	abilities	ability	NOUN
easat-8773	175	11	in	in	ADP
easat-8773	175	12	process	process	NOUN
easat-8773	175	13	understanding	understanding	NOUN
easat-8773	175	14	and	and	CCONJ
easat-8773	175	15	simplifying	simplifying	NOUN
easat-8773	175	16	,	,	PUNCT
easat-8773	175	17	see	see	VERB
easat-8773	175	18	figure	figure	NOUN
easat-8773	175	19	3	3	NUM
easat-8773	175	20	.	.	NOUN
easat-8773	175	21	954	954	NUM
easat-8773	175	22	edelweiss	edelweiss	PROPN
easat-8773	175	23	applied	apply	VERB
easat-8773	175	24	science	science	NOUN
easat-8773	175	25	and	and	CCONJ
easat-8773	175	26	technology	technology	NOUN
easat-8773	175	27	issn	issn	PROPN
easat-8773	175	28	:	:	PUNCT
easat-8773	175	29	2576	2576	NUM
easat-8773	175	30	-	-	SYM
easat-8773	175	31	8484	8484	NUM
easat-8773	175	32	vol	vol	NOUN
easat-8773	175	33	.	.	PROPN
easat-8773	176	1	9	9	NUM
easat-8773	176	2	,	,	PUNCT
easat-8773	176	3	no	no	INTJ
easat-8773	176	4	.	.	NOUN
easat-8773	177	1	7	7	NUM
easat-8773	177	2	:	:	SYM
easat-8773	177	3	947	947	NUM
easat-8773	177	4	-	-	SYM
easat-8773	177	5	959	959	NUM
easat-8773	177	6	,	,	PUNCT
easat-8773	177	7	2025	2025	NUM
easat-8773	177	8	doi	doi	NOUN
easat-8773	177	9	:	:	PUNCT
easat-8773	177	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	177	11	©	©	PROPN
easat-8773	177	12	2025	2025	NUM
easat-8773	177	13	by	by	ADP
easat-8773	177	14	the	the	DET
easat-8773	177	15	authors	author	NOUN
easat-8773	177	16	;	;	PUNCT
easat-8773	177	17	licensee	licensee	PROPN
easat-8773	177	18	learning	learn	VERB
easat-8773	177	19	gate	gate	PROPN
easat-8773	177	20	figure	figure	NOUN
easat-8773	177	21	3	3	NUM
easat-8773	177	22	.	.	PUNCT
easat-8773	178	1	examples	example	NOUN
easat-8773	178	2	errors	error	NOUN
easat-8773	178	3	in	in	ADP
easat-8773	178	4	the	the	DET
easat-8773	178	5	understanding	understanding	NOUN
easat-8773	178	6	and	and	CCONJ
easat-8773	178	7	simplifying	simplifying	NOUN
easat-8773	178	8	process	process	NOUN
easat-8773	178	9	.	.	PUNCT
easat-8773	179	1	the	the	DET
easat-8773	179	2	interview	interview	NOUN
easat-8773	179	3	was	be	AUX
easat-8773	179	4	conducted	conduct	VERB
easat-8773	179	5	based	base	VERB
easat-8773	179	6	on	on	ADP
easat-8773	179	7	students	student	NOUN
easat-8773	179	8	'	'	PART
easat-8773	179	9	answers	answer	NOUN
easat-8773	179	10	to	to	PART
easat-8773	179	11	identify	identify	VERB
easat-8773	179	12	assumptions	assumption	NOUN
easat-8773	179	13	and	and	CCONJ
easat-8773	179	14	errors	error	NOUN
easat-8773	179	15	.	.	PUNCT
easat-8773	180	1	below	below	ADV
easat-8773	180	2	is	be	AUX
easat-8773	180	3	an	an	DET
easat-8773	180	4	excerpt	excerpt	NOUN
easat-8773	180	5	.	.	PUNCT
easat-8773	181	1	r	r	NOUN
easat-8773	181	2	:	:	PUNCT
easat-8773	181	3	actually	actually	ADV
easat-8773	181	4	,	,	PUNCT
easat-8773	181	5	the	the	DET
easat-8773	181	6	area	area	NOUN
easat-8773	181	7	of	of	ADP
easat-8773	181	8	a	a	DET
easat-8773	181	9	shape	shape	NOUN
easat-8773	181	10	is	be	AUX
easat-8773	181	11	found	find	VERB
easat-8773	181	12	by	by	ADP
easat-8773	181	13	multiplying	multiply	VERB
easat-8773	181	14	its	its	PRON
easat-8773	181	15	length	length	NOUN
easat-8773	181	16	by	by	ADP
easat-8773	181	17	its	its	PRON
easat-8773	181	18	width	width	NOUN
easat-8773	181	19	,	,	PUNCT
easat-8773	181	20	not	not	PART
easat-8773	181	21	by	by	ADP
easat-8773	181	22	subtracting	subtract	VERB
easat-8773	181	23	.	.	PUNCT
easat-8773	182	1	have	have	AUX
easat-8773	182	2	you	you	PRON
easat-8773	182	3	ever	ever	ADV
easat-8773	182	4	used	use	VERB
easat-8773	182	5	the	the	DET
easat-8773	182	6	area	area	NOUN
easat-8773	182	7	formula	formula	NOUN
easat-8773	182	8	before	before	ADV
easat-8773	182	9	?	?	PUNCT
easat-8773	183	1	s	s	X
easat-8773	183	2	:	:	PUNCT
easat-8773	183	3	hmm	hmm	INTJ
easat-8773	183	4	…	…	PUNCT
easat-8773	183	5	i	i	PRON
easat-8773	183	6	know	know	VERB
easat-8773	183	7	there	there	PRON
easat-8773	183	8	is	be	VERB
easat-8773	183	9	an	an	DET
easat-8773	183	10	area	area	NOUN
easat-8773	183	11	formula	formula	NOUN
easat-8773	183	12	,	,	PUNCT
easat-8773	183	13	but	but	CCONJ
easat-8773	183	14	i	i	PRON
easat-8773	183	15	have	have	VERB
easat-8773	183	16	trouble	trouble	NOUN
easat-8773	183	17	remembering	remember	VERB
easat-8773	183	18	it	it	PRON
easat-8773	183	19	r	r	NOUN
easat-8773	183	20	:	:	PUNCT
easat-8773	183	21	the	the	DET
easat-8773	183	22	area	area	NOUN
easat-8773	183	23	of	of	ADP
easat-8773	183	24	talawang	talawang	NOUN
easat-8773	183	25	is	be	AUX
easat-8773	183	26	calculated	calculate	VERB
easat-8773	183	27	by	by	ADP
easat-8773	183	28	multiplying	multiply	VERB
easat-8773	183	29	its	its	PRON
easat-8773	183	30	length	length	NOUN
easat-8773	183	31	by	by	ADP
easat-8773	183	32	its	its	PRON
easat-8773	183	33	width	width	NOUN
easat-8773	183	34	.	.	PUNCT
easat-8773	184	1	if	if	SCONJ
easat-8773	184	2	the	the	DET
easat-8773	184	3	length	length	NOUN
easat-8773	184	4	is	be	AUX
easat-8773	184	5	200	200	NUM
easat-8773	184	6	cm	cm	NOUN
easat-8773	184	7	and	and	CCONJ
easat-8773	184	8	the	the	DET
easat-8773	184	9	width	width	NOUN
easat-8773	184	10	is	be	AUX
easat-8773	184	11	50	50	NUM
easat-8773	184	12	cm	cm	NOUN
easat-8773	184	13	,	,	PUNCT
easat-8773	184	14	how	how	SCONJ
easat-8773	184	15	do	do	AUX
easat-8773	184	16	you	you	PRON
easat-8773	184	17	think	think	VERB
easat-8773	184	18	the	the	DET
easat-8773	184	19	calculation	calculation	NOUN
easat-8773	184	20	should	should	AUX
easat-8773	184	21	be	be	AUX
easat-8773	184	22	done	do	VERB
easat-8773	184	23	?	?	PUNCT
easat-8773	185	1	s	s	VERB
easat-8773	185	2	:	:	PUNCT
easat-8773	185	3	so	so	ADV
easat-8773	185	4	,	,	PUNCT
easat-8773	185	5	i	i	PRON
easat-8773	185	6	should	should	AUX
easat-8773	185	7	multiply	multiply	VERB
easat-8773	185	8	200	200	NUM
easat-8773	185	9	×	×	NOUN
easat-8773	185	10	50	50	NUM
easat-8773	185	11	?	?	PUNCT
easat-8773	186	1	the	the	DET
easat-8773	186	2	student	student	NOUN
easat-8773	186	3	's	's	PART
easat-8773	186	4	confusion	confusion	NOUN
easat-8773	186	5	arises	arise	VERB
easat-8773	186	6	not	not	PART
easat-8773	186	7	from	from	ADP
easat-8773	186	8	misinterpretation	misinterpretation	NOUN
easat-8773	186	9	of	of	ADP
easat-8773	186	10	the	the	DET
easat-8773	186	11	problem	problem	NOUN
easat-8773	186	12	context	context	NOUN
easat-8773	186	13	,	,	PUNCT
easat-8773	186	14	but	but	CCONJ
easat-8773	186	15	from	from	ADP
easat-8773	186	16	gaps	gap	NOUN
easat-8773	186	17	in	in	ADP
easat-8773	186	18	recalling	recall	VERB
easat-8773	186	19	basic	basic	ADJ
easat-8773	186	20	mathematical	mathematical	ADJ
easat-8773	186	21	knowledge	knowledge	NOUN
easat-8773	186	22	,	,	PUNCT
easat-8773	186	23	specifically	specifically	ADV
easat-8773	186	24	the	the	DET
easat-8773	186	25	formula	formula	NOUN
easat-8773	186	26	for	for	ADP
easat-8773	186	27	area	area	NOUN
easat-8773	186	28	.	.	PUNCT
easat-8773	187	1	although	although	SCONJ
easat-8773	187	2	the	the	DET
easat-8773	187	3	student	student	NOUN
easat-8773	187	4	eventually	eventually	ADV
easat-8773	187	5	arrived	arrive	VERB
easat-8773	187	6	at	at	ADP
easat-8773	187	7	the	the	DET
easat-8773	187	8	correct	correct	ADJ
easat-8773	187	9	operation	operation	NOUN
easat-8773	187	10	with	with	ADP
easat-8773	187	11	guidance	guidance	NOUN
easat-8773	187	12	,	,	PUNCT
easat-8773	187	13	the	the	DET
easat-8773	187	14	initial	initial	ADJ
easat-8773	187	15	inclination	inclination	NOUN
easat-8773	187	16	to	to	PART
easat-8773	187	17	subtract	subtract	VERB
easat-8773	187	18	suggests	suggest	VERB
easat-8773	187	19	a	a	DET
easat-8773	187	20	misapplication	misapplication	NOUN
easat-8773	187	21	of	of	ADP
easat-8773	187	22	prior	prior	ADJ
easat-8773	187	23	knowledge	knowledge	NOUN
easat-8773	187	24	.	.	PUNCT
easat-8773	188	1	the	the	DET
easat-8773	188	2	dialogue	dialogue	NOUN
easat-8773	188	3	also	also	ADV
easat-8773	188	4	highlights	highlight	VERB
easat-8773	188	5	a	a	DET
easat-8773	188	6	passive	passive	ADJ
easat-8773	188	7	engagement	engagement	NOUN
easat-8773	188	8	with	with	ADP
easat-8773	188	9	mathematical	mathematical	ADJ
easat-8773	188	10	rules	rule	NOUN
easat-8773	188	11	the	the	DET
easat-8773	188	12	student	student	NOUN
easat-8773	188	13	indicates	indicate	VERB
easat-8773	188	14	awareness	awareness	NOUN
easat-8773	188	15	of	of	ADP
easat-8773	188	16	the	the	DET
easat-8773	188	17	formula	formula	NOUN
easat-8773	188	18	's	's	PART
easat-8773	188	19	existence	existence	NOUN
easat-8773	188	20	but	but	CCONJ
easat-8773	188	21	lacks	lack	VERB
easat-8773	188	22	confidence	confidence	NOUN
easat-8773	188	23	and	and	CCONJ
easat-8773	188	24	fluency	fluency	NOUN
easat-8773	188	25	in	in	ADP
easat-8773	188	26	applying	apply	VERB
easat-8773	188	27	it	it	PRON
easat-8773	188	28	.	.	PUNCT
easat-8773	189	1	this	this	PRON
easat-8773	189	2	points	point	VERB
easat-8773	189	3	to	to	ADP
easat-8773	189	4	challenges	challenge	NOUN
easat-8773	189	5	in	in	ADP
easat-8773	189	6	simplifying	simplify	VERB
easat-8773	189	7	the	the	DET
easat-8773	189	8	situation	situation	NOUN
easat-8773	189	9	into	into	ADP
easat-8773	189	10	a	a	DET
easat-8773	189	11	solvable	solvable	ADJ
easat-8773	189	12	mathematical	mathematical	ADJ
easat-8773	189	13	structure	structure	NOUN
easat-8773	189	14	,	,	PUNCT
easat-8773	189	15	where	where	SCONJ
easat-8773	189	16	foundational	foundational	ADJ
easat-8773	189	17	misunderstandings	misunderstanding	NOUN
easat-8773	189	18	create	create	VERB
easat-8773	189	19	barriers	barrier	NOUN
easat-8773	189	20	before	before	SCONJ
easat-8773	189	21	any	any	DET
easat-8773	189	22	formal	formal	ADJ
easat-8773	189	23	modeling	modeling	NOUN
easat-8773	189	24	takes	take	VERB
easat-8773	189	25	place	place	NOUN
easat-8773	189	26	.	.	PUNCT
easat-8773	190	1	this	this	DET
easat-8773	190	2	case	case	NOUN
easat-8773	190	3	emphasizes	emphasize	VERB
easat-8773	190	4	that	that	SCONJ
easat-8773	190	5	errors	error	NOUN
easat-8773	190	6	in	in	ADP
easat-8773	190	7	early	early	ADJ
easat-8773	190	8	modeling	modeling	NOUN
easat-8773	190	9	stages	stage	NOUN
easat-8773	190	10	often	often	ADV
easat-8773	190	11	stem	stem	VERB
easat-8773	190	12	from	from	ADP
easat-8773	190	13	low	low	ADJ
easat-8773	190	14	confidence	confidence	NOUN
easat-8773	190	15	in	in	ADP
easat-8773	190	16	fundamental	fundamental	ADJ
easat-8773	190	17	skills	skill	NOUN
easat-8773	190	18	.	.	PUNCT
easat-8773	191	1	before	before	ADP
easat-8773	191	2	advancing	advance	VERB
easat-8773	191	3	into	into	ADP
easat-8773	191	4	more	more	ADJ
easat-8773	191	5	complex	complex	ADJ
easat-8773	191	6	phases	phase	NOUN
easat-8773	191	7	,	,	PUNCT
easat-8773	191	8	first	first	ADV
easat-8773	191	9	reinforce	reinforce	VERB
easat-8773	191	10	basic	basic	ADJ
easat-8773	191	11	conceptual	conceptual	ADJ
easat-8773	191	12	fluency	fluency	NOUN
easat-8773	191	13	to	to	PART
easat-8773	191	14	ensure	ensure	VERB
easat-8773	191	15	that	that	DET
easat-8773	191	16	simplification	simplification	NOUN
easat-8773	191	17	is	be	AUX
easat-8773	191	18	grounded	ground	VERB
easat-8773	191	19	in	in	ADP
easat-8773	191	20	correct	correct	ADJ
easat-8773	191	21	mathematical	mathematical	ADJ
easat-8773	191	22	reasoning	reasoning	NOUN
easat-8773	191	23	.	.	PUNCT
easat-8773	192	1	example	example	NOUN
easat-8773	192	2	error	error	NOUN
easat-8773	192	3	made	make	VERB
easat-8773	192	4	by	by	ADP
easat-8773	192	5	student	student	NOUN
easat-8773	192	6	with	with	ADP
easat-8773	192	7	medium	medium	ADJ
easat-8773	192	8	level	level	NOUN
easat-8773	192	9	mathematical	mathematical	ADJ
easat-8773	192	10	abilities	ability	NOUN
easat-8773	192	11	in	in	ADP
easat-8773	192	12	process	process	NOUN
easat-8773	192	13	mathematizing	mathematize	VERB
easat-8773	192	14	,	,	PUNCT
easat-8773	192	15	see	see	VERB
easat-8773	192	16	figure	figure	NOUN
easat-8773	192	17	4	4	NUM
easat-8773	192	18	.	.	PUNCT
easat-8773	192	19	figure	figure	VERB
easat-8773	192	20	4	4	NUM
easat-8773	192	21	.	.	NOUN
easat-8773	192	22	example	example	NOUN
easat-8773	192	23	of	of	ADP
easat-8773	192	24	errors	error	NOUN
easat-8773	192	25	in	in	ADP
easat-8773	192	26	the	the	DET
easat-8773	192	27	mathematizing	mathematizing	NOUN
easat-8773	192	28	process	process	NOUN
easat-8773	192	29	.	.	PUNCT
easat-8773	193	1	the	the	DET
easat-8773	193	2	interview	interview	NOUN
easat-8773	193	3	was	be	AUX
easat-8773	193	4	conducted	conduct	VERB
easat-8773	193	5	based	base	VERB
easat-8773	193	6	on	on	ADP
easat-8773	193	7	students	student	NOUN
easat-8773	193	8	'	'	PART
easat-8773	193	9	answers	answer	NOUN
easat-8773	193	10	to	to	PART
easat-8773	193	11	identify	identify	VERB
easat-8773	193	12	assumptions	assumption	NOUN
easat-8773	193	13	and	and	CCONJ
easat-8773	193	14	errors	error	NOUN
easat-8773	193	15	.	.	PUNCT
easat-8773	194	1	below	below	ADV
easat-8773	194	2	is	be	AUX
easat-8773	194	3	an	an	DET
easat-8773	194	4	excerpt	excerpt	NOUN
easat-8773	194	5	.	.	PUNCT
easat-8773	195	1	955	955	NUM
easat-8773	195	2	edelweiss	edelweiss	PROPN
easat-8773	195	3	applied	apply	VERB
easat-8773	195	4	science	science	NOUN
easat-8773	195	5	and	and	CCONJ
easat-8773	195	6	technology	technology	NOUN
easat-8773	195	7	issn	issn	PROPN
easat-8773	195	8	:	:	PUNCT
easat-8773	195	9	2576	2576	NUM
easat-8773	195	10	-	-	SYM
easat-8773	195	11	8484	8484	NUM
easat-8773	195	12	vol	vol	NOUN
easat-8773	195	13	.	.	PROPN
easat-8773	196	1	9	9	NUM
easat-8773	196	2	,	,	PUNCT
easat-8773	196	3	no	no	INTJ
easat-8773	196	4	.	.	NOUN
easat-8773	197	1	7	7	NUM
easat-8773	197	2	:	:	SYM
easat-8773	197	3	947	947	NUM
easat-8773	197	4	-	-	SYM
easat-8773	197	5	959	959	NUM
easat-8773	197	6	,	,	PUNCT
easat-8773	197	7	2025	2025	NUM
easat-8773	197	8	doi	doi	NOUN
easat-8773	197	9	:	:	PUNCT
easat-8773	197	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	197	11	©	©	PROPN
easat-8773	197	12	2025	2025	NUM
easat-8773	197	13	by	by	ADP
easat-8773	197	14	the	the	DET
easat-8773	197	15	authors	author	NOUN
easat-8773	197	16	;	;	PUNCT
easat-8773	197	17	licensee	licensee	NOUN
easat-8773	197	18	learning	learn	VERB
easat-8773	197	19	gate	gate	NOUN
easat-8773	197	20	r	r	NOUN
easat-8773	197	21	:	:	PUNCT
easat-8773	197	22	are	be	AUX
easat-8773	197	23	you	you	PRON
easat-8773	197	24	assumed	assume	VERB
easat-8773	197	25	each	each	DET
easat-8773	197	26	group	group	NOUN
easat-8773	197	27	required	require	VERB
easat-8773	197	28	a	a	DET
easat-8773	197	29	proportional	proportional	ADJ
easat-8773	197	30	number	number	NOUN
easat-8773	197	31	of	of	ADP
easat-8773	197	32	feathers	feather	NOUN
easat-8773	197	33	,	,	PUNCT
easat-8773	197	34	but	but	CCONJ
easat-8773	197	35	did	do	AUX
easat-8773	197	36	the	the	DET
easat-8773	197	37	problem	problem	NOUN
easat-8773	197	38	state	state	NOUN
easat-8773	197	39	this	this	PRON
easat-8773	197	40	explicitly	explicitly	ADV
easat-8773	197	41	?	?	PUNCT
easat-8773	198	1	s	s	VERB
easat-8773	198	2	:	:	PUNCT
easat-8773	198	3	i	i	PRON
easat-8773	198	4	assumed	assume	VERB
easat-8773	198	5	that	that	SCONJ
easat-8773	198	6	the	the	DET
easat-8773	198	7	same	same	ADJ
easat-8773	198	8	factor	factor	NOUN
easat-8773	198	9	should	should	AUX
easat-8773	198	10	apply	apply	VERB
easat-8773	198	11	to	to	ADP
easat-8773	198	12	men	man	NOUN
easat-8773	198	13	,	,	PUNCT
easat-8773	198	14	women	woman	NOUN
easat-8773	198	15	,	,	PUNCT
easat-8773	198	16	and	and	CCONJ
easat-8773	198	17	commanders	commander	NOUN
easat-8773	198	18	.	.	PUNCT
easat-8773	199	1	r	r	X
easat-8773	199	2	:	:	PUNCT
easat-8773	199	3	that	that	PRON
easat-8773	199	4	’s	’	VERB
easat-8773	199	5	a	a	DET
easat-8773	199	6	common	common	ADJ
easat-8773	199	7	error	error	NOUN
easat-8773	199	8	.	.	PUNCT
easat-8773	200	1	in	in	ADP
easat-8773	200	2	your	your	PRON
easat-8773	200	3	final	final	ADJ
easat-8773	200	4	step	step	NOUN
easat-8773	200	5	,	,	PUNCT
easat-8773	200	6	you	you	PRON
easat-8773	200	7	wrote	write	VERB
easat-8773	200	8	3	3	NUM
easat-8773	200	9	ruai	ruai	NOUN
easat-8773	200	10	feathers	feather	NOUN
easat-8773	200	11	=	=	PUNCT
easat-8773	200	12	71	71	NUM
easat-8773	200	13	+	+	CCONJ
easat-8773	200	14	9	9	NUM
easat-8773	200	15	+	+	CCONJ
easat-8773	200	16	6	6	NUM
easat-8773	200	17	=	=	SYM
easat-8773	200	18	86	86	NUM
easat-8773	200	19	ruai	ruai	NOUN
easat-8773	200	20	feathers	feather	NOUN
easat-8773	200	21	.	.	PUNCT
easat-8773	201	1	what	what	PRON
easat-8773	201	2	does	do	AUX
easat-8773	201	3	the	the	DET
easat-8773	201	4	left	left	ADJ
easat-8773	201	5	-	-	PUNCT
easat-8773	201	6	hand	hand	NOUN
easat-8773	201	7	side	side	NOUN
easat-8773	201	8	of	of	ADP
easat-8773	201	9	the	the	DET
easat-8773	201	10	equation	equation	NOUN
easat-8773	201	11	represent	represent	VERB
easat-8773	201	12	?	?	PUNCT
easat-8773	202	1	s	s	VERB
easat-8773	202	2	:	:	PUNCT
easat-8773	203	1	i	i	PRON
easat-8773	203	2	was	be	AUX
easat-8773	203	3	trying	try	VERB
easat-8773	203	4	to	to	PART
easat-8773	203	5	show	show	VERB
easat-8773	203	6	the	the	DET
easat-8773	203	7	total	total	ADJ
easat-8773	203	8	number	number	NOUN
easat-8773	203	9	of	of	ADP
easat-8773	203	10	feathers	feather	NOUN
easat-8773	203	11	.	.	PUNCT
easat-8773	204	1	r	r	X
easat-8773	204	2	:	:	PUNCT
easat-8773	204	3	the	the	DET
easat-8773	204	4	way	way	NOUN
easat-8773	204	5	it	it	PRON
easat-8773	204	6	is	be	AUX
easat-8773	204	7	written	write	VERB
easat-8773	204	8	,	,	PUNCT
easat-8773	204	9	3	3	NUM
easat-8773	204	10	ruai	ruai	NOUN
easat-8773	204	11	feathers	feather	NOUN
easat-8773	204	12	=	=	SYM
easat-8773	204	13	86	86	NUM
easat-8773	204	14	ruai	ruai	NOUN
easat-8773	204	15	feathers	feather	NOUN
easat-8773	204	16	,	,	PUNCT
easat-8773	204	17	suggests	suggest	VERB
easat-8773	204	18	that	that	SCONJ
easat-8773	204	19	3	3	NUM
easat-8773	204	20	feathers	feather	NOUN
easat-8773	204	21	are	be	AUX
easat-8773	204	22	equal	equal	ADJ
easat-8773	204	23	to	to	ADP
easat-8773	204	24	86	86	NUM
easat-8773	204	25	,	,	PUNCT
easat-8773	204	26	which	which	PRON
easat-8773	204	27	is	be	AUX
easat-8773	204	28	incorrect	incorrect	ADJ
easat-8773	204	29	.	.	PUNCT
easat-8773	205	1	the	the	DET
easat-8773	205	2	student	student	NOUN
easat-8773	205	3	demonstrates	demonstrate	VERB
easat-8773	205	4	a	a	DET
easat-8773	205	5	misunderstanding	misunderstanding	NOUN
easat-8773	205	6	of	of	ADP
easat-8773	205	7	representational	representational	ADJ
easat-8773	205	8	equivalence	equivalence	NOUN
easat-8773	205	9	.	.	PUNCT
easat-8773	206	1	by	by	ADP
easat-8773	206	2	writing	write	VERB
easat-8773	206	3	3	3	NUM
easat-8773	206	4	ruai	ruai	NOUN
easat-8773	206	5	feathers	feather	NOUN
easat-8773	206	6	=	=	SYM
easat-8773	206	7	86	86	NUM
easat-8773	206	8	ruai	ruai	NOUN
easat-8773	206	9	feathers	feather	NOUN
easat-8773	206	10	,	,	PUNCT
easat-8773	206	11	they	they	PRON
easat-8773	206	12	not	not	PART
easat-8773	206	13	only	only	ADV
easat-8773	206	14	misrepresented	misrepresent	VERB
easat-8773	206	15	a	a	DET
easat-8773	206	16	relationship	relationship	NOUN
easat-8773	206	17	but	but	CCONJ
easat-8773	206	18	also	also	ADV
easat-8773	206	19	introduced	introduce	VERB
easat-8773	206	20	an	an	DET
easat-8773	206	21	illogical	illogical	ADJ
easat-8773	206	22	equation	equation	NOUN
easat-8773	206	23	suggesting	suggest	VERB
easat-8773	206	24	direct	direct	ADJ
easat-8773	206	25	equality	equality	NOUN
easat-8773	206	26	between	between	ADP
easat-8773	206	27	unequal	unequal	ADJ
easat-8773	206	28	quantities	quantity	NOUN
easat-8773	206	29	.	.	PUNCT
easat-8773	207	1	this	this	PRON
easat-8773	207	2	indicates	indicate	VERB
easat-8773	207	3	a	a	DET
easat-8773	207	4	failure	failure	NOUN
easat-8773	207	5	to	to	PART
easat-8773	207	6	distinguish	distinguish	VERB
easat-8773	207	7	between	between	ADP
easat-8773	207	8	symbolic	symbolic	ADJ
easat-8773	207	9	representation	representation	NOUN
easat-8773	207	10	and	and	CCONJ
easat-8773	207	11	real	real	ADJ
easat-8773	207	12	-	-	PUNCT
easat-8773	207	13	world	world	NOUN
easat-8773	207	14	meaning	meaning	NOUN
easat-8773	207	15	,	,	PUNCT
easat-8773	207	16	a	a	DET
easat-8773	207	17	key	key	ADJ
easat-8773	207	18	element	element	NOUN
easat-8773	207	19	in	in	ADP
easat-8773	207	20	mathematical	mathematical	ADJ
easat-8773	207	21	modeling	modeling	NOUN
easat-8773	207	22	literacy	literacy	NOUN
easat-8773	207	23	.	.	PUNCT
easat-8773	208	1	further	far	ADV
easat-8773	208	2	,	,	PUNCT
easat-8773	208	3	the	the	DET
easat-8773	208	4	assumption	assumption	NOUN
easat-8773	208	5	that	that	SCONJ
easat-8773	208	6	a	a	DET
easat-8773	208	7	uniform	uniform	ADJ
easat-8773	208	8	proportion	proportion	NOUN
easat-8773	208	9	could	could	AUX
easat-8773	208	10	be	be	AUX
easat-8773	208	11	applied	apply	VERB
easat-8773	208	12	to	to	ADP
easat-8773	208	13	all	all	DET
easat-8773	208	14	groups	group	NOUN
easat-8773	208	15	(	(	PUNCT
easat-8773	208	16	men	man	NOUN
easat-8773	208	17	,	,	PUNCT
easat-8773	208	18	women	woman	NOUN
easat-8773	208	19	,	,	PUNCT
easat-8773	208	20	commanders	commander	NOUN
easat-8773	208	21	)	)	PUNCT
easat-8773	208	22	without	without	ADP
easat-8773	208	23	justification	justification	NOUN
easat-8773	208	24	from	from	ADP
easat-8773	208	25	the	the	DET
easat-8773	208	26	problem	problem	NOUN
easat-8773	208	27	context	context	NOUN
easat-8773	208	28	reflects	reflect	VERB
easat-8773	208	29	a	a	DET
easat-8773	208	30	premature	premature	ADJ
easat-8773	208	31	generalization	generalization	NOUN
easat-8773	208	32	.	.	PUNCT
easat-8773	209	1	this	this	DET
easat-8773	209	2	example	example	NOUN
easat-8773	209	3	highlights	highlight	VERB
easat-8773	209	4	that	that	PRON
easat-8773	209	5	error	error	NOUN
easat-8773	209	6	during	during	ADP
easat-8773	209	7	the	the	DET
easat-8773	209	8	mathematizing	mathematizing	NOUN
easat-8773	209	9	process	process	NOUN
easat-8773	209	10	often	often	ADV
easat-8773	209	11	stem	stem	VERB
easat-8773	209	12	from	from	ADP
easat-8773	209	13	inappropriate	inappropriate	ADJ
easat-8773	209	14	assumptions	assumption	NOUN
easat-8773	209	15	and	and	CCONJ
easat-8773	209	16	misuse	misuse	NOUN
easat-8773	209	17	of	of	ADP
easat-8773	209	18	mathematical	mathematical	ADJ
easat-8773	209	19	language	language	NOUN
easat-8773	209	20	or	or	CCONJ
easat-8773	209	21	symbols	symbol	NOUN
easat-8773	209	22	.	.	PUNCT
easat-8773	210	1	the	the	DET
easat-8773	210	2	misrepresentation	misrepresentation	NOUN
easat-8773	210	3	of	of	ADP
easat-8773	210	4	relationships	relationship	NOUN
easat-8773	210	5	and	and	CCONJ
easat-8773	210	6	failure	failure	NOUN
easat-8773	210	7	to	to	PART
easat-8773	210	8	verify	verify	VERB
easat-8773	210	9	the	the	DET
easat-8773	210	10	logic	logic	NOUN
easat-8773	210	11	behind	behind	ADP
easat-8773	210	12	model	model	NOUN
easat-8773	210	13	construction	construction	NOUN
easat-8773	210	14	underscore	underscore	VERB
easat-8773	210	15	the	the	DET
easat-8773	210	16	need	need	NOUN
easat-8773	210	17	for	for	ADP
easat-8773	210	18	instruction	instruction	NOUN
easat-8773	210	19	that	that	PRON
easat-8773	210	20	emphasizes	emphasize	VERB
easat-8773	210	21	critical	critical	ADJ
easat-8773	210	22	thinking	thinking	NOUN
easat-8773	210	23	,	,	PUNCT
easat-8773	210	24	contextual	contextual	ADJ
easat-8773	210	25	sensitivity	sensitivity	NOUN
easat-8773	210	26	,	,	PUNCT
easat-8773	210	27	and	and	CCONJ
easat-8773	210	28	representational	representational	ADJ
easat-8773	210	29	accuracy	accuracy	NOUN
easat-8773	210	30	in	in	ADP
easat-8773	210	31	modeling	model	VERB
easat-8773	210	32	activities	activity	NOUN
easat-8773	210	33	.	.	PUNCT
easat-8773	211	1	example	example	NOUN
easat-8773	211	2	error	error	NOUN
easat-8773	211	3	made	make	VERB
easat-8773	211	4	by	by	ADP
easat-8773	211	5	student	student	NOUN
easat-8773	211	6	with	with	ADP
easat-8773	211	7	medium	medium	ADJ
easat-8773	211	8	level	level	NOUN
easat-8773	211	9	mathematical	mathematical	ADJ
easat-8773	211	10	abilities	ability	NOUN
easat-8773	211	11	in	in	ADP
easat-8773	211	12	process	process	NOUN
easat-8773	211	13	working	work	VERB
easat-8773	211	14	mathematically	mathematically	ADV
easat-8773	211	15	,	,	PUNCT
easat-8773	211	16	see	see	VERB
easat-8773	211	17	figure	figure	NOUN
easat-8773	211	18	5	5	NUM
easat-8773	211	19	.	.	PUNCT
easat-8773	211	20	figure	figure	NOUN
easat-8773	211	21	5	5	NUM
easat-8773	211	22	.	.	NOUN
easat-8773	211	23	example	example	NOUN
easat-8773	211	24	of	of	ADP
easat-8773	211	25	errors	error	NOUN
easat-8773	211	26	in	in	ADP
easat-8773	211	27	the	the	DET
easat-8773	211	28	working	work	VERB
easat-8773	211	29	mathematically	mathematically	ADV
easat-8773	211	30	process	process	NOUN
easat-8773	211	31	.	.	PUNCT
easat-8773	212	1	the	the	DET
easat-8773	212	2	interview	interview	NOUN
easat-8773	212	3	was	be	AUX
easat-8773	212	4	conducted	conduct	VERB
easat-8773	212	5	based	base	VERB
easat-8773	212	6	on	on	ADP
easat-8773	212	7	students	student	NOUN
easat-8773	212	8	'	'	PART
easat-8773	212	9	answers	answer	NOUN
easat-8773	212	10	to	to	PART
easat-8773	212	11	identify	identify	VERB
easat-8773	212	12	assumptions	assumption	NOUN
easat-8773	212	13	and	and	CCONJ
easat-8773	212	14	errors	error	NOUN
easat-8773	212	15	.	.	PUNCT
easat-8773	213	1	below	below	ADV
easat-8773	213	2	is	be	AUX
easat-8773	213	3	an	an	DET
easat-8773	213	4	excerpt	excerpt	NOUN
easat-8773	213	5	.	.	PUNCT
easat-8773	214	1	r	r	NOUN
easat-8773	214	2	:	:	PUNCT
easat-8773	214	3	that	that	PRON
easat-8773	214	4	is	be	AUX
easat-8773	214	5	the	the	DET
easat-8773	214	6	correct	correct	ADJ
easat-8773	214	7	approach	approach	NOUN
easat-8773	214	8	.	.	PUNCT
easat-8773	215	1	however	however	ADV
easat-8773	215	2	,	,	PUNCT
easat-8773	215	3	let	let	VERB
easat-8773	215	4	's	us	PRON
easat-8773	215	5	review	review	VERB
easat-8773	215	6	your	your	PRON
easat-8773	215	7	calculations	calculation	NOUN
easat-8773	215	8	.	.	PUNCT
easat-8773	216	1	in	in	ADP
easat-8773	216	2	one	one	NUM
easat-8773	216	3	of	of	ADP
easat-8773	216	4	your	your	PRON
easat-8773	216	5	steps	step	NOUN
easat-8773	216	6	,	,	PUNCT
easat-8773	216	7	you	you	PRON
easat-8773	216	8	wrote	write	VERB
easat-8773	216	9	"	"	PUNCT
easat-8773	216	10	102	102	NUM
easat-8773	216	11	×	×	NOUN
easat-8773	216	12	270	270	NUM
easat-8773	216	13	=	=	SYM
easat-8773	216	14	27.540	27.540	NUM
easat-8773	216	15	.	.	PUNCT
easat-8773	216	16	"	"	PUNCT
easat-8773	217	1	do	do	AUX
easat-8773	217	2	you	you	PRON
easat-8773	217	3	think	think	VERB
easat-8773	217	4	this	this	DET
easat-8773	217	5	result	result	NOUN
easat-8773	217	6	makes	make	VERB
easat-8773	217	7	sense	sense	NOUN
easat-8773	217	8	?	?	PUNCT
easat-8773	218	1	s	s	VERB
easat-8773	218	2	:	:	PUNCT
easat-8773	218	3	hmm	hmm	INTJ
easat-8773	218	4	…	…	PUNCT
easat-8773	218	5	it	it	PRON
easat-8773	218	6	should	should	AUX
easat-8773	218	7	be	be	AUX
easat-8773	218	8	correct	correct	ADJ
easat-8773	218	9	because	because	SCONJ
easat-8773	218	10	i	i	PRON
easat-8773	218	11	added	add	VERB
easat-8773	218	12	the	the	DET
easat-8773	218	13	areas	area	NOUN
easat-8773	218	14	and	and	CCONJ
easat-8773	218	15	multiplied	multiply	VERB
easat-8773	218	16	them	they	PRON
easat-8773	218	17	.	.	PUNCT
easat-8773	219	1	r	r	NOUN
easat-8773	219	2	:	:	PUNCT
easat-8773	219	3	actually	actually	ADV
easat-8773	219	4	,	,	PUNCT
easat-8773	219	5	there	there	PRON
easat-8773	219	6	is	be	VERB
easat-8773	219	7	an	an	DET
easat-8773	219	8	error	error	NOUN
easat-8773	219	9	in	in	ADP
easat-8773	219	10	the	the	DET
easat-8773	219	11	mathematical	mathematical	ADJ
easat-8773	219	12	operation	operation	NOUN
easat-8773	219	13	at	at	ADP
easat-8773	219	14	this	this	DET
easat-8773	219	15	stage	stage	NOUN
easat-8773	219	16	.	.	PUNCT
easat-8773	220	1	the	the	DET
easat-8773	220	2	total	total	ADJ
easat-8773	220	3	area	area	NOUN
easat-8773	220	4	should	should	AUX
easat-8773	220	5	be	be	AUX
easat-8773	220	6	calculated	calculate	VERB
easat-8773	220	7	by	by	ADP
easat-8773	220	8	addition	addition	NOUN
easat-8773	220	9	,	,	PUNCT
easat-8773	220	10	not	not	PART
easat-8773	220	11	multiplication	multiplication	NOUN
easat-8773	220	12	.	.	PUNCT
easat-8773	221	1	s	s	PART
easat-8773	221	2	:	:	PUNCT
easat-8773	222	1	oh	oh	INTJ
easat-8773	222	2	,	,	PUNCT
easat-8773	222	3	i	i	PRON
easat-8773	222	4	see	see	VERB
easat-8773	222	5	!	!	PUNCT
easat-8773	223	1	i	i	PRON
easat-8773	223	2	should	should	AUX
easat-8773	223	3	have	have	AUX
easat-8773	223	4	just	just	ADV
easat-8773	223	5	added	add	VERB
easat-8773	223	6	the	the	DET
easat-8773	223	7	values	value	NOUN
easat-8773	223	8	instead	instead	ADV
easat-8773	223	9	of	of	ADP
easat-8773	223	10	multiplying	multiply	VERB
easat-8773	223	11	them	they	PRON
easat-8773	223	12	.	.	PUNCT
easat-8773	224	1	the	the	DET
easat-8773	224	2	student	student	NOUN
easat-8773	224	3	's	's	PART
easat-8773	224	4	error	error	NOUN
easat-8773	224	5	lies	lie	VERB
easat-8773	224	6	not	not	PART
easat-8773	224	7	in	in	ADP
easat-8773	224	8	the	the	DET
easat-8773	224	9	approach	approach	NOUN
easat-8773	224	10	,	,	PUNCT
easat-8773	224	11	but	but	CCONJ
easat-8773	224	12	in	in	ADP
easat-8773	224	13	executing	execute	VERB
easat-8773	224	14	the	the	DET
easat-8773	224	15	correct	correct	ADJ
easat-8773	224	16	mathematical	mathematical	ADJ
easat-8773	224	17	operation	operation	NOUN
easat-8773	224	18	.	.	PUNCT
easat-8773	225	1	while	while	SCONJ
easat-8773	225	2	they	they	PRON
easat-8773	225	3	understood	understand	VERB
easat-8773	225	4	that	that	SCONJ
easat-8773	225	5	area	area	NOUN
easat-8773	225	6	values	value	NOUN
easat-8773	225	7	needed	need	VERB
easat-8773	225	8	to	to	PART
easat-8773	225	9	be	be	AUX
easat-8773	225	10	combined	combine	VERB
easat-8773	225	11	,	,	PUNCT
easat-8773	225	12	they	they	PRON
easat-8773	225	13	mistakenly	mistakenly	ADV
easat-8773	225	14	applied	apply	VERB
easat-8773	225	15	multiplication	multiplication	NOUN
easat-8773	225	16	instead	instead	ADV
easat-8773	225	17	of	of	ADP
easat-8773	225	18	addition	addition	NOUN
easat-8773	225	19	demonstrating	demonstrate	VERB
easat-8773	225	20	a	a	DET
easat-8773	225	21	misalignment	misalignment	NOUN
easat-8773	225	22	between	between	ADP
easat-8773	225	23	procedural	procedural	ADJ
easat-8773	225	24	execution	execution	NOUN
easat-8773	225	25	and	and	CCONJ
easat-8773	225	26	conceptual	conceptual	ADJ
easat-8773	225	27	understanding	understanding	NOUN
easat-8773	225	28	.	.	PUNCT
easat-8773	226	1	this	this	PRON
easat-8773	226	2	suggests	suggest	VERB
easat-8773	226	3	that	that	SCONJ
easat-8773	226	4	while	while	SCONJ
easat-8773	226	5	the	the	DET
easat-8773	226	6	student	student	NOUN
easat-8773	226	7	may	may	AUX
easat-8773	226	8	possess	possess	VERB
easat-8773	226	9	surface	surface	NOUN
easat-8773	226	10	-	-	PUNCT
easat-8773	226	11	level	level	NOUN
easat-8773	226	12	familiarity	familiarity	NOUN
easat-8773	226	13	with	with	ADP
easat-8773	226	14	problem	problem	NOUN
easat-8773	226	15	requirements	requirement	NOUN
easat-8773	226	16	,	,	PUNCT
easat-8773	226	17	their	their	PRON
easat-8773	226	18	decision	decision	NOUN
easat-8773	226	19	-	-	PUNCT
easat-8773	226	20	making	making	NOUN
easat-8773	226	21	during	during	ADP
easat-8773	226	22	the	the	DET
easat-8773	226	23	calculation	calculation	NOUN
easat-8773	226	24	phase	phase	NOUN
easat-8773	226	25	is	be	AUX
easat-8773	226	26	mechanical	mechanical	ADJ
easat-8773	226	27	rather	rather	ADV
easat-8773	226	28	than	than	ADP
easat-8773	226	29	reflective	reflective	ADJ
easat-8773	226	30	.	.	PUNCT
easat-8773	227	1	956	956	NUM
easat-8773	227	2	edelweiss	edelweiss	PROPN
easat-8773	227	3	applied	apply	VERB
easat-8773	227	4	science	science	NOUN
easat-8773	227	5	and	and	CCONJ
easat-8773	227	6	technology	technology	NOUN
easat-8773	227	7	issn	issn	PROPN
easat-8773	227	8	:	:	PUNCT
easat-8773	227	9	2576	2576	NUM
easat-8773	227	10	-	-	SYM
easat-8773	227	11	8484	8484	NUM
easat-8773	227	12	vol	vol	NOUN
easat-8773	227	13	.	.	PROPN
easat-8773	228	1	9	9	NUM
easat-8773	228	2	,	,	PUNCT
easat-8773	228	3	no	no	INTJ
easat-8773	228	4	.	.	NOUN
easat-8773	229	1	7	7	NUM
easat-8773	229	2	:	:	SYM
easat-8773	229	3	947	947	NUM
easat-8773	229	4	-	-	SYM
easat-8773	229	5	959	959	NUM
easat-8773	229	6	,	,	PUNCT
easat-8773	229	7	2025	2025	NUM
easat-8773	229	8	doi	doi	NOUN
easat-8773	229	9	:	:	PUNCT
easat-8773	229	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	229	11	©	©	PROPN
easat-8773	229	12	2025	2025	NUM
easat-8773	229	13	by	by	ADP
easat-8773	229	14	the	the	DET
easat-8773	229	15	authors	author	NOUN
easat-8773	229	16	;	;	PUNCT
easat-8773	229	17	licensee	licensee	PROPN
easat-8773	229	18	learning	learning	NOUN
easat-8773	229	19	gate	gate	VERB
easat-8773	229	20	the	the	DET
easat-8773	229	21	fact	fact	NOUN
easat-8773	229	22	that	that	SCONJ
easat-8773	229	23	the	the	DET
easat-8773	229	24	student	student	NOUN
easat-8773	229	25	misunderstood	misunderstood	VERB
easat-8773	229	26	the	the	DET
easat-8773	229	27	purpose	purpose	NOUN
easat-8773	229	28	of	of	ADP
easat-8773	229	29	multiplication	multiplication	NOUN
easat-8773	229	30	versus	versus	ADP
easat-8773	229	31	addition	addition	NOUN
easat-8773	229	32	in	in	ADP
easat-8773	229	33	context	context	NOUN
easat-8773	229	34	also	also	ADV
easat-8773	229	35	highlights	highlight	VERB
easat-8773	229	36	weaknesses	weakness	NOUN
easat-8773	229	37	in	in	ADP
easat-8773	229	38	interpreting	interpret	VERB
easat-8773	229	39	quantitative	quantitative	ADJ
easat-8773	229	40	relationships	relationship	NOUN
easat-8773	229	41	between	between	ADP
easat-8773	229	42	mathematical	mathematical	ADJ
easat-8773	229	43	entities	entity	NOUN
easat-8773	229	44	.	.	PUNCT
easat-8773	230	1	this	this	DET
easat-8773	230	2	example	example	NOUN
easat-8773	230	3	illustrates	illustrate	VERB
easat-8773	230	4	that	that	SCONJ
easat-8773	230	5	errors	error	NOUN
easat-8773	230	6	during	during	ADP
easat-8773	230	7	the	the	DET
easat-8773	230	8	working	working	NOUN
easat-8773	230	9	mathematically	mathematically	ADV
easat-8773	230	10	phases	phase	NOUN
easat-8773	230	11	are	be	AUX
easat-8773	230	12	not	not	PART
easat-8773	230	13	always	always	ADV
easat-8773	230	14	due	due	ADJ
easat-8773	230	15	to	to	ADP
easat-8773	230	16	conceptual	conceptual	ADJ
easat-8773	230	17	misunderstanding	misunderstanding	NOUN
easat-8773	230	18	,	,	PUNCT
easat-8773	230	19	but	but	CCONJ
easat-8773	230	20	may	may	AUX
easat-8773	230	21	stem	stem	VERB
easat-8773	230	22	from	from	ADP
easat-8773	230	23	flawed	flawed	ADJ
easat-8773	230	24	operational	operational	ADJ
easat-8773	230	25	decisions	decision	NOUN
easat-8773	230	26	.	.	PUNCT
easat-8773	231	1	instructional	instructional	ADJ
easat-8773	231	2	emphasis	emphasis	NOUN
easat-8773	231	3	should	should	AUX
easat-8773	231	4	therefore	therefore	ADV
easat-8773	231	5	include	include	VERB
easat-8773	231	6	not	not	PART
easat-8773	231	7	only	only	ADV
easat-8773	231	8	the	the	DET
easat-8773	231	9	mastery	mastery	NOUN
easat-8773	231	10	of	of	ADP
easat-8773	231	11	concepts	concept	NOUN
easat-8773	231	12	and	and	CCONJ
easat-8773	231	13	procedures	procedure	NOUN
easat-8773	231	14	,	,	PUNCT
easat-8773	231	15	but	but	CCONJ
easat-8773	231	16	also	also	ADV
easat-8773	231	17	guided	guide	VERB
easat-8773	231	18	reflection	reflection	NOUN
easat-8773	231	19	on	on	ADP
easat-8773	231	20	the	the	DET
easat-8773	231	21	logic	logic	NOUN
easat-8773	231	22	behind	behind	ADP
easat-8773	231	23	chosen	choose	VERB
easat-8773	231	24	operations	operation	NOUN
easat-8773	231	25	.	.	PUNCT
easat-8773	232	1	example	example	NOUN
easat-8773	232	2	error	error	NOUN
easat-8773	232	3	made	make	VERB
easat-8773	232	4	by	by	ADP
easat-8773	232	5	student	student	NOUN
easat-8773	232	6	with	with	ADP
easat-8773	232	7	high	high	ADJ
easat-8773	232	8	level	level	NOUN
easat-8773	232	9	mathematical	mathematical	ADJ
easat-8773	232	10	abilities	ability	NOUN
easat-8773	232	11	in	in	ADP
easat-8773	232	12	process	process	NOUN
easat-8773	232	13	interpreting	interpret	VERB
easat-8773	232	14	and	and	CCONJ
easat-8773	232	15	validating	validate	VERB
easat-8773	232	16	,	,	PUNCT
easat-8773	232	17	see	see	VERB
easat-8773	232	18	figure	figure	NOUN
easat-8773	232	19	6	6	NUM
easat-8773	232	20	.	.	PUNCT
easat-8773	232	21	figure	figure	VERB
easat-8773	232	22	6	6	NUM
easat-8773	232	23	.	.	NOUN
easat-8773	232	24	example	example	NOUN
easat-8773	232	25	of	of	ADP
easat-8773	232	26	errors	error	NOUN
easat-8773	232	27	in	in	ADP
easat-8773	232	28	the	the	DET
easat-8773	232	29	interpreting	interpreting	NOUN
easat-8773	232	30	and	and	CCONJ
easat-8773	232	31	validating	validate	VERB
easat-8773	232	32	process	process	NOUN
easat-8773	232	33	.	.	PUNCT
easat-8773	233	1	the	the	DET
easat-8773	233	2	interview	interview	NOUN
easat-8773	233	3	was	be	AUX
easat-8773	233	4	conducted	conduct	VERB
easat-8773	233	5	based	base	VERB
easat-8773	233	6	on	on	ADP
easat-8773	233	7	students	student	NOUN
easat-8773	233	8	'	'	PART
easat-8773	233	9	answers	answer	NOUN
easat-8773	233	10	to	to	PART
easat-8773	233	11	identify	identify	VERB
easat-8773	233	12	assumptions	assumption	NOUN
easat-8773	233	13	and	and	CCONJ
easat-8773	233	14	errors	error	NOUN
easat-8773	233	15	.	.	PUNCT
easat-8773	234	1	below	below	ADV
easat-8773	234	2	is	be	AUX
easat-8773	234	3	an	an	DET
easat-8773	234	4	excerpt	excerpt	NOUN
easat-8773	234	5	.	.	PUNCT
easat-8773	235	1	r	r	X
easat-8773	235	2	:	:	PUNCT
easat-8773	235	3	alright	alright	INTJ
easat-8773	235	4	,	,	PUNCT
easat-8773	235	5	based	base	VERB
easat-8773	235	6	on	on	ADP
easat-8773	235	7	what	what	PRON
easat-8773	235	8	you	you	PRON
easat-8773	235	9	wrote	write	VERB
easat-8773	235	10	,	,	PUNCT
easat-8773	235	11	do	do	AUX
easat-8773	235	12	you	you	PRON
easat-8773	235	13	think	think	VERB
easat-8773	235	14	your	your	PRON
easat-8773	235	15	answer	answer	NOUN
easat-8773	235	16	is	be	AUX
easat-8773	235	17	correct	correct	ADJ
easat-8773	235	18	?	?	PUNCT
easat-8773	236	1	s	s	X
easat-8773	236	2	:	:	PUNCT
easat-8773	236	3	hmm	hmm	INTJ
easat-8773	236	4	…	…	PUNCT
easat-8773	236	5	it	it	PRON
easat-8773	236	6	should	should	AUX
easat-8773	236	7	be	be	AUX
easat-8773	236	8	correct	correct	ADJ
easat-8773	236	9	because	because	SCONJ
easat-8773	236	10	i	i	PRON
easat-8773	236	11	multiplied	multiply	VERB
easat-8773	236	12	the	the	DET
easat-8773	236	13	length	length	NOUN
easat-8773	236	14	and	and	CCONJ
easat-8773	236	15	width	width	NOUN
easat-8773	236	16	.	.	PUNCT
easat-8773	237	1	r	r	X
easat-8773	237	2	:	:	PUNCT
easat-8773	237	3	actually	actually	ADV
easat-8773	237	4	,	,	PUNCT
easat-8773	237	5	there	there	PRON
easat-8773	237	6	is	be	VERB
easat-8773	237	7	an	an	DET
easat-8773	237	8	error	error	NOUN
easat-8773	237	9	in	in	ADP
easat-8773	237	10	the	the	DET
easat-8773	237	11	unit	unit	NOUN
easat-8773	237	12	notation	notation	NOUN
easat-8773	237	13	.	.	PUNCT
easat-8773	238	1	when	when	SCONJ
easat-8773	238	2	calculating	calculate	VERB
easat-8773	238	3	area	area	NOUN
easat-8773	238	4	,	,	PUNCT
easat-8773	238	5	the	the	DET
easat-8773	238	6	unit	unit	NOUN
easat-8773	238	7	should	should	AUX
easat-8773	238	8	not	not	PART
easat-8773	238	9	be	be	AUX
easat-8773	238	10	cm	cm	ADJ
easat-8773	238	11	,	,	PUNCT
easat-8773	238	12	but	but	CCONJ
easat-8773	238	13	cm²	cm²	PROPN
easat-8773	238	14	,	,	PUNCT
easat-8773	238	15	because	because	SCONJ
easat-8773	238	16	area	area	NOUN
easat-8773	238	17	represents	represent	VERB
easat-8773	238	18	two	two	NUM
easat-8773	238	19	dimensions	dimension	NOUN
easat-8773	238	20	,	,	PUNCT
easat-8773	238	21	not	not	PART
easat-8773	238	22	one	one	NUM
easat-8773	238	23	dimension	dimension	NOUN
easat-8773	238	24	like	like	ADP
easat-8773	238	25	length	length	NOUN
easat-8773	238	26	or	or	CCONJ
easat-8773	238	27	width	width	NOUN
easat-8773	238	28	.	.	PUNCT
easat-8773	239	1	s	s	VERB
easat-8773	239	2	:	:	PUNCT
easat-8773	239	3	i	i	PRON
easat-8773	239	4	wrote	write	VERB
easat-8773	239	5	cm	cm	PROPN
easat-8773	239	6	without	without	ADP
easat-8773	239	7	realizing	realize	VERB
easat-8773	239	8	that	that	SCONJ
easat-8773	239	9	it	it	PRON
easat-8773	239	10	should	should	AUX
easat-8773	239	11	have	have	AUX
easat-8773	239	12	been	be	AUX
easat-8773	239	13	cm²	cm²	ADJ
easat-8773	239	14	.	.	PUNCT
easat-8773	240	1	this	this	DET
easat-8773	240	2	interview	interview	NOUN
easat-8773	240	3	illustrates	illustrate	VERB
easat-8773	240	4	a	a	DET
easat-8773	240	5	subtle	subtle	ADJ
easat-8773	240	6	yet	yet	CCONJ
easat-8773	240	7	impactful	impactful	ADJ
easat-8773	240	8	error	error	NOUN
easat-8773	240	9	that	that	PRON
easat-8773	240	10	reflects	reflect	VERB
easat-8773	240	11	a	a	DET
easat-8773	240	12	student	student	NOUN
easat-8773	240	13	’s	’s	PART
easat-8773	240	14	incomplete	incomplete	ADJ
easat-8773	240	15	understanding	understanding	NOUN
easat-8773	240	16	of	of	ADP
easat-8773	240	17	mathematical	mathematical	ADJ
easat-8773	240	18	conventions	convention	NOUN
easat-8773	240	19	specifically	specifically	ADV
easat-8773	240	20	unit	unit	NOUN
easat-8773	240	21	usage	usage	NOUN
easat-8773	240	22	when	when	SCONJ
easat-8773	240	23	interpreting	interpret	VERB
easat-8773	240	24	and	and	CCONJ
easat-8773	240	25	validating	validate	VERB
easat-8773	240	26	a	a	DET
easat-8773	240	27	solution	solution	NOUN
easat-8773	240	28	.	.	PUNCT
easat-8773	241	1	the	the	DET
easat-8773	241	2	student	student	NOUN
easat-8773	241	3	correctly	correctly	ADV
easat-8773	241	4	performed	perform	VERB
easat-8773	241	5	the	the	DET
easat-8773	241	6	procedure	procedure	NOUN
easat-8773	241	7	(	(	PUNCT
easat-8773	241	8	multiplying	multiply	VERB
easat-8773	241	9	length	length	NOUN
easat-8773	241	10	by	by	ADP
easat-8773	241	11	width	width	NOUN
easat-8773	241	12	)	)	PUNCT
easat-8773	241	13	,	,	PUNCT
easat-8773	241	14	but	but	CCONJ
easat-8773	241	15	failed	fail	VERB
easat-8773	241	16	to	to	PART
easat-8773	241	17	recognize	recognize	VERB
easat-8773	241	18	the	the	DET
easat-8773	241	19	dimensional	dimensional	ADJ
easat-8773	241	20	implications	implication	NOUN
easat-8773	241	21	of	of	ADP
easat-8773	241	22	their	their	PRON
easat-8773	241	23	result	result	NOUN
easat-8773	241	24	,	,	PUNCT
easat-8773	241	25	indicating	indicate	VERB
easat-8773	241	26	that	that	SCONJ
easat-8773	241	27	procedural	procedural	ADJ
easat-8773	241	28	fluency	fluency	NOUN
easat-8773	241	29	is	be	AUX
easat-8773	241	30	not	not	PART
easat-8773	241	31	always	always	ADV
easat-8773	241	32	accompanied	accompany	VERB
easat-8773	241	33	by	by	ADP
easat-8773	241	34	conceptual	conceptual	ADJ
easat-8773	241	35	awareness	awareness	NOUN
easat-8773	241	36	.	.	PUNCT
easat-8773	242	1	this	this	PRON
easat-8773	242	2	aligns	align	VERB
easat-8773	242	3	with	with	ADP
easat-8773	242	4	prior	prior	ADJ
easat-8773	242	5	results	result	NOUN
easat-8773	242	6	suggesting	suggest	VERB
easat-8773	242	7	that	that	SCONJ
easat-8773	242	8	the	the	DET
easat-8773	242	9	validation	validation	NOUN
easat-8773	242	10	process	process	NOUN
easat-8773	242	11	poses	pose	VERB
easat-8773	242	12	significant	significant	ADJ
easat-8773	242	13	cognitive	cognitive	ADJ
easat-8773	242	14	demands	demand	NOUN
easat-8773	242	15	,	,	PUNCT
easat-8773	242	16	particularly	particularly	ADV
easat-8773	242	17	in	in	ADP
easat-8773	242	18	transitioning	transition	VERB
easat-8773	242	19	from	from	ADP
easat-8773	242	20	computation	computation	NOUN
easat-8773	242	21	to	to	ADP
easat-8773	242	22	interpretation	interpretation	NOUN
easat-8773	242	23	.	.	PUNCT
easat-8773	243	1	this	this	DET
easat-8773	243	2	instance	instance	NOUN
easat-8773	243	3	reinforces	reinforce	VERB
easat-8773	243	4	the	the	DET
easat-8773	243	5	errors	error	NOUN
easat-8773	243	6	in	in	ADP
easat-8773	243	7	the	the	DET
easat-8773	243	8	interpreting	interpreting	NOUN
easat-8773	243	9	and	and	CCONJ
easat-8773	243	10	validating	validate	VERB
easat-8773	243	11	phases	phase	NOUN
easat-8773	243	12	are	be	AUX
easat-8773	243	13	not	not	PART
easat-8773	243	14	merely	merely	ADV
easat-8773	243	15	technical	technical	ADJ
easat-8773	243	16	,	,	PUNCT
easat-8773	243	17	but	but	CCONJ
easat-8773	243	18	point	point	VERB
easat-8773	243	19	to	to	ADP
easat-8773	243	20	deeper	deep	ADJ
easat-8773	243	21	issues	issue	NOUN
easat-8773	243	22	in	in	ADP
easat-8773	243	23	students	student	NOUN
easat-8773	243	24	’	'	PUNCT
easat-8773	243	25	conceptual	conceptual	ADJ
easat-8773	243	26	understanding	understanding	NOUN
easat-8773	243	27	and	and	CCONJ
easat-8773	243	28	metacognitive	metacognitive	ADJ
easat-8773	243	29	monitoring	monitoring	NOUN
easat-8773	243	30	.	.	PUNCT
easat-8773	244	1	it	it	PRON
easat-8773	244	2	highlights	highlight	VERB
easat-8773	244	3	the	the	DET
easat-8773	244	4	importance	importance	NOUN
easat-8773	244	5	of	of	ADP
easat-8773	244	6	fostering	foster	VERB
easat-8773	244	7	reflective	reflective	ADJ
easat-8773	244	8	thinking	thinking	NOUN
easat-8773	244	9	and	and	CCONJ
easat-8773	244	10	dimensional	dimensional	ADJ
easat-8773	244	11	reasoning	reasoning	NOUN
easat-8773	244	12	in	in	ADP
easat-8773	244	13	mathematical	mathematical	ADJ
easat-8773	244	14	modeling	modeling	NOUN
easat-8773	244	15	instruction	instruction	NOUN
easat-8773	244	16	.	.	PUNCT
easat-8773	245	1	5	5	X
easat-8773	245	2	.	.	X
easat-8773	245	3	discussion	discussion	NOUN
easat-8773	245	4	the	the	DET
easat-8773	245	5	results	result	NOUN
easat-8773	245	6	reveal	reveal	VERB
easat-8773	245	7	the	the	DET
easat-8773	245	8	students	student	NOUN
easat-8773	245	9	exhibit	exhibit	VERB
easat-8773	245	10	significant	significant	ADJ
easat-8773	245	11	and	and	CCONJ
easat-8773	245	12	varied	varied	ADJ
easat-8773	245	13	errors	error	NOUN
easat-8773	245	14	across	across	ADP
easat-8773	245	15	all	all	DET
easat-8773	245	16	stages	stage	NOUN
easat-8773	245	17	of	of	ADP
easat-8773	245	18	mathematical	mathematical	ADJ
easat-8773	245	19	modeling	modeling	NOUN
easat-8773	245	20	processes	process	NOUN
easat-8773	245	21	.	.	PUNCT
easat-8773	246	1	these	these	DET
easat-8773	246	2	errors	error	NOUN
easat-8773	246	3	are	be	AUX
easat-8773	246	4	closely	closely	ADV
easat-8773	246	5	tied	tie	VERB
easat-8773	246	6	to	to	ADP
easat-8773	246	7	their	their	PRON
easat-8773	246	8	mathematical	mathematical	ADJ
easat-8773	246	9	proficiency	proficiency	NOUN
easat-8773	246	10	,	,	PUNCT
easat-8773	246	11	with	with	ADP
easat-8773	246	12	low	low	ADJ
easat-8773	246	13	and	and	CCONJ
easat-8773	246	14	medium	medium	ADJ
easat-8773	246	15	ability	ability	NOUN
easat-8773	246	16	students	student	NOUN
easat-8773	246	17	experiencing	experience	VERB
easat-8773	246	18	errors	error	NOUN
easat-8773	246	19	from	from	ADP
easat-8773	246	20	the	the	DET
easat-8773	246	21	earliest	early	ADJ
easat-8773	246	22	phases	phase	NOUN
easat-8773	246	23	such	such	ADJ
easat-8773	246	24	as	as	ADP
easat-8773	246	25	understanding	understanding	NOUN
easat-8773	246	26	and	and	CCONJ
easat-8773	246	27	simplifying	simplifying	NOUN
easat-8773	246	28	,	,	PUNCT
easat-8773	246	29	while	while	SCONJ
easat-8773	246	30	even	even	ADV
easat-8773	246	31	high	high	ADJ
easat-8773	246	32	ability	ability	NOUN
easat-8773	246	33	students	student	NOUN
easat-8773	246	34	demonstrate	demonstrate	VERB
easat-8773	246	35	challenges	challenge	NOUN
easat-8773	246	36	at	at	ADP
easat-8773	246	37	more	more	ADV
easat-8773	246	38	advanced	advanced	ADJ
easat-8773	246	39	stages	stage	NOUN
easat-8773	246	40	like	like	ADP
easat-8773	246	41	interpreting	interpret	VERB
easat-8773	246	42	and	and	CCONJ
easat-8773	246	43	validating	validate	VERB
easat-8773	246	44	.	.	PUNCT
easat-8773	247	1	957	957	NUM
easat-8773	247	2	edelweiss	edelweiss	PROPN
easat-8773	247	3	applied	apply	VERB
easat-8773	247	4	science	science	NOUN
easat-8773	247	5	and	and	CCONJ
easat-8773	247	6	technology	technology	NOUN
easat-8773	247	7	issn	issn	PROPN
easat-8773	247	8	:	:	PUNCT
easat-8773	247	9	2576	2576	NUM
easat-8773	247	10	-	-	SYM
easat-8773	247	11	8484	8484	NUM
easat-8773	247	12	vol	vol	NOUN
easat-8773	247	13	.	.	PROPN
easat-8773	248	1	9	9	NUM
easat-8773	248	2	,	,	PUNCT
easat-8773	248	3	no	no	INTJ
easat-8773	248	4	.	.	NOUN
easat-8773	249	1	7	7	NUM
easat-8773	249	2	:	:	SYM
easat-8773	249	3	947	947	NUM
easat-8773	249	4	-	-	SYM
easat-8773	249	5	959	959	NUM
easat-8773	249	6	,	,	PUNCT
easat-8773	249	7	2025	2025	NUM
easat-8773	249	8	doi	doi	NOUN
easat-8773	249	9	:	:	PUNCT
easat-8773	249	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	249	11	©	©	PROPN
easat-8773	249	12	2025	2025	NUM
easat-8773	249	13	by	by	ADP
easat-8773	249	14	the	the	DET
easat-8773	249	15	authors	author	NOUN
easat-8773	249	16	;	;	PUNCT
easat-8773	249	17	licensee	licensee	PROPN
easat-8773	249	18	learning	learn	VERB
easat-8773	249	19	gate	gate	NOUN
easat-8773	249	20	errors	error	NOUN
easat-8773	249	21	often	often	ADV
easat-8773	249	22	occurred	occur	VERB
easat-8773	249	23	simultaneously	simultaneously	ADV
easat-8773	249	24	or	or	CCONJ
easat-8773	249	25	in	in	ADP
easat-8773	249	26	succession	succession	NOUN
easat-8773	249	27	,	,	PUNCT
easat-8773	249	28	reflecting	reflect	VERB
easat-8773	249	29	not	not	PART
easat-8773	249	30	only	only	ADV
easat-8773	249	31	conceptual	conceptual	ADJ
easat-8773	249	32	misunderstanding	misunderstanding	NOUN
easat-8773	249	33	but	but	CCONJ
easat-8773	249	34	also	also	ADV
easat-8773	249	35	lapses	lapse	NOUN
easat-8773	249	36	in	in	ADP
easat-8773	249	37	procedural	procedural	ADJ
easat-8773	249	38	fluency	fluency	NOUN
easat-8773	249	39	and	and	CCONJ
easat-8773	249	40	metacognitive	metacognitive	ADJ
easat-8773	249	41	oversight	oversight	NOUN
easat-8773	249	42	.	.	PUNCT
easat-8773	250	1	in	in	ADP
easat-8773	250	2	the	the	DET
easat-8773	250	3	initial	initial	ADJ
easat-8773	250	4	understanding	understanding	NOUN
easat-8773	250	5	phase	phase	NOUN
easat-8773	250	6	,	,	PUNCT
easat-8773	250	7	many	many	ADJ
easat-8773	250	8	students	student	NOUN
easat-8773	250	9	particularly	particularly	ADV
easat-8773	250	10	those	those	PRON
easat-8773	250	11	with	with	ADP
easat-8773	250	12	lower	low	ADJ
easat-8773	250	13	ability	ability	NOUN
easat-8773	250	14	struggles	struggle	VERB
easat-8773	250	15	to	to	PART
easat-8773	250	16	grasp	grasp	VERB
easat-8773	250	17	the	the	DET
easat-8773	250	18	context	context	NOUN
easat-8773	250	19	or	or	CCONJ
easat-8773	250	20	intent	intent	NOUN
easat-8773	250	21	of	of	ADP
easat-8773	250	22	the	the	DET
easat-8773	250	23	task	task	NOUN
easat-8773	250	24	.	.	PUNCT
easat-8773	251	1	this	this	PRON
easat-8773	251	2	aligns	align	VERB
easat-8773	251	3	with	with	ADP
easat-8773	251	4	prior	prior	ADJ
easat-8773	251	5	research	research	NOUN
easat-8773	251	6	suggesting	suggest	VERB
easat-8773	251	7	that	that	SCONJ
easat-8773	251	8	students	student	NOUN
easat-8773	251	9	often	often	ADV
easat-8773	251	10	attempt	attempt	VERB
easat-8773	251	11	to	to	PART
easat-8773	251	12	solve	solve	VERB
easat-8773	251	13	problems	problem	NOUN
easat-8773	251	14	without	without	ADP
easat-8773	251	15	thoroughly	thoroughly	ADV
easat-8773	251	16	reading	read	VERB
easat-8773	251	17	or	or	CCONJ
easat-8773	251	18	understanding	understand	VERB
easat-8773	251	19	the	the	DET
easat-8773	251	20	context	context	NOUN
easat-8773	251	21	[	[	X
easat-8773	251	22	10	10	NUM
easat-8773	251	23	,	,	PUNCT
easat-8773	251	24	11	11	NUM
easat-8773	251	25	]	]	PUNCT
easat-8773	251	26	.	.	PUNCT
easat-8773	252	1	one	one	NUM
easat-8773	252	2	contributing	contribute	VERB
easat-8773	252	3	factor	factor	NOUN
easat-8773	252	4	may	may	AUX
easat-8773	252	5	be	be	AUX
easat-8773	252	6	the	the	DET
easat-8773	252	7	unfamiliar	unfamiliar	ADJ
easat-8773	252	8	structure	structure	NOUN
easat-8773	252	9	of	of	ADP
easat-8773	252	10	modeling	modeling	NOUN
easat-8773	252	11	problem	problem	NOUN
easat-8773	252	12	compared	compare	VERB
easat-8773	252	13	to	to	ADP
easat-8773	252	14	conventional	conventional	ADJ
easat-8773	252	15	classroom	classroom	NOUN
easat-8773	252	16	exercises	exercise	NOUN
easat-8773	252	17	.	.	PUNCT
easat-8773	253	1	in	in	ADP
easat-8773	253	2	the	the	DET
easat-8773	253	3	simplifying	simplifying	NOUN
easat-8773	253	4	and	and	CCONJ
easat-8773	253	5	mathematizing	mathematizing	NOUN
easat-8773	253	6	process	process	NOUN
easat-8773	253	7	,	,	PUNCT
easat-8773	253	8	errors	error	NOUN
easat-8773	253	9	arose	arise	VERB
easat-8773	253	10	when	when	SCONJ
easat-8773	253	11	students	student	NOUN
easat-8773	253	12	failed	fail	VERB
easat-8773	253	13	to	to	PART
easat-8773	253	14	filter	filter	VERB
easat-8773	253	15	essential	essential	ADJ
easat-8773	253	16	information	information	NOUN
easat-8773	253	17	or	or	CCONJ
easat-8773	253	18	made	make	VERB
easat-8773	253	19	incorrect	incorrect	ADJ
easat-8773	253	20	assumptions	assumption	NOUN
easat-8773	253	21	,	,	PUNCT
easat-8773	253	22	often	often	ADV
easat-8773	253	23	applying	apply	VERB
easat-8773	253	24	proportional	proportional	ADJ
easat-8773	253	25	reasoning	reasoning	NOUN
easat-8773	253	26	without	without	ADP
easat-8773	253	27	contextual	contextual	ADJ
easat-8773	253	28	justification	justification	NOUN
easat-8773	253	29	.	.	PUNCT
easat-8773	254	1	this	this	PRON
easat-8773	254	2	consistent	consistent	ADJ
easat-8773	254	3	with	with	ADP
easat-8773	254	4	results	result	NOUN
easat-8773	254	5	who	who	PRON
easat-8773	254	6	noted	note	VERB
easat-8773	254	7	that	that	SCONJ
easat-8773	254	8	simplification	simplification	NOUN
easat-8773	254	9	is	be	AUX
easat-8773	254	10	particularly	particularly	ADV
easat-8773	254	11	difficult	difficult	ADJ
easat-8773	254	12	when	when	SCONJ
easat-8773	254	13	student	student	NOUN
easat-8773	254	14	lack	lack	VERB
easat-8773	254	15	real	real	ADJ
easat-8773	254	16	-	-	PUNCT
easat-8773	254	17	world	world	NOUN
easat-8773	254	18	experience	experience	NOUN
easat-8773	254	19	related	relate	VERB
easat-8773	254	20	to	to	ADP
easat-8773	254	21	the	the	DET
easat-8773	254	22	problem	problem	NOUN
easat-8773	254	23	situation	situation	NOUN
easat-8773	254	24	[	[	X
easat-8773	254	25	8	8	NUM
easat-8773	254	26	,	,	PUNCT
easat-8773	254	27	22	22	NUM
easat-8773	254	28	]	]	PUNCT
easat-8773	254	29	.	.	PUNCT
easat-8773	255	1	the	the	DET
easat-8773	255	2	transition	transition	NOUN
easat-8773	255	3	from	from	ADP
easat-8773	255	4	realworld	realworld	PROPN
easat-8773	255	5	context	context	PROPN
easat-8773	255	6	to	to	ADP
easat-8773	255	7	a	a	DET
easat-8773	255	8	mathematical	mathematical	ADJ
easat-8773	255	9	model	model	NOUN
easat-8773	255	10	proved	prove	VERB
easat-8773	255	11	especially	especially	ADV
easat-8773	255	12	challenging	challenge	VERB
easat-8773	255	13	for	for	ADP
easat-8773	255	14	students	student	NOUN
easat-8773	255	15	with	with	ADP
easat-8773	255	16	weaker	weak	ADJ
easat-8773	255	17	conceptual	conceptual	ADJ
easat-8773	255	18	foundations	foundation	NOUN
easat-8773	255	19	[	[	X
easat-8773	255	20	9	9	NUM
easat-8773	255	21	,	,	PUNCT
easat-8773	255	22	23	23	NUM
easat-8773	255	23	]	]	PUNCT
easat-8773	255	24	.	.	PUNCT
easat-8773	256	1	the	the	DET
easat-8773	256	2	working	work	VERB
easat-8773	256	3	mathematically	mathematically	ADV
easat-8773	256	4	process	process	NOUN
easat-8773	256	5	presented	present	VERB
easat-8773	256	6	frequent	frequent	ADJ
easat-8773	256	7	errors	error	NOUN
easat-8773	256	8	,	,	PUNCT
easat-8773	256	9	especially	especially	ADV
easat-8773	256	10	among	among	ADP
easat-8773	256	11	students	student	NOUN
easat-8773	256	12	with	with	ADP
easat-8773	256	13	medium	medium	ADJ
easat-8773	256	14	mathematical	mathematical	ADJ
easat-8773	256	15	ability	ability	NOUN
easat-8773	256	16	.	.	PUNCT
easat-8773	257	1	common	common	ADJ
easat-8773	257	2	errors	error	NOUN
easat-8773	257	3	included	include	VERB
easat-8773	257	4	incorrect	incorrect	ADJ
easat-8773	257	5	operations	operation	NOUN
easat-8773	257	6	such	such	ADJ
easat-8773	257	7	as	as	ADP
easat-8773	257	8	unjustified	unjustified	ADJ
easat-8773	257	9	multiplication	multiplication	NOUN
easat-8773	257	10	or	or	CCONJ
easat-8773	257	11	flawed	flawed	ADJ
easat-8773	257	12	addition	addition	NOUN
easat-8773	257	13	,	,	PUNCT
easat-8773	257	14	suggesting	suggest	VERB
easat-8773	257	15	a	a	DET
easat-8773	257	16	lack	lack	NOUN
easat-8773	257	17	of	of	ADP
easat-8773	257	18	procedural	procedural	ADJ
easat-8773	257	19	fluency	fluency	NOUN
easat-8773	257	20	and	and	CCONJ
easat-8773	257	21	number	number	NOUN
easat-8773	257	22	sense	sense	NOUN
easat-8773	257	23	.	.	PUNCT
easat-8773	258	1	in	in	ADP
easat-8773	258	2	the	the	DET
easat-8773	258	3	interpreting	interpreting	NOUN
easat-8773	258	4	and	and	CCONJ
easat-8773	258	5	validating	validate	VERB
easat-8773	258	6	process	process	NOUN
easat-8773	258	7	,	,	PUNCT
easat-8773	258	8	even	even	ADV
easat-8773	258	9	high	high	ADJ
easat-8773	258	10	-	-	PUNCT
easat-8773	258	11	ability	ability	NOUN
easat-8773	258	12	students	student	NOUN
easat-8773	258	13	made	make	VERB
easat-8773	258	14	notable	notable	ADJ
easat-8773	258	15	errors	error	NOUN
easat-8773	258	16	.	.	PUNCT
easat-8773	259	1	while	while	SCONJ
easat-8773	259	2	they	they	PRON
easat-8773	259	3	were	be	AUX
easat-8773	259	4	often	often	ADV
easat-8773	259	5	successful	successful	ADJ
easat-8773	259	6	in	in	ADP
easat-8773	259	7	producing	produce	VERB
easat-8773	259	8	a	a	DET
easat-8773	259	9	correct	correct	ADJ
easat-8773	259	10	mathematical	mathematical	ADJ
easat-8773	259	11	solution	solution	NOUN
easat-8773	259	12	,	,	PUNCT
easat-8773	259	13	they	they	PRON
easat-8773	259	14	rarely	rarely	ADV
easat-8773	259	15	questioned	question	VERB
easat-8773	259	16	or	or	CCONJ
easat-8773	259	17	verified	verify	VERB
easat-8773	259	18	the	the	DET
easat-8773	259	19	relevance	relevance	NOUN
easat-8773	259	20	of	of	ADP
easat-8773	259	21	their	their	PRON
easat-8773	259	22	answer	answer	NOUN
easat-8773	259	23	within	within	ADP
easat-8773	259	24	the	the	DET
easat-8773	259	25	context	context	NOUN
easat-8773	259	26	of	of	ADP
easat-8773	259	27	the	the	DET
easat-8773	259	28	problem	problem	NOUN
easat-8773	259	29	[	[	X
easat-8773	259	30	11	11	NUM
easat-8773	259	31	]	]	PUNCT
easat-8773	259	32	.	.	PUNCT
easat-8773	260	1	this	this	PRON
easat-8773	260	2	highlights	highlight	VERB
easat-8773	260	3	a	a	DET
easat-8773	260	4	weakness	weakness	NOUN
easat-8773	260	5	in	in	ADP
easat-8773	260	6	metacognitive	metacognitive	ADJ
easat-8773	260	7	reflection	reflection	NOUN
easat-8773	260	8	and	and	CCONJ
easat-8773	260	9	a	a	DET
easat-8773	260	10	tendency	tendency	NOUN
easat-8773	260	11	to	to	PART
easat-8773	260	12	treat	treat	VERB
easat-8773	260	13	validation	validation	NOUN
easat-8773	260	14	as	as	ADP
easat-8773	260	15	a	a	DET
easat-8773	260	16	superficial	superficial	ADJ
easat-8773	260	17	check	check	NOUN
easat-8773	260	18	rather	rather	ADV
easat-8773	260	19	than	than	ADP
easat-8773	260	20	critical	critical	ADJ
easat-8773	260	21	evaluation	evaluation	NOUN
easat-8773	260	22	step	step	NOUN
easat-8773	260	23	[	[	X
easat-8773	260	24	24	24	NUM
easat-8773	260	25	,	,	PUNCT
easat-8773	260	26	25	25	NUM
easat-8773	260	27	]	]	PUNCT
easat-8773	260	28	.	.	PUNCT
easat-8773	261	1	these	these	PRON
easat-8773	261	2	results	result	VERB
easat-8773	261	3	multifaceted	multifaceted	ADJ
easat-8773	261	4	nature	nature	NOUN
easat-8773	261	5	of	of	ADP
easat-8773	261	6	mathematical	mathematical	ADJ
easat-8773	261	7	modeling	modeling	NOUN
easat-8773	261	8	competence	competence	NOUN
easat-8773	261	9	,	,	PUNCT
easat-8773	261	10	involves	involve	VERB
easat-8773	261	11	a	a	DET
easat-8773	261	12	constellation	constellation	NOUN
easat-8773	261	13	of	of	ADP
easat-8773	261	14	interrelated	interrelated	ADJ
easat-8773	261	15	sub	sub	NOUN
easat-8773	261	16	-	-	NOUN
easat-8773	261	17	competencies	competency	NOUN
easat-8773	261	18	that	that	PRON
easat-8773	261	19	must	must	AUX
easat-8773	261	20	be	be	AUX
easat-8773	261	21	developed	develop	VERB
easat-8773	261	22	holistically	holistically	ADV
easat-8773	261	23	throughout	throughout	ADP
easat-8773	261	24	the	the	DET
easat-8773	261	25	modeling	modeling	NOUN
easat-8773	261	26	process	process	NOUN
easat-8773	261	27	[	[	X
easat-8773	261	28	26	26	NUM
easat-8773	261	29	]	]	PUNCT
easat-8773	261	30	.	.	PUNCT
easat-8773	262	1	the	the	DET
easat-8773	262	2	persistence	persistence	NOUN
easat-8773	262	3	of	of	ADP
easat-8773	262	4	errors	error	NOUN
easat-8773	262	5	across	across	ADP
easat-8773	262	6	all	all	DET
easat-8773	262	7	stages	stage	NOUN
easat-8773	262	8	particularly	particularly	ADV
easat-8773	262	9	in	in	ADP
easat-8773	262	10	simplifying	simplifying	NOUN
easat-8773	262	11	,	,	PUNCT
easat-8773	262	12	mathematizing	mathematizing	NOUN
easat-8773	262	13	,	,	PUNCT
easat-8773	262	14	and	and	CCONJ
easat-8773	262	15	validating	validate	VERB
easat-8773	262	16	suggests	suggest	VERB
easat-8773	262	17	that	that	SCONJ
easat-8773	262	18	students	student	NOUN
easat-8773	262	19	may	may	AUX
easat-8773	262	20	lack	lack	VERB
easat-8773	262	21	not	not	PART
easat-8773	262	22	only	only	ADV
easat-8773	262	23	procedural	procedural	ADJ
easat-8773	262	24	fluency	fluency	NOUN
easat-8773	262	25	but	but	CCONJ
easat-8773	262	26	also	also	ADV
easat-8773	262	27	the	the	DET
easat-8773	262	28	broader	broad	ADJ
easat-8773	262	29	competencies	competency	NOUN
easat-8773	262	30	necessary	necessary	ADJ
easat-8773	262	31	to	to	PART
easat-8773	262	32	navigate	navigate	VERB
easat-8773	262	33	real	real	ADJ
easat-8773	262	34	-	-	PUNCT
easat-8773	262	35	world	world	NOUN
easat-8773	262	36	contexts	context	NOUN
easat-8773	262	37	mathematically	mathematically	ADV
easat-8773	262	38	.	.	PUNCT
easat-8773	263	1	moreover	moreover	ADV
easat-8773	263	2	,	,	PUNCT
easat-8773	263	3	the	the	DET
easat-8773	263	4	affective	affective	ADJ
easat-8773	263	5	and	and	CCONJ
easat-8773	263	6	metacognitive	metacognitive	ADJ
easat-8773	263	7	dimensions	dimension	NOUN
easat-8773	263	8	of	of	ADP
easat-8773	263	9	modeling	modeling	NOUN
easat-8773	263	10	appear	appear	VERB
easat-8773	263	11	to	to	PART
easat-8773	263	12	play	play	VERB
easat-8773	263	13	a	a	DET
easat-8773	263	14	critical	critical	ADJ
easat-8773	263	15	role	role	NOUN
easat-8773	263	16	in	in	ADP
easat-8773	263	17	shaping	shape	VERB
easat-8773	263	18	students	student	NOUN
easat-8773	263	19	’	'	PUNCT
easat-8773	263	20	engagement	engagement	NOUN
easat-8773	263	21	and	and	CCONJ
easat-8773	263	22	perseverance	perseverance	NOUN
easat-8773	263	23	[	[	X
easat-8773	263	24	27	27	NUM
easat-8773	263	25	]	]	PUNCT
easat-8773	263	26	.	.	PUNCT
easat-8773	264	1	their	their	PRON
easat-8773	264	2	study	study	NOUN
easat-8773	264	3	emphasizes	emphasize	VERB
easat-8773	264	4	that	that	SCONJ
easat-8773	264	5	learners	learner	NOUN
easat-8773	264	6	’	'	PUNCT
easat-8773	264	7	beliefs	belief	NOUN
easat-8773	264	8	and	and	CCONJ
easat-8773	264	9	dispositions	disposition	NOUN
easat-8773	264	10	significantly	significantly	ADV
easat-8773	264	11	influence	influence	VERB
easat-8773	264	12	how	how	SCONJ
easat-8773	264	13	they	they	PRON
easat-8773	264	14	approach	approach	VERB
easat-8773	264	15	and	and	CCONJ
easat-8773	264	16	sustain	sustain	VERB
easat-8773	264	17	modeling	modeling	NOUN
easat-8773	264	18	test	test	NOUN
easat-8773	264	19	.	.	PUNCT
easat-8773	265	1	these	these	DET
easat-8773	265	2	challenges	challenge	NOUN
easat-8773	265	3	further	far	ADV
easat-8773	265	4	resonate	resonate	VERB
easat-8773	265	5	that	that	SCONJ
easat-8773	265	6	modeling	model	VERB
easat-8773	265	7	tasks	task	NOUN
easat-8773	265	8	present	present	VERB
easat-8773	265	9	a	a	DET
easat-8773	265	10	dual	dual	ADJ
easat-8773	265	11	challenge	challenge	NOUN
easat-8773	265	12	:	:	PUNCT
easat-8773	265	13	grappling	grapple	VERB
easat-8773	265	14	with	with	ADP
easat-8773	265	15	mathematical	mathematical	ADJ
easat-8773	265	16	demands	demand	NOUN
easat-8773	265	17	while	while	SCONJ
easat-8773	265	18	simultaneously	simultaneously	ADV
easat-8773	265	19	navigating	navigate	VERB
easat-8773	265	20	the	the	DET
easat-8773	265	21	purpose	purpose	NOUN
easat-8773	265	22	and	and	CCONJ
easat-8773	265	23	intent	intent	NOUN
easat-8773	265	24	of	of	ADP
easat-8773	265	25	the	the	DET
easat-8773	265	26	activity	activity	NOUN
easat-8773	265	27	[	[	X
easat-8773	265	28	28	28	NUM
easat-8773	265	29	]	]	PUNCT
easat-8773	265	30	.	.	PUNCT
easat-8773	266	1	this	this	DET
easat-8773	266	2	tension	tension	NOUN
easat-8773	266	3	may	may	AUX
easat-8773	266	4	contribute	contribute	VERB
easat-8773	266	5	to	to	ADP
easat-8773	266	6	persistent	persistent	ADJ
easat-8773	266	7	errors	error	NOUN
easat-8773	266	8	,	,	PUNCT
easat-8773	266	9	particularly	particularly	ADV
easat-8773	266	10	when	when	SCONJ
easat-8773	266	11	students	student	NOUN
easat-8773	266	12	interpret	interpret	VERB
easat-8773	266	13	modeling	modeling	NOUN
easat-8773	266	14	solely	solely	ADV
easat-8773	266	15	as	as	ADP
easat-8773	266	16	application	application	NOUN
easat-8773	266	17	rather	rather	ADV
easat-8773	266	18	than	than	ADP
easat-8773	266	19	exploration	exploration	NOUN
easat-8773	266	20	.	.	PUNCT
easat-8773	267	1	modeling	model	VERB
easat-8773	267	2	not	not	PART
easat-8773	267	3	just	just	ADV
easat-8773	267	4	as	as	ADP
easat-8773	267	5	the	the	DET
easat-8773	267	6	application	application	NOUN
easat-8773	267	7	of	of	ADP
easat-8773	267	8	existing	exist	VERB
easat-8773	267	9	knowledge	knowledge	NOUN
easat-8773	267	10	,	,	PUNCT
easat-8773	267	11	but	but	CCONJ
easat-8773	267	12	as	as	ADP
easat-8773	267	13	a	a	DET
easat-8773	267	14	generative	generative	ADJ
easat-8773	267	15	process	process	NOUN
easat-8773	267	16	through	through	ADP
easat-8773	267	17	which	which	PRON
easat-8773	267	18	mathematical	mathematical	ADJ
easat-8773	267	19	ideas	idea	NOUN
easat-8773	267	20	are	be	AUX
easat-8773	267	21	actively	actively	ADV
easat-8773	267	22	constructed	construct	VERB
easat-8773	267	23	and	and	CCONJ
easat-8773	267	24	refined	refine	VERB
easat-8773	267	25	[	[	PUNCT
easat-8773	267	26	29	29	NUM
easat-8773	267	27	]	]	SYM
easat-8773	267	28	.	.	PUNCT
easat-8773	268	1	6	6	X
easat-8773	268	2	.	.	X
easat-8773	268	3	conclusion	conclusion	NOUN
easat-8773	268	4	the	the	DET
easat-8773	268	5	study	study	NOUN
easat-8773	268	6	shows	show	VERB
easat-8773	268	7	that	that	SCONJ
easat-8773	268	8	errors	error	NOUN
easat-8773	268	9	in	in	ADP
easat-8773	268	10	mathematical	mathematical	ADJ
easat-8773	268	11	modeling	modeling	NOUN
easat-8773	268	12	arise	arise	NOUN
easat-8773	268	13	across	across	ADP
easat-8773	268	14	multiple	multiple	ADJ
easat-8773	268	15	stages	stage	NOUN
easat-8773	268	16	:	:	PUNCT
easat-8773	269	1	understanding	understanding	NOUN
easat-8773	269	2	,	,	PUNCT
easat-8773	269	3	simplifying	simplify	VERB
easat-8773	269	4	,	,	PUNCT
easat-8773	269	5	working	work	VERB
easat-8773	269	6	mathematically	mathematically	ADV
easat-8773	269	7	,	,	PUNCT
easat-8773	269	8	interpreting	interpreting	NOUN
easat-8773	269	9	,	,	PUNCT
easat-8773	269	10	and	and	CCONJ
easat-8773	269	11	validating	validate	VERB
easat-8773	269	12	:	:	PUNCT
easat-8773	269	13	due	due	ADP
easat-8773	269	14	to	to	ADP
easat-8773	269	15	difficulties	difficulty	NOUN
easat-8773	269	16	in	in	ADP
easat-8773	269	17	conceptual	conceptual	ADJ
easat-8773	269	18	comprehension	comprehension	NOUN
easat-8773	269	19	,	,	PUNCT
easat-8773	269	20	procedural	procedural	ADJ
easat-8773	269	21	fluency	fluency	NOUN
easat-8773	269	22	,	,	PUNCT
easat-8773	269	23	and	and	CCONJ
easat-8773	269	24	translating	translate	VERB
easat-8773	269	25	real	real	ADJ
easat-8773	269	26	-	-	PUNCT
easat-8773	269	27	world	world	NOUN
easat-8773	269	28	problems	problem	NOUN
easat-8773	269	29	into	into	ADP
easat-8773	269	30	mathematical	mathematical	ADJ
easat-8773	269	31	forms	form	NOUN
easat-8773	269	32	.	.	PUNCT
easat-8773	270	1	misinterpretations	misinterpretation	NOUN
easat-8773	270	2	,	,	PUNCT
easat-8773	270	3	incorrect	incorrect	ADJ
easat-8773	270	4	assumptions	assumption	NOUN
easat-8773	270	5	,	,	PUNCT
easat-8773	270	6	computational	computational	ADJ
easat-8773	270	7	errors	error	NOUN
easat-8773	270	8	,	,	PUNCT
easat-8773	270	9	and	and	CCONJ
easat-8773	270	10	gaps	gap	NOUN
easat-8773	270	11	in	in	ADP
easat-8773	270	12	logical	logical	ADJ
easat-8773	270	13	reasoning	reasoning	NOUN
easat-8773	270	14	further	far	ADV
easat-8773	270	15	contribute	contribute	VERB
easat-8773	270	16	to	to	ADP
easat-8773	270	17	these	these	DET
easat-8773	270	18	errors	error	NOUN
easat-8773	270	19	.	.	PUNCT
easat-8773	271	1	deficiencies	deficiency	NOUN
easat-8773	271	2	in	in	ADP
easat-8773	271	3	validation	validation	NOUN
easat-8773	271	4	indicate	indicate	VERB
easat-8773	271	5	a	a	DET
easat-8773	271	6	lack	lack	NOUN
easat-8773	271	7	of	of	ADP
easat-8773	271	8	reflection	reflection	NOUN
easat-8773	271	9	and	and	CCONJ
easat-8773	271	10	critical	critical	ADJ
easat-8773	271	11	evaluation	evaluation	NOUN
easat-8773	271	12	,	,	PUNCT
easat-8773	271	13	impacting	impact	VERB
easat-8773	271	14	the	the	DET
easat-8773	271	15	accuracy	accuracy	NOUN
easat-8773	271	16	of	of	ADP
easat-8773	271	17	students	student	NOUN
easat-8773	271	18	’	'	PUNCT
easat-8773	271	19	models	model	NOUN
easat-8773	271	20	.	.	PUNCT
easat-8773	272	1	the	the	DET
easat-8773	272	2	study	study	NOUN
easat-8773	272	3	confirms	confirm	VERB
easat-8773	272	4	that	that	SCONJ
easat-8773	272	5	errors	error	NOUN
easat-8773	272	6	in	in	ADP
easat-8773	272	7	students	student	NOUN
easat-8773	272	8	’	'	PUNCT
easat-8773	272	9	mathematical	mathematical	ADJ
easat-8773	272	10	modeling	modeling	NOUN
easat-8773	272	11	processes	process	NOUN
easat-8773	272	12	occur	occur	VERB
easat-8773	272	13	at	at	ADP
easat-8773	272	14	multiple	multiple	ADJ
easat-8773	272	15	stages	stage	NOUN
easat-8773	272	16	,	,	PUNCT
easat-8773	272	17	with	with	ADP
easat-8773	272	18	distinct	distinct	ADJ
easat-8773	272	19	patterns	pattern	NOUN
easat-8773	272	20	based	base	VERB
easat-8773	272	21	on	on	ADP
easat-8773	272	22	mathematical	mathematical	ADJ
easat-8773	272	23	ability	ability	NOUN
easat-8773	272	24	levels	level	NOUN
easat-8773	272	25	.	.	PUNCT
easat-8773	273	1	moreover	moreover	ADV
easat-8773	273	2	,	,	PUNCT
easat-8773	273	3	the	the	DET
easat-8773	273	4	analysis	analysis	NOUN
easat-8773	273	5	results	result	NOUN
easat-8773	273	6	obtained	obtain	VERB
easat-8773	273	7	67	67	NUM
easat-8773	273	8	students	student	NOUN
easat-8773	273	9	who	who	PRON
easat-8773	273	10	made	make	VERB
easat-8773	273	11	errors	error	NOUN
easat-8773	273	12	.	.	PUNCT
easat-8773	274	1	67	67	NUM
easat-8773	274	2	students	student	NOUN
easat-8773	274	3	made	make	VERB
easat-8773	274	4	errors	error	NOUN
easat-8773	274	5	,	,	PUNCT
easat-8773	274	6	including	include	VERB
easat-8773	274	7	39	39	NUM
easat-8773	274	8	boys	boy	NOUN
easat-8773	274	9	and	and	CCONJ
easat-8773	274	10	28	28	NUM
easat-8773	274	11	girls	girl	NOUN
easat-8773	274	12	.	.	PUNCT
easat-8773	275	1	errors	error	NOUN
easat-8773	275	2	in	in	ADP
easat-8773	275	3	understanding	understanding	NOUN
easat-8773	275	4	(	(	PUNCT
easat-8773	275	5	31.59	31.59	NUM
easat-8773	275	6	%	%	NOUN
easat-8773	275	7	)	)	PUNCT
easat-8773	275	8	,	,	PUNCT
easat-8773	275	9	simplifying	simplify	VERB
easat-8773	275	10	(	(	PUNCT
easat-8773	275	11	37.84	37.84	NUM
easat-8773	275	12	%	%	NOUN
easat-8773	275	13	)	)	PUNCT
easat-8773	275	14	,	,	PUNCT
easat-8773	275	15	mathematizing	mathematize	VERB
easat-8773	275	16	(	(	PUNCT
easat-8773	275	17	39.58	39.58	NUM
easat-8773	275	18	%	%	NOUN
easat-8773	275	19	)	)	PUNCT
easat-8773	275	20	,	,	PUNCT
easat-8773	275	21	with	with	ADP
easat-8773	275	22	the	the	DET
easat-8773	275	23	most	most	ADV
easat-8773	275	24	common	common	ADJ
easat-8773	275	25	errors	error	NOUN
easat-8773	275	26	were	be	AUX
easat-8773	275	27	in	in	ADP
easat-8773	275	28	working	work	VERB
easat-8773	275	29	mathematically	mathematically	ADV
easat-8773	275	30	(	(	PUNCT
easat-8773	275	31	43.75	43.75	NUM
easat-8773	275	32	%	%	NOUN
easat-8773	275	33	)	)	PUNCT
easat-8773	275	34	,	,	PUNCT
easat-8773	275	35	interpreting	interpret	VERB
easat-8773	275	36	(	(	PUNCT
easat-8773	275	37	45.48	45.48	NUM
easat-8773	275	38	%	%	NOUN
easat-8773	275	39	)	)	PUNCT
easat-8773	275	40	,	,	PUNCT
easat-8773	275	41	and	and	CCONJ
easat-8773	275	42	validating	validate	VERB
easat-8773	275	43	(	(	PUNCT
easat-8773	275	44	47.56	47.56	NUM
easat-8773	275	45	%	%	NOUN
easat-8773	275	46	)	)	PUNCT
easat-8773	275	47	.	.	PUNCT
easat-8773	276	1	errors	error	NOUN
easat-8773	276	2	in	in	ADP
easat-8773	276	3	understanding	understanding	NOUN
easat-8773	276	4	were	be	AUX
easat-8773	276	5	most	most	ADV
easat-8773	276	6	frequent	frequent	ADJ
easat-8773	276	7	among	among	ADP
easat-8773	276	8	low	low	ADJ
easat-8773	276	9	-	-	PUNCT
easat-8773	276	10	ability	ability	NOUN
easat-8773	276	11	students	student	NOUN
easat-8773	276	12	,	,	PUNCT
easat-8773	276	13	suggesting	suggest	VERB
easat-8773	276	14	difficulties	difficulty	NOUN
easat-8773	276	15	in	in	ADP
easat-8773	276	16	grasping	grasp	VERB
easat-8773	276	17	problem	problem	NOUN
easat-8773	276	18	contexts	contexts	NOUN
easat-8773	276	19	.	.	PUNCT
easat-8773	277	1	medium	medium	ADJ
easat-8773	277	2	-	-	PUNCT
easat-8773	277	3	ability	ability	NOUN
easat-8773	277	4	students	student	NOUN
easat-8773	277	5	struggled	struggle	VERB
easat-8773	277	6	most	most	ADV
easat-8773	277	7	in	in	ADP
easat-8773	277	8	working	work	VERB
easat-8773	277	9	mathematically	mathematically	ADV
easat-8773	277	10	,	,	PUNCT
easat-8773	277	11	indicating	indicate	VERB
easat-8773	277	12	challenges	challenge	NOUN
easat-8773	277	13	in	in	ADP
easat-8773	277	14	applying	apply	VERB
easat-8773	277	15	formulas	formula	NOUN
easat-8773	277	16	and	and	CCONJ
easat-8773	277	17	performing	perform	VERB
easat-8773	277	18	calculations	calculation	NOUN
easat-8773	277	19	.	.	PUNCT
easat-8773	278	1	high	high	ADJ
easat-8773	278	2	-	-	PUNCT
easat-8773	278	3	ability	ability	NOUN
easat-8773	278	4	students	student	NOUN
easat-8773	278	5	showed	show	VERB
easat-8773	278	6	more	more	ADJ
easat-8773	278	7	errors	error	NOUN
easat-8773	278	8	in	in	ADP
easat-8773	278	9	interpreting	interpret	VERB
easat-8773	278	10	and	and	CCONJ
easat-8773	278	11	validating	validate	VERB
easat-8773	278	12	,	,	PUNCT
easat-8773	278	13	revealing	reveal	VERB
easat-8773	278	14	errors	error	NOUN
easat-8773	278	15	in	in	ADP
easat-8773	278	16	critically	critically	ADV
easat-8773	278	17	evaluating	evaluate	VERB
easat-8773	278	18	solutions	solution	NOUN
easat-8773	278	19	.	.	PUNCT
easat-8773	279	1	958	958	NUM
easat-8773	279	2	edelweiss	edelweiss	PROPN
easat-8773	279	3	applied	apply	VERB
easat-8773	279	4	science	science	NOUN
easat-8773	279	5	and	and	CCONJ
easat-8773	279	6	technology	technology	NOUN
easat-8773	279	7	issn	issn	PROPN
easat-8773	279	8	:	:	PUNCT
easat-8773	279	9	2576	2576	NUM
easat-8773	279	10	-	-	SYM
easat-8773	279	11	8484	8484	NUM
easat-8773	279	12	vol	vol	NOUN
easat-8773	279	13	.	.	PROPN
easat-8773	280	1	9	9	NUM
easat-8773	280	2	,	,	PUNCT
easat-8773	280	3	no	no	INTJ
easat-8773	280	4	.	.	NOUN
easat-8773	281	1	7	7	NUM
easat-8773	281	2	:	:	SYM
easat-8773	281	3	947	947	NUM
easat-8773	281	4	-	-	SYM
easat-8773	281	5	959	959	NUM
easat-8773	281	6	,	,	PUNCT
easat-8773	281	7	2025	2025	NUM
easat-8773	281	8	doi	doi	NOUN
easat-8773	281	9	:	:	PUNCT
easat-8773	281	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	281	11	©	©	PROPN
easat-8773	281	12	2025	2025	NUM
easat-8773	281	13	by	by	ADP
easat-8773	281	14	the	the	DET
easat-8773	281	15	authors	author	NOUN
easat-8773	281	16	;	;	PUNCT
easat-8773	281	17	licensee	licensee	PROPN
easat-8773	281	18	learning	learning	NOUN
easat-8773	281	19	gate	gate	NOUN
easat-8773	281	20	further	further	ADJ
easat-8773	281	21	research	research	NOUN
easat-8773	281	22	can	can	AUX
easat-8773	281	23	be	be	AUX
easat-8773	281	24	developing	develop	VERB
easat-8773	281	25	learning	learn	VERB
easat-8773	281	26	approaches	approach	NOUN
easat-8773	281	27	or	or	CCONJ
easat-8773	281	28	interventions	intervention	NOUN
easat-8773	281	29	that	that	PRON
easat-8773	281	30	are	be	AUX
easat-8773	281	31	tailored	tailor	VERB
easat-8773	281	32	to	to	ADP
easat-8773	281	33	the	the	DET
easat-8773	281	34	level	level	NOUN
easat-8773	281	35	of	of	ADP
easat-8773	281	36	student	student	NOUN
easat-8773	281	37	ability	ability	NOUN
easat-8773	281	38	.	.	PUNCT
easat-8773	282	1	low	low	ADJ
easat-8773	282	2	-	-	PUNCT
easat-8773	282	3	ability	ability	NOUN
easat-8773	282	4	students	student	NOUN
easat-8773	282	5	need	need	VERB
easat-8773	282	6	support	support	NOUN
easat-8773	282	7	in	in	ADP
easat-8773	282	8	understanding	understand	VERB
easat-8773	282	9	the	the	DET
easat-8773	282	10	context	context	NOUN
easat-8773	282	11	of	of	ADP
easat-8773	282	12	the	the	DET
easat-8773	282	13	problem	problem	NOUN
easat-8773	282	14	,	,	PUNCT
easat-8773	282	15	for	for	ADP
easat-8773	282	16	example	example	NOUN
easat-8773	282	17	through	through	ADP
easat-8773	282	18	the	the	DET
easat-8773	282	19	use	use	NOUN
easat-8773	282	20	of	of	ADP
easat-8773	282	21	scaffolding	scaffolding	NOUN
easat-8773	282	22	,	,	PUNCT
easat-8773	282	23	visualization	visualization	NOUN
easat-8773	282	24	,	,	PUNCT
easat-8773	282	25	and	and	CCONJ
easat-8773	282	26	simple	simple	ADJ
easat-8773	282	27	language	language	NOUN
easat-8773	282	28	.	.	PUNCT
easat-8773	283	1	medium	medium	ADJ
easat-8773	283	2	-	-	PUNCT
easat-8773	283	3	ability	ability	NOUN
easat-8773	283	4	students	student	NOUN
easat-8773	283	5	need	need	VERB
easat-8773	283	6	to	to	PART
easat-8773	283	7	be	be	AUX
easat-8773	283	8	strengthened	strengthen	VERB
easat-8773	283	9	in	in	ADP
easat-8773	283	10	aspects	aspect	NOUN
easat-8773	283	11	of	of	ADP
easat-8773	283	12	procedural	procedural	ADJ
easat-8773	283	13	skills	skill	NOUN
easat-8773	283	14	,	,	PUNCT
easat-8773	283	15	such	such	ADJ
easat-8773	283	16	as	as	ADP
easat-8773	283	17	practicing	practice	VERB
easat-8773	283	18	concept	concept	NOUN
easat-8773	283	19	mastery	mastery	NOUN
easat-8773	283	20	and	and	CCONJ
easat-8773	283	21	applying	apply	VERB
easat-8773	283	22	formulas	formula	NOUN
easat-8773	283	23	.	.	PUNCT
easat-8773	284	1	high	high	ADJ
easat-8773	284	2	-	-	PUNCT
easat-8773	284	3	ability	ability	NOUN
easat-8773	284	4	students	student	NOUN
easat-8773	284	5	should	should	AUX
easat-8773	284	6	be	be	AUX
easat-8773	284	7	facilitated	facilitate	VERB
easat-8773	284	8	with	with	ADP
easat-8773	284	9	reflective	reflective	ADJ
easat-8773	284	10	,	,	PUNCT
easat-8773	284	11	evaluative	evaluative	ADJ
easat-8773	284	12	,	,	PUNCT
easat-8773	284	13	and	and	CCONJ
easat-8773	284	14	open	open	ADJ
easat-8773	284	15	activities	activity	NOUN
easat-8773	284	16	towards	towards	ADP
easat-8773	284	17	multiple	multiple	ADJ
easat-8773	284	18	representations	representation	NOUN
easat-8773	284	19	to	to	PART
easat-8773	284	20	deepen	deepen	VERB
easat-8773	284	21	their	their	PRON
easat-8773	284	22	understanding	understanding	NOUN
easat-8773	284	23	of	of	ADP
easat-8773	284	24	the	the	DET
easat-8773	284	25	model	model	NOUN
easat-8773	284	26	contextually	contextually	ADV
easat-8773	284	27	.	.	PUNCT
easat-8773	285	1	there	there	PRON
easat-8773	285	2	needs	need	VERB
easat-8773	285	3	to	to	PART
easat-8773	285	4	be	be	AUX
easat-8773	285	5	scaffolding	scaffold	VERB
easat-8773	285	6	action	action	NOUN
easat-8773	285	7	at	at	ADP
easat-8773	285	8	the	the	DET
easat-8773	285	9	interpreting	interpreting	NOUN
easat-8773	285	10	and	and	CCONJ
easat-8773	285	11	validating	validate	VERB
easat-8773	285	12	process	process	NOUN
easat-8773	285	13	because	because	SCONJ
easat-8773	285	14	they	they	PRON
easat-8773	285	15	are	be	AUX
easat-8773	285	16	the	the	DET
easat-8773	285	17	highest	high	ADJ
easat-8773	285	18	errors	error	NOUN
easat-8773	285	19	made	make	VERB
easat-8773	285	20	by	by	ADP
easat-8773	285	21	students	student	NOUN
easat-8773	285	22	at	at	ADP
easat-8773	285	23	these	these	DET
easat-8773	285	24	two	two	NUM
easat-8773	285	25	final	final	ADJ
easat-8773	285	26	stages	stage	NOUN
easat-8773	285	27	,	,	PUNCT
easat-8773	285	28	it	it	PRON
easat-8773	285	29	is	be	AUX
easat-8773	285	30	important	important	ADJ
easat-8773	285	31	to	to	PART
easat-8773	285	32	include	include	VERB
easat-8773	285	33	activities	activity	NOUN
easat-8773	285	34	such	such	ADJ
easat-8773	285	35	as	as	ADP
easat-8773	285	36	group	group	NOUN
easat-8773	285	37	discussions	discussion	NOUN
easat-8773	285	38	,	,	PUNCT
easat-8773	285	39	self	self	NOUN
easat-8773	285	40	-	-	PUNCT
easat-8773	285	41	assessment	assessment	NOUN
easat-8773	285	42	,	,	PUNCT
easat-8773	285	43	and	and	CCONJ
easat-8773	285	44	peer	peer	NOUN
easat-8773	285	45	review	review	NOUN
easat-8773	285	46	to	to	PART
easat-8773	285	47	foster	foster	ADJ
easat-8773	285	48	students	student	NOUN
easat-8773	285	49	'	'	PART
easat-8773	285	50	critical	critical	ADJ
easat-8773	285	51	thinking	thinking	NOUN
easat-8773	285	52	and	and	CCONJ
easat-8773	285	53	self	self	NOUN
easat-8773	285	54	-	-	PUNCT
easat-8773	285	55	reflection	reflection	NOUN
easat-8773	285	56	skills	skill	NOUN
easat-8773	285	57	.	.	PUNCT
easat-8773	286	1	institutional	institutional	ADJ
easat-8773	286	2	review	review	PROPN
easat-8773	286	3	board	board	NOUN
easat-8773	286	4	statement	statement	NOUN
easat-8773	286	5	:	:	PUNCT
easat-8773	286	6	this	this	DET
easat-8773	286	7	study	study	NOUN
easat-8773	286	8	was	be	AUX
easat-8773	286	9	reviewed	review	VERB
easat-8773	286	10	and	and	CCONJ
easat-8773	286	11	approved	approve	VERB
easat-8773	286	12	by	by	ADP
easat-8773	286	13	the	the	DET
easat-8773	286	14	institutional	institutional	ADJ
easat-8773	286	15	review	review	PROPN
easat-8773	286	16	board	board	NOUN
easat-8773	286	17	of	of	ADP
easat-8773	286	18	universitas	universitas	PROPN
easat-8773	286	19	negeri	negeri	PROPN
easat-8773	286	20	surabaya	surabaya	PROPN
easat-8773	286	21	,	,	PUNCT
easat-8773	286	22	indonesia	indonesia	PROPN
easat-8773	286	23	,	,	PUNCT
easat-8773	286	24	under	under	ADP
easat-8773	286	25	protocol	protocol	NOUN
easat-8773	286	26	number	number	NOUN
easat-8773	286	27	(	(	PUNCT
easat-8773	286	28	letter	letter	NOUN
easat-8773	286	29	number	number	NOUN
easat-8773	286	30	:	:	PUNCT
easat-8773	286	31	b/23583	b/23583	NOUN
easat-8773	286	32	/	/	SYM
easat-8773	286	33	un38.3	un38.3	ADJ
easat-8773	286	34	/	/	SYM
easat-8773	286	35	lt.02.02/2023	lt.02.02/2023	PROPN
easat-8773	286	36	)	)	PUNCT
easat-8773	286	37	.	.	PUNCT
easat-8773	287	1	all	all	DET
easat-8773	287	2	procedures	procedure	NOUN
easat-8773	287	3	followed	follow	VERB
easat-8773	287	4	the	the	DET
easat-8773	287	5	ethical	ethical	ADJ
easat-8773	287	6	standards	standard	NOUN
easat-8773	287	7	of	of	ADP
easat-8773	287	8	the	the	DET
easat-8773	287	9	institution	institution	NOUN
easat-8773	287	10	.	.	PUNCT
easat-8773	288	1	informed	inform	VERB
easat-8773	288	2	consent	consent	NOUN
easat-8773	288	3	was	be	AUX
easat-8773	288	4	obtained	obtain	VERB
easat-8773	288	5	from	from	ADP
easat-8773	288	6	all	all	DET
easat-8773	288	7	participants	participant	NOUN
easat-8773	288	8	prior	prior	ADV
easat-8773	288	9	to	to	ADP
easat-8773	288	10	data	data	NOUN
easat-8773	288	11	collection	collection	NOUN
easat-8773	288	12	.	.	PUNCT
easat-8773	289	1	transparency	transparency	NOUN
easat-8773	289	2	:	:	PUNCT
easat-8773	289	3	the	the	DET
easat-8773	289	4	authors	author	NOUN
easat-8773	289	5	confirm	confirm	VERB
easat-8773	289	6	that	that	SCONJ
easat-8773	289	7	the	the	DET
easat-8773	289	8	manuscript	manuscript	NOUN
easat-8773	289	9	is	be	AUX
easat-8773	289	10	an	an	DET
easat-8773	289	11	honest	honest	ADJ
easat-8773	289	12	,	,	PUNCT
easat-8773	289	13	accurate	accurate	ADJ
easat-8773	289	14	,	,	PUNCT
easat-8773	289	15	and	and	CCONJ
easat-8773	289	16	transparent	transparent	ADJ
easat-8773	289	17	account	account	NOUN
easat-8773	289	18	of	of	ADP
easat-8773	289	19	the	the	DET
easat-8773	289	20	study	study	NOUN
easat-8773	289	21	;	;	PUNCT
easat-8773	289	22	that	that	SCONJ
easat-8773	289	23	no	no	DET
easat-8773	289	24	vital	vital	ADJ
easat-8773	289	25	features	feature	NOUN
easat-8773	289	26	of	of	ADP
easat-8773	289	27	the	the	DET
easat-8773	289	28	study	study	NOUN
easat-8773	289	29	have	have	AUX
easat-8773	289	30	been	be	AUX
easat-8773	289	31	omitted	omit	VERB
easat-8773	289	32	;	;	PUNCT
easat-8773	289	33	and	and	CCONJ
easat-8773	289	34	that	that	SCONJ
easat-8773	289	35	any	any	DET
easat-8773	289	36	discrepancies	discrepancy	NOUN
easat-8773	289	37	from	from	ADP
easat-8773	289	38	the	the	DET
easat-8773	289	39	study	study	NOUN
easat-8773	289	40	as	as	SCONJ
easat-8773	289	41	planned	plan	VERB
easat-8773	289	42	have	have	AUX
easat-8773	289	43	been	be	AUX
easat-8773	289	44	explained	explain	VERB
easat-8773	289	45	.	.	PUNCT
easat-8773	290	1	this	this	DET
easat-8773	290	2	study	study	NOUN
easat-8773	290	3	followed	follow	VERB
easat-8773	290	4	all	all	DET
easat-8773	290	5	ethical	ethical	ADJ
easat-8773	290	6	practices	practice	NOUN
easat-8773	290	7	during	during	ADP
easat-8773	290	8	writing	writing	NOUN
easat-8773	290	9	.	.	PUNCT
easat-8773	291	1	acknowledgments	acknowledgment	NOUN
easat-8773	291	2	:	:	PUNCT
easat-8773	292	1	i	i	PRON
easat-8773	292	2	would	would	AUX
easat-8773	292	3	like	like	VERB
easat-8773	292	4	to	to	PART
easat-8773	292	5	thank	thank	VERB
easat-8773	292	6	you	you	PRON
easat-8773	292	7	funding	fund	VERB
easat-8773	292	8	for	for	ADP
easat-8773	292	9	this	this	DET
easat-8773	292	10	study	study	NOUN
easat-8773	292	11	.	.	PUNCT
easat-8773	293	1	this	this	DET
easat-8773	293	2	study	study	NOUN
easat-8773	293	3	was	be	AUX
easat-8773	293	4	supported	support	VERB
easat-8773	293	5	by	by	ADP
easat-8773	293	6	santo	santo	PROPN
easat-8773	293	7	agustinus	agustinus	PROPN
easat-8773	293	8	hippo	hippo	PROPN
easat-8773	293	9	university	university	PROPN
easat-8773	293	10	catholic	catholic	PROPN
easat-8773	293	11	in	in	ADP
easat-8773	293	12	west	west	PROPN
easat-8773	293	13	kalimantan	kalimantan	PROPN
easat-8773	293	14	.	.	PUNCT
easat-8773	294	1	the	the	DET
easat-8773	294	2	first	first	ADJ
easat-8773	294	3	authors	author	NOUN
easat-8773	294	4	would	would	AUX
easat-8773	294	5	like	like	VERB
easat-8773	294	6	to	to	PART
easat-8773	294	7	extend	extend	VERB
easat-8773	294	8	their	their	PRON
easat-8773	294	9	gratitude	gratitude	NOUN
easat-8773	294	10	to	to	ADP
easat-8773	294	11	the	the	DET
easat-8773	294	12	mayor	mayor	NOUN
easat-8773	294	13	of	of	ADP
easat-8773	294	14	landak	landak	PROPN
easat-8773	294	15	regency	regency	PROPN
easat-8773	294	16	,	,	PUNCT
easat-8773	294	17	the	the	DET
easat-8773	294	18	principals	principal	NOUN
easat-8773	294	19	of	of	ADP
easat-8773	294	20	smp	smp	PROPN
easat-8773	294	21	st	st	PROPN
easat-8773	294	22	.	.	PROPN
easat-8773	294	23	benediktus	benediktus	PROPN
easat-8773	294	24	,	,	PUNCT
easat-8773	294	25	and	and	CCONJ
easat-8773	294	26	all	all	DET
easat-8773	294	27	the	the	DET
easat-8773	294	28	teachers	teacher	NOUN
easat-8773	294	29	and	and	CCONJ
easat-8773	294	30	students	student	NOUN
easat-8773	294	31	for	for	ADP
easat-8773	294	32	their	their	PRON
easat-8773	294	33	participation	participation	NOUN
easat-8773	294	34	in	in	ADP
easat-8773	294	35	this	this	DET
easat-8773	294	36	study	study	NOUN
easat-8773	294	37	.	.	PUNCT
easat-8773	295	1	copyright	copyright	NOUN
easat-8773	295	2	:	:	PUNCT
easat-8773	295	3	©	©	PROPN
easat-8773	295	4	2025	2025	NUM
easat-8773	295	5	by	by	ADP
easat-8773	295	6	the	the	DET
easat-8773	295	7	authors	author	NOUN
easat-8773	295	8	.	.	PUNCT
easat-8773	296	1	this	this	DET
easat-8773	296	2	open	open	ADJ
easat-8773	296	3	-	-	PUNCT
easat-8773	296	4	access	access	NOUN
easat-8773	296	5	article	article	NOUN
easat-8773	296	6	is	be	AUX
easat-8773	296	7	distributed	distribute	VERB
easat-8773	296	8	under	under	ADP
easat-8773	296	9	the	the	DET
easat-8773	296	10	terms	term	NOUN
easat-8773	296	11	and	and	CCONJ
easat-8773	296	12	conditions	condition	NOUN
easat-8773	296	13	of	of	ADP
easat-8773	296	14	the	the	DET
easat-8773	296	15	creative	creative	ADJ
easat-8773	296	16	commons	common	NOUN
easat-8773	296	17	attribution	attribution	NOUN
easat-8773	296	18	(	(	PUNCT
easat-8773	296	19	cc	cc	NOUN
easat-8773	296	20	by	by	ADP
easat-8773	296	21	)	)	PUNCT
easat-8773	296	22	license	license	NOUN
easat-8773	296	23	(	(	PUNCT
easat-8773	296	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-8773	296	25	)	)	PUNCT
easat-8773	296	26	.	.	PUNCT
easat-8773	297	1	references	reference	NOUN
easat-8773	297	2	[	[	X
easat-8773	297	3	1	1	NUM
easat-8773	297	4	]	]	X
easat-8773	297	5	g.	g.	PROPN
easat-8773	297	6	kaiser	kaiser	PROPN
easat-8773	297	7	,	,	PUNCT
easat-8773	297	8	"	"	PUNCT
easat-8773	297	9	modelling	modelling	NOUN
easat-8773	297	10	and	and	CCONJ
easat-8773	297	11	modelling	model	VERB
easat-8773	297	12	competencies	competency	NOUN
easat-8773	297	13	in	in	ADP
easat-8773	297	14	school	school	NOUN
easat-8773	297	15	.	.	PUNCT
easat-8773	298	1	in	in	ADP
easat-8773	298	2	c.	c.	PROPN
easat-8773	298	3	haines	haine	NOUN
easat-8773	298	4	,	,	PUNCT
easat-8773	298	5	p.	p.	PROPN
easat-8773	298	6	galbraith	galbraith	PROPN
easat-8773	298	7	,	,	PUNCT
easat-8773	298	8	w.	w.	PROPN
easat-8773	298	9	blum	blum	PROPN
easat-8773	298	10	,	,	PUNCT
easat-8773	298	11	&	&	CCONJ
easat-8773	298	12	s.	s.	PROPN
easat-8773	298	13	khan	khan	PROPN
easat-8773	298	14	(	(	PUNCT
easat-8773	298	15	eds	ed	NOUN
easat-8773	298	16	.	.	PUNCT
easat-8773	298	17	)	)	PUNCT
easat-8773	298	18	,	,	PUNCT
easat-8773	298	19	mathematical	mathematical	ADJ
easat-8773	298	20	modelling	modelling	NOUN
easat-8773	298	21	(	(	PUNCT
easat-8773	298	22	ictma	ictma	NOUN
easat-8773	298	23	12	12	NUM
easat-8773	298	24	):	):	PUNCT
easat-8773	298	25	education	education	NOUN
easat-8773	298	26	,	,	PUNCT
easat-8773	298	27	engineering	engineering	NOUN
easat-8773	298	28	and	and	CCONJ
easat-8773	298	29	economics	economic	NOUN
easat-8773	298	30	,	,	PUNCT
easat-8773	298	31	"	"	PUNCT
easat-8773	298	32	in	in	ADP
easat-8773	298	33	proceedings	proceeding	NOUN
easat-8773	298	34	from	from	ADP
easat-8773	298	35	the	the	DET
easat-8773	298	36	twelfth	twelfth	ADJ
easat-8773	298	37	international	international	ADJ
easat-8773	298	38	conference	conference	NOUN
easat-8773	298	39	on	on	ADP
easat-8773	298	40	the	the	DET
easat-8773	298	41	teaching	teaching	NOUN
easat-8773	298	42	of	of	ADP
easat-8773	298	43	mathematical	mathematical	ADJ
easat-8773	298	44	modelling	modelling	NOUN
easat-8773	298	45	and	and	CCONJ
easat-8773	298	46	applications	application	NOUN
easat-8773	298	47	,	,	PUNCT
easat-8773	298	48	110–119	110–119	NUM
easat-8773	298	49	.	.	NUM
easat-8773	298	50	,	,	PUNCT
easat-8773	298	51	2007	2007	NUM
easat-8773	298	52	.	.	PUNCT
easat-8773	299	1	[	[	X
easat-8773	299	2	2	2	X
easat-8773	299	3	]	]	PUNCT
easat-8773	299	4	j.	j.	PROPN
easat-8773	299	5	m.	m.	PROPN
easat-8773	299	6	suh	suh	PROPN
easat-8773	299	7	and	and	CCONJ
easat-8773	299	8	p.	p.	PROPN
easat-8773	299	9	seshaiyer	seshaiyer	PROPN
easat-8773	299	10	,	,	PUNCT
easat-8773	299	11	modeling	model	VERB
easat-8773	299	12	mathematical	mathematical	ADJ
easat-8773	299	13	ideas	idea	NOUN
easat-8773	299	14	,	,	PUNCT
easat-8773	299	15	developing	develop	VERB
easat-8773	299	16	strategic	strategic	ADJ
easat-8773	299	17	competence	competence	NOUN
easat-8773	299	18	in	in	ADP
easat-8773	299	19	elementary	elementary	ADJ
easat-8773	299	20	and	and	CCONJ
easat-8773	299	21	middle	middle	ADJ
easat-8773	299	22	school	school	NOUN
easat-8773	299	23	.	.	PUNCT
easat-8773	300	1	lanham	lanham	PROPN
easat-8773	300	2	,	,	PUNCT
easat-8773	300	3	md	md	PROPN
easat-8773	300	4	:	:	PUNCT
easat-8773	300	5	rowman	rowman	PROPN
easat-8773	300	6	&	&	CCONJ
easat-8773	300	7	littlefield	littlefield	PROPN
easat-8773	300	8	,	,	PUNCT
easat-8773	300	9	2017	2017	NUM
easat-8773	300	10	.	.	PUNCT
easat-8773	301	1	[	[	X
easat-8773	301	2	3	3	X
easat-8773	301	3	]	]	X
easat-8773	301	4	d.	d.	NOUN
easat-8773	301	5	milinković	milinković	PROPN
easat-8773	301	6	and	and	CCONJ
easat-8773	301	7	m.	m.	NOUN
easat-8773	301	8	ćurčić	ćurčić	NOUN
easat-8773	301	9	,	,	PUNCT
easat-8773	301	10	"	"	PUNCT
easat-8773	301	11	mathematical	mathematical	ADJ
easat-8773	301	12	modeling	modeling	NOUN
easat-8773	301	13	of	of	ADP
easat-8773	301	14	natural	natural	ADJ
easat-8773	301	15	and	and	CCONJ
easat-8773	301	16	social	social	ADJ
easat-8773	301	17	context	context	NOUN
easat-8773	301	18	at	at	ADP
easat-8773	301	19	preschool	preschool	ADJ
easat-8773	301	20	level	level	NOUN
easat-8773	301	21	of	of	ADP
easat-8773	301	22	education	education	NOUN
easat-8773	301	23	[	[	X
easat-8773	301	24	matematičko	matematičko	NOUN
easat-8773	301	25	modeliranje	modeliranje	NOUN
easat-8773	301	26	prirodnog	prirodnog	NOUN
easat-8773	302	1	i	i	PRON
easat-8773	302	2	društvenog	društvenog	VERB
easat-8773	302	3	konteksta	konteksta	PROPN
easat-8773	302	4	u	u	PROPN
easat-8773	302	5	predškolsko	predškolsko	ADV
easat-8773	302	6	doba	doba	PROPN
easat-8773	302	7	]	]	PUNCT
easat-8773	302	8	,	,	PUNCT
easat-8773	302	9	"	"	PUNCT
easat-8773	302	10	croatian	croatian	ADJ
easat-8773	302	11	journal	journal	NOUN
easat-8773	302	12	of	of	ADP
easat-8773	302	13	education	education	NOUN
easat-8773	302	14	,	,	PUNCT
easat-8773	302	15	vol	vol	NOUN
easat-8773	302	16	.	.	PROPN
easat-8773	302	17	20	20	NUM
easat-8773	302	18	,	,	PUNCT
easat-8773	302	19	pp	pp	ADJ
easat-8773	302	20	.	.	PUNCT
easat-8773	303	1	157	157	NUM
easat-8773	303	2	-	-	SYM
easat-8773	303	3	174	174	NUM
easat-8773	303	4	,	,	PUNCT
easat-8773	303	5	2018	2018	NUM
easat-8773	303	6	.	.	PUNCT
easat-8773	304	1	https://doi.org/10.15516/cje.v20i0.3036	https://doi.org/10.15516/cje.v20i0.3036	X
easat-8773	305	1	[	[	X
easat-8773	305	2	4	4	X
easat-8773	305	3	]	]	X
easat-8773	305	4	g.	g.	PROPN
easat-8773	305	5	a.	a.	PROPN
easat-8773	305	6	stillman	stillman	PROPN
easat-8773	305	7	,	,	PUNCT
easat-8773	305	8	"	"	PUNCT
easat-8773	305	9	applications	application	NOUN
easat-8773	305	10	and	and	CCONJ
easat-8773	305	11	modelling	model	VERB
easat-8773	305	12	research	research	NOUN
easat-8773	305	13	in	in	ADP
easat-8773	305	14	secondary	secondary	ADJ
easat-8773	305	15	classrooms	classroom	NOUN
easat-8773	305	16	:	:	PUNCT
easat-8773	305	17	what	what	PRON
easat-8773	305	18	have	have	AUX
easat-8773	305	19	we	we	PRON
easat-8773	305	20	learnt	learn	VERB
easat-8773	305	21	?	?	PUNCT
easat-8773	305	22	,	,	PUNCT
easat-8773	305	23	"	"	PUNCT
easat-8773	305	24	in	in	ADP
easat-8773	305	25	selected	select	VERB
easat-8773	305	26	regular	regular	ADJ
easat-8773	305	27	lectures	lecture	NOUN
easat-8773	305	28	from	from	ADP
easat-8773	305	29	the	the	DET
easat-8773	305	30	12th	12th	ADJ
easat-8773	305	31	international	international	ADJ
easat-8773	305	32	congress	congress	PROPN
easat-8773	305	33	on	on	ADP
easat-8773	305	34	mathematical	mathematical	ADJ
easat-8773	305	35	education	education	NOUN
easat-8773	305	36	,	,	PUNCT
easat-8773	305	37	2015	2015	NUM
easat-8773	305	38	:	:	PUNCT
easat-8773	305	39	springer	springer	NOUN
easat-8773	305	40	,	,	PUNCT
easat-8773	305	41	pp	pp	ADP
easat-8773	305	42	.	.	PUNCT
easat-8773	306	1	791	791	NUM
easat-8773	306	2	-	-	SYM
easat-8773	306	3	805	805	NUM
easat-8773	306	4	.	.	PUNCT
easat-8773	307	1	[	[	X
easat-8773	307	2	5	5	X
easat-8773	307	3	]	]	PUNCT
easat-8773	307	4	w.	w.	PROPN
easat-8773	307	5	blum	blum	PROPN
easat-8773	307	6	and	and	CCONJ
easat-8773	307	7	d.	d.	PROPN
easat-8773	307	8	leiss	leiss	PROPN
easat-8773	307	9	,	,	PUNCT
easat-8773	307	10	"	"	PUNCT
easat-8773	307	11	how	how	SCONJ
easat-8773	307	12	do	do	AUX
easat-8773	307	13	students	student	NOUN
easat-8773	307	14	and	and	CCONJ
easat-8773	307	15	teachers	teacher	NOUN
easat-8773	307	16	deal	deal	VERB
easat-8773	307	17	with	with	ADP
easat-8773	307	18	modelling	modelling	NOUN
easat-8773	307	19	problems	problem	NOUN
easat-8773	307	20	?	?	PUNCT
easat-8773	308	1	in	in	ADP
easat-8773	308	2	c.	c.	PROPN
easat-8773	308	3	haines	haine	NOUN
easat-8773	308	4	,	,	PUNCT
easat-8773	308	5	p.	p.	PROPN
easat-8773	308	6	galbraith	galbraith	PROPN
easat-8773	308	7	,	,	PUNCT
easat-8773	308	8	w.	w.	PROPN
easat-8773	308	9	blum	blum	PROPN
easat-8773	308	10	,	,	PUNCT
easat-8773	308	11	&	&	CCONJ
easat-8773	308	12	s.	s.	PROPN
easat-8773	308	13	khan	khan	PROPN
easat-8773	308	14	(	(	PUNCT
easat-8773	308	15	eds	ed	NOUN
easat-8773	308	16	.	.	PUNCT
easat-8773	308	17	)	)	PUNCT
easat-8773	308	18	,	,	PUNCT
easat-8773	308	19	mathematical	mathematical	ADJ
easat-8773	308	20	modelling	modelling	NOUN
easat-8773	308	21	(	(	PUNCT
easat-8773	308	22	ictma	ictma	NOUN
easat-8773	308	23	12	12	NUM
easat-8773	308	24	):	):	PUNCT
easat-8773	308	25	education	education	NOUN
easat-8773	308	26	,	,	PUNCT
easat-8773	308	27	engineering	engineering	NOUN
easat-8773	308	28	and	and	CCONJ
easat-8773	308	29	economics	economic	NOUN
easat-8773	308	30	,	,	PUNCT
easat-8773	308	31	"	"	PUNCT
easat-8773	308	32	in	in	ADP
easat-8773	308	33	proceedings	proceeding	NOUN
easat-8773	308	34	from	from	ADP
easat-8773	308	35	the	the	DET
easat-8773	308	36	twelfth	twelfth	ADJ
easat-8773	308	37	international	international	ADJ
easat-8773	308	38	conference	conference	NOUN
easat-8773	308	39	on	on	ADP
easat-8773	308	40	the	the	DET
easat-8773	308	41	teaching	teaching	NOUN
easat-8773	308	42	of	of	ADP
easat-8773	308	43	mathematical	mathematical	ADJ
easat-8773	308	44	modelling	modelling	NOUN
easat-8773	308	45	and	and	CCONJ
easat-8773	308	46	applications	application	NOUN
easat-8773	308	47	,	,	PUNCT
easat-8773	308	48	222–231	222–231	NUM
easat-8773	308	49	,	,	PUNCT
easat-8773	308	50	2007	2007	NUM
easat-8773	308	51	.	.	PUNCT
easat-8773	309	1	[	[	X
easat-8773	309	2	6	6	NUM
easat-8773	309	3	]	]	X
easat-8773	309	4	g.	g.	PROPN
easat-8773	309	5	greefrath	greefrath	PROPN
easat-8773	309	6	and	and	CCONJ
easat-8773	309	7	k.	k.	PROPN
easat-8773	309	8	vorhölter	vorhölter	PROPN
easat-8773	309	9	,	,	PUNCT
easat-8773	309	10	teaching	teaching	NOUN
easat-8773	309	11	and	and	CCONJ
easat-8773	309	12	learning	learn	VERB
easat-8773	309	13	mathematical	mathematical	ADJ
easat-8773	309	14	modelling	modelling	NOUN
easat-8773	309	15	:	:	PUNCT
easat-8773	309	16	approaches	approach	NOUN
easat-8773	309	17	and	and	CCONJ
easat-8773	309	18	developments	development	NOUN
easat-8773	309	19	from	from	ADP
easat-8773	309	20	german	german	ADJ
easat-8773	309	21	speaking	speak	VERB
easat-8773	309	22	countries	country	NOUN
easat-8773	309	23	.	.	PUNCT
easat-8773	310	1	cham	cham	PROPN
easat-8773	310	2	,	,	PUNCT
easat-8773	310	3	switzerland	switzerland	PROPN
easat-8773	310	4	:	:	PUNCT
easat-8773	310	5	springer	springer	NOUN
easat-8773	310	6	,	,	PUNCT
easat-8773	310	7	2016	2016	NUM
easat-8773	310	8	.	.	PUNCT
easat-8773	311	1	[	[	X
easat-8773	311	2	7	7	X
easat-8773	311	3	]	]	X
easat-8773	311	4	h.	h.	PROPN
easat-8773	311	5	m.	m.	NOUN
easat-8773	311	6	doerr	doerr	PROPN
easat-8773	311	7	and	and	CCONJ
easat-8773	311	8	l.	l.	PROPN
easat-8773	311	9	d.	d.	PROPN
easat-8773	311	10	english	english	PROPN
easat-8773	311	11	,	,	PUNCT
easat-8773	311	12	"	"	PUNCT
easat-8773	311	13	a	a	DET
easat-8773	311	14	modeling	modeling	NOUN
easat-8773	311	15	perspective	perspective	NOUN
easat-8773	311	16	on	on	ADP
easat-8773	311	17	students	student	NOUN
easat-8773	311	18	'	'	PART
easat-8773	311	19	mathematical	mathematical	ADJ
easat-8773	311	20	reasoning	reasoning	NOUN
easat-8773	311	21	about	about	ADP
easat-8773	311	22	data	datum	NOUN
easat-8773	311	23	,	,	PUNCT
easat-8773	311	24	"	"	PUNCT
easat-8773	311	25	journal	journal	NOUN
easat-8773	311	26	for	for	ADP
easat-8773	311	27	research	research	NOUN
easat-8773	311	28	in	in	ADP
easat-8773	311	29	mathematics	mathematics	PROPN
easat-8773	311	30	education	education	NOUN
easat-8773	311	31	,	,	PUNCT
easat-8773	311	32	vol	vol	NOUN
easat-8773	311	33	.	.	PROPN
easat-8773	311	34	34	34	NUM
easat-8773	311	35	,	,	PUNCT
easat-8773	311	36	no	no	INTJ
easat-8773	311	37	.	.	NOUN
easat-8773	311	38	2	2	NUM
easat-8773	311	39	,	,	PUNCT
easat-8773	311	40	pp	pp	ADJ
easat-8773	311	41	.	.	PUNCT
easat-8773	312	1	110	110	NUM
easat-8773	312	2	-	-	SYM
easat-8773	312	3	136	136	NUM
easat-8773	312	4	,	,	PUNCT
easat-8773	312	5	2003	2003	NUM
easat-8773	312	6	.	.	PUNCT
easat-8773	313	1	https://doi.org/10.2307/30034902	https://doi.org/10.2307/30034902	VERB
easat-8773	314	1	[	[	X
easat-8773	314	2	8	8	NUM
easat-8773	314	3	]	]	PUNCT
easat-8773	314	4	k.	k.	NOUN
easat-8773	314	5	maaß	maaß	PROPN
easat-8773	314	6	,	,	PUNCT
easat-8773	314	7	"	"	PUNCT
easat-8773	314	8	what	what	PRON
easat-8773	314	9	are	be	AUX
easat-8773	314	10	modelling	model	VERB
easat-8773	314	11	competencies	competency	NOUN
easat-8773	314	12	?	?	PUNCT
easat-8773	314	13	,	,	PUNCT
easat-8773	314	14	"	"	PUNCT
easat-8773	314	15	zdm	zdm	NOUN
easat-8773	314	16	,	,	PUNCT
easat-8773	314	17	vol	vol	NOUN
easat-8773	314	18	.	.	PROPN
easat-8773	315	1	38	38	NUM
easat-8773	315	2	,	,	PUNCT
easat-8773	315	3	pp	pp	ADJ
easat-8773	315	4	.	.	PUNCT
easat-8773	316	1	113	113	NUM
easat-8773	316	2	-	-	SYM
easat-8773	316	3	142	142	NUM
easat-8773	316	4	,	,	PUNCT
easat-8773	316	5	2006	2006	NUM
easat-8773	316	6	.	.	PUNCT
easat-8773	317	1	[	[	X
easat-8773	317	2	9	9	NUM
easat-8773	317	3	]	]	PUNCT
easat-8773	317	4	p.	p.	NOUN
easat-8773	317	5	galbraith	galbraith	PROPN
easat-8773	317	6	and	and	CCONJ
easat-8773	317	7	g.	g.	PROPN
easat-8773	317	8	stillman	stillman	PROPN
easat-8773	317	9	,	,	PUNCT
easat-8773	317	10	"	"	PUNCT
easat-8773	317	11	a	a	DET
easat-8773	317	12	framework	framework	NOUN
easat-8773	317	13	for	for	ADP
easat-8773	317	14	identifying	identify	VERB
easat-8773	317	15	student	student	NOUN
easat-8773	317	16	blockages	blockage	NOUN
easat-8773	317	17	during	during	ADP
easat-8773	317	18	transitions	transition	NOUN
easat-8773	317	19	in	in	ADP
easat-8773	317	20	the	the	DET
easat-8773	317	21	modelling	modelling	NOUN
easat-8773	317	22	process	process	NOUN
easat-8773	317	23	,	,	PUNCT
easat-8773	317	24	"	"	PUNCT
easat-8773	317	25	zdm	zdm	NOUN
easat-8773	317	26	,	,	PUNCT
easat-8773	317	27	vol	vol	NOUN
easat-8773	317	28	.	.	PROPN
easat-8773	318	1	38	38	NUM
easat-8773	318	2	,	,	PUNCT
easat-8773	318	3	pp	pp	ADJ
easat-8773	318	4	.	.	PUNCT
easat-8773	319	1	143	143	NUM
easat-8773	319	2	-	-	SYM
easat-8773	319	3	162	162	NUM
easat-8773	319	4	,	,	PUNCT
easat-8773	319	5	2006	2006	NUM
easat-8773	319	6	.	.	PUNCT
easat-8773	320	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-8773	321	1	https://doi.org/10.15516/cje.v20i0.3036	https://doi.org/10.15516/cje.v20i0.3036	PROPN
easat-8773	321	2	https://doi.org/10.2307/30034902	https://doi.org/10.2307/30034902	VERB
easat-8773	321	3	959	959	NUM
easat-8773	321	4	edelweiss	edelweiss	PROPN
easat-8773	321	5	applied	apply	VERB
easat-8773	321	6	science	science	NOUN
easat-8773	321	7	and	and	CCONJ
easat-8773	321	8	technology	technology	NOUN
easat-8773	321	9	issn	issn	PROPN
easat-8773	321	10	:	:	PUNCT
easat-8773	321	11	2576	2576	NUM
easat-8773	321	12	-	-	SYM
easat-8773	321	13	8484	8484	NUM
easat-8773	321	14	vol	vol	NOUN
easat-8773	321	15	.	.	PROPN
easat-8773	322	1	9	9	NUM
easat-8773	322	2	,	,	PUNCT
easat-8773	322	3	no	no	INTJ
easat-8773	322	4	.	.	NOUN
easat-8773	323	1	7	7	NUM
easat-8773	323	2	:	:	SYM
easat-8773	323	3	947	947	NUM
easat-8773	323	4	-	-	SYM
easat-8773	323	5	959	959	NUM
easat-8773	323	6	,	,	PUNCT
easat-8773	323	7	2025	2025	NUM
easat-8773	323	8	doi	doi	NOUN
easat-8773	323	9	:	:	PUNCT
easat-8773	323	10	10.55214/25768484.v9i7.8773	10.55214/25768484.v9i7.8773	NUM
easat-8773	323	11	©	©	PROPN
easat-8773	323	12	2025	2025	NUM
easat-8773	323	13	by	by	ADP
easat-8773	323	14	the	the	DET
easat-8773	323	15	authors	author	NOUN
easat-8773	323	16	;	;	PUNCT
easat-8773	323	17	licensee	licensee	PROPN
easat-8773	323	18	learning	learning	NOUN
easat-8773	323	19	gate	gate	NOUN
easat-8773	324	1	[	[	X
easat-8773	324	2	10	10	NUM
easat-8773	324	3	]	]	X
easat-8773	324	4	j.	j.	PROPN
easat-8773	324	5	plath	plath	PROPN
easat-8773	324	6	and	and	CCONJ
easat-8773	324	7	d.	d.	PROPN
easat-8773	324	8	leiss	leiss	PROPN
easat-8773	324	9	,	,	PUNCT
easat-8773	324	10	"	"	PUNCT
easat-8773	324	11	the	the	DET
easat-8773	324	12	impact	impact	NOUN
easat-8773	324	13	of	of	ADP
easat-8773	324	14	linguistic	linguistic	ADJ
easat-8773	324	15	complexity	complexity	NOUN
easat-8773	324	16	on	on	ADP
easat-8773	324	17	the	the	DET
easat-8773	324	18	solution	solution	NOUN
easat-8773	324	19	of	of	ADP
easat-8773	324	20	mathematical	mathematical	ADJ
easat-8773	324	21	modelling	modelling	NOUN
easat-8773	324	22	tasks	task	NOUN
easat-8773	324	23	,	,	PUNCT
easat-8773	324	24	"	"	PUNCT
easat-8773	324	25	zdm	zdm	NOUN
easat-8773	324	26	,	,	PUNCT
easat-8773	324	27	vol	vol	NOUN
easat-8773	324	28	.	.	PROPN
easat-8773	324	29	50	50	NUM
easat-8773	324	30	,	,	PUNCT
easat-8773	324	31	pp	pp	ADJ
easat-8773	324	32	.	.	PUNCT
easat-8773	324	33	159	159	NUM
easat-8773	324	34	-	-	SYM
easat-8773	324	35	171	171	NUM
easat-8773	324	36	,	,	PUNCT
easat-8773	324	37	2018	2018	NUM
easat-8773	324	38	.	.	PUNCT
easat-8773	325	1	[	[	X
easat-8773	325	2	11	11	NUM
easat-8773	325	3	]	]	X
easat-8773	325	4	w.	w.	PROPN
easat-8773	325	5	blum	blum	PROPN
easat-8773	325	6	,	,	PUNCT
easat-8773	325	7	"	"	PUNCT
easat-8773	325	8	quality	quality	NOUN
easat-8773	325	9	teaching	teaching	NOUN
easat-8773	325	10	of	of	ADP
easat-8773	325	11	mathematical	mathematical	ADJ
easat-8773	325	12	modelling	modelling	NOUN
easat-8773	325	13	:	:	PUNCT
easat-8773	325	14	what	what	PRON
easat-8773	325	15	do	do	AUX
easat-8773	325	16	we	we	PRON
easat-8773	325	17	know	know	VERB
easat-8773	325	18	,	,	PUNCT
easat-8773	325	19	what	what	PRON
easat-8773	325	20	can	can	AUX
easat-8773	325	21	we	we	PRON
easat-8773	325	22	do	do	VERB
easat-8773	325	23	?	?	PUNCT
easat-8773	326	1	in	in	ADP
easat-8773	326	2	s.	s.	PROPN
easat-8773	326	3	j.	j.	PROPN
easat-8773	326	4	cho	cho	PROPN
easat-8773	326	5	(	(	PUNCT
easat-8773	326	6	ed	ed	NOUN
easat-8773	326	7	.	.	PUNCT
easat-8773	326	8	)	)	PUNCT
easat-8773	326	9	,	,	PUNCT
easat-8773	326	10	"	"	PUNCT
easat-8773	326	11	in	in	ADP
easat-8773	326	12	the	the	DET
easat-8773	326	13	proceedings	proceeding	NOUN
easat-8773	326	14	of	of	ADP
easat-8773	326	15	the	the	DET
easat-8773	326	16	12th	12th	ADJ
easat-8773	326	17	international	international	ADJ
easat-8773	326	18	congress	congress	PROPN
easat-8773	326	19	on	on	ADP
easat-8773	326	20	mathematical	mathematical	ADJ
easat-8773	326	21	education	education	NOUN
easat-8773	326	22	,	,	PUNCT
easat-8773	326	23	73–96	73–96	NUM
easat-8773	326	24	,	,	PUNCT
easat-8773	326	25	2015	2015	NUM
easat-8773	326	26	.	.	PUNCT
easat-8773	327	1	[	[	X
easat-8773	327	2	12	12	NUM
easat-8773	327	3	]	]	PUNCT
easat-8773	327	4	m.	m.	NOUN
easat-8773	327	5	cevikbas	cevikbas	NOUN
easat-8773	327	6	,	,	PUNCT
easat-8773	327	7	g.	g.	PROPN
easat-8773	327	8	kaiser	kaiser	PROPN
easat-8773	327	9	,	,	PUNCT
easat-8773	327	10	and	and	CCONJ
easat-8773	327	11	s.	s.	PROPN
easat-8773	327	12	schukajlow	schukajlow	PROPN
easat-8773	327	13	,	,	PUNCT
easat-8773	327	14	"	"	PUNCT
easat-8773	327	15	a	a	DET
easat-8773	327	16	systematic	systematic	ADJ
easat-8773	327	17	literature	literature	NOUN
easat-8773	327	18	review	review	NOUN
easat-8773	327	19	of	of	ADP
easat-8773	327	20	the	the	DET
easat-8773	327	21	current	current	ADJ
easat-8773	327	22	discussion	discussion	NOUN
easat-8773	327	23	on	on	ADP
easat-8773	327	24	mathematical	mathematical	ADJ
easat-8773	327	25	modelling	modelling	NOUN
easat-8773	327	26	competencies	competency	NOUN
easat-8773	327	27	:	:	PUNCT
easat-8773	327	28	state	state	NOUN
easat-8773	327	29	-	-	PUNCT
easat-8773	327	30	of	of	ADP
easat-8773	327	31	-	-	PUNCT
easat-8773	327	32	the	the	DET
easat-8773	327	33	-	-	PUNCT
easat-8773	327	34	art	art	NOUN
easat-8773	327	35	developments	development	NOUN
easat-8773	327	36	in	in	ADP
easat-8773	327	37	conceptualizing	conceptualize	VERB
easat-8773	327	38	,	,	PUNCT
easat-8773	327	39	measuring	measure	VERB
easat-8773	327	40	,	,	PUNCT
easat-8773	327	41	and	and	CCONJ
easat-8773	327	42	fostering	foster	VERB
easat-8773	327	43	,	,	PUNCT
easat-8773	327	44	"	"	PUNCT
easat-8773	327	45	educational	educational	ADJ
easat-8773	327	46	studies	study	NOUN
easat-8773	327	47	in	in	ADP
easat-8773	327	48	mathematics	mathematic	NOUN
easat-8773	327	49	,	,	PUNCT
easat-8773	327	50	vol	vol	NOUN
easat-8773	327	51	.	.	PROPN
easat-8773	327	52	109	109	NUM
easat-8773	327	53	,	,	PUNCT
easat-8773	327	54	no	no	INTJ
easat-8773	327	55	.	.	NOUN
easat-8773	327	56	2	2	NUM
easat-8773	327	57	,	,	PUNCT
easat-8773	327	58	pp	pp	ADJ
easat-8773	327	59	.	.	PUNCT
easat-8773	327	60	205	205	NUM
easat-8773	327	61	-	-	SYM
easat-8773	327	62	236	236	NUM
easat-8773	327	63	,	,	PUNCT
easat-8773	327	64	2022	2022	NUM
easat-8773	327	65	.	.	PUNCT
easat-8773	327	66	https://doi.org/10.1007/s10649-021-10104-6	https://doi.org/10.1007/s10649-021-10104-6	PROPN
easat-8773	328	1	[	[	X
easat-8773	328	2	13	13	NUM
easat-8773	328	3	]	]	PUNCT
easat-8773	328	4	j.	j.	PROPN
easat-8773	328	5	c.	c.	PROPN
easat-8773	328	6	barbosa	barbosa	PROPN
easat-8773	328	7	,	,	PUNCT
easat-8773	328	8	"	"	PUNCT
easat-8773	328	9	mathematical	mathematical	ADJ
easat-8773	328	10	modelling	modelling	NOUN
easat-8773	328	11	in	in	ADP
easat-8773	328	12	classroom	classroom	NOUN
easat-8773	328	13	:	:	PUNCT
easat-8773	328	14	a	a	DET
easat-8773	328	15	socio	socio	NOUN
easat-8773	328	16	-	-	PUNCT
easat-8773	328	17	critical	critical	ADJ
easat-8773	328	18	and	and	CCONJ
easat-8773	328	19	discursive	discursive	ADJ
easat-8773	328	20	perspective	perspective	NOUN
easat-8773	328	21	,	,	PUNCT
easat-8773	328	22	"	"	PUNCT
easat-8773	328	23	zdm	zdm	NOUN
easat-8773	328	24	,	,	PUNCT
easat-8773	328	25	vol	vol	NOUN
easat-8773	328	26	.	.	PROPN
easat-8773	329	1	38	38	NUM
easat-8773	329	2	,	,	PUNCT
easat-8773	329	3	pp	pp	ADJ
easat-8773	329	4	.	.	PUNCT
easat-8773	330	1	293	293	NUM
easat-8773	330	2	-	-	SYM
easat-8773	330	3	301	301	NUM
easat-8773	330	4	,	,	PUNCT
easat-8773	330	5	2006	2006	NUM
easat-8773	330	6	.	.	PUNCT
easat-8773	331	1	[	[	X
easat-8773	331	2	14	14	NUM
easat-8773	331	3	]	]	X
easat-8773	331	4	w.	w.	PROPN
easat-8773	331	5	blum	blum	PROPN
easat-8773	331	6	and	and	CCONJ
easat-8773	331	7	d.	d.	PROPN
easat-8773	331	8	leiß	leiß	PROPN
easat-8773	331	9	,	,	PUNCT
easat-8773	331	10	mathematical	mathematical	ADJ
easat-8773	331	11	modelling	modelling	NOUN
easat-8773	331	12	(	(	PUNCT
easat-8773	331	13	ictma	ictma	NOUN
easat-8773	331	14	12	12	NUM
easat-8773	331	15	):	):	PUNCT
easat-8773	331	16	education	education	NOUN
easat-8773	331	17	,	,	PUNCT
easat-8773	331	18	engineering	engineering	NOUN
easat-8773	331	19	and	and	CCONJ
easat-8773	331	20	economics	economic	NOUN
easat-8773	331	21	.	.	PUNCT
easat-8773	332	1	how	how	SCONJ
easat-8773	332	2	do	do	AUX
easat-8773	332	3	students	student	NOUN
easat-8773	332	4	and	and	CCONJ
easat-8773	332	5	teachers	teacher	NOUN
easat-8773	332	6	deal	deal	VERB
easat-8773	332	7	with	with	ADP
easat-8773	332	8	mathematical	mathematical	ADJ
easat-8773	332	9	modelling	modelling	NOUN
easat-8773	332	10	problems	problem	NOUN
easat-8773	332	11	?	?	PUNCT
easat-8773	333	1	the	the	DET
easat-8773	333	2	example	example	NOUN
easat-8773	333	3	sugarloaf	sugarloaf	PROPN
easat-8773	333	4	and	and	CCONJ
easat-8773	333	5	the	the	DET
easat-8773	333	6	disum	disum	NOUN
easat-8773	333	7	project	project	NOUN
easat-8773	333	8	.	.	PUNCT
easat-8773	334	1	amsterdam	amsterdam	PROPN
easat-8773	334	2	,	,	PUNCT
easat-8773	334	3	the	the	DET
easat-8773	334	4	netherlands	netherlands	PROPN
easat-8773	334	5	:	:	PUNCT
easat-8773	334	6	elsevier	elsevier	NOUN
easat-8773	334	7	,	,	PUNCT
easat-8773	334	8	2007	2007	NUM
easat-8773	334	9	.	.	PUNCT
easat-8773	335	1	[	[	X
easat-8773	335	2	15	15	NUM
easat-8773	335	3	]	]	X
easat-8773	335	4	g.	g.	PROPN
easat-8773	335	5	kaiser	kaiser	PROPN
easat-8773	335	6	and	and	CCONJ
easat-8773	335	7	b.	b.	PROPN
easat-8773	335	8	sriraman	sriraman	PROPN
easat-8773	335	9	,	,	PUNCT
easat-8773	335	10	"	"	PUNCT
easat-8773	335	11	a	a	DET
easat-8773	335	12	global	global	ADJ
easat-8773	335	13	survey	survey	NOUN
easat-8773	335	14	of	of	ADP
easat-8773	335	15	international	international	ADJ
easat-8773	335	16	perspectives	perspective	NOUN
easat-8773	335	17	on	on	ADP
easat-8773	335	18	modelling	modelling	NOUN
easat-8773	335	19	in	in	ADP
easat-8773	335	20	mathematics	mathematic	NOUN
easat-8773	335	21	education	education	NOUN
easat-8773	335	22	,	,	PUNCT
easat-8773	335	23	"	"	PUNCT
easat-8773	335	24	zdm	zdm	NOUN
easat-8773	335	25	,	,	PUNCT
easat-8773	335	26	vol	vol	NOUN
easat-8773	335	27	.	.	PROPN
easat-8773	336	1	38	38	NUM
easat-8773	336	2	,	,	PUNCT
easat-8773	336	3	pp	pp	ADJ
easat-8773	336	4	.	.	PUNCT
easat-8773	337	1	302	302	NUM
easat-8773	337	2	-	-	SYM
easat-8773	337	3	310	310	NUM
easat-8773	337	4	,	,	PUNCT
easat-8773	337	5	2006	2006	NUM
easat-8773	337	6	.	.	PUNCT
easat-8773	338	1	[	[	X
easat-8773	338	2	16	16	NUM
easat-8773	338	3	]	]	X
easat-8773	338	4	c.	c.	PROPN
easat-8773	338	5	hankeln	hankeln	PROPN
easat-8773	338	6	,	,	PUNCT
easat-8773	338	7	c.	c.	PROPN
easat-8773	338	8	adamek	adamek	PROPN
easat-8773	338	9	,	,	PUNCT
easat-8773	338	10	and	and	CCONJ
easat-8773	338	11	g.	g.	PROPN
easat-8773	338	12	greefrath	greefrath	PROPN
easat-8773	338	13	,	,	PUNCT
easat-8773	338	14	assessing	assess	VERB
easat-8773	338	15	sub	sub	NOUN
easat-8773	338	16	-	-	NOUN
easat-8773	338	17	competencies	competency	NOUN
easat-8773	338	18	of	of	ADP
easat-8773	338	19	mathematical	mathematical	ADJ
easat-8773	338	20	modelling	modelling	NOUN
easat-8773	338	21	—	—	PUNCT
easat-8773	338	22	development	development	NOUN
easat-8773	338	23	of	of	ADP
easat-8773	338	24	a	a	DET
easat-8773	338	25	new	new	ADJ
easat-8773	338	26	test	test	NOUN
easat-8773	338	27	instrument	instrument	NOUN
easat-8773	338	28	.	.	PUNCT
easat-8773	339	1	in	in	ADP
easat-8773	339	2	g.	g.	PROPN
easat-8773	339	3	stillman	stillman	PROPN
easat-8773	339	4	&	&	CCONJ
easat-8773	339	5	j.	j.	PROPN
easat-8773	339	6	p.	p.	PROPN
easat-8773	339	7	brown	brown	PROPN
easat-8773	339	8	(	(	PUNCT
easat-8773	339	9	eds	ed	NOUN
easat-8773	339	10	.	.	PUNCT
easat-8773	339	11	)	)	PUNCT
easat-8773	339	12	,	,	PUNCT
easat-8773	339	13	lines	line	NOUN
easat-8773	339	14	of	of	ADP
easat-8773	339	15	inquiry	inquiry	NOUN
easat-8773	339	16	in	in	ADP
easat-8773	339	17	mathematical	mathematical	ADJ
easat-8773	339	18	modelling	modelling	NOUN
easat-8773	339	19	research	research	NOUN
easat-8773	339	20	in	in	ADP
easat-8773	339	21	education	education	NOUN
easat-8773	339	22	.	.	PUNCT
easat-8773	340	1	cham	cham	PROPN
easat-8773	340	2	:	:	PUNCT
easat-8773	340	3	springer	springer	NOUN
easat-8773	340	4	,	,	PUNCT
easat-8773	340	5	2019	2019	NUM
easat-8773	340	6	.	.	PUNCT
easat-8773	341	1	[	[	X
easat-8773	341	2	17	17	NUM
easat-8773	341	3	]	]	X
easat-8773	341	4	r.	r.	PROPN
easat-8773	341	5	lesh	lesh	PROPN
easat-8773	341	6	and	and	CCONJ
easat-8773	341	7	j.	j.	PROPN
easat-8773	341	8	s.	s.	PROPN
easat-8773	341	9	zawojewski	zawojewski	PROPN
easat-8773	341	10	,	,	PUNCT
easat-8773	341	11	problem	problem	NOUN
easat-8773	341	12	solving	solving	NOUN
easat-8773	341	13	and	and	CCONJ
easat-8773	341	14	modeling	modeling	NOUN
easat-8773	341	15	.	.	PUNCT
easat-8773	342	1	in	in	ADP
easat-8773	342	2	f.	f.	PROPN
easat-8773	342	3	k.	k.	PROPN
easat-8773	342	4	lester	lester	PROPN
easat-8773	342	5	jr	jr	PROPN
easat-8773	342	6	.	.	PROPN
easat-8773	343	1	(	(	PUNCT
easat-8773	343	2	ed	ed	NOUN
easat-8773	343	3	.	.	PUNCT
easat-8773	343	4	)	)	PUNCT
easat-8773	343	5	,	,	PUNCT
easat-8773	343	6	second	second	ADJ
easat-8773	343	7	handbook	handbook	NOUN
easat-8773	343	8	of	of	ADP
easat-8773	343	9	research	research	NOUN
easat-8773	343	10	on	on	ADP
easat-8773	343	11	mathematics	mathematic	NOUN
easat-8773	343	12	teaching	teaching	NOUN
easat-8773	343	13	and	and	CCONJ
easat-8773	343	14	learning	learning	NOUN
easat-8773	343	15	.	.	PUNCT
easat-8773	344	1	charlotte	charlotte	PROPN
easat-8773	344	2	,	,	PUNCT
easat-8773	344	3	nc	nc	PROPN
easat-8773	344	4	:	:	PUNCT
easat-8773	344	5	information	information	NOUN
easat-8773	344	6	age	age	NOUN
easat-8773	344	7	publishing	publishing	NOUN
easat-8773	344	8	,	,	PUNCT
easat-8773	344	9	2007	2007	NUM
easat-8773	344	10	.	.	PUNCT
easat-8773	345	1	[	[	X
easat-8773	345	2	18	18	NUM
easat-8773	345	3	]	]	PUNCT
easat-8773	345	4	k.	k.	NOUN
easat-8773	345	5	maaß	maaß	PROPN
easat-8773	345	6	,	,	PUNCT
easat-8773	345	7	"	"	PUNCT
easat-8773	345	8	barriers	barrier	NOUN
easat-8773	345	9	and	and	CCONJ
easat-8773	345	10	opportunities	opportunity	NOUN
easat-8773	345	11	for	for	ADP
easat-8773	345	12	the	the	DET
easat-8773	345	13	integration	integration	NOUN
easat-8773	345	14	of	of	ADP
easat-8773	345	15	modelling	modelling	NOUN
easat-8773	345	16	in	in	ADP
easat-8773	345	17	mathematics	mathematics	NOUN
easat-8773	345	18	classes	class	NOUN
easat-8773	345	19	:	:	PUNCT
easat-8773	345	20	results	result	NOUN
easat-8773	345	21	of	of	ADP
easat-8773	345	22	an	an	DET
easat-8773	345	23	empirical	empirical	ADJ
easat-8773	345	24	study	study	NOUN
easat-8773	345	25	,	,	PUNCT
easat-8773	345	26	"	"	PUNCT
easat-8773	345	27	teaching	teach	VERB
easat-8773	345	28	mathematics	mathematic	NOUN
easat-8773	345	29	and	and	CCONJ
easat-8773	345	30	its	its	PRON
easat-8773	345	31	applications	application	NOUN
easat-8773	345	32	:	:	PUNCT
easat-8773	345	33	international	international	ADJ
easat-8773	345	34	journal	journal	NOUN
easat-8773	345	35	of	of	ADP
easat-8773	345	36	the	the	DET
easat-8773	345	37	i	i	PROPN
easat-8773	345	38	m	m	PROPN
easat-8773	345	39	a	a	PROPN
easat-8773	345	40	,	,	PUNCT
easat-8773	345	41	vol	vol	NOUN
easat-8773	345	42	.	.	PROPN
easat-8773	345	43	24	24	NUM
easat-8773	345	44	,	,	PUNCT
easat-8773	345	45	no	no	INTJ
easat-8773	345	46	.	.	NOUN
easat-8773	345	47	2	2	NUM
easat-8773	345	48	-	-	SYM
easat-8773	345	49	3	3	NUM
easat-8773	345	50	,	,	PUNCT
easat-8773	345	51	pp	pp	ADJ
easat-8773	345	52	.	.	PUNCT
easat-8773	346	1	61	61	NUM
easat-8773	346	2	-	-	SYM
easat-8773	346	3	74	74	NUM
easat-8773	346	4	,	,	PUNCT
easat-8773	346	5	2005	2005	NUM
easat-8773	346	6	.	.	PUNCT
easat-8773	347	1	[	[	X
easat-8773	347	2	19	19	NUM
easat-8773	347	3	]	]	PUNCT
easat-8773	347	4	z.	z.	PROPN
easat-8773	347	5	kohen	kohen	PROPN
easat-8773	347	6	and	and	CCONJ
easat-8773	347	7	d.	d.	PROPN
easat-8773	347	8	orenstein	orenstein	PROPN
easat-8773	347	9	,	,	PUNCT
easat-8773	347	10	"	"	PUNCT
easat-8773	347	11	mathematical	mathematical	ADJ
easat-8773	347	12	modeling	modeling	NOUN
easat-8773	347	13	of	of	ADP
easat-8773	347	14	tech	tech	NOUN
easat-8773	347	15	-	-	PUNCT
easat-8773	347	16	related	relate	VERB
easat-8773	347	17	real	real	ADJ
easat-8773	347	18	-	-	PUNCT
easat-8773	347	19	world	world	NOUN
easat-8773	347	20	problems	problem	NOUN
easat-8773	347	21	for	for	ADP
easat-8773	347	22	secondary	secondary	ADJ
easat-8773	347	23	school	school	NOUN
easat-8773	347	24	-	-	PUNCT
easat-8773	347	25	level	level	NOUN
easat-8773	347	26	mathematics	mathematic	NOUN
easat-8773	347	27	,	,	PUNCT
easat-8773	347	28	"	"	PUNCT
easat-8773	347	29	educational	educational	ADJ
easat-8773	347	30	studies	study	NOUN
easat-8773	347	31	in	in	ADP
easat-8773	347	32	mathematics	mathematic	NOUN
easat-8773	347	33	,	,	PUNCT
easat-8773	347	34	vol	vol	NOUN
easat-8773	347	35	.	.	PUNCT
easat-8773	348	1	107	107	NUM
easat-8773	348	2	,	,	PUNCT
easat-8773	348	3	no	no	INTJ
easat-8773	348	4	.	.	NOUN
easat-8773	348	5	1	1	NUM
easat-8773	348	6	,	,	PUNCT
easat-8773	348	7	pp	pp	ADJ
easat-8773	348	8	.	.	PUNCT
easat-8773	349	1	71	71	NUM
easat-8773	349	2	-	-	SYM
easat-8773	349	3	91	91	NUM
easat-8773	349	4	,	,	PUNCT
easat-8773	349	5	2021	2021	NUM
easat-8773	349	6	.	.	PUNCT
easat-8773	350	1	[	[	X
easat-8773	350	2	20	20	NUM
easat-8773	350	3	]	]	PUNCT
easat-8773	350	4	m.	m.	PROPN
easat-8773	350	5	a.	a.	PROPN
easat-8773	350	6	newman	newman	PROPN
easat-8773	350	7	,	,	PUNCT
easat-8773	350	8	"	"	PUNCT
easat-8773	350	9	an	an	DET
easat-8773	350	10	analysis	analysis	NOUN
easat-8773	350	11	of	of	ADP
easat-8773	350	12	sixth	sixth	ADJ
easat-8773	350	13	-	-	PUNCT
easat-8773	350	14	grade	grade	NOUN
easat-8773	350	15	pupil	pupil	NOUN
easat-8773	350	16	's	's	PART
easat-8773	350	17	error	error	NOUN
easat-8773	350	18	on	on	ADP
easat-8773	350	19	written	write	VERB
easat-8773	350	20	mathematical	mathematical	ADJ
easat-8773	350	21	tasks	task	NOUN
easat-8773	350	22	,	,	PUNCT
easat-8773	350	23	"	"	PUNCT
easat-8773	350	24	victorian	victorian	ADJ
easat-8773	350	25	institute	institute	NOUN
easat-8773	350	26	for	for	ADP
easat-8773	350	27	educational	educational	ADJ
easat-8773	350	28	research	research	NOUN
easat-8773	350	29	bulletin	bulletin	NOUN
easat-8773	350	30	,	,	PUNCT
easat-8773	350	31	vol	vol	NOUN
easat-8773	350	32	.	.	PROPN
easat-8773	350	33	39	39	NUM
easat-8773	350	34	,	,	PUNCT
easat-8773	350	35	pp	pp	ADJ
easat-8773	350	36	.	.	PUNCT
easat-8773	351	1	31	31	NUM
easat-8773	351	2	-	-	SYM
easat-8773	351	3	43	43	NUM
easat-8773	351	4	,	,	PUNCT
easat-8773	351	5	1977	1977	NUM
easat-8773	351	6	.	.	PUNCT
easat-8773	352	1	[	[	X
easat-8773	352	2	21	21	NUM
easat-8773	352	3	]	]	PUNCT
easat-8773	352	4	a.	a.	NOUN
easat-8773	352	5	wijaya	wijaya	PROPN
easat-8773	352	6	,	,	PUNCT
easat-8773	352	7	m.	m.	PROPN
easat-8773	352	8	van	van	PROPN
easat-8773	352	9	den	den	PROPN
easat-8773	352	10	heuvel	heuvel	PROPN
easat-8773	352	11	-	-	PUNCT
easat-8773	352	12	panhuizen	panhuizen	PROPN
easat-8773	352	13	,	,	PUNCT
easat-8773	352	14	m.	m.	NOUN
easat-8773	352	15	doorman	doorman	NOUN
easat-8773	352	16	,	,	PUNCT
easat-8773	352	17	and	and	CCONJ
easat-8773	352	18	a.	a.	NOUN
easat-8773	352	19	robitzsch	robitzsch	PROPN
easat-8773	352	20	,	,	PUNCT
easat-8773	352	21	"	"	PUNCT
easat-8773	352	22	difficulties	difficulty	NOUN
easat-8773	352	23	in	in	ADP
easat-8773	352	24	solving	solve	VERB
easat-8773	352	25	context	context	NOUN
easat-8773	352	26	-	-	PUNCT
easat-8773	352	27	based	base	VERB
easat-8773	352	28	pisa	pisa	PROPN
easat-8773	352	29	mathematics	mathematic	NOUN
easat-8773	352	30	tasks	task	NOUN
easat-8773	352	31	:	:	PUNCT
easat-8773	352	32	an	an	DET
easat-8773	352	33	analysis	analysis	NOUN
easat-8773	352	34	of	of	ADP
easat-8773	352	35	students	student	NOUN
easat-8773	352	36	’	’	PART
easat-8773	352	37	errors	error	NOUN
easat-8773	352	38	,	,	PUNCT
easat-8773	352	39	"	"	PUNCT
easat-8773	352	40	the	the	DET
easat-8773	352	41	mathematics	mathematic	NOUN
easat-8773	352	42	enthusiast	enthusiast	NOUN
easat-8773	352	43	,	,	PUNCT
easat-8773	352	44	vol	vol	NOUN
easat-8773	352	45	.	.	PROPN
easat-8773	352	46	11	11	NUM
easat-8773	352	47	,	,	PUNCT
easat-8773	352	48	no	no	INTJ
easat-8773	352	49	.	.	NOUN
easat-8773	352	50	3	3	NUM
easat-8773	352	51	,	,	PUNCT
easat-8773	352	52	pp	pp	ADJ
easat-8773	352	53	.	.	PUNCT
easat-8773	353	1	555	555	NUM
easat-8773	353	2	-	-	SYM
easat-8773	353	3	584	584	NUM
easat-8773	353	4	,	,	PUNCT
easat-8773	353	5	2014	2014	NUM
easat-8773	353	6	.	.	PUNCT
easat-8773	354	1	[	[	X
easat-8773	354	2	22	22	NUM
easat-8773	354	3	]	]	X
easat-8773	354	4	w.	w.	PROPN
easat-8773	354	5	blum	blum	PROPN
easat-8773	354	6	,	,	PUNCT
easat-8773	354	7	can	can	AUX
easat-8773	354	8	modelling	modelling	NOUN
easat-8773	354	9	be	be	AUX
easat-8773	354	10	taught	teach	VERB
easat-8773	354	11	and	and	CCONJ
easat-8773	354	12	learnt	learn	VERB
easat-8773	354	13	?	?	PUNCT
easat-8773	355	1	some	some	DET
easat-8773	355	2	answers	answer	NOUN
easat-8773	355	3	from	from	ADP
easat-8773	355	4	empirical	empirical	ADJ
easat-8773	355	5	research	research	NOUN
easat-8773	355	6	.	.	PUNCT
easat-8773	356	1	in	in	ADP
easat-8773	356	2	g.	g.	PROPN
easat-8773	356	3	kaiser	kaiser	PROPN
easat-8773	356	4	,	,	PUNCT
easat-8773	356	5	w.	w.	PROPN
easat-8773	356	6	blum	blum	PROPN
easat-8773	356	7	,	,	PUNCT
easat-8773	356	8	r.	r.	PROPN
easat-8773	356	9	borromeo	borromeo	PROPN
easat-8773	356	10	ferri	ferri	PROPN
easat-8773	356	11	,	,	PUNCT
easat-8773	356	12	&	&	CCONJ
easat-8773	356	13	g.	g.	PROPN
easat-8773	356	14	stillman	stillman	PROPN
easat-8773	356	15	(	(	PUNCT
easat-8773	356	16	eds	eds	PROPN
easat-8773	356	17	.	.	PUNCT
easat-8773	356	18	)	)	PUNCT
easat-8773	356	19	,	,	PUNCT
easat-8773	356	20	trends	trend	NOUN
easat-8773	356	21	in	in	ADP
easat-8773	356	22	teaching	teaching	NOUN
easat-8773	356	23	and	and	CCONJ
easat-8773	356	24	learning	learning	NOUN
easat-8773	356	25	of	of	ADP
easat-8773	356	26	mathematical	mathematical	ADJ
easat-8773	356	27	modelling	modelling	NOUN
easat-8773	356	28	.	.	PUNCT
easat-8773	357	1	dordrecht	dordrecht	NOUN
easat-8773	357	2	:	:	PUNCT
easat-8773	357	3	springer	springer	NOUN
easat-8773	357	4	,	,	PUNCT
easat-8773	357	5	2011	2011	NUM
easat-8773	357	6	.	.	PUNCT
easat-8773	358	1	[	[	X
easat-8773	358	2	23	23	NUM
easat-8773	358	3	]	]	X
easat-8773	358	4	s.	s.	PROPN
easat-8773	358	5	schaap	schaap	PROPN
easat-8773	358	6	,	,	PUNCT
easat-8773	358	7	p.	p.	NOUN
easat-8773	358	8	vos	vos	NOUN
easat-8773	358	9	,	,	PUNCT
easat-8773	358	10	and	and	CCONJ
easat-8773	358	11	m.	m.	NOUN
easat-8773	358	12	goedhart	goedhart	NOUN
easat-8773	358	13	,	,	PUNCT
easat-8773	358	14	students	student	NOUN
easat-8773	358	15	overcoming	overcome	VERB
easat-8773	358	16	blockages	blockage	NOUN
easat-8773	358	17	while	while	SCONJ
easat-8773	358	18	building	build	VERB
easat-8773	358	19	a	a	DET
easat-8773	358	20	mathematical	mathematical	ADJ
easat-8773	358	21	model	model	NOUN
easat-8773	358	22	:	:	PUNCT
easat-8773	358	23	exploring	explore	VERB
easat-8773	358	24	a	a	DET
easat-8773	358	25	framework	framework	NOUN
easat-8773	358	26	.	.	PUNCT
easat-8773	359	1	in	in	ADP
easat-8773	359	2	g.	g.	PROPN
easat-8773	359	3	kaiser	kaiser	PROPN
easat-8773	359	4	,	,	PUNCT
easat-8773	359	5	w.	w.	PROPN
easat-8773	359	6	blum	blum	PROPN
easat-8773	359	7	,	,	PUNCT
easat-8773	359	8	r.	r.	PROPN
easat-8773	359	9	borromeo	borromeo	PROPN
easat-8773	359	10	ferri	ferri	PROPN
easat-8773	359	11	,	,	PUNCT
easat-8773	359	12	&	&	CCONJ
easat-8773	359	13	g.	g.	PROPN
easat-8773	359	14	stillman	stillman	PROPN
easat-8773	359	15	(	(	PUNCT
easat-8773	359	16	eds	eds	PROPN
easat-8773	359	17	.	.	PUNCT
easat-8773	359	18	)	)	PUNCT
easat-8773	359	19	,	,	PUNCT
easat-8773	359	20	trends	trend	NOUN
easat-8773	359	21	in	in	ADP
easat-8773	359	22	teaching	teaching	NOUN
easat-8773	359	23	and	and	CCONJ
easat-8773	359	24	learning	learning	NOUN
easat-8773	359	25	of	of	ADP
easat-8773	359	26	mathematical	mathematical	ADJ
easat-8773	359	27	modelling	modelling	NOUN
easat-8773	359	28	.	.	PUNCT
easat-8773	360	1	dordrecht	dordrecht	NOUN
easat-8773	360	2	:	:	PUNCT
easat-8773	360	3	springer	springer	NOUN
easat-8773	360	4	,	,	PUNCT
easat-8773	360	5	2011	2011	NUM
easat-8773	360	6	.	.	PUNCT
easat-8773	361	1	[	[	X
easat-8773	361	2	24	24	NUM
easat-8773	361	3	]	]	PUNCT
easat-8773	361	4	r.	r.	PROPN
easat-8773	361	5	b.	b.	PROPN
easat-8773	361	6	ferri	ferri	PROPN
easat-8773	361	7	,	,	PUNCT
easat-8773	361	8	"	"	PUNCT
easat-8773	361	9	theoretical	theoretical	ADJ
easat-8773	361	10	and	and	CCONJ
easat-8773	361	11	empirical	empirical	ADJ
easat-8773	361	12	differentiations	differentiation	NOUN
easat-8773	361	13	of	of	ADP
easat-8773	361	14	phases	phase	NOUN
easat-8773	361	15	in	in	ADP
easat-8773	361	16	the	the	DET
easat-8773	361	17	modelling	modelling	NOUN
easat-8773	361	18	process	process	NOUN
easat-8773	361	19	,	,	PUNCT
easat-8773	361	20	"	"	PUNCT
easat-8773	361	21	zdm	zdm	NOUN
easat-8773	361	22	,	,	PUNCT
easat-8773	361	23	vol	vol	NOUN
easat-8773	361	24	.	.	PROPN
easat-8773	361	25	38	38	NUM
easat-8773	361	26	,	,	PUNCT
easat-8773	361	27	pp	pp	ADJ
easat-8773	361	28	.	.	PUNCT
easat-8773	362	1	86	86	NUM
easat-8773	362	2	-	-	SYM
easat-8773	362	3	95	95	NUM
easat-8773	362	4	,	,	PUNCT
easat-8773	362	5	2006	2006	NUM
easat-8773	362	6	.	.	PUNCT
easat-8773	363	1	[	[	X
easat-8773	363	2	25	25	NUM
easat-8773	363	3	]	]	X
easat-8773	363	4	w.	w.	PROPN
easat-8773	363	5	blum	blum	PROPN
easat-8773	363	6	and	and	CCONJ
easat-8773	363	7	r.	r.	PROPN
easat-8773	363	8	borromeo	borromeo	PROPN
easat-8773	363	9	ferri	ferri	PROPN
easat-8773	363	10	,	,	PUNCT
easat-8773	363	11	"	"	PUNCT
easat-8773	363	12	mathematical	mathematical	ADJ
easat-8773	363	13	modelling	modelling	NOUN
easat-8773	363	14	:	:	PUNCT
easat-8773	363	15	can	can	AUX
easat-8773	363	16	it	it	PRON
easat-8773	363	17	be	be	AUX
easat-8773	363	18	taught	teach	VERB
easat-8773	363	19	and	and	CCONJ
easat-8773	363	20	learnt	learn	VERB
easat-8773	363	21	,	,	PUNCT
easat-8773	363	22	"	"	PUNCT
easat-8773	363	23	journal	journal	NOUN
easat-8773	363	24	of	of	ADP
easat-8773	363	25	mathematical	mathematical	ADJ
easat-8773	363	26	modelling	modelling	NOUN
easat-8773	363	27	and	and	CCONJ
easat-8773	363	28	application	application	NOUN
easat-8773	363	29	,	,	PUNCT
easat-8773	363	30	vol	vol	NOUN
easat-8773	363	31	.	.	PROPN
easat-8773	364	1	1	1	NUM
easat-8773	364	2	,	,	PUNCT
easat-8773	364	3	no	no	INTJ
easat-8773	364	4	.	.	NOUN
easat-8773	364	5	1	1	NUM
easat-8773	364	6	,	,	PUNCT
easat-8773	364	7	pp	pp	ADJ
easat-8773	364	8	.	.	PUNCT
easat-8773	365	1	45	45	NUM
easat-8773	365	2	-	-	SYM
easat-8773	365	3	58	58	NUM
easat-8773	365	4	,	,	PUNCT
easat-8773	365	5	2009	2009	NUM
easat-8773	365	6	.	.	PUNCT
easat-8773	366	1	[	[	X
easat-8773	366	2	26	26	NUM
easat-8773	366	3	]	]	PUNCT
easat-8773	366	4	m.	m.	NOUN
easat-8773	366	5	blomhøj	blomhøj	NOUN
easat-8773	366	6	and	and	CCONJ
easat-8773	366	7	t.	t.	PROPN
easat-8773	366	8	h.	h.	PROPN
easat-8773	366	9	jensen	jensen	PROPN
easat-8773	366	10	,	,	PUNCT
easat-8773	366	11	"	"	PUNCT
easat-8773	366	12	developing	develop	VERB
easat-8773	366	13	mathematical	mathematical	ADJ
easat-8773	366	14	modelling	modelling	NOUN
easat-8773	366	15	competence	competence	NOUN
easat-8773	366	16	:	:	PUNCT
easat-8773	366	17	conceptual	conceptual	ADJ
easat-8773	366	18	clarification	clarification	NOUN
easat-8773	366	19	and	and	CCONJ
easat-8773	366	20	educational	educational	ADJ
easat-8773	366	21	planning	planning	NOUN
easat-8773	366	22	,	,	PUNCT
easat-8773	366	23	"	"	PUNCT
easat-8773	366	24	teaching	teach	VERB
easat-8773	366	25	mathematics	mathematic	NOUN
easat-8773	366	26	and	and	CCONJ
easat-8773	366	27	its	its	PRON
easat-8773	366	28	applications	application	NOUN
easat-8773	366	29	:	:	PUNCT
easat-8773	366	30	an	an	DET
easat-8773	366	31	international	international	ADJ
easat-8773	366	32	journal	journal	NOUN
easat-8773	366	33	of	of	ADP
easat-8773	366	34	the	the	DET
easat-8773	366	35	i	i	PROPN
easat-8773	366	36	m	m	PROPN
easat-8773	366	37	a	a	PROPN
easat-8773	366	38	,	,	PUNCT
easat-8773	366	39	vol	vol	NOUN
easat-8773	366	40	.	.	PROPN
easat-8773	367	1	22	22	NUM
easat-8773	367	2	,	,	PUNCT
easat-8773	367	3	no	no	INTJ
easat-8773	367	4	.	.	NOUN
easat-8773	367	5	3	3	NUM
easat-8773	367	6	,	,	PUNCT
easat-8773	367	7	pp	pp	ADJ
easat-8773	367	8	.	.	PUNCT
easat-8773	368	1	123	123	NUM
easat-8773	368	2	-	-	SYM
easat-8773	368	3	139	139	NUM
easat-8773	368	4	,	,	PUNCT
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easat-8773	368	6	.	.	PUNCT
easat-8773	369	1	https://doi.org/10.1093/teamat/22.3.123	https://doi.org/10.1093/teamat/22.3.123	NOUN
easat-8773	370	1	[	[	X
easat-8773	370	2	27	27	NUM
easat-8773	370	3	]	]	X
easat-8773	370	4	p.	p.	NOUN
easat-8773	370	5	biccard	biccard	PROPN
easat-8773	370	6	and	and	CCONJ
easat-8773	370	7	d.	d.	PROPN
easat-8773	370	8	wessels	wessels	PROPN
easat-8773	370	9	,	,	PUNCT
easat-8773	370	10	"	"	PUNCT
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easat-8773	370	12	of	of	ADP
easat-8773	370	13	affective	affective	NOUN
easat-8773	370	14	modelling	modelling	NOUN
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easat-8773	370	16	in	in	ADP
easat-8773	370	17	primary	primary	ADJ
easat-8773	370	18	school	school	NOUN
easat-8773	370	19	learners	learner	NOUN
easat-8773	370	20	,	,	PUNCT
easat-8773	370	21	"	"	PUNCT
easat-8773	370	22	pythagoras	pythagoras	X
easat-8773	370	23	,	,	PUNCT
easat-8773	370	24	vol	vol	NOUN
easat-8773	370	25	.	.	PROPN
easat-8773	370	26	32	32	NUM
easat-8773	370	27	,	,	PUNCT
easat-8773	370	28	no	no	INTJ
easat-8773	370	29	.	.	NOUN
easat-8773	370	30	1	1	NUM
easat-8773	370	31	,	,	PUNCT
easat-8773	370	32	pp	pp	ADJ
easat-8773	370	33	.	.	PUNCT
easat-8773	371	1	1	1	NUM
easat-8773	371	2	-	-	SYM
easat-8773	371	3	9	9	NUM
easat-8773	371	4	,	,	PUNCT
easat-8773	371	5	2011	2011	NUM
easat-8773	371	6	.	.	PUNCT
easat-8773	372	1	https://doi.org/10.4102/pythagoras.v32i1.20	https://doi.org/10.4102/pythagoras.v32i1.20	PROPN
easat-8773	373	1	[	[	X
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easat-8773	373	3	]	]	X
easat-8773	373	4	g.	g.	PROPN
easat-8773	373	5	a.	a.	PROPN
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easat-8773	373	7	,	,	PUNCT
easat-8773	373	8	j.	j.	PROPN
easat-8773	373	9	p.	p.	PROPN
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easat-8773	373	13	p.	p.	PROPN
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easat-8773	373	15	,	,	PUNCT
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easat-8773	373	17	in	in	ADP
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easat-8773	373	19	challenges	challenge	NOUN
easat-8773	373	20	:	:	PUNCT
easat-8773	373	21	intents	intent	NOUN
easat-8773	373	22	and	and	CCONJ
easat-8773	373	23	purposes	purpose	NOUN
easat-8773	373	24	.	.	PUNCT
easat-8773	374	1	in	in	ADP
easat-8773	374	2	g.	g.	PROPN
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easat-8773	374	4	,	,	PUNCT
easat-8773	374	5	g.	g.	PROPN
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easat-8773	374	7	,	,	PUNCT
easat-8773	374	8	w.	w.	PROPN
easat-8773	374	9	blum	blum	PROPN
easat-8773	374	10	,	,	PUNCT
easat-8773	374	11	&	&	CCONJ
easat-8773	374	12	j.	j.	PROPN
easat-8773	374	13	p.	p.	PROPN
easat-8773	374	14	brown	brown	PROPN
easat-8773	374	15	(	(	PUNCT
easat-8773	374	16	eds	ed	NOUN
easat-8773	374	17	.	.	PUNCT
easat-8773	374	18	)	)	PUNCT
easat-8773	374	19	,	,	PUNCT
easat-8773	374	20	teaching	teach	VERB
easat-8773	374	21	mathematical	mathematical	ADJ
easat-8773	374	22	modelling	modelling	NOUN
easat-8773	374	23	:	:	PUNCT
easat-8773	374	24	connecting	connect	VERB
easat-8773	374	25	to	to	ADP
easat-8773	374	26	research	research	NOUN
easat-8773	374	27	and	and	CCONJ
easat-8773	374	28	practice	practice	NOUN
easat-8773	374	29	.	.	PUNCT
easat-8773	375	1	dordrecht	dordrecht	PROPN
easat-8773	375	2	:	:	PUNCT
easat-8773	375	3	springer	springer	PROPN
easat-8773	375	4	netherlands	netherlands	PROPN
easat-8773	375	5	,	,	PUNCT
easat-8773	375	6	2013	2013	NUM
easat-8773	375	7	.	.	PUNCT
easat-8773	376	1	[	[	X
easat-8773	376	2	29	29	NUM
easat-8773	376	3	]	]	X
easat-8773	376	4	r.	r.	PROPN
easat-8773	376	5	lesh	lesh	PROPN
easat-8773	376	6	and	and	CCONJ
easat-8773	376	7	b.	b.	PROPN
easat-8773	376	8	caylor	caylor	PROPN
easat-8773	376	9	,	,	PUNCT
easat-8773	376	10	"	"	PUNCT
easat-8773	376	11	introduction	introduction	NOUN
easat-8773	376	12	to	to	ADP
easat-8773	376	13	the	the	DET
easat-8773	376	14	special	special	ADJ
easat-8773	376	15	issue	issue	NOUN
easat-8773	376	16	:	:	PUNCT
easat-8773	376	17	modeling	modeling	NOUN
easat-8773	376	18	as	as	ADP
easat-8773	376	19	application	application	NOUN
easat-8773	376	20	versus	versus	ADP
easat-8773	376	21	modeling	modeling	NOUN
easat-8773	376	22	as	as	ADP
easat-8773	376	23	a	a	DET
easat-8773	376	24	way	way	NOUN
easat-8773	376	25	to	to	PART
easat-8773	376	26	create	create	VERB
easat-8773	376	27	mathematics	mathematic	NOUN
easat-8773	376	28	,	,	PUNCT
easat-8773	376	29	"	"	PUNCT
easat-8773	376	30	international	international	ADJ
easat-8773	376	31	journal	journal	NOUN
easat-8773	376	32	of	of	ADP
easat-8773	376	33	computers	computer	NOUN
easat-8773	376	34	for	for	ADP
easat-8773	376	35	mathematical	mathematical	ADJ
easat-8773	376	36	learning	learning	NOUN
easat-8773	376	37	,	,	PUNCT
easat-8773	376	38	vol	vol	NOUN
easat-8773	376	39	.	.	PROPN
easat-8773	376	40	12	12	NUM
easat-8773	376	41	,	,	PUNCT
easat-8773	376	42	pp	pp	ADJ
easat-8773	376	43	.	.	PUNCT
easat-8773	377	1	173	173	NUM
easat-8773	377	2	-	-	SYM
easat-8773	377	3	194	194	NUM
easat-8773	377	4	,	,	PUNCT
easat-8773	377	5	2007	2007	NUM
easat-8773	377	6	.	.	PUNCT
easat-8773	378	1	https://doi.org/10.1007/s10649-021-10104-6	https://doi.org/10.1007/s10649-021-10104-6	PROPN
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easat-8773	379	1	https://doi.org/10.4102/pythagoras.v32i1.20	https://doi.org/10.4102/pythagoras.v32i1.20	PROPN