id	sid	tid	token	lemma	pos
easat-6229	1	1	edelweiss	edelweiss	PROPN
easat-6229	1	2	applied	apply	VERB
easat-6229	1	3	science	science	NOUN
easat-6229	1	4	and	and	CCONJ
easat-6229	1	5	technology	technology	NOUN
easat-6229	1	6	issn	issn	PROPN
easat-6229	1	7	:	:	PUNCT
easat-6229	1	8	2576	2576	NUM
easat-6229	1	9	-	-	SYM
easat-6229	1	10	8484	8484	NUM
easat-6229	1	11	vol	vol	NOUN
easat-6229	1	12	.	.	PROPN
easat-6229	2	1	9	9	NUM
easat-6229	2	2	,	,	PUNCT
easat-6229	2	3	no	no	INTJ
easat-6229	2	4	.	.	NOUN
easat-6229	2	5	4	4	NUM
easat-6229	2	6	,	,	PUNCT
easat-6229	2	7	1240	1240	NUM
easat-6229	2	8	-	-	SYM
easat-6229	2	9	1251	1251	NUM
easat-6229	2	10	2025	2025	NUM
easat-6229	2	11	publisher	publisher	NOUN
easat-6229	2	12	:	:	PUNCT
easat-6229	2	13	learning	learn	VERB
easat-6229	2	14	gate	gate	NOUN
easat-6229	2	15	doi	doi	PROPN
easat-6229	2	16	:	:	PUNCT
easat-6229	2	17	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	2	18	©	©	ADP
easat-6229	2	19	2025	2025	NUM
easat-6229	2	20	by	by	ADP
easat-6229	2	21	the	the	DET
easat-6229	2	22	authors	author	NOUN
easat-6229	2	23	;	;	PUNCT
easat-6229	2	24	licensee	licensee	PROPN
easat-6229	2	25	learning	learning	NOUN
easat-6229	2	26	gate	gate	NOUN
easat-6229	3	1	©	©	PROPN
easat-6229	3	2	2025	2025	NUM
easat-6229	3	3	by	by	ADP
easat-6229	3	4	the	the	DET
easat-6229	3	5	authors	author	NOUN
easat-6229	3	6	;	;	PUNCT
easat-6229	3	7	licensee	licensee	PROPN
easat-6229	3	8	learning	learning	NOUN
easat-6229	3	9	gate	gate	NOUN
easat-6229	3	10	history	history	NOUN
easat-6229	3	11	:	:	PUNCT
easat-6229	3	12	received	receive	VERB
easat-6229	3	13	:	:	PUNCT
easat-6229	3	14	19	19	NUM
easat-6229	3	15	february	february	NOUN
easat-6229	3	16	2025	2025	NUM
easat-6229	3	17	;	;	PUNCT
easat-6229	3	18	revised	revise	VERB
easat-6229	3	19	:	:	PUNCT
easat-6229	3	20	17	17	NUM
easat-6229	3	21	march	march	NOUN
easat-6229	3	22	2025	2025	NUM
easat-6229	3	23	;	;	PUNCT
easat-6229	3	24	accepted	accept	VERB
easat-6229	3	25	:	:	PUNCT
easat-6229	3	26	21	21	NUM
easat-6229	3	27	march	march	NOUN
easat-6229	3	28	2025	2025	NUM
easat-6229	3	29	;	;	PUNCT
easat-6229	3	30	published	publish	VERB
easat-6229	3	31	:	:	PUNCT
easat-6229	3	32	14	14	NUM
easat-6229	3	33	april	april	PROPN
easat-6229	3	34	2025	2025	NUM
easat-6229	3	35	*	*	PUNCT
easat-6229	3	36	correspondence	correspondence	NOUN
easat-6229	3	37	:	:	PUNCT
easat-6229	3	38	s.b.waluya@mail.unnes.ac.id	s.b.waluya@mail.unnes.ac.id	PROPN
easat-6229	3	39	grow	grow	NOUN
easat-6229	3	40	proof	proof	NOUN
easat-6229	3	41	ability	ability	NOUN
easat-6229	3	42	student	student	NOUN
easat-6229	3	43	through	through	ADP
easat-6229	3	44	mathematical	mathematical	ADJ
easat-6229	3	45	working	working	NOUN
easat-6229	3	46	space	space	NOUN
easat-6229	3	47	strategies	strategy	NOUN
easat-6229	3	48	isnani1	isnani1	PROPN
easat-6229	3	49	,	,	PUNCT
easat-6229	3	50	s.b	s.b	PROPN
easat-6229	3	51	.	.	PROPN
easat-6229	3	52	waluya2	waluya2	PROPN
easat-6229	3	53	*	*	PUNCT
easat-6229	3	54	,	,	PUNCT
easat-6229	3	55	dwijanto3	dwijanto3	PROPN
easat-6229	3	56	,	,	PUNCT
easat-6229	3	57	t.s.n	t.s.n	NOUN
easat-6229	3	58	.	.	PUNCT
easat-6229	4	1	asih4	asih4	PROPN
easat-6229	4	2	1,2,3,4department	1,2,3,4department	NUM
easat-6229	4	3	mathematics	mathematic	NOUN
easat-6229	4	4	education	education	NOUN
easat-6229	4	5	universitas	universita	NOUN
easat-6229	4	6	negeri	negeri	PROPN
easat-6229	4	7	semarang	semarang	PROPN
easat-6229	4	8	,	,	PUNCT
easat-6229	4	9	indonesia	indonesia	PROPN
easat-6229	4	10	;	;	PUNCT
easat-6229	4	11	s.b.waluya@mail.unnes.ac.id	s.b.waluya@mail.unnes.ac.id	PROPN
easat-6229	4	12	(	(	PUNCT
easat-6229	4	13	s.b.w	s.b.w	ADJ
easat-6229	4	14	.	.	PUNCT
easat-6229	4	15	)	)	PUNCT
easat-6229	4	16	.	.	PUNCT
easat-6229	5	1	abstract	abstract	ADV
easat-6229	5	2	:	:	PUNCT
easat-6229	5	3	this	this	DET
easat-6229	5	4	research	research	NOUN
easat-6229	5	5	aims	aim	VERB
easat-6229	5	6	to	to	PART
easat-6229	5	7	assist	assist	VERB
easat-6229	5	8	students	student	NOUN
easat-6229	5	9	in	in	ADP
easat-6229	5	10	solving	solve	VERB
easat-6229	5	11	mathematical	mathematical	ADJ
easat-6229	5	12	proof	proof	NOUN
easat-6229	5	13	problems	problem	NOUN
easat-6229	5	14	.	.	PUNCT
easat-6229	6	1	this	this	DET
easat-6229	6	2	qualitative	qualitative	ADJ
easat-6229	6	3	study	study	NOUN
easat-6229	6	4	investigates	investigate	VERB
easat-6229	6	5	the	the	DET
easat-6229	6	6	proving	proving	NOUN
easat-6229	6	7	ability	ability	NOUN
easat-6229	6	8	of	of	ADP
easat-6229	6	9	mathematics	mathematics	NOUN
easat-6229	6	10	education	education	NOUN
easat-6229	6	11	students	student	NOUN
easat-6229	6	12	in	in	ADP
easat-6229	6	13	the	the	DET
easat-6229	6	14	real	real	ADJ
easat-6229	6	15	analysis	analysis	NOUN
easat-6229	6	16	course	course	NOUN
easat-6229	6	17	,	,	PUNCT
easat-6229	6	18	with	with	ADP
easat-6229	6	19	a	a	DET
easat-6229	6	20	special	special	ADJ
easat-6229	6	21	focus	focus	NOUN
easat-6229	6	22	on	on	ADP
easat-6229	6	23	sequence	sequence	NOUN
easat-6229	6	24	material	material	NOUN
easat-6229	6	25	.	.	PUNCT
easat-6229	7	1	the	the	DET
easat-6229	7	2	research	research	NOUN
easat-6229	7	3	design	design	NOUN
easat-6229	7	4	incorporates	incorporate	VERB
easat-6229	7	5	experiments	experiment	NOUN
easat-6229	7	6	to	to	PART
easat-6229	7	7	evaluate	evaluate	VERB
easat-6229	7	8	the	the	DET
easat-6229	7	9	effectiveness	effectiveness	NOUN
easat-6229	7	10	of	of	ADP
easat-6229	7	11	the	the	DET
easat-6229	7	12	strategies	strategy	NOUN
easat-6229	7	13	used	use	VERB
easat-6229	7	14	.	.	PUNCT
easat-6229	8	1	participants	participant	NOUN
easat-6229	8	2	are	be	AUX
easat-6229	8	3	students	student	NOUN
easat-6229	8	4	who	who	PRON
easat-6229	8	5	take	take	VERB
easat-6229	8	6	part	part	NOUN
easat-6229	8	7	in	in	ADP
easat-6229	8	8	the	the	DET
easat-6229	8	9	real	real	ADJ
easat-6229	8	10	analysis	analysis	NOUN
easat-6229	8	11	program	program	NOUN
easat-6229	8	12	at	at	ADP
easat-6229	8	13	private	private	ADJ
easat-6229	8	14	universities	university	NOUN
easat-6229	8	15	in	in	ADP
easat-6229	8	16	the	the	DET
easat-6229	8	17	northern	northern	ADJ
easat-6229	8	18	coastal	coastal	ADJ
easat-6229	8	19	region	region	NOUN
easat-6229	8	20	of	of	ADP
easat-6229	8	21	western	western	ADJ
easat-6229	8	22	central	central	ADJ
easat-6229	8	23	java	java	PROPN
easat-6229	8	24	,	,	PUNCT
easat-6229	8	25	indonesia	indonesia	PROPN
easat-6229	8	26	,	,	PUNCT
easat-6229	8	27	specifically	specifically	ADV
easat-6229	8	28	in	in	ADP
easat-6229	8	29	tegal	tegal	ADJ
easat-6229	8	30	city	city	NOUN
easat-6229	8	31	during	during	ADP
easat-6229	8	32	the	the	DET
easat-6229	8	33	2022/2023	2022/2023	NUM
easat-6229	8	34	academic	academic	ADJ
easat-6229	8	35	year	year	NOUN
easat-6229	8	36	.	.	PUNCT
easat-6229	9	1	three	three	NUM
easat-6229	9	2	study	study	NOUN
easat-6229	9	3	participants	participant	NOUN
easat-6229	9	4	were	be	AUX
easat-6229	9	5	selected	select	VERB
easat-6229	9	6	,	,	PUNCT
easat-6229	9	7	each	each	PRON
easat-6229	9	8	representing	represent	VERB
easat-6229	9	9	a	a	DET
easat-6229	9	10	different	different	ADJ
easat-6229	9	11	level	level	NOUN
easat-6229	9	12	of	of	ADP
easat-6229	9	13	evidentiary	evidentiary	ADJ
easat-6229	9	14	ability	ability	NOUN
easat-6229	9	15	.	.	PUNCT
easat-6229	10	1	data	datum	NOUN
easat-6229	10	2	is	be	AUX
easat-6229	10	3	collected	collect	VERB
easat-6229	10	4	through	through	ADP
easat-6229	10	5	work	work	NOUN
easat-6229	10	6	documents	document	NOUN
easat-6229	10	7	,	,	PUNCT
easat-6229	10	8	interviews	interview	NOUN
easat-6229	10	9	,	,	PUNCT
easat-6229	10	10	and	and	CCONJ
easat-6229	10	11	structured	structured	ADJ
easat-6229	10	12	testing	testing	NOUN
easat-6229	10	13	,	,	PUNCT
easat-6229	10	14	and	and	CCONJ
easat-6229	10	15	then	then	ADV
easat-6229	10	16	analyzed	analyze	VERB
easat-6229	10	17	using	use	VERB
easat-6229	10	18	iterative	iterative	NOUN
easat-6229	10	19	techniques	technique	NOUN
easat-6229	10	20	,	,	PUNCT
easat-6229	10	21	including	include	VERB
easat-6229	10	22	data	data	NOUN
easat-6229	10	23	condensation	condensation	NOUN
easat-6229	10	24	,	,	PUNCT
easat-6229	10	25	data	datum	NOUN
easat-6229	10	26	exposure	exposure	NOUN
easat-6229	10	27	,	,	PUNCT
easat-6229	10	28	and	and	CCONJ
easat-6229	10	29	verification	verification	NOUN
easat-6229	10	30	.	.	PUNCT
easat-6229	11	1	the	the	DET
easat-6229	11	2	findings	finding	NOUN
easat-6229	11	3	show	show	VERB
easat-6229	11	4	that	that	SCONJ
easat-6229	11	5	most	most	ADJ
easat-6229	11	6	students	student	NOUN
easat-6229	11	7	can	can	AUX
easat-6229	11	8	follow	follow	VERB
easat-6229	11	9	the	the	DET
easat-6229	11	10	evidence	evidence	NOUN
easat-6229	11	11	and	and	CCONJ
easat-6229	11	12	correct	correct	VERB
easat-6229	11	13	their	their	PRON
easat-6229	11	14	mistakes	mistake	NOUN
easat-6229	11	15	.	.	PUNCT
easat-6229	12	1	in	in	ADP
easat-6229	12	2	the	the	DET
easat-6229	12	3	future	future	NOUN
easat-6229	12	4	,	,	PUNCT
easat-6229	12	5	this	this	DET
easat-6229	12	6	research	research	NOUN
easat-6229	12	7	will	will	AUX
easat-6229	12	8	prioritize	prioritize	VERB
easat-6229	12	9	developments	development	NOUN
easat-6229	12	10	related	relate	VERB
easat-6229	12	11	to	to	ADP
easat-6229	12	12	proof	proof	NOUN
easat-6229	12	13	to	to	PART
easat-6229	12	14	improve	improve	VERB
easat-6229	12	15	quality	quality	NOUN
easat-6229	12	16	-	-	PUNCT
easat-6229	12	17	proof	proof	ADJ
easat-6229	12	18	capabilities	capability	NOUN
easat-6229	12	19	and	and	CCONJ
easat-6229	12	20	explore	explore	VERB
easat-6229	12	21	the	the	DET
easat-6229	12	22	obstacles	obstacle	NOUN
easat-6229	12	23	faced	face	VERB
easat-6229	12	24	in	in	ADP
easat-6229	12	25	studying	study	VERB
easat-6229	12	26	proof	proof	ADJ
easat-6229	12	27	problems	problem	NOUN
easat-6229	12	28	.	.	PUNCT
easat-6229	13	1	this	this	DET
easat-6229	13	2	research	research	NOUN
easat-6229	13	3	can	can	AUX
easat-6229	13	4	ultimately	ultimately	ADV
easat-6229	13	5	contribute	contribute	VERB
easat-6229	13	6	to	to	ADP
easat-6229	13	7	more	more	ADV
easat-6229	13	8	effective	effective	ADJ
easat-6229	13	9	teaching	teaching	NOUN
easat-6229	13	10	of	of	ADP
easat-6229	13	11	real	real	ADJ
easat-6229	13	12	analysis	analysis	NOUN
easat-6229	13	13	by	by	ADP
easat-6229	13	14	providing	provide	VERB
easat-6229	13	15	a	a	DET
easat-6229	13	16	deeper	deep	ADJ
easat-6229	13	17	understanding	understanding	NOUN
easat-6229	13	18	of	of	ADP
easat-6229	13	19	the	the	DET
easat-6229	13	20	evidence	evidence	NOUN
easat-6229	13	21	problem	problem	NOUN
easat-6229	13	22	that	that	PRON
easat-6229	13	23	can	can	AUX
easat-6229	13	24	be	be	AUX
easat-6229	13	25	easily	easily	ADV
easat-6229	13	26	learned	learn	VERB
easat-6229	13	27	.	.	PUNCT
easat-6229	14	1	keywords	keyword	NOUN
easat-6229	14	2	:	:	PUNCT
easat-6229	14	3	mathematical	mathematical	ADJ
easat-6229	14	4	working	working	NOUN
easat-6229	14	5	space	space	NOUN
easat-6229	14	6	strategy	strategy	NOUN
easat-6229	14	7	,	,	PUNCT
easat-6229	14	8	model	model	NOUN
easat-6229	14	9	guided	guide	VERB
easat-6229	14	10	discovery	discovery	NOUN
easat-6229	14	11	learning	learning	NOUN
easat-6229	14	12	,	,	PUNCT
easat-6229	14	13	proof	proof	NOUN
easat-6229	14	14	ability	ability	NOUN
easat-6229	14	15	,	,	PUNCT
easat-6229	14	16	real	real	ADJ
easat-6229	14	17	analysis	analysis	NOUN
easat-6229	14	18	.	.	PUNCT
easat-6229	15	1	1	1	X
easat-6229	15	2	.	.	X
easat-6229	15	3	introduction	introduction	NOUN
easat-6229	15	4	the	the	DET
easat-6229	15	5	ability	ability	NOUN
easat-6229	15	6	to	to	PART
easat-6229	15	7	process	process	VERB
easat-6229	15	8	evidence	evidence	NOUN
easat-6229	15	9	is	be	AUX
easat-6229	15	10	essential	essential	ADJ
easat-6229	15	11	for	for	ADP
easat-6229	15	12	mathematics	mathematics	NOUN
easat-6229	15	13	education	education	NOUN
easat-6229	15	14	students	student	NOUN
easat-6229	15	15	,	,	PUNCT
easat-6229	15	16	as	as	SCONJ
easat-6229	15	17	it	it	PRON
easat-6229	15	18	directly	directly	ADV
easat-6229	15	19	influences	influence	VERB
easat-6229	15	20	their	their	PRON
easat-6229	15	21	proficiency	proficiency	NOUN
easat-6229	15	22	in	in	ADP
easat-6229	15	23	developing	develop	VERB
easat-6229	15	24	working	working	NOUN
easat-6229	15	25	memory	memory	NOUN
easat-6229	15	26	and	and	CCONJ
easat-6229	15	27	cognition	cognition	NOUN
easat-6229	15	28	,	,	PUNCT
easat-6229	15	29	both	both	PRON
easat-6229	15	30	of	of	ADP
easat-6229	15	31	which	which	PRON
easat-6229	15	32	impact	impact	VERB
easat-6229	15	33	their	their	PRON
easat-6229	15	34	ability	ability	NOUN
easat-6229	15	35	to	to	PART
easat-6229	15	36	construct	construct	VERB
easat-6229	15	37	proofs	proof	NOUN
easat-6229	16	1	[	[	X
easat-6229	16	2	1	1	NUM
easat-6229	16	3	]	]	PUNCT
easat-6229	16	4	.	.	PUNCT
easat-6229	17	1	additionally	additionally	ADV
easat-6229	17	2	,	,	PUNCT
easat-6229	17	3	a	a	DET
easat-6229	17	4	solid	solid	ADJ
easat-6229	17	5	understanding	understanding	NOUN
easat-6229	17	6	of	of	ADP
easat-6229	17	7	basic	basic	ADJ
easat-6229	17	8	mathematical	mathematical	ADJ
easat-6229	17	9	concepts	concept	NOUN
easat-6229	17	10	is	be	AUX
easat-6229	17	11	required	require	VERB
easat-6229	17	12	[	[	X
easat-6229	17	13	2	2	NUM
easat-6229	17	14	]	]	PUNCT
easat-6229	17	15	.	.	PUNCT
easat-6229	18	1	the	the	DET
easat-6229	18	2	creation	creation	NOUN
easat-6229	18	3	,	,	PUNCT
easat-6229	18	4	construction	construction	NOUN
easat-6229	18	5	,	,	PUNCT
easat-6229	18	6	and	and	CCONJ
easat-6229	18	7	communication	communication	NOUN
easat-6229	18	8	of	of	ADP
easat-6229	18	9	mathematical	mathematical	ADJ
easat-6229	18	10	knowledge	knowledge	NOUN
easat-6229	18	11	heavily	heavily	ADV
easat-6229	18	12	rely	rely	VERB
easat-6229	18	13	on	on	ADP
easat-6229	18	14	evidence	evidence	NOUN
easat-6229	18	15	,	,	PUNCT
easat-6229	18	16	enabling	enable	VERB
easat-6229	18	17	mathematicians	mathematician	NOUN
easat-6229	18	18	to	to	PART
easat-6229	18	19	persuade	persuade	VERB
easat-6229	18	20	others	other	NOUN
easat-6229	18	21	of	of	ADP
easat-6229	18	22	the	the	DET
easat-6229	18	23	correctness	correctness	NOUN
easat-6229	18	24	of	of	ADP
easat-6229	18	25	their	their	PRON
easat-6229	18	26	ideas	idea	NOUN
easat-6229	18	27	and	and	CCONJ
easat-6229	18	28	statements	statement	NOUN
easat-6229	18	29	[	[	X
easat-6229	18	30	1	1	NUM
easat-6229	18	31	,	,	PUNCT
easat-6229	18	32	3	3	NUM
easat-6229	18	33	]	]	PUNCT
easat-6229	18	34	.	.	PUNCT
easat-6229	19	1	further	far	ADV
easat-6229	19	2	emphasizes	emphasize	VERB
easat-6229	19	3	that	that	SCONJ
easat-6229	19	4	a	a	DET
easat-6229	19	5	strong	strong	ADJ
easat-6229	19	6	grasp	grasp	NOUN
easat-6229	19	7	of	of	ADP
easat-6229	19	8	mathematical	mathematical	ADJ
easat-6229	19	9	concepts	concept	NOUN
easat-6229	19	10	is	be	AUX
easat-6229	19	11	crucial	crucial	ADJ
easat-6229	19	12	for	for	ADP
easat-6229	19	13	building	build	VERB
easat-6229	19	14	robust	robust	ADJ
easat-6229	19	15	evidence	evidence	NOUN
easat-6229	19	16	.	.	PUNCT
easat-6229	20	1	the	the	DET
easat-6229	20	2	process	process	NOUN
easat-6229	20	3	of	of	ADP
easat-6229	20	4	discovering	discover	VERB
easat-6229	20	5	,	,	PUNCT
easat-6229	20	6	verifying	verifying	NOUN
easat-6229	20	7	,	,	PUNCT
easat-6229	20	8	explaining	explain	VERB
easat-6229	20	9	,	,	PUNCT
easat-6229	20	10	systematizing	systematizing	NOUN
easat-6229	20	11	,	,	PUNCT
easat-6229	20	12	and	and	CCONJ
easat-6229	20	13	communicating	communicate	VERB
easat-6229	20	14	mathematical	mathematical	ADJ
easat-6229	20	15	knowledge	knowledge	NOUN
easat-6229	20	16	relies	rely	VERB
easat-6229	20	17	heavily	heavily	ADV
easat-6229	20	18	on	on	ADP
easat-6229	20	19	evidence	evidence	NOUN
easat-6229	20	20	.	.	PUNCT
easat-6229	21	1	students	student	NOUN
easat-6229	21	2	must	must	AUX
easat-6229	21	3	be	be	AUX
easat-6229	21	4	able	able	ADJ
easat-6229	21	5	to	to	PART
easat-6229	21	6	provide	provide	VERB
easat-6229	21	7	reasonable	reasonable	ADJ
easat-6229	21	8	justifications	justification	NOUN
easat-6229	21	9	and	and	CCONJ
easat-6229	21	10	demonstrate	demonstrate	VERB
easat-6229	21	11	that	that	SCONJ
easat-6229	21	12	mathematical	mathematical	ADJ
easat-6229	21	13	statements	statement	NOUN
easat-6229	21	14	are	be	AUX
easat-6229	21	15	correct	correct	ADJ
easat-6229	21	16	.	.	PUNCT
easat-6229	22	1	proofs	proof	NOUN
easat-6229	22	2	can	can	AUX
easat-6229	22	3	lead	lead	VERB
easat-6229	22	4	to	to	ADP
easat-6229	22	5	new	new	ADJ
easat-6229	22	6	insights	insight	NOUN
easat-6229	22	7	,	,	PUNCT
easat-6229	22	8	discoveries	discovery	NOUN
easat-6229	22	9	,	,	PUNCT
easat-6229	22	10	and	and	CCONJ
easat-6229	22	11	developments	development	NOUN
easat-6229	22	12	[	[	X
easat-6229	22	13	4	4	NUM
easat-6229	22	14	,	,	PUNCT
easat-6229	22	15	5	5	NUM
easat-6229	22	16	]	]	PUNCT
easat-6229	22	17	.	.	PUNCT
easat-6229	23	1	the	the	DET
easat-6229	23	2	real	real	ADJ
easat-6229	23	3	analysis	analysis	NOUN
easat-6229	23	4	course	course	NOUN
easat-6229	23	5	in	in	ADP
easat-6229	23	6	the	the	DET
easat-6229	23	7	department	department	NOUN
easat-6229	23	8	of	of	ADP
easat-6229	23	9	mathematics	mathematics	PROPN
easat-6229	23	10	and	and	CCONJ
easat-6229	23	11	mathematics	mathematic	NOUN
easat-6229	23	12	education	education	NOUN
easat-6229	23	13	is	be	AUX
easat-6229	23	14	rich	rich	ADJ
easat-6229	23	15	in	in	ADP
easat-6229	23	16	evidentiary	evidentiary	ADJ
easat-6229	23	17	content	content	NOUN
easat-6229	23	18	.	.	PUNCT
easat-6229	24	1	real	real	ADJ
easat-6229	24	2	analysis	analysis	NOUN
easat-6229	24	3	is	be	AUX
easat-6229	24	4	a	a	DET
easat-6229	24	5	complex	complex	ADJ
easat-6229	24	6	subject	subject	NOUN
easat-6229	24	7	that	that	PRON
easat-6229	24	8	requires	require	VERB
easat-6229	24	9	deep	deep	ADJ
easat-6229	24	10	thinking	thinking	NOUN
easat-6229	24	11	.	.	PUNCT
easat-6229	25	1	building	building	NOUN
easat-6229	25	2	and	and	CCONJ
easat-6229	25	3	understanding	understand	VERB
easat-6229	25	4	evidence	evidence	NOUN
easat-6229	25	5	necessitates	necessitate	VERB
easat-6229	25	6	a	a	DET
easat-6229	25	7	strong	strong	ADJ
easat-6229	25	8	grasp	grasp	NOUN
easat-6229	25	9	of	of	ADP
easat-6229	25	10	mathematical	mathematical	ADJ
easat-6229	25	11	concepts	concept	NOUN
easat-6229	25	12	.	.	PUNCT
easat-6229	26	1	before	before	ADP
easat-6229	26	2	studying	study	VERB
easat-6229	26	3	real	real	ADJ
easat-6229	26	4	analysis	analysis	NOUN
easat-6229	26	5	,	,	PUNCT
easat-6229	26	6	students	student	NOUN
easat-6229	26	7	must	must	AUX
easat-6229	26	8	be	be	AUX
easat-6229	26	9	prepared	prepare	VERB
easat-6229	26	10	to	to	PART
easat-6229	26	11	comprehend	comprehend	VERB
easat-6229	26	12	the	the	DET
easat-6229	26	13	evidence	evidence	NOUN
easat-6229	26	14	presented	present	VERB
easat-6229	26	15	.	.	PUNCT
easat-6229	27	1	additionally	additionally	ADV
easat-6229	27	2	,	,	PUNCT
easat-6229	27	3	they	they	PRON
easat-6229	27	4	must	must	AUX
easat-6229	27	5	develop	develop	VERB
easat-6229	27	6	an	an	DET
easat-6229	27	7	understanding	understanding	NOUN
easat-6229	27	8	of	of	ADP
easat-6229	27	9	proof	proof	NOUN
easat-6229	27	10	and	and	CCONJ
easat-6229	27	11	enhance	enhance	VERB
easat-6229	27	12	their	their	PRON
easat-6229	27	13	problem	problem	NOUN
easat-6229	27	14	-	-	PUNCT
easat-6229	27	15	solving	solve	VERB
easat-6229	27	16	skills	skill	NOUN
easat-6229	27	17	.	.	PUNCT
easat-6229	28	1	both	both	PRON
easat-6229	28	2	of	of	ADP
easat-6229	28	3	these	these	DET
easat-6229	28	4	abilities	ability	NOUN
easat-6229	28	5	can	can	AUX
easat-6229	28	6	be	be	AUX
easat-6229	28	7	cultivated	cultivate	VERB
easat-6229	28	8	through	through	ADP
easat-6229	28	9	the	the	DET
easat-6229	28	10	practice	practice	NOUN
easat-6229	28	11	of	of	ADP
easat-6229	28	12	solving	solve	VERB
easat-6229	28	13	problems	problem	NOUN
easat-6229	28	14	related	relate	VERB
easat-6229	28	15	to	to	ADP
easat-6229	28	16	proofs	proof	NOUN
easat-6229	28	17	[	[	X
easat-6229	28	18	6	6	NUM
easat-6229	28	19	]	]	PUNCT
easat-6229	28	20	.	.	PUNCT
easat-6229	29	1	most	most	ADJ
easat-6229	29	2	students	student	NOUN
easat-6229	29	3	of	of	ADP
easat-6229	29	4	mathematics	mathematic	NOUN
easat-6229	29	5	and	and	CCONJ
easat-6229	29	6	mathematics	mathematic	NOUN
easat-6229	29	7	education	education	NOUN
easat-6229	29	8	consider	consider	VERB
easat-6229	29	9	real	real	ADJ
easat-6229	29	10	analysis	analysis	NOUN
easat-6229	29	11	to	to	PART
easat-6229	29	12	be	be	AUX
easat-6229	29	13	a	a	DET
easat-6229	29	14	very	very	ADV
easat-6229	29	15	difficult	difficult	ADJ
easat-6229	29	16	subject	subject	NOUN
easat-6229	29	17	.	.	PUNCT
easat-6229	30	1	many	many	ADJ
easat-6229	30	2	students	student	NOUN
easat-6229	30	3	are	be	AUX
easat-6229	30	4	unfamiliar	unfamiliar	ADJ
easat-6229	30	5	with	with	ADP
easat-6229	30	6	the	the	DET
easat-6229	30	7	concept	concept	NOUN
easat-6229	30	8	of	of	ADP
easat-6229	30	9	proof	proof	NOUN
easat-6229	30	10	and	and	CCONJ
easat-6229	30	11	struggle	struggle	VERB
easat-6229	30	12	to	to	PART
easat-6229	30	13	understand	understand	VERB
easat-6229	30	14	it	it	PRON
easat-6229	30	15	.	.	PUNCT
easat-6229	31	1	to	to	PART
easat-6229	31	2	enhance	enhance	VERB
easat-6229	31	3	students	student	NOUN
easat-6229	31	4	'	'	PART
easat-6229	31	5	ability	ability	NOUN
easat-6229	31	6	to	to	PART
easat-6229	31	7	comprehend	comprehend	VERB
easat-6229	31	8	and	and	CCONJ
easat-6229	31	9	construct	construct	VERB
easat-6229	31	10	evidence	evidence	NOUN
easat-6229	31	11	,	,	PUNCT
easat-6229	31	12	they	they	PRON
easat-6229	31	13	must	must	AUX
easat-6229	31	14	develop	develop	VERB
easat-6229	31	15	confidence	confidence	NOUN
easat-6229	31	16	in	in	ADP
easat-6229	31	17	their	their	PRON
easat-6229	31	18	reasoning	reasoning	NOUN
easat-6229	31	19	skills	skill	NOUN
easat-6229	31	20	.	.	PUNCT
easat-6229	32	1	unfortunately	unfortunately	ADV
easat-6229	32	2	,	,	PUNCT
easat-6229	32	3	many	many	ADJ
easat-6229	32	4	college	college	NOUN
easat-6229	32	5	students	student	NOUN
easat-6229	32	6	possess	possess	VERB
easat-6229	32	7	a	a	DET
easat-6229	32	8	fixed	fix	VERB
easat-6229	32	9	mindset	mindset	NOUN
easat-6229	32	10	when	when	SCONJ
easat-6229	32	11	it	it	PRON
easat-6229	32	12	comes	come	VERB
easat-6229	32	13	to	to	ADP
easat-6229	32	14	learning	learn	VERB
easat-6229	32	15	mathematics	mathematic	NOUN
easat-6229	32	16	,	,	PUNCT
easat-6229	32	17	which	which	PRON
easat-6229	32	18	leads	lead	VERB
easat-6229	32	19	to	to	ADP
easat-6229	32	20	a	a	DET
easat-6229	32	21	lack	lack	NOUN
easat-6229	32	22	of	of	ADP
easat-6229	32	23	confidence	confidence	NOUN
easat-6229	32	24	in	in	ADP
easat-6229	32	25	understanding	understanding	NOUN
easat-6229	32	26	and	and	CCONJ
easat-6229	32	27	constructing	construct	VERB
easat-6229	32	28	evidence	evidence	NOUN
easat-6229	32	29	1241	1241	NUM
easat-6229	32	30	edelweiss	edelweiss	PROPN
easat-6229	32	31	applied	apply	VERB
easat-6229	32	32	science	science	NOUN
easat-6229	32	33	and	and	CCONJ
easat-6229	32	34	technology	technology	NOUN
easat-6229	32	35	issn	issn	PROPN
easat-6229	32	36	:	:	PUNCT
easat-6229	32	37	2576	2576	NUM
easat-6229	32	38	-	-	SYM
easat-6229	32	39	8484	8484	NUM
easat-6229	32	40	vol	vol	NOUN
easat-6229	32	41	.	.	PROPN
easat-6229	33	1	9	9	NUM
easat-6229	33	2	,	,	PUNCT
easat-6229	33	3	no	no	INTJ
easat-6229	33	4	.	.	NOUN
easat-6229	33	5	4	4	NUM
easat-6229	33	6	:	:	SYM
easat-6229	33	7	1240	1240	NUM
easat-6229	33	8	-	-	SYM
easat-6229	33	9	1251	1251	NUM
easat-6229	33	10	,	,	PUNCT
easat-6229	33	11	2025	2025	NUM
easat-6229	33	12	doi	doi	NOUN
easat-6229	33	13	:	:	PUNCT
easat-6229	33	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	33	15	©	©	ADP
easat-6229	33	16	2025	2025	NUM
easat-6229	33	17	by	by	ADP
easat-6229	33	18	the	the	DET
easat-6229	33	19	authors	author	NOUN
easat-6229	33	20	;	;	PUNCT
easat-6229	33	21	licensee	licensee	PROPN
easat-6229	33	22	learning	learning	NOUN
easat-6229	33	23	gate	gate	NOUN
easat-6229	34	1	[	[	X
easat-6229	34	2	5	5	NUM
easat-6229	34	3	]	]	PUNCT
easat-6229	34	4	.	.	PUNCT
easat-6229	35	1	the	the	DET
easat-6229	35	2	epistemology	epistemology	NOUN
easat-6229	35	3	of	of	ADP
easat-6229	35	4	students	student	NOUN
easat-6229	35	5	in	in	ADP
easat-6229	35	6	the	the	DET
easat-6229	35	7	real	real	ADJ
easat-6229	35	8	analysis	analysis	NOUN
easat-6229	35	9	course	course	NOUN
easat-6229	35	10	reveals	reveal	VERB
easat-6229	35	11	several	several	ADJ
easat-6229	35	12	challenges	challenge	NOUN
easat-6229	35	13	they	they	PRON
easat-6229	35	14	face	face	VERB
easat-6229	35	15	when	when	SCONJ
easat-6229	35	16	studying	study	VERB
easat-6229	35	17	proofs	proof	NOUN
easat-6229	35	18	.	.	PUNCT
easat-6229	36	1	these	these	DET
easat-6229	36	2	challenges	challenge	NOUN
easat-6229	36	3	include	include	VERB
easat-6229	36	4	difficulties	difficulty	NOUN
easat-6229	36	5	in	in	ADP
easat-6229	36	6	understanding	understand	VERB
easat-6229	36	7	concepts	concept	NOUN
easat-6229	36	8	(	(	PUNCT
easat-6229	36	9	definitions	definition	NOUN
easat-6229	36	10	)	)	PUNCT
easat-6229	36	11	,	,	PUNCT
easat-6229	36	12	uncertainty	uncertainty	NOUN
easat-6229	36	13	about	about	ADP
easat-6229	36	14	how	how	SCONJ
easat-6229	36	15	to	to	PART
easat-6229	36	16	begin	begin	VERB
easat-6229	36	17	constructing	construct	VERB
easat-6229	36	18	proofs	proof	NOUN
easat-6229	36	19	,	,	PUNCT
easat-6229	36	20	lack	lack	NOUN
easat-6229	36	21	of	of	ADP
easat-6229	36	22	knowledge	knowledge	NOUN
easat-6229	36	23	regarding	regard	VERB
easat-6229	36	24	the	the	DET
easat-6229	36	25	application	application	NOUN
easat-6229	36	26	of	of	ADP
easat-6229	36	27	known	know	VERB
easat-6229	36	28	definitions	definition	NOUN
easat-6229	36	29	and	and	CCONJ
easat-6229	36	30	principles	principle	NOUN
easat-6229	36	31	,	,	PUNCT
easat-6229	36	32	and	and	CCONJ
easat-6229	36	33	confusion	confusion	NOUN
easat-6229	36	34	about	about	ADP
easat-6229	36	35	what	what	PRON
easat-6229	36	36	needs	need	VERB
easat-6229	36	37	to	to	PART
easat-6229	36	38	be	be	AUX
easat-6229	36	39	proven	prove	VERB
easat-6229	36	40	[	[	X
easat-6229	36	41	7	7	NUM
easat-6229	36	42	,	,	PUNCT
easat-6229	36	43	8	8	NUM
easat-6229	36	44	]	]	PUNCT
easat-6229	36	45	.	.	PUNCT
easat-6229	37	1	students	student	NOUN
easat-6229	37	2	often	often	ADV
easat-6229	37	3	struggle	struggle	VERB
easat-6229	37	4	to	to	PART
easat-6229	37	5	understand	understand	VERB
easat-6229	37	6	the	the	DET
easat-6229	37	7	role	role	NOUN
easat-6229	37	8	and	and	CCONJ
easat-6229	37	9	function	function	NOUN
easat-6229	37	10	of	of	ADP
easat-6229	37	11	proof	proof	NOUN
easat-6229	37	12	in	in	ADP
easat-6229	37	13	mathematics	mathematic	NOUN
easat-6229	37	14	,	,	PUNCT
easat-6229	37	15	both	both	CCONJ
easat-6229	37	16	in	in	ADP
easat-6229	37	17	the	the	DET
easat-6229	37	18	short	short	ADJ
easat-6229	37	19	and	and	CCONJ
easat-6229	37	20	long	long	ADJ
easat-6229	37	21	term	term	NOUN
easat-6229	37	22	.	.	PUNCT
easat-6229	38	1	evidence	evidence	NOUN
easat-6229	38	2	is	be	AUX
easat-6229	38	3	crucial	crucial	ADJ
easat-6229	38	4	for	for	ADP
easat-6229	38	5	verifying	verify	VERB
easat-6229	38	6	the	the	DET
easat-6229	38	7	correctness	correctness	NOUN
easat-6229	38	8	of	of	ADP
easat-6229	38	9	statements	statement	NOUN
easat-6229	38	10	,	,	PUNCT
easat-6229	38	11	providing	provide	VERB
easat-6229	38	12	logical	logical	ADJ
easat-6229	38	13	arguments	argument	NOUN
easat-6229	38	14	,	,	PUNCT
easat-6229	38	15	constructing	construct	VERB
easat-6229	38	16	new	new	ADJ
easat-6229	38	17	mathematics	mathematic	NOUN
easat-6229	38	18	,	,	PUNCT
easat-6229	38	19	and	and	CCONJ
easat-6229	38	20	communicating	communicate	VERB
easat-6229	38	21	mathematical	mathematical	ADJ
easat-6229	38	22	concepts	concept	NOUN
easat-6229	38	23	.	.	PUNCT
easat-6229	39	1	it	it	PRON
easat-6229	39	2	also	also	ADV
easat-6229	39	3	plays	play	VERB
easat-6229	39	4	a	a	DET
easat-6229	39	5	vital	vital	ADJ
easat-6229	39	6	role	role	NOUN
easat-6229	39	7	in	in	ADP
easat-6229	39	8	systematizing	systematize	VERB
easat-6229	39	9	statements	statement	NOUN
easat-6229	39	10	within	within	ADP
easat-6229	39	11	axiomatic	axiomatic	ADJ
easat-6229	39	12	systems	system	NOUN
easat-6229	39	13	[	[	X
easat-6229	39	14	9	9	NUM
easat-6229	39	15	]	]	PUNCT
easat-6229	39	16	.	.	PUNCT
easat-6229	40	1	the	the	DET
easat-6229	40	2	application	application	NOUN
easat-6229	40	3	of	of	ADP
easat-6229	40	4	evidence	evidence	NOUN
easat-6229	40	5	in	in	ADP
easat-6229	40	6	mathematics	mathematics	NOUN
easat-6229	40	7	education	education	NOUN
easat-6229	40	8	is	be	AUX
easat-6229	40	9	essential	essential	ADJ
easat-6229	40	10	because	because	SCONJ
easat-6229	40	11	it	it	PRON
easat-6229	40	12	enhances	enhance	VERB
easat-6229	40	13	critical	critical	ADJ
easat-6229	40	14	thinking	thinking	NOUN
easat-6229	40	15	and	and	CCONJ
easat-6229	40	16	problem	problem	NOUN
easat-6229	40	17	-	-	PUNCT
easat-6229	40	18	solving	solve	VERB
easat-6229	40	19	skills[10	skills[10	NOUN
easat-6229	40	20	]	]	PUNCT
easat-6229	40	21	.	.	PUNCT
easat-6229	41	1	the	the	DET
easat-6229	41	2	imparting	imparting	NOUN
easat-6229	41	3	of	of	ADP
easat-6229	41	4	ideas	idea	NOUN
easat-6229	41	5	,	,	PUNCT
easat-6229	41	6	the	the	DET
easat-6229	41	7	development	development	NOUN
easat-6229	41	8	and	and	CCONJ
easat-6229	41	9	communication	communication	NOUN
easat-6229	41	10	of	of	ADP
easat-6229	41	11	knowledge	knowledge	NOUN
easat-6229	41	12	,	,	PUNCT
easat-6229	41	13	and	and	CCONJ
easat-6229	41	14	the	the	DET
easat-6229	41	15	contribution	contribution	NOUN
easat-6229	41	16	to	to	ADP
easat-6229	41	17	the	the	DET
easat-6229	41	18	development	development	NOUN
easat-6229	41	19	of	of	ADP
easat-6229	41	20	mathematics	mathematic	NOUN
easat-6229	41	21	are	be	AUX
easat-6229	41	22	all	all	PRON
easat-6229	41	23	significant	significant	ADJ
easat-6229	41	24	aspects	aspect	NOUN
easat-6229	41	25	of	of	ADP
easat-6229	41	26	proof	proof	NOUN
easat-6229	41	27	.	.	PUNCT
easat-6229	42	1	by	by	ADP
easat-6229	42	2	emphasizing	emphasize	VERB
easat-6229	42	3	these	these	DET
easat-6229	42	4	aspects	aspect	NOUN
easat-6229	42	5	,	,	PUNCT
easat-6229	42	6	educators	educator	NOUN
easat-6229	42	7	can	can	AUX
easat-6229	42	8	better	well	ADV
easat-6229	42	9	support	support	VERB
easat-6229	42	10	students	student	NOUN
easat-6229	42	11	in	in	ADP
easat-6229	42	12	their	their	PRON
easat-6229	42	13	understanding	understanding	NOUN
easat-6229	42	14	and	and	CCONJ
easat-6229	42	15	application	application	NOUN
easat-6229	42	16	of	of	ADP
easat-6229	42	17	mathematical	mathematical	ADJ
easat-6229	42	18	proofs	proof	NOUN
easat-6229	42	19	[	[	X
easat-6229	42	20	11	11	NUM
easat-6229	42	21	]	]	PUNCT
easat-6229	42	22	.	.	PUNCT
easat-6229	43	1	1.1	1.1	NUM
easat-6229	43	2	.	.	PUNCT
easat-6229	44	1	the	the	DET
easat-6229	44	2	needs	need	NOUN
easat-6229	44	3	of	of	ADP
easat-6229	44	4	students	student	NOUN
easat-6229	44	5	the	the	DET
easat-6229	44	6	guided	guide	VERB
easat-6229	44	7	discovery	discovery	NOUN
easat-6229	44	8	learning	learn	VERB
easat-6229	44	9	learning	learn	VERB
easat-6229	44	10	model	model	NOUN
easat-6229	44	11	has	have	VERB
easat-6229	44	12	a	a	DET
easat-6229	44	13	positive	positive	ADJ
easat-6229	44	14	impact	impact	NOUN
easat-6229	44	15	on	on	ADP
easat-6229	44	16	comprehension	comprehension	NOUN
easat-6229	44	17	skills	skill	NOUN
easat-6229	44	18	and	and	CCONJ
easat-6229	44	19	mathematical	mathematical	ADJ
easat-6229	44	20	skills	skill	NOUN
easat-6229	44	21	,	,	PUNCT
easat-6229	44	22	while	while	SCONJ
easat-6229	44	23	the	the	DET
easat-6229	44	24	benefits	benefit	NOUN
easat-6229	44	25	of	of	ADP
easat-6229	44	26	the	the	DET
easat-6229	44	27	guided	guide	VERB
easat-6229	44	28	discovery	discovery	NOUN
easat-6229	44	29	learning	learn	VERB
easat-6229	44	30	model	model	NOUN
easat-6229	44	31	on	on	ADP
easat-6229	44	32	mathematics	mathematic	NOUN
easat-6229	44	33	learning	learning	NOUN
easat-6229	44	34	are	be	AUX
easat-6229	44	35	:	:	PUNCT
easat-6229	44	36	(	(	PUNCT
easat-6229	44	37	1	1	X
easat-6229	44	38	)	)	PUNCT
easat-6229	44	39	improvement	improvement	NOUN
easat-6229	44	40	of	of	ADP
easat-6229	44	41	conceptual	conceptual	ADJ
easat-6229	44	42	comprehension	comprehension	NOUN
easat-6229	44	43	:	:	PUNCT
easat-6229	44	44	research	research	NOUN
easat-6229	44	45	conducted	conduct	VERB
easat-6229	44	46	by	by	ADP
easat-6229	44	47	dumitraşcu	dumitraşcu	NOUN
easat-6229	45	1	[	[	X
easat-6229	45	2	12	12	NUM
easat-6229	45	3	]	]	PUNCT
easat-6229	45	4	shows	show	VERB
easat-6229	45	5	that	that	SCONJ
easat-6229	45	6	the	the	DET
easat-6229	45	7	integration	integration	NOUN
easat-6229	45	8	of	of	ADP
easat-6229	45	9	guided	guide	VERB
easat-6229	45	10	discovery	discovery	NOUN
easat-6229	45	11	learning	learning	NOUN
easat-6229	45	12	in	in	ADP
easat-6229	45	13	real	real	ADJ
easat-6229	45	14	analysis	analysis	NOUN
easat-6229	45	15	teaching	teaching	NOUN
easat-6229	45	16	allows	allow	VERB
easat-6229	45	17	students	student	NOUN
easat-6229	45	18	to	to	PART
easat-6229	45	19	understand	understand	VERB
easat-6229	45	20	concepts	concept	NOUN
easat-6229	45	21	more	more	ADV
easat-6229	45	22	deeply	deeply	ADV
easat-6229	45	23	compared	compare	VERB
easat-6229	45	24	to	to	ADP
easat-6229	45	25	conventional	conventional	ADJ
easat-6229	45	26	approaches	approach	NOUN
easat-6229	45	27	.	.	PUNCT
easat-6229	46	1	(	(	PUNCT
easat-6229	46	2	2	2	NUM
easat-6229	46	3	)	)	PUNCT
easat-6229	46	4	.	.	PUNCT
easat-6229	47	1	development	development	NOUN
easat-6229	47	2	of	of	ADP
easat-6229	47	3	critical	critical	ADJ
easat-6229	47	4	thinking	thinking	NOUN
easat-6229	47	5	skills	skill	NOUN
easat-6229	47	6	:	:	PUNCT
easat-6229	47	7	a	a	DET
easat-6229	47	8	study	study	NOUN
easat-6229	47	9	by	by	ADP
easat-6229	47	10	kariman	kariman	NOUN
easat-6229	47	11	,	,	PUNCT
easat-6229	47	12	et	et	PROPN
easat-6229	47	13	al	al	PROPN
easat-6229	47	14	.	.	PUNCT
easat-6229	48	1	[	[	X
easat-6229	48	2	13	13	NUM
easat-6229	48	3	]	]	PUNCT
easat-6229	48	4	confirms	confirm	VERB
easat-6229	48	5	that	that	SCONJ
easat-6229	48	6	the	the	DET
easat-6229	48	7	guided	guide	VERB
easat-6229	48	8	discovery	discovery	NOUN
easat-6229	48	9	learning	learning	NOUN
easat-6229	48	10	model	model	NOUN
easat-6229	48	11	,	,	PUNCT
easat-6229	48	12	when	when	SCONJ
easat-6229	48	13	combined	combine	VERB
easat-6229	48	14	with	with	ADP
easat-6229	48	15	argument	argument	NOUN
easat-6229	48	16	mapping	mapping	NOUN
easat-6229	48	17	,	,	PUNCT
easat-6229	48	18	can	can	AUX
easat-6229	48	19	improve	improve	VERB
easat-6229	48	20	students	student	NOUN
easat-6229	48	21	'	'	PART
easat-6229	48	22	critical	critical	ADJ
easat-6229	48	23	thinking	thinking	NOUN
easat-6229	48	24	skills	skill	NOUN
easat-6229	48	25	in	in	ADP
easat-6229	48	26	understanding	understand	VERB
easat-6229	48	27	the	the	DET
easat-6229	48	28	changes	change	NOUN
easat-6229	48	29	that	that	PRON
easat-6229	48	30	occur	occur	VERB
easat-6229	48	31	in	in	ADP
easat-6229	48	32	the	the	DET
easat-6229	48	33	environment	environment	NOUN
easat-6229	48	34	.	.	PUNCT
easat-6229	49	1	(	(	PUNCT
easat-6229	49	2	3	3	NUM
easat-6229	49	3	)	)	PUNCT
easat-6229	49	4	.	.	PUNCT
easat-6229	50	1	improvement	improvement	NOUN
easat-6229	50	2	of	of	ADP
easat-6229	50	3	practice	practice	NOUN
easat-6229	50	4	skills	skill	NOUN
easat-6229	50	5	:	:	PUNCT
easat-6229	50	6	aagesen	aagesen	ADJ
easat-6229	50	7	,	,	PUNCT
easat-6229	50	8	et	et	PROPN
easat-6229	50	9	al	al	PROPN
easat-6229	50	10	.	.	PUNCT
easat-6229	51	1	[	[	X
easat-6229	51	2	14	14	NUM
easat-6229	51	3	]	]	PUNCT
easat-6229	51	4	found	find	VERB
easat-6229	51	5	that	that	SCONJ
easat-6229	51	6	the	the	DET
easat-6229	51	7	application	application	NOUN
easat-6229	51	8	of	of	ADP
easat-6229	51	9	guided	guide	VERB
easat-6229	51	10	discovery	discovery	NOUN
easat-6229	51	11	learning	learn	VERB
easat-6229	51	12	in	in	ADP
easat-6229	51	13	surgical	surgical	ADJ
easat-6229	51	14	skills	skill	NOUN
easat-6229	51	15	courses	course	NOUN
easat-6229	51	16	was	be	AUX
easat-6229	51	17	more	more	ADV
easat-6229	51	18	effective	effective	ADJ
easat-6229	51	19	in	in	ADP
easat-6229	51	20	improving	improve	VERB
easat-6229	51	21	students	student	NOUN
easat-6229	51	22	'	'	PART
easat-6229	51	23	understanding	understanding	NOUN
easat-6229	51	24	and	and	CCONJ
easat-6229	51	25	practical	practical	ADJ
easat-6229	51	26	skills	skill	NOUN
easat-6229	51	27	compared	compare	VERB
easat-6229	51	28	to	to	ADP
easat-6229	51	29	traditional	traditional	ADJ
easat-6229	51	30	teaching	teaching	NOUN
easat-6229	51	31	methods	method	NOUN
easat-6229	51	32	.	.	PUNCT
easat-6229	52	1	(	(	PUNCT
easat-6229	52	2	4	4	NUM
easat-6229	52	3	)	)	PUNCT
easat-6229	52	4	.	.	PUNCT
easat-6229	53	1	positive	positive	ADJ
easat-6229	53	2	impact	impact	NOUN
easat-6229	53	3	in	in	ADP
easat-6229	53	4	mathematics	mathematics	NOUN
easat-6229	53	5	education	education	NOUN
easat-6229	53	6	:	:	PUNCT
easat-6229	53	7	kariman	kariman	NOUN
easat-6229	53	8	,	,	PUNCT
easat-6229	53	9	et	et	PROPN
easat-6229	53	10	al	al	PROPN
easat-6229	53	11	.	.	PUNCT
easat-6229	54	1	[	[	X
easat-6229	54	2	13	13	NUM
easat-6229	54	3	]	]	PUNCT
easat-6229	54	4	shows	show	VERB
easat-6229	54	5	that	that	SCONJ
easat-6229	54	6	modules	module	NOUN
easat-6229	54	7	based	base	VERB
easat-6229	54	8	on	on	ADP
easat-6229	54	9	guided	guide	VERB
easat-6229	54	10	discovery	discovery	NOUN
easat-6229	54	11	learning	learning	NOUN
easat-6229	54	12	are	be	AUX
easat-6229	54	13	able	able	ADJ
easat-6229	54	14	to	to	PART
easat-6229	54	15	improve	improve	VERB
easat-6229	54	16	students	student	NOUN
easat-6229	54	17	'	'	PART
easat-6229	54	18	understanding	understanding	NOUN
easat-6229	54	19	of	of	ADP
easat-6229	54	20	concepts	concept	NOUN
easat-6229	54	21	and	and	CCONJ
easat-6229	54	22	critical	critical	ADJ
easat-6229	54	23	thinking	thinking	NOUN
easat-6229	54	24	skills	skill	NOUN
easat-6229	54	25	in	in	ADP
easat-6229	54	26	the	the	DET
easat-6229	54	27	field	field	NOUN
easat-6229	54	28	of	of	ADP
easat-6229	54	29	mathematics	mathematic	NOUN
easat-6229	54	30	.	.	PUNCT
easat-6229	55	1	(	(	PUNCT
easat-6229	55	2	5	5	NUM
easat-6229	55	3	)	)	PUNCT
easat-6229	55	4	.	.	PUNCT
easat-6229	56	1	technology	technology	NOUN
easat-6229	56	2	support	support	NOUN
easat-6229	56	3	for	for	ADP
easat-6229	56	4	interactive	interactive	ADJ
easat-6229	56	5	learning	learning	NOUN
easat-6229	56	6	:	:	PUNCT
easat-6229	56	7	kniha	kniha	PROPN
easat-6229	56	8	,	,	PUNCT
easat-6229	56	9	et	et	PROPN
easat-6229	56	10	al	al	PROPN
easat-6229	56	11	.	.	PUNCT
easat-6229	57	1	[	[	X
easat-6229	57	2	15	15	NUM
easat-6229	57	3	]	]	PUNCT
easat-6229	57	4	reveals	reveal	VERB
easat-6229	57	5	that	that	SCONJ
easat-6229	57	6	the	the	DET
easat-6229	57	7	combination	combination	NOUN
easat-6229	57	8	of	of	ADP
easat-6229	57	9	guided	guide	VERB
easat-6229	57	10	discovery	discovery	NOUN
easat-6229	57	11	learning	learning	NOUN
easat-6229	57	12	and	and	CCONJ
easat-6229	57	13	technology	technology	NOUN
easat-6229	57	14	,	,	PUNCT
easat-6229	57	15	such	such	ADJ
easat-6229	57	16	as	as	ADP
easat-6229	57	17	video	video	NOUN
easat-6229	57	18	-	-	PUNCT
easat-6229	57	19	based	base	VERB
easat-6229	57	20	teaching	teaching	NOUN
easat-6229	57	21	,	,	PUNCT
easat-6229	57	22	results	result	NOUN
easat-6229	57	23	in	in	ADP
easat-6229	57	24	better	well	ADJ
easat-6229	57	25	outcomes	outcome	NOUN
easat-6229	57	26	in	in	ADP
easat-6229	57	27	oral	oral	ADJ
easat-6229	57	28	surgical	surgical	ADJ
easat-6229	57	29	skills	skill	NOUN
easat-6229	57	30	training	training	NOUN
easat-6229	57	31	.	.	PUNCT
easat-6229	58	1	(	(	PUNCT
easat-6229	58	2	6	6	NUM
easat-6229	58	3	)	)	PUNCT
easat-6229	58	4	.	.	PUNCT
easat-6229	59	1	increased	increase	VERB
easat-6229	59	2	interest	interest	NOUN
easat-6229	59	3	and	and	CCONJ
easat-6229	59	4	motivation	motivation	NOUN
easat-6229	59	5	:	:	PUNCT
easat-6229	59	6	studies	study	NOUN
easat-6229	59	7	by	by	ADP
easat-6229	59	8	nurhayani	nurhayani	PROPN
easat-6229	59	9	,	,	PUNCT
easat-6229	59	10	et	et	PROPN
easat-6229	59	11	al	al	PROPN
easat-6229	59	12	.	.	PUNCT
easat-6229	60	1	[	[	X
easat-6229	60	2	16	16	NUM
easat-6229	60	3	]	]	PUNCT
easat-6229	60	4	show	show	VERB
easat-6229	60	5	that	that	SCONJ
easat-6229	60	6	the	the	DET
easat-6229	60	7	application	application	NOUN
easat-6229	60	8	of	of	ADP
easat-6229	60	9	guided	guide	VERB
easat-6229	60	10	discovery	discovery	NOUN
easat-6229	60	11	learning	learning	NOUN
easat-6229	60	12	can	can	AUX
easat-6229	60	13	increase	increase	VERB
easat-6229	60	14	students	student	NOUN
easat-6229	60	15	'	'	PART
easat-6229	60	16	interest	interest	NOUN
easat-6229	60	17	in	in	ADP
easat-6229	60	18	learning	learn	VERB
easat-6229	60	19	mathematics	mathematic	NOUN
easat-6229	60	20	and	and	CCONJ
easat-6229	60	21	encourage	encourage	VERB
easat-6229	60	22	them	they	PRON
easat-6229	60	23	to	to	PART
easat-6229	60	24	be	be	AUX
easat-6229	60	25	more	more	ADV
easat-6229	60	26	active	active	ADJ
easat-6229	60	27	in	in	ADP
easat-6229	60	28	the	the	DET
easat-6229	60	29	learning	learning	NOUN
easat-6229	60	30	process	process	NOUN
easat-6229	60	31	.	.	PUNCT
easat-6229	61	1	next	next	ADJ
easat-6229	61	2	for	for	ADP
easat-6229	61	3	the	the	DET
easat-6229	61	4	concept	concept	NOUN
easat-6229	61	5	of	of	ADP
easat-6229	61	6	mathematical	mathematical	ADJ
easat-6229	61	7	working	working	NOUN
easat-6229	61	8	space	space	NOUN
easat-6229	61	9	is	be	AUX
easat-6229	61	10	a	a	DET
easat-6229	61	11	theoretical	theoretical	ADJ
easat-6229	61	12	and	and	CCONJ
easat-6229	61	13	methodological	methodological	ADJ
easat-6229	61	14	model	model	NOUN
easat-6229	61	15	applied	apply	VERB
easat-6229	61	16	in	in	ADP
easat-6229	61	17	mathematics	mathematics	PROPN
easat-6229	61	18	education	education	NOUN
easat-6229	61	19	research	research	NOUN
easat-6229	61	20	to	to	PART
easat-6229	61	21	analyze	analyze	VERB
easat-6229	61	22	and	and	CCONJ
easat-6229	61	23	understand	understand	VERB
easat-6229	61	24	mathematical	mathematical	ADJ
easat-6229	61	25	activities	activity	NOUN
easat-6229	61	26	carried	carry	VERB
easat-6229	61	27	out	out	ADP
easat-6229	61	28	by	by	ADP
easat-6229	61	29	students	student	NOUN
easat-6229	61	30	and	and	CCONJ
easat-6229	61	31	teachers	teacher	NOUN
easat-6229	61	32	.	.	PUNCT
easat-6229	62	1	this	this	DET
easat-6229	62	2	model	model	NOUN
easat-6229	62	3	integrates	integrate	VERB
easat-6229	62	4	the	the	DET
easat-6229	62	5	epistemological	epistemological	ADJ
easat-6229	62	6	and	and	CCONJ
easat-6229	62	7	cognitive	cognitive	ADJ
easat-6229	62	8	aspects	aspect	NOUN
easat-6229	62	9	of	of	ADP
easat-6229	62	10	mathematical	mathematical	ADJ
easat-6229	62	11	activities	activity	NOUN
easat-6229	62	12	,	,	PUNCT
easat-6229	62	13	which	which	PRON
easat-6229	62	14	are	be	AUX
easat-6229	62	15	organized	organize	VERB
easat-6229	62	16	in	in	ADP
easat-6229	62	17	two	two	NUM
easat-6229	62	18	main	main	ADJ
easat-6229	62	19	domains	domain	NOUN
easat-6229	62	20	:	:	PUNCT
easat-6229	62	21	the	the	DET
easat-6229	62	22	epistemological	epistemological	ADJ
easat-6229	62	23	domain	domain	NOUN
easat-6229	62	24	and	and	CCONJ
easat-6229	62	25	the	the	DET
easat-6229	62	26	cognitive	cognitive	ADJ
easat-6229	62	27	domain	domain	NOUN
easat-6229	62	28	[	[	X
easat-6229	62	29	17	17	NUM
easat-6229	62	30	-	-	SYM
easat-6229	62	31	19	19	NUM
easat-6229	62	32	]	]	PUNCT
easat-6229	62	33	.	.	PUNCT
easat-6229	63	1	the	the	DET
easat-6229	63	2	mathematical	mathematical	ADJ
easat-6229	63	3	working	working	NOUN
easat-6229	63	4	space	space	NOUN
easat-6229	63	5	is	be	AUX
easat-6229	63	6	characterized	characterize	VERB
easat-6229	63	7	by	by	ADP
easat-6229	63	8	three	three	NUM
easat-6229	63	9	interconnected	interconnected	ADJ
easat-6229	63	10	dimensions	dimension	NOUN
easat-6229	63	11	,	,	PUNCT
easat-6229	63	12	which	which	PRON
easat-6229	63	13	are	be	AUX
easat-6229	63	14	crucial	crucial	ADJ
easat-6229	63	15	for	for	ADP
easat-6229	63	16	carrying	carry	VERB
easat-6229	63	17	out	out	ADP
easat-6229	63	18	thorough	thorough	ADJ
easat-6229	63	19	mathematical	mathematical	ADJ
easat-6229	63	20	activities	activity	NOUN
easat-6229	63	21	:	:	PUNCT
easat-6229	63	22	semiotic	semiotic	ADJ
easat-6229	63	23	dimension	dimension	NOUN
easat-6229	63	24	:	:	PUNCT
easat-6229	63	25	refers	refer	VERB
easat-6229	63	26	to	to	ADP
easat-6229	63	27	the	the	DET
easat-6229	63	28	use	use	NOUN
easat-6229	63	29	of	of	ADP
easat-6229	63	30	signs	sign	NOUN
easat-6229	63	31	and	and	CCONJ
easat-6229	63	32	symbols	symbol	NOUN
easat-6229	63	33	in	in	ADP
easat-6229	63	34	mathematical	mathematical	ADJ
easat-6229	63	35	reasoning	reasoning	NOUN
easat-6229	63	36	and	and	CCONJ
easat-6229	63	37	communication	communication	NOUN
easat-6229	63	38	processes	process	NOUN
easat-6229	63	39	[	[	X
easat-6229	63	40	19	19	NUM
easat-6229	63	41	,	,	PUNCT
easat-6229	63	42	20	20	NUM
easat-6229	63	43	]	]	PUNCT
easat-6229	63	44	.	.	PUNCT
easat-6229	64	1	instrumental	instrumental	ADJ
easat-6229	64	2	dimension	dimension	NOUN
easat-6229	64	3	:	:	PUNCT
easat-6229	64	4	involves	involve	VERB
easat-6229	64	5	tools	tool	NOUN
easat-6229	64	6	and	and	CCONJ
easat-6229	64	7	instruments	instrument	NOUN
easat-6229	64	8	,	,	PUNCT
easat-6229	64	9	both	both	CCONJ
easat-6229	64	10	physical	physical	ADJ
easat-6229	64	11	and	and	CCONJ
easat-6229	64	12	digital	digital	ADJ
easat-6229	64	13	,	,	PUNCT
easat-6229	64	14	used	use	VERB
easat-6229	64	15	in	in	ADP
easat-6229	64	16	the	the	DET
easat-6229	64	17	execution	execution	NOUN
easat-6229	64	18	of	of	ADP
easat-6229	64	19	mathematical	mathematical	ADJ
easat-6229	64	20	tasks	task	NOUN
easat-6229	64	21	[	[	X
easat-6229	64	22	17	17	NUM
easat-6229	64	23	]	]	PUNCT
easat-6229	64	24	.	.	PUNCT
easat-6229	65	1	discursive	discursive	ADJ
easat-6229	65	2	dimension	dimension	NOUN
easat-6229	65	3	:	:	PUNCT
easat-6229	65	4	deals	deal	NOUN
easat-6229	65	5	with	with	ADP
easat-6229	65	6	the	the	DET
easat-6229	65	7	language	language	NOUN
easat-6229	65	8	and	and	CCONJ
easat-6229	65	9	discourse	discourse	NOUN
easat-6229	65	10	applied	apply	VERB
easat-6229	65	11	in	in	ADP
easat-6229	65	12	explanations	explanation	NOUN
easat-6229	65	13	and	and	CCONJ
easat-6229	65	14	mathematical	mathematical	ADJ
easat-6229	65	15	arguments	argument	NOUN
easat-6229	65	16	[	[	X
easat-6229	65	17	19	19	NUM
easat-6229	65	18	]	]	PUNCT
easat-6229	65	19	.	.	PUNCT
easat-6229	66	1	mathematical	mathematical	ADJ
easat-6229	66	2	woking	woking	NOUN
easat-6229	66	3	space	space	NOUN
easat-6229	66	4	has	have	VERB
easat-6229	66	5	the	the	DET
easat-6229	66	6	following	follow	VERB
easat-6229	66	7	benefits	benefit	NOUN
easat-6229	66	8	:	:	PUNCT
easat-6229	66	9	(	(	PUNCT
easat-6229	66	10	1	1	NUM
easat-6229	66	11	)	)	PUNCT
easat-6229	66	12	.	.	PUNCT
easat-6229	67	1	holistic	holistic	ADJ
easat-6229	67	2	understanding	understanding	NOUN
easat-6229	67	3	:	:	PUNCT
easat-6229	67	4	by	by	ADP
easat-6229	67	5	integrating	integrate	VERB
easat-6229	67	6	epistemological	epistemological	ADJ
easat-6229	67	7	and	and	CCONJ
easat-6229	67	8	cognitive	cognitive	ADJ
easat-6229	67	9	aspects	aspect	NOUN
easat-6229	67	10	,	,	PUNCT
easat-6229	67	11	mathematical	mathematical	ADJ
easat-6229	67	12	woking	woking	NOUN
easat-6229	67	13	space	space	NOUN
easat-6229	67	14	provides	provide	VERB
easat-6229	67	15	a	a	DET
easat-6229	67	16	comprehensive	comprehensive	ADJ
easat-6229	67	17	framework	framework	NOUN
easat-6229	67	18	for	for	ADP
easat-6229	67	19	understanding	understand	VERB
easat-6229	67	20	mathematical	mathematical	ADJ
easat-6229	67	21	activities	activity	NOUN
easat-6229	67	22	[	[	X
easat-6229	67	23	19	19	NUM
easat-6229	67	24	,	,	PUNCT
easat-6229	67	25	20	20	NUM
easat-6229	67	26	]	]	PUNCT
easat-6229	67	27	.	.	PUNCT
easat-6229	68	1	(	(	PUNCT
easat-6229	68	2	2	2	NUM
easat-6229	68	3	)	)	PUNCT
easat-6229	68	4	.	.	PUNCT
easat-6229	69	1	identification	identification	NOUN
easat-6229	69	2	of	of	ADP
easat-6229	69	3	misunderstandings	misunderstanding	NOUN
easat-6229	69	4	:	:	PUNCT
easat-6229	69	5	this	this	DET
easat-6229	69	6	model	model	NOUN
easat-6229	69	7	serves	serve	VERB
easat-6229	69	8	to	to	PART
easat-6229	69	9	identify	identify	VERB
easat-6229	69	10	and	and	CCONJ
easat-6229	69	11	address	address	VERB
easat-6229	69	12	misunderstandings	misunderstanding	NOUN
easat-6229	69	13	that	that	PRON
easat-6229	69	14	may	may	AUX
easat-6229	69	15	not	not	PART
easat-6229	69	16	be	be	AUX
easat-6229	69	17	directly	directly	ADV
easat-6229	69	18	detected	detect	VERB
easat-6229	69	19	by	by	ADP
easat-6229	69	20	teachers	teacher	NOUN
easat-6229	69	21	[	[	X
easat-6229	69	22	17	17	NUM
easat-6229	69	23	]	]	PUNCT
easat-6229	69	24	.	.	PUNCT
easat-6229	70	1	(	(	PUNCT
easat-6229	70	2	3	3	NUM
easat-6229	70	3	)	)	PUNCT
easat-6229	70	4	.	.	PUNCT
easat-6229	71	1	improvement	improvement	NOUN
easat-6229	71	2	of	of	ADP
easat-6229	71	3	teaching	teaching	NOUN
easat-6229	71	4	practices	practice	NOUN
easat-6229	71	5	:	:	PUNCT
easat-6229	71	6	mathematical	mathematical	ADJ
easat-6229	71	7	woking	woking	NOUN
easat-6229	71	8	space	space	NOUN
easat-6229	71	9	offers	offer	VERB
easat-6229	71	10	a	a	DET
easat-6229	71	11	structured	structured	ADJ
easat-6229	71	12	approach	approach	NOUN
easat-6229	71	13	to	to	ADP
easat-6229	71	14	improving	improve	VERB
easat-6229	71	15	teaching	teaching	NOUN
easat-6229	71	16	practices	practice	NOUN
easat-6229	71	17	by	by	ADP
easat-6229	71	18	emphasizing	emphasize	VERB
easat-6229	71	19	the	the	DET
easat-6229	71	20	interaction	interaction	NOUN
easat-6229	71	21	between	between	ADP
easat-6229	71	22	different	different	ADJ
easat-6229	71	23	dimensions	dimension	NOUN
easat-6229	71	24	in	in	ADP
easat-6229	71	25	mathematics	mathematics	NOUN
easat-6229	71	26	activities	activity	NOUN
easat-6229	71	27	[	[	X
easat-6229	71	28	18	18	NUM
easat-6229	71	29	]	]	PUNCT
easat-6229	71	30	.	.	PUNCT
easat-6229	72	1	1242	1242	NUM
easat-6229	72	2	edelweiss	edelweiss	PROPN
easat-6229	72	3	applied	apply	VERB
easat-6229	72	4	science	science	NOUN
easat-6229	72	5	and	and	CCONJ
easat-6229	72	6	technology	technology	NOUN
easat-6229	72	7	issn	issn	PROPN
easat-6229	72	8	:	:	PUNCT
easat-6229	72	9	2576	2576	NUM
easat-6229	72	10	-	-	SYM
easat-6229	72	11	8484	8484	NUM
easat-6229	72	12	vol	vol	NOUN
easat-6229	72	13	.	.	PROPN
easat-6229	73	1	9	9	NUM
easat-6229	73	2	,	,	PUNCT
easat-6229	73	3	no	no	INTJ
easat-6229	73	4	.	.	NOUN
easat-6229	73	5	4	4	NUM
easat-6229	73	6	:	:	SYM
easat-6229	73	7	1240	1240	NUM
easat-6229	73	8	-	-	SYM
easat-6229	73	9	1251	1251	NUM
easat-6229	73	10	,	,	PUNCT
easat-6229	73	11	2025	2025	NUM
easat-6229	73	12	doi	doi	NOUN
easat-6229	73	13	:	:	PUNCT
easat-6229	73	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	73	15	©	©	ADP
easat-6229	73	16	2025	2025	NUM
easat-6229	73	17	by	by	ADP
easat-6229	73	18	the	the	DET
easat-6229	73	19	authors	author	NOUN
easat-6229	73	20	;	;	PUNCT
easat-6229	73	21	licensee	licensee	PROPN
easat-6229	73	22	learning	learning	NOUN
easat-6229	73	23	gate	gate	NOUN
easat-6229	73	24	based	base	VERB
easat-6229	73	25	on	on	ADP
easat-6229	73	26	the	the	DET
easat-6229	73	27	above	above	ADJ
easat-6229	73	28	proof	proof	ADJ
easat-6229	73	29	problem	problem	NOUN
easat-6229	73	30	,	,	PUNCT
easat-6229	73	31	students	student	NOUN
easat-6229	73	32	need	need	VERB
easat-6229	73	33	a	a	DET
easat-6229	73	34	supportive	supportive	ADJ
easat-6229	73	35	and	and	CCONJ
easat-6229	73	36	inclusive	inclusive	ADJ
easat-6229	73	37	learning	learn	VERB
easat-6229	73	38	environment	environment	NOUN
easat-6229	73	39	to	to	PART
easat-6229	73	40	enhance	enhance	VERB
easat-6229	73	41	their	their	PRON
easat-6229	73	42	evidentiary	evidentiary	ADJ
easat-6229	73	43	skills	skill	NOUN
easat-6229	73	44	.	.	PUNCT
easat-6229	74	1	a	a	DET
easat-6229	74	2	well	well	ADV
easat-6229	74	3	-	-	PUNCT
easat-6229	74	4	designed	design	VERB
easat-6229	74	5	learning	learning	NOUN
easat-6229	74	6	setting	set	VERB
easat-6229	74	7	encourages	encourage	VERB
easat-6229	74	8	students	student	NOUN
easat-6229	74	9	to	to	PART
easat-6229	74	10	identify	identify	VERB
easat-6229	74	11	patterns	pattern	NOUN
easat-6229	74	12	,	,	PUNCT
easat-6229	74	13	ask	ask	VERB
easat-6229	74	14	questions	question	NOUN
easat-6229	74	15	,	,	PUNCT
easat-6229	74	16	and	and	CCONJ
easat-6229	74	17	seek	seek	VERB
easat-6229	74	18	help	help	NOUN
easat-6229	74	19	when	when	SCONJ
easat-6229	74	20	necessary	necessary	ADJ
easat-6229	74	21	.	.	PUNCT
easat-6229	75	1	additionally	additionally	ADV
easat-6229	75	2	,	,	PUNCT
easat-6229	75	3	prior	prior	ADJ
easat-6229	75	4	knowledge	knowledge	NOUN
easat-6229	75	5	significantly	significantly	ADV
easat-6229	75	6	impacts	impact	VERB
easat-6229	75	7	student	student	NOUN
easat-6229	75	8	learning	learning	NOUN
easat-6229	75	9	in	in	ADP
easat-6229	75	10	the	the	DET
easat-6229	75	11	classroom	classroom	NOUN
easat-6229	75	12	baki	baki	PROPN
easat-6229	76	1	[	[	X
easat-6229	76	2	21	21	NUM
easat-6229	76	3	]	]	PUNCT
easat-6229	76	4	.	.	PUNCT
easat-6229	77	1	a	a	DET
easat-6229	77	2	caring	caring	ADJ
easat-6229	77	3	,	,	PUNCT
easat-6229	77	4	consistent	consistent	ADJ
easat-6229	77	5	,	,	PUNCT
easat-6229	77	6	and	and	CCONJ
easat-6229	77	7	inclusive	inclusive	ADJ
easat-6229	77	8	environment	environment	NOUN
easat-6229	77	9	is	be	AUX
easat-6229	77	10	essential	essential	ADJ
easat-6229	77	11	for	for	SCONJ
easat-6229	77	12	students	student	NOUN
easat-6229	77	13	to	to	PART
easat-6229	77	14	overcome	overcome	VERB
easat-6229	77	15	difficulties	difficulty	NOUN
easat-6229	77	16	,	,	PUNCT
easat-6229	77	17	take	take	VERB
easat-6229	77	18	risks	risk	NOUN
easat-6229	77	19	,	,	PUNCT
easat-6229	77	20	speak	speak	VERB
easat-6229	77	21	up	up	ADP
easat-6229	77	22	,	,	PUNCT
easat-6229	77	23	and	and	CCONJ
easat-6229	77	24	ask	ask	VERB
easat-6229	77	25	for	for	ADP
easat-6229	77	26	help	help	NOUN
easat-6229	77	27	.	.	PUNCT
easat-6229	77	28	"	"	PUNCT
easat-6229	78	1	the	the	DET
easat-6229	78	2	chosen	choose	VERB
easat-6229	78	3	learning	learning	NOUN
easat-6229	78	4	model	model	NOUN
easat-6229	78	5	must	must	AUX
easat-6229	78	6	meet	meet	VERB
easat-6229	78	7	the	the	DET
easat-6229	78	8	needs	need	NOUN
easat-6229	78	9	and	and	CCONJ
easat-6229	78	10	conditions	condition	NOUN
easat-6229	78	11	of	of	ADP
easat-6229	78	12	students	student	NOUN
easat-6229	78	13	[	[	X
easat-6229	78	14	22	22	NUM
easat-6229	78	15	]	]	PUNCT
easat-6229	78	16	.	.	PUNCT
easat-6229	79	1	a	a	DET
easat-6229	79	2	learning	learning	NOUN
easat-6229	79	3	model	model	NOUN
easat-6229	79	4	known	know	VERB
easat-6229	79	5	as	as	ADP
easat-6229	79	6	guided	guide	VERB
easat-6229	79	7	discovery	discovery	NOUN
easat-6229	79	8	learning	learning	NOUN
easat-6229	79	9	encourages	encourage	VERB
easat-6229	79	10	students	student	NOUN
easat-6229	79	11	to	to	PART
easat-6229	79	12	investigate	investigate	VERB
easat-6229	79	13	and	and	CCONJ
easat-6229	79	14	develop	develop	VERB
easat-6229	79	15	their	their	PRON
easat-6229	79	16	concepts	concept	NOUN
easat-6229	79	17	.	.	PUNCT
easat-6229	80	1	this	this	DET
easat-6229	80	2	model	model	NOUN
easat-6229	80	3	allows	allow	VERB
easat-6229	80	4	students	student	NOUN
easat-6229	80	5	to	to	PART
easat-6229	80	6	enhance	enhance	VERB
easat-6229	80	7	their	their	PRON
easat-6229	80	8	critical	critical	ADJ
easat-6229	80	9	problem	problem	NOUN
easat-6229	80	10	-	-	PUNCT
easat-6229	80	11	solving	solve	VERB
easat-6229	80	12	and	and	CCONJ
easat-6229	80	13	critical	critical	ADJ
easat-6229	80	14	thinking	thinking	NOUN
easat-6229	80	15	skills	skill	NOUN
easat-6229	80	16	,	,	PUNCT
easat-6229	80	17	with	with	ADP
easat-6229	80	18	lecturers	lecturer	NOUN
easat-6229	80	19	serving	serve	VERB
easat-6229	80	20	as	as	ADP
easat-6229	80	21	facilitators	facilitator	NOUN
easat-6229	80	22	who	who	PRON
easat-6229	80	23	analyze	analyze	VERB
easat-6229	80	24	the	the	DET
easat-6229	80	25	challenges	challenge	NOUN
easat-6229	80	26	students	student	NOUN
easat-6229	80	27	face	face	VERB
easat-6229	80	28	to	to	PART
easat-6229	80	29	help	help	VERB
easat-6229	80	30	them	they	PRON
easat-6229	80	31	solve	solve	VERB
easat-6229	80	32	problems	problem	NOUN
easat-6229	80	33	[	[	X
easat-6229	80	34	14	14	NUM
easat-6229	80	35	-	-	SYM
easat-6229	80	36	16	16	NUM
easat-6229	80	37	,	,	PUNCT
easat-6229	80	38	23	23	NUM
easat-6229	80	39	]	]	PUNCT
easat-6229	80	40	.	.	PUNCT
easat-6229	81	1	strategies	strategy	NOUN
easat-6229	81	2	are	be	AUX
easat-6229	81	3	essential	essential	ADJ
easat-6229	81	4	because	because	SCONJ
easat-6229	81	5	they	they	PRON
easat-6229	81	6	help	help	VERB
easat-6229	81	7	students	student	NOUN
easat-6229	81	8	manage	manage	VERB
easat-6229	81	9	their	their	PRON
easat-6229	81	10	thoughts	thought	NOUN
easat-6229	81	11	during	during	ADP
easat-6229	81	12	evidentiary	evidentiary	ADJ
easat-6229	81	13	activities	activity	NOUN
easat-6229	81	14	.	.	PUNCT
easat-6229	82	1	to	to	PART
easat-6229	82	2	maximize	maximize	VERB
easat-6229	82	3	the	the	DET
easat-6229	82	4	impact	impact	NOUN
easat-6229	82	5	on	on	ADP
easat-6229	82	6	learning	learn	VERB
easat-6229	82	7	objectives	objective	NOUN
easat-6229	82	8	,	,	PUNCT
easat-6229	82	9	evidence	evidence	NOUN
easat-6229	82	10	-	-	PUNCT
easat-6229	82	11	based	base	VERB
easat-6229	82	12	strategies	strategy	NOUN
easat-6229	82	13	must	must	AUX
easat-6229	82	14	be	be	AUX
easat-6229	82	15	carefully	carefully	ADV
easat-6229	82	16	selected	select	VERB
easat-6229	82	17	[	[	PUNCT
easat-6229	82	18	24	24	NUM
easat-6229	82	19	]	]	PUNCT
easat-6229	82	20	.	.	PUNCT
easat-6229	83	1	this	this	DET
easat-6229	83	2	study	study	NOUN
easat-6229	83	3	employs	employ	VERB
easat-6229	83	4	the	the	DET
easat-6229	83	5	mathematical	mathematical	ADJ
easat-6229	83	6	working	working	NOUN
easat-6229	83	7	space	space	NOUN
easat-6229	83	8	strategy	strategy	NOUN
easat-6229	83	9	,	,	PUNCT
easat-6229	83	10	which	which	PRON
easat-6229	83	11	incorporates	incorporate	VERB
easat-6229	83	12	semiotics	semiotic	NOUN
easat-6229	83	13	to	to	PART
easat-6229	83	14	connect	connect	VERB
easat-6229	83	15	representations	representation	NOUN
easat-6229	83	16	that	that	PRON
easat-6229	83	17	visualize	visualize	VERB
easat-6229	83	18	mathematical	mathematical	ADJ
easat-6229	83	19	problems	problem	NOUN
easat-6229	83	20	.	.	PUNCT
easat-6229	84	1	the	the	DET
easat-6229	84	2	instrumental	instrumental	ADJ
easat-6229	84	3	origin	origin	NOUN
easat-6229	84	4	represents	represent	VERB
easat-6229	84	5	the	the	DET
easat-6229	84	6	stage	stage	NOUN
easat-6229	84	7	where	where	SCONJ
easat-6229	84	8	the	the	DET
easat-6229	84	9	knowledge	knowledge	NOUN
easat-6229	84	10	gathered	gather	VERB
easat-6229	84	11	can	can	AUX
easat-6229	84	12	be	be	AUX
easat-6229	84	13	utilized	utilize	VERB
easat-6229	84	14	to	to	PART
easat-6229	84	15	construct	construct	VERB
easat-6229	84	16	evidence	evidence	NOUN
easat-6229	84	17	.	.	PUNCT
easat-6229	85	1	when	when	SCONJ
easat-6229	85	2	this	this	DET
easat-6229	85	3	evidence	evidence	NOUN
easat-6229	85	4	is	be	AUX
easat-6229	85	5	validated	validate	VERB
easat-6229	85	6	,	,	PUNCT
easat-6229	85	7	it	it	PRON
easat-6229	85	8	is	be	AUX
easat-6229	85	9	referred	refer	VERB
easat-6229	85	10	to	to	ADP
easat-6229	85	11	as	as	ADP
easat-6229	85	12	genesis	genesis	PROPN
easat-6229	85	13	[	[	X
easat-6229	85	14	17	17	NUM
easat-6229	85	15	,	,	PUNCT
easat-6229	85	16	25	25	NUM
easat-6229	85	17	,	,	PUNCT
easat-6229	85	18	26	26	NUM
easat-6229	85	19	]	]	PUNCT
easat-6229	85	20	.	.	PUNCT
easat-6229	86	1	the	the	DET
easat-6229	86	2	discussion	discussion	NOUN
easat-6229	86	3	material	material	NOUN
easat-6229	86	4	worksheet	worksheet	NOUN
easat-6229	86	5	serves	serve	VERB
easat-6229	86	6	as	as	ADP
easat-6229	86	7	a	a	DET
easat-6229	86	8	vital	vital	ADJ
easat-6229	86	9	learning	learning	NOUN
easat-6229	86	10	tool	tool	NOUN
easat-6229	86	11	in	in	ADP
easat-6229	86	12	this	this	DET
easat-6229	86	13	study	study	NOUN
easat-6229	86	14	.	.	PUNCT
easat-6229	87	1	this	this	DET
easat-6229	87	2	worksheet	worksheet	NOUN
easat-6229	87	3	employs	employ	VERB
easat-6229	87	4	the	the	DET
easat-6229	87	5	mathematical	mathematical	ADJ
easat-6229	87	6	working	working	NOUN
easat-6229	87	7	space	space	NOUN
easat-6229	87	8	strategy	strategy	NOUN
easat-6229	87	9	,	,	PUNCT
easat-6229	87	10	which	which	PRON
easat-6229	87	11	includes	include	VERB
easat-6229	87	12	sequence	sequence	NOUN
easat-6229	87	13	material	material	NOUN
easat-6229	87	14	[	[	X
easat-6229	87	15	27	27	NUM
easat-6229	87	16	]	]	PUNCT
easat-6229	87	17	.	.	PUNCT
easat-6229	88	1	the	the	DET
easat-6229	88	2	content	content	NOUN
easat-6229	88	3	utilized	utilize	VERB
easat-6229	88	4	in	in	ADP
easat-6229	88	5	this	this	DET
easat-6229	88	6	paper	paper	NOUN
easat-6229	88	7	is	be	AUX
easat-6229	88	8	derived	derive	VERB
easat-6229	88	9	from	from	ADP
easat-6229	88	10	comprehensive	comprehensive	ADJ
easat-6229	88	11	semiotic	semiotic	ADJ
easat-6229	88	12	sources	source	NOUN
easat-6229	88	13	[	[	X
easat-6229	88	14	28	28	NUM
easat-6229	88	15	]	]	PUNCT
easat-6229	88	16	.	.	PUNCT
easat-6229	89	1	the	the	DET
easat-6229	89	2	worksheet	worksheet	NOUN
easat-6229	89	3	encompasses	encompass	VERB
easat-6229	89	4	the	the	DET
easat-6229	89	5	background	background	NOUN
easat-6229	89	6	,	,	PUNCT
easat-6229	89	7	core	core	NOUN
easat-6229	89	8	concepts	concept	NOUN
easat-6229	89	9	,	,	PUNCT
easat-6229	89	10	and	and	CCONJ
easat-6229	89	11	attributes	attribute	NOUN
easat-6229	89	12	of	of	ADP
easat-6229	89	13	each	each	DET
easat-6229	89	14	available	available	ADJ
easat-6229	89	15	definition	definition	NOUN
easat-6229	89	16	.	.	PUNCT
easat-6229	90	1	subsequently	subsequently	ADV
easat-6229	90	2	,	,	PUNCT
easat-6229	90	3	through	through	ADP
easat-6229	90	4	group	group	NOUN
easat-6229	90	5	discussions	discussion	NOUN
easat-6229	90	6	,	,	PUNCT
easat-6229	90	7	students	student	NOUN
easat-6229	90	8	are	be	AUX
easat-6229	90	9	required	require	VERB
easat-6229	90	10	to	to	PART
easat-6229	90	11	interpret	interpret	VERB
easat-6229	90	12	each	each	DET
easat-6229	90	13	definition	definition	NOUN
easat-6229	90	14	in	in	ADP
easat-6229	90	15	language	language	NOUN
easat-6229	90	16	that	that	PRON
easat-6229	90	17	is	be	AUX
easat-6229	90	18	easy	easy	ADJ
easat-6229	90	19	to	to	PART
easat-6229	90	20	understand	understand	VERB
easat-6229	90	21	.	.	PUNCT
easat-6229	91	1	furthermore	furthermore	ADV
easat-6229	91	2	,	,	PUNCT
easat-6229	91	3	every	every	DET
easat-6229	91	4	lemma	lemma	PROPN
easat-6229	91	5	,	,	PUNCT
easat-6229	91	6	theorem	theorem	VERB
easat-6229	91	7	,	,	PUNCT
easat-6229	91	8	or	or	CCONJ
easat-6229	91	9	proof	proof	NOUN
easat-6229	91	10	problem	problem	NOUN
easat-6229	91	11	incorporates	incorporate	VERB
easat-6229	91	12	a	a	DET
easat-6229	91	13	semiotic	semiotic	ADJ
easat-6229	91	14	,	,	PUNCT
easat-6229	91	15	instrumental	instrumental	ADJ
easat-6229	91	16	,	,	PUNCT
easat-6229	91	17	and	and	CCONJ
easat-6229	91	18	discursive	discursive	ADJ
easat-6229	91	19	foundation	foundation	NOUN
easat-6229	91	20	.	.	PUNCT
easat-6229	92	1	the	the	DET
easat-6229	92	2	discussion	discussion	NOUN
easat-6229	92	3	material	material	NOUN
easat-6229	92	4	worksheet	worksheet	NOUN
easat-6229	92	5	is	be	AUX
easat-6229	92	6	specifically	specifically	ADV
easat-6229	92	7	designed	design	VERB
easat-6229	92	8	to	to	PART
easat-6229	92	9	aid	aid	VERB
easat-6229	92	10	students	student	NOUN
easat-6229	92	11	in	in	ADP
easat-6229	92	12	learning	learn	VERB
easat-6229	92	13	real	real	ADJ
easat-6229	92	14	analysis	analysis	NOUN
easat-6229	92	15	.	.	PUNCT
easat-6229	93	1	mathematical	mathematical	ADJ
easat-6229	93	2	research	research	NOUN
easat-6229	93	3	related	relate	VERB
easat-6229	93	4	to	to	ADP
easat-6229	93	5	proof	proof	NOUN
easat-6229	93	6	and	and	CCONJ
easat-6229	93	7	learning	learn	VERB
easat-6229	93	8	using	use	VERB
easat-6229	93	9	the	the	DET
easat-6229	93	10	mathematical	mathematical	ADJ
easat-6229	93	11	working	working	NOUN
easat-6229	93	12	space	space	NOUN
easat-6229	93	13	strategy	strategy	NOUN
easat-6229	93	14	has	have	AUX
easat-6229	93	15	demonstrated	demonstrate	VERB
easat-6229	93	16	success	success	NOUN
easat-6229	93	17	.	.	PUNCT
easat-6229	94	1	for	for	ADP
easat-6229	94	2	instance	instance	NOUN
easat-6229	94	3	,	,	PUNCT
easat-6229	94	4	found	find	VERB
easat-6229	94	5	positive	positive	ADJ
easat-6229	94	6	outcomes	outcome	NOUN
easat-6229	94	7	in	in	ADP
easat-6229	94	8	evidentiary	evidentiary	ADJ
easat-6229	94	9	problems	problem	NOUN
easat-6229	94	10	in	in	ADP
easat-6229	94	11	geometry	geometry	NOUN
easat-6229	94	12	gómez	gómez	NOUN
easat-6229	94	13	-	-	PUNCT
easat-6229	94	14	chacón	chacón	PROPN
easat-6229	94	15	and	and	CCONJ
easat-6229	94	16	kuzniak	kuzniak	PROPN
easat-6229	95	1	[	[	X
easat-6229	95	2	18	18	NUM
easat-6229	95	3	]	]	PUNCT
easat-6229	95	4	applied	apply	VERB
easat-6229	95	5	this	this	DET
easat-6229	95	6	strategy	strategy	NOUN
easat-6229	95	7	in	in	ADP
easat-6229	95	8	evidentiary	evidentiary	ADJ
easat-6229	95	9	research	research	NOUN
easat-6229	95	10	on	on	ADP
easat-6229	95	11	functional	functional	ADJ
easat-6229	95	12	problems	problem	NOUN
easat-6229	95	13	minh	minh	ADV
easat-6229	95	14	and	and	CCONJ
easat-6229	95	15	lagrange	lagrange	PROPN
easat-6229	95	16	[	[	X
easat-6229	95	17	29	29	NUM
easat-6229	95	18	]	]	PUNCT
easat-6229	95	19	and	and	CCONJ
easat-6229	95	20	reported	report	VERB
easat-6229	95	21	success	success	NOUN
easat-6229	95	22	in	in	ADP
easat-6229	95	23	the	the	DET
easat-6229	95	24	study	study	NOUN
easat-6229	95	25	of	of	ADP
easat-6229	95	26	histogram	histogram	NOUN
easat-6229	95	27	problems	problem	NOUN
easat-6229	95	28	derouet	derouet	VERB
easat-6229	95	29	and	and	CCONJ
easat-6229	95	30	parzysz	parzysz	NOUN
easat-6229	95	31	[	[	X
easat-6229	95	32	28	28	NUM
easat-6229	95	33	]	]	PUNCT
easat-6229	95	34	noting	note	VERB
easat-6229	95	35	that	that	SCONJ
easat-6229	95	36	its	its	PRON
easat-6229	95	37	application	application	NOUN
easat-6229	95	38	helps	help	VERB
easat-6229	95	39	students	student	NOUN
easat-6229	95	40	improve	improve	VERB
easat-6229	95	41	their	their	PRON
easat-6229	95	42	creative	creative	ADJ
easat-6229	95	43	reasoning	reasoning	NOUN
easat-6229	95	44	and	and	CCONJ
easat-6229	95	45	successfully	successfully	ADV
easat-6229	95	46	solve	solve	VERB
easat-6229	95	47	mathematical	mathematical	ADJ
easat-6229	95	48	problems	problem	NOUN
easat-6229	95	49	[	[	X
easat-6229	95	50	28	28	NUM
easat-6229	95	51	,	,	PUNCT
easat-6229	95	52	30	30	NUM
easat-6229	95	53	-	-	SYM
easat-6229	95	54	34	34	NUM
easat-6229	95	55	]	]	PUNCT
easat-6229	95	56	.	.	PUNCT
easat-6229	96	1	therefore	therefore	ADV
easat-6229	96	2	,	,	PUNCT
easat-6229	96	3	it	it	PRON
easat-6229	96	4	is	be	AUX
easat-6229	96	5	evident	evident	ADJ
easat-6229	96	6	that	that	SCONJ
easat-6229	96	7	there	there	PRON
easat-6229	96	8	are	be	VERB
easat-6229	96	9	distinctions	distinction	NOUN
easat-6229	96	10	between	between	ADP
easat-6229	96	11	previous	previous	ADJ
easat-6229	96	12	research	research	NOUN
easat-6229	96	13	and	and	CCONJ
easat-6229	96	14	the	the	DET
easat-6229	96	15	current	current	ADJ
easat-6229	96	16	study	study	NOUN
easat-6229	96	17	,	,	PUNCT
easat-6229	96	18	particularly	particularly	ADV
easat-6229	96	19	as	as	SCONJ
easat-6229	96	20	this	this	DET
easat-6229	96	21	research	research	NOUN
easat-6229	96	22	examines	examine	VERB
easat-6229	96	23	the	the	DET
easat-6229	96	24	evidentiary	evidentiary	ADJ
easat-6229	96	25	process	process	NOUN
easat-6229	96	26	in	in	ADP
easat-6229	96	27	real	real	ADJ
easat-6229	96	28	analysis	analysis	NOUN
easat-6229	96	29	through	through	ADP
easat-6229	96	30	the	the	DET
easat-6229	96	31	stages	stage	NOUN
easat-6229	96	32	of	of	ADP
easat-6229	96	33	visualization	visualization	NOUN
easat-6229	96	34	,	,	PUNCT
easat-6229	96	35	construction	construction	NOUN
easat-6229	96	36	,	,	PUNCT
easat-6229	96	37	and	and	CCONJ
easat-6229	96	38	validation	validation	NOUN
easat-6229	96	39	to	to	PART
easat-6229	96	40	optimize	optimize	VERB
easat-6229	96	41	the	the	DET
easat-6229	96	42	development	development	NOUN
easat-6229	96	43	of	of	ADP
easat-6229	96	44	proof	proof	NOUN
easat-6229	96	45	skills	skill	NOUN
easat-6229	96	46	in	in	ADP
easat-6229	96	47	real	real	ADJ
easat-6229	96	48	analysis	analysis	NOUN
easat-6229	96	49	lectures	lecture	NOUN
easat-6229	96	50	,	,	PUNCT
easat-6229	96	51	research	research	NOUN
easat-6229	96	52	must	must	AUX
easat-6229	96	53	be	be	AUX
easat-6229	96	54	conducted	conduct	VERB
easat-6229	96	55	.	.	PUNCT
easat-6229	97	1	additionally	additionally	ADV
easat-6229	97	2	,	,	PUNCT
easat-6229	97	3	to	to	PART
easat-6229	97	4	assess	assess	VERB
easat-6229	97	5	the	the	DET
easat-6229	97	6	ability	ability	NOUN
easat-6229	97	7	of	of	ADP
easat-6229	97	8	prospective	prospective	ADJ
easat-6229	97	9	mathematics	mathematic	NOUN
easat-6229	97	10	teachers	teacher	NOUN
easat-6229	97	11	to	to	PART
easat-6229	97	12	solve	solve	VERB
easat-6229	97	13	mathematical	mathematical	ADJ
easat-6229	97	14	proof	proof	NOUN
easat-6229	97	15	problems	problem	NOUN
easat-6229	97	16	,	,	PUNCT
easat-6229	97	17	qualitative	qualitative	ADJ
easat-6229	97	18	research	research	NOUN
easat-6229	97	19	was	be	AUX
easat-6229	97	20	carried	carry	VERB
easat-6229	97	21	out	out	ADP
easat-6229	97	22	involving	involve	VERB
easat-6229	97	23	several	several	ADJ
easat-6229	97	24	mathematics	mathematic	NOUN
easat-6229	97	25	teacher	teacher	NOUN
easat-6229	97	26	candidates	candidate	NOUN
easat-6229	97	27	.	.	PUNCT
easat-6229	98	1	this	this	DET
easat-6229	98	2	research	research	NOUN
easat-6229	98	3	aims	aim	VERB
easat-6229	98	4	to	to	PART
easat-6229	98	5	enhance	enhance	VERB
easat-6229	98	6	the	the	DET
easat-6229	98	7	mathematical	mathematical	ADJ
easat-6229	98	8	proof	proof	NOUN
easat-6229	98	9	abilities	ability	NOUN
easat-6229	98	10	of	of	ADP
easat-6229	98	11	prospective	prospective	ADJ
easat-6229	98	12	mathematics	mathematic	NOUN
easat-6229	98	13	teachers	teacher	NOUN
easat-6229	98	14	in	in	ADP
easat-6229	98	15	completing	complete	VERB
easat-6229	98	16	the	the	DET
easat-6229	98	17	process	process	NOUN
easat-6229	98	18	of	of	ADP
easat-6229	98	19	proving	prove	VERB
easat-6229	98	20	sequence	sequence	NOUN
easat-6229	98	21	material	material	NOUN
easat-6229	98	22	within	within	ADP
easat-6229	98	23	the	the	DET
easat-6229	98	24	real	real	ADJ
easat-6229	98	25	analysis	analysis	NOUN
easat-6229	98	26	course	course	NOUN
easat-6229	98	27	by	by	ADP
easat-6229	98	28	utilizing	utilize	VERB
easat-6229	98	29	the	the	DET
easat-6229	98	30	guided	guide	VERB
easat-6229	98	31	discovery	discovery	NOUN
easat-6229	98	32	learning	learning	NOUN
easat-6229	98	33	model	model	NOUN
easat-6229	98	34	and	and	CCONJ
easat-6229	98	35	the	the	DET
easat-6229	98	36	mathematical	mathematical	ADJ
easat-6229	98	37	working	working	NOUN
easat-6229	98	38	space	space	NOUN
easat-6229	98	39	strategy	strategy	NOUN
easat-6229	98	40	.	.	PUNCT
easat-6229	99	1	2	2	X
easat-6229	99	2	.	.	X
easat-6229	99	3	method	method	PROPN
easat-6229	99	4	2.1	2.1	NUM
easat-6229	99	5	.	.	PUNCT
easat-6229	100	1	research	research	NOUN
easat-6229	100	2	design	design	VERB
easat-6229	100	3	a	a	DET
easat-6229	100	4	qualitative	qualitative	ADJ
easat-6229	100	5	approach	approach	NOUN
easat-6229	100	6	is	be	AUX
easat-6229	100	7	employed	employ	VERB
easat-6229	100	8	in	in	ADP
easat-6229	100	9	this	this	DET
easat-6229	100	10	study	study	NOUN
easat-6229	100	11	to	to	PART
easat-6229	100	12	examine	examine	VERB
easat-6229	100	13	the	the	DET
easat-6229	100	14	ability	ability	NOUN
easat-6229	100	15	of	of	ADP
easat-6229	100	16	prospective	prospective	ADJ
easat-6229	100	17	mathematics	mathematic	NOUN
easat-6229	100	18	teachers	teacher	NOUN
easat-6229	100	19	to	to	PART
easat-6229	100	20	solve	solve	VERB
easat-6229	100	21	proof	proof	NOUN
easat-6229	100	22	problems	problem	NOUN
easat-6229	100	23	related	relate	VERB
easat-6229	100	24	to	to	ADP
easat-6229	100	25	sequence	sequence	NOUN
easat-6229	100	26	material	material	NOUN
easat-6229	100	27	in	in	ADP
easat-6229	100	28	the	the	DET
easat-6229	100	29	real	real	ADJ
easat-6229	100	30	analysis	analysis	NOUN
easat-6229	100	31	course	course	NOUN
easat-6229	100	32	.	.	PUNCT
easat-6229	101	1	an	an	DET
easat-6229	101	2	experimental	experimental	ADJ
easat-6229	101	3	design	design	NOUN
easat-6229	101	4	is	be	AUX
easat-6229	101	5	utilized	utilize	VERB
easat-6229	101	6	for	for	ADP
easat-6229	101	7	the	the	DET
easat-6229	101	8	research	research	NOUN
easat-6229	101	9	.	.	PUNCT
easat-6229	102	1	the	the	DET
easat-6229	102	2	focus	focus	NOUN
easat-6229	102	3	of	of	ADP
easat-6229	102	4	this	this	DET
easat-6229	102	5	study	study	NOUN
easat-6229	102	6	is	be	AUX
easat-6229	102	7	on	on	ADP
easat-6229	102	8	three	three	NUM
easat-6229	102	9	subjects	subject	NOUN
easat-6229	102	10	who	who	PRON
easat-6229	102	11	are	be	AUX
easat-6229	102	12	considered	consider	VERB
easat-6229	102	13	to	to	PART
easat-6229	102	14	meet	meet	VERB
easat-6229	102	15	the	the	DET
easat-6229	102	16	objectives	objective	NOUN
easat-6229	102	17	of	of	ADP
easat-6229	102	18	the	the	DET
easat-6229	102	19	research	research	NOUN
easat-6229	102	20	.	.	PUNCT
easat-6229	103	1	2.2	2.2	NUM
easat-6229	103	2	.	.	PUNCT
easat-6229	104	1	research	research	NOUN
easat-6229	104	2	subject	subject	NOUN
easat-6229	104	3	this	this	DET
easat-6229	104	4	research	research	NOUN
easat-6229	104	5	involved	involve	VERB
easat-6229	104	6	27	27	NUM
easat-6229	104	7	strata	strata	NOUN
easat-6229	104	8	one	one	NUM
easat-6229	104	9	mathematics	mathematic	NOUN
easat-6229	104	10	education	education	NOUN
easat-6229	104	11	students	student	NOUN
easat-6229	104	12	who	who	PRON
easat-6229	104	13	were	be	AUX
easat-6229	104	14	enrolled	enrol	VERB
easat-6229	104	15	in	in	ADP
easat-6229	104	16	the	the	DET
easat-6229	104	17	real	real	ADJ
easat-6229	104	18	analysis	analysis	NOUN
easat-6229	104	19	course	course	NOUN
easat-6229	104	20	.	.	PUNCT
easat-6229	105	1	after	after	SCONJ
easat-6229	105	2	the	the	DET
easat-6229	105	3	students	student	NOUN
easat-6229	105	4	learned	learn	VERB
easat-6229	105	5	the	the	DET
easat-6229	105	6	material	material	NOUN
easat-6229	105	7	in	in	ADP
easat-6229	105	8	sequence	sequence	NOUN
easat-6229	105	9	for	for	ADP
easat-6229	105	10	six	six	NUM
easat-6229	105	11	meetings	meeting	NOUN
easat-6229	105	12	,	,	PUNCT
easat-6229	105	13	a	a	DET
easat-6229	105	14	test	test	NOUN
easat-6229	105	15	was	be	AUX
easat-6229	105	16	conducted	conduct	VERB
easat-6229	105	17	in	in	ADP
easat-6229	105	18	the	the	DET
easat-6229	105	19	seventh	seventh	ADJ
easat-6229	105	20	meeting	meeting	NOUN
easat-6229	105	21	to	to	PART
easat-6229	105	22	measure	measure	VERB
easat-6229	105	23	their	their	PRON
easat-6229	105	24	proof	proof	ADJ
easat-6229	105	25	abilities	ability	NOUN
easat-6229	105	26	.	.	PUNCT
easat-6229	106	1	based	base	VERB
easat-6229	106	2	on	on	ADP
easat-6229	106	3	the	the	DET
easat-6229	106	4	test	test	NOUN
easat-6229	106	5	results	result	NOUN
easat-6229	106	6	,	,	PUNCT
easat-6229	106	7	the	the	DET
easat-6229	106	8	students	student	NOUN
easat-6229	106	9	1243	1243	NUM
easat-6229	106	10	edelweiss	edelweiss	PROPN
easat-6229	106	11	applied	apply	VERB
easat-6229	106	12	science	science	NOUN
easat-6229	106	13	and	and	CCONJ
easat-6229	106	14	technology	technology	NOUN
easat-6229	106	15	issn	issn	PROPN
easat-6229	106	16	:	:	PUNCT
easat-6229	106	17	2576	2576	NUM
easat-6229	106	18	-	-	SYM
easat-6229	106	19	8484	8484	NUM
easat-6229	106	20	vol	vol	NOUN
easat-6229	106	21	.	.	PROPN
easat-6229	107	1	9	9	NUM
easat-6229	107	2	,	,	PUNCT
easat-6229	107	3	no	no	INTJ
easat-6229	107	4	.	.	NOUN
easat-6229	107	5	4	4	NUM
easat-6229	107	6	:	:	SYM
easat-6229	107	7	1240	1240	NUM
easat-6229	107	8	-	-	SYM
easat-6229	107	9	1251	1251	NUM
easat-6229	107	10	,	,	PUNCT
easat-6229	107	11	2025	2025	NUM
easat-6229	107	12	doi	doi	NOUN
easat-6229	107	13	:	:	PUNCT
easat-6229	107	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	107	15	©	©	ADP
easat-6229	107	16	2025	2025	NUM
easat-6229	107	17	by	by	ADP
easat-6229	107	18	the	the	DET
easat-6229	107	19	authors	author	NOUN
easat-6229	107	20	;	;	PUNCT
easat-6229	107	21	licensee	licensee	PROPN
easat-6229	107	22	learning	learning	NOUN
easat-6229	107	23	gate	gate	NOUN
easat-6229	107	24	were	be	AUX
easat-6229	107	25	categorized	categorize	VERB
easat-6229	107	26	into	into	ADP
easat-6229	107	27	three	three	NUM
easat-6229	107	28	groups	group	NOUN
easat-6229	107	29	:	:	PUNCT
easat-6229	107	30	very	very	ADV
easat-6229	107	31	good	good	ADJ
easat-6229	107	32	(	(	PUNCT
easat-6229	107	33	l	l	NOUN
easat-6229	107	34	)	)	PUNCT
easat-6229	107	35	,	,	PUNCT
easat-6229	107	36	medium	medium	NOUN
easat-6229	107	37	(	(	PUNCT
easat-6229	107	38	m	m	NOUN
easat-6229	107	39	)	)	PUNCT
easat-6229	107	40	,	,	PUNCT
easat-6229	107	41	and	and	CCONJ
easat-6229	107	42	poor	poor	ADJ
easat-6229	107	43	(	(	PUNCT
easat-6229	107	44	s	s	NOUN
easat-6229	107	45	)	)	PUNCT
easat-6229	107	46	.	.	PUNCT
easat-6229	108	1	three	three	NUM
easat-6229	108	2	students	student	NOUN
easat-6229	108	3	from	from	ADP
easat-6229	108	4	each	each	DET
easat-6229	108	5	group	group	NOUN
easat-6229	108	6	were	be	AUX
easat-6229	108	7	randomly	randomly	ADV
easat-6229	108	8	selected	select	VERB
easat-6229	108	9	.	.	PUNCT
easat-6229	109	1	the	the	DET
easat-6229	109	2	lecturer	lecturer	NOUN
easat-6229	109	3	then	then	ADV
easat-6229	109	4	recommended	recommend	VERB
easat-6229	109	5	five	five	NUM
easat-6229	109	6	students	student	NOUN
easat-6229	109	7	out	out	ADP
easat-6229	109	8	of	of	ADP
easat-6229	109	9	the	the	DET
easat-6229	109	10	nine	nine	NUM
easat-6229	109	11	selected	select	VERB
easat-6229	109	12	,	,	PUNCT
easat-6229	109	13	but	but	CCONJ
easat-6229	109	14	only	only	ADV
easat-6229	109	15	three	three	NUM
easat-6229	109	16	l2	l2	NOUN
easat-6229	109	17	,	,	PUNCT
easat-6229	109	18	m5	m5	NOUN
easat-6229	109	19	,	,	PUNCT
easat-6229	109	20	and	and	CCONJ
easat-6229	109	21	s3	s3	PROPN
easat-6229	109	22	students	student	NOUN
easat-6229	109	23	were	be	AUX
easat-6229	109	24	willing	willing	ADJ
easat-6229	109	25	to	to	PART
easat-6229	109	26	take	take	VERB
easat-6229	109	27	part	part	NOUN
easat-6229	109	28	in	in	ADP
easat-6229	109	29	the	the	DET
easat-6229	109	30	research	research	NOUN
easat-6229	109	31	.	.	PUNCT
easat-6229	110	1	2.3	2.3	NUM
easat-6229	110	2	.	.	PUNCT
easat-6229	110	3	data	datum	NOUN
easat-6229	110	4	collection	collection	NOUN
easat-6229	110	5	data	datum	NOUN
easat-6229	110	6	on	on	ADP
easat-6229	110	7	mathematical	mathematical	ADJ
easat-6229	110	8	proof	proof	NOUN
easat-6229	110	9	ability	ability	NOUN
easat-6229	110	10	were	be	AUX
easat-6229	110	11	collected	collect	VERB
easat-6229	110	12	through	through	ADP
easat-6229	110	13	semi	semi	ADJ
easat-6229	110	14	-	-	ADJ
easat-6229	110	15	structured	structured	ADJ
easat-6229	110	16	tests	test	NOUN
easat-6229	110	17	and	and	CCONJ
easat-6229	110	18	interviews	interview	NOUN
easat-6229	110	19	.	.	PUNCT
easat-6229	111	1	the	the	DET
easat-6229	111	2	test	test	NOUN
easat-6229	111	3	consists	consist	VERB
easat-6229	111	4	of	of	ADP
easat-6229	111	5	six	six	NUM
easat-6229	111	6	descriptive	descriptive	ADJ
easat-6229	111	7	questions	question	NOUN
easat-6229	111	8	that	that	PRON
easat-6229	111	9	address	address	VERB
easat-6229	111	10	the	the	DET
easat-6229	111	11	following	follow	VERB
easat-6229	111	12	topics	topic	NOUN
easat-6229	111	13	:	:	PUNCT
easat-6229	111	14	the	the	DET
easat-6229	111	15	limit	limit	NOUN
easat-6229	111	16	of	of	ADP
easat-6229	111	17	a	a	DET
easat-6229	111	18	sequence	sequence	NOUN
easat-6229	111	19	,	,	PUNCT
easat-6229	111	20	the	the	DET
easat-6229	111	21	squeeze	squeeze	NOUN
easat-6229	111	22	theorem	theorem	NOUN
easat-6229	111	23	,	,	PUNCT
easat-6229	111	24	sequence	sequence	NOUN
easat-6229	111	25	ratios	ratio	NOUN
easat-6229	111	26	,	,	PUNCT
easat-6229	111	27	monotone	monotone	ADJ
easat-6229	111	28	sequences	sequence	NOUN
easat-6229	111	29	,	,	PUNCT
easat-6229	111	30	subsequences	subsequence	NOUN
easat-6229	111	31	,	,	PUNCT
easat-6229	111	32	and	and	CCONJ
easat-6229	111	33	cauchy	cauchy	ADJ
easat-6229	111	34	sequences	sequence	NOUN
easat-6229	111	35	.	.	PUNCT
easat-6229	112	1	then	then	ADV
easat-6229	112	2	three	three	NUM
easat-6229	112	3	subjects	subject	NOUN
easat-6229	112	4	were	be	AUX
easat-6229	112	5	selected	select	VERB
easat-6229	112	6	for	for	ADP
easat-6229	112	7	the	the	DET
easat-6229	112	8	interview	interview	NOUN
easat-6229	112	9	.	.	PUNCT
easat-6229	113	1	tests	test	NOUN
easat-6229	113	2	were	be	AUX
easat-6229	113	3	administered	administer	VERB
easat-6229	113	4	to	to	PART
easat-6229	113	5	assess	assess	VERB
easat-6229	113	6	students	student	NOUN
easat-6229	113	7	'	'	PART
easat-6229	113	8	abilities	ability	NOUN
easat-6229	113	9	in	in	ADP
easat-6229	113	10	completing	complete	VERB
easat-6229	113	11	the	the	DET
easat-6229	113	12	evidentiary	evidentiary	ADJ
easat-6229	113	13	process	process	NOUN
easat-6229	113	14	.	.	PUNCT
easat-6229	114	1	the	the	DET
easat-6229	114	2	criteria	criterion	NOUN
easat-6229	114	3	for	for	ADP
easat-6229	114	4	evaluating	evaluate	VERB
easat-6229	114	5	students	student	NOUN
easat-6229	114	6	'	'	PART
easat-6229	114	7	abilities	ability	NOUN
easat-6229	114	8	in	in	ADP
easat-6229	114	9	solving	solve	VERB
easat-6229	114	10	evidentiary	evidentiary	NOUN
easat-6229	114	11	problems	problem	NOUN
easat-6229	114	12	are	be	AUX
easat-6229	114	13	presented	present	VERB
easat-6229	114	14	in	in	ADP
easat-6229	114	15	table	table	NOUN
easat-6229	114	16	1	1	NUM
easat-6229	114	17	below	below	ADV
easat-6229	114	18	.	.	PUNCT
easat-6229	115	1	table	table	NOUN
easat-6229	115	2	1	1	NUM
easat-6229	115	3	.	.	PUNCT
easat-6229	115	4	criteria	criterion	NOUN
easat-6229	115	5	for	for	ADP
easat-6229	115	6	proof	proof	NOUN
easat-6229	115	7	.	.	PUNCT
easat-6229	116	1	number	number	NOUN
easat-6229	116	2	rumus	rumus	NOUN
easat-6229	116	3	criterion	criterion	NOUN
easat-6229	116	4	1	1	NUM
easat-6229	116	5	.	.	PUNCT
easat-6229	117	1	𝑥	𝑥	PRON
easat-6229	117	2	≥	≥	NUM
easat-6229	117	3	�	�	NOUN
easat-6229	117	4	̅	̅	NOUN
easat-6229	117	5	�	�	NOUN
easat-6229	117	6	+	+	CCONJ
easat-6229	117	7	𝑑.	𝑑.	NOUN
easat-6229	117	8	𝑠	𝑠	X
easat-6229	117	9	tall	tall	ADJ
easat-6229	117	10	(	(	PUNCT
easat-6229	117	11	l	l	NOUN
easat-6229	117	12	)	)	PUNCT
easat-6229	117	13	2	2	NUM
easat-6229	117	14	�	�	NOUN
easat-6229	117	15	̅	̅	NOUN
easat-6229	117	16	�	�	NOUN
easat-6229	117	17	−	−	NOUN
easat-6229	117	18	𝑠.	𝑠.	NOUN
easat-6229	117	19	𝑑	𝑑	NOUN
easat-6229	117	20	≤	≤	NUM
easat-6229	117	21	𝑥	𝑥	ADP
easat-6229	117	22	<	<	X
easat-6229	117	23	�	�	PROPN
easat-6229	117	24	̅	̅	NOUN
easat-6229	117	25	�	�	NOUN
easat-6229	117	26	+	+	CCONJ
easat-6229	117	27	𝑑.	𝑑.	NOUN
easat-6229	117	28	𝑠	𝑠	AUX
easat-6229	117	29	keep	keep	VERB
easat-6229	117	30	(	(	PUNCT
easat-6229	117	31	m	m	NOUN
easat-6229	117	32	)	)	PUNCT
easat-6229	117	33	3	3	NUM
easat-6229	117	34	𝑥	𝑥	PROPN
easat-6229	117	35	≤	≤	NUM
easat-6229	117	36	�	�	NOUN
easat-6229	117	37	̅	̅	NOUN
easat-6229	117	38	�	�	NOUN
easat-6229	117	39	−	−	PROPN
easat-6229	117	40	𝑑.	𝑑.	NOUN
easat-6229	117	41	𝑠	𝑠	X
easat-6229	117	42	low	low	INTJ
easat-6229	117	43	(	(	PUNCT
easat-6229	117	44	s	s	NOUN
easat-6229	117	45	)	)	PUNCT
easat-6229	117	46	during	during	ADP
easat-6229	117	47	the	the	DET
easat-6229	117	48	interview	interview	NOUN
easat-6229	117	49	,	,	PUNCT
easat-6229	117	50	students	student	NOUN
easat-6229	117	51	were	be	AUX
easat-6229	117	52	presented	present	VERB
easat-6229	117	53	with	with	ADP
easat-6229	117	54	problems	problem	NOUN
easat-6229	117	55	related	relate	VERB
easat-6229	117	56	to	to	ADP
easat-6229	117	57	the	the	DET
easat-6229	117	58	sequence	sequence	NOUN
easat-6229	117	59	material	material	NOUN
easat-6229	117	60	and	and	CCONJ
easat-6229	117	61	its	its	PRON
easat-6229	117	62	connection	connection	NOUN
easat-6229	117	63	to	to	ADP
easat-6229	117	64	the	the	DET
easat-6229	117	65	proof	proof	ADJ
easat-6229	117	66	process	process	NOUN
easat-6229	117	67	.	.	PUNCT
easat-6229	118	1	the	the	DET
easat-6229	118	2	purpose	purpose	NOUN
easat-6229	118	3	of	of	ADP
easat-6229	118	4	this	this	DET
easat-6229	118	5	interview	interview	NOUN
easat-6229	118	6	method	method	NOUN
easat-6229	118	7	is	be	AUX
easat-6229	118	8	to	to	PART
easat-6229	118	9	gain	gain	VERB
easat-6229	118	10	deeper	deep	ADJ
easat-6229	118	11	insights	insight	NOUN
easat-6229	118	12	into	into	ADP
easat-6229	118	13	the	the	DET
easat-6229	118	14	students	student	NOUN
easat-6229	118	15	'	'	PART
easat-6229	118	16	proof	proof	NOUN
easat-6229	118	17	processes	process	NOUN
easat-6229	118	18	when	when	SCONJ
easat-6229	118	19	solving	solve	VERB
easat-6229	118	20	evidentiary	evidentiary	NOUN
easat-6229	118	21	problems	problem	NOUN
easat-6229	118	22	.	.	PUNCT
easat-6229	119	1	the	the	DET
easat-6229	119	2	following	follow	VERB
easat-6229	119	3	indicators	indicator	NOUN
easat-6229	119	4	are	be	AUX
easat-6229	119	5	used	use	VERB
easat-6229	119	6	to	to	PART
easat-6229	119	7	measure	measure	VERB
easat-6229	119	8	the	the	DET
easat-6229	119	9	ability	ability	NOUN
easat-6229	119	10	in	in	ADP
easat-6229	119	11	mathematical	mathematical	ADJ
easat-6229	119	12	proof	proof	NOUN
easat-6229	119	13	:	:	PUNCT
easat-6229	119	14	1	1	X
easat-6229	119	15	)	)	PUNCT
easat-6229	119	16	reading	reading	NOUN
easat-6229	119	17	of	of	ADP
easat-6229	119	18	evidence	evidence	NOUN
easat-6229	119	19	with	with	ADP
easat-6229	119	20	its	its	PRON
easat-6229	119	21	evidentiary	evidentiary	ADJ
easat-6229	119	22	aspects	aspect	NOUN
easat-6229	119	23	,	,	PUNCT
easat-6229	119	24	which	which	PRON
easat-6229	119	25	includes	include	VERB
easat-6229	119	26	making	make	VERB
easat-6229	119	27	hypotheses	hypothesis	NOUN
easat-6229	119	28	(	(	PUNCT
easat-6229	119	29	conjectures	conjecture	NOUN
easat-6229	119	30	)	)	PUNCT
easat-6229	119	31	based	base	VERB
easat-6229	119	32	on	on	ADP
easat-6229	119	33	the	the	DET
easat-6229	119	34	patterns	pattern	NOUN
easat-6229	119	35	and	and	CCONJ
easat-6229	119	36	characteristics	characteristic	NOUN
easat-6229	119	37	of	of	ADP
easat-6229	119	38	several	several	ADJ
easat-6229	119	39	statements	statement	NOUN
easat-6229	119	40	,	,	PUNCT
easat-6229	119	41	as	as	ADV
easat-6229	119	42	well	well	ADV
easat-6229	119	43	as	as	ADP
easat-6229	119	44	proving	prove	VERB
easat-6229	119	45	the	the	DET
easat-6229	119	46	obtained	obtain	VERB
easat-6229	119	47	conjectures	conjecture	NOUN
easat-6229	119	48	through	through	ADP
easat-6229	119	49	deduction	deduction	NOUN
easat-6229	119	50	;	;	PUNCT
easat-6229	119	51	2	2	X
easat-6229	119	52	)	)	PUNCT
easat-6229	119	53	evidence	evidence	NOUN
easat-6229	119	54	construction	construction	NOUN
easat-6229	119	55	with	with	ADP
easat-6229	119	56	its	its	PRON
easat-6229	119	57	evidentiary	evidentiary	ADJ
easat-6229	119	58	aspect	aspect	NOUN
easat-6229	119	59	,	,	PUNCT
easat-6229	119	60	which	which	PRON
easat-6229	119	61	involves	involve	VERB
easat-6229	119	62	applying	apply	VERB
easat-6229	119	63	definitions	definition	NOUN
easat-6229	119	64	and	and	CCONJ
easat-6229	119	65	related	related	ADJ
easat-6229	119	66	characteristics	characteristic	NOUN
easat-6229	119	67	,	,	PUNCT
easat-6229	119	68	sequencing	sequence	VERB
easat-6229	119	69	the	the	DET
easat-6229	119	70	evidentiary	evidentiary	NOUN
easat-6229	119	71	and	and	CCONJ
easat-6229	119	72	construction	construction	NOUN
easat-6229	119	73	steps	step	NOUN
easat-6229	119	74	into	into	ADP
easat-6229	119	75	formal	formal	ADJ
easat-6229	119	76	evidence	evidence	NOUN
easat-6229	119	77	,	,	PUNCT
easat-6229	119	78	and	and	CCONJ
easat-6229	119	79	demonstrating	demonstrate	VERB
easat-6229	119	80	the	the	DET
easat-6229	119	81	ability	ability	NOUN
easat-6229	119	82	to	to	PART
easat-6229	119	83	use	use	VERB
easat-6229	119	84	premises	premise	NOUN
easat-6229	119	85	,	,	PUNCT
easat-6229	119	86	definitions	definition	NOUN
easat-6229	119	87	,	,	PUNCT
easat-6229	119	88	or	or	CCONJ
easat-6229	119	89	theorems	theorem	NOUN
easat-6229	119	90	associated	associate	VERB
easat-6229	119	91	with	with	ADP
easat-6229	119	92	the	the	DET
easat-6229	119	93	statement	statement	NOUN
easat-6229	119	94	to	to	PART
easat-6229	119	95	build	build	VERB
easat-6229	119	96	valid	valid	ADJ
easat-6229	119	97	evidence	evidence	NOUN
easat-6229	119	98	.	.	PUNCT
easat-6229	120	1	2.4	2.4	NUM
easat-6229	120	2	.	.	X
easat-6229	120	3	analyzing	analyze	VERB
easat-6229	120	4	of	of	ADP
easat-6229	120	5	data	datum	NOUN
easat-6229	120	6	to	to	PART
easat-6229	120	7	analyze	analyze	VERB
easat-6229	120	8	the	the	DET
easat-6229	120	9	test	test	NOUN
easat-6229	120	10	and	and	CCONJ
easat-6229	120	11	interview	interview	NOUN
easat-6229	120	12	data	datum	NOUN
easat-6229	120	13	,	,	PUNCT
easat-6229	120	14	with	with	ADP
easat-6229	120	15	interactive	interactive	ADJ
easat-6229	120	16	techniques	technique	NOUN
easat-6229	120	17	,	,	PUNCT
easat-6229	120	18	namely	namely	ADV
easat-6229	120	19	data	datum	NOUN
easat-6229	120	20	condensation	condensation	NOUN
easat-6229	120	21	,	,	PUNCT
easat-6229	120	22	exposure	exposure	NOUN
easat-6229	120	23	,	,	PUNCT
easat-6229	120	24	and	and	CCONJ
easat-6229	120	25	verification	verification	NOUN
easat-6229	120	26	.	.	PUNCT
easat-6229	121	1	the	the	DET
easat-6229	121	2	purpose	purpose	NOUN
easat-6229	121	3	of	of	ADP
easat-6229	121	4	this	this	DET
easat-6229	121	5	study	study	NOUN
easat-6229	121	6	is	be	AUX
easat-6229	121	7	to	to	PART
easat-6229	121	8	improve	improve	VERB
easat-6229	121	9	students	student	NOUN
easat-6229	121	10	'	'	PART
easat-6229	121	11	ability	ability	NOUN
easat-6229	121	12	in	in	ADP
easat-6229	121	13	the	the	DET
easat-6229	121	14	mathematical	mathematical	ADJ
easat-6229	121	15	proof	proof	NOUN
easat-6229	121	16	process	process	NOUN
easat-6229	121	17	by	by	ADP
easat-6229	121	18	helping	help	VERB
easat-6229	121	19	to	to	PART
easat-6229	121	20	solve	solve	VERB
easat-6229	121	21	the	the	DET
easat-6229	121	22	problems	problem	NOUN
easat-6229	121	23	they	they	PRON
easat-6229	121	24	write	write	VERB
easat-6229	121	25	for	for	ADP
easat-6229	121	26	analysis	analysis	NOUN
easat-6229	121	27	and	and	CCONJ
easat-6229	121	28	then	then	ADV
easat-6229	121	29	analyzing	analyze	VERB
easat-6229	121	30	indicators	indicator	NOUN
easat-6229	121	31	that	that	PRON
easat-6229	121	32	show	show	VERB
easat-6229	121	33	proof	proof	ADJ
easat-6229	121	34	ability	ability	NOUN
easat-6229	121	35	.	.	PUNCT
easat-6229	122	1	it	it	PRON
easat-6229	122	2	is	be	AUX
easat-6229	122	3	hoped	hope	VERB
easat-6229	122	4	that	that	SCONJ
easat-6229	122	5	the	the	DET
easat-6229	122	6	new	new	ADJ
easat-6229	122	7	findings	finding	NOUN
easat-6229	122	8	will	will	AUX
easat-6229	122	9	result	result	VERB
easat-6229	122	10	in	in	ADP
easat-6229	122	11	practical	practical	ADJ
easat-6229	122	12	,	,	PUNCT
easat-6229	122	13	measurable	measurable	ADJ
easat-6229	122	14	,	,	PUNCT
easat-6229	122	15	and	and	CCONJ
easat-6229	122	16	applicable	applicable	ADJ
easat-6229	122	17	measures	measure	NOUN
easat-6229	122	18	that	that	PRON
easat-6229	122	19	can	can	AUX
easat-6229	122	20	contribute	contribute	VERB
easat-6229	122	21	to	to	ADP
easat-6229	122	22	mathematics	mathematic	NOUN
easat-6229	122	23	education	education	NOUN
easat-6229	122	24	.	.	PUNCT
easat-6229	123	1	3	3	X
easat-6229	123	2	.	.	NOUN
easat-6229	123	3	results	result	NOUN
easat-6229	123	4	and	and	CCONJ
easat-6229	123	5	discussion	discussion	NOUN
easat-6229	123	6	3.1	3.1	NUM
easat-6229	123	7	.	.	PUNCT
easat-6229	124	1	implementation	implementation	NOUN
easat-6229	124	2	students	student	NOUN
easat-6229	124	3	in	in	ADP
easat-6229	124	4	the	the	DET
easat-6229	124	5	mathematics	mathematic	NOUN
easat-6229	124	6	education	education	NOUN
easat-6229	124	7	study	study	NOUN
easat-6229	124	8	program	program	NOUN
easat-6229	124	9	at	at	ADP
easat-6229	124	10	pancasakti	pancasakti	ADJ
easat-6229	124	11	tegal	tegal	ADJ
easat-6229	124	12	university	university	NOUN
easat-6229	124	13	use	use	VERB
easat-6229	124	14	the	the	DET
easat-6229	124	15	guided	guide	VERB
easat-6229	124	16	discovery	discovery	NOUN
easat-6229	124	17	learning	learning	NOUN
easat-6229	124	18	model	model	NOUN
easat-6229	124	19	in	in	ADP
easat-6229	124	20	conjunction	conjunction	NOUN
easat-6229	124	21	with	with	ADP
easat-6229	124	22	the	the	DET
easat-6229	124	23	mathematical	mathematical	ADJ
easat-6229	124	24	working	working	NOUN
easat-6229	124	25	space	space	NOUN
easat-6229	124	26	strategy	strategy	NOUN
easat-6229	124	27	to	to	PART
easat-6229	124	28	engage	engage	VERB
easat-6229	124	29	in	in	ADP
easat-6229	124	30	the	the	DET
easat-6229	124	31	real	real	ADJ
easat-6229	124	32	analysis	analysis	NOUN
easat-6229	124	33	of	of	ADP
easat-6229	124	34	sequence	sequence	NOUN
easat-6229	124	35	material	material	NOUN
easat-6229	124	36	.	.	PUNCT
easat-6229	125	1	the	the	DET
easat-6229	125	2	students	student	NOUN
easat-6229	125	3	do	do	AUX
easat-6229	125	4	not	not	PART
easat-6229	125	5	feel	feel	VERB
easat-6229	125	6	burdened	burden	VERB
easat-6229	125	7	by	by	ADP
easat-6229	125	8	the	the	DET
easat-6229	125	9	learning	learning	NOUN
easat-6229	125	10	model	model	NOUN
easat-6229	125	11	used	use	VERB
easat-6229	125	12	during	during	ADP
easat-6229	125	13	lectures	lecture	NOUN
easat-6229	125	14	.	.	PUNCT
easat-6229	126	1	to	to	PART
easat-6229	126	2	solve	solve	VERB
easat-6229	126	3	the	the	DET
easat-6229	126	4	problem	problem	NOUN
easat-6229	126	5	of	of	ADP
easat-6229	126	6	proof	proof	NOUN
easat-6229	126	7	,	,	PUNCT
easat-6229	126	8	students	student	NOUN
easat-6229	126	9	can	can	AUX
easat-6229	126	10	investigate	investigate	VERB
easat-6229	126	11	the	the	DET
easat-6229	126	12	findings	finding	NOUN
easat-6229	126	13	and	and	CCONJ
easat-6229	126	14	seek	seek	VERB
easat-6229	126	15	assistance	assistance	NOUN
easat-6229	126	16	from	from	ADP
easat-6229	126	17	the	the	DET
easat-6229	126	18	teacher	teacher	NOUN
easat-6229	126	19	if	if	SCONJ
easat-6229	126	20	needed	need	VERB
easat-6229	126	21	to	to	PART
easat-6229	126	22	work	work	VERB
easat-6229	126	23	through	through	ADP
easat-6229	126	24	the	the	DET
easat-6229	126	25	mathematical	mathematical	ADJ
easat-6229	126	26	proof	proof	NOUN
easat-6229	126	27	they	they	PRON
easat-6229	126	28	are	be	AUX
easat-6229	126	29	faced	face	VERB
easat-6229	126	30	with	with	ADP
easat-6229	126	31	.	.	PUNCT
easat-6229	127	1	in	in	ADP
easat-6229	127	2	addition	addition	NOUN
easat-6229	127	3	,	,	PUNCT
easat-6229	127	4	the	the	DET
easat-6229	127	5	use	use	NOUN
easat-6229	127	6	of	of	ADP
easat-6229	127	7	the	the	DET
easat-6229	127	8	mathematical	mathematical	ADJ
easat-6229	127	9	working	working	NOUN
easat-6229	127	10	space	space	NOUN
easat-6229	127	11	strategy	strategy	NOUN
easat-6229	127	12	for	for	ADP
easat-6229	127	13	discussion	discussion	NOUN
easat-6229	127	14	material	material	NOUN
easat-6229	127	15	is	be	AUX
easat-6229	127	16	very	very	ADV
easat-6229	127	17	helpful	helpful	ADJ
easat-6229	127	18	for	for	ADP
easat-6229	127	19	students	student	NOUN
easat-6229	127	20	in	in	ADP
easat-6229	127	21	addressing	address	VERB
easat-6229	127	22	proving	prove	VERB
easat-6229	127	23	problems	problem	NOUN
easat-6229	127	24	in	in	ADP
easat-6229	127	25	real	real	ADJ
easat-6229	127	26	analysis	analysis	NOUN
easat-6229	127	27	.	.	PUNCT
easat-6229	128	1	the	the	DET
easat-6229	128	2	worksheet	worksheet	NOUN
easat-6229	128	3	for	for	ADP
easat-6229	128	4	the	the	DET
easat-6229	128	5	discussion	discussion	NOUN
easat-6229	128	6	material	material	NOUN
easat-6229	128	7	on	on	ADP
easat-6229	128	8	sequences	sequence	NOUN
easat-6229	128	9	contains	contain	VERB
easat-6229	128	10	definitions	definition	NOUN
easat-6229	128	11	,	,	PUNCT
easat-6229	128	12	theorems	theorem	NOUN
easat-6229	128	13	,	,	PUNCT
easat-6229	128	14	and	and	CCONJ
easat-6229	128	15	proof	proof	ADJ
easat-6229	128	16	questions	question	NOUN
easat-6229	128	17	.	.	PUNCT
easat-6229	129	1	each	each	DET
easat-6229	129	2	definition	definition	NOUN
easat-6229	129	3	is	be	AUX
easat-6229	129	4	accompanied	accompany	VERB
easat-6229	129	5	by	by	ADP
easat-6229	129	6	attributes	attribute	NOUN
easat-6229	129	7	that	that	PRON
easat-6229	129	8	are	be	AUX
easat-6229	129	9	useful	useful	ADJ
easat-6229	129	10	for	for	ADP
easat-6229	129	11	sequencing	sequence	VERB
easat-6229	129	12	the	the	DET
easat-6229	129	13	evidentiary	evidentiary	ADJ
easat-6229	129	14	steps	step	NOUN
easat-6229	129	15	,	,	PUNCT
easat-6229	129	16	which	which	PRON
easat-6229	129	17	greatly	greatly	ADV
easat-6229	129	18	assists	assist	VERB
easat-6229	129	19	students	student	NOUN
easat-6229	129	20	in	in	ADP
easat-6229	129	21	their	their	PRON
easat-6229	129	22	proof	proof	ADJ
easat-6229	129	23	work	work	NOUN
easat-6229	129	24	.	.	PUNCT
easat-6229	130	1	furthermore	furthermore	ADV
easat-6229	130	2	,	,	PUNCT
easat-6229	130	3	for	for	ADP
easat-6229	130	4	every	every	DET
easat-6229	130	5	definition	definition	NOUN
easat-6229	130	6	,	,	PUNCT
easat-6229	130	7	theorem	theorem	ADJ
easat-6229	130	8	,	,	PUNCT
easat-6229	130	9	lemma	lemma	PROPN
easat-6229	130	10	,	,	PUNCT
easat-6229	130	11	or	or	CCONJ
easat-6229	130	12	proof	proof	ADJ
easat-6229	130	13	problem	problem	NOUN
easat-6229	130	14	,	,	PUNCT
easat-6229	130	15	students	student	NOUN
easat-6229	130	16	must	must	AUX
easat-6229	130	17	be	be	AUX
easat-6229	130	18	able	able	ADJ
easat-6229	130	19	to	to	PART
easat-6229	130	20	interpret	interpret	VERB
easat-6229	130	21	it	it	PRON
easat-6229	130	22	in	in	ADP
easat-6229	130	23	language	language	NOUN
easat-6229	130	24	that	that	PRON
easat-6229	130	25	is	be	AUX
easat-6229	130	26	easy	easy	ADJ
easat-6229	130	27	to	to	PART
easat-6229	130	28	understand	understand	VERB
easat-6229	130	29	and	and	CCONJ
easat-6229	130	30	conveys	convey	VERB
easat-6229	130	31	a	a	DET
easat-6229	130	32	clear	clear	ADJ
easat-6229	130	33	meaning	meaning	NOUN
easat-6229	130	34	.	.	PUNCT
easat-6229	131	1	1244	1244	NUM
easat-6229	131	2	edelweiss	edelweiss	PROPN
easat-6229	131	3	applied	apply	VERB
easat-6229	131	4	science	science	NOUN
easat-6229	131	5	and	and	CCONJ
easat-6229	131	6	technology	technology	NOUN
easat-6229	131	7	issn	issn	PROPN
easat-6229	131	8	:	:	PUNCT
easat-6229	131	9	2576	2576	NUM
easat-6229	131	10	-	-	SYM
easat-6229	131	11	8484	8484	NUM
easat-6229	131	12	vol	vol	NOUN
easat-6229	131	13	.	.	PROPN
easat-6229	132	1	9	9	NUM
easat-6229	132	2	,	,	PUNCT
easat-6229	132	3	no	no	INTJ
easat-6229	132	4	.	.	NOUN
easat-6229	132	5	4	4	NUM
easat-6229	132	6	:	:	SYM
easat-6229	132	7	1240	1240	NUM
easat-6229	132	8	-	-	SYM
easat-6229	132	9	1251	1251	NUM
easat-6229	132	10	,	,	PUNCT
easat-6229	132	11	2025	2025	NUM
easat-6229	132	12	doi	doi	NOUN
easat-6229	132	13	:	:	PUNCT
easat-6229	132	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	132	15	©	©	ADP
easat-6229	132	16	2025	2025	NUM
easat-6229	132	17	by	by	ADP
easat-6229	132	18	the	the	DET
easat-6229	132	19	authors	author	NOUN
easat-6229	132	20	;	;	PUNCT
easat-6229	132	21	licensee	licensee	PROPN
easat-6229	132	22	learning	learning	NOUN
easat-6229	132	23	gate	gate	NOUN
easat-6229	132	24	this	this	DET
easat-6229	132	25	interpretation	interpretation	NOUN
easat-6229	132	26	can	can	AUX
easat-6229	132	27	be	be	AUX
easat-6229	132	28	facilitated	facilitate	VERB
easat-6229	132	29	through	through	ADP
easat-6229	132	30	discussions	discussion	NOUN
easat-6229	132	31	within	within	ADP
easat-6229	132	32	their	their	PRON
easat-6229	132	33	groups	group	NOUN
easat-6229	132	34	.	.	PUNCT
easat-6229	133	1	furthermore	furthermore	ADV
easat-6229	133	2	,	,	PUNCT
easat-6229	133	3	each	each	PRON
easat-6229	133	4	theorem	theorem	PROPN
easat-6229	133	5	,	,	PUNCT
easat-6229	133	6	lemma	lemma	PROPN
easat-6229	133	7	,	,	PUNCT
easat-6229	133	8	and	and	CCONJ
easat-6229	133	9	proof	proof	NOUN
easat-6229	133	10	question	question	NOUN
easat-6229	133	11	are	be	AUX
easat-6229	133	12	accompanied	accompany	VERB
easat-6229	133	13	by	by	ADP
easat-6229	133	14	a	a	DET
easat-6229	133	15	background	background	NOUN
easat-6229	133	16	,	,	PUNCT
easat-6229	133	17	premise	premise	NOUN
easat-6229	133	18	,	,	PUNCT
easat-6229	133	19	and	and	CCONJ
easat-6229	133	20	conclusion	conclusion	NOUN
easat-6229	133	21	.	.	PUNCT
easat-6229	134	1	the	the	DET
easat-6229	134	2	premise	premise	NOUN
easat-6229	134	3	serves	serve	VERB
easat-6229	134	4	as	as	ADP
easat-6229	134	5	the	the	DET
easat-6229	134	6	first	first	ADJ
easat-6229	134	7	step	step	NOUN
easat-6229	134	8	in	in	ADP
easat-6229	134	9	the	the	DET
easat-6229	134	10	proof	proof	NOUN
easat-6229	134	11	and	and	CCONJ
easat-6229	134	12	should	should	AUX
easat-6229	134	13	lead	lead	VERB
easat-6229	134	14	to	to	ADP
easat-6229	134	15	the	the	DET
easat-6229	134	16	conclusion	conclusion	NOUN
easat-6229	134	17	as	as	ADP
easat-6229	134	18	the	the	DET
easat-6229	134	19	result	result	NOUN
easat-6229	134	20	.	.	PUNCT
easat-6229	135	1	similarly	similarly	ADV
easat-6229	135	2	,	,	PUNCT
easat-6229	135	3	the	the	DET
easat-6229	135	4	construction	construction	NOUN
easat-6229	135	5	of	of	ADP
easat-6229	135	6	evidence	evidence	NOUN
easat-6229	135	7	should	should	AUX
easat-6229	135	8	be	be	AUX
easat-6229	135	9	supported	support	VERB
easat-6229	135	10	by	by	ADP
easat-6229	135	11	relevant	relevant	ADJ
easat-6229	135	12	facts	fact	NOUN
easat-6229	135	13	and	and	CCONJ
easat-6229	135	14	should	should	AUX
easat-6229	135	15	sequence	sequence	VERB
easat-6229	135	16	the	the	DET
easat-6229	135	17	available	available	ADJ
easat-6229	135	18	evidentiary	evidentiary	ADJ
easat-6229	135	19	steps	step	NOUN
easat-6229	135	20	to	to	PART
easat-6229	135	21	obtain	obtain	VERB
easat-6229	135	22	a	a	DET
easat-6229	135	23	valid	valid	ADJ
easat-6229	135	24	construction	construction	NOUN
easat-6229	135	25	.	.	PUNCT
easat-6229	136	1	after	after	ADP
easat-6229	136	2	that	that	PRON
easat-6229	136	3	,	,	PUNCT
easat-6229	136	4	the	the	DET
easat-6229	136	5	premises	premise	NOUN
easat-6229	136	6	,	,	PUNCT
easat-6229	136	7	definitions	definition	NOUN
easat-6229	136	8	,	,	PUNCT
easat-6229	136	9	theorems	theorem	NOUN
easat-6229	136	10	,	,	PUNCT
easat-6229	136	11	or	or	CCONJ
easat-6229	136	12	problems	problem	NOUN
easat-6229	136	13	that	that	PRON
easat-6229	136	14	have	have	AUX
easat-6229	136	15	been	be	AUX
easat-6229	136	16	studied	study	VERB
easat-6229	136	17	about	about	ADP
easat-6229	136	18	the	the	DET
easat-6229	136	19	statement	statement	NOUN
easat-6229	136	20	can	can	AUX
easat-6229	136	21	be	be	AUX
easat-6229	136	22	used	use	VERB
easat-6229	136	23	to	to	PART
easat-6229	136	24	build	build	VERB
easat-6229	136	25	the	the	DET
easat-6229	136	26	evidence	evidence	NOUN
easat-6229	136	27	construction	construction	NOUN
easat-6229	136	28	.	.	PUNCT
easat-6229	137	1	it	it	PRON
easat-6229	137	2	is	be	AUX
easat-6229	137	3	also	also	ADV
easat-6229	137	4	advisable	advisable	ADJ
easat-6229	137	5	to	to	PART
easat-6229	137	6	conduct	conduct	VERB
easat-6229	137	7	a	a	DET
easat-6229	137	8	preliminary	preliminary	ADJ
easat-6229	137	9	analysis	analysis	NOUN
easat-6229	137	10	when	when	SCONJ
easat-6229	137	11	solving	solve	VERB
easat-6229	137	12	evidentiary	evidentiary	NOUN
easat-6229	137	13	problems	problem	NOUN
easat-6229	137	14	to	to	PART
easat-6229	137	15	avoid	avoid	VERB
easat-6229	137	16	mistakes	mistake	NOUN
easat-6229	137	17	in	in	ADP
easat-6229	137	18	gathering	gather	VERB
easat-6229	137	19	the	the	DET
easat-6229	137	20	facts	fact	NOUN
easat-6229	137	21	to	to	PART
easat-6229	137	22	be	be	AUX
easat-6229	137	23	used	use	VERB
easat-6229	137	24	.	.	PUNCT
easat-6229	138	1	the	the	DET
easat-6229	138	2	results	result	NOUN
easat-6229	138	3	of	of	ADP
easat-6229	138	4	the	the	DET
easat-6229	138	5	interviews	interview	NOUN
easat-6229	138	6	conducted	conduct	VERB
easat-6229	138	7	with	with	ADP
easat-6229	138	8	students	student	NOUN
easat-6229	138	9	after	after	SCONJ
easat-6229	138	10	they	they	PRON
easat-6229	138	11	completed	complete	VERB
easat-6229	138	12	the	the	DET
easat-6229	138	13	real	real	ADJ
easat-6229	138	14	analysis	analysis	NOUN
easat-6229	138	15	lesson	lesson	NOUN
easat-6229	138	16	in	in	ADP
easat-6229	138	17	this	this	DET
easat-6229	138	18	study	study	NOUN
easat-6229	138	19	are	be	AUX
easat-6229	138	20	as	as	SCONJ
easat-6229	138	21	follows	follow	VERB
easat-6229	138	22	:	:	PUNCT
easat-6229	138	23	t	t	X
easat-6229	138	24	:	:	PUNCT
easat-6229	138	25	what	what	PRON
easat-6229	138	26	are	be	AUX
easat-6229	138	27	your	your	PRON
easat-6229	138	28	thoughts	thought	NOUN
easat-6229	138	29	on	on	ADP
easat-6229	138	30	learning	learn	VERB
easat-6229	138	31	in	in	ADP
easat-6229	138	32	this	this	DET
easat-6229	138	33	sequence	sequence	NOUN
easat-6229	138	34	of	of	ADP
easat-6229	138	35	materials	material	NOUN
easat-6229	138	36	?	?	PUNCT
easat-6229	139	1	l2	l2	NOUN
easat-6229	139	2	:	:	PUNCT
easat-6229	140	1	i	i	PRON
easat-6229	140	2	enjoy	enjoy	VERB
easat-6229	140	3	using	use	VERB
easat-6229	140	4	this	this	DET
easat-6229	140	5	learning	learning	NOUN
easat-6229	140	6	approach	approach	NOUN
easat-6229	140	7	because	because	SCONJ
easat-6229	140	8	it	it	PRON
easat-6229	140	9	helps	help	VERB
easat-6229	140	10	me	i	PRON
easat-6229	140	11	complete	complete	VERB
easat-6229	140	12	this	this	DET
easat-6229	140	13	worksheet	worksheet	NOUN
easat-6229	140	14	and	and	CCONJ
easat-6229	140	15	other	other	ADJ
easat-6229	140	16	tasks	task	NOUN
easat-6229	140	17	effectively	effectively	ADV
easat-6229	140	18	and	and	CCONJ
easat-6229	140	19	on	on	ADP
easat-6229	140	20	time	time	NOUN
easat-6229	140	21	.	.	PUNCT
easat-6229	141	1	m5	m5	NOUN
easat-6229	141	2	:	:	PUNCT
easat-6229	141	3	i	i	PRON
easat-6229	141	4	find	find	VERB
easat-6229	141	5	it	it	PRON
easat-6229	141	6	very	very	ADV
easat-6229	141	7	helpful	helpful	ADJ
easat-6229	141	8	because	because	SCONJ
easat-6229	141	9	it	it	PRON
easat-6229	141	10	used	use	VERB
easat-6229	141	11	to	to	PART
easat-6229	141	12	be	be	AUX
easat-6229	141	13	quite	quite	ADV
easat-6229	141	14	difficult	difficult	ADJ
easat-6229	141	15	for	for	SCONJ
easat-6229	141	16	me	i	PRON
easat-6229	141	17	to	to	PART
easat-6229	141	18	study	study	VERB
easat-6229	141	19	the	the	DET
easat-6229	141	20	problem	problem	NOUN
easat-6229	141	21	of	of	ADP
easat-6229	141	22	proof	proof	NOUN
easat-6229	141	23	.	.	PUNCT
easat-6229	142	1	however	however	ADV
easat-6229	142	2	,	,	PUNCT
easat-6229	142	3	now	now	ADV
easat-6229	142	4	i	i	PRON
easat-6229	142	5	am	be	AUX
easat-6229	142	6	better	well	ADJ
easat-6229	142	7	at	at	ADP
easat-6229	142	8	completing	complete	VERB
easat-6229	142	9	it	it	PRON
easat-6229	142	10	,	,	PUNCT
easat-6229	142	11	thanks	thank	NOUN
easat-6229	142	12	to	to	ADP
easat-6229	142	13	the	the	DET
easat-6229	142	14	guidance	guidance	NOUN
easat-6229	142	15	of	of	ADP
easat-6229	142	16	my	my	PRON
easat-6229	142	17	lecturers	lecturer	NOUN
easat-6229	142	18	,	,	PUNCT
easat-6229	142	19	who	who	PRON
easat-6229	142	20	are	be	AUX
easat-6229	142	21	always	always	ADV
easat-6229	142	22	watching	watch	VERB
easat-6229	142	23	over	over	ADP
easat-6229	142	24	me	i	PRON
easat-6229	142	25	.	.	PUNCT
easat-6229	143	1	s3	s3	NOUN
easat-6229	143	2	:	:	PUNCT
easat-6229	143	3	fear	fear	NOUN
easat-6229	143	4	and	and	CCONJ
easat-6229	143	5	laziness	laziness	NOUN
easat-6229	143	6	,	,	PUNCT
easat-6229	143	7	which	which	PRON
easat-6229	143	8	often	often	ADV
easat-6229	143	9	arose	arise	VERB
easat-6229	143	10	when	when	SCONJ
easat-6229	143	11	studying	study	VERB
easat-6229	143	12	the	the	DET
easat-6229	143	13	problem	problem	NOUN
easat-6229	143	14	of	of	ADP
easat-6229	143	15	proof	proof	NOUN
easat-6229	143	16	,	,	PUNCT
easat-6229	143	17	are	be	AUX
easat-6229	143	18	now	now	ADV
easat-6229	143	19	gradually	gradually	ADV
easat-6229	143	20	disappearing	disappear	VERB
easat-6229	143	21	.	.	PUNCT
easat-6229	144	1	understanding	understand	VERB
easat-6229	144	2	evidence	evidence	NOUN
easat-6229	144	3	learning	learn	VERB
easat-6229	144	4	today	today	NOUN
easat-6229	144	5	is	be	AUX
easat-6229	144	6	easier	easy	ADJ
easat-6229	144	7	than	than	ADP
easat-6229	144	8	ever	ever	ADV
easat-6229	144	9	.	.	PUNCT
easat-6229	145	1	t	t	PROPN
easat-6229	145	2	:	:	PUNCT
easat-6229	145	3	what	what	PRON
easat-6229	145	4	are	be	AUX
easat-6229	145	5	your	your	PRON
easat-6229	145	6	thoughts	thought	NOUN
easat-6229	145	7	on	on	ADP
easat-6229	145	8	the	the	DET
easat-6229	145	9	strategies	strategy	NOUN
easat-6229	145	10	used	use	VERB
easat-6229	145	11	to	to	PART
easat-6229	145	12	learn	learn	VERB
easat-6229	145	13	real	real	ADJ
easat-6229	145	14	analysis	analysis	NOUN
easat-6229	145	15	?	?	PUNCT
easat-6229	146	1	l2	l2	NOUN
easat-6229	146	2	:	:	PUNCT
easat-6229	147	1	i	i	PRON
easat-6229	147	2	think	think	VERB
easat-6229	147	3	it	it	PRON
easat-6229	147	4	’s	’	VERB
easat-6229	147	5	fun	fun	NOUN
easat-6229	147	6	and	and	CCONJ
easat-6229	147	7	easy	easy	ADJ
easat-6229	147	8	to	to	PART
easat-6229	147	9	use	use	VERB
easat-6229	147	10	for	for	ADP
easat-6229	147	11	other	other	ADJ
easat-6229	147	12	proof	proof	ADJ
easat-6229	147	13	materials	material	NOUN
easat-6229	147	14	.	.	PUNCT
easat-6229	148	1	m5	m5	NOUN
easat-6229	148	2	:	:	PUNCT
easat-6229	148	3	i	i	PRON
easat-6229	148	4	will	will	AUX
easat-6229	148	5	use	use	VERB
easat-6229	148	6	this	this	DET
easat-6229	148	7	strategy	strategy	NOUN
easat-6229	148	8	when	when	SCONJ
easat-6229	148	9	necessary	necessary	ADJ
easat-6229	148	10	so	so	SCONJ
easat-6229	148	11	that	that	SCONJ
easat-6229	148	12	i	i	PRON
easat-6229	148	13	can	can	AUX
easat-6229	148	14	master	master	VERB
easat-6229	148	15	the	the	DET
easat-6229	148	16	proof	proof	NOUN
easat-6229	148	17	correctly	correctly	ADV
easat-6229	148	18	.	.	PUNCT
easat-6229	149	1	s3	s3	PROPN
easat-6229	149	2	:	:	PUNCT
easat-6229	149	3	this	this	DET
easat-6229	149	4	strategy	strategy	NOUN
easat-6229	149	5	has	have	AUX
easat-6229	149	6	opened	open	VERB
easat-6229	149	7	my	my	PRON
easat-6229	149	8	eyes	eye	NOUN
easat-6229	149	9	to	to	ADP
easat-6229	149	10	the	the	DET
easat-6229	149	11	concept	concept	NOUN
easat-6229	149	12	of	of	ADP
easat-6229	149	13	proof	proof	NOUN
easat-6229	149	14	.	.	PUNCT
easat-6229	150	1	based	base	VERB
easat-6229	150	2	on	on	ADP
easat-6229	150	3	the	the	DET
easat-6229	150	4	results	result	NOUN
easat-6229	150	5	of	of	ADP
easat-6229	150	6	the	the	DET
easat-6229	150	7	interview	interview	NOUN
easat-6229	150	8	,	,	PUNCT
easat-6229	150	9	it	it	PRON
easat-6229	150	10	can	can	AUX
easat-6229	150	11	be	be	AUX
easat-6229	150	12	seen	see	VERB
easat-6229	150	13	that	that	SCONJ
easat-6229	150	14	l2	l2	NOUN
easat-6229	150	15	students	student	NOUN
easat-6229	150	16	,	,	PUNCT
easat-6229	150	17	who	who	PRON
easat-6229	150	18	previously	previously	ADV
easat-6229	150	19	almost	almost	ADV
easat-6229	150	20	understood	understand	VERB
easat-6229	150	21	mathematical	mathematical	ADJ
easat-6229	150	22	proof	proof	NOUN
easat-6229	150	23	problems	problem	NOUN
easat-6229	150	24	,	,	PUNCT
easat-6229	150	25	have	have	AUX
easat-6229	150	26	become	become	VERB
easat-6229	150	27	even	even	ADV
easat-6229	150	28	better	well	ADJ
easat-6229	150	29	.	.	PUNCT
easat-6229	151	1	m5	m5	NOUN
easat-6229	151	2	students	student	NOUN
easat-6229	151	3	,	,	PUNCT
easat-6229	151	4	who	who	PRON
easat-6229	151	5	were	be	AUX
easat-6229	151	6	previously	previously	ADV
easat-6229	151	7	still	still	ADV
easat-6229	151	8	confused	confuse	VERB
easat-6229	151	9	about	about	ADP
easat-6229	151	10	proof	proof	NOUN
easat-6229	151	11	problems	problem	NOUN
easat-6229	151	12	,	,	PUNCT
easat-6229	151	13	have	have	AUX
easat-6229	151	14	also	also	ADV
easat-6229	151	15	improved	improve	VERB
easat-6229	151	16	.	.	PUNCT
easat-6229	152	1	additionally	additionally	ADV
easat-6229	152	2	,	,	PUNCT
easat-6229	152	3	s3	s3	PROPN
easat-6229	152	4	students	student	NOUN
easat-6229	152	5	,	,	PUNCT
easat-6229	152	6	who	who	PRON
easat-6229	152	7	were	be	AUX
easat-6229	152	8	previously	previously	ADV
easat-6229	152	9	still	still	ADV
easat-6229	152	10	afraid	afraid	ADJ
easat-6229	152	11	of	of	ADP
easat-6229	152	12	proof	proof	NOUN
easat-6229	152	13	problems	problem	NOUN
easat-6229	152	14	,	,	PUNCT
easat-6229	152	15	now	now	ADV
easat-6229	152	16	feel	feel	VERB
easat-6229	152	17	comfortable	comfortable	ADJ
easat-6229	152	18	learning	learning	NOUN
easat-6229	152	19	about	about	ADP
easat-6229	152	20	proof	proof	NOUN
easat-6229	152	21	.	.	PUNCT
easat-6229	153	1	3.2	3.2	NUM
easat-6229	153	2	.	.	PUNCT
easat-6229	153	3	troubleshooting	troubleshooting	NOUN
easat-6229	153	4	based	base	VERB
easat-6229	153	5	on	on	ADP
easat-6229	153	6	the	the	DET
easat-6229	153	7	two	two	NUM
easat-6229	153	8	completion	completion	NOUN
easat-6229	153	9	indicators	indicator	NOUN
easat-6229	153	10	used	use	VERB
easat-6229	153	11	and	and	CCONJ
easat-6229	153	12	the	the	DET
easat-6229	153	13	six	six	NUM
easat-6229	153	14	available	available	ADJ
easat-6229	153	15	questions	question	NOUN
easat-6229	153	16	.	.	PUNCT
easat-6229	154	1	the	the	DET
easat-6229	154	2	three	three	NUM
easat-6229	154	3	students	student	NOUN
easat-6229	154	4	can	can	AUX
easat-6229	154	5	complete	complete	VERB
easat-6229	154	6	the	the	DET
easat-6229	154	7	proof	proof	NOUN
easat-6229	154	8	correctly	correctly	ADV
easat-6229	154	9	on	on	ADP
easat-6229	154	10	the	the	DET
easat-6229	154	11	sequence	sequence	NOUN
easat-6229	154	12	ratio	ratio	NOUN
easat-6229	154	13	problem	problem	NOUN
easat-6229	154	14	because	because	SCONJ
easat-6229	154	15	each	each	PRON
easat-6229	154	16	of	of	ADP
easat-6229	154	17	them	they	PRON
easat-6229	154	18	can	can	AUX
easat-6229	154	19	perform	perform	VERB
easat-6229	154	20	the	the	DET
easat-6229	154	21	initial	initial	ADJ
easat-6229	154	22	analysis	analysis	NOUN
easat-6229	154	23	correctly	correctly	ADV
easat-6229	154	24	,	,	PUNCT
easat-6229	154	25	thereby	thereby	ADV
easat-6229	154	26	enabling	enable	VERB
easat-6229	154	27	them	they	PRON
easat-6229	154	28	to	to	PART
easat-6229	154	29	proceed	proceed	VERB
easat-6229	154	30	with	with	ADP
easat-6229	154	31	a	a	DET
easat-6229	154	32	simple	simple	ADJ
easat-6229	154	33	valid	valid	ADJ
easat-6229	154	34	proof	proof	NOUN
easat-6229	154	35	.	.	PUNCT
easat-6229	155	1	in	in	ADP
easat-6229	155	2	the	the	DET
easat-6229	155	3	problem	problem	NOUN
easat-6229	155	4	of	of	ADP
easat-6229	155	5	the	the	DET
easat-6229	155	6	squeeze	squeeze	NOUN
easat-6229	155	7	theorem	theorem	NOUN
easat-6229	155	8	,	,	PUNCT
easat-6229	155	9	l2	l2	NOUN
easat-6229	155	10	and	and	CCONJ
easat-6229	155	11	m5	m5	NOUN
easat-6229	155	12	students	student	NOUN
easat-6229	155	13	can	can	AUX
easat-6229	155	14	solve	solve	VERB
easat-6229	155	15	this	this	DET
easat-6229	155	16	simple	simple	ADJ
easat-6229	155	17	proof	proof	NOUN
easat-6229	155	18	because	because	SCONJ
easat-6229	155	19	they	they	PRON
easat-6229	155	20	can	can	AUX
easat-6229	155	21	correctly	correctly	ADV
easat-6229	155	22	determine	determine	VERB
easat-6229	155	23	the	the	DET
easat-6229	155	24	premise	premise	NOUN
easat-6229	155	25	,	,	PUNCT
easat-6229	155	26	making	make	VERB
easat-6229	155	27	it	it	PRON
easat-6229	155	28	easier	easy	ADJ
easat-6229	155	29	for	for	SCONJ
easat-6229	155	30	them	they	PRON
easat-6229	155	31	to	to	PART
easat-6229	155	32	apply	apply	VERB
easat-6229	155	33	it	it	PRON
easat-6229	155	34	.	.	PUNCT
easat-6229	156	1	additionally	additionally	ADV
easat-6229	156	2	,	,	PUNCT
easat-6229	156	3	l2	l2	NOUN
easat-6229	156	4	and	and	CCONJ
easat-6229	156	5	m5	m5	NOUN
easat-6229	156	6	students	student	NOUN
easat-6229	156	7	can	can	AUX
easat-6229	156	8	provide	provide	VERB
easat-6229	156	9	valid	valid	ADJ
easat-6229	156	10	examples	example	NOUN
easat-6229	156	11	of	of	ADP
easat-6229	156	12	divergent	divergent	ADJ
easat-6229	156	13	sequences	sequence	NOUN
easat-6229	156	14	because	because	SCONJ
easat-6229	156	15	they	they	PRON
easat-6229	156	16	both	both	PRON
easat-6229	156	17	understand	understand	VERB
easat-6229	156	18	the	the	DET
easat-6229	156	19	definition	definition	NOUN
easat-6229	156	20	of	of	ADP
easat-6229	156	21	convergent	convergent	NOUN
easat-6229	156	22	sequences	sequence	NOUN
easat-6229	156	23	well	well	ADV
easat-6229	156	24	.	.	PUNCT
easat-6229	157	1	meanwhile	meanwhile	ADV
easat-6229	157	2	,	,	PUNCT
easat-6229	157	3	only	only	ADV
easat-6229	157	4	l2	l2	NOUN
easat-6229	157	5	students	student	NOUN
easat-6229	157	6	can	can	AUX
easat-6229	157	7	solve	solve	VERB
easat-6229	157	8	the	the	DET
easat-6229	157	9	problem	problem	NOUN
easat-6229	157	10	of	of	ADP
easat-6229	157	11	cauchy	cauchy	ADJ
easat-6229	157	12	sequence	sequence	NOUN
easat-6229	157	13	and	and	CCONJ
easat-6229	157	14	sequence	sequence	NOUN
easat-6229	157	15	limits	limit	NOUN
easat-6229	157	16	.	.	PUNCT
easat-6229	158	1	l2	l2	NOUN
easat-6229	158	2	students	student	NOUN
easat-6229	158	3	can	can	AUX
easat-6229	158	4	show	show	VERB
easat-6229	158	5	the	the	DET
easat-6229	158	6	final	final	ADJ
easat-6229	158	7	results	result	NOUN
easat-6229	158	8	of	of	ADP
easat-6229	158	9	the	the	DET
easat-6229	158	10	proof	proof	NOUN
easat-6229	158	11	in	in	ADP
easat-6229	158	12	these	these	DET
easat-6229	158	13	two	two	NUM
easat-6229	158	14	questions	question	NOUN
easat-6229	158	15	.	.	PUNCT
easat-6229	159	1	the	the	DET
easat-6229	159	2	student	student	NOUN
easat-6229	159	3	conducted	conduct	VERB
easat-6229	159	4	an	an	DET
easat-6229	159	5	initial	initial	ADJ
easat-6229	159	6	analysis	analysis	NOUN
easat-6229	159	7	to	to	PART
easat-6229	159	8	obtain	obtain	VERB
easat-6229	159	9	the	the	DET
easat-6229	159	10	final	final	ADJ
easat-6229	159	11	result	result	NOUN
easat-6229	159	12	and	and	CCONJ
easat-6229	159	13	then	then	ADV
easat-6229	159	14	organized	organize	VERB
easat-6229	159	15	the	the	DET
easat-6229	159	16	proof	proof	NOUN
easat-6229	159	17	steps	step	NOUN
easat-6229	159	18	to	to	PART
easat-6229	159	19	achieve	achieve	VERB
easat-6229	159	20	a	a	DET
easat-6229	159	21	valid	valid	ADJ
easat-6229	159	22	outcome	outcome	NOUN
easat-6229	159	23	.	.	PUNCT
easat-6229	160	1	while	while	SCONJ
easat-6229	160	2	m5	m5	ADJ
easat-6229	160	3	students	student	NOUN
easat-6229	160	4	only	only	ADV
easat-6229	160	5	possess	possess	VERB
easat-6229	160	6	the	the	DET
easat-6229	160	7	ability	ability	NOUN
easat-6229	160	8	to	to	PART
easat-6229	160	9	conduct	conduct	VERB
easat-6229	160	10	a	a	DET
easat-6229	160	11	preliminary	preliminary	ADJ
easat-6229	160	12	analysis	analysis	NOUN
easat-6229	160	13	on	on	ADP
easat-6229	160	14	the	the	DET
easat-6229	160	15	sequence	sequence	NOUN
easat-6229	160	16	limit	limit	NOUN
easat-6229	160	17	problem	problem	NOUN
easat-6229	160	18	,	,	PUNCT
easat-6229	160	19	their	their	PRON
easat-6229	160	20	proof	proof	NOUN
easat-6229	160	21	is	be	AUX
easat-6229	160	22	not	not	PART
easat-6229	160	23	constructive	constructive	ADJ
easat-6229	160	24	.	.	PUNCT
easat-6229	161	1	in	in	ADP
easat-6229	161	2	the	the	DET
easat-6229	161	3	case	case	NOUN
easat-6229	161	4	of	of	ADP
easat-6229	161	5	the	the	DET
easat-6229	161	6	monotone	monotone	ADJ
easat-6229	161	7	sequence	sequence	NOUN
easat-6229	161	8	problem	problem	NOUN
easat-6229	161	9	,	,	PUNCT
easat-6229	161	10	there	there	PRON
easat-6229	161	11	is	be	VERB
easat-6229	161	12	no	no	DET
easat-6229	161	13	single	single	ADJ
easat-6229	161	14	criterion	criterion	NOUN
easat-6229	161	15	that	that	PRON
easat-6229	161	16	can	can	AUX
easat-6229	161	17	complement	complement	VERB
easat-6229	161	18	valid	valid	ADJ
easat-6229	161	19	evidence	evidence	NOUN
easat-6229	161	20	.	.	PUNCT
easat-6229	162	1	only	only	ADV
easat-6229	162	2	l2	l2	NOUN
easat-6229	162	3	students	student	NOUN
easat-6229	162	4	can	can	AUX
easat-6229	162	5	perform	perform	VERB
easat-6229	162	6	the	the	DET
easat-6229	162	7	initial	initial	ADJ
easat-6229	162	8	analysis	analysis	NOUN
easat-6229	162	9	correctly	correctly	ADV
easat-6229	162	10	;	;	PUNCT
easat-6229	162	11	however	however	ADV
easat-6229	162	12	,	,	PUNCT
easat-6229	162	13	they	they	PRON
easat-6229	162	14	were	be	AUX
easat-6229	162	15	not	not	PART
easat-6229	162	16	careful	careful	ADJ
easat-6229	162	17	when	when	SCONJ
easat-6229	162	18	executing	execute	VERB
easat-6229	162	19	the	the	DET
easat-6229	162	20	evidentiary	evidentiary	ADJ
easat-6229	162	21	steps	step	NOUN
easat-6229	162	22	,	,	PUNCT
easat-6229	162	23	which	which	PRON
easat-6229	162	24	prevented	prevent	VERB
easat-6229	162	25	them	they	PRON
easat-6229	162	26	from	from	ADP
easat-6229	162	27	arriving	arrive	VERB
easat-6229	162	28	at	at	ADP
easat-6229	162	29	correct	correct	ADJ
easat-6229	162	30	conclusions	conclusion	NOUN
easat-6229	162	31	.	.	PUNCT
easat-6229	163	1	the	the	DET
easat-6229	163	2	test	test	NOUN
easat-6229	163	3	conducted	conduct	VERB
easat-6229	163	4	on	on	ADP
easat-6229	163	5	the	the	DET
easat-6229	163	6	sequence	sequence	NOUN
easat-6229	163	7	material	material	NOUN
easat-6229	163	8	is	be	AUX
easat-6229	163	9	designed	design	VERB
easat-6229	163	10	to	to	PART
easat-6229	163	11	assess	assess	VERB
easat-6229	163	12	students	student	NOUN
easat-6229	163	13	'	'	PART
easat-6229	163	14	mathematical	mathematical	ADJ
easat-6229	163	15	proof	proof	NOUN
easat-6229	163	16	abilities	ability	NOUN
easat-6229	163	17	in	in	ADP
easat-6229	163	18	solving	solve	VERB
easat-6229	163	19	problems	problem	NOUN
easat-6229	163	20	.	.	PUNCT
easat-6229	164	1	students	student	NOUN
easat-6229	164	2	are	be	AUX
easat-6229	164	3	required	require	VERB
easat-6229	164	4	to	to	PART
easat-6229	164	5	answer	answer	VERB
easat-6229	164	6	six	six	NUM
easat-6229	164	7	evidence	evidence	NOUN
easat-6229	164	8	-	-	PUNCT
easat-6229	164	9	oriented	orient	VERB
easat-6229	164	10	questions	question	NOUN
easat-6229	164	11	.	.	PUNCT
easat-6229	165	1	the	the	DET
easat-6229	165	2	focus	focus	NOUN
easat-6229	165	3	of	of	ADP
easat-6229	165	4	the	the	DET
easat-6229	165	5	test	test	NOUN
easat-6229	165	6	analysis	analysis	NOUN
easat-6229	165	7	is	be	AUX
easat-6229	165	8	on	on	ADP
easat-6229	165	9	indicators	indicator	NOUN
easat-6229	165	10	of	of	ADP
easat-6229	165	11	the	the	DET
easat-6229	165	12	student	student	NOUN
easat-6229	165	13	's	's	PART
easat-6229	165	14	mathematical	mathematical	ADJ
easat-6229	165	15	proof	proof	NOUN
easat-6229	165	16	performance	performance	NOUN
easat-6229	165	17	,	,	PUNCT
easat-6229	165	18	as	as	SCONJ
easat-6229	165	19	shown	show	VERB
easat-6229	165	20	in	in	ADP
easat-6229	165	21	table	table	NOUN
easat-6229	165	22	2	2	NUM
easat-6229	165	23	1245	1245	NUM
easat-6229	165	24	edelweiss	edelweiss	PROPN
easat-6229	165	25	applied	apply	VERB
easat-6229	165	26	science	science	NOUN
easat-6229	165	27	and	and	CCONJ
easat-6229	165	28	technology	technology	NOUN
easat-6229	165	29	issn	issn	PROPN
easat-6229	165	30	:	:	PUNCT
easat-6229	165	31	2576	2576	NUM
easat-6229	165	32	-	-	SYM
easat-6229	165	33	8484	8484	NUM
easat-6229	165	34	vol	vol	NOUN
easat-6229	165	35	.	.	PROPN
easat-6229	166	1	9	9	NUM
easat-6229	166	2	,	,	PUNCT
easat-6229	166	3	no	no	INTJ
easat-6229	166	4	.	.	NOUN
easat-6229	166	5	4	4	NUM
easat-6229	166	6	:	:	SYM
easat-6229	166	7	1240	1240	NUM
easat-6229	166	8	-	-	SYM
easat-6229	166	9	1251	1251	NUM
easat-6229	166	10	,	,	PUNCT
easat-6229	166	11	2025	2025	NUM
easat-6229	166	12	doi	doi	NOUN
easat-6229	166	13	:	:	PUNCT
easat-6229	166	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	166	15	©	©	ADP
easat-6229	166	16	2025	2025	NUM
easat-6229	166	17	by	by	ADP
easat-6229	166	18	the	the	DET
easat-6229	166	19	authors	author	NOUN
easat-6229	166	20	;	;	PUNCT
easat-6229	166	21	licensee	licensee	PROPN
easat-6229	166	22	learning	learn	VERB
easat-6229	166	23	gate	gate	NOUN
easat-6229	166	24	table	table	NOUN
easat-6229	166	25	2	2	NUM
easat-6229	166	26	.	.	PUNCT
easat-6229	166	27	evidentiary	evidentiary	ADJ
easat-6229	166	28	ability	ability	NOUN
easat-6229	166	29	and	and	CCONJ
easat-6229	166	30	measured	measure	VERB
easat-6229	166	31	aspect	aspect	NOUN
easat-6229	166	32	.	.	PUNCT
easat-6229	167	1	number	number	NOUN
easat-6229	167	2	indicators	indicator	NOUN
easat-6229	167	3	measured	measure	VERB
easat-6229	167	4	aspects	aspect	NOUN
easat-6229	167	5	submaterials	submaterial	NOUN
easat-6229	167	6	l2	l2	NOUN
easat-6229	167	7	m5	m5	NOUN
easat-6229	167	8	s3	s3	PROPN
easat-6229	167	9	1	1	NUM
easat-6229	167	10	.	.	PUNCT
easat-6229	168	1	reading	read	VERB
easat-6229	168	2	evidence	evidence	NOUN
easat-6229	168	3	make	make	VERB
easat-6229	168	4	a	a	DET
easat-6229	168	5	hypothesis	hypothesis	NOUN
easat-6229	168	6	(	(	PUNCT
easat-6229	168	7	conjecture	conjecture	NOUN
easat-6229	168	8	)	)	PUNCT
easat-6229	168	9	based	base	VERB
easat-6229	168	10	on	on	ADP
easat-6229	168	11	the	the	DET
easat-6229	168	12	pattern	pattern	NOUN
easat-6229	168	13	and	and	CCONJ
easat-6229	168	14	nature	nature	NOUN
easat-6229	168	15	of	of	ADP
easat-6229	168	16	several	several	ADJ
easat-6229	168	17	statements	statement	NOUN
easat-6229	168	18	and	and	CCONJ
easat-6229	168	19	prove	prove	VERB
easat-6229	168	20	the	the	DET
easat-6229	168	21	obtained	obtain	VERB
easat-6229	168	22	conjecture	conjecture	NOUN
easat-6229	168	23	by	by	ADP
easat-6229	168	24	deduction	deduction	NOUN
easat-6229	168	25	.	.	PUNCT
easat-6229	169	1	squeeze	squeeze	NOUN
easat-6229	169	2	theorem	theorem	NOUN
easat-6229	169	3	√	√	PROPN
easat-6229	169	4	√	√	NUM
easat-6229	169	5	×	×	PROPN
easat-6229	169	6	cauchy	cauchy	NOUN
easat-6229	169	7	sequence	sequence	NOUN
easat-6229	169	8	√	√	ADP
easat-6229	169	9	×	×	PROPN
easat-6229	169	10	×	×	NOUN
easat-6229	169	11	2	2	NUM
easat-6229	169	12	.	.	PUNCT
easat-6229	169	13	constructing	construct	VERB
easat-6229	169	14	evidence	evidence	NOUN
easat-6229	169	15	ability	ability	NOUN
easat-6229	169	16	to	to	PART
easat-6229	169	17	apply	apply	VERB
easat-6229	169	18	definitions	definition	NOUN
easat-6229	169	19	and	and	CCONJ
easat-6229	169	20	related	related	ADJ
easat-6229	169	21	properties	property	NOUN
easat-6229	169	22	and	and	CCONJ
easat-6229	169	23	sequence	sequence	NOUN
easat-6229	169	24	the	the	DET
easat-6229	169	25	steps	step	NOUN
easat-6229	169	26	of	of	ADP
easat-6229	169	27	proof	proof	NOUN
easat-6229	169	28	and	and	CCONJ
easat-6229	169	29	construction	construction	NOUN
easat-6229	169	30	into	into	ADP
easat-6229	169	31	formal	formal	ADJ
easat-6229	169	32	evidence	evidence	NOUN
easat-6229	169	33	.	.	PUNCT
easat-6229	170	1	sequence	sequence	NOUN
easat-6229	170	2	limit	limit	NOUN
easat-6229	170	3	√	√	NUM
easat-6229	170	4	×	×	NOUN
easat-6229	170	5	×	×	NOUN
easat-6229	170	6	sequence	sequence	NOUN
easat-6229	170	7	ratio	ratio	NOUN
easat-6229	170	8	√	√	NOUN
easat-6229	170	9	√	√	NUM
easat-6229	170	10	√	√	VERB
easat-6229	170	11	ability	ability	NOUN
easat-6229	170	12	to	to	PART
easat-6229	170	13	use	use	VERB
easat-6229	170	14	premises	premise	NOUN
easat-6229	170	15	,	,	PUNCT
easat-6229	170	16	definitions	definition	NOUN
easat-6229	170	17	,	,	PUNCT
easat-6229	170	18	or	or	CCONJ
easat-6229	170	19	statementrelated	statementrelate	VERB
easat-6229	170	20	theorems	theorem	NOUN
easat-6229	170	21	to	to	PART
easat-6229	170	22	build	build	VERB
easat-6229	170	23	a	a	DET
easat-6229	170	24	proof	proof	ADJ
easat-6229	170	25	monoton	monoton	NOUN
easat-6229	170	26	sequence	sequence	NOUN
easat-6229	170	27	×	×	NOUN
easat-6229	170	28	×	×	NOUN
easat-6229	170	29	×	×	NOUN
easat-6229	170	30	subsequences	subsequence	VERB
easat-6229	170	31	√	√	PROPN
easat-6229	170	32	√	√	NUM
easat-6229	170	33	×	×	NOUN
easat-6229	170	34	based	base	VERB
easat-6229	170	35	on	on	ADP
easat-6229	170	36	the	the	DET
easat-6229	170	37	results	result	NOUN
easat-6229	170	38	of	of	ADP
easat-6229	170	39	solving	solve	VERB
easat-6229	170	40	the	the	DET
easat-6229	170	41	questions	question	NOUN
easat-6229	170	42	above	above	ADV
easat-6229	170	43	,	,	PUNCT
easat-6229	170	44	it	it	PRON
easat-6229	170	45	was	be	AUX
easat-6229	170	46	found	find	VERB
easat-6229	170	47	that	that	SCONJ
easat-6229	170	48	l2	l2	NOUN
easat-6229	170	49	students	student	NOUN
easat-6229	170	50	already	already	ADV
easat-6229	170	51	understood	understand	VERB
easat-6229	170	52	the	the	DET
easat-6229	170	53	concept	concept	NOUN
easat-6229	170	54	of	of	ADP
easat-6229	170	55	proof	proof	NOUN
easat-6229	170	56	,	,	PUNCT
easat-6229	170	57	grasped	grasp	VERB
easat-6229	170	58	the	the	DET
easat-6229	170	59	flow	flow	NOUN
easat-6229	170	60	of	of	ADP
easat-6229	170	61	proof	proof	NOUN
easat-6229	170	62	,	,	PUNCT
easat-6229	170	63	and	and	CCONJ
easat-6229	170	64	could	could	AUX
easat-6229	170	65	draw	draw	VERB
easat-6229	170	66	valid	valid	ADJ
easat-6229	170	67	conclusions	conclusion	NOUN
easat-6229	170	68	.	.	PUNCT
easat-6229	171	1	meanwhile	meanwhile	ADV
easat-6229	171	2	,	,	PUNCT
easat-6229	171	3	s3	s3	PROPN
easat-6229	171	4	students	student	NOUN
easat-6229	171	5	do	do	AUX
easat-6229	171	6	not	not	PART
easat-6229	171	7	thoroughly	thoroughly	ADV
easat-6229	171	8	understand	understand	VERB
easat-6229	171	9	the	the	DET
easat-6229	171	10	concept	concept	NOUN
easat-6229	171	11	of	of	ADP
easat-6229	171	12	proof	proof	NOUN
easat-6229	171	13	and	and	CCONJ
easat-6229	171	14	can	can	AUX
easat-6229	171	15	not	not	PART
easat-6229	171	16	follow	follow	VERB
easat-6229	171	17	the	the	DET
easat-6229	171	18	evidence	evidence	NOUN
easat-6229	171	19	that	that	PRON
easat-6229	171	20	has	have	AUX
easat-6229	171	21	been	be	AUX
easat-6229	171	22	examined	examine	VERB
easat-6229	171	23	.	.	PUNCT
easat-6229	172	1	3.3	3.3	NUM
easat-6229	172	2	.	.	PUNCT
easat-6229	172	3	results	result	NOUN
easat-6229	172	4	of	of	ADP
easat-6229	172	5	evidentiary	evidentiary	ADJ
easat-6229	172	6	ability	ability	NOUN
easat-6229	172	7	the	the	DET
easat-6229	172	8	evidentiary	evidentiary	ADJ
easat-6229	172	9	test	test	NOUN
easat-6229	172	10	was	be	AUX
easat-6229	172	11	conducted	conduct	VERB
easat-6229	172	12	at	at	ADP
easat-6229	172	13	the	the	DET
easat-6229	172	14	seventh	seventh	ADJ
easat-6229	172	15	meeting	meeting	NOUN
easat-6229	172	16	after	after	SCONJ
easat-6229	172	17	the	the	DET
easat-6229	172	18	sequence	sequence	NOUN
easat-6229	172	19	material	material	NOUN
easat-6229	172	20	was	be	AUX
easat-6229	172	21	completed	complete	VERB
easat-6229	172	22	.	.	PUNCT
easat-6229	173	1	table	table	NOUN
easat-6229	173	2	1	1	NUM
easat-6229	173	3	shows	show	VERB
easat-6229	173	4	how	how	SCONJ
easat-6229	173	5	to	to	PART
easat-6229	173	6	calculate	calculate	VERB
easat-6229	173	7	the	the	DET
easat-6229	173	8	evidentiary	evidentiary	ADJ
easat-6229	173	9	criteria	criterion	NOUN
easat-6229	173	10	based	base	VERB
easat-6229	173	11	on	on	ADP
easat-6229	173	12	the	the	DET
easat-6229	173	13	test	test	NOUN
easat-6229	173	14	results	result	NOUN
easat-6229	173	15	,	,	PUNCT
easat-6229	173	16	while	while	SCONJ
easat-6229	173	17	table	table	NOUN
easat-6229	173	18	3	3	NUM
easat-6229	173	19	presents	present	VERB
easat-6229	173	20	the	the	DET
easat-6229	173	21	results	result	NOUN
easat-6229	173	22	of	of	ADP
easat-6229	173	23	the	the	DET
easat-6229	173	24	evidentiary	evidentiary	ADJ
easat-6229	173	25	criteria	criterion	NOUN
easat-6229	173	26	,	,	PUNCT
easat-6229	173	27	namely	namely	ADV
easat-6229	173	28	:	:	PUNCT
easat-6229	173	29	table	table	NOUN
easat-6229	173	30	3	3	NUM
easat-6229	173	31	.	.	PUNCT
easat-6229	173	32	results	result	NOUN
easat-6229	173	33	of	of	ADP
easat-6229	173	34	evidentiary	evidentiary	ADJ
easat-6229	173	35	criteria	criterion	NOUN
easat-6229	173	36	number	number	NOUN
easat-6229	173	37	types	type	NOUN
easat-6229	173	38	of	of	ADP
easat-6229	173	39	categories	category	NOUN
easat-6229	173	40	a	a	DET
easat-6229	173	41	large	large	ADJ
easat-6229	173	42	number	number	NOUN
easat-6229	173	43	of	of	ADP
easat-6229	173	44	students	student	NOUN
easat-6229	173	45	1	1	NUM
easat-6229	173	46	.	.	PUNCT
easat-6229	174	1	the	the	DET
easat-6229	174	2	upper	upper	ADJ
easat-6229	174	3	category	category	NOUN
easat-6229	174	4	(	(	PUNCT
easat-6229	174	5	l	l	NOUN
easat-6229	174	6	)	)	PUNCT
easat-6229	174	7	16	16	NUM
easat-6229	174	8	2	2	NUM
easat-6229	174	9	.	.	PUNCT
easat-6229	175	1	the	the	DET
easat-6229	175	2	middle	middle	ADJ
easat-6229	175	3	category	category	NOUN
easat-6229	175	4	(	(	PUNCT
easat-6229	175	5	m	m	NOUN
easat-6229	175	6	)	)	PUNCT
easat-6229	175	7	6	6	NUM
easat-6229	175	8	3	3	NUM
easat-6229	175	9	.	.	PUNCT
easat-6229	176	1	the	the	DET
easat-6229	176	2	lower	low	ADJ
easat-6229	176	3	category	category	NOUN
easat-6229	176	4	(	(	PUNCT
easat-6229	176	5	s	s	NOUN
easat-6229	176	6	)	)	PUNCT
easat-6229	176	7	3	3	NUM
easat-6229	176	8	observations	observation	NOUN
easat-6229	176	9	made	make	VERB
easat-6229	176	10	in	in	ADP
easat-6229	176	11	each	each	DET
easat-6229	176	12	category	category	NOUN
easat-6229	176	13	showed	show	VERB
easat-6229	176	14	that	that	SCONJ
easat-6229	176	15	high	high	ADJ
easat-6229	176	16	-	-	PUNCT
easat-6229	176	17	achieving	achieve	VERB
easat-6229	176	18	students	student	NOUN
easat-6229	176	19	enjoyed	enjoy	VERB
easat-6229	176	20	using	use	VERB
easat-6229	176	21	the	the	DET
easat-6229	176	22	newly	newly	ADV
easat-6229	176	23	learned	learn	VERB
easat-6229	176	24	lessons	lesson	NOUN
easat-6229	176	25	,	,	PUNCT
easat-6229	176	26	and	and	CCONJ
easat-6229	176	27	the	the	DET
easat-6229	176	28	discussion	discussion	NOUN
easat-6229	176	29	material	material	NOUN
easat-6229	176	30	worksheets	worksheet	NOUN
easat-6229	176	31	made	make	VERB
easat-6229	176	32	learning	learn	VERB
easat-6229	176	33	about	about	ADP
easat-6229	176	34	evidence	evidence	NOUN
easat-6229	176	35	easier	easy	ADJ
easat-6229	176	36	.	.	PUNCT
easat-6229	177	1	students	student	NOUN
easat-6229	177	2	engage	engage	VERB
easat-6229	177	3	in	in	ADP
easat-6229	177	4	group	group	NOUN
easat-6229	177	5	discussions	discussion	NOUN
easat-6229	177	6	on	on	ADP
easat-6229	177	7	this	this	DET
easat-6229	177	8	worksheet	worksheet	NOUN
easat-6229	177	9	,	,	PUNCT
easat-6229	177	10	allowing	allow	VERB
easat-6229	177	11	them	they	PRON
easat-6229	177	12	to	to	PART
easat-6229	177	13	grasp	grasp	VERB
easat-6229	177	14	the	the	DET
easat-6229	177	15	concept	concept	NOUN
easat-6229	177	16	of	of	ADP
easat-6229	177	17	proof	proof	NOUN
easat-6229	177	18	more	more	ADV
easat-6229	177	19	easily	easily	ADV
easat-6229	177	20	.	.	PUNCT
easat-6229	178	1	if	if	SCONJ
easat-6229	178	2	students	student	NOUN
easat-6229	178	3	read	read	VERB
easat-6229	178	4	the	the	DET
easat-6229	178	5	evidence	evidence	NOUN
easat-6229	178	6	correctly	correctly	ADV
easat-6229	178	7	and	and	CCONJ
easat-6229	178	8	carefully	carefully	ADV
easat-6229	178	9	,	,	PUNCT
easat-6229	178	10	they	they	PRON
easat-6229	178	11	can	can	AUX
easat-6229	178	12	understand	understand	VERB
easat-6229	178	13	it	it	PRON
easat-6229	178	14	better	well	ADV
easat-6229	178	15	.	.	PUNCT
easat-6229	179	1	they	they	PRON
easat-6229	179	2	can	can	AUX
easat-6229	179	3	easily	easily	ADV
easat-6229	179	4	and	and	CCONJ
easat-6229	179	5	accurately	accurately	ADV
easat-6229	179	6	interpret	interpret	VERB
easat-6229	179	7	all	all	DET
easat-6229	179	8	the	the	DET
easat-6229	179	9	definitions	definition	NOUN
easat-6229	179	10	,	,	PUNCT
easat-6229	179	11	theorems	theorem	NOUN
easat-6229	179	12	,	,	PUNCT
easat-6229	179	13	lemmas	lemmas	ADJ
easat-6229	179	14	,	,	PUNCT
easat-6229	179	15	and	and	CCONJ
easat-6229	179	16	evidentiary	evidentiary	ADJ
easat-6229	179	17	problems	problem	NOUN
easat-6229	179	18	presented	present	VERB
easat-6229	179	19	in	in	ADP
easat-6229	179	20	the	the	DET
easat-6229	179	21	worksheet	worksheet	NOUN
easat-6229	179	22	.	.	PUNCT
easat-6229	180	1	additionally	additionally	ADV
easat-6229	180	2	,	,	PUNCT
easat-6229	180	3	students	student	NOUN
easat-6229	180	4	can	can	AUX
easat-6229	180	5	use	use	VERB
easat-6229	180	6	the	the	DET
easat-6229	180	7	strategies	strategy	NOUN
easat-6229	180	8	provided	provide	VERB
easat-6229	180	9	in	in	ADP
easat-6229	180	10	the	the	DET
easat-6229	180	11	worksheet	worksheet	NOUN
easat-6229	180	12	to	to	PART
easat-6229	180	13	construct	construct	VERB
easat-6229	180	14	evidence	evidence	NOUN
easat-6229	180	15	.	.	PUNCT
easat-6229	181	1	students	student	NOUN
easat-6229	181	2	already	already	ADV
easat-6229	181	3	understand	understand	VERB
easat-6229	181	4	the	the	DET
easat-6229	181	5	concepts	concept	NOUN
easat-6229	181	6	,	,	PUNCT
easat-6229	181	7	definitions	definition	NOUN
easat-6229	181	8	,	,	PUNCT
easat-6229	181	9	and	and	CCONJ
easat-6229	181	10	theorems	theorem	NOUN
easat-6229	181	11	,	,	PUNCT
easat-6229	181	12	allowing	allow	VERB
easat-6229	181	13	them	they	PRON
easat-6229	181	14	to	to	PART
easat-6229	181	15	comprehend	comprehend	VERB
easat-6229	181	16	the	the	DET
easat-6229	181	17	steps	step	NOUN
easat-6229	181	18	of	of	ADP
easat-6229	181	19	proof	proof	NOUN
easat-6229	181	20	correctly	correctly	ADV
easat-6229	181	21	.	.	PUNCT
easat-6229	182	1	most	most	ADJ
easat-6229	182	2	students	student	NOUN
easat-6229	182	3	can	can	AUX
easat-6229	182	4	identify	identify	VERB
easat-6229	182	5	and	and	CCONJ
easat-6229	182	6	correct	correct	ADJ
easat-6229	182	7	symbols	symbol	NOUN
easat-6229	182	8	,	,	PUNCT
easat-6229	182	9	statements	statement	NOUN
easat-6229	182	10	,	,	PUNCT
easat-6229	182	11	and	and	CCONJ
easat-6229	182	12	premises	premise	NOUN
easat-6229	182	13	in	in	ADP
easat-6229	182	14	incorrect	incorrect	ADJ
easat-6229	182	15	proof	proof	NOUN
easat-6229	182	16	steps	step	NOUN
easat-6229	182	17	or	or	CCONJ
easat-6229	182	18	provide	provide	VERB
easat-6229	182	19	reasons	reason	NOUN
easat-6229	182	20	for	for	ADP
easat-6229	182	21	these	these	DET
easat-6229	182	22	errors	error	NOUN
easat-6229	182	23	.	.	PUNCT
easat-6229	183	1	they	they	PRON
easat-6229	183	2	can	can	AUX
easat-6229	183	3	also	also	ADV
easat-6229	183	4	apply	apply	VERB
easat-6229	183	5	the	the	DET
easat-6229	183	6	evidentiary	evidentiary	ADJ
easat-6229	183	7	steps	step	NOUN
easat-6229	183	8	to	to	ADP
easat-6229	183	9	similar	similar	ADJ
easat-6229	183	10	statements	statement	NOUN
easat-6229	183	11	.	.	PUNCT
easat-6229	184	1	furthermore	furthermore	ADV
easat-6229	184	2	,	,	PUNCT
easat-6229	184	3	students	student	NOUN
easat-6229	184	4	successfully	successfully	ADV
easat-6229	184	5	use	use	VERB
easat-6229	184	6	relevant	relevant	ADJ
easat-6229	184	7	premises	premise	NOUN
easat-6229	184	8	,	,	PUNCT
easat-6229	184	9	definitions	definition	NOUN
easat-6229	184	10	,	,	PUNCT
easat-6229	184	11	or	or	CCONJ
easat-6229	184	12	theorems	theorem	NOUN
easat-6229	184	13	to	to	PART
easat-6229	184	14	construct	construct	VERB
easat-6229	184	15	evidence	evidence	NOUN
easat-6229	184	16	.	.	PUNCT
easat-6229	185	1	students	student	NOUN
easat-6229	185	2	in	in	ADP
easat-6229	185	3	this	this	DET
easat-6229	185	4	class	class	NOUN
easat-6229	185	5	can	can	AUX
easat-6229	185	6	understand	understand	VERB
easat-6229	185	7	and	and	CCONJ
easat-6229	185	8	follow	follow	VERB
easat-6229	185	9	evidence	evidence	NOUN
easat-6229	185	10	effectively	effectively	ADV
easat-6229	185	11	.	.	PUNCT
easat-6229	186	1	finally	finally	ADV
easat-6229	186	2	,	,	PUNCT
easat-6229	186	3	students	student	NOUN
easat-6229	186	4	with	with	ADP
easat-6229	186	5	high	high	ADJ
easat-6229	186	6	grades	grade	NOUN
easat-6229	186	7	can	can	AUX
easat-6229	186	8	easily	easily	ADV
easat-6229	186	9	provide	provide	VERB
easat-6229	186	10	accurate	accurate	ADJ
easat-6229	186	11	and	and	CCONJ
easat-6229	186	12	valid	valid	ADJ
easat-6229	186	13	conclusions	conclusion	NOUN
easat-6229	186	14	.	.	PUNCT
easat-6229	187	1	the	the	DET
easat-6229	187	2	results	result	NOUN
easat-6229	187	3	of	of	ADP
easat-6229	187	4	the	the	DET
easat-6229	187	5	work	work	NOUN
easat-6229	187	6	on	on	ADP
easat-6229	187	7	the	the	DET
easat-6229	187	8	cauchy	cauchy	ADJ
easat-6229	187	9	sequence	sequence	NOUN
easat-6229	187	10	carried	carry	VERB
easat-6229	187	11	out	out	ADP
easat-6229	187	12	by	by	ADP
easat-6229	187	13	l2	l2	NOUN
easat-6229	187	14	are	be	AUX
easat-6229	187	15	as	as	SCONJ
easat-6229	187	16	follows	follow	VERB
easat-6229	187	17	:	:	PUNCT
easat-6229	187	18	1246	1246	NUM
easat-6229	187	19	edelweiss	edelweiss	PROPN
easat-6229	187	20	applied	apply	VERB
easat-6229	187	21	science	science	NOUN
easat-6229	187	22	and	and	CCONJ
easat-6229	187	23	technology	technology	NOUN
easat-6229	187	24	issn	issn	PROPN
easat-6229	187	25	:	:	PUNCT
easat-6229	187	26	2576	2576	NUM
easat-6229	187	27	-	-	SYM
easat-6229	187	28	8484	8484	NUM
easat-6229	187	29	vol	vol	NOUN
easat-6229	187	30	.	.	PROPN
easat-6229	188	1	9	9	NUM
easat-6229	188	2	,	,	PUNCT
easat-6229	188	3	no	no	INTJ
easat-6229	188	4	.	.	NOUN
easat-6229	188	5	4	4	NUM
easat-6229	188	6	:	:	SYM
easat-6229	188	7	1240	1240	NUM
easat-6229	188	8	-	-	SYM
easat-6229	188	9	1251	1251	NUM
easat-6229	188	10	,	,	PUNCT
easat-6229	188	11	2025	2025	NUM
easat-6229	188	12	doi	doi	NOUN
easat-6229	188	13	:	:	PUNCT
easat-6229	188	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	188	15	©	©	ADP
easat-6229	188	16	2025	2025	NUM
easat-6229	188	17	by	by	ADP
easat-6229	188	18	the	the	DET
easat-6229	188	19	authors	author	NOUN
easat-6229	188	20	;	;	PUNCT
easat-6229	188	21	licensee	licensee	PROPN
easat-6229	188	22	learning	learn	VERB
easat-6229	188	23	gate	gate	NOUN
easat-6229	188	24	figure	figure	NOUN
easat-6229	188	25	1	1	NUM
easat-6229	188	26	.	.	PUNCT
easat-6229	188	27	high	high	ADJ
easat-6229	188	28	category	category	NOUN
easat-6229	188	29	performance	performance	NOUN
easat-6229	188	30	result	result	NOUN
easat-6229	188	31	(	(	PUNCT
easat-6229	188	32	l2	l2	NOUN
easat-6229	188	33	)	)	PUNCT
easat-6229	188	34	.	.	PUNCT
easat-6229	189	1	the	the	DET
easat-6229	189	2	results	result	NOUN
easat-6229	189	3	of	of	ADP
easat-6229	189	4	the	the	DET
easat-6229	189	5	lecturer	lecturer	NOUN
easat-6229	189	6	's	's	PART
easat-6229	189	7	(	(	PUNCT
easat-6229	189	8	t	t	NOUN
easat-6229	189	9	)	)	PUNCT
easat-6229	189	10	interview	interview	NOUN
easat-6229	189	11	with	with	ADP
easat-6229	189	12	the	the	DET
easat-6229	189	13	students	student	NOUN
easat-6229	189	14	(	(	PUNCT
easat-6229	189	15	l2	l2	PROPN
easat-6229	189	16	)	)	PUNCT
easat-6229	189	17	are	be	AUX
easat-6229	189	18	as	as	SCONJ
easat-6229	189	19	follows	follow	VERB
easat-6229	189	20	:	:	PUNCT
easat-6229	189	21	t	t	X
easat-6229	189	22	:	:	PUNCT
easat-6229	189	23	what	what	PRON
easat-6229	189	24	do	do	AUX
easat-6229	189	25	you	you	PRON
easat-6229	189	26	think	think	VERB
easat-6229	189	27	of	of	ADP
easat-6229	189	28	this	this	DET
easat-6229	189	29	material	material	NOUN
easat-6229	189	30	sequence	sequence	NOUN
easat-6229	189	31	during	during	ADP
easat-6229	189	32	the	the	DET
easat-6229	189	33	lecture	lecture	NOUN
easat-6229	189	34	?	?	PUNCT
easat-6229	190	1	l2	l2	NOUN
easat-6229	190	2	:	:	PUNCT
easat-6229	190	3	increase	increase	VERB
easat-6229	190	4	knowledge	knowledge	NOUN
easat-6229	190	5	of	of	ADP
easat-6229	190	6	the	the	DET
easat-6229	190	7	problem	problem	NOUN
easat-6229	190	8	of	of	ADP
easat-6229	190	9	proof	proof	NOUN
easat-6229	190	10	.	.	PUNCT
easat-6229	191	1	t	t	PROPN
easat-6229	191	2	:	:	PUNCT
easat-6229	191	3	how	how	SCONJ
easat-6229	191	4	to	to	PART
easat-6229	191	5	complete	complete	VERB
easat-6229	191	6	the	the	DET
easat-6229	191	7	evidence	evidence	NOUN
easat-6229	191	8	related	relate	VERB
easat-6229	191	9	to	to	ADP
easat-6229	191	10	the	the	DET
easat-6229	191	11	problem	problem	NOUN
easat-6229	191	12	of	of	ADP
easat-6229	191	13	proof	proof	NOUN
easat-6229	191	14	?	?	PUNCT
easat-6229	192	1	l2	l2	NOUN
easat-6229	192	2	:	:	PUNCT
easat-6229	192	3	before	before	ADP
easat-6229	192	4	embarking	embark	VERB
easat-6229	192	5	on	on	ADP
easat-6229	192	6	proving	prove	VERB
easat-6229	192	7	a	a	DET
easat-6229	192	8	theorem	theorem	NOUN
easat-6229	192	9	,	,	PUNCT
easat-6229	192	10	it	it	PRON
easat-6229	192	11	is	be	AUX
easat-6229	192	12	indispensable	indispensable	ADJ
easat-6229	192	13	to	to	PART
easat-6229	192	14	thoroughly	thoroughly	ADV
easat-6229	192	15	comprehend	comprehend	VERB
easat-6229	192	16	the	the	DET
easat-6229	192	17	underlying	underlie	VERB
easat-6229	192	18	problem	problem	NOUN
easat-6229	192	19	and	and	CCONJ
easat-6229	192	20	then	then	ADV
easat-6229	192	21	do	do	VERB
easat-6229	192	22	the	the	DET
easat-6229	192	23	initial	initial	ADJ
easat-6229	192	24	analysis	analysis	NOUN
easat-6229	192	25	t	t	NOUN
easat-6229	192	26	:	:	PUNCT
easat-6229	192	27	why	why	SCONJ
easat-6229	192	28	do	do	AUX
easat-6229	192	29	you	you	PRON
easat-6229	192	30	need	need	VERB
easat-6229	192	31	to	to	PART
easat-6229	192	32	understand	understand	VERB
easat-6229	192	33	the	the	DET
easat-6229	192	34	meaning	meaning	NOUN
easat-6229	192	35	of	of	ADP
easat-6229	192	36	the	the	DET
easat-6229	192	37	problem	problem	NOUN
easat-6229	192	38	?	?	PUNCT
easat-6229	193	1	l2	l2	NOUN
easat-6229	193	2	:	:	PUNCT
easat-6229	193	3	understanding	understand	VERB
easat-6229	193	4	the	the	DET
easat-6229	193	5	problem	problem	NOUN
easat-6229	193	6	makes	make	VERB
easat-6229	193	7	it	it	PRON
easat-6229	193	8	easy	easy	ADJ
easat-6229	193	9	to	to	PART
easat-6229	193	10	identify	identify	VERB
easat-6229	193	11	the	the	DET
easat-6229	193	12	premise	premise	NOUN
easat-6229	193	13	and	and	CCONJ
easat-6229	193	14	conclude	conclude	VERB
easat-6229	193	15	what	what	PRON
easat-6229	193	16	needs	need	VERB
easat-6229	193	17	to	to	PART
easat-6229	193	18	be	be	AUX
easat-6229	193	19	proven	prove	VERB
easat-6229	193	20	.	.	PUNCT
easat-6229	194	1	with	with	ADP
easat-6229	194	2	clarity	clarity	NOUN
easat-6229	194	3	about	about	ADP
easat-6229	194	4	these	these	DET
easat-6229	194	5	points	point	NOUN
easat-6229	194	6	,	,	PUNCT
easat-6229	194	7	you	you	PRON
easat-6229	194	8	can	can	AUX
easat-6229	194	9	then	then	ADV
easat-6229	194	10	take	take	VERB
easat-6229	194	11	the	the	DET
easat-6229	194	12	required	require	VERB
easat-6229	194	13	evidentiary	evidentiary	ADJ
easat-6229	194	14	steps	step	NOUN
easat-6229	194	15	to	to	PART
easat-6229	194	16	arrive	arrive	VERB
easat-6229	194	17	at	at	ADP
easat-6229	194	18	your	your	PRON
easat-6229	194	19	conclusion	conclusion	NOUN
easat-6229	194	20	.	.	PUNCT
easat-6229	195	1	each	each	DET
easat-6229	195	2	step	step	NOUN
easat-6229	195	3	builds	build	VERB
easat-6229	195	4	upon	upon	SCONJ
easat-6229	195	5	the	the	DET
easat-6229	195	6	last	last	ADJ
easat-6229	195	7	,	,	PUNCT
easat-6229	195	8	creating	create	VERB
easat-6229	195	9	a	a	DET
easat-6229	195	10	logical	logical	ADJ
easat-6229	195	11	sequence	sequence	NOUN
easat-6229	195	12	that	that	PRON
easat-6229	195	13	leads	lead	VERB
easat-6229	195	14	directly	directly	ADV
easat-6229	195	15	to	to	ADP
easat-6229	195	16	your	your	PRON
easat-6229	195	17	desired	desire	VERB
easat-6229	195	18	outcome	outcome	NOUN
easat-6229	195	19	.	.	PUNCT
easat-6229	196	1	thus	thus	ADV
easat-6229	196	2	,	,	PUNCT
easat-6229	196	3	clear	clear	ADJ
easat-6229	196	4	comprehension	comprehension	NOUN
easat-6229	196	5	simplifies	simplify	VERB
easat-6229	196	6	the	the	DET
easat-6229	196	7	process	process	NOUN
easat-6229	196	8	of	of	ADP
easat-6229	196	9	constructing	construct	VERB
easat-6229	196	10	a	a	DET
easat-6229	196	11	valid	valid	ADJ
easat-6229	196	12	proof	proof	NOUN
easat-6229	196	13	.	.	PUNCT
easat-6229	197	1	t	t	PROPN
easat-6229	197	2	:	:	PUNCT
easat-6229	197	3	what	what	PRON
easat-6229	197	4	is	be	AUX
easat-6229	197	5	the	the	DET
easat-6229	197	6	need	need	NOUN
easat-6229	197	7	for	for	ADP
easat-6229	197	8	an	an	DET
easat-6229	197	9	initial	initial	ADJ
easat-6229	197	10	analysis	analysis	NOUN
easat-6229	197	11	l2	l2	NOUN
easat-6229	197	12	:	:	PUNCT
easat-6229	197	13	to	to	PART
easat-6229	197	14	facilitate	facilitate	VERB
easat-6229	197	15	proof	proof	NOUN
easat-6229	197	16	,	,	PUNCT
easat-6229	197	17	in	in	ADP
easat-6229	197	18	this	this	DET
easat-6229	197	19	row	row	NOUN
easat-6229	197	20	problem	problem	NOUN
easat-6229	197	21	,	,	PUNCT
easat-6229	197	22	the	the	DET
easat-6229	197	23	theories	theory	NOUN
easat-6229	197	24	used	use	VERB
easat-6229	197	25	to	to	PART
easat-6229	197	26	prove	prove	VERB
easat-6229	197	27	convergent	convergent	NOUN
easat-6229	197	28	rows	row	NOUN
easat-6229	197	29	are	be	AUX
easat-6229	197	30	numerous	numerous	ADJ
easat-6229	197	31	so	so	SCONJ
easat-6229	197	32	that	that	SCONJ
easat-6229	197	33	by	by	ADP
easat-6229	197	34	conducting	conduct	VERB
easat-6229	197	35	a	a	DET
easat-6229	197	36	preliminary	preliminary	ADJ
easat-6229	197	37	analysis	analysis	NOUN
easat-6229	197	38	,	,	PUNCT
easat-6229	197	39	we	we	PRON
easat-6229	197	40	can	can	AUX
easat-6229	197	41	determine	determine	VERB
easat-6229	197	42	the	the	DET
easat-6229	197	43	right	right	ADJ
easat-6229	197	44	theory	theory	NOUN
easat-6229	197	45	that	that	PRON
easat-6229	197	46	corresponds	correspond	VERB
easat-6229	197	47	to	to	ADP
easat-6229	197	48	the	the	DET
easat-6229	197	49	characteristics	characteristic	NOUN
easat-6229	197	50	of	of	ADP
easat-6229	197	51	the	the	DET
easat-6229	197	52	problem	problem	NOUN
easat-6229	197	53	.	.	PUNCT
easat-6229	198	1	to	to	PART
easat-6229	198	2	do	do	VERB
easat-6229	198	3	this	this	PRON
easat-6229	198	4	,	,	PUNCT
easat-6229	198	5	do	do	VERB
easat-6229	198	6	a	a	DET
easat-6229	198	7	preliminary	preliminary	ADJ
easat-6229	198	8	analysis	analysis	NOUN
easat-6229	198	9	first	first	ADV
easat-6229	198	10	,	,	PUNCT
easat-6229	198	11	as	as	SCONJ
easat-6229	198	12	is	be	AUX
easat-6229	198	13	done	do	VERB
easat-6229	198	14	in	in	ADP
easat-6229	198	15	the	the	DET
easat-6229	198	16	cauchy	cauchy	PROPN
easat-6229	198	17	row	row	NOUN
easat-6229	198	18	problem	problem	NOUN
easat-6229	198	19	,	,	PUNCT
easat-6229	198	20	so	so	SCONJ
easat-6229	198	21	that	that	SCONJ
easat-6229	198	22	it	it	PRON
easat-6229	198	23	is	be	AUX
easat-6229	198	24	easy	easy	ADJ
easat-6229	198	25	to	to	PART
easat-6229	198	26	determine	determine	VERB
easat-6229	198	27	the	the	DET
easat-6229	198	28	value	value	NOUN
easat-6229	198	29	.	.	PUNCT
easat-6229	199	1	𝜀	𝜀	PROPN
easat-6229	199	2	2𝐴	2𝐴	NOUN
easat-6229	199	3	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
easat-6229	199	4	𝜀	𝜀	PROPN
easat-6229	199	5	2𝐵	2𝐵	NOUN
easat-6229	199	6	for	for	ADP
easat-6229	199	7	each	each	DET
easat-6229	199	8	row	row	NOUN
easat-6229	199	9	,	,	PUNCT
easat-6229	199	10	so	so	SCONJ
easat-6229	199	11	that	that	SCONJ
easat-6229	199	12	if	if	SCONJ
easat-6229	199	13	the	the	DET
easat-6229	199	14	two	two	NUM
easat-6229	199	15	rows	row	NOUN
easat-6229	199	16	are	be	AUX
easat-6229	199	17	added	add	VERB
easat-6229	199	18	together	together	ADV
easat-6229	199	19	it	it	PRON
easat-6229	199	20	will	will	AUX
easat-6229	199	21	yield	yield	VERB
easat-6229	199	22	ε	ε	PROPN
easat-6229	199	23	.	.	PUNCT
easat-6229	200	1	students	student	NOUN
easat-6229	200	2	in	in	ADP
easat-6229	200	3	the	the	DET
easat-6229	200	4	middle	middle	ADJ
easat-6229	200	5	category	category	NOUN
easat-6229	200	6	(	(	PUNCT
easat-6229	200	7	m	m	NOUN
easat-6229	200	8	)	)	PUNCT
easat-6229	200	9	have	have	AUX
easat-6229	200	10	expressed	express	VERB
easat-6229	200	11	their	their	PRON
easat-6229	200	12	satisfaction	satisfaction	NOUN
easat-6229	200	13	with	with	ADP
easat-6229	200	14	the	the	DET
easat-6229	200	15	newly	newly	ADV
easat-6229	200	16	implemented	implement	VERB
easat-6229	200	17	learning	learning	NOUN
easat-6229	200	18	model	model	NOUN
easat-6229	200	19	,	,	PUNCT
easat-6229	200	20	although	although	SCONJ
easat-6229	200	21	they	they	PRON
easat-6229	200	22	still	still	ADV
easat-6229	200	23	request	request	VERB
easat-6229	200	24	continuous	continuous	ADJ
easat-6229	200	25	support	support	NOUN
easat-6229	200	26	from	from	ADP
easat-6229	200	27	their	their	PRON
easat-6229	200	28	lecturers	lecturer	NOUN
easat-6229	200	29	.	.	PUNCT
easat-6229	201	1	their	their	PRON
easat-6229	201	2	understanding	understanding	NOUN
easat-6229	201	3	of	of	ADP
easat-6229	201	4	the	the	DET
easat-6229	201	5	steps	step	NOUN
easat-6229	201	6	involved	involve	VERB
easat-6229	201	7	in	in	ADP
easat-6229	201	8	proof	proof	NOUN
easat-6229	201	9	and	and	CCONJ
easat-6229	201	10	the	the	DET
easat-6229	201	11	application	application	NOUN
easat-6229	201	12	of	of	ADP
easat-6229	201	13	definitions	definition	NOUN
easat-6229	201	14	for	for	ADP
easat-6229	201	15	proving	prove	VERB
easat-6229	201	16	concepts	concept	NOUN
easat-6229	201	17	has	have	AUX
easat-6229	201	18	notably	notably	ADV
easat-6229	201	19	improved	improve	VERB
easat-6229	201	20	.	.	PUNCT
easat-6229	202	1	below	below	ADV
easat-6229	202	2	is	be	AUX
easat-6229	202	3	one	one	NUM
easat-6229	202	4	of	of	ADP
easat-6229	202	5	the	the	DET
easat-6229	202	6	tests	test	NOUN
easat-6229	202	7	works	work	VERB
easat-6229	202	8	on	on	ADP
easat-6229	202	9	cauchy	cauchy	ADJ
easat-6229	202	10	sequence	sequence	NOUN
easat-6229	202	11	problems	problem	NOUN
easat-6229	202	12	completed	complete	VERB
easat-6229	202	13	by	by	ADP
easat-6229	202	14	a	a	DET
easat-6229	202	15	student	student	NOUN
easat-6229	202	16	in	in	ADP
easat-6229	202	17	the	the	DET
easat-6229	202	18	intermediate	intermediate	ADJ
easat-6229	202	19	category	category	NOUN
easat-6229	202	20	,	,	PUNCT
easat-6229	202	21	identified	identify	VERB
easat-6229	202	22	as	as	ADP
easat-6229	202	23	m5	m5	PROPN
easat-6229	202	24	.	.	PUNCT
easat-6229	203	1	this	this	DET
easat-6229	203	2	work	work	NOUN
easat-6229	203	3	reflects	reflect	VERB
easat-6229	203	4	their	their	PRON
easat-6229	203	5	enhanced	enhanced	ADJ
easat-6229	203	6	grasp	grasp	NOUN
easat-6229	203	7	of	of	ADP
easat-6229	203	8	the	the	DET
easat-6229	203	9	material	material	NOUN
easat-6229	203	10	and	and	CCONJ
easat-6229	203	11	demonstrates	demonstrate	VERB
easat-6229	203	12	their	their	PRON
easat-6229	203	13	ability	ability	NOUN
easat-6229	203	14	to	to	PART
easat-6229	203	15	apply	apply	VERB
easat-6229	203	16	the	the	DET
easat-6229	203	17	concepts	concept	NOUN
easat-6229	203	18	learned	learn	VERB
easat-6229	203	19	effectively	effectively	ADV
easat-6229	203	20	.	.	PUNCT
easat-6229	204	1	the	the	DET
easat-6229	204	2	results	result	NOUN
easat-6229	204	3	indicated	indicate	VERB
easat-6229	204	4	that	that	SCONJ
easat-6229	204	5	students	student	NOUN
easat-6229	204	6	in	in	ADP
easat-6229	204	7	the	the	DET
easat-6229	204	8	middle	middle	ADJ
easat-6229	204	9	category	category	NOUN
easat-6229	204	10	(	(	PUNCT
easat-6229	204	11	m	m	NOUN
easat-6229	204	12	)	)	PUNCT
easat-6229	204	13	expressed	express	VERB
easat-6229	204	14	satisfaction	satisfaction	NOUN
easat-6229	204	15	with	with	ADP
easat-6229	204	16	the	the	DET
easat-6229	204	17	new	new	ADJ
easat-6229	204	18	learning	learning	NOUN
easat-6229	204	19	model	model	NOUN
easat-6229	204	20	.	.	PUNCT
easat-6229	205	1	however	however	ADV
easat-6229	205	2	,	,	PUNCT
easat-6229	205	3	they	they	PRON
easat-6229	205	4	emphasized	emphasize	VERB
easat-6229	205	5	the	the	DET
easat-6229	205	6	need	need	NOUN
easat-6229	205	7	for	for	SCONJ
easat-6229	205	8	ongoing	ongoing	ADJ
easat-6229	205	9	support	support	NOUN
easat-6229	205	10	from	from	ADP
easat-6229	205	11	their	their	PRON
easat-6229	205	12	lecturers	lecturer	NOUN
easat-6229	205	13	to	to	PART
easat-6229	205	14	enhance	enhance	VERB
easat-6229	205	15	their	their	PRON
easat-6229	205	16	learning	learning	NOUN
easat-6229	205	17	experience	experience	NOUN
easat-6229	205	18	.	.	PUNCT
easat-6229	206	1	these	these	DET
easat-6229	206	2	students	student	NOUN
easat-6229	206	3	reported	report	VERB
easat-6229	206	4	gaining	gain	VERB
easat-6229	206	5	a	a	DET
easat-6229	206	6	deeper	deep	ADJ
easat-6229	206	7	understanding	understanding	NOUN
easat-6229	206	8	of	of	ADP
easat-6229	206	9	the	the	DET
easat-6229	206	10	proof	proof	ADJ
easat-6229	206	11	process	process	NOUN
easat-6229	206	12	and	and	CCONJ
easat-6229	206	13	the	the	DET
easat-6229	206	14	application	application	NOUN
easat-6229	206	15	of	of	ADP
easat-6229	206	16	definitions	definition	NOUN
easat-6229	206	17	in	in	ADP
easat-6229	206	18	mathematical	mathematical	ADJ
easat-6229	206	19	proofs	proof	NOUN
easat-6229	206	20	.	.	PUNCT
easat-6229	207	1	an	an	DET
easat-6229	207	2	example	example	NOUN
easat-6229	207	3	of	of	ADP
easat-6229	207	4	an	an	DET
easat-6229	207	5	exam	exam	NOUN
easat-6229	207	6	question	question	NOUN
easat-6229	207	7	related	relate	VERB
easat-6229	207	8	to	to	ADP
easat-6229	207	9	the	the	DET
easat-6229	207	10	cauchy	cauchy	ADJ
easat-6229	207	11	sequence	sequence	NOUN
easat-6229	207	12	,	,	PUNCT
easat-6229	207	13	designed	design	VERB
easat-6229	207	14	for	for	ADP
easat-6229	207	15	students	student	NOUN
easat-6229	207	16	in	in	ADP
easat-6229	207	17	the	the	DET
easat-6229	207	18	intermediate	intermediate	ADJ
easat-6229	207	19	category	category	NOUN
easat-6229	207	20	,	,	PUNCT
easat-6229	207	21	is	be	AUX
easat-6229	207	22	provided	provide	VERB
easat-6229	207	23	below	below	ADP
easat-6229	207	24	.	.	PUNCT
easat-6229	208	1	1247	1247	NUM
easat-6229	208	2	edelweiss	edelweiss	PROPN
easat-6229	208	3	applied	apply	VERB
easat-6229	208	4	science	science	NOUN
easat-6229	208	5	and	and	CCONJ
easat-6229	208	6	technology	technology	NOUN
easat-6229	208	7	issn	issn	PROPN
easat-6229	208	8	:	:	PUNCT
easat-6229	208	9	2576	2576	NUM
easat-6229	208	10	-	-	SYM
easat-6229	208	11	8484	8484	NUM
easat-6229	208	12	vol	vol	NOUN
easat-6229	208	13	.	.	PROPN
easat-6229	209	1	9	9	NUM
easat-6229	209	2	,	,	PUNCT
easat-6229	209	3	no	no	INTJ
easat-6229	209	4	.	.	NOUN
easat-6229	209	5	4	4	NUM
easat-6229	209	6	:	:	SYM
easat-6229	209	7	1240	1240	NUM
easat-6229	209	8	-	-	SYM
easat-6229	209	9	1251	1251	NUM
easat-6229	209	10	,	,	PUNCT
easat-6229	209	11	2025	2025	NUM
easat-6229	209	12	doi	doi	NOUN
easat-6229	209	13	:	:	PUNCT
easat-6229	209	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	209	15	©	©	ADP
easat-6229	209	16	2025	2025	NUM
easat-6229	209	17	by	by	ADP
easat-6229	209	18	the	the	DET
easat-6229	209	19	authors	author	NOUN
easat-6229	209	20	;	;	PUNCT
easat-6229	209	21	licensee	licensee	PROPN
easat-6229	209	22	learning	learn	VERB
easat-6229	209	23	gate	gate	NOUN
easat-6229	209	24	figure	figure	NOUN
easat-6229	209	25	2	2	NUM
easat-6229	209	26	.	.	NOUN
easat-6229	209	27	medium	medium	ADJ
easat-6229	209	28	category	category	NOUN
easat-6229	209	29	test	test	NOUN
easat-6229	209	30	answer	answer	NOUN
easat-6229	209	31	result	result	NOUN
easat-6229	209	32	(	(	PUNCT
easat-6229	209	33	m5	m5	NOUN
easat-6229	209	34	)	)	PUNCT
easat-6229	209	35	the	the	DET
easat-6229	209	36	results	result	NOUN
easat-6229	209	37	of	of	ADP
easat-6229	209	38	the	the	DET
easat-6229	209	39	interviews	interview	NOUN
easat-6229	209	40	conducted	conduct	VERB
easat-6229	209	41	by	by	ADP
easat-6229	209	42	m5	m5	ADJ
easat-6229	209	43	lecturers	lecturer	NOUN
easat-6229	209	44	and	and	CCONJ
easat-6229	209	45	students	student	NOUN
easat-6229	209	46	revealed	reveal	VERB
easat-6229	209	47	that	that	SCONJ
easat-6229	209	48	students	student	NOUN
easat-6229	209	49	in	in	ADP
easat-6229	209	50	category	category	NOUN
easat-6229	209	51	m	m	VERB
easat-6229	209	52	still	still	ADV
easat-6229	209	53	experience	experience	VERB
easat-6229	209	54	confusion	confusion	NOUN
easat-6229	209	55	when	when	SCONJ
easat-6229	209	56	verifying	verify	VERB
easat-6229	209	57	mathematical	mathematical	ADJ
easat-6229	209	58	statements	statement	NOUN
easat-6229	209	59	to	to	PART
easat-6229	209	60	determine	determine	VERB
easat-6229	209	61	their	their	PRON
easat-6229	209	62	validity	validity	NOUN
easat-6229	209	63	.	.	PUNCT
easat-6229	210	1	although	although	SCONJ
easat-6229	210	2	they	they	PRON
easat-6229	210	3	have	have	AUX
easat-6229	210	4	learned	learn	VERB
easat-6229	210	5	various	various	ADJ
easat-6229	210	6	methods	method	NOUN
easat-6229	210	7	for	for	ADP
easat-6229	210	8	constructing	construct	VERB
easat-6229	210	9	valid	valid	ADJ
easat-6229	210	10	proofs	proof	NOUN
easat-6229	210	11	,	,	PUNCT
easat-6229	210	12	they	they	PRON
easat-6229	210	13	struggle	struggle	VERB
easat-6229	210	14	with	with	ADP
easat-6229	210	15	how	how	SCONJ
easat-6229	210	16	to	to	PART
easat-6229	210	17	appropriately	appropriately	ADV
easat-6229	210	18	utilize	utilize	VERB
easat-6229	210	19	premises	premise	NOUN
easat-6229	210	20	,	,	PUNCT
easat-6229	210	21	definitions	definition	NOUN
easat-6229	210	22	,	,	PUNCT
easat-6229	210	23	or	or	CCONJ
easat-6229	210	24	statements	statement	NOUN
easat-6229	210	25	related	relate	VERB
easat-6229	210	26	to	to	ADP
easat-6229	210	27	theorems	theorem	NOUN
easat-6229	210	28	in	in	ADP
easat-6229	210	29	their	their	PRON
easat-6229	210	30	reasoning	reasoning	NOUN
easat-6229	210	31	.	.	PUNCT
easat-6229	211	1	these	these	DET
easat-6229	211	2	students	student	NOUN
easat-6229	211	3	can	can	AUX
easat-6229	211	4	follow	follow	VERB
easat-6229	211	5	the	the	DET
easat-6229	211	6	provided	provide	VERB
easat-6229	211	7	evidence	evidence	NOUN
easat-6229	211	8	but	but	CCONJ
easat-6229	211	9	find	find	VERB
easat-6229	211	10	it	it	PRON
easat-6229	211	11	challenging	challenge	VERB
easat-6229	211	12	to	to	PART
easat-6229	211	13	articulate	articulate	VERB
easat-6229	211	14	how	how	SCONJ
easat-6229	211	15	,	,	PUNCT
easat-6229	211	16	why	why	SCONJ
easat-6229	211	17	,	,	PUNCT
easat-6229	211	18	or	or	CCONJ
easat-6229	211	19	where	where	SCONJ
easat-6229	211	20	any	any	DET
easat-6229	211	21	discrepancies	discrepancy	NOUN
easat-6229	211	22	in	in	ADP
easat-6229	211	23	the	the	DET
easat-6229	211	24	proof	proof	NOUN
easat-6229	211	25	may	may	AUX
easat-6229	211	26	exist	exist	VERB
easat-6229	211	27	.	.	PUNCT
easat-6229	212	1	t	t	NOUN
easat-6229	212	2	:	:	PUNCT
easat-6229	212	3	what	what	PRON
easat-6229	212	4	do	do	AUX
easat-6229	212	5	you	you	PRON
easat-6229	212	6	think	think	VERB
easat-6229	212	7	of	of	ADP
easat-6229	212	8	the	the	DET
easat-6229	212	9	new	new	ADJ
easat-6229	212	10	atmosphere	atmosphere	NOUN
easat-6229	212	11	presented	present	VERB
easat-6229	212	12	in	in	ADP
easat-6229	212	13	this	this	DET
easat-6229	212	14	sequence	sequence	NOUN
easat-6229	212	15	material	material	NOUN
easat-6229	212	16	?	?	PUNCT
easat-6229	213	1	m5	m5	NOUN
easat-6229	213	2	:	:	PUNCT
easat-6229	213	3	it	it	PRON
easat-6229	213	4	is	be	AUX
easat-6229	213	5	better	well	ADJ
easat-6229	213	6	than	than	ADP
easat-6229	213	7	ever	ever	ADV
easat-6229	213	8	t	t	NOUN
easat-6229	213	9	:	:	PUNCT
easat-6229	213	10	what	what	PRON
easat-6229	213	11	do	do	AUX
easat-6229	213	12	you	you	PRON
easat-6229	213	13	think	think	VERB
easat-6229	213	14	of	of	ADP
easat-6229	213	15	the	the	DET
easat-6229	213	16	use	use	NOUN
easat-6229	213	17	of	of	ADP
easat-6229	213	18	worksheets	worksheet	NOUN
easat-6229	213	19	on	on	ADP
easat-6229	213	20	sequence	sequence	NOUN
easat-6229	213	21	material	material	NOUN
easat-6229	213	22	?	?	PUNCT
easat-6229	214	1	m5	m5	NOUN
easat-6229	214	2	:	:	PUNCT
easat-6229	214	3	i	i	PRON
easat-6229	214	4	find	find	VERB
easat-6229	214	5	it	it	PRON
easat-6229	214	6	relatively	relatively	ADV
easat-6229	214	7	easy	easy	ADJ
easat-6229	214	8	to	to	PART
easat-6229	214	9	understand	understand	VERB
easat-6229	214	10	,	,	PUNCT
easat-6229	214	11	despite	despite	SCONJ
easat-6229	214	12	needing	need	VERB
easat-6229	214	13	some	some	DET
easat-6229	214	14	effort	effort	NOUN
easat-6229	214	15	at	at	ADP
easat-6229	214	16	times	time	NOUN
easat-6229	214	17	.	.	PUNCT
easat-6229	215	1	nonetheless	nonetheless	ADV
easat-6229	215	2	,	,	PUNCT
easat-6229	215	3	i	i	PRON
easat-6229	215	4	regularly	regularly	ADV
easat-6229	215	5	seek	seek	VERB
easat-6229	215	6	clarification	clarification	NOUN
easat-6229	215	7	from	from	ADP
easat-6229	215	8	our	our	PRON
easat-6229	215	9	instructor	instructor	NOUN
easat-6229	215	10	.	.	PUNCT
easat-6229	216	1	t	t	PROPN
easat-6229	216	2	:	:	PUNCT
easat-6229	216	3	what	what	PRON
easat-6229	216	4	causes	cause	VERB
easat-6229	216	5	difficulty	difficulty	NOUN
easat-6229	216	6	for	for	ADP
easat-6229	216	7	you	you	PRON
easat-6229	216	8	in	in	ADP
easat-6229	216	9	solving	solve	VERB
easat-6229	216	10	the	the	DET
easat-6229	216	11	evidence	evidence	NOUN
easat-6229	216	12	questions	question	NOUN
easat-6229	216	13	involving	involve	VERB
easat-6229	216	14	cauchy	cauchy	ADJ
easat-6229	216	15	sequences	sequence	NOUN
easat-6229	216	16	?	?	PUNCT
easat-6229	217	1	m5	m5	NOUN
easat-6229	217	2	:	:	PUNCT
easat-6229	217	3	i	i	PRON
easat-6229	217	4	do	do	AUX
easat-6229	217	5	n't	not	PART
easat-6229	217	6	perform	perform	VERB
easat-6229	217	7	the	the	DET
easat-6229	217	8	initial	initial	ADJ
easat-6229	217	9	analysis	analysis	NOUN
easat-6229	217	10	,	,	PUNCT
easat-6229	217	11	so	so	CCONJ
easat-6229	217	12	when	when	SCONJ
easat-6229	217	13	the	the	DET
easat-6229	217	14	proof	proof	NOUN
easat-6229	217	15	fails	fail	VERB
easat-6229	217	16	to	to	PART
easat-6229	217	17	determine	determine	VERB
easat-6229	217	18	the	the	DET
easat-6229	217	19	value	value	NOUN
easat-6229	217	20	for	for	ADP
easat-6229	217	21	every	every	DET
easat-6229	217	22	sequence	sequence	NOUN
easat-6229	217	23	ε	ε	PROPN
easat-6229	217	24	students	student	NOUN
easat-6229	217	25	from	from	ADP
easat-6229	217	26	the	the	DET
easat-6229	217	27	lower	low	ADJ
easat-6229	217	28	category	category	NOUN
easat-6229	217	29	(	(	PUNCT
easat-6229	217	30	s	s	X
easat-6229	217	31	)	)	PUNCT
easat-6229	217	32	appreciated	appreciate	VERB
easat-6229	217	33	the	the	DET
easat-6229	217	34	new	new	ADJ
easat-6229	217	35	learning	learning	NOUN
easat-6229	217	36	approach	approach	NOUN
easat-6229	217	37	.	.	PUNCT
easat-6229	218	1	however	however	ADV
easat-6229	218	2	,	,	PUNCT
easat-6229	218	3	this	this	DET
easat-6229	218	4	group	group	NOUN
easat-6229	218	5	takes	take	VERB
easat-6229	218	6	longer	long	ADV
easat-6229	218	7	to	to	PART
easat-6229	218	8	comprehend	comprehend	VERB
easat-6229	218	9	the	the	DET
easat-6229	218	10	worksheets	worksheet	NOUN
easat-6229	218	11	compared	compare	VERB
easat-6229	218	12	to	to	ADP
easat-6229	218	13	students	student	NOUN
easat-6229	218	14	from	from	ADP
easat-6229	218	15	the	the	DET
easat-6229	218	16	other	other	ADJ
easat-6229	218	17	two	two	NUM
easat-6229	218	18	categories	category	NOUN
easat-6229	218	19	.	.	PUNCT
easat-6229	219	1	this	this	DET
easat-6229	219	2	type	type	NOUN
easat-6229	219	3	of	of	ADP
easat-6229	219	4	understanding	understanding	NOUN
easat-6229	219	5	of	of	ADP
easat-6229	219	6	valid	valid	ADJ
easat-6229	219	7	proofs	proof	NOUN
easat-6229	219	8	requires	require	VERB
easat-6229	219	9	repeated	repeat	VERB
easat-6229	219	10	reinforcement	reinforcement	NOUN
easat-6229	219	11	.	.	PUNCT
easat-6229	220	1	figure	figure	NOUN
easat-6229	220	2	3	3	NUM
easat-6229	220	3	.	.	PUNCT
easat-6229	220	4	low	low	ADJ
easat-6229	220	5	category	category	NOUN
easat-6229	220	6	test	test	NOUN
easat-6229	220	7	answer	answer	NOUN
easat-6229	220	8	(	(	PUNCT
easat-6229	220	9	s3	s3	PROPN
easat-6229	220	10	)	)	PUNCT
easat-6229	220	11	.	.	PUNCT
easat-6229	221	1	the	the	DET
easat-6229	221	2	findings	finding	NOUN
easat-6229	221	3	from	from	ADP
easat-6229	221	4	the	the	DET
easat-6229	221	5	interviews	interview	NOUN
easat-6229	221	6	conducted	conduct	VERB
easat-6229	221	7	with	with	ADP
easat-6229	221	8	lecturers	lecturer	NOUN
easat-6229	221	9	and	and	CCONJ
easat-6229	221	10	s3	s3	PROPN
easat-6229	221	11	students	student	NOUN
easat-6229	221	12	indicate	indicate	VERB
easat-6229	221	13	that	that	SCONJ
easat-6229	221	14	understanding	understand	VERB
easat-6229	221	15	the	the	DET
easat-6229	221	16	nature	nature	NOUN
easat-6229	221	17	of	of	ADP
easat-6229	221	18	certain	certain	ADJ
easat-6229	221	19	statements	statement	NOUN
easat-6229	221	20	and	and	CCONJ
easat-6229	221	21	hypotheses	hypothesis	NOUN
easat-6229	221	22	(	(	PUNCT
easat-6229	221	23	conjectures	conjecture	NOUN
easat-6229	221	24	)	)	PUNCT
easat-6229	221	25	based	base	VERB
easat-6229	221	26	on	on	ADP
easat-6229	221	27	patterns	pattern	NOUN
easat-6229	221	28	,	,	PUNCT
easat-6229	221	29	as	as	ADV
easat-6229	221	30	well	well	ADV
easat-6229	221	31	1248	1248	NUM
easat-6229	221	32	edelweiss	edelweiss	PROPN
easat-6229	221	33	applied	apply	VERB
easat-6229	221	34	science	science	NOUN
easat-6229	221	35	and	and	CCONJ
easat-6229	221	36	technology	technology	NOUN
easat-6229	221	37	issn	issn	PROPN
easat-6229	221	38	:	:	PUNCT
easat-6229	221	39	2576	2576	NUM
easat-6229	221	40	-	-	SYM
easat-6229	221	41	8484	8484	NUM
easat-6229	221	42	vol	vol	NOUN
easat-6229	221	43	.	.	PROPN
easat-6229	222	1	9	9	NUM
easat-6229	222	2	,	,	PUNCT
easat-6229	222	3	no	no	INTJ
easat-6229	222	4	.	.	NOUN
easat-6229	222	5	4	4	NUM
easat-6229	222	6	:	:	SYM
easat-6229	222	7	1240	1240	NUM
easat-6229	222	8	-	-	SYM
easat-6229	222	9	1251	1251	NUM
easat-6229	222	10	,	,	PUNCT
easat-6229	222	11	2025	2025	NUM
easat-6229	222	12	doi	doi	NOUN
easat-6229	222	13	:	:	PUNCT
easat-6229	222	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	222	15	©	©	ADP
easat-6229	222	16	2025	2025	NUM
easat-6229	222	17	by	by	ADP
easat-6229	222	18	the	the	DET
easat-6229	222	19	authors	author	NOUN
easat-6229	222	20	;	;	PUNCT
easat-6229	222	21	licensee	licensee	PROPN
easat-6229	222	22	learning	learning	NOUN
easat-6229	222	23	gate	gate	NOUN
easat-6229	222	24	as	as	ADP
easat-6229	222	25	proving	prove	VERB
easat-6229	222	26	these	these	DET
easat-6229	222	27	hypotheses	hypothesis	NOUN
easat-6229	222	28	deductively	deductively	ADV
easat-6229	222	29	,	,	PUNCT
easat-6229	222	30	often	often	ADV
easat-6229	222	31	proves	prove	VERB
easat-6229	222	32	challenging	challenging	ADJ
easat-6229	222	33	.	.	PUNCT
easat-6229	223	1	students	student	NOUN
easat-6229	223	2	are	be	AUX
easat-6229	223	3	hesitant	hesitant	ADJ
easat-6229	223	4	to	to	PART
easat-6229	223	5	organize	organize	VERB
easat-6229	223	6	the	the	DET
easat-6229	223	7	evidentiary	evidentiary	ADJ
easat-6229	223	8	steps	step	NOUN
easat-6229	223	9	and	and	CCONJ
easat-6229	223	10	convert	convert	VERB
easat-6229	223	11	them	they	PRON
easat-6229	223	12	into	into	ADP
easat-6229	223	13	formal	formal	ADJ
easat-6229	223	14	proofs	proof	NOUN
easat-6229	223	15	using	use	VERB
easat-6229	223	16	relevant	relevant	ADJ
easat-6229	223	17	definitions	definition	NOUN
easat-6229	223	18	or	or	CCONJ
easat-6229	223	19	characteristics	characteristic	NOUN
easat-6229	223	20	.	.	PUNCT
easat-6229	224	1	this	this	DET
easat-6229	224	2	difficulty	difficulty	NOUN
easat-6229	224	3	is	be	AUX
easat-6229	224	4	compounded	compound	VERB
easat-6229	224	5	for	for	ADP
easat-6229	224	6	students	student	NOUN
easat-6229	224	7	in	in	ADP
easat-6229	224	8	category	category	NOUN
easat-6229	224	9	s	s	NOUN
easat-6229	224	10	,	,	PUNCT
easat-6229	224	11	who	who	PRON
easat-6229	224	12	can	can	AUX
easat-6229	224	13	only	only	ADV
easat-6229	224	14	grasp	grasp	VERB
easat-6229	224	15	a	a	DET
easat-6229	224	16	small	small	ADJ
easat-6229	224	17	portion	portion	NOUN
easat-6229	224	18	of	of	ADP
easat-6229	224	19	the	the	DET
easat-6229	224	20	evidence	evidence	NOUN
easat-6229	224	21	being	be	AUX
easat-6229	224	22	studied	study	VERB
easat-6229	224	23	,	,	PUNCT
easat-6229	224	24	making	make	VERB
easat-6229	224	25	it	it	PRON
easat-6229	224	26	hard	hard	ADJ
easat-6229	224	27	for	for	SCONJ
easat-6229	224	28	them	they	PRON
easat-6229	224	29	to	to	PART
easat-6229	224	30	initiate	initiate	VERB
easat-6229	224	31	the	the	DET
easat-6229	224	32	evaluation	evaluation	NOUN
easat-6229	224	33	process	process	NOUN
easat-6229	224	34	.	.	PUNCT
easat-6229	225	1	t	t	PROPN
easat-6229	225	2	:	:	PUNCT
easat-6229	225	3	are	be	AUX
easat-6229	225	4	you	you	PRON
easat-6229	225	5	happy	happy	ADJ
easat-6229	225	6	when	when	SCONJ
easat-6229	225	7	you	you	PRON
easat-6229	225	8	sit	sit	VERB
easat-6229	225	9	in	in	ADP
easat-6229	225	10	a	a	DET
easat-6229	225	11	group	group	NOUN
easat-6229	225	12	and	and	CCONJ
easat-6229	225	13	discuss	discuss	VERB
easat-6229	225	14	the	the	DET
easat-6229	225	15	evidence	evidence	NOUN
easat-6229	225	16	with	with	ADP
easat-6229	225	17	your	your	PRON
easat-6229	225	18	friends	friend	NOUN
easat-6229	225	19	s3	s3	PROPN
easat-6229	225	20	:	:	PUNCT
easat-6229	225	21	very	very	ADV
easat-6229	225	22	happy	happy	ADJ
easat-6229	225	23	t	t	PROPN
easat-6229	225	24	:	:	PUNCT
easat-6229	225	25	what	what	PRON
easat-6229	225	26	do	do	AUX
easat-6229	225	27	you	you	PRON
easat-6229	225	28	think	think	VERB
easat-6229	225	29	about	about	ADP
easat-6229	225	30	using	use	VERB
easat-6229	225	31	discussion	discussion	NOUN
easat-6229	225	32	material	material	NOUN
easat-6229	225	33	worksheets	worksheet	NOUN
easat-6229	225	34	with	with	ADP
easat-6229	225	35	the	the	DET
easat-6229	225	36	mathematical	mathematical	ADJ
easat-6229	225	37	working	working	NOUN
easat-6229	225	38	space	space	NOUN
easat-6229	225	39	strategy	strategy	NOUN
easat-6229	225	40	while	while	SCONJ
easat-6229	225	41	focusing	focus	VERB
easat-6229	225	42	on	on	ADP
easat-6229	225	43	sequence	sequence	NOUN
easat-6229	225	44	material	material	NOUN
easat-6229	225	45	?	?	PUNCT
easat-6229	226	1	s3	s3	NOUN
easat-6229	226	2	:	:	PUNCT
easat-6229	226	3	while	while	SCONJ
easat-6229	226	4	i	i	PRON
easat-6229	226	5	remain	remain	VERB
easat-6229	226	6	somewhat	somewhat	ADV
easat-6229	226	7	confused	confused	ADJ
easat-6229	226	8	,	,	PUNCT
easat-6229	226	9	this	this	DET
easat-6229	226	10	experience	experience	NOUN
easat-6229	226	11	has	have	AUX
easat-6229	226	12	increased	increase	VERB
easat-6229	226	13	my	my	PRON
easat-6229	226	14	enthusiasm	enthusiasm	NOUN
easat-6229	226	15	for	for	ADP
easat-6229	226	16	learning	learn	VERB
easat-6229	226	17	t	t	PROPN
easat-6229	226	18	:	:	PUNCT
easat-6229	226	19	what	what	PRON
easat-6229	226	20	causes	cause	VERB
easat-6229	226	21	you	you	PRON
easat-6229	226	22	to	to	PART
easat-6229	226	23	be	be	AUX
easat-6229	226	24	unable	unable	ADJ
easat-6229	226	25	to	to	PART
easat-6229	226	26	solve	solve	VERB
easat-6229	226	27	the	the	DET
easat-6229	226	28	cauchy	cauchy	ADJ
easat-6229	226	29	sequence	sequence	NOUN
easat-6229	226	30	problem	problem	NOUN
easat-6229	226	31	correctly	correctly	ADV
easat-6229	226	32	?	?	PUNCT
easat-6229	227	1	s3	s3	NOUN
easat-6229	227	2	:	:	PUNCT
easat-6229	227	3	i	i	PRON
easat-6229	227	4	forgot	forget	VERB
easat-6229	227	5	the	the	DET
easat-6229	227	6	definition	definition	NOUN
easat-6229	227	7	of	of	ADP
easat-6229	227	8	the	the	DET
easat-6229	227	9	cauchy	cauchy	ADJ
easat-6229	227	10	sequence	sequence	NOUN
easat-6229	227	11	.	.	PUNCT
easat-6229	228	1	the	the	DET
easat-6229	228	2	interview	interview	NOUN
easat-6229	228	3	indicates	indicate	VERB
easat-6229	228	4	that	that	SCONJ
easat-6229	228	5	the	the	DET
easat-6229	228	6	evidentiary	evidentiary	ADJ
easat-6229	228	7	indicators	indicator	NOUN
easat-6229	228	8	are	be	AUX
easat-6229	228	9	not	not	PART
easat-6229	228	10	being	be	AUX
easat-6229	228	11	prioritized	prioritize	VERB
easat-6229	228	12	by	by	ADP
easat-6229	228	13	s3	s3	PROPN
easat-6229	228	14	.	.	PROPN
easat-6229	229	1	4	4	NUM
easat-6229	229	2	.	.	X
easat-6229	229	3	discussion	discussion	NOUN
easat-6229	229	4	one	one	NUM
easat-6229	229	5	of	of	ADP
easat-6229	229	6	the	the	DET
easat-6229	229	7	benefits	benefit	NOUN
easat-6229	229	8	of	of	ADP
easat-6229	229	9	the	the	DET
easat-6229	229	10	guided	guide	VERB
easat-6229	229	11	discovery	discovery	NOUN
easat-6229	229	12	learning	learning	NOUN
easat-6229	229	13	model	model	NOUN
easat-6229	229	14	is	be	AUX
easat-6229	229	15	that	that	SCONJ
easat-6229	229	16	it	it	PRON
easat-6229	229	17	transforms	transform	VERB
easat-6229	229	18	the	the	DET
easat-6229	229	19	student	student	NOUN
easat-6229	229	20	learning	learn	VERB
easat-6229	229	21	environment	environment	NOUN
easat-6229	229	22	into	into	ADP
easat-6229	229	23	a	a	DET
easat-6229	229	24	more	more	ADV
easat-6229	229	25	active	active	ADJ
easat-6229	229	26	setting	setting	NOUN
easat-6229	229	27	,	,	PUNCT
easat-6229	229	28	encouraging	encourage	VERB
easat-6229	229	29	students	student	NOUN
easat-6229	229	30	to	to	PART
easat-6229	229	31	collaborate	collaborate	VERB
easat-6229	229	32	and	and	CCONJ
easat-6229	229	33	engage	engage	VERB
easat-6229	229	34	in	in	ADP
easat-6229	229	35	problem	problem	NOUN
easat-6229	229	36	-	-	PUNCT
easat-6229	229	37	solving	solve	VERB
easat-6229	229	38	activities	activity	NOUN
easat-6229	229	39	,	,	PUNCT
easat-6229	229	40	particularly	particularly	ADV
easat-6229	229	41	in	in	ADP
easat-6229	229	42	real	real	ADJ
easat-6229	229	43	analysis	analysis	NOUN
easat-6229	229	44	.	.	PUNCT
easat-6229	230	1	this	this	DET
easat-6229	230	2	outcome	outcome	NOUN
easat-6229	230	3	aligns	align	VERB
easat-6229	230	4	with	with	ADP
easat-6229	230	5	the	the	DET
easat-6229	230	6	findings	finding	NOUN
easat-6229	230	7	of	of	ADP
easat-6229	230	8	numerous	numerous	ADJ
easat-6229	230	9	studies	study	NOUN
easat-6229	230	10	that	that	PRON
easat-6229	230	11	employ	employ	VERB
easat-6229	230	12	this	this	DET
easat-6229	230	13	model	model	NOUN
easat-6229	230	14	in	in	ADP
easat-6229	230	15	exact	exact	ADJ
easat-6229	230	16	sciences	science	NOUN
easat-6229	230	17	,	,	PUNCT
easat-6229	230	18	demonstrating	demonstrate	VERB
easat-6229	230	19	its	its	PRON
easat-6229	230	20	efficacy	efficacy	NOUN
easat-6229	230	21	in	in	ADP
easat-6229	230	22	enhancing	enhance	VERB
easat-6229	230	23	student	student	NOUN
easat-6229	230	24	participation	participation	NOUN
easat-6229	230	25	and	and	CCONJ
easat-6229	230	26	improving	improve	VERB
easat-6229	230	27	learning	learn	VERB
easat-6229	230	28	outcomes	outcome	NOUN
easat-6229	230	29	.	.	PUNCT
easat-6229	231	1	similarly	similarly	ADV
easat-6229	231	2	,	,	PUNCT
easat-6229	231	3	applying	apply	VERB
easat-6229	231	4	this	this	DET
easat-6229	231	5	model	model	NOUN
easat-6229	231	6	to	to	PART
easat-6229	231	7	teach	teach	VERB
easat-6229	231	8	real	real	ADJ
easat-6229	231	9	analysis	analysis	NOUN
easat-6229	231	10	fosters	foster	VERB
easat-6229	231	11	greater	great	ADJ
easat-6229	231	12	student	student	NOUN
easat-6229	231	13	engagement	engagement	NOUN
easat-6229	231	14	in	in	ADP
easat-6229	231	15	evidentiary	evidentiary	ADJ
easat-6229	231	16	learning	learning	NOUN
easat-6229	231	17	.	.	PUNCT
easat-6229	232	1	studies	study	NOUN
easat-6229	232	2	have	have	AUX
easat-6229	232	3	shown	show	VERB
easat-6229	232	4	that	that	SCONJ
easat-6229	232	5	students	student	NOUN
easat-6229	232	6	who	who	PRON
easat-6229	232	7	use	use	VERB
easat-6229	232	8	the	the	DET
easat-6229	232	9	guided	guide	VERB
easat-6229	232	10	discovery	discovery	NOUN
easat-6229	232	11	learning	learning	NOUN
easat-6229	232	12	model	model	NOUN
easat-6229	232	13	in	in	ADP
easat-6229	232	14	real	real	ADJ
easat-6229	232	15	analysis	analysis	NOUN
easat-6229	232	16	achieve	achieve	VERB
easat-6229	232	17	a	a	DET
easat-6229	232	18	successful	successful	ADJ
easat-6229	232	19	comprehension	comprehension	NOUN
easat-6229	232	20	of	of	ADP
easat-6229	232	21	complex	complex	ADJ
easat-6229	232	22	concepts	concept	NOUN
easat-6229	232	23	[	[	X
easat-6229	232	24	12	12	NUM
easat-6229	232	25	]	]	PUNCT
easat-6229	232	26	.	.	PUNCT
easat-6229	233	1	despite	despite	SCONJ
easat-6229	233	2	feeling	feel	VERB
easat-6229	233	3	confused	confused	ADJ
easat-6229	233	4	when	when	SCONJ
easat-6229	233	5	learning	learn	VERB
easat-6229	233	6	real	real	ADJ
easat-6229	233	7	analysis	analysis	NOUN
easat-6229	233	8	,	,	PUNCT
easat-6229	233	9	the	the	DET
easat-6229	233	10	worksheet	worksheet	NOUN
easat-6229	233	11	discussion	discussion	NOUN
easat-6229	233	12	material	material	NOUN
easat-6229	233	13	has	have	AUX
easat-6229	233	14	been	be	AUX
easat-6229	233	15	prepared	prepare	VERB
easat-6229	233	16	with	with	ADP
easat-6229	233	17	the	the	DET
easat-6229	233	18	mathematical	mathematical	ADJ
easat-6229	233	19	working	working	NOUN
easat-6229	233	20	space	space	NOUN
easat-6229	233	21	strategy	strategy	NOUN
easat-6229	233	22	,	,	PUNCT
easat-6229	233	23	thereby	thereby	ADV
easat-6229	233	24	alleviating	alleviate	VERB
easat-6229	233	25	the	the	DET
easat-6229	233	26	burden	burden	NOUN
easat-6229	233	27	.	.	PUNCT
easat-6229	234	1	additionally	additionally	ADV
easat-6229	234	2	,	,	PUNCT
easat-6229	234	3	statements	statement	NOUN
easat-6229	234	4	indeed	indeed	ADV
easat-6229	234	5	require	require	VERB
easat-6229	234	6	guidance	guidance	NOUN
easat-6229	234	7	to	to	PART
easat-6229	234	8	make	make	VERB
easat-6229	234	9	learning	learn	VERB
easat-6229	234	10	both	both	CCONJ
easat-6229	234	11	meaningful	meaningful	ADJ
easat-6229	234	12	and	and	CCONJ
easat-6229	234	13	enjoyable	enjoyable	ADJ
easat-6229	234	14	[	[	X
easat-6229	234	15	35	35	NUM
easat-6229	234	16	]	]	PUNCT
easat-6229	234	17	.	.	PUNCT
easat-6229	235	1	this	this	DET
easat-6229	235	2	discussion	discussion	NOUN
easat-6229	235	3	material	material	NOUN
easat-6229	235	4	worksheet	worksheet	NOUN
easat-6229	235	5	is	be	AUX
easat-6229	235	6	structured	structure	VERB
easat-6229	235	7	with	with	ADP
easat-6229	235	8	a	a	DET
easat-6229	235	9	mathematical	mathematical	ADJ
easat-6229	235	10	workspace	workspace	NOUN
easat-6229	235	11	strategy	strategy	NOUN
easat-6229	235	12	that	that	PRON
easat-6229	235	13	aids	aid	VERB
easat-6229	235	14	students	student	NOUN
easat-6229	235	15	in	in	ADP
easat-6229	235	16	mastering	master	VERB
easat-6229	235	17	real	real	ADJ
easat-6229	235	18	analysis	analysis	NOUN
easat-6229	235	19	[	[	X
easat-6229	235	20	36	36	NUM
easat-6229	235	21	-	-	SYM
easat-6229	235	22	38	38	NUM
easat-6229	235	23	]	]	PUNCT
easat-6229	235	24	.	.	PUNCT
easat-6229	236	1	by	by	ADP
easat-6229	236	2	helping	help	VERB
easat-6229	236	3	students	student	NOUN
easat-6229	236	4	understand	understand	VERB
easat-6229	236	5	definitions	definition	NOUN
easat-6229	236	6	,	,	PUNCT
easat-6229	236	7	theorems	theorem	NOUN
easat-6229	236	8	,	,	PUNCT
easat-6229	236	9	lemmas	lemmas	ADJ
easat-6229	236	10	,	,	PUNCT
easat-6229	236	11	and	and	CCONJ
easat-6229	236	12	related	related	ADJ
easat-6229	236	13	problems	problem	NOUN
easat-6229	236	14	in	in	ADP
easat-6229	236	15	simple	simple	ADJ
easat-6229	236	16	language	language	NOUN
easat-6229	236	17	,	,	PUNCT
easat-6229	236	18	these	these	DET
easat-6229	236	19	worksheets	worksheet	NOUN
easat-6229	236	20	facilitate	facilitate	VERB
easat-6229	236	21	the	the	DET
easat-6229	236	22	development	development	NOUN
easat-6229	236	23	and	and	CCONJ
easat-6229	236	24	validation	validation	NOUN
easat-6229	236	25	of	of	ADP
easat-6229	236	26	evidence	evidence	NOUN
easat-6229	236	27	.	.	PUNCT
easat-6229	237	1	therefore	therefore	ADV
easat-6229	237	2	,	,	PUNCT
easat-6229	237	3	utilizing	utilize	VERB
easat-6229	237	4	this	this	DET
easat-6229	237	5	method	method	NOUN
easat-6229	237	6	enhances	enhance	VERB
easat-6229	237	7	the	the	DET
easat-6229	237	8	overall	overall	ADJ
easat-6229	237	9	learning	learning	NOUN
easat-6229	237	10	experience	experience	NOUN
easat-6229	237	11	for	for	ADP
easat-6229	237	12	students	student	NOUN
easat-6229	237	13	engaged	engage	VERB
easat-6229	237	14	in	in	ADP
easat-6229	237	15	real	real	ADJ
easat-6229	237	16	analysis	analysis	NOUN
easat-6229	237	17	.	.	PUNCT
easat-6229	238	1	understanding	understand	VERB
easat-6229	238	2	proofs	proof	NOUN
easat-6229	238	3	is	be	AUX
easat-6229	238	4	crucial	crucial	ADJ
easat-6229	238	5	for	for	ADP
easat-6229	238	6	demonstrating	demonstrate	VERB
easat-6229	238	7	theorems	theorem	NOUN
easat-6229	238	8	and	and	CCONJ
easat-6229	238	9	solving	solve	VERB
easat-6229	238	10	proof	proof	NOUN
easat-6229	238	11	problems	problem	NOUN
easat-6229	238	12	;	;	PUNCT
easat-6229	238	13	therefore	therefore	ADV
easat-6229	238	14	,	,	PUNCT
easat-6229	238	15	all	all	DET
easat-6229	238	16	students	student	NOUN
easat-6229	238	17	must	must	AUX
easat-6229	238	18	grasp	grasp	VERB
easat-6229	238	19	the	the	DET
easat-6229	238	20	concept	concept	NOUN
easat-6229	238	21	of	of	ADP
easat-6229	238	22	definitions	definition	NOUN
easat-6229	238	23	.	.	PUNCT
easat-6229	239	1	various	various	ADJ
easat-6229	239	2	approaches	approach	NOUN
easat-6229	239	3	can	can	AUX
easat-6229	239	4	enhance	enhance	VERB
easat-6229	239	5	students	student	NOUN
easat-6229	239	6	'	'	PART
easat-6229	239	7	thinking	thinking	NOUN
easat-6229	239	8	by	by	ADP
easat-6229	239	9	encouraging	encourage	VERB
easat-6229	239	10	them	they	PRON
easat-6229	239	11	to	to	PART
easat-6229	239	12	write	write	VERB
easat-6229	239	13	valid	valid	ADJ
easat-6229	239	14	proofs	proof	NOUN
easat-6229	239	15	[	[	X
easat-6229	239	16	39	39	NUM
easat-6229	239	17	]	]	PUNCT
easat-6229	239	18	.	.	PUNCT
easat-6229	240	1	by	by	ADP
easat-6229	240	2	employing	employ	VERB
easat-6229	240	3	the	the	DET
easat-6229	240	4	mathematical	mathematical	ADJ
easat-6229	240	5	working	working	NOUN
easat-6229	240	6	space	space	NOUN
easat-6229	240	7	strategy	strategy	NOUN
easat-6229	240	8	,	,	PUNCT
easat-6229	240	9	students	student	NOUN
easat-6229	240	10	can	can	AUX
easat-6229	240	11	more	more	ADV
easat-6229	240	12	easily	easily	ADV
easat-6229	240	13	comprehend	comprehend	VERB
easat-6229	240	14	the	the	DET
easat-6229	240	15	definitions	definition	NOUN
easat-6229	240	16	presented	present	VERB
easat-6229	240	17	in	in	ADP
easat-6229	240	18	the	the	DET
easat-6229	240	19	discussion	discussion	NOUN
easat-6229	240	20	material	material	NOUN
easat-6229	240	21	worksheets	worksheet	NOUN
easat-6229	240	22	.	.	PUNCT
easat-6229	241	1	every	every	DET
easat-6229	241	2	student	student	NOUN
easat-6229	241	3	should	should	AUX
easat-6229	241	4	be	be	AUX
easat-6229	241	5	familiar	familiar	ADJ
easat-6229	241	6	with	with	ADP
easat-6229	241	7	the	the	DET
easat-6229	241	8	background	background	NOUN
easat-6229	241	9	,	,	PUNCT
easat-6229	241	10	meaning	meaning	NOUN
easat-6229	241	11	,	,	PUNCT
easat-6229	241	12	and	and	CCONJ
easat-6229	241	13	characteristics	characteristic	NOUN
easat-6229	241	14	of	of	ADP
easat-6229	241	15	definitions	definition	NOUN
easat-6229	241	16	.	.	PUNCT
easat-6229	242	1	this	this	DET
easat-6229	242	2	knowledge	knowledge	NOUN
easat-6229	242	3	will	will	AUX
easat-6229	242	4	facilitate	facilitate	VERB
easat-6229	242	5	their	their	PRON
easat-6229	242	6	ability	ability	NOUN
easat-6229	242	7	to	to	PART
easat-6229	242	8	prove	prove	VERB
easat-6229	242	9	theorems	theorem	NOUN
easat-6229	242	10	and	and	CCONJ
easat-6229	242	11	solve	solve	VERB
easat-6229	242	12	proof	proof	NOUN
easat-6229	242	13	problems	problem	NOUN
easat-6229	242	14	,	,	PUNCT
easat-6229	242	15	making	make	VERB
easat-6229	242	16	the	the	DET
easat-6229	242	17	process	process	NOUN
easat-6229	242	18	significantly	significantly	ADV
easat-6229	242	19	easier	easy	ADJ
easat-6229	242	20	and	and	CCONJ
easat-6229	242	21	more	more	ADV
easat-6229	242	22	manageable	manageable	ADJ
easat-6229	242	23	.	.	PUNCT
easat-6229	243	1	during	during	ADP
easat-6229	243	2	lectures	lecture	NOUN
easat-6229	243	3	,	,	PUNCT
easat-6229	243	4	students	student	NOUN
easat-6229	243	5	often	often	ADV
easat-6229	243	6	engage	engage	VERB
easat-6229	243	7	in	in	ADP
easat-6229	243	8	group	group	NOUN
easat-6229	243	9	discussions	discussion	NOUN
easat-6229	243	10	to	to	PART
easat-6229	243	11	answer	answer	VERB
easat-6229	243	12	questions	question	NOUN
easat-6229	243	13	,	,	PUNCT
easat-6229	243	14	which	which	PRON
easat-6229	243	15	is	be	AUX
easat-6229	243	16	very	very	ADV
easat-6229	243	17	helpful	helpful	ADJ
easat-6229	243	18	in	in	ADP
easat-6229	243	19	finding	find	VERB
easat-6229	243	20	solutions	solution	NOUN
easat-6229	243	21	[	[	X
easat-6229	243	22	13	13	NUM
easat-6229	243	23	]	]	PUNCT
easat-6229	243	24	.	.	PUNCT
easat-6229	244	1	the	the	DET
easat-6229	244	2	guided	guide	VERB
easat-6229	244	3	discovery	discovery	NOUN
easat-6229	244	4	learning	learning	NOUN
easat-6229	244	5	model	model	NOUN
easat-6229	244	6	is	be	AUX
easat-6229	244	7	particularly	particularly	ADV
easat-6229	244	8	effective	effective	ADJ
easat-6229	244	9	in	in	ADP
easat-6229	244	10	realanalysis	realanalysis	NOUN
easat-6229	244	11	education	education	NOUN
easat-6229	244	12	[	[	X
easat-6229	244	13	12	12	NUM
easat-6229	244	14	,	,	PUNCT
easat-6229	244	15	39	39	NUM
easat-6229	244	16	]	]	PUNCT
easat-6229	244	17	.	.	PUNCT
easat-6229	245	1	at	at	ADP
easat-6229	245	2	the	the	DET
easat-6229	245	3	end	end	NOUN
easat-6229	245	4	of	of	ADP
easat-6229	245	5	each	each	DET
easat-6229	245	6	session	session	NOUN
easat-6229	245	7	,	,	PUNCT
easat-6229	245	8	students	student	NOUN
easat-6229	245	9	work	work	VERB
easat-6229	245	10	individually	individually	ADV
easat-6229	245	11	on	on	ADP
easat-6229	245	12	evidence	evidence	NOUN
easat-6229	245	13	-	-	PUNCT
easat-6229	245	14	related	relate	VERB
easat-6229	245	15	questions	question	NOUN
easat-6229	245	16	,	,	PUNCT
easat-6229	245	17	which	which	PRON
easat-6229	245	18	encourages	encourage	VERB
easat-6229	245	19	them	they	PRON
easat-6229	245	20	to	to	PART
easat-6229	245	21	enhance	enhance	VERB
easat-6229	245	22	their	their	PRON
easat-6229	245	23	proof	proof	NOUN
easat-6229	245	24	skills	skill	NOUN
easat-6229	245	25	.	.	PUNCT
easat-6229	246	1	additionally	additionally	ADV
easat-6229	246	2	,	,	PUNCT
easat-6229	246	3	the	the	DET
easat-6229	246	4	discussion	discussion	NOUN
easat-6229	246	5	material	material	NOUN
easat-6229	246	6	worksheets	worksheet	NOUN
easat-6229	246	7	have	have	AUX
easat-6229	246	8	significantly	significantly	ADV
easat-6229	246	9	aided	aid	VERB
easat-6229	246	10	students	student	NOUN
easat-6229	246	11	in	in	ADP
easat-6229	246	12	learning	learn	VERB
easat-6229	246	13	real	real	ADJ
easat-6229	246	14	analysis	analysis	NOUN
easat-6229	246	15	and	and	CCONJ
easat-6229	246	16	overcoming	overcome	VERB
easat-6229	246	17	various	various	ADJ
easat-6229	246	18	learning	learn	VERB
easat-6229	246	19	difficulties	difficulty	NOUN
easat-6229	246	20	.	.	PUNCT
easat-6229	247	1	worksheets	worksheet	NOUN
easat-6229	247	2	that	that	PRON
easat-6229	247	3	incorporate	incorporate	VERB
easat-6229	247	4	mathematical	mathematical	ADJ
easat-6229	247	5	workspace	workspace	NOUN
easat-6229	247	6	strategies	strategy	NOUN
easat-6229	247	7	are	be	AUX
easat-6229	247	8	especially	especially	ADV
easat-6229	247	9	beneficial	beneficial	ADJ
easat-6229	247	10	for	for	ADP
easat-6229	247	11	understanding	understand	VERB
easat-6229	247	12	proofs	proof	NOUN
easat-6229	247	13	[	[	X
easat-6229	247	14	17	17	NUM
easat-6229	247	15	,	,	PUNCT
easat-6229	247	16	19	19	NUM
easat-6229	247	17	,	,	PUNCT
easat-6229	247	18	26	26	NUM
easat-6229	247	19	,	,	PUNCT
easat-6229	247	20	40	40	NUM
easat-6229	247	21	,	,	PUNCT
easat-6229	247	22	41	41	NUM
easat-6229	247	23	]	]	PUNCT
easat-6229	247	24	.	.	PUNCT
easat-6229	248	1	the	the	DET
easat-6229	248	2	use	use	NOUN
easat-6229	248	3	of	of	ADP
easat-6229	248	4	discussion	discussion	NOUN
easat-6229	248	5	material	material	NOUN
easat-6229	248	6	worksheets	worksheet	NOUN
easat-6229	248	7	significantly	significantly	ADV
easat-6229	248	8	aids	aid	VERB
easat-6229	248	9	students	student	NOUN
easat-6229	248	10	in	in	ADP
easat-6229	248	11	mastering	master	VERB
easat-6229	248	12	real	real	ADJ
easat-6229	248	13	analysis	analysis	NOUN
easat-6229	248	14	.	.	PUNCT
easat-6229	249	1	initially	initially	ADV
easat-6229	249	2	,	,	PUNCT
easat-6229	249	3	students	student	NOUN
easat-6229	249	4	often	often	ADV
easat-6229	249	5	struggle	struggle	VERB
easat-6229	249	6	with	with	ADP
easat-6229	249	7	proving	prove	VERB
easat-6229	249	8	concepts	concept	NOUN
easat-6229	249	9	they	they	PRON
easat-6229	249	10	encounter	encounter	VERB
easat-6229	249	11	;	;	PUNCT
easat-6229	249	12	however	however	ADV
easat-6229	249	13	,	,	PUNCT
easat-6229	249	14	flexible	flexible	ADJ
easat-6229	249	15	worksheets	worksheet	NOUN
easat-6229	249	16	can	can	AUX
easat-6229	249	17	help	help	VERB
easat-6229	249	18	mitigate	mitigate	VERB
easat-6229	249	19	these	these	DET
easat-6229	249	20	challenges	challenge	NOUN
easat-6229	249	21	.	.	PUNCT
easat-6229	250	1	many	many	ADJ
easat-6229	250	2	students	student	NOUN
easat-6229	250	3	report	report	VERB
easat-6229	250	4	that	that	SCONJ
easat-6229	250	5	these	these	DET
easat-6229	250	6	worksheets	worksheet	NOUN
easat-6229	250	7	are	be	AUX
easat-6229	250	8	instrumental	instrumental	ADJ
easat-6229	250	9	in	in	ADP
easat-6229	250	10	analyzing	analyze	VERB
easat-6229	250	11	mathematical	mathematical	ADJ
easat-6229	250	12	problems	problem	NOUN
easat-6229	250	13	.	.	PUNCT
easat-6229	251	1	once	once	SCONJ
easat-6229	251	2	students	student	NOUN
easat-6229	251	3	have	have	VERB
easat-6229	251	4	a	a	DET
easat-6229	251	5	solid	solid	ADJ
easat-6229	251	6	grasp	grasp	NOUN
easat-6229	251	7	of	of	ADP
easat-6229	251	8	the	the	DET
easat-6229	251	9	fundamentals	fundamental	NOUN
easat-6229	251	10	of	of	ADP
easat-6229	251	11	analysis	analysis	NOUN
easat-6229	251	12	and	and	CCONJ
easat-6229	251	13	proof	proof	NOUN
easat-6229	251	14	techniques	technique	NOUN
easat-6229	251	15	,	,	PUNCT
easat-6229	251	16	they	they	PRON
easat-6229	251	17	find	find	VERB
easat-6229	251	18	it	it	PRON
easat-6229	251	19	easier	easy	ADJ
easat-6229	251	20	to	to	PART
easat-6229	251	21	tackle	tackle	VERB
easat-6229	251	22	more	more	ADV
easat-6229	251	23	complex	complex	ADJ
easat-6229	251	24	mathematical	mathematical	ADJ
easat-6229	251	25	problems	problem	NOUN
easat-6229	251	26	.	.	PUNCT
easat-6229	252	1	this	this	PRON
easat-6229	252	2	indicates	indicate	VERB
easat-6229	252	3	that	that	SCONJ
easat-6229	252	4	mastering	master	VERB
easat-6229	252	5	proof	proof	NOUN
easat-6229	252	6	concepts	concept	NOUN
easat-6229	252	7	lays	lay	VERB
easat-6229	252	8	a	a	DET
easat-6229	252	9	strong	strong	ADJ
easat-6229	252	10	foundation	foundation	NOUN
easat-6229	252	11	for	for	ADP
easat-6229	252	12	further	far	ADV
easat-6229	252	13	learning	learn	VERB
easat-6229	252	14	[	[	PUNCT
easat-6229	252	15	42	42	NUM
easat-6229	252	16	-	-	SYM
easat-6229	252	17	44	44	NUM
easat-6229	252	18	]	]	PUNCT
easat-6229	252	19	.	.	PUNCT
easat-6229	253	1	support	support	VERB
easat-6229	253	2	this	this	DET
easat-6229	253	3	notion	notion	NOUN
easat-6229	253	4	,	,	PUNCT
easat-6229	253	5	1249	1249	NUM
easat-6229	253	6	edelweiss	edelweiss	PROPN
easat-6229	253	7	applied	apply	VERB
easat-6229	253	8	science	science	NOUN
easat-6229	253	9	and	and	CCONJ
easat-6229	253	10	technology	technology	NOUN
easat-6229	253	11	issn	issn	PROPN
easat-6229	253	12	:	:	PUNCT
easat-6229	253	13	2576	2576	NUM
easat-6229	253	14	-	-	SYM
easat-6229	253	15	8484	8484	NUM
easat-6229	253	16	vol	vol	NOUN
easat-6229	253	17	.	.	PROPN
easat-6229	254	1	9	9	NUM
easat-6229	254	2	,	,	PUNCT
easat-6229	254	3	no	no	INTJ
easat-6229	254	4	.	.	NOUN
easat-6229	254	5	4	4	NUM
easat-6229	254	6	:	:	SYM
easat-6229	254	7	1240	1240	NUM
easat-6229	254	8	-	-	SYM
easat-6229	254	9	1251	1251	NUM
easat-6229	254	10	,	,	PUNCT
easat-6229	254	11	2025	2025	NUM
easat-6229	254	12	doi	doi	NOUN
easat-6229	254	13	:	:	PUNCT
easat-6229	254	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	254	15	©	©	ADP
easat-6229	254	16	2025	2025	NUM
easat-6229	254	17	by	by	ADP
easat-6229	254	18	the	the	DET
easat-6229	254	19	authors	author	NOUN
easat-6229	254	20	;	;	PUNCT
easat-6229	254	21	licensee	licensee	PROPN
easat-6229	254	22	learning	learn	VERB
easat-6229	254	23	gate	gate	PROPN
easat-6229	254	24	suggesting	suggest	VERB
easat-6229	254	25	that	that	SCONJ
easat-6229	254	26	once	once	SCONJ
easat-6229	254	27	students	student	NOUN
easat-6229	254	28	understand	understand	VERB
easat-6229	254	29	the	the	DET
easat-6229	254	30	concept	concept	NOUN
easat-6229	254	31	of	of	ADP
easat-6229	254	32	proof	proof	NOUN
easat-6229	254	33	,	,	PUNCT
easat-6229	254	34	they	they	PRON
easat-6229	254	35	are	be	AUX
easat-6229	254	36	better	well	ADV
easat-6229	254	37	equipped	equip	VERB
easat-6229	254	38	to	to	PART
easat-6229	254	39	demonstrate	demonstrate	VERB
easat-6229	254	40	their	their	PRON
easat-6229	254	41	knowledge	knowledge	NOUN
easat-6229	254	42	effectively	effectively	ADV
easat-6229	254	43	[	[	X
easat-6229	254	44	45	45	NUM
easat-6229	254	45	]	]	PUNCT
easat-6229	254	46	.	.	PUNCT
easat-6229	255	1	one	one	NUM
easat-6229	255	2	of	of	ADP
easat-6229	255	3	the	the	DET
easat-6229	255	4	findings	finding	NOUN
easat-6229	255	5	is	be	AUX
easat-6229	255	6	that	that	SCONJ
easat-6229	255	7	students	student	NOUN
easat-6229	255	8	are	be	AUX
easat-6229	255	9	motivated	motivated	ADJ
easat-6229	255	10	to	to	PART
easat-6229	255	11	tackle	tackle	VERB
easat-6229	255	12	proof	proof	NOUN
easat-6229	255	13	questions	question	NOUN
easat-6229	255	14	after	after	ADP
easat-6229	255	15	implementing	implement	VERB
easat-6229	255	16	the	the	DET
easat-6229	255	17	strategies	strategy	NOUN
easat-6229	255	18	used	use	VERB
easat-6229	255	19	.	.	PUNCT
easat-6229	256	1	the	the	DET
easat-6229	256	2	lecturer	lecturer	NOUN
easat-6229	256	3	incorporated	incorporate	VERB
easat-6229	256	4	several	several	ADJ
easat-6229	256	5	proof	proof	ADJ
easat-6229	256	6	questions	question	NOUN
easat-6229	256	7	to	to	PART
easat-6229	256	8	ensure	ensure	VERB
easat-6229	256	9	that	that	SCONJ
easat-6229	256	10	students	student	NOUN
easat-6229	256	11	do	do	AUX
easat-6229	256	12	not	not	PART
easat-6229	256	13	feel	feel	VERB
easat-6229	256	14	overwhelmed	overwhelmed	ADJ
easat-6229	256	15	by	by	ADP
easat-6229	256	16	their	their	PRON
easat-6229	256	17	assignments	assignment	NOUN
easat-6229	256	18	.	.	PUNCT
easat-6229	257	1	research	research	NOUN
easat-6229	257	2	by	by	ADP
easat-6229	257	3	aisyah	aisyah	PROPN
easat-6229	257	4	,	,	PUNCT
easat-6229	257	5	et	et	PROPN
easat-6229	257	6	al	al	PROPN
easat-6229	257	7	.	.	PUNCT
easat-6229	258	1	[	[	X
easat-6229	258	2	46	46	NUM
easat-6229	258	3	]	]	PUNCT
easat-6229	258	4	found	find	VERB
easat-6229	258	5	that	that	SCONJ
easat-6229	258	6	when	when	SCONJ
easat-6229	258	7	teachers	teacher	NOUN
easat-6229	258	8	frequently	frequently	ADV
easat-6229	258	9	provide	provide	VERB
easat-6229	258	10	proof	proof	ADJ
easat-6229	258	11	questions	question	NOUN
easat-6229	258	12	,	,	PUNCT
easat-6229	258	13	it	it	PRON
easat-6229	258	14	allows	allow	VERB
easat-6229	258	15	students	student	NOUN
easat-6229	258	16	to	to	PART
easat-6229	258	17	practice	practice	VERB
easat-6229	258	18	their	their	PRON
easat-6229	258	19	reasoning	reasoning	NOUN
easat-6229	258	20	skills	skill	NOUN
easat-6229	258	21	.	.	PUNCT
easat-6229	259	1	this	this	DET
easat-6229	259	2	practice	practice	NOUN
easat-6229	259	3	positively	positively	ADV
easat-6229	259	4	impacts	impact	VERB
easat-6229	259	5	students	student	NOUN
easat-6229	259	6	,	,	PUNCT
easat-6229	259	7	as	as	SCONJ
easat-6229	259	8	they	they	PRON
easat-6229	259	9	become	become	VERB
easat-6229	259	10	accustomed	accustomed	ADJ
easat-6229	259	11	to	to	ADP
easat-6229	259	12	solving	solve	VERB
easat-6229	259	13	problems	problem	NOUN
easat-6229	259	14	related	relate	VERB
easat-6229	259	15	to	to	ADP
easat-6229	259	16	proofs	proof	NOUN
easat-6229	259	17	.	.	PUNCT
easat-6229	260	1	5	5	X
easat-6229	260	2	.	.	X
easat-6229	260	3	conclusion	conclusion	NOUN
easat-6229	260	4	in	in	ADP
easat-6229	260	5	real	real	ADJ
easat-6229	260	6	analysis	analysis	NOUN
easat-6229	260	7	learning	learning	NOUN
easat-6229	260	8	,	,	PUNCT
easat-6229	260	9	the	the	DET
easat-6229	260	10	guided	guide	VERB
easat-6229	260	11	discovery	discovery	NOUN
easat-6229	260	12	learning	learning	NOUN
easat-6229	260	13	model	model	NOUN
easat-6229	260	14	is	be	AUX
easat-6229	260	15	highly	highly	ADV
easat-6229	260	16	effective	effective	ADJ
easat-6229	260	17	because	because	SCONJ
easat-6229	260	18	it	it	PRON
easat-6229	260	19	encourages	encourage	VERB
easat-6229	260	20	students	student	NOUN
easat-6229	260	21	to	to	PART
easat-6229	260	22	approach	approach	VERB
easat-6229	260	23	problems	problem	NOUN
easat-6229	260	24	as	as	ADP
easat-6229	260	25	proofs	proof	NOUN
easat-6229	260	26	.	.	PUNCT
easat-6229	261	1	by	by	ADP
easat-6229	261	2	utilizing	utilize	VERB
easat-6229	261	3	the	the	DET
easat-6229	261	4	mathematical	mathematical	ADJ
easat-6229	261	5	working	working	NOUN
easat-6229	261	6	space	space	NOUN
easat-6229	261	7	strategy	strategy	NOUN
easat-6229	261	8	,	,	PUNCT
easat-6229	261	9	discussion	discussion	NOUN
easat-6229	261	10	material	material	NOUN
easat-6229	261	11	worksheets	worksheet	NOUN
easat-6229	261	12	can	can	AUX
easat-6229	261	13	significantly	significantly	ADV
easat-6229	261	14	aid	aid	VERB
easat-6229	261	15	students	student	NOUN
easat-6229	261	16	in	in	ADP
easat-6229	261	17	understanding	understand	VERB
easat-6229	261	18	proof	proof	NOUN
easat-6229	261	19	concepts	concept	NOUN
easat-6229	261	20	.	.	PUNCT
easat-6229	262	1	this	this	DET
easat-6229	262	2	effectiveness	effectiveness	NOUN
easat-6229	262	3	stems	stem	VERB
easat-6229	262	4	from	from	ADP
easat-6229	262	5	the	the	DET
easat-6229	262	6	fact	fact	NOUN
easat-6229	262	7	that	that	SCONJ
easat-6229	262	8	the	the	DET
easat-6229	262	9	worksheets	worksheet	NOUN
easat-6229	262	10	incorporate	incorporate	VERB
easat-6229	262	11	visualization	visualization	NOUN
easat-6229	262	12	,	,	PUNCT
easat-6229	262	13	construction	construction	NOUN
easat-6229	262	14	,	,	PUNCT
easat-6229	262	15	and	and	CCONJ
easat-6229	262	16	validation	validation	NOUN
easat-6229	262	17	elements	element	NOUN
easat-6229	262	18	,	,	PUNCT
easat-6229	262	19	which	which	PRON
easat-6229	262	20	enhance	enhance	VERB
easat-6229	262	21	the	the	DET
easat-6229	262	22	learning	learning	NOUN
easat-6229	262	23	experience	experience	NOUN
easat-6229	262	24	.	.	PUNCT
easat-6229	263	1	the	the	DET
easat-6229	263	2	mathematical	mathematical	ADJ
easat-6229	263	3	working	working	NOUN
easat-6229	263	4	space	space	NOUN
easat-6229	263	5	strategy	strategy	NOUN
easat-6229	263	6	facilitates	facilitate	VERB
easat-6229	263	7	representation	representation	NOUN
easat-6229	263	8	,	,	PUNCT
easat-6229	263	9	visualization	visualization	NOUN
easat-6229	263	10	,	,	PUNCT
easat-6229	263	11	and	and	CCONJ
easat-6229	263	12	construction	construction	NOUN
easat-6229	263	13	to	to	PART
easat-6229	263	14	prove	prove	VERB
easat-6229	263	15	or	or	CCONJ
easat-6229	263	16	validate	validate	VERB
easat-6229	263	17	evidence	evidence	NOUN
easat-6229	263	18	.	.	PUNCT
easat-6229	264	1	this	this	DET
easat-6229	264	2	visualization	visualization	NOUN
easat-6229	264	3	helps	help	VERB
easat-6229	264	4	students	student	NOUN
easat-6229	264	5	better	well	ADV
easat-6229	264	6	understand	understand	VERB
easat-6229	264	7	concepts	concept	NOUN
easat-6229	264	8	and	and	CCONJ
easat-6229	264	9	definitions	definition	NOUN
easat-6229	264	10	.	.	PUNCT
easat-6229	265	1	additionally	additionally	ADV
easat-6229	265	2	,	,	PUNCT
easat-6229	265	3	it	it	PRON
easat-6229	265	4	enables	enable	VERB
easat-6229	265	5	students	student	NOUN
easat-6229	265	6	to	to	PART
easat-6229	265	7	use	use	VERB
easat-6229	265	8	definitions	definition	NOUN
easat-6229	265	9	as	as	ADP
easat-6229	265	10	a	a	DET
easat-6229	265	11	foundation	foundation	NOUN
easat-6229	265	12	for	for	ADP
easat-6229	265	13	providing	provide	VERB
easat-6229	265	14	reasoning	reasoning	NOUN
easat-6229	265	15	behind	behind	ADP
easat-6229	265	16	the	the	DET
easat-6229	265	17	correct	correct	ADJ
easat-6229	265	18	proof	proof	NOUN
easat-6229	265	19	steps	step	NOUN
easat-6229	265	20	or	or	CCONJ
easat-6229	265	21	for	for	ADP
easat-6229	265	22	correcting	correct	VERB
easat-6229	265	23	symbols	symbol	NOUN
easat-6229	265	24	,	,	PUNCT
easat-6229	265	25	statements	statement	NOUN
easat-6229	265	26	,	,	PUNCT
easat-6229	265	27	and	and	CCONJ
easat-6229	265	28	premises	premise	NOUN
easat-6229	265	29	in	in	ADP
easat-6229	265	30	the	the	DET
easat-6229	265	31	case	case	NOUN
easat-6229	265	32	of	of	ADP
easat-6229	265	33	incorrect	incorrect	ADJ
easat-6229	265	34	proof	proof	NOUN
easat-6229	265	35	steps	step	NOUN
easat-6229	265	36	.	.	PUNCT
easat-6229	266	1	students	student	NOUN
easat-6229	266	2	possess	possess	VERB
easat-6229	266	3	a	a	DET
easat-6229	266	4	thorough	thorough	ADJ
easat-6229	266	5	comprehension	comprehension	NOUN
easat-6229	266	6	of	of	ADP
easat-6229	266	7	definitions	definition	NOUN
easat-6229	266	8	,	,	PUNCT
easat-6229	266	9	enabling	enable	VERB
easat-6229	266	10	them	they	PRON
easat-6229	266	11	to	to	PART
easat-6229	266	12	analyze	analyze	VERB
easat-6229	266	13	mathematical	mathematical	ADJ
easat-6229	266	14	statements	statement	NOUN
easat-6229	266	15	and	and	CCONJ
easat-6229	266	16	determine	determine	VERB
easat-6229	266	17	whether	whether	SCONJ
easat-6229	266	18	they	they	PRON
easat-6229	266	19	are	be	AUX
easat-6229	266	20	true	true	ADJ
easat-6229	266	21	or	or	CCONJ
easat-6229	266	22	false	false	ADJ
easat-6229	266	23	through	through	ADP
easat-6229	266	24	the	the	DET
easat-6229	266	25	application	application	NOUN
easat-6229	266	26	of	of	ADP
easat-6229	266	27	example	example	NOUN
easat-6229	266	28	rejections	rejection	NOUN
easat-6229	266	29	.	.	PUNCT
easat-6229	267	1	they	they	PRON
easat-6229	267	2	also	also	ADV
easat-6229	267	3	excel	excel	VERB
easat-6229	267	4	at	at	ADP
easat-6229	267	5	organizing	organize	VERB
easat-6229	267	6	and	and	CCONJ
easat-6229	267	7	rearranging	rearrange	VERB
easat-6229	267	8	factual	factual	ADJ
easat-6229	267	9	information	information	NOUN
easat-6229	267	10	while	while	SCONJ
easat-6229	267	11	sequencing	sequence	VERB
easat-6229	267	12	the	the	DET
easat-6229	267	13	steps	step	NOUN
easat-6229	267	14	required	require	VERB
easat-6229	267	15	to	to	PART
easat-6229	267	16	construct	construct	VERB
easat-6229	267	17	valid	valid	ADJ
easat-6229	267	18	arguments	argument	NOUN
easat-6229	267	19	.	.	PUNCT
easat-6229	268	1	furthermore	furthermore	ADV
easat-6229	268	2	,	,	PUNCT
easat-6229	268	3	students	student	NOUN
easat-6229	268	4	can	can	AUX
easat-6229	268	5	connect	connect	VERB
easat-6229	268	6	established	establish	VERB
easat-6229	268	7	knowledge	knowledge	NOUN
easat-6229	268	8	regarding	regard	VERB
easat-6229	268	9	the	the	DET
easat-6229	268	10	statement	statement	NOUN
easat-6229	268	11	to	to	ADP
easat-6229	268	12	the	the	DET
easat-6229	268	13	claims	claim	NOUN
easat-6229	268	14	needing	need	VERB
easat-6229	268	15	verification	verification	NOUN
easat-6229	268	16	.	.	PUNCT
easat-6229	269	1	to	to	PART
easat-6229	269	2	build	build	VERB
easat-6229	269	3	robust	robust	ADJ
easat-6229	269	4	evidence	evidence	NOUN
easat-6229	269	5	,	,	PUNCT
easat-6229	269	6	these	these	DET
easat-6229	269	7	facts	fact	NOUN
easat-6229	269	8	can	can	AUX
easat-6229	269	9	be	be	AUX
easat-6229	269	10	integrated	integrate	VERB
easat-6229	269	11	into	into	ADP
easat-6229	269	12	existing	exist	VERB
easat-6229	269	13	definitions	definition	NOUN
easat-6229	269	14	,	,	PUNCT
easat-6229	269	15	theorems	theorem	NOUN
easat-6229	269	16	,	,	PUNCT
easat-6229	269	17	or	or	CCONJ
easat-6229	269	18	previously	previously	ADV
easat-6229	269	19	proven	prove	VERB
easat-6229	269	20	assertions	assertion	NOUN
easat-6229	269	21	related	relate	VERB
easat-6229	269	22	to	to	ADP
easat-6229	269	23	the	the	DET
easat-6229	269	24	statement	statement	NOUN
easat-6229	269	25	.	.	PUNCT
easat-6229	270	1	discussion	discussion	NOUN
easat-6229	270	2	can	can	AUX
easat-6229	270	3	be	be	AUX
easat-6229	270	4	an	an	DET
easat-6229	270	5	effective	effective	ADJ
easat-6229	270	6	strategy	strategy	NOUN
easat-6229	270	7	to	to	PART
easat-6229	270	8	encourage	encourage	VERB
easat-6229	270	9	democratic	democratic	ADJ
easat-6229	270	10	habits	habit	NOUN
easat-6229	270	11	,	,	PUNCT
easat-6229	270	12	increase	increase	VERB
easat-6229	270	13	student	student	NOUN
easat-6229	270	14	enthusiasm	enthusiasm	NOUN
easat-6229	270	15	,	,	PUNCT
easat-6229	270	16	and	and	CCONJ
easat-6229	270	17	enhance	enhance	VERB
easat-6229	270	18	intellectual	intellectual	ADJ
easat-6229	270	19	intelligence	intelligence	NOUN
easat-6229	270	20	.	.	PUNCT
easat-6229	271	1	after	after	ADP
easat-6229	271	2	learning	learn	VERB
easat-6229	271	3	real	real	ADJ
easat-6229	271	4	analysis	analysis	NOUN
easat-6229	271	5	through	through	ADP
easat-6229	271	6	worksheets	worksheet	NOUN
easat-6229	271	7	that	that	PRON
easat-6229	271	8	utilize	utilize	VERB
easat-6229	271	9	the	the	DET
easat-6229	271	10	mathematical	mathematical	ADJ
easat-6229	271	11	working	working	NOUN
easat-6229	271	12	space	space	NOUN
easat-6229	271	13	strategy	strategy	NOUN
easat-6229	271	14	,	,	PUNCT
easat-6229	271	15	students	student	NOUN
easat-6229	271	16	demonstrate	demonstrate	VERB
easat-6229	271	17	several	several	ADJ
easat-6229	271	18	competencies	competency	NOUN
easat-6229	271	19	:	:	PUNCT
easat-6229	271	20	they	they	PRON
easat-6229	271	21	can	can	AUX
easat-6229	271	22	understand	understand	VERB
easat-6229	271	23	general	general	ADJ
easat-6229	271	24	statements	statement	NOUN
easat-6229	271	25	and	and	CCONJ
easat-6229	271	26	test	test	VERB
easat-6229	271	27	them	they	PRON
easat-6229	271	28	with	with	ADP
easat-6229	271	29	examples	example	NOUN
easat-6229	271	30	;	;	PUNCT
easat-6229	271	31	identify	identify	VERB
easat-6229	271	32	errors	error	NOUN
easat-6229	271	33	in	in	ADP
easat-6229	271	34	proofs	proof	NOUN
easat-6229	271	35	and	and	CCONJ
easat-6229	271	36	correct	correct	VERB
easat-6229	271	37	them	they	PRON
easat-6229	271	38	;	;	PUNCT
easat-6229	271	39	and	and	CCONJ
easat-6229	271	40	draw	draw	VERB
easat-6229	271	41	accurate	accurate	ADJ
easat-6229	271	42	conclusions	conclusion	NOUN
easat-6229	271	43	.	.	PUNCT
easat-6229	272	1	the	the	DET
easat-6229	272	2	implementation	implementation	NOUN
easat-6229	272	3	of	of	ADP
easat-6229	272	4	evidence	evidence	NOUN
easat-6229	272	5	-	-	PUNCT
easat-6229	272	6	based	base	VERB
easat-6229	272	7	strategies	strategy	NOUN
easat-6229	272	8	,	,	PUNCT
easat-6229	272	9	such	such	ADJ
easat-6229	272	10	as	as	ADP
easat-6229	272	11	visualization	visualization	NOUN
easat-6229	272	12	,	,	PUNCT
easat-6229	272	13	discussion	discussion	NOUN
easat-6229	272	14	,	,	PUNCT
easat-6229	272	15	and	and	CCONJ
easat-6229	272	16	manipulation	manipulation	NOUN
easat-6229	272	17	,	,	PUNCT
easat-6229	272	18	significantly	significantly	ADV
easat-6229	272	19	contributes	contribute	VERB
easat-6229	272	20	to	to	ADP
easat-6229	272	21	improving	improve	VERB
easat-6229	272	22	the	the	DET
easat-6229	272	23	learning	learning	NOUN
easat-6229	272	24	experience	experience	NOUN
easat-6229	272	25	in	in	ADP
easat-6229	272	26	real	real	ADJ
easat-6229	272	27	analysis	analysis	NOUN
easat-6229	272	28	.	.	PUNCT
easat-6229	273	1	this	this	DET
easat-6229	273	2	study	study	NOUN
easat-6229	273	3	focuses	focus	VERB
easat-6229	273	4	on	on	ADP
easat-6229	273	5	real	real	ADJ
easat-6229	273	6	analysis	analysis	NOUN
easat-6229	273	7	,	,	PUNCT
easat-6229	273	8	specifically	specifically	ADV
easat-6229	273	9	the	the	DET
easat-6229	273	10	material	material	NOUN
easat-6229	273	11	related	relate	VERB
easat-6229	273	12	to	to	ADP
easat-6229	273	13	sequences	sequence	NOUN
easat-6229	273	14	.	.	PUNCT
easat-6229	274	1	the	the	DET
easat-6229	274	2	primary	primary	ADJ
easat-6229	274	3	objective	objective	NOUN
easat-6229	274	4	is	be	AUX
easat-6229	274	5	to	to	PART
easat-6229	274	6	prove	prove	VERB
easat-6229	274	7	the	the	DET
easat-6229	274	8	convergence	convergence	NOUN
easat-6229	274	9	of	of	ADP
easat-6229	274	10	sequences	sequence	NOUN
easat-6229	274	11	.	.	PUNCT
easat-6229	275	1	bartle	bartle	PROPN
easat-6229	275	2	's	's	PART
easat-6229	275	3	approach	approach	NOUN
easat-6229	275	4	utilizes	utilize	VERB
easat-6229	275	5	a	a	DET
easat-6229	275	6	variety	variety	NOUN
easat-6229	275	7	of	of	ADP
easat-6229	275	8	theorems	theorem	NOUN
easat-6229	275	9	and	and	CCONJ
easat-6229	275	10	definitions	definition	NOUN
easat-6229	275	11	for	for	ADP
easat-6229	275	12	this	this	DET
easat-6229	275	13	purpose	purpose	NOUN
easat-6229	275	14	,	,	PUNCT
easat-6229	275	15	with	with	ADP
easat-6229	275	16	each	each	DET
easat-6229	275	17	session	session	NOUN
easat-6229	275	18	dedicated	dedicate	VERB
easat-6229	275	19	to	to	ADP
easat-6229	275	20	discussing	discuss	VERB
easat-6229	275	21	theorems	theorem	NOUN
easat-6229	275	22	that	that	PRON
easat-6229	275	23	help	help	AUX
easat-6229	275	24	establish	establish	VERB
easat-6229	275	25	the	the	DET
easat-6229	275	26	convergence	convergence	NOUN
easat-6229	275	27	of	of	ADP
easat-6229	275	28	sequences	sequence	NOUN
easat-6229	275	29	.	.	PUNCT
easat-6229	276	1	as	as	ADP
easat-6229	276	2	a	a	DET
easat-6229	276	3	result	result	NOUN
easat-6229	276	4	,	,	PUNCT
easat-6229	276	5	students	student	NOUN
easat-6229	276	6	gain	gain	VERB
easat-6229	276	7	a	a	DET
easat-6229	276	8	clear	clear	ADJ
easat-6229	276	9	understanding	understanding	NOUN
easat-6229	276	10	and	and	CCONJ
easat-6229	276	11	can	can	AUX
easat-6229	276	12	effectively	effectively	ADV
easat-6229	276	13	apply	apply	VERB
easat-6229	276	14	these	these	DET
easat-6229	276	15	theorems	theorem	NOUN
easat-6229	276	16	to	to	PART
easat-6229	276	17	solve	solve	VERB
easat-6229	276	18	problems	problem	NOUN
easat-6229	276	19	.	.	PUNCT
easat-6229	277	1	after	after	ADP
easat-6229	277	2	completing	complete	VERB
easat-6229	277	3	the	the	DET
easat-6229	277	4	material	material	NOUN
easat-6229	277	5	,	,	PUNCT
easat-6229	277	6	students	student	NOUN
easat-6229	277	7	take	take	VERB
easat-6229	277	8	a	a	DET
easat-6229	277	9	test	test	NOUN
easat-6229	277	10	;	;	PUNCT
easat-6229	277	11	however	however	ADV
easat-6229	277	12	,	,	PUNCT
easat-6229	277	13	they	they	PRON
easat-6229	277	14	often	often	ADV
easat-6229	277	15	find	find	VERB
easat-6229	277	16	it	it	PRON
easat-6229	277	17	challenging	challenge	VERB
easat-6229	277	18	to	to	PART
easat-6229	277	19	determine	determine	VERB
easat-6229	277	20	which	which	PRON
easat-6229	277	21	theorem	theorem	VERB
easat-6229	277	22	applies	applie	NOUN
easat-6229	277	23	to	to	ADP
easat-6229	277	24	specific	specific	ADJ
easat-6229	277	25	problems	problem	NOUN
easat-6229	277	26	.	.	PUNCT
easat-6229	278	1	it	it	PRON
easat-6229	278	2	is	be	AUX
easat-6229	278	3	essential	essential	ADJ
easat-6229	278	4	for	for	SCONJ
easat-6229	278	5	students	student	NOUN
easat-6229	278	6	to	to	PART
easat-6229	278	7	correctly	correctly	ADV
easat-6229	278	8	utilize	utilize	VERB
easat-6229	278	9	theorems	theorem	NOUN
easat-6229	278	10	and	and	CCONJ
easat-6229	278	11	definitions	definition	NOUN
easat-6229	278	12	relevant	relevant	ADJ
easat-6229	278	13	to	to	ADP
easat-6229	278	14	the	the	DET
easat-6229	278	15	problems	problem	NOUN
easat-6229	278	16	they	they	PRON
easat-6229	278	17	encounter	encounter	VERB
easat-6229	278	18	.	.	PUNCT
easat-6229	279	1	to	to	PART
easat-6229	279	2	address	address	VERB
easat-6229	279	3	this	this	DET
easat-6229	279	4	issue	issue	NOUN
easat-6229	279	5	,	,	PUNCT
easat-6229	279	6	a	a	DET
easat-6229	279	7	discussion	discussion	NOUN
easat-6229	279	8	material	material	NOUN
easat-6229	279	9	worksheet	worksheet	NOUN
easat-6229	279	10	was	be	AUX
easat-6229	279	11	developed	develop	VERB
easat-6229	279	12	using	use	VERB
easat-6229	279	13	the	the	DET
easat-6229	279	14	mathematical	mathematical	ADJ
easat-6229	279	15	working	working	NOUN
easat-6229	279	16	space	space	NOUN
easat-6229	279	17	strategy	strategy	NOUN
easat-6229	279	18	.	.	PUNCT
easat-6229	280	1	the	the	DET
easat-6229	280	2	implementation	implementation	NOUN
easat-6229	280	3	of	of	ADP
easat-6229	280	4	these	these	DET
easat-6229	280	5	worksheets	worksheet	NOUN
easat-6229	280	6	enhances	enhance	VERB
easat-6229	280	7	student	student	NOUN
easat-6229	280	8	engagement	engagement	NOUN
easat-6229	280	9	in	in	ADP
easat-6229	280	10	learning	learn	VERB
easat-6229	280	11	real	real	ADJ
easat-6229	280	12	analysis	analysis	NOUN
easat-6229	280	13	,	,	PUNCT
easat-6229	280	14	encouraging	encourage	VERB
easat-6229	280	15	lecturers	lecturer	NOUN
easat-6229	280	16	to	to	PART
easat-6229	280	17	pose	pose	VERB
easat-6229	280	18	questions	question	NOUN
easat-6229	280	19	that	that	PRON
easat-6229	280	20	require	require	VERB
easat-6229	280	21	evidence	evidence	NOUN
easat-6229	280	22	-	-	PUNCT
easat-6229	280	23	based	base	VERB
easat-6229	280	24	reasoning	reasoning	NOUN
easat-6229	280	25	.	.	PUNCT
easat-6229	281	1	students	student	NOUN
easat-6229	281	2	benefit	benefit	VERB
easat-6229	281	3	from	from	ADP
easat-6229	281	4	applying	apply	VERB
easat-6229	281	5	the	the	DET
easat-6229	281	6	strategies	strategy	NOUN
easat-6229	281	7	outlined	outline	VERB
easat-6229	281	8	in	in	ADP
easat-6229	281	9	these	these	DET
easat-6229	281	10	worksheets	worksheet	NOUN
easat-6229	281	11	,	,	PUNCT
easat-6229	281	12	as	as	SCONJ
easat-6229	281	13	they	they	PRON
easat-6229	281	14	assist	assist	VERB
easat-6229	281	15	in	in	ADP
easat-6229	281	16	tackling	tackle	VERB
easat-6229	281	17	proof	proof	NOUN
easat-6229	281	18	-	-	PUNCT
easat-6229	281	19	related	relate	VERB
easat-6229	281	20	problems	problem	NOUN
easat-6229	281	21	.	.	PUNCT
easat-6229	282	1	transparency	transparency	NOUN
easat-6229	282	2	:	:	PUNCT
easat-6229	282	3	the	the	DET
easat-6229	282	4	authors	author	NOUN
easat-6229	282	5	confirm	confirm	VERB
easat-6229	282	6	that	that	SCONJ
easat-6229	282	7	the	the	DET
easat-6229	282	8	manuscript	manuscript	NOUN
easat-6229	282	9	is	be	AUX
easat-6229	282	10	an	an	DET
easat-6229	282	11	honest	honest	ADJ
easat-6229	282	12	,	,	PUNCT
easat-6229	282	13	accurate	accurate	ADJ
easat-6229	282	14	,	,	PUNCT
easat-6229	282	15	and	and	CCONJ
easat-6229	282	16	transparent	transparent	ADJ
easat-6229	282	17	account	account	NOUN
easat-6229	282	18	of	of	ADP
easat-6229	282	19	the	the	DET
easat-6229	282	20	study	study	NOUN
easat-6229	282	21	;	;	PUNCT
easat-6229	282	22	that	that	SCONJ
easat-6229	282	23	no	no	DET
easat-6229	282	24	vital	vital	ADJ
easat-6229	282	25	features	feature	NOUN
easat-6229	282	26	of	of	ADP
easat-6229	282	27	the	the	DET
easat-6229	282	28	study	study	NOUN
easat-6229	282	29	have	have	AUX
easat-6229	282	30	been	be	AUX
easat-6229	282	31	omitted	omit	VERB
easat-6229	282	32	;	;	PUNCT
easat-6229	282	33	and	and	CCONJ
easat-6229	282	34	that	that	SCONJ
easat-6229	282	35	any	any	DET
easat-6229	282	36	discrepancies	discrepancy	NOUN
easat-6229	282	37	from	from	ADP
easat-6229	282	38	the	the	DET
easat-6229	282	39	study	study	NOUN
easat-6229	282	40	as	as	SCONJ
easat-6229	282	41	planned	plan	VERB
easat-6229	282	42	have	have	AUX
easat-6229	282	43	been	be	AUX
easat-6229	282	44	explained	explain	VERB
easat-6229	282	45	.	.	PUNCT
easat-6229	283	1	this	this	DET
easat-6229	283	2	study	study	NOUN
easat-6229	283	3	followed	follow	VERB
easat-6229	283	4	all	all	DET
easat-6229	283	5	ethical	ethical	ADJ
easat-6229	283	6	practices	practice	NOUN
easat-6229	283	7	during	during	ADP
easat-6229	283	8	writing	writing	NOUN
easat-6229	283	9	.	.	PUNCT
easat-6229	284	1	1250	1250	NUM
easat-6229	284	2	edelweiss	edelweiss	PROPN
easat-6229	284	3	applied	apply	VERB
easat-6229	284	4	science	science	NOUN
easat-6229	284	5	and	and	CCONJ
easat-6229	284	6	technology	technology	NOUN
easat-6229	284	7	issn	issn	PROPN
easat-6229	284	8	:	:	PUNCT
easat-6229	284	9	2576	2576	NUM
easat-6229	284	10	-	-	SYM
easat-6229	284	11	8484	8484	NUM
easat-6229	284	12	vol	vol	NOUN
easat-6229	284	13	.	.	PROPN
easat-6229	285	1	9	9	NUM
easat-6229	285	2	,	,	PUNCT
easat-6229	285	3	no	no	INTJ
easat-6229	285	4	.	.	NOUN
easat-6229	285	5	4	4	NUM
easat-6229	285	6	:	:	SYM
easat-6229	285	7	1240	1240	NUM
easat-6229	285	8	-	-	SYM
easat-6229	285	9	1251	1251	NUM
easat-6229	285	10	,	,	PUNCT
easat-6229	285	11	2025	2025	NUM
easat-6229	285	12	doi	doi	NOUN
easat-6229	285	13	:	:	PUNCT
easat-6229	285	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
easat-6229	285	15	©	©	ADP
easat-6229	285	16	2025	2025	NUM
easat-6229	285	17	by	by	ADP
easat-6229	285	18	the	the	DET
easat-6229	285	19	authors	author	NOUN
easat-6229	285	20	;	;	PUNCT
easat-6229	286	1	licensee	licensee	PROPN
easat-6229	286	2	learning	learn	VERB
easat-6229	286	3	gate	gate	NOUN
easat-6229	286	4	copyright	copyright	NOUN
easat-6229	286	5	:	:	PUNCT
easat-6229	286	6	©	©	PROPN
easat-6229	286	7	2025	2025	NUM
easat-6229	286	8	by	by	ADP
easat-6229	286	9	the	the	DET
easat-6229	286	10	authors	author	NOUN
easat-6229	286	11	.	.	PUNCT
easat-6229	287	1	this	this	DET
easat-6229	287	2	open	open	ADJ
easat-6229	287	3	-	-	PUNCT
easat-6229	287	4	access	access	NOUN
easat-6229	287	5	article	article	NOUN
easat-6229	287	6	is	be	AUX
easat-6229	287	7	distributed	distribute	VERB
easat-6229	287	8	under	under	ADP
easat-6229	287	9	the	the	DET
easat-6229	287	10	terms	term	NOUN
easat-6229	287	11	and	and	CCONJ
easat-6229	287	12	conditions	condition	NOUN
easat-6229	287	13	of	of	ADP
easat-6229	287	14	the	the	DET
easat-6229	287	15	creative	creative	ADJ
easat-6229	287	16	commons	common	NOUN
easat-6229	287	17	attribution	attribution	NOUN
easat-6229	287	18	(	(	PUNCT
easat-6229	287	19	cc	cc	NOUN
easat-6229	287	20	by	by	ADP
easat-6229	287	21	)	)	PUNCT
easat-6229	287	22	license	license	NOUN
easat-6229	287	23	(	(	PUNCT
easat-6229	287	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-6229	287	25	)	)	PUNCT
easat-6229	287	26	.	.	PUNCT
easat-6229	288	1	references	reference	NOUN
easat-6229	288	2	[	[	X
easat-6229	288	3	1	1	NUM
easat-6229	288	4	]	]	PUNCT
easat-6229	288	5	h.	h.	PROPN
easat-6229	288	6	rocha	rocha	PROPN
easat-6229	288	7	,	,	PUNCT
easat-6229	288	8	"	"	PUNCT
easat-6229	288	9	mathematical	mathematical	ADJ
easat-6229	288	10	proof	proof	NOUN
easat-6229	288	11	:	:	PUNCT
easat-6229	288	12	from	from	ADP
easat-6229	288	13	mathematics	mathematics	PROPN
easat-6229	288	14	to	to	ADP
easat-6229	288	15	school	school	NOUN
easat-6229	288	16	mathematics	mathematic	NOUN
easat-6229	288	17	,	,	PUNCT
easat-6229	288	18	"	"	PUNCT
easat-6229	288	19	philosophical	philosophical	ADJ
easat-6229	288	20	transactions	transaction	NOUN
easat-6229	288	21	of	of	ADP
easat-6229	288	22	the	the	DET
easat-6229	288	23	royal	royal	ADJ
easat-6229	288	24	society	society	NOUN
easat-6229	288	25	a	a	PRON
easat-6229	288	26	,	,	PUNCT
easat-6229	288	27	vol	vol	NOUN
easat-6229	288	28	.	.	PROPN
easat-6229	288	29	377	377	NUM
easat-6229	288	30	,	,	PUNCT
easat-6229	288	31	no	no	NOUN
easat-6229	288	32	.	.	NOUN
easat-6229	288	33	2140	2140	NUM
easat-6229	288	34	,	,	PUNCT
easat-6229	288	35	p.	p.	NOUN
easat-6229	288	36	20180045	20180045	NUM
easat-6229	288	37	,	,	PUNCT
easat-6229	288	38	2019	2019	NUM
easat-6229	288	39	.	.	PUNCT
easat-6229	289	1	https://doi.org/10.1098/rsta.2018.0045	https://doi.org/10.1098/rsta.2018.0045	PROPN
easat-6229	289	2	[	[	X
easat-6229	289	3	2	2	X
easat-6229	289	4	]	]	PUNCT
easat-6229	289	5	e.	e.	PROPN
easat-6229	289	6	bettinger	bettinger	PROPN
easat-6229	289	7	,	,	PUNCT
easat-6229	289	8	s.	s.	PROPN
easat-6229	289	9	ludvigsen	ludvigsen	PROPN
easat-6229	289	10	,	,	PUNCT
easat-6229	289	11	m.	m.	PROPN
easat-6229	289	12	rege	rege	PROPN
easat-6229	289	13	,	,	PUNCT
easat-6229	289	14	i.	i.	PROPN
easat-6229	289	15	f.	f.	PROPN
easat-6229	289	16	solli	solli	PROPN
easat-6229	289	17	,	,	PUNCT
easat-6229	289	18	and	and	CCONJ
easat-6229	289	19	d.	d.	PROPN
easat-6229	289	20	yeager	yeager	PROPN
easat-6229	289	21	,	,	PUNCT
easat-6229	289	22	"	"	PUNCT
easat-6229	289	23	increasing	increase	VERB
easat-6229	289	24	perseverance	perseverance	NOUN
easat-6229	289	25	in	in	ADP
easat-6229	289	26	math	math	NOUN
easat-6229	289	27	:	:	PUNCT
easat-6229	289	28	evidence	evidence	NOUN
easat-6229	289	29	from	from	ADP
easat-6229	289	30	a	a	DET
easat-6229	289	31	field	field	NOUN
easat-6229	289	32	experiment	experiment	NOUN
easat-6229	289	33	in	in	ADP
easat-6229	289	34	norway	norway	PROPN
easat-6229	289	35	,	,	PUNCT
easat-6229	289	36	"	"	PUNCT
easat-6229	289	37	journal	journal	NOUN
easat-6229	289	38	of	of	ADP
easat-6229	289	39	economic	economic	ADJ
easat-6229	289	40	behavior	behavior	NOUN
easat-6229	289	41	&	&	CCONJ
easat-6229	289	42	organization	organization	PROPN
easat-6229	289	43	,	,	PUNCT
easat-6229	289	44	vol	vol	NOUN
easat-6229	289	45	.	.	PROPN
easat-6229	289	46	146	146	NUM
easat-6229	289	47	,	,	PUNCT
easat-6229	289	48	pp	pp	ADJ
easat-6229	289	49	.	.	PUNCT
easat-6229	290	1	1	1	NUM
easat-6229	290	2	-	-	SYM
easat-6229	290	3	15	15	NUM
easat-6229	290	4	,	,	PUNCT
easat-6229	290	5	2018	2018	NUM
easat-6229	290	6	.	.	PUNCT
easat-6229	291	1	https://doi.org/10.1016/j.jebo.2017.11.032	https://doi.org/10.1016/j.jebo.2017.11.032	PRON
easat-6229	292	1	[	[	X
easat-6229	292	2	3	3	NUM
easat-6229	292	3	]	]	X
easat-6229	292	4	l.	l.	PROPN
easat-6229	292	5	cragg	cragg	PROPN
easat-6229	292	6	and	and	CCONJ
easat-6229	292	7	c.	c.	PROPN
easat-6229	292	8	gilmore	gilmore	PROPN
easat-6229	292	9	,	,	PUNCT
easat-6229	292	10	"	"	PUNCT
easat-6229	292	11	skills	skill	VERB
easat-6229	292	12	underlying	underlying	ADJ
easat-6229	292	13	mathematics	mathematic	NOUN
easat-6229	292	14	:	:	PUNCT
easat-6229	292	15	the	the	DET
easat-6229	292	16	role	role	NOUN
easat-6229	292	17	of	of	ADP
easat-6229	292	18	executive	executive	ADJ
easat-6229	292	19	function	function	NOUN
easat-6229	292	20	in	in	ADP
easat-6229	292	21	the	the	DET
easat-6229	292	22	development	development	NOUN
easat-6229	292	23	of	of	ADP
easat-6229	292	24	mathematics	mathematic	NOUN
easat-6229	292	25	proficiency	proficiency	NOUN
easat-6229	292	26	,	,	PUNCT
easat-6229	292	27	"	"	PUNCT
easat-6229	292	28	trends	trend	NOUN
easat-6229	292	29	in	in	ADP
easat-6229	292	30	neuroscience	neuroscience	NOUN
easat-6229	292	31	and	and	CCONJ
easat-6229	292	32	education	education	NOUN
easat-6229	292	33	,	,	PUNCT
easat-6229	292	34	vol	vol	NOUN
easat-6229	292	35	.	.	PROPN
easat-6229	292	36	3	3	NUM
easat-6229	292	37	,	,	PUNCT
easat-6229	292	38	no	no	INTJ
easat-6229	292	39	.	.	NOUN
easat-6229	292	40	2	2	NUM
easat-6229	292	41	,	,	PUNCT
easat-6229	292	42	pp	pp	ADJ
easat-6229	292	43	.	.	PUNCT
easat-6229	293	1	63	63	NUM
easat-6229	293	2	-	-	SYM
easat-6229	293	3	68	68	NUM
easat-6229	293	4	,	,	PUNCT
easat-6229	293	5	2014	2014	NUM
easat-6229	293	6	.	.	PUNCT
easat-6229	294	1	https://doi.org/10.1016/j.tine.2013.12.001	https://doi.org/10.1016/j.tine.2013.12.001	VERB
easat-6229	294	2	[	[	PUNCT
easat-6229	294	3	4	4	X
easat-6229	294	4	]	]	PUNCT
easat-6229	294	5	t.	t.	NOUN
easat-6229	294	6	cadwalladerolsker	cadwalladerolsker	NOUN
easat-6229	294	7	,	,	PUNCT
easat-6229	294	8	"	"	PUNCT
easat-6229	294	9	what	what	PRON
easat-6229	294	10	do	do	AUX
easat-6229	294	11	we	we	PRON
easat-6229	294	12	mean	mean	VERB
easat-6229	294	13	by	by	ADP
easat-6229	294	14	mathematical	mathematical	ADJ
easat-6229	294	15	proof	proof	NOUN
easat-6229	294	16	?	?	PUNCT
easat-6229	294	17	,	,	PUNCT
easat-6229	294	18	"	"	PUNCT
easat-6229	294	19	journal	journal	NOUN
easat-6229	294	20	of	of	ADP
easat-6229	294	21	humanistic	humanistic	ADJ
easat-6229	294	22	mathematics	mathematic	NOUN
easat-6229	294	23	,	,	PUNCT
easat-6229	294	24	vol	vol	NOUN
easat-6229	294	25	.	.	PROPN
easat-6229	294	26	1	1	NUM
easat-6229	294	27	,	,	PUNCT
easat-6229	294	28	no	no	INTJ
easat-6229	294	29	.	.	NOUN
easat-6229	294	30	1	1	NUM
easat-6229	294	31	,	,	PUNCT
easat-6229	294	32	pp	pp	ADJ
easat-6229	294	33	.	.	PUNCT
easat-6229	295	1	33	33	NUM
easat-6229	295	2	-	-	SYM
easat-6229	295	3	60	60	NUM
easat-6229	295	4	,	,	PUNCT
easat-6229	295	5	2011	2011	NUM
easat-6229	295	6	.	.	PUNCT
easat-6229	296	1	https://doi.org/10.5642/jhummath.201101.04	https://doi.org/10.5642/jhummath.201101.04	X
easat-6229	297	1	[	[	X
easat-6229	297	2	5	5	NUM
easat-6229	297	3	]	]	PUNCT
easat-6229	297	4	d.	d.	PROPN
easat-6229	297	5	a.	a.	PROPN
easat-6229	297	6	stylianou	stylianou	PROPN
easat-6229	297	7	,	,	PUNCT
easat-6229	297	8	m.	m.	PROPN
easat-6229	297	9	l.	l.	PROPN
easat-6229	297	10	blanton	blanton	PROPN
easat-6229	297	11	,	,	PUNCT
easat-6229	297	12	and	and	CCONJ
easat-6229	297	13	o.	o.	PROPN
easat-6229	297	14	rotou	rotou	PROPN
easat-6229	297	15	,	,	PUNCT
easat-6229	297	16	"	"	PUNCT
easat-6229	297	17	undergraduate	undergraduate	ADJ
easat-6229	297	18	students	student	NOUN
easat-6229	297	19	’	’	PART
easat-6229	297	20	understanding	understanding	NOUN
easat-6229	297	21	of	of	ADP
easat-6229	297	22	proof	proof	NOUN
easat-6229	297	23	:	:	PUNCT
easat-6229	297	24	relationships	relationship	NOUN
easat-6229	297	25	between	between	ADP
easat-6229	297	26	proof	proof	ADJ
easat-6229	297	27	conceptions	conception	NOUN
easat-6229	297	28	,	,	PUNCT
easat-6229	297	29	beliefs	belief	NOUN
easat-6229	297	30	,	,	PUNCT
easat-6229	297	31	and	and	CCONJ
easat-6229	297	32	classroom	classroom	NOUN
easat-6229	297	33	experiences	experience	NOUN
easat-6229	297	34	with	with	ADP
easat-6229	297	35	learning	learn	VERB
easat-6229	297	36	proof	proof	NOUN
easat-6229	297	37	,	,	PUNCT
easat-6229	297	38	"	"	PUNCT
easat-6229	297	39	international	international	ADJ
easat-6229	297	40	journal	journal	NOUN
easat-6229	297	41	of	of	ADP
easat-6229	297	42	research	research	NOUN
easat-6229	297	43	in	in	ADP
easat-6229	297	44	undergraduate	undergraduate	ADJ
easat-6229	297	45	mathematics	mathematic	NOUN
easat-6229	297	46	education	education	NOUN
easat-6229	297	47	,	,	PUNCT
easat-6229	297	48	vol	vol	NOUN
easat-6229	297	49	.	.	PROPN
easat-6229	297	50	1	1	NUM
easat-6229	297	51	,	,	PUNCT
easat-6229	297	52	pp	pp	ADJ
easat-6229	297	53	.	.	PUNCT
easat-6229	298	1	91	91	NUM
easat-6229	298	2	-	-	SYM
easat-6229	298	3	134	134	NUM
easat-6229	298	4	,	,	PUNCT
easat-6229	298	5	2015	2015	NUM
easat-6229	298	6	.	.	PUNCT
easat-6229	299	1	https://doi.org/10.1007/s40753-015-0003-0	https://doi.org/10.1007/s40753-015-0003-0	X
easat-6229	300	1	[	[	X
easat-6229	300	2	6	6	NUM
easat-6229	300	3	]	]	PUNCT
easat-6229	300	4	t.	t.	PROPN
easat-6229	300	5	b.	b.	PROPN
easat-6229	300	6	l.	l.	PROPN
easat-6229	300	7	tran	tran	PROPN
easat-6229	300	8	,	,	PUNCT
easat-6229	300	9	t.	t.	PROPN
easat-6229	300	10	n.	n.	PROPN
easat-6229	300	11	ho	ho	PROPN
easat-6229	300	12	,	,	PUNCT
easat-6229	300	13	s.	s.	PROPN
easat-6229	300	14	v.	v.	PROPN
easat-6229	300	15	mackenzie	mackenzie	PROPN
easat-6229	300	16	,	,	PUNCT
easat-6229	300	17	and	and	CCONJ
easat-6229	300	18	l.	l.	PROPN
easat-6229	300	19	k.	k.	PROPN
easat-6229	300	20	le	le	PROPN
easat-6229	300	21	,	,	PUNCT
easat-6229	300	22	"	"	PUNCT
easat-6229	300	23	developing	develop	VERB
easat-6229	300	24	assessment	assessment	NOUN
easat-6229	300	25	criteria	criterion	NOUN
easat-6229	300	26	of	of	ADP
easat-6229	300	27	a	a	DET
easat-6229	300	28	lesson	lesson	NOUN
easat-6229	300	29	for	for	ADP
easat-6229	300	30	creativity	creativity	NOUN
easat-6229	300	31	to	to	PART
easat-6229	300	32	promote	promote	VERB
easat-6229	300	33	teaching	teaching	NOUN
easat-6229	300	34	for	for	ADP
easat-6229	300	35	creativity	creativity	NOUN
easat-6229	300	36	,	,	PUNCT
easat-6229	300	37	"	"	PUNCT
easat-6229	300	38	thinking	thinking	NOUN
easat-6229	300	39	skills	skill	NOUN
easat-6229	300	40	and	and	CCONJ
easat-6229	300	41	creativity	creativity	NOUN
easat-6229	300	42	,	,	PUNCT
easat-6229	300	43	vol	vol	NOUN
easat-6229	300	44	.	.	PROPN
easat-6229	300	45	25	25	NUM
easat-6229	300	46	,	,	PUNCT
easat-6229	300	47	pp	pp	ADJ
easat-6229	300	48	.	.	PUNCT
easat-6229	301	1	10	10	NUM
easat-6229	301	2	-	-	SYM
easat-6229	301	3	26	26	NUM
easat-6229	301	4	,	,	PUNCT
easat-6229	301	5	2017	2017	NUM
easat-6229	301	6	.	.	PUNCT
easat-6229	302	1	https://doi.org/10.1016/j.tsc.2017.05.006	https://doi.org/10.1016/j.tsc.2017.05.006	NOUN
easat-6229	303	1	[	[	X
easat-6229	303	2	7	7	X
easat-6229	303	3	]	]	X
easat-6229	303	4	h.	h.	PROPN
easat-6229	303	5	b.	b.	PROPN
easat-6229	303	6	chand	chand	PROPN
easat-6229	303	7	,	,	PUNCT
easat-6229	303	8	"	"	PUNCT
easat-6229	303	9	difficulties	difficulty	NOUN
easat-6229	303	10	experienced	experience	VERB
easat-6229	303	11	by	by	ADP
easat-6229	303	12	undergraduate	undergraduate	ADJ
easat-6229	303	13	students	student	NOUN
easat-6229	303	14	in	in	ADP
easat-6229	303	15	proving	prove	VERB
easat-6229	303	16	theorems	theorem	NOUN
easat-6229	303	17	of	of	ADP
easat-6229	303	18	real	real	ADJ
easat-6229	303	19	analysis	analysis	NOUN
easat-6229	303	20	,	,	PUNCT
easat-6229	303	21	"	"	PUNCT
easat-6229	303	22	scholars	scholar	NOUN
easat-6229	303	23	'	'	PART
easat-6229	303	24	journal	journal	NOUN
easat-6229	303	25	,	,	PUNCT
easat-6229	303	26	pp	pp	ADJ
easat-6229	303	27	.	.	PUNCT
easat-6229	304	1	149	149	NUM
easat-6229	304	2	-	-	SYM
easat-6229	304	3	163	163	NUM
easat-6229	304	4	,	,	PUNCT
easat-6229	304	5	2021	2021	NUM
easat-6229	304	6	.	.	PUNCT
easat-6229	305	1	https://doi.org/10.3126/scholars.v4i1.42475	https://doi.org/10.3126/scholars.v4i1.42475	PROPN
easat-6229	305	2	[	[	X
easat-6229	305	3	8	8	NUM
easat-6229	305	4	]	]	X
easat-6229	305	5	i.	i.	NOUN
easat-6229	305	6	widiati	widiati	PROPN
easat-6229	305	7	and	and	CCONJ
easat-6229	305	8	a.	a.	NOUN
easat-6229	305	9	sthephani	sthephani	PROPN
easat-6229	305	10	,	,	PUNCT
easat-6229	305	11	"	"	PUNCT
easat-6229	305	12	difficulties	difficultie	VERB
easat-6229	305	13	analysis	analysis	NOUN
easat-6229	305	14	of	of	ADP
easat-6229	305	15	mathematics	mathematics	NOUN
easat-6229	305	16	education	education	NOUN
easat-6229	305	17	students	student	NOUN
easat-6229	305	18	on	on	ADP
easat-6229	305	19	the	the	DET
easat-6229	305	20	real	real	ADJ
easat-6229	305	21	analysis	analysis	NOUN
easat-6229	305	22	subject	subject	ADJ
easat-6229	305	23	,	,	PUNCT
easat-6229	305	24	"	"	PUNCT
easat-6229	305	25	presented	present	VERB
easat-6229	305	26	at	at	ADP
easat-6229	305	27	the	the	DET
easat-6229	305	28	in	in	ADJ
easat-6229	305	29	journal	journal	PROPN
easat-6229	305	30	of	of	ADP
easat-6229	305	31	physics	physics	PROPN
easat-6229	305	32	:	:	PUNCT
easat-6229	305	33	conference	conference	NOUN
easat-6229	305	34	series	series	NOUN
easat-6229	305	35	(	(	PUNCT
easat-6229	305	36	vol	vol	NOUN
easat-6229	305	37	.	.	PROPN
easat-6229	305	38	1088	1088	NUM
easat-6229	305	39	,	,	PUNCT
easat-6229	305	40	no	no	INTJ
easat-6229	305	41	.	.	NOUN
easat-6229	305	42	1	1	NUM
easat-6229	305	43	,	,	PUNCT
easat-6229	305	44	p.	p.	NOUN
easat-6229	305	45	012037	012037	NUM
easat-6229	305	46	)	)	PUNCT
easat-6229	305	47	.	.	PUNCT
easat-6229	306	1	iop	iop	PROPN
easat-6229	306	2	publishing	publishing	NOUN
easat-6229	306	3	,	,	PUNCT
easat-6229	306	4	2018	2018	NUM
easat-6229	306	5	.	.	PUNCT
easat-6229	307	1	[	[	X
easat-6229	307	2	9	9	NUM
easat-6229	307	3	]	]	PUNCT
easat-6229	307	4	a.	a.	NOUN
easat-6229	307	5	bordg	bordg	ADV
easat-6229	307	6	,	,	PUNCT
easat-6229	307	7	"	"	PUNCT
easat-6229	307	8	a	a	DET
easat-6229	307	9	replication	replication	NOUN
easat-6229	307	10	crisis	crisis	NOUN
easat-6229	307	11	in	in	ADP
easat-6229	307	12	mathematics	mathematic	NOUN
easat-6229	307	13	?	?	PUNCT
easat-6229	307	14	,	,	PUNCT
easat-6229	307	15	"	"	PUNCT
easat-6229	307	16	the	the	DET
easat-6229	307	17	mathematical	mathematical	ADJ
easat-6229	307	18	intelligencer	intelligencer	NOUN
easat-6229	307	19	,	,	PUNCT
easat-6229	307	20	pp	pp	ADJ
easat-6229	307	21	.	.	PUNCT
easat-6229	308	1	1	1	NUM
easat-6229	308	2	-	-	SYM
easat-6229	308	3	5	5	NUM
easat-6229	308	4	,	,	PUNCT
easat-6229	308	5	2021	2021	NUM
easat-6229	308	6	.	.	PUNCT
easat-6229	309	1	https://doi.org/10.1007/s00283-020-10037-7	https://doi.org/10.1007/s00283-020-10037-7	NOUN
easat-6229	310	1	[	[	X
easat-6229	310	2	10	10	NUM
easat-6229	310	3	]	]	X
easat-6229	310	4	g.	g.	PROPN
easat-6229	310	5	güler	güler	PROPN
easat-6229	310	6	,	,	PUNCT
easat-6229	310	7	"	"	PUNCT
easat-6229	310	8	the	the	DET
easat-6229	310	9	difficulties	difficulty	NOUN
easat-6229	310	10	experienced	experience	VERB
easat-6229	310	11	in	in	ADP
easat-6229	310	12	teaching	teach	VERB
easat-6229	310	13	proof	proof	NOUN
easat-6229	310	14	to	to	ADP
easat-6229	310	15	prospective	prospective	ADJ
easat-6229	310	16	mathematics	mathematic	NOUN
easat-6229	310	17	teachers	teacher	NOUN
easat-6229	310	18	:	:	PUNCT
easat-6229	310	19	academician	academician	NOUN
easat-6229	310	20	views	view	NOUN
easat-6229	310	21	,	,	PUNCT
easat-6229	310	22	"	"	PUNCT
easat-6229	310	23	higher	high	ADJ
easat-6229	310	24	education	education	NOUN
easat-6229	310	25	studies	study	NOUN
easat-6229	310	26	,	,	PUNCT
easat-6229	310	27	vol	vol	NOUN
easat-6229	310	28	.	.	PROPN
easat-6229	310	29	6	6	NUM
easat-6229	310	30	,	,	PUNCT
easat-6229	310	31	no	no	INTJ
easat-6229	310	32	.	.	NOUN
easat-6229	310	33	1	1	NUM
easat-6229	310	34	,	,	PUNCT
easat-6229	310	35	pp	pp	ADJ
easat-6229	310	36	.	.	PUNCT
easat-6229	310	37	145	145	NUM
easat-6229	310	38	-	-	SYM
easat-6229	310	39	158	158	NUM
easat-6229	310	40	,	,	PUNCT
easat-6229	310	41	2016	2016	NUM
easat-6229	310	42	.	.	PUNCT
easat-6229	311	1	https://doi.org/10.5539/hrs.v6n1p145	https://doi.org/10.5539/hrs.v6n1p145	PROPN
easat-6229	312	1	[	[	X
easat-6229	312	2	11	11	NUM
easat-6229	312	3	]	]	X
easat-6229	312	4	v.	v.	ADP
easat-6229	312	5	durand	durand	PROPN
easat-6229	312	6	-	-	PUNCT
easat-6229	312	7	guerrier	guerrier	NOUN
easat-6229	312	8	,	,	PUNCT
easat-6229	312	9	p.	p.	NOUN
easat-6229	312	10	boero	boero	NOUN
easat-6229	312	11	,	,	PUNCT
easat-6229	312	12	n.	n.	NOUN
easat-6229	312	13	douek	douek	PROPN
easat-6229	312	14	,	,	PUNCT
easat-6229	312	15	s.	s.	PROPN
easat-6229	312	16	s.	s.	PROPN
easat-6229	312	17	epp	epp	PROPN
easat-6229	312	18	,	,	PUNCT
easat-6229	312	19	and	and	CCONJ
easat-6229	312	20	d.	d.	PROPN
easat-6229	312	21	tanguay	tanguay	PROPN
easat-6229	312	22	,	,	PUNCT
easat-6229	312	23	"	"	PUNCT
easat-6229	312	24	examining	examine	VERB
easat-6229	312	25	the	the	DET
easat-6229	312	26	role	role	NOUN
easat-6229	312	27	of	of	ADP
easat-6229	312	28	logic	logic	NOUN
easat-6229	312	29	in	in	ADP
easat-6229	312	30	teaching	teaching	NOUN
easat-6229	312	31	proof	proof	NOUN
easat-6229	312	32	,	,	PUNCT
easat-6229	312	33	"	"	PUNCT
easat-6229	312	34	vol	vol	NOUN
easat-6229	312	35	.	.	PROPN
easat-6229	312	36	15	15	NUM
easat-6229	312	37	,	,	PUNCT
easat-6229	312	38	2012	2012	NUM
easat-6229	312	39	.	.	PUNCT
easat-6229	313	1	https://doi.org/10.1007/978-94-007-2129-6_16	https://doi.org/10.1007/978-94-007-2129-6_16	NOUN
easat-6229	313	2	[	[	X
easat-6229	313	3	12	12	NUM
easat-6229	313	4	]	]	X
easat-6229	313	5	d.	d.	PROPN
easat-6229	313	6	dumitraşcu	dumitraşcu	PROPN
easat-6229	313	7	,	,	PUNCT
easat-6229	313	8	"	"	PUNCT
easat-6229	313	9	integration	integration	NOUN
easat-6229	313	10	of	of	ADP
easat-6229	313	11	guided	guide	VERB
easat-6229	313	12	discovery	discovery	NOUN
easat-6229	313	13	in	in	ADP
easat-6229	313	14	the	the	DET
easat-6229	313	15	teaching	teaching	NOUN
easat-6229	313	16	of	of	ADP
easat-6229	313	17	real	real	ADJ
easat-6229	313	18	analysis	analysis	NOUN
easat-6229	313	19	,	,	PUNCT
easat-6229	313	20	"	"	PUNCT
easat-6229	313	21	primus	primus	PROPN
easat-6229	313	22	,	,	PUNCT
easat-6229	313	23	vol	vol	NOUN
easat-6229	313	24	.	.	PROPN
easat-6229	313	25	19	19	NUM
easat-6229	313	26	,	,	PUNCT
easat-6229	313	27	no	no	INTJ
easat-6229	313	28	.	.	NOUN
easat-6229	313	29	4	4	NUM
easat-6229	313	30	,	,	PUNCT
easat-6229	313	31	pp	pp	ADJ
easat-6229	313	32	.	.	PUNCT
easat-6229	314	1	370	370	NUM
easat-6229	314	2	-	-	SYM
easat-6229	314	3	380	380	NUM
easat-6229	314	4	,	,	PUNCT
easat-6229	314	5	2009	2009	NUM
easat-6229	314	6	.	.	PUNCT
easat-6229	315	1	https://doi.org/10.1080/10511970802072368	https://doi.org/10.1080/10511970802072368	X
easat-6229	316	1	[	[	X
easat-6229	316	2	13	13	NUM
easat-6229	316	3	]	]	X
easat-6229	316	4	d.	d.	PROPN
easat-6229	316	5	kariman	kariman	PROPN
easat-6229	316	6	,	,	PUNCT
easat-6229	316	7	y.	y.	PROPN
easat-6229	316	8	harisman	harisman	PROPN
easat-6229	316	9	,	,	PUNCT
easat-6229	316	10	a.	a.	NOUN
easat-6229	316	11	sovia	sovia	NOUN
easat-6229	316	12	,	,	PUNCT
easat-6229	316	13	and	and	CCONJ
easat-6229	316	14	r.	r.	PROPN
easat-6229	316	15	c.	c.	PROPN
easat-6229	316	16	i.	i.	PROPN
easat-6229	316	17	prahmana	prahmana	PROPN
easat-6229	316	18	,	,	PUNCT
easat-6229	316	19	"	"	PUNCT
easat-6229	316	20	effectiveness	effectiveness	NOUN
easat-6229	316	21	of	of	ADP
easat-6229	316	22	guided	guide	VERB
easat-6229	316	23	discovery	discovery	NOUN
easat-6229	316	24	-	-	PUNCT
easat-6229	316	25	based	base	VERB
easat-6229	316	26	module	module	NOUN
easat-6229	316	27	:	:	PUNCT
easat-6229	316	28	a	a	DET
easat-6229	316	29	case	case	NOUN
easat-6229	316	30	study	study	NOUN
easat-6229	316	31	in	in	ADP
easat-6229	316	32	padang	padang	PROPN
easat-6229	316	33	city	city	PROPN
easat-6229	316	34	,	,	PUNCT
easat-6229	316	35	indonesia	indonesia	PROPN
easat-6229	316	36	,	,	PUNCT
easat-6229	316	37	"	"	PUNCT
easat-6229	316	38	journal	journal	NOUN
easat-6229	316	39	on	on	ADP
easat-6229	316	40	mathematics	mathematics	PROPN
easat-6229	316	41	education	education	NOUN
easat-6229	316	42	,	,	PUNCT
easat-6229	316	43	vol	vol	NOUN
easat-6229	316	44	.	.	PROPN
easat-6229	316	45	10	10	NUM
easat-6229	316	46	,	,	PUNCT
easat-6229	316	47	no	no	INTJ
easat-6229	316	48	.	.	NOUN
easat-6229	316	49	2	2	NUM
easat-6229	316	50	,	,	PUNCT
easat-6229	316	51	pp	pp	ADJ
easat-6229	316	52	.	.	PUNCT
easat-6229	317	1	239	239	NUM
easat-6229	317	2	-	-	SYM
easat-6229	317	3	250	250	NUM
easat-6229	317	4	,	,	PUNCT
easat-6229	317	5	2019	2019	NUM
easat-6229	317	6	.	.	PUNCT
easat-6229	318	1	https://doi.org/10.22342/jme.10.2.6610.239-250	https://doi.org/10.22342/jme.10.2.6610.239-250	PROPN
easat-6229	319	1	[	[	X
easat-6229	319	2	14	14	NUM
easat-6229	319	3	]	]	PUNCT
easat-6229	319	4	a.	a.	PROPN
easat-6229	319	5	h.	h.	PROPN
easat-6229	319	6	aagesen	aagesen	PROPN
easat-6229	319	7	et	et	PROPN
easat-6229	319	8	al	al	PROPN
easat-6229	319	9	.	.	PROPN
easat-6229	319	10	,	,	PUNCT
easat-6229	319	11	"	"	PUNCT
easat-6229	319	12	the	the	DET
easat-6229	319	13	benefits	benefit	NOUN
easat-6229	319	14	of	of	ADP
easat-6229	319	15	tying	tie	VERB
easat-6229	319	16	yourself	yourself	PRON
easat-6229	319	17	in	in	ADP
easat-6229	319	18	knots	knot	NOUN
easat-6229	319	19	:	:	PUNCT
easat-6229	319	20	unraveling	unravel	VERB
easat-6229	319	21	the	the	DET
easat-6229	319	22	learning	learn	VERB
easat-6229	319	23	mechanisms	mechanism	NOUN
easat-6229	319	24	of	of	ADP
easat-6229	319	25	guided	guide	VERB
easat-6229	319	26	discovery	discovery	NOUN
easat-6229	319	27	learning	learning	NOUN
easat-6229	319	28	in	in	ADP
easat-6229	319	29	an	an	DET
easat-6229	319	30	open	open	ADJ
easat-6229	319	31	surgical	surgical	ADJ
easat-6229	319	32	skills	skill	NOUN
easat-6229	319	33	course	course	NOUN
easat-6229	319	34	,	,	PUNCT
easat-6229	319	35	"	"	PUNCT
easat-6229	319	36	academic	academic	ADJ
easat-6229	319	37	medicine	medicine	NOUN
easat-6229	319	38	,	,	PUNCT
easat-6229	319	39	vol	vol	NOUN
easat-6229	319	40	.	.	PROPN
easat-6229	319	41	95	95	NUM
easat-6229	319	42	,	,	PUNCT
easat-6229	319	43	no	no	INTJ
easat-6229	319	44	.	.	NOUN
easat-6229	319	45	11s	11s	NUM
easat-6229	319	46	,	,	PUNCT
easat-6229	319	47	pp	pp	ADP
easat-6229	319	48	.	.	PUNCT
easat-6229	319	49	s37	s37	NOUN
easat-6229	319	50	-	-	PUNCT
easat-6229	319	51	s43	s43	NOUN
easat-6229	319	52	,	,	PUNCT
easat-6229	319	53	2020	2020	NUM
easat-6229	319	54	.	.	PUNCT
easat-6229	320	1	https://doi.org/10.1097/acm.0000000000003646	https://doi.org/10.1097/acm.0000000000003646	NOUN
easat-6229	321	1	[	[	X
easat-6229	321	2	15	15	NUM
easat-6229	321	3	]	]	PUNCT
easat-6229	321	4	k.	k.	PROPN
easat-6229	321	5	kniha	kniha	VERB
easat-6229	321	6	et	et	PROPN
easat-6229	321	7	al	al	PROPN
easat-6229	321	8	.	.	PROPN
easat-6229	321	9	,	,	PUNCT
easat-6229	321	10	"	"	PUNCT
easat-6229	321	11	guided	guide	VERB
easat-6229	321	12	discovery	discovery	NOUN
easat-6229	321	13	learning	learning	NOUN
easat-6229	321	14	:	:	PUNCT
easat-6229	321	15	a	a	DET
easat-6229	321	16	follow‐up	follow‐up	ADJ
easat-6229	321	17	study	study	NOUN
easat-6229	321	18	of	of	ADP
easat-6229	321	19	try‐it‐yourself	try‐it‐yourself	PRON
easat-6229	321	20	surgery	surgery	NOUN
easat-6229	321	21	and	and	CCONJ
easat-6229	321	22	subsequent	subsequent	ADJ
easat-6229	321	23	video‐assisted	video‐assisted	ADJ
easat-6229	321	24	teaching	teaching	NOUN
easat-6229	321	25	for	for	ADP
easat-6229	321	26	oral	oral	ADJ
easat-6229	321	27	surgical	surgical	ADJ
easat-6229	321	28	skills	skill	NOUN
easat-6229	321	29	training	training	NOUN
easat-6229	321	30	,	,	PUNCT
easat-6229	321	31	"	"	PUNCT
easat-6229	321	32	european	european	ADJ
easat-6229	321	33	journal	journal	NOUN
easat-6229	321	34	of	of	ADP
easat-6229	321	35	dental	dental	ADJ
easat-6229	321	36	education	education	NOUN
easat-6229	321	37	,	,	PUNCT
easat-6229	321	38	vol	vol	NOUN
easat-6229	321	39	.	.	PROPN
easat-6229	321	40	27	27	NUM
easat-6229	321	41	,	,	PUNCT
easat-6229	321	42	no	no	INTJ
easat-6229	321	43	.	.	NOUN
easat-6229	321	44	1	1	NUM
easat-6229	321	45	,	,	PUNCT
easat-6229	321	46	pp	pp	ADJ
easat-6229	321	47	.	.	PUNCT
easat-6229	322	1	29	29	NUM
easat-6229	322	2	-	-	SYM
easat-6229	322	3	35	35	NUM
easat-6229	322	4	,	,	PUNCT
easat-6229	322	5	2023	2023	NUM
easat-6229	322	6	.	.	PUNCT
easat-6229	323	1	https://doi.org/10.1111/eje.12772	https://doi.org/10.1111/eje.12772	NOUN
easat-6229	323	2	[	[	X
easat-6229	323	3	16	16	NUM
easat-6229	323	4	]	]	X
easat-6229	323	5	n.	n.	PROPN
easat-6229	323	6	nurhayani	nurhayani	PROPN
easat-6229	323	7	,	,	PUNCT
easat-6229	323	8	r.	r.	PROPN
easat-6229	323	9	rosnawati	rosnawati	PROPN
easat-6229	323	10	,	,	PUNCT
easat-6229	323	11	and	and	CCONJ
easat-6229	323	12	t.	t.	PROPN
easat-6229	323	13	amimah	amimah	PROPN
easat-6229	323	14	,	,	PUNCT
easat-6229	323	15	"	"	PUNCT
easat-6229	323	16	optimization	optimization	NOUN
easat-6229	323	17	of	of	ADP
easat-6229	323	18	guided	guide	VERB
easat-6229	323	19	discovery	discovery	NOUN
easat-6229	323	20	learning	learning	NOUN
easat-6229	323	21	models	model	NOUN
easat-6229	323	22	to	to	PART
easat-6229	323	23	increase	increase	VERB
easat-6229	323	24	students	student	NOUN
easat-6229	323	25	’	’	PART
easat-6229	323	26	interest	interest	NOUN
easat-6229	323	27	in	in	ADP
easat-6229	323	28	mathematics	mathematic	NOUN
easat-6229	323	29	,	,	PUNCT
easat-6229	323	30	"	"	PUNCT
easat-6229	323	31	infin	infin	NOUN
easat-6229	323	32	.	.	PUNCT
easat-6229	324	1	j	j	PROPN
easat-6229	324	2	,	,	PUNCT
easat-6229	324	3	vol	vol	NOUN
easat-6229	324	4	.	.	PROPN
easat-6229	324	5	9	9	NUM
easat-6229	324	6	,	,	PUNCT
easat-6229	324	7	no	no	INTJ
easat-6229	324	8	.	.	NOUN
easat-6229	324	9	1	1	NUM
easat-6229	324	10	,	,	PUNCT
easat-6229	324	11	p.	p.	NOUN
easat-6229	324	12	69	69	NUM
easat-6229	324	13	,	,	PUNCT
easat-6229	324	14	2020	2020	NUM
easat-6229	324	15	.	.	PUNCT
easat-6229	325	1	https://doi.org/10.22460/infinity.v9i1.p69-80	https://doi.org/10.22460/infinity.v9i1.p69-80	PRON
easat-6229	326	1	[	[	X
easat-6229	326	2	17	17	NUM
easat-6229	326	3	]	]	PUNCT
easat-6229	326	4	a.	a.	NOUN
easat-6229	326	5	kuzniak	kuzniak	PROPN
easat-6229	326	6	and	and	CCONJ
easat-6229	326	7	a.	a.	NOUN
easat-6229	326	8	nechache	nechache	PROPN
easat-6229	326	9	,	,	PUNCT
easat-6229	326	10	"	"	PUNCT
easat-6229	326	11	on	on	ADP
easat-6229	326	12	forms	form	NOUN
easat-6229	326	13	of	of	ADP
easat-6229	326	14	geometric	geometric	ADJ
easat-6229	326	15	work	work	NOUN
easat-6229	326	16	:	:	PUNCT
easat-6229	326	17	a	a	DET
easat-6229	326	18	study	study	NOUN
easat-6229	326	19	with	with	ADP
easat-6229	326	20	pre	pre	ADJ
easat-6229	326	21	-	-	ADJ
easat-6229	326	22	service	service	ADJ
easat-6229	326	23	teachers	teacher	NOUN
easat-6229	326	24	based	base	VERB
easat-6229	326	25	on	on	ADP
easat-6229	326	26	the	the	DET
easat-6229	326	27	theory	theory	NOUN
easat-6229	326	28	of	of	ADP
easat-6229	326	29	mathematical	mathematical	ADJ
easat-6229	326	30	working	working	NOUN
easat-6229	326	31	spaces	space	NOUN
easat-6229	326	32	,	,	PUNCT
easat-6229	326	33	"	"	PUNCT
easat-6229	326	34	educational	educational	ADJ
easat-6229	326	35	studies	study	NOUN
easat-6229	326	36	in	in	ADP
easat-6229	326	37	mathematics	mathematic	NOUN
easat-6229	326	38	,	,	PUNCT
easat-6229	326	39	vol	vol	NOUN
easat-6229	326	40	.	.	PROPN
easat-6229	326	41	106	106	NUM
easat-6229	326	42	,	,	PUNCT
easat-6229	326	43	no	no	INTJ
easat-6229	326	44	.	.	NOUN
easat-6229	326	45	2	2	NUM
easat-6229	326	46	,	,	PUNCT
easat-6229	326	47	pp	pp	ADJ
easat-6229	326	48	.	.	PUNCT
easat-6229	327	1	271	271	NUM
easat-6229	327	2	-	-	SYM
easat-6229	327	3	289	289	NUM
easat-6229	327	4	,	,	PUNCT
easat-6229	327	5	2021	2021	NUM
easat-6229	327	6	.	.	PUNCT
easat-6229	327	7	https://doi.org/10.1007/s10649-020-10011-2	https://doi.org/10.1007/s10649-020-10011-2	NUM
easat-6229	328	1	[	[	X
easat-6229	328	2	18	18	NUM
easat-6229	328	3	]	]	X
easat-6229	328	4	i.	i.	PROPN
easat-6229	328	5	m.	m.	PROPN
easat-6229	328	6	gómez	gómez	PROPN
easat-6229	328	7	-	-	PUNCT
easat-6229	328	8	chacón	chacón	PROPN
easat-6229	328	9	and	and	CCONJ
easat-6229	328	10	a.	a.	PROPN
easat-6229	328	11	kuzniak	kuzniak	PROPN
easat-6229	328	12	,	,	PUNCT
easat-6229	328	13	"	"	PUNCT
easat-6229	328	14	spaces	space	NOUN
easat-6229	328	15	for	for	ADP
easat-6229	328	16	geometric	geometric	ADJ
easat-6229	328	17	work	work	NOUN
easat-6229	328	18	:	:	PUNCT
easat-6229	328	19	figural	figural	NOUN
easat-6229	328	20	,	,	PUNCT
easat-6229	328	21	instrumental	instrumental	ADJ
easat-6229	328	22	,	,	PUNCT
easat-6229	328	23	and	and	CCONJ
easat-6229	328	24	discursive	discursive	ADJ
easat-6229	328	25	geneses	genesis	NOUN
easat-6229	328	26	of	of	ADP
easat-6229	328	27	reasoning	reasoning	NOUN
easat-6229	328	28	in	in	ADP
easat-6229	328	29	a	a	DET
easat-6229	328	30	technological	technological	ADJ
easat-6229	328	31	environment	environment	NOUN
easat-6229	328	32	,	,	PUNCT
easat-6229	328	33	"	"	PUNCT
easat-6229	328	34	international	international	ADJ
easat-6229	328	35	journal	journal	NOUN
easat-6229	328	36	of	of	ADP
easat-6229	328	37	science	science	NOUN
easat-6229	328	38	and	and	CCONJ
easat-6229	328	39	mathematics	mathematic	NOUN
easat-6229	328	40	education	education	NOUN
easat-6229	328	41	,	,	PUNCT
easat-6229	328	42	vol	vol	NOUN
easat-6229	328	43	.	.	PROPN
easat-6229	328	44	13	13	NUM
easat-6229	328	45	,	,	PUNCT
easat-6229	328	46	pp	pp	ADJ
easat-6229	328	47	.	.	PUNCT
easat-6229	328	48	201226	201226	NUM
easat-6229	328	49	,	,	PUNCT
easat-6229	328	50	2015	2015	NUM
easat-6229	328	51	.	.	PUNCT
easat-6229	329	1	https://doi.org/10.1007/s10763-013-9462-4	https://doi.org/10.1007/s10763-013-9462-4	NUM
easat-6229	330	1	[	[	X
easat-6229	330	2	19	19	NUM
easat-6229	330	3	]	]	X
easat-6229	330	4	e.	e.	PROPN
easat-6229	330	5	m.	m.	PROPN
easat-6229	330	6	delgadillo	delgadillo	PROPN
easat-6229	330	7	and	and	CCONJ
easat-6229	330	8	l.	l.	PROPN
easat-6229	330	9	vivier	vivier	PROPN
easat-6229	330	10	,	,	PUNCT
easat-6229	330	11	"	"	PUNCT
easat-6229	330	12	mathematical	mathematical	ADJ
easat-6229	330	13	working	working	NOUN
easat-6229	330	14	space	space	NOUN
easat-6229	330	15	and	and	CCONJ
easat-6229	330	16	paradigms	paradigm	VERB
easat-6229	330	17	as	as	ADP
easat-6229	330	18	an	an	DET
easat-6229	330	19	analysis	analysis	NOUN
easat-6229	330	20	tool	tool	NOUN
easat-6229	330	21	for	for	ADP
easat-6229	330	22	the	the	DET
easat-6229	330	23	teaching	teaching	NOUN
easat-6229	330	24	and	and	CCONJ
easat-6229	330	25	learning	learning	NOUN
easat-6229	330	26	of	of	ADP
easat-6229	330	27	analysis	analysis	NOUN
easat-6229	330	28	,	,	PUNCT
easat-6229	330	29	"	"	PUNCT
easat-6229	330	30	zdm	zdm	NOUN
easat-6229	330	31	,	,	PUNCT
easat-6229	330	32	vol	vol	NOUN
easat-6229	330	33	.	.	PROPN
easat-6229	330	34	48	48	NUM
easat-6229	330	35	,	,	PUNCT
easat-6229	330	36	pp	pp	ADJ
easat-6229	330	37	.	.	PUNCT
easat-6229	331	1	739	739	NUM
easat-6229	331	2	-	-	SYM
easat-6229	331	3	754	754	NUM
easat-6229	331	4	,	,	PUNCT
easat-6229	331	5	2016	2016	NUM
easat-6229	331	6	.	.	PUNCT
easat-6229	332	1	https://doi.org/10.1007/s11858-016-0777-9	https://doi.org/10.1007/s11858-016-0777-9	X
easat-6229	333	1	[	[	X
easat-6229	333	2	20	20	NUM
easat-6229	333	3	]	]	PUNCT
easat-6229	333	4	a.	a.	NOUN
easat-6229	333	5	kuzniak	kuzniak	PROPN
easat-6229	333	6	,	,	PUNCT
easat-6229	333	7	d.	d.	PROPN
easat-6229	333	8	tanguay	tanguay	PROPN
easat-6229	333	9	,	,	PUNCT
easat-6229	333	10	and	and	CCONJ
easat-6229	333	11	i.	i.	PROPN
easat-6229	333	12	elia	elia	PROPN
easat-6229	333	13	,	,	PUNCT
easat-6229	333	14	"	"	PUNCT
easat-6229	333	15	mathematical	mathematical	ADJ
easat-6229	333	16	working	working	NOUN
easat-6229	333	17	spaces	space	NOUN
easat-6229	333	18	in	in	ADP
easat-6229	333	19	schooling	schooling	NOUN
easat-6229	333	20	:	:	PUNCT
easat-6229	333	21	an	an	DET
easat-6229	333	22	introduction	introduction	NOUN
easat-6229	333	23	,	,	PUNCT
easat-6229	333	24	"	"	PUNCT
easat-6229	333	25	zdm	zdm	NOUN
easat-6229	333	26	,	,	PUNCT
easat-6229	333	27	vol	vol	NOUN
easat-6229	333	28	.	.	PROPN
easat-6229	333	29	48	48	NUM
easat-6229	333	30	,	,	PUNCT
easat-6229	333	31	pp	pp	ADJ
easat-6229	333	32	.	.	PUNCT
easat-6229	334	1	721	721	NUM
easat-6229	334	2	-	-	SYM
easat-6229	334	3	737	737	NUM
easat-6229	334	4	,	,	PUNCT
easat-6229	334	5	2016	2016	NUM
easat-6229	334	6	.	.	PUNCT
easat-6229	335	1	[	[	X
easat-6229	335	2	21	21	NUM
easat-6229	335	3	]	]	X
easat-6229	335	4	m.	m.	NOUN
easat-6229	335	5	baki	baki	PROPN
easat-6229	335	6	,	,	PUNCT
easat-6229	335	7	"	"	PUNCT
easat-6229	335	8	the	the	DET
easat-6229	335	9	development	development	NOUN
easat-6229	335	10	of	of	ADP
easat-6229	335	11	mathematical	mathematical	ADJ
easat-6229	335	12	knowledge	knowledge	NOUN
easat-6229	335	13	for	for	ADP
easat-6229	335	14	teaching	teaching	NOUN
easat-6229	335	15	of	of	ADP
easat-6229	335	16	mathematics	mathematics	NOUN
easat-6229	335	17	teachers	teacher	NOUN
easat-6229	335	18	in	in	ADP
easat-6229	335	19	lesson	lesson	NOUN
easat-6229	335	20	analysis	analysis	NOUN
easat-6229	335	21	process	process	NOUN
easat-6229	335	22	,	,	PUNCT
easat-6229	335	23	"	"	PUNCT
easat-6229	335	24	european	european	ADJ
easat-6229	335	25	journal	journal	NOUN
easat-6229	335	26	of	of	ADP
easat-6229	335	27	educational	educational	ADJ
easat-6229	335	28	research	research	NOUN
easat-6229	335	29	,	,	PUNCT
easat-6229	335	30	vol	vol	NOUN
easat-6229	335	31	.	.	PROPN
easat-6229	335	32	5	5	NUM
easat-6229	335	33	,	,	PUNCT
easat-6229	335	34	no	no	INTJ
easat-6229	335	35	.	.	NOUN
easat-6229	335	36	4	4	NUM
easat-6229	335	37	,	,	PUNCT
easat-6229	335	38	pp	pp	ADJ
easat-6229	335	39	.	.	PUNCT
easat-6229	336	1	165	165	NUM
easat-6229	336	2	-	-	SYM
easat-6229	336	3	171	171	NUM
easat-6229	336	4	,	,	PUNCT
easat-6229	336	5	2016	2016	NUM
easat-6229	336	6	.	.	PUNCT
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easat-6229	338	17	https://doi.org/10.1007/s10763-013-9462-4	https://doi.org/10.1007/s10763-013-9462-4	NUM
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easat-6229	338	19	https://doi.org/10.12973/eu-jer.5.4.165	https://doi.org/10.12973/eu-jer.5.4.165	PROPN
easat-6229	338	20	https://doi.org/10.12973/eu-jer.5.4.165	https://doi.org/10.12973/eu-jer.5.4.165	PROPN
easat-6229	338	21	1251	1251	NUM
easat-6229	338	22	edelweiss	edelweiss	PROPN
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easat-6229	338	25	and	and	CCONJ
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easat-6229	338	27	issn	issn	PROPN
easat-6229	338	28	:	:	PUNCT
easat-6229	338	29	2576	2576	NUM
easat-6229	338	30	-	-	SYM
easat-6229	338	31	8484	8484	NUM
easat-6229	338	32	vol	vol	NOUN
easat-6229	338	33	.	.	PROPN
easat-6229	339	1	9	9	NUM
easat-6229	339	2	,	,	PUNCT
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easat-6229	339	4	.	.	NOUN
easat-6229	339	5	4	4	NUM
easat-6229	339	6	:	:	SYM
easat-6229	339	7	1240	1240	NUM
easat-6229	339	8	-	-	SYM
easat-6229	339	9	1251	1251	NUM
easat-6229	339	10	,	,	PUNCT
easat-6229	339	11	2025	2025	NUM
easat-6229	339	12	doi	doi	NOUN
easat-6229	339	13	:	:	PUNCT
easat-6229	339	14	10.55214/25768484.v9i4.6229	10.55214/25768484.v9i4.6229	NUM
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easat-6229	339	20	;	;	PUNCT
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easat-6229	339	22	learning	learning	NOUN
easat-6229	339	23	gate	gate	NOUN
easat-6229	340	1	[	[	X
easat-6229	340	2	22	22	NUM
easat-6229	340	3	]	]	PUNCT
easat-6229	340	4	w.	w.	PROPN
easat-6229	340	5	winarso	winarso	PROPN
easat-6229	340	6	and	and	CCONJ
easat-6229	340	7	a.	a.	PROPN
easat-6229	340	8	a.	a.	NOUN
easat-6229	340	9	haqq	haqq	NOUN
easat-6229	340	10	,	,	PUNCT
easat-6229	340	11	"	"	PUNCT
easat-6229	340	12	where	where	SCONJ
easat-6229	340	13	exactly	exactly	ADV
easat-6229	340	14	for	for	ADP
easat-6229	340	15	enhance	enhance	NOUN
easat-6229	340	16	critical	critical	ADJ
easat-6229	340	17	and	and	CCONJ
easat-6229	340	18	creative	creative	ADJ
easat-6229	340	19	thinking	thinking	NOUN
easat-6229	340	20	:	:	PUNCT
easat-6229	340	21	the	the	DET
easat-6229	340	22	use	use	NOUN
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easat-6229	340	24	problem	problem	NOUN
easat-6229	340	25	posing	pose	VERB
easat-6229	340	26	or	or	CCONJ
easat-6229	340	27	contextual	contextual	ADJ
easat-6229	340	28	learning	learning	NOUN
easat-6229	340	29	,	,	PUNCT
easat-6229	340	30	"	"	PUNCT
easat-6229	340	31	european	european	ADJ
easat-6229	340	32	journal	journal	NOUN
easat-6229	340	33	of	of	ADP
easat-6229	340	34	educational	educational	ADJ
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easat-6229	340	37	vol	vol	NOUN
easat-6229	340	38	.	.	PROPN
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easat-6229	340	40	,	,	PUNCT
easat-6229	340	41	no	no	INTJ
easat-6229	340	42	.	.	NOUN
easat-6229	340	43	2	2	NUM
easat-6229	340	44	,	,	PUNCT
easat-6229	340	45	pp	pp	ADJ
easat-6229	340	46	.	.	PUNCT
easat-6229	340	47	877	877	NUM
easat-6229	340	48	-	-	SYM
easat-6229	340	49	887	887	NUM
easat-6229	340	50	,	,	PUNCT
easat-6229	340	51	2020	2020	NUM
easat-6229	340	52	.	.	PUNCT
easat-6229	341	1	https://doi.org/10.12973/eu-jer.9.2.877	https://doi.org/10.12973/eu-jer.9.2.877	VERB
easat-6229	341	2	[	[	X
easat-6229	341	3	23	23	NUM
easat-6229	341	4	]	]	X
easat-6229	341	5	y.	y.	NOUN
easat-6229	341	6	yerimadesi	yerimadesi	PROPN
easat-6229	341	7	et	et	PROPN
easat-6229	341	8	al	al	PROPN
easat-6229	341	9	.	.	PROPN
easat-6229	341	10	,	,	PUNCT
easat-6229	341	11	"	"	PUNCT
easat-6229	341	12	guided	guide	VERB
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easat-6229	341	14	learning	learning	NOUN
easat-6229	341	15	-	-	PUNCT
easat-6229	341	16	based	base	VERB
easat-6229	341	17	chemistry	chemistry	NOUN
easat-6229	341	18	e	e	NOUN
easat-6229	341	19	-	-	NOUN
easat-6229	341	20	module	module	NOUN
easat-6229	341	21	and	and	CCONJ
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easat-6229	341	28	-	-	PUNCT
easat-6229	341	29	order	order	NOUN
easat-6229	341	30	thinking	thinking	NOUN
easat-6229	341	31	skills	skill	NOUN
easat-6229	341	32	,	,	PUNCT
easat-6229	341	33	"	"	PUNCT
easat-6229	341	34	jurnal	jurnal	ADJ
easat-6229	341	35	pendidikan	pendidikan	PROPN
easat-6229	341	36	ipa	ipa	PROPN
easat-6229	341	37	indonesia	indonesia	PROPN
easat-6229	341	38	,	,	PUNCT
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easat-6229	341	40	.	.	PROPN
easat-6229	341	41	12	12	NUM
easat-6229	341	42	,	,	PUNCT
easat-6229	341	43	no	no	INTJ
easat-6229	341	44	.	.	NOUN
easat-6229	341	45	1	1	NUM
easat-6229	341	46	,	,	PUNCT
easat-6229	341	47	pp	pp	ADJ
easat-6229	341	48	.	.	PUNCT
easat-6229	342	1	168	168	NUM
easat-6229	342	2	-	-	SYM
easat-6229	342	3	177	177	NUM
easat-6229	342	4	,	,	PUNCT
easat-6229	342	5	2023	2023	NUM
easat-6229	342	6	.	.	PUNCT
easat-6229	343	1	https://doi.org/10.15294/jpii.v12i1.42130	https://doi.org/10.15294/jpii.v12i1.42130	X
easat-6229	344	1	[	[	X
easat-6229	344	2	24	24	NUM
easat-6229	344	3	]	]	PUNCT
easat-6229	344	4	r.	r.	PROPN
easat-6229	344	5	w.	w.	PROPN
easat-6229	344	6	y.	y.	PROPN
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easat-6229	344	10	.	.	PROPN
easat-6229	344	11	,	,	PUNCT
easat-6229	344	12	"	"	PUNCT
easat-6229	344	13	systematic	systematic	ADJ
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easat-6229	344	15	review	review	NOUN
easat-6229	344	16	on	on	ADP
easat-6229	344	17	the	the	DET
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easat-6229	344	20	-	-	PUNCT
easat-6229	344	21	year	year	NOUN
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easat-6229	344	30	"	"	PUNCT
easat-6229	344	31	infinity	infinity	NOUN
easat-6229	344	32	journal	journal	NOUN
easat-6229	344	33	,	,	PUNCT
easat-6229	344	34	vol	vol	NOUN
easat-6229	344	35	.	.	PROPN
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easat-6229	344	37	,	,	PUNCT
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easat-6229	344	40	2	2	NUM
easat-6229	344	41	,	,	PUNCT
easat-6229	344	42	pp	pp	ADJ
easat-6229	344	43	.	.	PUNCT
easat-6229	345	1	243	243	NUM
easat-6229	345	2	-	-	SYM
easat-6229	345	3	260	260	NUM
easat-6229	345	4	,	,	PUNCT
easat-6229	345	5	2023	2023	NUM
easat-6229	345	6	.	.	PUNCT
easat-6229	346	1	https://doi.org/10.22460/infinity.v12i2.p243260	https://doi.org/10.22460/infinity.v12i2.p243260	NOUN
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easat-6229	346	4	]	]	PUNCT
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easat-6229	346	8	and	and	CCONJ
easat-6229	346	9	a.	a.	PROPN
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easat-6229	346	11	,	,	PUNCT
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easat-6229	346	13	the	the	DET
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easat-6229	346	18	model	model	NOUN
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easat-6229	346	20	mathematical	mathematical	ADJ
easat-6229	346	21	critical	critical	ADJ
easat-6229	346	22	thinking	thinking	NOUN
easat-6229	346	23	ability	ability	NOUN
easat-6229	346	24	,	,	PUNCT
easat-6229	346	25	"	"	PUNCT
easat-6229	346	26	international	international	ADJ
easat-6229	346	27	journal	journal	NOUN
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easat-6229	346	30	,	,	PUNCT
easat-6229	346	31	vol	vol	NOUN
easat-6229	346	32	.	.	PROPN
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easat-6229	346	37	1	1	NUM
easat-6229	346	38	,	,	PUNCT
easat-6229	346	39	pp	pp	ADJ
easat-6229	346	40	.	.	PUNCT
easat-6229	347	1	727	727	NUM
easat-6229	347	2	-	-	SYM
easat-6229	347	3	742	742	NUM
easat-6229	347	4	,	,	PUNCT
easat-6229	347	5	2021	2021	NUM
easat-6229	347	6	.	.	PUNCT
easat-6229	348	1	[	[	X
easat-6229	348	2	26	26	NUM
easat-6229	348	3	]	]	X
easat-6229	348	4	i.	i.	PROPN
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easat-6229	348	12	,	,	PUNCT
easat-6229	348	13	a.	a.	NOUN
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easat-6229	348	16	and	and	CCONJ
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easat-6229	348	18	e.	e.	PROPN
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easat-6229	348	21	,	,	PUNCT
easat-6229	348	22	"	"	PUNCT
easat-6229	348	23	students	student	NOUN
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easat-6229	348	31	focusing	focus	VERB
easat-6229	348	32	on	on	ADP
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easat-6229	348	34	,	,	PUNCT
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easat-6229	348	36	and	and	CCONJ
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easat-6229	348	38	,	,	PUNCT
easat-6229	348	39	"	"	PUNCT
easat-6229	348	40	zdm	zdm	NOUN
easat-6229	348	41	,	,	PUNCT
easat-6229	348	42	vol	vol	NOUN
easat-6229	348	43	.	.	PROPN
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easat-6229	348	45	,	,	PUNCT
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easat-6229	348	48	6	6	NUM
easat-6229	348	49	,	,	PUNCT
easat-6229	348	50	pp	pp	ADJ
easat-6229	348	51	.	.	PUNCT
easat-6229	348	52	895	895	NUM
easat-6229	348	53	-	-	NUM
easat-6229	348	54	907	907	NUM
easat-6229	348	55	,	,	PUNCT
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easat-6229	348	57	.	.	PUNCT
easat-6229	349	1	[	[	X
easat-6229	349	2	27	27	NUM
easat-6229	349	3	]	]	X
easat-6229	349	4	r.	r.	PROPN
easat-6229	349	5	g.	g.	PROPN
easat-6229	349	6	bartle	bartle	PROPN
easat-6229	349	7	and	and	CCONJ
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easat-6229	349	9	r.	r.	PROPN
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easat-6229	349	14	real	real	ADJ
easat-6229	349	15	analysis	analysis	NOUN
easat-6229	349	16	.	.	PUNCT
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easat-6229	350	2	wiley	wiley	PROPN
easat-6229	350	3	&	&	CCONJ
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easat-6229	350	5	,	,	PUNCT
easat-6229	350	6	inc	inc	PROPN
easat-6229	350	7	.	.	PROPN
easat-6229	350	8	,	,	PUNCT
easat-6229	350	9	2000	2000	NUM
easat-6229	350	10	.	.	PUNCT
easat-6229	351	1	[	[	X
easat-6229	351	2	28	28	NUM
easat-6229	351	3	]	]	X
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easat-6229	351	6	and	and	CCONJ
easat-6229	351	7	b.	b.	PROPN
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easat-6229	351	9	,	,	PUNCT
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easat-6229	351	13	histograms	histogram	NOUN
easat-6229	351	14	be	be	AUX
easat-6229	351	15	useful	useful	ADJ
easat-6229	351	16	for	for	ADP
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easat-6229	351	18	continuous	continuous	ADJ
easat-6229	351	19	probability	probability	NOUN
easat-6229	351	20	distributions	distribution	NOUN
easat-6229	351	21	?	?	PUNCT
easat-6229	351	22	,	,	PUNCT
easat-6229	351	23	"	"	PUNCT
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easat-6229	351	25	,	,	PUNCT
easat-6229	351	26	vol	vol	NOUN
easat-6229	351	27	.	.	PROPN
easat-6229	352	1	48	48	NUM
easat-6229	352	2	,	,	PUNCT
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easat-6229	352	6	,	,	PUNCT
easat-6229	352	7	pp	pp	ADJ
easat-6229	352	8	.	.	PUNCT
easat-6229	353	1	757	757	PROPN
easat-6229	353	2	-	-	SYM
easat-6229	353	3	773	773	NUM
easat-6229	353	4	,	,	PUNCT
easat-6229	353	5	2016	2016	NUM
easat-6229	353	6	.	.	PUNCT
easat-6229	354	1	[	[	X
easat-6229	354	2	29	29	NUM
easat-6229	354	3	]	]	PUNCT
easat-6229	354	4	t.	t.	PROPN
easat-6229	354	5	k.	k.	PROPN
easat-6229	354	6	minh	minh	PROPN
easat-6229	354	7	and	and	CCONJ
easat-6229	354	8	j.-b	j.-b	PROPN
easat-6229	354	9	.	.	PUNCT
easat-6229	355	1	lagrange	lagrange	PROPN
easat-6229	355	2	,	,	PUNCT
easat-6229	355	3	"	"	PUNCT
easat-6229	355	4	connected	connected	ADJ
easat-6229	355	5	functional	functional	ADJ
easat-6229	355	6	working	working	NOUN
easat-6229	355	7	spaces	space	NOUN
easat-6229	355	8	:	:	PUNCT
easat-6229	355	9	a	a	DET
easat-6229	355	10	framework	framework	NOUN
easat-6229	355	11	for	for	ADP
easat-6229	355	12	the	the	DET
easat-6229	355	13	teaching	teaching	NOUN
easat-6229	355	14	and	and	CCONJ
easat-6229	355	15	learning	learning	NOUN
easat-6229	355	16	of	of	ADP
easat-6229	355	17	functions	function	NOUN
easat-6229	355	18	at	at	ADP
easat-6229	355	19	upper	upper	ADJ
easat-6229	355	20	secondary	secondary	ADJ
easat-6229	355	21	level	level	NOUN
easat-6229	355	22	,	,	PUNCT
easat-6229	355	23	"	"	PUNCT
easat-6229	355	24	zdm	zdm	NOUN
easat-6229	355	25	,	,	PUNCT
easat-6229	355	26	vol	vol	NOUN
easat-6229	355	27	.	.	PROPN
easat-6229	355	28	48	48	NUM
easat-6229	355	29	,	,	PUNCT
easat-6229	355	30	no	no	INTJ
easat-6229	355	31	.	.	NOUN
easat-6229	355	32	6	6	NUM
easat-6229	355	33	,	,	PUNCT
easat-6229	355	34	pp	pp	ADJ
easat-6229	355	35	.	.	PUNCT
easat-6229	356	1	793	793	NUM
easat-6229	356	2	-	-	SYM
easat-6229	356	3	807	807	NUM
easat-6229	356	4	,	,	PUNCT
easat-6229	356	5	2016	2016	NUM
easat-6229	356	6	.	.	PUNCT
easat-6229	357	1	https://doi.org/10.1007/s11858-0160774-z	https://doi.org/10.1007/s11858-0160774-z	PROPN
easat-6229	357	2	[	[	PUNCT
easat-6229	357	3	30	30	NUM
easat-6229	357	4	]	]	X
easat-6229	357	5	a.	a.	NOUN
easat-6229	357	6	bacelo	bacelo	NOUN
easat-6229	357	7	and	and	CCONJ
easat-6229	357	8	i.	i.	PROPN
easat-6229	357	9	m.	m.	PROPN
easat-6229	357	10	gomez	gomez	PROPN
easat-6229	357	11	-	-	PUNCT
easat-6229	357	12	chacon	chacon	PROPN
easat-6229	357	13	,	,	PUNCT
easat-6229	357	14	"	"	PUNCT
easat-6229	357	15	characterising	characterise	VERB
easat-6229	357	16	algorithmic	algorithmic	ADJ
easat-6229	357	17	thinking	thinking	NOUN
easat-6229	357	18	:	:	PUNCT
easat-6229	357	19	a	a	DET
easat-6229	357	20	university	university	NOUN
easat-6229	357	21	study	study	NOUN
easat-6229	357	22	of	of	ADP
easat-6229	357	23	unplugged	unplugged	PROPN
easat-6229	357	24	activities	activity	NOUN
easat-6229	357	25	✰	✰	VERB
easat-6229	357	26	,	,	PUNCT
easat-6229	357	27	"	"	PUNCT
easat-6229	357	28	thinking	thinking	NOUN
easat-6229	357	29	skills	skill	NOUN
easat-6229	357	30	and	and	CCONJ
easat-6229	357	31	creativity	creativity	NOUN
easat-6229	357	32	,	,	PUNCT
easat-6229	357	33	vol	vol	NOUN
easat-6229	357	34	.	.	PROPN
easat-6229	358	1	48	48	NUM
easat-6229	358	2	,	,	PUNCT
easat-6229	358	3	p.	p.	NOUN
easat-6229	358	4	101284	101284	NUM
easat-6229	358	5	,	,	PUNCT
easat-6229	358	6	2023	2023	NUM
easat-6229	358	7	.	.	PUNCT
easat-6229	359	1	https://doi.org/10.1016/j.tsc.2023.101284	https://doi.org/10.1016/j.tsc.2023.101284	PUNCT
easat-6229	360	1	[	[	X
easat-6229	360	2	31	31	NUM
easat-6229	360	3	]	]	PUNCT
easat-6229	360	4	t.	t.	PROPN
easat-6229	360	5	bauer	bauer	PROPN
easat-6229	360	6	,	,	PUNCT
easat-6229	360	7	r.	r.	PROPN
easat-6229	360	8	biehler	biehler	NOUN
easat-6229	360	9	,	,	PUNCT
easat-6229	360	10	and	and	CCONJ
easat-6229	360	11	e.	e.	PROPN
easat-6229	360	12	lankeit	lankeit	PROPN
easat-6229	360	13	,	,	PUNCT
easat-6229	360	14	"	"	PUNCT
easat-6229	360	15	conceptests	conceptest	NOUN
easat-6229	360	16	in	in	ADP
easat-6229	360	17	undergraduate	undergraduate	ADJ
easat-6229	360	18	real	real	ADJ
easat-6229	360	19	analysis	analysis	NOUN
easat-6229	360	20	:	:	PUNCT
easat-6229	360	21	comparing	compare	VERB
easat-6229	360	22	peer	peer	NOUN
easat-6229	360	23	discussion	discussion	NOUN
easat-6229	360	24	and	and	CCONJ
easat-6229	360	25	instructional	instructional	ADJ
easat-6229	360	26	explanation	explanation	NOUN
easat-6229	360	27	settings	setting	NOUN
easat-6229	360	28	,	,	PUNCT
easat-6229	360	29	"	"	PUNCT
easat-6229	360	30	international	international	ADJ
easat-6229	360	31	journal	journal	NOUN
easat-6229	360	32	of	of	ADP
easat-6229	360	33	research	research	NOUN
easat-6229	360	34	in	in	ADP
easat-6229	360	35	undergraduate	undergraduate	ADJ
easat-6229	360	36	mathematics	mathematic	NOUN
easat-6229	360	37	education	education	NOUN
easat-6229	360	38	,	,	PUNCT
easat-6229	360	39	vol	vol	NOUN
easat-6229	360	40	.	.	PROPN
easat-6229	360	41	9	9	NUM
easat-6229	360	42	,	,	PUNCT
easat-6229	360	43	no	no	INTJ
easat-6229	360	44	.	.	NOUN
easat-6229	360	45	2	2	NUM
easat-6229	360	46	,	,	PUNCT
easat-6229	360	47	pp	pp	ADJ
easat-6229	360	48	.	.	PUNCT
easat-6229	360	49	426	426	NUM
easat-6229	360	50	-	-	SYM
easat-6229	360	51	460	460	NUM
easat-6229	360	52	,	,	PUNCT
easat-6229	360	53	2023	2023	NUM
easat-6229	360	54	.	.	PUNCT
easat-6229	361	1	https://doi.org/10.1007/s40753-022-00167-y	https://doi.org/10.1007/s40753-022-00167-y	NOUN
easat-6229	361	2	[	[	X
easat-6229	361	3	32	32	NUM
easat-6229	361	4	]	]	PUNCT
easat-6229	361	5	m.-h	m.-h	NOUN
easat-6229	361	6	.	.	PUNCT
easat-6229	362	1	shih	shih	PROPN
easat-6229	362	2	and	and	CCONJ
easat-6229	362	3	w.-p	w.-p	PROPN
easat-6229	362	4	.	.	PUNCT
easat-6229	363	1	sung	sung	PROPN
easat-6229	363	2	,	,	PUNCT
easat-6229	363	3	"	"	PUNCT
easat-6229	363	4	shaking	shake	VERB
easat-6229	363	5	table	table	NOUN
easat-6229	363	6	test	test	NOUN
easat-6229	363	7	and	and	CCONJ
easat-6229	363	8	verification	verification	NOUN
easat-6229	363	9	of	of	ADP
easat-6229	363	10	development	development	NOUN
easat-6229	363	11	of	of	ADP
easat-6229	363	12	an	an	DET
easat-6229	363	13	accumulated	accumulate	VERB
easat-6229	363	14	semi	semi	ADJ
easat-6229	363	15	-	-	ADJ
easat-6229	363	16	active	active	ADJ
easat-6229	363	17	hydraulic	hydraulic	ADJ
easat-6229	363	18	damper	damper	NOUN
easat-6229	363	19	as	as	ADP
easat-6229	363	20	an	an	DET
easat-6229	363	21	active	active	ADJ
easat-6229	363	22	interaction	interaction	NOUN
easat-6229	363	23	control	control	NOUN
easat-6229	363	24	device	device	NOUN
easat-6229	363	25	,	,	PUNCT
easat-6229	363	26	"	"	PUNCT
easat-6229	363	27	sādhanā	sādhanā	ADJ
easat-6229	363	28	,	,	PUNCT
easat-6229	363	29	vol	vol	NOUN
easat-6229	363	30	.	.	PROPN
easat-6229	363	31	41	41	NUM
easat-6229	363	32	,	,	PUNCT
easat-6229	363	33	pp	pp	ADJ
easat-6229	363	34	.	.	PUNCT
easat-6229	364	1	1425	1425	NUM
easat-6229	364	2	-	-	SYM
easat-6229	364	3	1442	1442	NUM
easat-6229	364	4	,	,	PUNCT
easat-6229	364	5	2016	2016	NUM
easat-6229	364	6	.	.	PUNCT
easat-6229	365	1	https://doi.org/10.1007/s12046-016-0570-z	https://doi.org/10.1007/s12046-016-0570-z	PROPN
easat-6229	366	1	[	[	X
easat-6229	366	2	33	33	NUM
easat-6229	366	3	]	]	PUNCT
easat-6229	366	4	z.	z.	PROPN
easat-6229	366	5	k.	k.	PROPN
easat-6229	366	6	szabo	szabo	PROPN
easat-6229	366	7	,	,	PUNCT
easat-6229	366	8	p.	p.	PROPN
easat-6229	366	9	körtesi	körtesi	PROPN
easat-6229	366	10	,	,	PUNCT
easat-6229	366	11	j.	j.	PROPN
easat-6229	366	12	guncaga	guncaga	PROPN
easat-6229	366	13	,	,	PUNCT
easat-6229	366	14	d.	d.	PROPN
easat-6229	366	15	szabo	szabo	PROPN
easat-6229	366	16	,	,	PUNCT
easat-6229	366	17	and	and	CCONJ
easat-6229	366	18	r.	r.	PROPN
easat-6229	366	19	neag	neag	PROPN
easat-6229	366	20	,	,	PUNCT
easat-6229	366	21	"	"	PUNCT
easat-6229	366	22	examples	example	NOUN
easat-6229	366	23	of	of	ADP
easat-6229	366	24	problem	problem	NOUN
easat-6229	366	25	-	-	PUNCT
easat-6229	366	26	solving	solve	VERB
easat-6229	366	27	strategies	strategy	NOUN
easat-6229	366	28	in	in	ADP
easat-6229	366	29	mathematics	mathematics	NOUN
easat-6229	366	30	education	education	NOUN
easat-6229	366	31	supporting	support	VERB
easat-6229	366	32	the	the	DET
easat-6229	366	33	sustainability	sustainability	NOUN
easat-6229	366	34	of	of	ADP
easat-6229	366	35	21st	21st	ADJ
easat-6229	366	36	-	-	PUNCT
easat-6229	366	37	century	century	NOUN
easat-6229	366	38	skills	skill	NOUN
easat-6229	366	39	,	,	PUNCT
easat-6229	366	40	"	"	PUNCT
easat-6229	366	41	sustainability	sustainability	NOUN
easat-6229	366	42	,	,	PUNCT
easat-6229	366	43	vol	vol	NOUN
easat-6229	366	44	.	.	PROPN
easat-6229	367	1	12	12	NUM
easat-6229	367	2	,	,	PUNCT
easat-6229	367	3	no	no	INTJ
easat-6229	367	4	.	.	NOUN
easat-6229	367	5	23	23	NUM
easat-6229	367	6	,	,	PUNCT
easat-6229	367	7	p.	p.	NOUN
easat-6229	367	8	10113	10113	NUM
easat-6229	367	9	,	,	PUNCT
easat-6229	367	10	2020	2020	NUM
easat-6229	367	11	.	.	PUNCT
easat-6229	368	1	https://doi.org/10.3390/su122310113	https://doi.org/10.3390/su122310113	PUNCT
easat-6229	369	1	[	[	X
easat-6229	369	2	34	34	NUM
easat-6229	369	3	]	]	X
easat-6229	369	4	j.	j.	PROPN
easat-6229	369	5	lithner	lithner	PROPN
easat-6229	369	6	,	,	PUNCT
easat-6229	369	7	"	"	PUNCT
easat-6229	369	8	principles	principle	NOUN
easat-6229	369	9	for	for	ADP
easat-6229	369	10	designing	design	VERB
easat-6229	369	11	mathematical	mathematical	ADJ
easat-6229	369	12	tasks	task	NOUN
easat-6229	369	13	that	that	PRON
easat-6229	369	14	enhance	enhance	VERB
easat-6229	369	15	imitative	imitative	ADJ
easat-6229	369	16	and	and	CCONJ
easat-6229	369	17	creative	creative	ADJ
easat-6229	369	18	reasoning	reasoning	NOUN
easat-6229	369	19	,	,	PUNCT
easat-6229	369	20	"	"	PUNCT
easat-6229	369	21	zdm	zdm	NOUN
easat-6229	369	22	,	,	PUNCT
easat-6229	369	23	vol	vol	NOUN
easat-6229	369	24	.	.	PROPN
easat-6229	369	25	49	49	NUM
easat-6229	369	26	,	,	PUNCT
easat-6229	369	27	no	no	INTJ
easat-6229	369	28	.	.	NOUN
easat-6229	369	29	6	6	NUM
easat-6229	369	30	,	,	PUNCT
easat-6229	369	31	pp	pp	ADJ
easat-6229	369	32	.	.	PUNCT
easat-6229	370	1	937	937	NUM
easat-6229	370	2	-	-	SYM
easat-6229	370	3	949	949	NUM
easat-6229	370	4	,	,	PUNCT
easat-6229	370	5	2017	2017	NUM
easat-6229	370	6	.	.	PUNCT
easat-6229	371	1	https://doi.org/10.1007/s11858-017-0867-3	https://doi.org/10.1007/s11858-017-0867-3	X
easat-6229	372	1	[	[	X
easat-6229	372	2	35	35	NUM
easat-6229	372	3	]	]	PUNCT
easat-6229	372	4	k.	k.	PROPN
easat-6229	372	5	weber	weber	PROPN
easat-6229	372	6	,	,	PUNCT
easat-6229	372	7	"	"	PUNCT
easat-6229	372	8	effective	effective	ADJ
easat-6229	372	9	proof	proof	NOUN
easat-6229	372	10	reading	read	VERB
easat-6229	372	11	strategies	strategy	NOUN
easat-6229	372	12	for	for	ADP
easat-6229	372	13	comprehending	comprehending	ADJ
easat-6229	372	14	mathematical	mathematical	ADJ
easat-6229	372	15	proofs	proof	NOUN
easat-6229	372	16	,	,	PUNCT
easat-6229	372	17	"	"	PUNCT
easat-6229	372	18	international	international	ADJ
easat-6229	372	19	journal	journal	NOUN
easat-6229	372	20	of	of	ADP
easat-6229	372	21	research	research	NOUN
easat-6229	372	22	in	in	ADP
easat-6229	372	23	undergraduate	undergraduate	ADJ
easat-6229	372	24	mathematics	mathematic	NOUN
easat-6229	372	25	education	education	NOUN
easat-6229	372	26	,	,	PUNCT
easat-6229	372	27	vol	vol	NOUN
easat-6229	372	28	.	.	PROPN
easat-6229	372	29	1	1	NUM
easat-6229	372	30	,	,	PUNCT
easat-6229	372	31	pp	pp	ADJ
easat-6229	372	32	.	.	PUNCT
easat-6229	372	33	289	289	NUM
easat-6229	372	34	-	-	SYM
easat-6229	372	35	314	314	NUM
easat-6229	372	36	,	,	PUNCT
easat-6229	372	37	2015	2015	NUM
easat-6229	372	38	.	.	PUNCT
easat-6229	373	1	https://doi.org/10.1007/s40753-0150011-0	https://doi.org/10.1007/s40753-0150011-0	ADJ
easat-6229	373	2	[	[	PUNCT
easat-6229	373	3	36	36	NUM
easat-6229	373	4	]	]	X
easat-6229	373	5	y.	y.	NOUN
easat-6229	373	6	zengin	zengin	NOUN
easat-6229	373	7	,	,	PUNCT
easat-6229	373	8	"	"	PUNCT
easat-6229	373	9	development	development	NOUN
easat-6229	373	10	of	of	ADP
easat-6229	373	11	mathematical	mathematical	ADJ
easat-6229	373	12	connection	connection	NOUN
easat-6229	373	13	skills	skill	NOUN
easat-6229	373	14	in	in	ADP
easat-6229	373	15	a	a	DET
easat-6229	373	16	dynamic	dynamic	ADJ
easat-6229	373	17	learning	learning	NOUN
easat-6229	373	18	environment	environment	NOUN
easat-6229	373	19	,	,	PUNCT
easat-6229	373	20	"	"	PUNCT
easat-6229	373	21	education	education	NOUN
easat-6229	373	22	and	and	CCONJ
easat-6229	373	23	information	information	NOUN
easat-6229	373	24	technologies	technology	NOUN
easat-6229	373	25	,	,	PUNCT
easat-6229	373	26	vol	vol	NOUN
easat-6229	373	27	.	.	PROPN
easat-6229	374	1	24	24	NUM
easat-6229	374	2	,	,	PUNCT
easat-6229	374	3	no	no	INTJ
easat-6229	374	4	.	.	NOUN
easat-6229	374	5	3	3	NUM
easat-6229	374	6	,	,	PUNCT
easat-6229	374	7	pp	pp	ADJ
easat-6229	374	8	.	.	PUNCT
easat-6229	375	1	2175	2175	NUM
easat-6229	375	2	-	-	SYM
easat-6229	375	3	2194	2194	NUM
easat-6229	375	4	,	,	PUNCT
easat-6229	375	5	2019	2019	NUM
easat-6229	375	6	.	.	PUNCT
easat-6229	376	1	https://doi.org/10.1007/s10639-019-09870-x	https://doi.org/10.1007/s10639-019-09870-x	VERB
easat-6229	377	1	[	[	X
easat-6229	377	2	37	37	NUM
easat-6229	377	3	]	]	PUNCT
easat-6229	377	4	a.	a.	NOUN
easat-6229	377	5	t.	t.	PROPN
easat-6229	377	6	ottenbreit	ottenbreit	PROPN
easat-6229	377	7	-	-	PUNCT
easat-6229	377	8	leftwich	leftwich	PROPN
easat-6229	377	9	,	,	PUNCT
easat-6229	377	10	k.	k.	PROPN
easat-6229	377	11	d.	d.	PROPN
easat-6229	377	12	glazewski	glazewski	PROPN
easat-6229	377	13	,	,	PUNCT
easat-6229	377	14	t.	t.	PROPN
easat-6229	377	15	j.	j.	PROPN
easat-6229	377	16	newby	newby	PROPN
easat-6229	377	17	,	,	PUNCT
easat-6229	377	18	and	and	CCONJ
easat-6229	377	19	p.	p.	NOUN
easat-6229	377	20	a.	a.	PROPN
easat-6229	377	21	ertmer	ertmer	PROPN
easat-6229	377	22	,	,	PUNCT
easat-6229	377	23	"	"	PUNCT
easat-6229	377	24	teacher	teacher	NOUN
easat-6229	377	25	value	value	NOUN
easat-6229	377	26	beliefs	belief	NOUN
easat-6229	377	27	associated	associate	VERB
easat-6229	377	28	with	with	ADP
easat-6229	377	29	using	use	VERB
easat-6229	377	30	technology	technology	NOUN
easat-6229	377	31	:	:	PUNCT
easat-6229	377	32	addressing	address	VERB
easat-6229	377	33	professional	professional	ADJ
easat-6229	377	34	and	and	CCONJ
easat-6229	377	35	student	student	NOUN
easat-6229	377	36	needs	need	NOUN
easat-6229	377	37	,	,	PUNCT
easat-6229	377	38	"	"	PUNCT
easat-6229	377	39	computers	computer	NOUN
easat-6229	377	40	&	&	CCONJ
easat-6229	377	41	education	education	NOUN
easat-6229	377	42	,	,	PUNCT
easat-6229	377	43	vol	vol	NOUN
easat-6229	377	44	.	.	PROPN
easat-6229	378	1	55	55	NUM
easat-6229	378	2	,	,	PUNCT
easat-6229	378	3	no	no	INTJ
easat-6229	378	4	.	.	NOUN
easat-6229	378	5	3	3	NUM
easat-6229	378	6	,	,	PUNCT
easat-6229	378	7	pp	pp	ADJ
easat-6229	378	8	.	.	PUNCT
easat-6229	379	1	1321	1321	NUM
easat-6229	379	2	-	-	SYM
easat-6229	379	3	1335	1335	NUM
easat-6229	379	4	,	,	PUNCT
easat-6229	379	5	2010	2010	NUM
easat-6229	379	6	.	.	PUNCT
easat-6229	380	1	[	[	X
easat-6229	380	2	38	38	NUM
easat-6229	380	3	]	]	PUNCT
easat-6229	380	4	m.	m.	PROPN
easat-6229	380	5	k.	k.	PROPN
easat-6229	380	6	stein	stein	PROPN
easat-6229	380	7	,	,	PUNCT
easat-6229	380	8	j.	j.	PROPN
easat-6229	380	9	l.	l.	PROPN
easat-6229	380	10	russell	russell	PROPN
easat-6229	380	11	,	,	PUNCT
easat-6229	380	12	v.	v.	PROPN
easat-6229	380	13	bill	bill	PROPN
easat-6229	380	14	,	,	PUNCT
easat-6229	380	15	r.	r.	PROPN
easat-6229	380	16	correnti	correnti	PROPN
easat-6229	380	17	,	,	PUNCT
easat-6229	380	18	and	and	CCONJ
easat-6229	380	19	l.	l.	PROPN
easat-6229	380	20	speranzo	speranzo	PROPN
easat-6229	380	21	,	,	PUNCT
easat-6229	380	22	"	"	PUNCT
easat-6229	380	23	coach	coach	NOUN
easat-6229	380	24	learning	learn	VERB
easat-6229	380	25	to	to	PART
easat-6229	380	26	help	help	VERB
easat-6229	380	27	teachers	teacher	NOUN
easat-6229	380	28	learn	learn	VERB
easat-6229	380	29	to	to	PART
easat-6229	380	30	enact	enact	VERB
easat-6229	380	31	conceptually	conceptually	ADV
easat-6229	380	32	rich	rich	ADJ
easat-6229	380	33	,	,	PUNCT
easat-6229	380	34	student	student	NOUN
easat-6229	380	35	-	-	PUNCT
easat-6229	380	36	focused	focus	VERB
easat-6229	380	37	mathematics	mathematic	NOUN
easat-6229	380	38	lessons	lesson	NOUN
easat-6229	380	39	,	,	PUNCT
easat-6229	380	40	"	"	PUNCT
easat-6229	380	41	journal	journal	NOUN
easat-6229	380	42	of	of	ADP
easat-6229	380	43	mathematics	mathematics	PROPN
easat-6229	380	44	teacher	teacher	NOUN
easat-6229	380	45	education	education	NOUN
easat-6229	380	46	,	,	PUNCT
easat-6229	380	47	pp	pp	ADJ
easat-6229	380	48	.	.	PUNCT
easat-6229	381	1	1	1	NUM
easat-6229	381	2	-	-	SYM
easat-6229	381	3	26	26	NUM
easat-6229	381	4	,	,	PUNCT
easat-6229	381	5	2022	2022	NUM
easat-6229	381	6	.	.	PUNCT
easat-6229	382	1	[	[	X
easat-6229	382	2	39	39	NUM
easat-6229	382	3	]	]	PUNCT
easat-6229	382	4	a.	a.	NOUN
easat-6229	382	5	stefanowicz	stefanowicz	PROPN
easat-6229	382	6	,	,	PUNCT
easat-6229	382	7	j.	j.	PROPN
easat-6229	382	8	kyle	kyle	PROPN
easat-6229	382	9	,	,	PUNCT
easat-6229	382	10	and	and	CCONJ
easat-6229	382	11	m.	m.	PROPN
easat-6229	382	12	grove	grove	PROPN
easat-6229	382	13	,	,	PUNCT
easat-6229	382	14	"	"	PUNCT
easat-6229	382	15	proofs	proof	NOUN
easat-6229	382	16	and	and	CCONJ
easat-6229	382	17	mathematical	mathematical	ADJ
easat-6229	382	18	reasoning	reasoning	NOUN
easat-6229	382	19	university	university	NOUN
easat-6229	382	20	of	of	ADP
easat-6229	382	21	birmingham	birmingham	PROPN
easat-6229	382	22	,	,	PUNCT
easat-6229	382	23	"	"	PUNCT
easat-6229	382	24	ed	ed	NOUN
easat-6229	382	25	:	:	PUNCT
easat-6229	382	26	september	september	PROPN
easat-6229	382	27	,	,	PUNCT
easat-6229	382	28	2014	2014	NUM
easat-6229	382	29	.	.	PUNCT
easat-6229	383	1	[	[	X
easat-6229	383	2	40	40	NUM
easat-6229	383	3	]	]	PUNCT
easat-6229	383	4	m.	m.	NOUN
easat-6229	383	5	rodd	rodd	PROPN
easat-6229	383	6	,	,	PUNCT
easat-6229	383	7	"	"	PUNCT
easat-6229	383	8	transition	transition	NOUN
easat-6229	383	9	from	from	ADP
easat-6229	383	10	"	"	PUNCT
easat-6229	383	11	it	it	PRON
easat-6229	383	12	looks	look	VERB
easat-6229	383	13	like	like	SCONJ
easat-6229	383	14	"	"	PUNCT
easat-6229	383	15	to	to	PART
easat-6229	383	16	"	"	PUNCT
easat-6229	383	17	it	it	PRON
easat-6229	383	18	has	have	VERB
easat-6229	383	19	to	to	PART
easat-6229	383	20	be	be	AUX
easat-6229	383	21	"	"	PUNCT
easat-6229	383	22	in	in	ADP
easat-6229	383	23	a	a	DET
easat-6229	383	24	geometric	geometric	ADJ
easat-6229	383	25	workspace	workspace	NOUN
easat-6229	383	26	:	:	PUNCT
easat-6229	383	27	affect	affect	VERB
easat-6229	383	28	and	and	CCONJ
easat-6229	383	29	attention	attention	NOUN
easat-6229	383	30	,	,	PUNCT
easat-6229	383	31	"	"	PUNCT
easat-6229	383	32	bolema	bolema	NOUN
easat-6229	383	33	:	:	PUNCT
easat-6229	383	34	boletim	boletim	PROPN
easat-6229	383	35	de	de	PROPN
easat-6229	383	36	educação	educação	PROPN
easat-6229	383	37	matemática	matemática	PROPN
easat-6229	383	38	,	,	PUNCT
easat-6229	383	39	vol	vol	NOUN
easat-6229	383	40	.	.	PROPN
easat-6229	383	41	30	30	NUM
easat-6229	383	42	,	,	PUNCT
easat-6229	383	43	pp	pp	ADJ
easat-6229	383	44	.	.	PUNCT
easat-6229	384	1	142	142	NUM
easat-6229	384	2	-	-	SYM
easat-6229	384	3	164	164	NUM
easat-6229	384	4	,	,	PUNCT
easat-6229	384	5	2016	2016	NUM
easat-6229	384	6	.	.	PUNCT
easat-6229	385	1	https://doi.org/10.1590/1980-4415v30n54a07	https://doi.org/10.1590/1980-4415v30n54a07	VERB
easat-6229	385	2	[	[	X
easat-6229	385	3	41	41	NUM
easat-6229	385	4	]	]	PUNCT
easat-6229	385	5	m.	m.	NOUN
easat-6229	385	6	santos	santos	PROPN
easat-6229	385	7	-	-	PUNCT
easat-6229	385	8	trigo	trigo	PROPN
easat-6229	385	9	,	,	PUNCT
easat-6229	385	10	l.	l.	PROPN
easat-6229	385	11	moreno	moreno	PROPN
easat-6229	385	12	-	-	PUNCT
easat-6229	385	13	armella	armella	PROPN
easat-6229	385	14	,	,	PUNCT
easat-6229	385	15	and	and	CCONJ
easat-6229	385	16	m.	m.	PROPN
easat-6229	385	17	camacho	camacho	PROPN
easat-6229	385	18	-	-	PUNCT
easat-6229	385	19	machín	machín	NOUN
easat-6229	385	20	,	,	PUNCT
easat-6229	385	21	"	"	PUNCT
easat-6229	385	22	problem	problem	NOUN
easat-6229	385	23	solving	solving	NOUN
easat-6229	385	24	and	and	CCONJ
easat-6229	385	25	the	the	DET
easat-6229	385	26	use	use	NOUN
easat-6229	385	27	of	of	ADP
easat-6229	385	28	digital	digital	ADJ
easat-6229	385	29	technologies	technology	NOUN
easat-6229	385	30	within	within	ADP
easat-6229	385	31	the	the	DET
easat-6229	385	32	mathematical	mathematical	ADJ
easat-6229	385	33	working	work	VERB
easat-6229	385	34	space	space	NOUN
easat-6229	385	35	framework	framework	NOUN
easat-6229	385	36	,	,	PUNCT
easat-6229	385	37	"	"	PUNCT
easat-6229	385	38	zdm	zdm	NOUN
easat-6229	385	39	,	,	PUNCT
easat-6229	385	40	vol	vol	NOUN
easat-6229	385	41	.	.	PROPN
easat-6229	386	1	48	48	NUM
easat-6229	386	2	,	,	PUNCT
easat-6229	386	3	pp	pp	ADJ
easat-6229	386	4	.	.	PUNCT
easat-6229	387	1	827	827	NUM
easat-6229	387	2	-	-	SYM
easat-6229	387	3	842	842	NUM
easat-6229	387	4	,	,	PUNCT
easat-6229	387	5	2016	2016	NUM
easat-6229	387	6	.	.	PUNCT
easat-6229	388	1	https://doi.org/10.1007/s11858-016-0757-0	https://doi.org/10.1007/s11858-016-0757-0	PRON
easat-6229	389	1	[	[	X
easat-6229	389	2	42	42	NUM
easat-6229	389	3	]	]	PUNCT
easat-6229	389	4	m.	m.	NOUN
easat-6229	389	5	omar	omar	PROPN
easat-6229	389	6	,	,	PUNCT
easat-6229	389	7	g.	g.	PROPN
easat-6229	389	8	karakok	karakok	PROPN
easat-6229	389	9	,	,	PUNCT
easat-6229	389	10	m.	m.	PROPN
easat-6229	389	11	savic	savic	PROPN
easat-6229	389	12	,	,	PUNCT
easat-6229	389	13	h.	h.	PROPN
easat-6229	389	14	e.	e.	PROPN
easat-6229	389	15	turkey	turkey	PROPN
easat-6229	389	16	,	,	PUNCT
easat-6229	389	17	and	and	CCONJ
easat-6229	389	18	g.	g.	PROPN
easat-6229	389	19	tang	tang	PROPN
easat-6229	389	20	,	,	PUNCT
easat-6229	389	21	"	"	PUNCT
easat-6229	389	22	i	i	PRON
easat-6229	389	23	felt	feel	VERB
easat-6229	389	24	like	like	ADP
easat-6229	389	25	a	a	DET
easat-6229	389	26	mathematician	mathematician	NOUN
easat-6229	389	27	:	:	PUNCT
easat-6229	389	28	problems	problem	NOUN
easat-6229	389	29	and	and	CCONJ
easat-6229	389	30	assessment	assessment	NOUN
easat-6229	389	31	to	to	PART
easat-6229	389	32	promote	promote	VERB
easat-6229	389	33	creative	creative	ADJ
easat-6229	389	34	effort	effort	NOUN
easat-6229	389	35	,	,	PUNCT
easat-6229	389	36	"	"	PUNCT
easat-6229	389	37	primus	primus	PROPN
easat-6229	389	38	,	,	PUNCT
easat-6229	389	39	vol	vol	NOUN
easat-6229	389	40	.	.	PROPN
easat-6229	389	41	29	29	NUM
easat-6229	389	42	,	,	PUNCT
easat-6229	389	43	no	no	INTJ
easat-6229	389	44	.	.	NOUN
easat-6229	389	45	1	1	NUM
easat-6229	389	46	,	,	PUNCT
easat-6229	389	47	pp	pp	ADJ
easat-6229	389	48	.	.	PUNCT
easat-6229	390	1	82	82	NUM
easat-6229	390	2	-	-	SYM
easat-6229	390	3	102	102	NUM
easat-6229	390	4	,	,	PUNCT
easat-6229	390	5	2019	2019	NUM
easat-6229	390	6	.	.	PUNCT
easat-6229	391	1	[	[	X
easat-6229	391	2	43	43	NUM
easat-6229	391	3	]	]	X
easat-6229	391	4	g.	g.	PROPN
easat-6229	391	5	hanna	hanna	PROPN
easat-6229	391	6	and	and	CCONJ
easat-6229	391	7	e.	e.	PROPN
easat-6229	391	8	barbeau	barbeau	PROPN
easat-6229	391	9	,	,	PUNCT
easat-6229	391	10	"	"	PUNCT
easat-6229	391	11	proofs	proof	NOUN
easat-6229	391	12	as	as	ADP
easat-6229	391	13	bearers	bearer	NOUN
easat-6229	391	14	of	of	ADP
easat-6229	391	15	mathematical	mathematical	ADJ
easat-6229	391	16	knowledge	knowledge	NOUN
easat-6229	391	17	,	,	PUNCT
easat-6229	391	18	"	"	PUNCT
easat-6229	391	19	zdm	zdm	PROPN
easat-6229	391	20	int	int	NOUN
easat-6229	391	21	.	.	PUNCT
easat-6229	392	1	j.	j.	PROPN
easat-6229	392	2	math	math	PROPN
easat-6229	392	3	.	.	PUNCT
easat-6229	393	1	educ	educ	PROPN
easat-6229	393	2	,	,	PUNCT
easat-6229	393	3	vol	vol	NOUN
easat-6229	393	4	.	.	PROPN
easat-6229	393	5	40	40	NUM
easat-6229	393	6	,	,	PUNCT
easat-6229	393	7	no	no	INTJ
easat-6229	393	8	.	.	NOUN
easat-6229	393	9	3	3	NUM
easat-6229	393	10	,	,	PUNCT
easat-6229	393	11	pp	pp	ADJ
easat-6229	393	12	.	.	PUNCT
easat-6229	394	1	345–353	345–353	NUM
easat-6229	394	2	,	,	PUNCT
easat-6229	394	3	2008	2008	NUM
easat-6229	394	4	.	.	PUNCT
easat-6229	394	5	https://doi.org/10.1007/s11858-008-0080-5	https://doi.org/10.1007/s11858-008-0080-5	NUM
easat-6229	395	1	[	[	X
easat-6229	395	2	44	44	NUM
easat-6229	395	3	]	]	PUNCT
easat-6229	395	4	p.	p.	NOUN
easat-6229	395	5	regier	regier	NOUN
easat-6229	395	6	and	and	CCONJ
easat-6229	395	7	m.	m.	NOUN
easat-6229	395	8	savic	savic	PROPN
easat-6229	395	9	,	,	PUNCT
easat-6229	395	10	"	"	PUNCT
easat-6229	395	11	how	how	SCONJ
easat-6229	395	12	teaching	teaching	NOUN
easat-6229	395	13	to	to	PART
easat-6229	395	14	foster	foster	VERB
easat-6229	395	15	mathematical	mathematical	ADJ
easat-6229	395	16	creativity	creativity	NOUN
easat-6229	395	17	may	may	AUX
easat-6229	395	18	impact	impact	VERB
easat-6229	395	19	student	student	NOUN
easat-6229	395	20	self	self	NOUN
easat-6229	395	21	-	-	PUNCT
easat-6229	395	22	efficacy	efficacy	NOUN
easat-6229	395	23	for	for	ADP
easat-6229	395	24	proving	prove	VERB
easat-6229	395	25	,	,	PUNCT
easat-6229	395	26	"	"	PUNCT
easat-6229	395	27	the	the	DET
easat-6229	395	28	journal	journal	NOUN
easat-6229	395	29	of	of	ADP
easat-6229	395	30	mathematical	mathematical	ADJ
easat-6229	395	31	behavior	behavior	NOUN
easat-6229	395	32	,	,	PUNCT
easat-6229	395	33	vol	vol	NOUN
easat-6229	395	34	.	.	PROPN
easat-6229	395	35	57	57	NUM
easat-6229	395	36	,	,	PUNCT
easat-6229	395	37	p.	p.	NOUN
easat-6229	395	38	100720	100720	NUM
easat-6229	395	39	,	,	PUNCT
easat-6229	395	40	2020	2020	NUM
easat-6229	395	41	.	.	PUNCT
easat-6229	396	1	[	[	X
easat-6229	396	2	45	45	NUM
easat-6229	396	3	]	]	PUNCT
easat-6229	396	4	m.	m.	NOUN
easat-6229	396	5	nadlifah	nadlifah	NOUN
easat-6229	396	6	and	and	CCONJ
easat-6229	396	7	s.	s.	PROPN
easat-6229	396	8	prabawanto	prabawanto	PROPN
easat-6229	396	9	,	,	PUNCT
easat-6229	396	10	"	"	PUNCT
easat-6229	396	11	mathematical	mathematical	ADJ
easat-6229	396	12	proof	proof	ADJ
easat-6229	396	13	construction	construction	NOUN
easat-6229	396	14	:	:	PUNCT
easat-6229	396	15	students	student	NOUN
easat-6229	396	16	’	'	PUNCT
easat-6229	396	17	ability	ability	NOUN
easat-6229	396	18	in	in	ADP
easat-6229	396	19	higher	high	ADJ
easat-6229	396	20	education	education	NOUN
easat-6229	396	21	,	,	PUNCT
easat-6229	396	22	"	"	PUNCT
easat-6229	396	23	in	in	ADP
easat-6229	396	24	journal	journal	NOUN
easat-6229	396	25	of	of	ADP
easat-6229	396	26	physics	physics	PROPN
easat-6229	396	27	:	:	PUNCT
easat-6229	396	28	conference	conference	NOUN
easat-6229	396	29	series	series	NOUN
easat-6229	396	30	,	,	PUNCT
easat-6229	396	31	2017	2017	NUM
easat-6229	396	32	,	,	PUNCT
easat-6229	396	33	vol	vol	NOUN
easat-6229	396	34	.	.	NOUN
easat-6229	396	35	895	895	NUM
easat-6229	396	36	,	,	PUNCT
easat-6229	396	37	no	no	INTJ
easat-6229	396	38	.	.	NOUN
easat-6229	396	39	1	1	NUM
easat-6229	396	40	,	,	PUNCT
easat-6229	396	41	p.	p.	NOUN
easat-6229	396	42	012094	012094	NUM
easat-6229	396	43	.	.	PUNCT
easat-6229	397	1	[	[	X
easat-6229	397	2	46	46	NUM
easat-6229	397	3	]	]	X
easat-6229	397	4	n.	n.	PROPN
easat-6229	397	5	aisyah	aisyah	PROPN
easat-6229	397	6	,	,	PUNCT
easat-6229	397	7	e.	e.	PROPN
easat-6229	397	8	susanti	susanti	PROPN
easat-6229	397	9	,	,	PUNCT
easat-6229	397	10	m.	m.	NOUN
easat-6229	397	11	meryansumayeka	meryansumayeka	PROPN
easat-6229	397	12	,	,	PUNCT
easat-6229	397	13	t.	t.	PROPN
easat-6229	397	14	y.	y.	PROPN
easat-6229	397	15	e.	e.	PROPN
easat-6229	397	16	siswono	siswono	PROPN
easat-6229	397	17	,	,	PUNCT
easat-6229	397	18	and	and	CCONJ
easat-6229	397	19	s.	s.	PROPN
easat-6229	397	20	m.	m.	PROPN
easat-6229	397	21	maat	maat	PROPN
easat-6229	397	22	,	,	PUNCT
easat-6229	397	23	"	"	PUNCT
easat-6229	397	24	proving	prove	VERB
easat-6229	397	25	geometry	geometry	NOUN
easat-6229	397	26	theorems	theorem	NOUN
easat-6229	397	27	:	:	PUNCT
easat-6229	397	28	student	student	NOUN
easat-6229	397	29	prospective	prospective	ADJ
easat-6229	397	30	teachers	teacher	NOUN
easat-6229	397	31	’	’	PART
easat-6229	397	32	perseverance	perseverance	NOUN
easat-6229	397	33	and	and	CCONJ
easat-6229	397	34	mathematical	mathematical	ADJ
easat-6229	397	35	reasoning	reasoning	NOUN
easat-6229	397	36	,	,	PUNCT
easat-6229	397	37	"	"	PUNCT
easat-6229	397	38	infinity	infinity	NOUN
easat-6229	397	39	journal	journal	NOUN
easat-6229	397	40	,	,	PUNCT
easat-6229	397	41	vol	vol	NOUN
easat-6229	397	42	.	.	PROPN
easat-6229	397	43	12	12	NUM
easat-6229	397	44	,	,	PUNCT
easat-6229	397	45	no	no	INTJ
easat-6229	397	46	.	.	NOUN
easat-6229	397	47	2	2	NUM
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easat-6229	397	54	,	,	PUNCT
easat-6229	397	55	2023	2023	NUM
easat-6229	397	56	.	.	PUNCT
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easat-6229	398	4	https://doi.org/10.22460/infinity.v12i2.p243-260	https://doi.org/10.22460/infinity.v12i2.p243-260	NOUN
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easat-6229	398	6	https://doi.org/10.1007/s11858-016-0774-z	https://doi.org/10.1007/s11858-016-0774-z	PROPN
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easat-6229	399	2	https://doi.org/10.1007/s40753-015-0011-0	https://doi.org/10.1007/s40753-015-0011-0	NUM
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