id	sid	tid	token	lemma	pos
cana-3074	1	1	communications	communication	NOUN
cana-3074	1	2	on	on	ADP
cana-3074	1	3	applied	apply	VERB
cana-3074	1	4	nonlinear	nonlinear	ADJ
cana-3074	1	5	analysis	analysis	NOUN
cana-3074	1	6	issn	issn	NOUN
cana-3074	1	7	:	:	PUNCT
cana-3074	1	8	1074	1074	NUM
cana-3074	1	9	-	-	PUNCT
cana-3074	1	10	133x	133x	NUM
cana-3074	1	11	vol	vol	NOUN
cana-3074	1	12	32	32	NUM
cana-3074	1	13	no	no	NOUN
cana-3074	1	14	.	.	PUNCT
cana-3074	2	1	5s	5s	NUM
cana-3074	2	2	(	(	PUNCT
cana-3074	2	3	2025	2025	NUM
cana-3074	2	4	)	)	PUNCT
cana-3074	2	5	268	268	NUM
cana-3074	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	3	2	geometrical	geometrical	ADJ
cana-3074	3	3	abstraction	abstraction	NOUN
cana-3074	3	4	on	on	ADP
cana-3074	3	5	van	van	PROPN
cana-3074	3	6	hiele	hiele	PROPN
cana-3074	3	7	levels	level	NOUN
cana-3074	3	8	among	among	ADP
cana-3074	3	9	mathematics	mathematics	NOUN
cana-3074	3	10	undergraduates	undergraduate	NOUN
cana-3074	3	11	asdar	asdar	NOUN
cana-3074	3	12	ahmad1*jumadila	ahmad1*jumadila	PROPN
cana-3074	3	13	purnama2	purnama2	PROPN
cana-3074	3	14	,	,	PUNCT
cana-3074	3	15	abdul	abdul	PROPN
cana-3074	3	16	rahman3	rahman3	PROPN
cana-3074	3	17	,	,	PUNCT
cana-3074	3	18	jeranah4	jeranah4	PROPN
cana-3074	3	19	1,2,3	1,2,3	NUM
cana-3074	3	20	universitas	universita	NOUN
cana-3074	3	21	negeri	negeri	NOUN
cana-3074	3	22	makassar	makassar	PROPN
cana-3074	3	23	4	4	NUM
cana-3074	3	24	stkip	stkip	VERB
cana-3074	3	25	ypup	ypup	NOUN
cana-3074	3	26	makassar	makassar	PROPN
cana-3074	3	27	*	*	PUNCT
cana-3074	3	28	corresponding	correspond	VERB
cana-3074	3	29	email	email	NOUN
cana-3074	3	30	:	:	PUNCT
cana-3074	3	31	asdar.ahmad@unm.ac.id	asdar.ahmad@unm.ac.id	NOUN
cana-3074	3	32	article	article	NOUN
cana-3074	3	33	history	history	NOUN
cana-3074	3	34	:	:	PUNCT
cana-3074	3	35	received	receive	VERB
cana-3074	3	36	:	:	PUNCT
cana-3074	3	37	07	07	NUM
cana-3074	3	38	-	-	SYM
cana-3074	3	39	10	10	NUM
cana-3074	3	40	-	-	PUNCT
cana-3074	3	41	2024	2024	NUM
cana-3074	3	42	revised	revise	VERB
cana-3074	3	43	:	:	PUNCT
cana-3074	3	44	27	27	NUM
cana-3074	3	45	-	-	SYM
cana-3074	3	46	11	11	NUM
cana-3074	3	47	-	-	PUNCT
cana-3074	3	48	2024	2024	NUM
cana-3074	3	49	accepted	accept	VERB
cana-3074	3	50	:	:	PUNCT
cana-3074	3	51	06	06	NUM
cana-3074	3	52	-	-	SYM
cana-3074	3	53	12	12	NUM
cana-3074	3	54	-	-	PUNCT
cana-3074	3	55	2024	2024	NUM
cana-3074	3	56	abstract	abstract	NOUN
cana-3074	3	57	:	:	PUNCT
cana-3074	3	58	this	this	DET
cana-3074	3	59	research	research	NOUN
cana-3074	3	60	aims	aim	VERB
cana-3074	3	61	to	to	PART
cana-3074	3	62	analyze	analyze	VERB
cana-3074	3	63	the	the	DET
cana-3074	3	64	geometrical	geometrical	ADJ
cana-3074	3	65	abstraction	abstraction	NOUN
cana-3074	3	66	on	on	ADP
cana-3074	3	67	van	van	PROPN
cana-3074	3	68	hiele	hiele	PROPN
cana-3074	3	69	levels	level	NOUN
cana-3074	3	70	among	among	ADP
cana-3074	3	71	mathematics	mathematics	NOUN
cana-3074	3	72	undergraduates	undergraduate	NOUN
cana-3074	3	73	at	at	ADP
cana-3074	3	74	the	the	DET
cana-3074	3	75	state	state	NOUN
cana-3074	3	76	university	university	PROPN
cana-3074	3	77	of	of	ADP
cana-3074	3	78	makassar	makassar	PROPN
cana-3074	3	79	by	by	ADP
cana-3074	3	80	utilizing	utilize	VERB
cana-3074	3	81	an	an	DET
cana-3074	3	82	explanatory	explanatory	ADJ
cana-3074	3	83	sequential	sequential	ADJ
cana-3074	3	84	mixed	mixed	ADJ
cana-3074	3	85	methods	method	NOUN
cana-3074	3	86	approach	approach	NOUN
cana-3074	3	87	.	.	PUNCT
cana-3074	4	1	research	research	NOUN
cana-3074	4	2	subjects	subject	NOUN
cana-3074	4	3	are	be	AUX
cana-3074	4	4	selected	select	VERB
cana-3074	4	5	by	by	ADP
cana-3074	4	6	using	use	VERB
cana-3074	4	7	a	a	DET
cana-3074	4	8	purposive	purposive	ADJ
cana-3074	4	9	sampling	sampling	NOUN
cana-3074	4	10	method	method	NOUN
cana-3074	4	11	from	from	ADP
cana-3074	4	12	each	each	DET
cana-3074	4	13	van	van	PROPN
cana-3074	4	14	hiele	hiele	PROPN
cana-3074	4	15	level	level	NOUN
cana-3074	4	16	to	to	PART
cana-3074	4	17	analyze	analyze	VERB
cana-3074	4	18	their	their	PRON
cana-3074	4	19	geometrical	geometrical	ADJ
cana-3074	4	20	abstractions	abstraction	NOUN
cana-3074	4	21	through	through	ADP
cana-3074	4	22	geometrical	geometrical	ADJ
cana-3074	4	23	abstraction	abstraction	NOUN
cana-3074	4	24	tests	test	NOUN
cana-3074	4	25	and	and	CCONJ
cana-3074	4	26	interviews	interview	NOUN
cana-3074	4	27	.	.	PUNCT
cana-3074	5	1	data	datum	NOUN
cana-3074	5	2	analysis	analysis	NOUN
cana-3074	5	3	includes	include	VERB
cana-3074	5	4	:	:	PUNCT
cana-3074	5	5	1	1	NUM
cana-3074	5	6	)	)	PUNCT
cana-3074	5	7	statistical	statistical	ADJ
cana-3074	5	8	analysis	analysis	NOUN
cana-3074	5	9	,	,	PUNCT
cana-3074	5	10	2	2	X
cana-3074	5	11	)	)	PUNCT
cana-3074	5	12	qualitative	qualitative	ADJ
cana-3074	5	13	data	datum	NOUN
cana-3074	5	14	collection	collection	NOUN
cana-3074	5	15	,	,	PUNCT
cana-3074	5	16	3	3	X
cana-3074	5	17	)	)	PUNCT
cana-3074	5	18	thematic	thematic	ADJ
cana-3074	5	19	analysis	analysis	NOUN
cana-3074	5	20	,	,	PUNCT
cana-3074	5	21	4	4	X
cana-3074	5	22	)	)	PUNCT
cana-3074	5	23	result	result	NOUN
cana-3074	5	24	interpretation	interpretation	NOUN
cana-3074	5	25	,	,	PUNCT
cana-3074	5	26	and	and	CCONJ
cana-3074	5	27	5	5	X
cana-3074	5	28	)	)	PUNCT
cana-3074	5	29	source	source	NOUN
cana-3074	5	30	triangulation	triangulation	NOUN
cana-3074	5	31	.	.	PUNCT
cana-3074	6	1	nvivo	nvivo	ADJ
cana-3074	6	2	12	12	NUM
cana-3074	6	3	software	software	NOUN
cana-3074	6	4	assists	assist	NOUN
cana-3074	6	5	in	in	ADP
cana-3074	6	6	coding	code	VERB
cana-3074	6	7	qualitative	qualitative	ADJ
cana-3074	6	8	data	datum	NOUN
cana-3074	6	9	.	.	PUNCT
cana-3074	7	1	results	result	NOUN
cana-3074	7	2	indicate	indicate	VERB
cana-3074	7	3	27.7	27.7	NUM
cana-3074	7	4	%	%	NOUN
cana-3074	7	5	of	of	ADP
cana-3074	7	6	undergraduates	undergraduate	NOUN
cana-3074	7	7	are	be	AUX
cana-3074	7	8	at	at	ADP
cana-3074	7	9	the	the	DET
cana-3074	7	10	visualization	visualization	NOUN
cana-3074	7	11	level	level	NOUN
cana-3074	7	12	,	,	PUNCT
cana-3074	7	13	37.2	37.2	NUM
cana-3074	7	14	%	%	NOUN
cana-3074	7	15	at	at	ADP
cana-3074	7	16	the	the	DET
cana-3074	7	17	analysis	analysis	NOUN
cana-3074	7	18	level	level	NOUN
cana-3074	7	19	,	,	PUNCT
cana-3074	7	20	14.1	14.1	NUM
cana-3074	7	21	%	%	NOUN
cana-3074	7	22	at	at	ADP
cana-3074	7	23	the	the	DET
cana-3074	7	24	informal	informal	ADJ
cana-3074	7	25	deduction	deduction	NOUN
cana-3074	7	26	level	level	NOUN
cana-3074	7	27	,	,	PUNCT
cana-3074	7	28	1.0	1.0	NUM
cana-3074	7	29	%	%	NOUN
cana-3074	7	30	at	at	ADP
cana-3074	7	31	the	the	DET
cana-3074	7	32	formal	formal	ADJ
cana-3074	7	33	deduction	deduction	NOUN
cana-3074	7	34	level	level	NOUN
cana-3074	7	35	,	,	PUNCT
cana-3074	7	36	and	and	CCONJ
cana-3074	7	37	2.6	2.6	NUM
cana-3074	7	38	%	%	NOUN
cana-3074	7	39	at	at	ADP
cana-3074	7	40	the	the	DET
cana-3074	7	41	rigor	rigor	NOUN
cana-3074	7	42	level	level	NOUN
cana-3074	7	43	.	.	PUNCT
cana-3074	8	1	on	on	ADP
cana-3074	8	2	the	the	DET
cana-3074	8	3	visualization	visualization	NOUN
cana-3074	8	4	level	level	NOUN
cana-3074	8	5	,	,	PUNCT
cana-3074	8	6	abstraction	abstraction	NOUN
cana-3074	8	7	involves	involve	VERB
cana-3074	8	8	understanding	understand	VERB
cana-3074	8	9	geometry	geometry	NOUN
cana-3074	8	10	concepts	concept	NOUN
cana-3074	8	11	contextually	contextually	ADV
cana-3074	8	12	.	.	PUNCT
cana-3074	9	1	on	on	ADP
cana-3074	9	2	the	the	DET
cana-3074	9	3	analysis	analysis	NOUN
cana-3074	9	4	level	level	NOUN
cana-3074	9	5	,	,	PUNCT
cana-3074	9	6	it	it	PRON
cana-3074	9	7	involves	involve	VERB
cana-3074	9	8	using	use	VERB
cana-3074	9	9	concepts	concept	NOUN
cana-3074	9	10	in	in	ADP
cana-3074	9	11	complex	complex	ADJ
cana-3074	9	12	contexts	contexts	NOUN
cana-3074	9	13	.	.	PUNCT
cana-3074	10	1	on	on	ADP
cana-3074	10	2	the	the	DET
cana-3074	10	3	informal	informal	ADJ
cana-3074	10	4	deduction	deduction	NOUN
cana-3074	10	5	level	level	NOUN
cana-3074	10	6	,	,	PUNCT
cana-3074	10	7	students	student	NOUN
cana-3074	10	8	connect	connect	VERB
cana-3074	10	9	geometry	geometry	NOUN
cana-3074	10	10	concepts	concept	NOUN
cana-3074	10	11	,	,	PUNCT
cana-3074	10	12	while	while	SCONJ
cana-3074	10	13	on	on	ADP
cana-3074	10	14	the	the	DET
cana-3074	10	15	formal	formal	ADJ
cana-3074	10	16	deduction	deduction	NOUN
cana-3074	10	17	level	level	NOUN
cana-3074	10	18	,	,	PUNCT
cana-3074	10	19	they	they	PRON
cana-3074	10	20	deepen	deepen	VERB
cana-3074	10	21	understanding	understanding	NOUN
cana-3074	10	22	through	through	ADP
cana-3074	10	23	mathematical	mathematical	ADJ
cana-3074	10	24	concepts	concept	NOUN
cana-3074	10	25	.	.	PUNCT
cana-3074	11	1	furthermore	furthermore	ADV
cana-3074	11	2	,	,	PUNCT
cana-3074	11	3	on	on	ADP
cana-3074	11	4	the	the	DET
cana-3074	11	5	rigor	rigor	NOUN
cana-3074	11	6	level	level	NOUN
cana-3074	11	7	,	,	PUNCT
cana-3074	11	8	students	student	NOUN
cana-3074	11	9	construct	construct	VERB
cana-3074	11	10	and	and	CCONJ
cana-3074	11	11	connect	connect	VERB
cana-3074	11	12	various	various	ADJ
cana-3074	11	13	mathematical	mathematical	ADJ
cana-3074	11	14	concepts	concept	NOUN
cana-3074	11	15	broadly	broadly	ADV
cana-3074	11	16	.	.	PUNCT
cana-3074	12	1	this	this	DET
cana-3074	12	2	study	study	NOUN
cana-3074	12	3	also	also	ADV
cana-3074	12	4	found	find	VERB
cana-3074	12	5	higher	high	ADJ
cana-3074	12	6	van	van	PROPN
cana-3074	12	7	hiele	hiele	PROPN
cana-3074	12	8	levels	level	NOUN
cana-3074	12	9	lead	lead	VERB
cana-3074	12	10	to	to	ADP
cana-3074	12	11	more	more	ADV
cana-3074	12	12	comprehensive	comprehensive	ADJ
cana-3074	12	13	geometrical	geometrical	ADJ
cana-3074	12	14	abstraction	abstraction	NOUN
cana-3074	12	15	.	.	PUNCT
cana-3074	13	1	future	future	ADJ
cana-3074	13	2	studies	study	NOUN
cana-3074	13	3	are	be	AUX
cana-3074	13	4	recommended	recommend	VERB
cana-3074	13	5	to	to	PART
cana-3074	13	6	explore	explore	VERB
cana-3074	13	7	the	the	DET
cana-3074	13	8	relationship	relationship	NOUN
cana-3074	13	9	between	between	ADP
cana-3074	13	10	van	van	PROPN
cana-3074	13	11	hiele	hiele	PROPN
cana-3074	13	12	levels	level	NOUN
cana-3074	13	13	and	and	CCONJ
cana-3074	13	14	geometrical	geometrical	ADJ
cana-3074	13	15	abstraction	abstraction	NOUN
cana-3074	13	16	.	.	PUNCT
cana-3074	14	1	keywords	keyword	NOUN
cana-3074	14	2	:	:	PUNCT
cana-3074	14	3	van	van	PROPN
cana-3074	14	4	hiele	hiele	PROPN
cana-3074	14	5	levels	level	NOUN
cana-3074	14	6	,	,	PUNCT
cana-3074	14	7	geometrical	geometrical	ADJ
cana-3074	14	8	abstraction	abstraction	NOUN
cana-3074	14	9	,	,	PUNCT
cana-3074	14	10	mathematics	mathematic	NOUN
cana-3074	14	11	undergraduates	undergraduate	NOUN
cana-3074	14	12	.	.	PUNCT
cana-3074	15	1	introduction	introduction	NOUN
cana-3074	15	2	geometry	geometry	NOUN
cana-3074	15	3	is	be	AUX
cana-3074	15	4	a	a	DET
cana-3074	15	5	branch	branch	NOUN
cana-3074	15	6	of	of	ADP
cana-3074	15	7	mathematics	mathematic	NOUN
cana-3074	15	8	that	that	PRON
cana-3074	15	9	explores	explore	VERB
cana-3074	15	10	the	the	DET
cana-3074	15	11	properties	property	NOUN
cana-3074	15	12	and	and	CCONJ
cana-3074	15	13	relationships	relationship	NOUN
cana-3074	15	14	of	of	ADP
cana-3074	15	15	points	point	NOUN
cana-3074	15	16	,	,	PUNCT
cana-3074	15	17	lines	line	NOUN
cana-3074	15	18	,	,	PUNCT
cana-3074	15	19	planes	plane	NOUN
cana-3074	15	20	,	,	PUNCT
cana-3074	15	21	solid	solid	ADJ
cana-3074	15	22	objects	object	NOUN
cana-3074	15	23	,	,	PUNCT
cana-3074	15	24	and	and	CCONJ
cana-3074	15	25	higher	higher	ADV
cana-3074	15	26	-	-	PUNCT
cana-3074	15	27	dimensional	dimensional	ADJ
cana-3074	15	28	analogs	analog	NOUN
cana-3074	15	29	which	which	PRON
cana-3074	15	30	plays	play	VERB
cana-3074	15	31	a	a	DET
cana-3074	15	32	vital	vital	ADJ
cana-3074	15	33	role	role	NOUN
cana-3074	15	34	in	in	ADP
cana-3074	15	35	developing	develop	VERB
cana-3074	15	36	students	student	NOUN
cana-3074	15	37	'	'	PART
cana-3074	15	38	spatial	spatial	ADJ
cana-3074	15	39	reasoning	reasoning	NOUN
cana-3074	15	40	and	and	CCONJ
cana-3074	15	41	problem	problem	NOUN
cana-3074	15	42	-	-	PUNCT
cana-3074	15	43	solving	solve	VERB
cana-3074	15	44	skills1	skills1	NOUN
cana-3074	15	45	.	.	PUNCT
cana-3074	16	1	chiossi	chiossi	PROPN
cana-3074	16	2	(	(	PUNCT
cana-3074	16	3	2021	2021	NUM
cana-3074	16	4	)	)	PUNCT
cana-3074	16	5	asserts	assert	VERB
cana-3074	16	6	that	that	SCONJ
cana-3074	16	7	geometry	geometry	NOUN
cana-3074	16	8	holds	hold	VERB
cana-3074	16	9	significance	significance	NOUN
cana-3074	16	10	for	for	ADP
cana-3074	16	11	mathematics	mathematics	NOUN
cana-3074	16	12	undergraduates	undergraduate	NOUN
cana-3074	16	13	as	as	SCONJ
cana-3074	16	14	it	it	PRON
cana-3074	16	15	lays	lay	VERB
cana-3074	16	16	a	a	DET
cana-3074	16	17	strong	strong	ADJ
cana-3074	16	18	foundation	foundation	NOUN
cana-3074	16	19	for	for	ADP
cana-3074	16	20	mathematical	mathematical	ADJ
cana-3074	16	21	thinking	thinking	NOUN
cana-3074	16	22	and	and	CCONJ
cana-3074	16	23	essential	essential	ADJ
cana-3074	16	24	visualization	visualization	NOUN
cana-3074	16	25	skills	skill	NOUN
cana-3074	16	26	,	,	PUNCT
cana-3074	16	27	crucial	crucial	ADJ
cana-3074	16	28	for	for	ADP
cana-3074	16	29	success	success	NOUN
cana-3074	16	30	in	in	ADP
cana-3074	16	31	higher	high	ADJ
cana-3074	16	32	-	-	PUNCT
cana-3074	16	33	level	level	NOUN
cana-3074	16	34	mathematics	mathematic	NOUN
cana-3074	16	35	.	.	PUNCT
cana-3074	17	1	however	however	ADV
cana-3074	17	2	,	,	PUNCT
cana-3074	17	3	geometry	geometry	NOUN
cana-3074	17	4	poses	pose	VERB
cana-3074	17	5	a	a	DET
cana-3074	17	6	challenge	challenge	NOUN
cana-3074	17	7	for	for	ADP
cana-3074	17	8	many	many	ADJ
cana-3074	17	9	students	student	NOUN
cana-3074	17	10	worldwide	worldwide	ADV
cana-3074	17	11	,	,	PUNCT
cana-3074	17	12	including	include	VERB
cana-3074	17	13	those	those	PRON
cana-3074	17	14	in	in	ADP
cana-3074	17	15	indonesia	indonesia	PROPN
cana-3074	17	16	2	2	NUM
cana-3074	17	17	.	.	PUNCT
cana-3074	18	1	students	student	NOUN
cana-3074	18	2	often	often	ADV
cana-3074	18	3	struggle	struggle	VERB
cana-3074	18	4	to	to	PART
cana-3074	18	5	grasp	grasp	VERB
cana-3074	18	6	geometry	geometry	NOUN
cana-3074	18	7	concepts	concept	NOUN
cana-3074	18	8	due	due	ADP
cana-3074	18	9	to	to	ADP
cana-3074	18	10	a	a	DET
cana-3074	18	11	lack	lack	NOUN
cana-3074	18	12	of	of	ADP
cana-3074	18	13	fundamental	fundamental	ADJ
cana-3074	18	14	knowledge	knowledge	NOUN
cana-3074	18	15	and	and	CCONJ
cana-3074	18	16	limited	limited	ADJ
cana-3074	18	17	geometry	geometry	NOUN
cana-3074	18	18	thinking	thinking	NOUN
cana-3074	18	19	skills	skill	VERB
cana-3074	18	20	3	3	NUM
cana-3074	18	21	.	.	PUNCT
cana-3074	18	22	according	accord	VERB
cana-3074	18	23	to	to	ADP
cana-3074	18	24	data	datum	NOUN
cana-3074	18	25	from	from	ADP
cana-3074	18	26	the	the	DET
cana-3074	18	27	program	program	NOUN
cana-3074	18	28	for	for	ADP
cana-3074	18	29	international	international	ADJ
cana-3074	18	30	student	student	NOUN
cana-3074	18	31	assessment	assessment	NOUN
cana-3074	18	32	(	(	PUNCT
cana-3074	18	33	pisa	pisa	PROPN
cana-3074	18	34	)	)	PUNCT
cana-3074	18	35	2022	2022	NUM
cana-3074	18	36	,	,	PUNCT
cana-3074	18	37	indonesia	indonesia	PROPN
cana-3074	18	38	's	's	PART
cana-3074	18	39	mathematics	mathematics	NOUN
cana-3074	18	40	proficiency	proficiency	NOUN
cana-3074	18	41	,	,	PUNCT
cana-3074	18	42	particularly	particularly	ADV
cana-3074	18	43	in	in	ADP
cana-3074	18	44	geometry	geometry	NOUN
cana-3074	18	45	,	,	PUNCT
cana-3074	18	46	tends	tend	VERB
cana-3074	18	47	to	to	PART
cana-3074	18	48	be	be	AUX
cana-3074	18	49	below	below	ADP
cana-3074	18	50	the	the	DET
cana-3074	18	51	oecd	oecd	PROPN
cana-3074	18	52	average	average	NOUN
cana-3074	18	53	,	,	PUNCT
cana-3074	18	54	with	with	ADP
cana-3074	18	55	indonesia	indonesia	PROPN
cana-3074	18	56	ranking	rank	VERB
cana-3074	18	57	63rd	63rd	NOUN
cana-3074	18	58	out	out	ADP
cana-3074	18	59	of	of	ADP
cana-3074	18	60	77	77	NUM
cana-3074	18	61	assessed	assessed	ADJ
cana-3074	18	62	countries	country	NOUN
cana-3074	18	63	4	4	NUM
cana-3074	18	64	.	.	SYM
cana-3074	18	65	1	1	NUM
cana-3074	18	66	chiossi	chiossi	ADJ
cana-3074	18	67	2021	2021	NUM
cana-3074	18	68	;	;	PUNCT
cana-3074	18	69	“	"	PUNCT
cana-3074	18	70	geometry	geometry	NOUN
cana-3074	18	71	”	"	PUNCT
cana-3074	18	72	2023	2023	NUM
cana-3074	18	73	2	2	NUM
cana-3074	18	74	naufal	naufal	NOUN
cana-3074	18	75	et	et	PROPN
cana-3074	18	76	al	al	PROPN
cana-3074	18	77	.	.	PROPN
cana-3074	18	78	2020	2020	NUM
cana-3074	18	79	;	;	PUNCT
cana-3074	18	80	purnomo	purnomo	VERB
cana-3074	18	81	2017	2017	NUM
cana-3074	18	82	3	3	NUM
cana-3074	18	83	ebissa	ebissa	NOUN
cana-3074	18	84	2020	2020	NUM
cana-3074	18	85	;	;	PUNCT
cana-3074	18	86	naufal	naufal	VERB
cana-3074	18	87	et	et	PROPN
cana-3074	18	88	al	al	PROPN
cana-3074	18	89	.	.	PROPN
cana-3074	18	90	2020	2020	NUM
cana-3074	18	91	4	4	NUM
cana-3074	18	92	oecd	oecd	PROPN
cana-3074	18	93	2023	2023	NUM
cana-3074	18	94	communications	communication	NOUN
cana-3074	18	95	on	on	ADP
cana-3074	18	96	applied	apply	VERB
cana-3074	18	97	nonlinear	nonlinear	ADJ
cana-3074	18	98	analysis	analysis	NOUN
cana-3074	18	99	issn	issn	NOUN
cana-3074	18	100	:	:	PUNCT
cana-3074	18	101	1074	1074	NUM
cana-3074	18	102	-	-	PUNCT
cana-3074	18	103	133x	133x	NUM
cana-3074	18	104	vol	vol	NOUN
cana-3074	18	105	32	32	NUM
cana-3074	18	106	no	no	NOUN
cana-3074	18	107	.	.	PUNCT
cana-3074	19	1	5s	5s	NUM
cana-3074	19	2	(	(	PUNCT
cana-3074	19	3	2025	2025	NUM
cana-3074	19	4	)	)	PUNCT
cana-3074	19	5	269	269	NUM
cana-3074	19	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	19	7	another	another	DET
cana-3074	19	8	study	study	NOUN
cana-3074	19	9	by	by	ADP
cana-3074	19	10	putri	putri	PROPN
cana-3074	19	11	and	and	CCONJ
cana-3074	19	12	nopriana	nopriana	PROPN
cana-3074	19	13	(	(	PUNCT
cana-3074	19	14	2019	2019	NUM
cana-3074	19	15	)	)	PUNCT
cana-3074	19	16	reveals	reveal	VERB
cana-3074	19	17	that	that	SCONJ
cana-3074	19	18	based	base	VERB
cana-3074	19	19	on	on	ADP
cana-3074	19	20	the	the	DET
cana-3074	19	21	levels	level	NOUN
cana-3074	19	22	of	of	ADP
cana-3074	19	23	geometric	geometric	ADJ
cana-3074	19	24	thinking	thinking	NOUN
cana-3074	19	25	using	use	VERB
cana-3074	19	26	the	the	DET
cana-3074	19	27	van	van	PROPN
cana-3074	19	28	hiele	hiele	PROPN
cana-3074	19	29	theory	theory	NOUN
cana-3074	19	30	,	,	PUNCT
cana-3074	19	31	approximately	approximately	ADV
cana-3074	19	32	15	15	NUM
cana-3074	19	33	%	%	NOUN
cana-3074	19	34	of	of	ADP
cana-3074	19	35	mathematics	mathematics	NOUN
cana-3074	19	36	undergraduates	undergraduate	NOUN
cana-3074	19	37	achieve	achieve	VERB
cana-3074	19	38	pre	pre	ADJ
cana-3074	19	39	-	-	ADJ
cana-3074	19	40	geometric	geometric	ADJ
cana-3074	19	41	thinking	thinking	NOUN
cana-3074	19	42	,	,	PUNCT
cana-3074	19	43	50	50	NUM
cana-3074	19	44	%	%	NOUN
cana-3074	19	45	are	be	AUX
cana-3074	19	46	at	at	ADP
cana-3074	19	47	the	the	DET
cana-3074	19	48	visualization	visualization	NOUN
cana-3074	19	49	level	level	NOUN
cana-3074	19	50	,	,	PUNCT
cana-3074	19	51	and	and	CCONJ
cana-3074	19	52	35	35	NUM
cana-3074	19	53	%	%	NOUN
cana-3074	19	54	are	be	AUX
cana-3074	19	55	at	at	ADP
cana-3074	19	56	the	the	DET
cana-3074	19	57	analysis	analysis	NOUN
cana-3074	19	58	level	level	NOUN
cana-3074	19	59	in	in	ADP
cana-3074	19	60	plane	plane	NOUN
cana-3074	19	61	analytical	analytical	ADJ
cana-3074	19	62	geometry	geometry	NOUN
cana-3074	19	63	,	,	PUNCT
cana-3074	19	64	particularly	particularly	ADV
cana-3074	19	65	concerning	concern	VERB
cana-3074	19	66	triangles	triangle	NOUN
cana-3074	19	67	.	.	PUNCT
cana-3074	20	1	the	the	DET
cana-3074	20	2	highest	high	ADJ
cana-3074	20	3	attained	attain	VERB
cana-3074	20	4	level	level	NOUN
cana-3074	20	5	of	of	ADP
cana-3074	20	6	geometric	geometric	ADJ
cana-3074	20	7	thinking	thinking	NOUN
cana-3074	20	8	is	be	AUX
cana-3074	20	9	analysis	analysis	NOUN
cana-3074	20	10	.	.	PUNCT
cana-3074	21	1	this	this	PRON
cana-3074	21	2	is	be	AUX
cana-3074	21	3	supported	support	VERB
cana-3074	21	4	by	by	ADP
cana-3074	21	5	observations	observation	NOUN
cana-3074	21	6	conducted	conduct	VERB
cana-3074	21	7	by	by	ADP
cana-3074	21	8	renanda	renanda	NOUN
cana-3074	21	9	et	et	PROPN
cana-3074	21	10	al	al	PROPN
cana-3074	21	11	.	.	PROPN
cana-3074	22	1	(	(	PUNCT
cana-3074	22	2	2023	2023	NUM
cana-3074	22	3	)	)	PUNCT
cana-3074	22	4	,	,	PUNCT
cana-3074	22	5	indicating	indicate	VERB
cana-3074	22	6	that	that	SCONJ
cana-3074	22	7	the	the	DET
cana-3074	22	8	van	van	PROPN
cana-3074	22	9	hiele	hiele	PROPN
cana-3074	22	10	levels	level	NOUN
cana-3074	22	11	among	among	ADP
cana-3074	22	12	mathematics	mathematics	NOUN
cana-3074	22	13	undergraduates	undergraduate	NOUN
cana-3074	22	14	are	be	AUX
cana-3074	22	15	still	still	ADV
cana-3074	22	16	primarily	primarily	ADV
cana-3074	22	17	at	at	ADP
cana-3074	22	18	the	the	DET
cana-3074	22	19	initial	initial	ADJ
cana-3074	22	20	stages	stage	NOUN
cana-3074	22	21	and	and	CCONJ
cana-3074	22	22	have	have	AUX
cana-3074	22	23	not	not	PART
cana-3074	22	24	fully	fully	ADV
cana-3074	22	25	developed	develop	VERB
cana-3074	22	26	.	.	PUNCT
cana-3074	23	1	widada	widada	PROPN
cana-3074	23	2	et	et	PROPN
cana-3074	23	3	al	al	PROPN
cana-3074	23	4	.	.	PROPN
cana-3074	24	1	(	(	PUNCT
cana-3074	24	2	2019	2019	NUM
cana-3074	24	3	)	)	PUNCT
cana-3074	24	4	stated	state	VERB
cana-3074	24	5	that	that	SCONJ
cana-3074	24	6	one	one	NUM
cana-3074	24	7	contributing	contribute	VERB
cana-3074	24	8	factor	factor	NOUN
cana-3074	24	9	to	to	ADP
cana-3074	24	10	geometric	geometric	ADJ
cana-3074	24	11	thinking	thinking	NOUN
cana-3074	24	12	ability	ability	NOUN
cana-3074	24	13	is	be	AUX
cana-3074	24	14	the	the	DET
cana-3074	24	15	abstraction	abstraction	NOUN
cana-3074	24	16	process	process	NOUN
cana-3074	24	17	.	.	PUNCT
cana-3074	25	1	students	student	NOUN
cana-3074	25	2	struggle	struggle	VERB
cana-3074	25	3	to	to	PART
cana-3074	25	4	grasp	grasp	VERB
cana-3074	25	5	geometric	geometric	ADJ
cana-3074	25	6	concepts	concept	NOUN
cana-3074	25	7	because	because	SCONJ
cana-3074	25	8	they	they	PRON
cana-3074	25	9	involve	involve	VERB
cana-3074	25	10	relatively	relatively	ADV
cana-3074	25	11	challenging	challenging	ADJ
cana-3074	25	12	processes	process	NOUN
cana-3074	25	13	such	such	ADJ
cana-3074	25	14	as	as	ADP
cana-3074	25	15	abstraction	abstraction	NOUN
cana-3074	25	16	.	.	PUNCT
cana-3074	26	1	trimurtini	trimurtini	NOUN
cana-3074	26	2	et	et	PROPN
cana-3074	26	3	al	al	PROPN
cana-3074	26	4	.	.	PROPN
cana-3074	27	1	(	(	PUNCT
cana-3074	27	2	2023	2023	NUM
cana-3074	27	3	)	)	PUNCT
cana-3074	27	4	also	also	ADV
cana-3074	27	5	found	find	VERB
cana-3074	27	6	that	that	SCONJ
cana-3074	27	7	the	the	DET
cana-3074	27	8	lack	lack	NOUN
cana-3074	27	9	of	of	ADP
cana-3074	27	10	geometric	geometric	ADJ
cana-3074	27	11	thinking	thinking	NOUN
cana-3074	27	12	ability	ability	NOUN
cana-3074	27	13	is	be	AUX
cana-3074	27	14	due	due	ADJ
cana-3074	27	15	to	to	ADP
cana-3074	27	16	students	student	NOUN
cana-3074	27	17	'	'	PART
cana-3074	27	18	inability	inability	NOUN
cana-3074	27	19	to	to	PART
cana-3074	27	20	think	think	VERB
cana-3074	27	21	abstractly	abstractly	ADV
cana-3074	27	22	about	about	ADP
cana-3074	27	23	geometric	geometric	ADJ
cana-3074	27	24	concepts	concept	NOUN
cana-3074	27	25	and	and	CCONJ
cana-3074	27	26	solve	solve	VERB
cana-3074	27	27	complex	complex	ADJ
cana-3074	27	28	problems	problem	NOUN
cana-3074	27	29	5	5	NUM
cana-3074	27	30	.	.	PUNCT
cana-3074	27	31	in	in	ADP
cana-3074	27	32	geometry	geometry	NOUN
cana-3074	27	33	learning	learning	NOUN
cana-3074	27	34	,	,	PUNCT
cana-3074	27	35	mitchelmore	mitchelmore	NOUN
cana-3074	27	36	and	and	CCONJ
cana-3074	27	37	white	white	ADJ
cana-3074	27	38	(	(	PUNCT
cana-3074	27	39	2007	2007	NUM
cana-3074	27	40	)	)	PUNCT
cana-3074	27	41	identified	identify	VERB
cana-3074	27	42	two	two	NUM
cana-3074	27	43	main	main	ADJ
cana-3074	27	44	theories	theory	NOUN
cana-3074	27	45	related	relate	VERB
cana-3074	27	46	to	to	ADP
cana-3074	27	47	the	the	DET
cana-3074	27	48	abstraction	abstraction	NOUN
cana-3074	27	49	process	process	NOUN
cana-3074	27	50	:	:	PUNCT
cana-3074	27	51	empirical	empirical	ADJ
cana-3074	27	52	abstraction	abstraction	NOUN
cana-3074	27	53	and	and	CCONJ
cana-3074	27	54	theoretical	theoretical	ADJ
cana-3074	27	55	abstraction	abstraction	NOUN
cana-3074	27	56	.	.	PUNCT
cana-3074	28	1	empirical	empirical	ADJ
cana-3074	28	2	abstraction	abstraction	NOUN
cana-3074	28	3	focus	focus	NOUN
cana-3074	28	4	on	on	ADP
cana-3074	28	5	recognizing	recognize	VERB
cana-3074	28	6	similarities	similarity	NOUN
cana-3074	28	7	and	and	CCONJ
cana-3074	28	8	then	then	ADV
cana-3074	28	9	translating	translate	VERB
cana-3074	28	10	these	these	DET
cana-3074	28	11	similarities	similarity	NOUN
cana-3074	28	12	into	into	ADP
cana-3074	28	13	new	new	ADJ
cana-3074	28	14	mental	mental	ADJ
cana-3074	28	15	constructs	construct	NOUN
cana-3074	28	16	,	,	PUNCT
cana-3074	28	17	resulting	result	VERB
cana-3074	28	18	in	in	ADP
cana-3074	28	19	concept	concept	NOUN
cana-3074	28	20	formation	formation	NOUN
cana-3074	28	21	.	.	PUNCT
cana-3074	29	1	additionally	additionally	ADV
cana-3074	29	2	,	,	PUNCT
cana-3074	29	3	theoretical	theoretical	ADJ
cana-3074	29	4	abstraction	abstraction	NOUN
cana-3074	29	5	,	,	PUNCT
cana-3074	29	6	focuses	focus	VERB
cana-3074	29	7	on	on	ADP
cana-3074	29	8	forming	form	VERB
cana-3074	29	9	concepts	concept	NOUN
cana-3074	29	10	consistent	consistent	ADJ
cana-3074	29	11	with	with	ADP
cana-3074	29	12	specific	specific	ADJ
cana-3074	29	13	theories	theory	NOUN
cana-3074	29	14	which	which	PRON
cana-3074	29	15	requires	require	VERB
cana-3074	29	16	a	a	DET
cana-3074	29	17	deeper	deep	ADJ
cana-3074	29	18	understanding	understanding	NOUN
cana-3074	29	19	and	and	CCONJ
cana-3074	29	20	generalization	generalization	NOUN
cana-3074	29	21	of	of	ADP
cana-3074	29	22	concrete	concrete	ADJ
cana-3074	29	23	information	information	NOUN
cana-3074	29	24	6	6	NUM
cana-3074	29	25	.	.	PUNCT
cana-3074	30	1	furthermore	furthermore	ADV
cana-3074	30	2	,	,	PUNCT
cana-3074	30	3	based	base	VERB
cana-3074	30	4	on	on	ADP
cana-3074	30	5	preliminary	preliminary	ADJ
cana-3074	30	6	observations	observation	NOUN
cana-3074	30	7	conducted	conduct	VERB
cana-3074	30	8	by	by	ADP
cana-3074	30	9	the	the	DET
cana-3074	30	10	researchers	researcher	NOUN
cana-3074	30	11	,	,	PUNCT
cana-3074	30	12	there	there	PRON
cana-3074	30	13	are	be	VERB
cana-3074	30	14	phenomena	phenomenon	NOUN
cana-3074	30	15	of	of	ADP
cana-3074	30	16	empirical	empirical	ADJ
cana-3074	30	17	and	and	CCONJ
cana-3074	30	18	theoretical	theoretical	ADJ
cana-3074	30	19	abstractions	abstraction	NOUN
cana-3074	30	20	playing	play	VERB
cana-3074	30	21	significant	significant	ADJ
cana-3074	30	22	roles	role	NOUN
cana-3074	30	23	in	in	ADP
cana-3074	30	24	every	every	DET
cana-3074	30	25	level	level	NOUN
cana-3074	30	26	of	of	ADP
cana-3074	30	27	van	van	PROPN
cana-3074	30	28	hiele	hiele	NOUN
cana-3074	30	29	.	.	PUNCT
cana-3074	31	1	the	the	DET
cana-3074	31	2	phenomena	phenomenon	NOUN
cana-3074	31	3	of	of	ADP
cana-3074	31	4	empirical	empirical	ADJ
cana-3074	31	5	abstraction	abstraction	NOUN
cana-3074	31	6	are	be	AUX
cana-3074	31	7	evident	evident	ADJ
cana-3074	31	8	in	in	ADP
cana-3074	31	9	students	student	NOUN
cana-3074	31	10	'	'	PART
cana-3074	31	11	ability	ability	NOUN
cana-3074	31	12	to	to	PART
cana-3074	31	13	observe	observe	VERB
cana-3074	31	14	,	,	PUNCT
cana-3074	31	15	measure	measure	NOUN
cana-3074	31	16	,	,	PUNCT
cana-3074	31	17	and	and	CCONJ
cana-3074	31	18	classify	classify	VERB
cana-3074	31	19	triangles	triangle	NOUN
cana-3074	31	20	based	base	VERB
cana-3074	31	21	on	on	ADP
cana-3074	31	22	their	their	PRON
cana-3074	31	23	properties	property	NOUN
cana-3074	31	24	when	when	SCONJ
cana-3074	31	25	working	work	VERB
cana-3074	31	26	on	on	ADP
cana-3074	31	27	van	van	PROPN
cana-3074	31	28	hiele	hiele	PROPN
cana-3074	31	29	level	level	NOUN
cana-3074	31	30	tests	test	NOUN
cana-3074	31	31	.	.	PUNCT
cana-3074	32	1	additionally	additionally	ADV
cana-3074	32	2	,	,	PUNCT
cana-3074	32	3	the	the	DET
cana-3074	32	4	phenomena	phenomenon	NOUN
cana-3074	32	5	of	of	ADP
cana-3074	32	6	theoretical	theoretical	ADJ
cana-3074	32	7	abstraction	abstraction	NOUN
cana-3074	32	8	are	be	AUX
cana-3074	32	9	depicted	depict	VERB
cana-3074	32	10	in	in	ADP
cana-3074	32	11	students	student	NOUN
cana-3074	32	12	'	'	PART
cana-3074	32	13	ability	ability	NOUN
cana-3074	32	14	to	to	PART
cana-3074	32	15	explain	explain	VERB
cana-3074	32	16	and	and	CCONJ
cana-3074	32	17	understand	understand	VERB
cana-3074	32	18	the	the	DET
cana-3074	32	19	conceptual	conceptual	ADJ
cana-3074	32	20	relationships	relationship	NOUN
cana-3074	32	21	underlying	underlie	VERB
cana-3074	32	22	geometric	geometric	ADJ
cana-3074	32	23	forms	form	NOUN
cana-3074	32	24	,	,	PUNCT
cana-3074	32	25	also	also	ADV
cana-3074	32	26	observed	observe	VERB
cana-3074	32	27	in	in	ADP
cana-3074	32	28	the	the	DET
cana-3074	32	29	van	van	PROPN
cana-3074	32	30	hiele	hiele	PROPN
cana-3074	32	31	level	level	NOUN
cana-3074	32	32	test	test	NOUN
cana-3074	32	33	process	process	NOUN
cana-3074	32	34	.	.	PUNCT
cana-3074	33	1	this	this	PRON
cana-3074	33	2	aligns	align	VERB
cana-3074	33	3	with	with	ADP
cana-3074	33	4	studies	study	NOUN
cana-3074	33	5	conducted	conduct	VERB
cana-3074	33	6	by	by	ADP
cana-3074	33	7	nurhasanah	nurhasanah	PROPN
cana-3074	33	8	et	et	PROPN
cana-3074	33	9	al	al	PROPN
cana-3074	33	10	.	.	PROPN
cana-3074	34	1	(	(	PUNCT
cana-3074	34	2	2013	2013	NUM
cana-3074	34	3	)	)	PUNCT
cana-3074	34	4	,	,	PUNCT
cana-3074	34	5	which	which	PRON
cana-3074	34	6	explain	explain	VERB
cana-3074	34	7	the	the	DET
cana-3074	34	8	aspects	aspect	NOUN
cana-3074	34	9	of	of	ADP
cana-3074	34	10	geometrical	geometrical	ADJ
cana-3074	34	11	abstraction	abstraction	NOUN
cana-3074	34	12	based	base	VERB
cana-3074	34	13	on	on	ADP
cana-3074	34	14	empirical	empirical	ADJ
cana-3074	34	15	and	and	CCONJ
cana-3074	34	16	theoretical	theoretical	ADJ
cana-3074	34	17	abstractions	abstraction	NOUN
cana-3074	34	18	at	at	ADP
cana-3074	34	19	each	each	DET
cana-3074	34	20	van	van	PROPN
cana-3074	34	21	hiele	hiele	PROPN
cana-3074	34	22	level	level	NOUN
cana-3074	34	23	in	in	ADP
cana-3074	34	24	geometry	geometry	NOUN
cana-3074	34	25	learning	learning	NOUN
cana-3074	34	26	.	.	PUNCT
cana-3074	35	1	therefore	therefore	ADV
cana-3074	35	2	,	,	PUNCT
cana-3074	35	3	to	to	PART
cana-3074	35	4	gain	gain	VERB
cana-3074	35	5	a	a	DET
cana-3074	35	6	deeper	deep	ADJ
cana-3074	35	7	and	and	CCONJ
cana-3074	35	8	comprehensive	comprehensive	ADJ
cana-3074	35	9	understanding	understanding	NOUN
cana-3074	35	10	of	of	ADP
cana-3074	35	11	mathematics	mathematic	NOUN
cana-3074	35	12	undergraduates	undergraduate	NOUN
cana-3074	35	13	'	'	PART
cana-3074	35	14	geometrical	geometrical	ADJ
cana-3074	35	15	abstraction	abstraction	NOUN
cana-3074	35	16	abilities	ability	NOUN
cana-3074	35	17	at	at	ADP
cana-3074	35	18	each	each	DET
cana-3074	35	19	van	van	PROPN
cana-3074	35	20	hiele	hiele	PROPN
cana-3074	35	21	level	level	NOUN
cana-3074	35	22	,	,	PUNCT
cana-3074	35	23	this	this	DET
cana-3074	35	24	research	research	NOUN
cana-3074	35	25	aims	aim	VERB
cana-3074	35	26	to	to	PART
cana-3074	35	27	analyze	analyze	VERB
cana-3074	35	28	and	and	CCONJ
cana-3074	35	29	provide	provide	VERB
cana-3074	35	30	a	a	DET
cana-3074	35	31	description	description	NOUN
cana-3074	35	32	of	of	ADP
cana-3074	35	33	geometrical	geometrical	ADJ
cana-3074	35	34	abstraction	abstraction	NOUN
cana-3074	35	35	at	at	ADP
cana-3074	35	36	each	each	DET
cana-3074	35	37	van	van	PROPN
cana-3074	35	38	hiele	hiele	PROPN
cana-3074	35	39	level	level	NOUN
cana-3074	35	40	among	among	ADP
cana-3074	35	41	mathematics	mathematic	NOUN
cana-3074	35	42	undergraduates	undergraduate	NOUN
cana-3074	35	43	.	.	PUNCT
cana-3074	36	1	literature	literature	NOUN
cana-3074	36	2	review	review	PROPN
cana-3074	36	3	van	van	PROPN
cana-3074	36	4	hiele	hiele	PROPN
cana-3074	36	5	levels	level	NOUN
cana-3074	36	6	in	in	ADP
cana-3074	36	7	the	the	DET
cana-3074	36	8	late	late	ADJ
cana-3074	36	9	1950s	1950	NOUN
cana-3074	36	10	in	in	ADP
cana-3074	36	11	the	the	DET
cana-3074	36	12	netherlands	netherlands	PROPN
cana-3074	36	13	,	,	PUNCT
cana-3074	36	14	dr	dr	PROPN
cana-3074	36	15	.	.	PROPN
cana-3074	36	16	pierre	pierre	PROPN
cana-3074	36	17	van	van	PROPN
cana-3074	36	18	hiele	hiele	PROPN
cana-3074	36	19	and	and	CCONJ
cana-3074	36	20	his	his	PRON
cana-3074	36	21	wife	wife	NOUN
cana-3074	36	22	,	,	PUNCT
cana-3074	36	23	dr	dr	PROPN
cana-3074	36	24	.	.	PROPN
cana-3074	36	25	dina	dina	PROPN
cana-3074	36	26	van	van	PROPN
cana-3074	36	27	hiele	hiele	PROPN
cana-3074	36	28	-	-	PUNCT
cana-3074	36	29	geldof	geldof	NOUN
cana-3074	36	30	,	,	PUNCT
cana-3074	36	31	after	after	ADP
cana-3074	36	32	studying	study	VERB
cana-3074	36	33	the	the	DET
cana-3074	36	34	challenges	challenge	NOUN
cana-3074	36	35	students	student	NOUN
cana-3074	36	36	faced	face	VERB
cana-3074	36	37	in	in	ADP
cana-3074	36	38	learning	learn	VERB
cana-3074	36	39	geometry	geometry	NOUN
cana-3074	36	40	,	,	PUNCT
cana-3074	36	41	introduced	introduce	VERB
cana-3074	36	42	the	the	DET
cana-3074	36	43	hierarchical	hierarchical	ADJ
cana-3074	36	44	levels	level	NOUN
cana-3074	36	45	of	of	ADP
cana-3074	36	46	geometric	geometric	ADJ
cana-3074	36	47	thinking	thinking	NOUN
cana-3074	36	48	known	know	VERB
cana-3074	36	49	as	as	ADP
cana-3074	36	50	the	the	DET
cana-3074	36	51	"	"	PUNCT
cana-3074	36	52	van	van	PROPN
cana-3074	36	53	hiele	hiele	PROPN
cana-3074	36	54	model	model	NOUN
cana-3074	36	55	"	"	PUNCT
cana-3074	36	56	or	or	CCONJ
cana-3074	36	57	"	"	PUNCT
cana-3074	36	58	van	van	PROPN
cana-3074	36	59	hiele	hiele	PROPN
cana-3074	36	60	theory	theory	NOUN
cana-3074	36	61	"	"	PUNCT
cana-3074	36	62	7	7	NUM
cana-3074	36	63	.	.	PUNCT
cana-3074	36	64	van	van	PROPN
cana-3074	36	65	hiele	hiele	PROPN
cana-3074	36	66	's	's	PART
cana-3074	36	67	theory	theory	NOUN
cana-3074	36	68	outlines	outline	VERB
cana-3074	36	69	five	five	NUM
cana-3074	36	70	levels	level	NOUN
cana-3074	36	71	of	of	ADP
cana-3074	36	72	geometric	geometric	ADJ
cana-3074	36	73	understanding	understanding	NOUN
cana-3074	36	74	that	that	PRON
cana-3074	36	75	describe	describe	VERB
cana-3074	36	76	the	the	DET
cana-3074	36	77	stages	stage	NOUN
cana-3074	36	78	of	of	ADP
cana-3074	36	79	students	student	NOUN
cana-3074	36	80	'	'	PART
cana-3074	36	81	geometric	geometric	ADJ
cana-3074	36	82	comprehension	comprehension	NOUN
cana-3074	36	83	.	.	PUNCT
cana-3074	37	1	these	these	DET
cana-3074	37	2	levels	level	NOUN
cana-3074	37	3	,	,	PUNCT
cana-3074	37	4	as	as	SCONJ
cana-3074	37	5	proposed	propose	VERB
cana-3074	37	6	by	by	ADP
cana-3074	37	7	van	van	PROPN
cana-3074	37	8	hiele	hiele	PROPN
cana-3074	37	9	(	(	PUNCT
cana-3074	37	10	1999	1999	NUM
cana-3074	37	11	):	):	PUNCT
cana-3074	37	12	1	1	X
cana-3074	37	13	)	)	PUNCT
cana-3074	37	14	visualization	visualization	NOUN
cana-3074	37	15	:	:	PUNCT
cana-3074	37	16	students	student	NOUN
cana-3074	37	17	can	can	AUX
cana-3074	37	18	identify	identify	VERB
cana-3074	37	19	basic	basic	ADJ
cana-3074	37	20	shapes	shape	NOUN
cana-3074	37	21	like	like	ADP
cana-3074	37	22	5	5	NUM
cana-3074	37	23	pavlovičová	pavlovičová	NOUN
cana-3074	37	24	&	&	CCONJ
cana-3074	37	25	bočková	bočková	PROPN
cana-3074	37	26	2021	2021	NUM
cana-3074	37	27	6	6	NUM
cana-3074	37	28	mitchelmore	mitchelmore	NOUN
cana-3074	37	29	&	&	CCONJ
cana-3074	37	30	white	white	PROPN
cana-3074	37	31	2007	2007	NUM
cana-3074	37	32	;	;	PUNCT
cana-3074	37	33	nurhasanah	nurhasanah	NOUN
cana-3074	37	34	et	et	PROPN
cana-3074	37	35	al	al	PROPN
cana-3074	37	36	.	.	PROPN
cana-3074	37	37	2013	2013	NUM
cana-3074	37	38	7	7	NUM
cana-3074	37	39	senk	senk	NOUN
cana-3074	37	40	et	et	PROPN
cana-3074	37	41	al	al	PROPN
cana-3074	37	42	.	.	PROPN
cana-3074	37	43	2022	2022	NUM
cana-3074	37	44	communications	communication	NOUN
cana-3074	37	45	on	on	ADP
cana-3074	37	46	applied	apply	VERB
cana-3074	37	47	nonlinear	nonlinear	ADJ
cana-3074	37	48	analysis	analysis	NOUN
cana-3074	37	49	issn	issn	NOUN
cana-3074	37	50	:	:	PUNCT
cana-3074	37	51	1074	1074	NUM
cana-3074	37	52	-	-	PUNCT
cana-3074	37	53	133x	133x	NUM
cana-3074	37	54	vol	vol	NOUN
cana-3074	37	55	32	32	NUM
cana-3074	37	56	no	no	NOUN
cana-3074	37	57	.	.	PUNCT
cana-3074	38	1	5s	5s	NUM
cana-3074	38	2	(	(	PUNCT
cana-3074	38	3	2025	2025	NUM
cana-3074	38	4	)	)	PUNCT
cana-3074	38	5	270	270	NUM
cana-3074	38	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	38	7	circles	circle	NOUN
cana-3074	38	8	or	or	CCONJ
cana-3074	38	9	squares	square	NOUN
cana-3074	38	10	but	but	CCONJ
cana-3074	38	11	may	may	AUX
cana-3074	38	12	not	not	PART
cana-3074	38	13	have	have	VERB
cana-3074	38	14	a	a	DET
cana-3074	38	15	clear	clear	ADJ
cana-3074	38	16	understanding	understanding	NOUN
cana-3074	38	17	of	of	ADP
cana-3074	38	18	their	their	PRON
cana-3074	38	19	defining	define	VERB
cana-3074	38	20	characteristics	characteristic	NOUN
cana-3074	38	21	or	or	CCONJ
cana-3074	38	22	the	the	DET
cana-3074	38	23	ability	ability	NOUN
cana-3074	38	24	to	to	PART
cana-3074	38	25	distinguish	distinguish	VERB
cana-3074	38	26	them	they	PRON
cana-3074	38	27	from	from	ADP
cana-3074	38	28	similar	similar	ADJ
cana-3074	38	29	shapes	shape	NOUN
cana-3074	38	30	,	,	PUNCT
cana-3074	38	31	2	2	X
cana-3074	38	32	)	)	PUNCT
cana-3074	38	33	analysis	analysis	NOUN
cana-3074	38	34	:	:	PUNCT
cana-3074	38	35	students	student	NOUN
cana-3074	38	36	begin	begin	VERB
cana-3074	38	37	to	to	PART
cana-3074	38	38	notice	notice	VERB
cana-3074	38	39	specific	specific	ADJ
cana-3074	38	40	details	detail	NOUN
cana-3074	38	41	of	of	ADP
cana-3074	38	42	geometric	geometric	ADJ
cana-3074	38	43	shapes	shape	NOUN
cana-3074	38	44	,	,	PUNCT
cana-3074	38	45	such	such	ADJ
cana-3074	38	46	as	as	ADP
cana-3074	38	47	the	the	DET
cana-3074	38	48	number	number	NOUN
cana-3074	38	49	of	of	ADP
cana-3074	38	50	sides	side	NOUN
cana-3074	38	51	and	and	CCONJ
cana-3074	38	52	angles	angle	NOUN
cana-3074	38	53	in	in	ADP
cana-3074	38	54	a	a	DET
cana-3074	38	55	triangle	triangle	NOUN
cana-3074	38	56	,	,	PUNCT
cana-3074	38	57	but	but	CCONJ
cana-3074	38	58	may	may	AUX
cana-3074	38	59	not	not	PART
cana-3074	38	60	fully	fully	ADV
cana-3074	38	61	understand	understand	VERB
cana-3074	38	62	the	the	DET
cana-3074	38	63	relationships	relationship	NOUN
cana-3074	38	64	between	between	ADP
cana-3074	38	65	different	different	ADJ
cana-3074	38	66	types	type	NOUN
cana-3074	38	67	of	of	ADP
cana-3074	38	68	triangles	triangle	NOUN
cana-3074	38	69	,	,	PUNCT
cana-3074	38	70	3	3	X
cana-3074	38	71	)	)	PUNCT
cana-3074	38	72	informal	informal	ADJ
cana-3074	38	73	deduction	deduction	NOUN
cana-3074	38	74	:	:	PUNCT
cana-3074	38	75	students	student	NOUN
cana-3074	38	76	start	start	VERB
cana-3074	38	77	to	to	PART
cana-3074	38	78	define	define	VERB
cana-3074	38	79	shapes	shape	NOUN
cana-3074	38	80	accurately	accurately	ADV
cana-3074	38	81	and	and	CCONJ
cana-3074	38	82	understand	understand	VERB
cana-3074	38	83	how	how	SCONJ
cana-3074	38	84	they	they	PRON
cana-3074	38	85	relate	relate	VERB
cana-3074	38	86	to	to	ADP
cana-3074	38	87	one	one	NUM
cana-3074	38	88	another	another	DET
cana-3074	38	89	,	,	PUNCT
cana-3074	38	90	4	4	X
cana-3074	38	91	)	)	PUNCT
cana-3074	38	92	formal	formal	ADJ
cana-3074	38	93	deduction	deduction	NOUN
cana-3074	38	94	:	:	PUNCT
cana-3074	38	95	students	student	NOUN
cana-3074	38	96	develop	develop	VERB
cana-3074	38	97	deductive	deductive	ADJ
cana-3074	38	98	reasoning	reasoning	NOUN
cana-3074	38	99	skills	skill	NOUN
cana-3074	38	100	,	,	PUNCT
cana-3074	38	101	enabling	enable	VERB
cana-3074	38	102	them	they	PRON
cana-3074	38	103	to	to	PART
cana-3074	38	104	understand	understand	VERB
cana-3074	38	105	and	and	CCONJ
cana-3074	38	106	prove	prove	VERB
cana-3074	38	107	geometric	geometric	ADJ
cana-3074	38	108	results	result	NOUN
cana-3074	38	109	while	while	SCONJ
cana-3074	38	110	recognizing	recognize	VERB
cana-3074	38	111	initial	initial	ADJ
cana-3074	38	112	assumptions	assumption	NOUN
cana-3074	38	113	,	,	PUNCT
cana-3074	38	114	5	5	X
cana-3074	38	115	)	)	PUNCT
cana-3074	38	116	rigor	rigor	NOUN
cana-3074	38	117	:	:	PUNCT
cana-3074	38	118	involves	involve	VERB
cana-3074	38	119	a	a	DET
cana-3074	38	120	deep	deep	ADJ
cana-3074	38	121	understanding	understanding	NOUN
cana-3074	38	122	of	of	ADP
cana-3074	38	123	the	the	DET
cana-3074	38	124	role	role	NOUN
cana-3074	38	125	of	of	ADP
cana-3074	38	126	axioms	axiom	NOUN
cana-3074	38	127	in	in	ADP
cana-3074	38	128	systematically	systematically	ADV
cana-3074	38	129	developing	develop	VERB
cana-3074	38	130	geometry	geometry	NOUN
cana-3074	38	131	.	.	PUNCT
cana-3074	39	1	van	van	PROPN
cana-3074	39	2	hiele	hiele	PROPN
cana-3074	39	3	emphasized	emphasize	VERB
cana-3074	39	4	that	that	SCONJ
cana-3074	39	5	student	student	NOUN
cana-3074	39	6	’s	’s	PART
cana-3074	39	7	progress	progress	NOUN
cana-3074	39	8	through	through	ADP
cana-3074	39	9	these	these	DET
cana-3074	39	10	levels	level	NOUN
cana-3074	39	11	hierarchically	hierarchically	ADV
cana-3074	39	12	,	,	PUNCT
cana-3074	39	13	although	although	SCONJ
cana-3074	39	14	not	not	PART
cana-3074	39	15	necessarily	necessarily	ADV
cana-3074	39	16	at	at	ADP
cana-3074	39	17	the	the	DET
cana-3074	39	18	same	same	ADJ
cana-3074	39	19	pace	pace	NOUN
cana-3074	39	20	or	or	CCONJ
cana-3074	39	21	age	age	NOUN
cana-3074	39	22	8	8	NUM
cana-3074	39	23	.	.	PUNCT
cana-3074	40	1	geometrical	geometrical	ADJ
cana-3074	40	2	abstraction	abstraction	NOUN
cana-3074	40	3	nurhasanah	nurhasanah	NOUN
cana-3074	40	4	et	et	PROPN
cana-3074	40	5	al	al	PROPN
cana-3074	40	6	.	.	PROPN
cana-3074	41	1	(	(	PUNCT
cana-3074	41	2	2013	2013	NUM
cana-3074	41	3	)	)	PUNCT
cana-3074	41	4	,	,	PUNCT
cana-3074	41	5	building	build	VERB
cana-3074	41	6	on	on	ADP
cana-3074	41	7	mitchelmore	mitchelmore	NOUN
cana-3074	41	8	and	and	CCONJ
cana-3074	41	9	white	white	ADJ
cana-3074	41	10	(	(	PUNCT
cana-3074	41	11	2007	2007	NUM
cana-3074	41	12	)	)	PUNCT
cana-3074	41	13	,	,	PUNCT
cana-3074	41	14	highlight	highlight	VERB
cana-3074	41	15	two	two	NUM
cana-3074	41	16	abstraction	abstraction	NOUN
cana-3074	41	17	processes	process	NOUN
cana-3074	41	18	in	in	ADP
cana-3074	41	19	geometry	geometry	NOUN
cana-3074	41	20	learning	learning	NOUN
cana-3074	41	21	:	:	PUNCT
cana-3074	41	22	empirical	empirical	ADJ
cana-3074	41	23	abstraction	abstraction	NOUN
cana-3074	41	24	and	and	CCONJ
cana-3074	41	25	theoretical	theoretical	ADJ
cana-3074	41	26	abstraction	abstraction	NOUN
cana-3074	41	27	.	.	PUNCT
cana-3074	42	1	empirical	empirical	ADJ
cana-3074	42	2	abstraction	abstraction	NOUN
cana-3074	42	3	relies	rely	VERB
cana-3074	42	4	on	on	ADP
cana-3074	42	5	direct	direct	ADJ
cana-3074	42	6	experiences	experience	NOUN
cana-3074	42	7	and	and	CCONJ
cana-3074	42	8	interactions	interaction	NOUN
cana-3074	42	9	with	with	ADP
cana-3074	42	10	geometric	geometric	ADJ
cana-3074	42	11	objects	object	NOUN
cana-3074	42	12	,	,	PUNCT
cana-3074	42	13	making	make	VERB
cana-3074	42	14	it	it	PRON
cana-3074	42	15	a	a	DET
cana-3074	42	16	natural	natural	ADJ
cana-3074	42	17	and	and	CCONJ
cana-3074	42	18	intuitive	intuitive	ADJ
cana-3074	42	19	process	process	NOUN
cana-3074	42	20	.	.	PUNCT
cana-3074	43	1	on	on	ADP
cana-3074	43	2	the	the	DET
cana-3074	43	3	other	other	ADJ
cana-3074	43	4	hand	hand	NOUN
cana-3074	43	5	,	,	PUNCT
cana-3074	43	6	theoretical	theoretical	ADJ
cana-3074	43	7	abstraction	abstraction	NOUN
cana-3074	43	8	involves	involve	VERB
cana-3074	43	9	a	a	DET
cana-3074	43	10	more	more	ADV
cana-3074	43	11	deliberate	deliberate	ADJ
cana-3074	43	12	and	and	CCONJ
cana-3074	43	13	structured	structured	ADJ
cana-3074	43	14	approach	approach	NOUN
cana-3074	43	15	to	to	AUX
cana-3074	43	16	concept	concept	NOUN
cana-3074	43	17	formation9	formation9	PROPN
cana-3074	43	18	.	.	PUNCT
cana-3074	44	1	it	it	PRON
cana-3074	44	2	involves	involve	VERB
cana-3074	44	3	activities	activity	NOUN
cana-3074	44	4	designed	design	VERB
cana-3074	44	5	to	to	PART
cana-3074	44	6	promote	promote	VERB
cana-3074	44	7	concept	concept	NOUN
cana-3074	44	8	formation	formation	NOUN
cana-3074	44	9	within	within	ADP
cana-3074	44	10	a	a	DET
cana-3074	44	11	specific	specific	ADJ
cana-3074	44	12	theoretical	theoretical	ADJ
cana-3074	44	13	framework	framework	NOUN
cana-3074	44	14	.	.	PUNCT
cana-3074	45	1	based	base	VERB
cana-3074	45	2	on	on	ADP
cana-3074	45	3	mitchelmore	mitchelmore	NOUN
cana-3074	45	4	and	and	CCONJ
cana-3074	45	5	white	white	ADJ
cana-3074	45	6	(	(	PUNCT
cana-3074	45	7	2007	2007	NUM
cana-3074	45	8	)	)	PUNCT
cana-3074	45	9	theories	theory	NOUN
cana-3074	45	10	of	of	ADP
cana-3074	45	11	empirical	empirical	ADJ
cana-3074	45	12	and	and	CCONJ
cana-3074	45	13	theoretical	theoretical	ADJ
cana-3074	45	14	abstraction	abstraction	NOUN
cana-3074	45	15	,	,	PUNCT
cana-3074	45	16	nurhasanah	nurhasanah	NOUN
cana-3074	45	17	et	et	PROPN
cana-3074	45	18	al	al	PROPN
cana-3074	45	19	.	.	PROPN
cana-3074	46	1	(	(	PUNCT
cana-3074	46	2	2013	2013	NUM
cana-3074	46	3	)	)	PUNCT
cana-3074	46	4	stated	state	VERB
cana-3074	46	5	that	that	SCONJ
cana-3074	46	6	abstraction	abstraction	NOUN
cana-3074	46	7	in	in	ADP
cana-3074	46	8	geometry	geometry	NOUN
cana-3074	46	9	learning	learning	NOUN
cana-3074	46	10	involves	involve	VERB
cana-3074	46	11	various	various	ADJ
cana-3074	46	12	aspects	aspect	NOUN
cana-3074	46	13	,	,	PUNCT
cana-3074	46	14	including	include	VERB
cana-3074	46	15	recognizing	recognize	VERB
cana-3074	46	16	object	object	NOUN
cana-3074	46	17	characteristics	characteristic	NOUN
cana-3074	46	18	through	through	ADP
cana-3074	46	19	direct	direct	ADJ
cana-3074	46	20	experience	experience	NOUN
cana-3074	46	21	,	,	PUNCT
cana-3074	46	22	forming	form	VERB
cana-3074	46	23	generalizations	generalization	NOUN
cana-3074	46	24	based	base	VERB
cana-3074	46	25	on	on	ADP
cana-3074	46	26	observed	observed	ADJ
cana-3074	46	27	patterns	pattern	NOUN
cana-3074	46	28	,	,	PUNCT
cana-3074	46	29	and	and	CCONJ
cana-3074	46	30	expressing	express	VERB
cana-3074	46	31	mathematical	mathematical	ADJ
cana-3074	46	32	objects	object	NOUN
cana-3074	46	33	using	use	VERB
cana-3074	46	34	symbols	symbol	NOUN
cana-3074	46	35	or	or	CCONJ
cana-3074	46	36	mathematical	mathematical	ADJ
cana-3074	46	37	language	language	NOUN
cana-3074	46	38	.	.	PUNCT
cana-3074	47	1	these	these	DET
cana-3074	47	2	aspects	aspect	NOUN
cana-3074	47	3	serve	serve	VERB
cana-3074	47	4	as	as	ADP
cana-3074	47	5	indicators	indicator	NOUN
cana-3074	47	6	to	to	PART
cana-3074	47	7	guide	guide	VERB
cana-3074	47	8	researchers	researcher	NOUN
cana-3074	47	9	in	in	ADP
cana-3074	47	10	exploring	explore	VERB
cana-3074	47	11	geometrical	geometrical	ADJ
cana-3074	47	12	abstraction	abstraction	NOUN
cana-3074	47	13	on	on	ADP
cana-3074	47	14	each	each	DET
cana-3074	47	15	van	van	PROPN
cana-3074	47	16	hiele	hiele	PROPN
cana-3074	47	17	level	level	NOUN
cana-3074	47	18	shown	show	VERB
cana-3074	47	19	in	in	ADP
cana-3074	47	20	table	table	NOUN
cana-3074	47	21	1	1	NUM
cana-3074	47	22	.	.	PUNCT
cana-3074	47	23	table	table	NOUN
cana-3074	47	24	1	1	NUM
cana-3074	47	25	.	.	PUNCT
cana-3074	48	1	indicators	indicator	NOUN
cana-3074	48	2	of	of	ADP
cana-3074	48	3	geometrical	geometrical	ADJ
cana-3074	48	4	abstraction	abstraction	NOUN
cana-3074	48	5	indicator	indicator	NOUN
cana-3074	48	6	aspect	aspect	NOUN
cana-3074	48	7	of	of	ADP
cana-3074	48	8	abstraction	abstraction	NOUN
cana-3074	48	9	direct	direct	ADJ
cana-3074	48	10	experience	experience	NOUN
cana-3074	48	11	recognizing	recognize	VERB
cana-3074	48	12	object	object	NOUN
cana-3074	48	13	characteristics	characteristic	NOUN
cana-3074	48	14	through	through	ADP
cana-3074	48	15	direct	direct	ADJ
cana-3074	48	16	experience	experience	NOUN
cana-3074	48	17	.	.	PUNCT
cana-3074	49	1	reality	reality	NOUN
cana-3074	49	2	or	or	CCONJ
cana-3074	49	3	imagination	imagination	NOUN
cana-3074	49	4	recognizing	recognize	VERB
cana-3074	49	5	object	object	NOUN
cana-3074	49	6	characteristics	characteristic	NOUN
cana-3074	49	7	,	,	PUNCT
cana-3074	49	8	whether	whether	SCONJ
cana-3074	49	9	manipulated	manipulate	VERB
cana-3074	49	10	in	in	ADP
cana-3074	49	11	real	real	ADJ
cana-3074	49	12	life	life	NOUN
cana-3074	49	13	or	or	CCONJ
cana-3074	49	14	imagined	imagine	VERB
cana-3074	49	15	.	.	PUNCT
cana-3074	50	1	pattern	pattern	NOUN
cana-3074	50	2	-	-	PUNCT
cana-3074	50	3	based	base	VERB
cana-3074	50	4	generalization	generalization	NOUN
cana-3074	50	5	forming	form	VERB
cana-3074	50	6	generalizations	generalization	NOUN
cana-3074	50	7	based	base	VERB
cana-3074	50	8	on	on	ADP
cana-3074	50	9	observed	observed	ADJ
cana-3074	50	10	patterns	pattern	NOUN
cana-3074	50	11	or	or	CCONJ
cana-3074	50	12	similarities	similarity	NOUN
cana-3074	50	13	.	.	PUNCT
cana-3074	51	1	mathematical	mathematical	ADJ
cana-3074	51	2	representation	representation	NOUN
cana-3074	51	3	expressing	express	VERB
cana-3074	51	4	mathematical	mathematical	ADJ
cana-3074	51	5	objects	object	NOUN
cana-3074	51	6	using	use	VERB
cana-3074	51	7	symbols	symbol	NOUN
cana-3074	51	8	or	or	CCONJ
cana-3074	51	9	mathematical	mathematical	ADJ
cana-3074	51	10	language	language	NOUN
cana-3074	51	11	.	.	PUNCT
cana-3074	52	1	integration	integration	NOUN
cana-3074	52	2	of	of	ADP
cana-3074	52	3	mathematical	mathematical	ADJ
cana-3074	52	4	concepts	concept	NOUN
cana-3074	52	5	building	build	VERB
cana-3074	52	6	relationships	relationship	NOUN
cana-3074	52	7	between	between	ADP
cana-3074	52	8	various	various	ADJ
cana-3074	52	9	mathematical	mathematical	ADJ
cana-3074	52	10	processes	process	NOUN
cana-3074	52	11	or	or	CCONJ
cana-3074	52	12	concepts	concept	NOUN
cana-3074	52	13	to	to	PART
cana-3074	52	14	develop	develop	VERB
cana-3074	52	15	new	new	ADJ
cana-3074	52	16	understanding	understanding	NOUN
cana-3074	52	17	.	.	PUNCT
cana-3074	53	1	real	real	ADJ
cana-3074	53	2	-	-	PUNCT
cana-3074	53	3	world	world	NOUN
cana-3074	53	4	relevance	relevance	NOUN
cana-3074	53	5	applying	apply	VERB
cana-3074	53	6	acquired	acquire	VERB
cana-3074	53	7	concepts	concept	NOUN
cana-3074	53	8	in	in	ADP
cana-3074	53	9	relevant	relevant	ADJ
cana-3074	53	10	real	real	ADJ
cana-3074	53	11	-	-	PUNCT
cana-3074	53	12	world	world	NOUN
cana-3074	53	13	contexts	contexts	NOUN
cana-3074	53	14	.	.	PUNCT
cana-3074	54	1	manipulation	manipulation	NOUN
cana-3074	54	2	of	of	ADP
cana-3074	54	3	abstract	abstract	ADJ
cana-3074	54	4	concepts	concept	NOUN
cana-3074	54	5	manipulating	manipulate	VERB
cana-3074	54	6	abstract	abstract	ADJ
cana-3074	54	7	mathematical	mathematical	ADJ
cana-3074	54	8	concepts	concept	NOUN
cana-3074	54	9	to	to	PART
cana-3074	54	10	solve	solve	VERB
cana-3074	54	11	problems	problem	NOUN
cana-3074	54	12	or	or	CCONJ
cana-3074	54	13	explore	explore	VERB
cana-3074	54	14	relationships	relationship	NOUN
cana-3074	54	15	.	.	PUNCT
cana-3074	55	1	mathematical	mathematical	ADJ
cana-3074	55	2	idealization	idealization	NOUN
cana-3074	55	3	idealizing	idealize	VERB
cana-3074	55	4	or	or	CCONJ
cana-3074	55	5	abstracting	abstract	VERB
cana-3074	55	6	physical	physical	ADJ
cana-3074	55	7	properties	property	NOUN
cana-3074	55	8	of	of	ADP
cana-3074	55	9	an	an	DET
cana-3074	55	10	object	object	NOUN
cana-3074	55	11	to	to	PART
cana-3074	55	12	focus	focus	VERB
cana-3074	55	13	on	on	ADP
cana-3074	55	14	its	its	PRON
cana-3074	55	15	mathematical	mathematical	ADJ
cana-3074	55	16	essence	essence	NOUN
cana-3074	55	17	.	.	PUNCT
cana-3074	56	1	8	8	NUM
cana-3074	56	2	senk	senk	NOUN
cana-3074	56	3	et	et	PROPN
cana-3074	56	4	al	al	PROPN
cana-3074	56	5	.	.	PROPN
cana-3074	56	6	2022	2022	NUM
cana-3074	56	7	9	9	NUM
cana-3074	56	8	mitchelmore	mitchelmore	NOUN
cana-3074	56	9	&	&	CCONJ
cana-3074	56	10	white	white	PROPN
cana-3074	56	11	2007	2007	NUM
cana-3074	56	12	communications	communication	NOUN
cana-3074	56	13	on	on	ADP
cana-3074	56	14	applied	apply	VERB
cana-3074	56	15	nonlinear	nonlinear	ADJ
cana-3074	56	16	analysis	analysis	NOUN
cana-3074	56	17	issn	issn	NOUN
cana-3074	56	18	:	:	PUNCT
cana-3074	56	19	1074	1074	NUM
cana-3074	56	20	-	-	PUNCT
cana-3074	56	21	133x	133x	NUM
cana-3074	56	22	vol	vol	NOUN
cana-3074	56	23	32	32	NUM
cana-3074	56	24	no	no	NOUN
cana-3074	56	25	.	.	PUNCT
cana-3074	57	1	5s	5s	NUM
cana-3074	57	2	(	(	PUNCT
cana-3074	57	3	2025	2025	NUM
cana-3074	57	4	)	)	PUNCT
cana-3074	57	5	271	271	NUM
cana-3074	57	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	57	7	research	research	NOUN
cana-3074	57	8	method	method	NOUN
cana-3074	57	9	this	this	DET
cana-3074	57	10	study	study	NOUN
cana-3074	57	11	aims	aim	VERB
cana-3074	57	12	to	to	PART
cana-3074	57	13	gain	gain	VERB
cana-3074	57	14	a	a	DET
cana-3074	57	15	deep	deep	ADJ
cana-3074	57	16	understanding	understanding	NOUN
cana-3074	57	17	of	of	ADP
cana-3074	57	18	the	the	DET
cana-3074	57	19	van	van	PROPN
cana-3074	57	20	hiele	hiele	PROPN
cana-3074	57	21	levels	level	NOUN
cana-3074	57	22	and	and	CCONJ
cana-3074	57	23	geometrical	geometrical	ADJ
cana-3074	57	24	abstraction	abstraction	NOUN
cana-3074	57	25	at	at	ADP
cana-3074	57	26	each	each	DET
cana-3074	57	27	van	van	PROPN
cana-3074	57	28	hiele	hiele	PROPN
cana-3074	57	29	level	level	NOUN
cana-3074	57	30	among	among	ADP
cana-3074	57	31	mathematics	mathematic	NOUN
cana-3074	57	32	undergraduates	undergraduate	NOUN
cana-3074	57	33	.	.	PUNCT
cana-3074	58	1	to	to	PART
cana-3074	58	2	enrich	enrich	VERB
cana-3074	58	3	the	the	DET
cana-3074	58	4	interpretation	interpretation	NOUN
cana-3074	58	5	of	of	ADP
cana-3074	58	6	findings	finding	NOUN
cana-3074	58	7	and	and	CCONJ
cana-3074	58	8	achieve	achieve	VERB
cana-3074	58	9	a	a	DET
cana-3074	58	10	comprehensive	comprehensive	ADJ
cana-3074	58	11	understanding	understanding	NOUN
cana-3074	58	12	of	of	ADP
cana-3074	58	13	geometrical	geometrical	ADJ
cana-3074	58	14	abstraction	abstraction	NOUN
cana-3074	58	15	at	at	ADP
cana-3074	58	16	each	each	DET
cana-3074	58	17	van	van	PROPN
cana-3074	58	18	hiele	hiele	PROPN
cana-3074	58	19	level	level	NOUN
cana-3074	58	20	,	,	PUNCT
cana-3074	58	21	an	an	DET
cana-3074	58	22	explanatory	explanatory	ADJ
cana-3074	58	23	sequential	sequential	ADJ
cana-3074	58	24	mixed	mixed	ADJ
cana-3074	58	25	methods	method	NOUN
cana-3074	58	26	approach	approach	NOUN
cana-3074	58	27	was	be	AUX
cana-3074	58	28	employed	employ	VERB
cana-3074	58	29	.	.	PUNCT
cana-3074	59	1	this	this	DET
cana-3074	59	2	approach	approach	NOUN
cana-3074	59	3	sequentially	sequentially	ADV
cana-3074	59	4	combines	combine	VERB
cana-3074	59	5	quantitative	quantitative	ADJ
cana-3074	59	6	and	and	CCONJ
cana-3074	59	7	qualitative	qualitative	ADJ
cana-3074	59	8	methods10	methods10	NOUN
cana-3074	59	9	.	.	PUNCT
cana-3074	60	1	initially	initially	ADV
cana-3074	60	2	,	,	PUNCT
cana-3074	60	3	quantitative	quantitative	ADJ
cana-3074	60	4	data	datum	NOUN
cana-3074	60	5	is	be	AUX
cana-3074	60	6	collected	collect	VERB
cana-3074	60	7	and	and	CCONJ
cana-3074	60	8	analyzed	analyze	VERB
cana-3074	60	9	to	to	PART
cana-3074	60	10	identify	identify	VERB
cana-3074	60	11	the	the	DET
cana-3074	60	12	van	van	PROPN
cana-3074	60	13	hiele	hiele	PROPN
cana-3074	60	14	levels	level	NOUN
cana-3074	60	15	among	among	ADP
cana-3074	60	16	the	the	DET
cana-3074	60	17	students	student	NOUN
cana-3074	60	18	.	.	PUNCT
cana-3074	61	1	subsequently	subsequently	ADV
cana-3074	61	2	,	,	PUNCT
cana-3074	61	3	qualitative	qualitative	ADJ
cana-3074	61	4	data	datum	NOUN
cana-3074	61	5	is	be	AUX
cana-3074	61	6	collected	collect	VERB
cana-3074	61	7	to	to	PART
cana-3074	61	8	explore	explore	VERB
cana-3074	61	9	geometrical	geometrical	ADJ
cana-3074	61	10	abstraction	abstraction	NOUN
cana-3074	61	11	at	at	ADP
cana-3074	61	12	each	each	DET
cana-3074	61	13	identified	identify	VERB
cana-3074	61	14	level	level	NOUN
cana-3074	61	15	.	.	PUNCT
cana-3074	62	1	this	this	DET
cana-3074	62	2	sequential	sequential	ADJ
cana-3074	62	3	approach	approach	NOUN
cana-3074	62	4	allows	allow	VERB
cana-3074	62	5	for	for	ADP
cana-3074	62	6	a	a	DET
cana-3074	62	7	deeper	deep	ADJ
cana-3074	62	8	exploration	exploration	NOUN
cana-3074	62	9	of	of	ADP
cana-3074	62	10	the	the	DET
cana-3074	62	11	research	research	NOUN
cana-3074	62	12	problem	problem	NOUN
cana-3074	62	13	by	by	ADP
cana-3074	62	14	using	use	VERB
cana-3074	62	15	qualitative	qualitative	ADJ
cana-3074	62	16	data	datum	NOUN
cana-3074	62	17	to	to	PART
cana-3074	62	18	explain	explain	VERB
cana-3074	62	19	and	and	CCONJ
cana-3074	62	20	elaborate	elaborate	VERB
cana-3074	62	21	on	on	ADP
cana-3074	62	22	quantitative	quantitative	ADJ
cana-3074	62	23	results	result	NOUN
cana-3074	62	24	.	.	PUNCT
cana-3074	63	1	data	datum	NOUN
cana-3074	63	2	source	source	NOUN
cana-3074	63	3	there	there	PRON
cana-3074	63	4	are	be	VERB
cana-3074	63	5	two	two	NUM
cana-3074	63	6	primary	primary	ADJ
cana-3074	63	7	data	datum	NOUN
cana-3074	63	8	sources	source	NOUN
cana-3074	63	9	and	and	CCONJ
cana-3074	63	10	one	one	NUM
cana-3074	63	11	secondary	secondary	ADJ
cana-3074	63	12	data	datum	NOUN
cana-3074	63	13	source	source	NOUN
cana-3074	63	14	in	in	ADP
cana-3074	63	15	this	this	DET
cana-3074	63	16	study	study	NOUN
cana-3074	63	17	.	.	PUNCT
cana-3074	64	1	the	the	DET
cana-3074	64	2	first	first	ADJ
cana-3074	64	3	primary	primary	ADJ
cana-3074	64	4	data	datum	NOUN
cana-3074	64	5	source	source	NOUN
cana-3074	64	6	focuses	focus	VERB
cana-3074	64	7	on	on	ADP
cana-3074	64	8	assessing	assess	VERB
cana-3074	64	9	the	the	DET
cana-3074	64	10	levels	level	NOUN
cana-3074	64	11	of	of	ADP
cana-3074	64	12	geometric	geometric	ADJ
cana-3074	64	13	thinking	thinking	NOUN
cana-3074	64	14	using	use	VERB
cana-3074	64	15	van	van	PROPN
cana-3074	64	16	hiele	hiele	PROPN
cana-3074	64	17	levels	level	NOUN
cana-3074	64	18	among	among	ADP
cana-3074	64	19	mathematics	mathematics	NOUN
cana-3074	64	20	undergraduates	undergraduate	NOUN
cana-3074	64	21	at	at	ADP
cana-3074	64	22	the	the	DET
cana-3074	64	23	state	state	NOUN
cana-3074	64	24	university	university	PROPN
cana-3074	64	25	of	of	ADP
cana-3074	64	26	makassar	makassar	PROPN
cana-3074	64	27	(	(	PUNCT
cana-3074	64	28	unm	unm	PROPN
cana-3074	64	29	)	)	PUNCT
cana-3074	64	30	.	.	PUNCT
cana-3074	65	1	the	the	DET
cana-3074	65	2	second	second	ADJ
cana-3074	65	3	primary	primary	ADJ
cana-3074	65	4	data	datum	NOUN
cana-3074	65	5	source	source	NOUN
cana-3074	65	6	involves	involve	VERB
cana-3074	65	7	evaluating	evaluate	VERB
cana-3074	65	8	geometrical	geometrical	ADJ
cana-3074	65	9	abstraction	abstraction	NOUN
cana-3074	65	10	within	within	ADP
cana-3074	65	11	the	the	DET
cana-3074	65	12	context	context	NOUN
cana-3074	65	13	of	of	ADP
cana-3074	65	14	triangles	triangle	NOUN
cana-3074	65	15	in	in	ADP
cana-3074	65	16	cartesian	cartesian	ADJ
cana-3074	65	17	coordinates	coordinate	NOUN
cana-3074	65	18	among	among	ADP
cana-3074	65	19	the	the	DET
cana-3074	65	20	mathematics	mathematic	NOUN
cana-3074	65	21	undergraduates	undergraduate	NOUN
cana-3074	65	22	.	.	PUNCT
cana-3074	66	1	moreover	moreover	ADV
cana-3074	66	2	,	,	PUNCT
cana-3074	66	3	secondary	secondary	ADJ
cana-3074	66	4	data	datum	NOUN
cana-3074	66	5	sources	source	NOUN
cana-3074	66	6	include	include	VERB
cana-3074	66	7	relevant	relevant	ADJ
cana-3074	66	8	theories	theory	NOUN
cana-3074	66	9	and	and	CCONJ
cana-3074	66	10	supporting	support	VERB
cana-3074	66	11	arguments	argument	NOUN
cana-3074	66	12	to	to	PART
cana-3074	66	13	provide	provide	VERB
cana-3074	66	14	a	a	DET
cana-3074	66	15	broader	broad	ADJ
cana-3074	66	16	context	context	NOUN
cana-3074	66	17	for	for	ADP
cana-3074	66	18	the	the	DET
cana-3074	66	19	research	research	NOUN
cana-3074	66	20	.	.	PUNCT
cana-3074	67	1	data	datum	NOUN
cana-3074	67	2	collection	collection	NOUN
cana-3074	67	3	technique	technique	NOUN
cana-3074	67	4	purposive	purposive	NOUN
cana-3074	67	5	sampling	sampling	NOUN
cana-3074	67	6	was	be	AUX
cana-3074	67	7	used	use	VERB
cana-3074	67	8	due	due	ADP
cana-3074	67	9	to	to	ADP
cana-3074	67	10	the	the	DET
cana-3074	67	11	specific	specific	ADJ
cana-3074	67	12	goal	goal	NOUN
cana-3074	67	13	of	of	ADP
cana-3074	67	14	understanding	understand	VERB
cana-3074	67	15	geometrical	geometrical	ADJ
cana-3074	67	16	abstraction	abstraction	NOUN
cana-3074	67	17	at	at	ADP
cana-3074	67	18	different	different	ADJ
cana-3074	67	19	van	van	PROPN
cana-3074	67	20	hiele	hiele	PROPN
cana-3074	67	21	levels	level	NOUN
cana-3074	67	22	11	11	NUM
cana-3074	67	23	.	.	PUNCT
cana-3074	68	1	this	this	DET
cana-3074	68	2	sampling	sampling	NOUN
cana-3074	68	3	method	method	NOUN
cana-3074	68	4	maximizes	maximize	VERB
cana-3074	68	5	the	the	DET
cana-3074	68	6	potential	potential	NOUN
cana-3074	68	7	for	for	ADP
cana-3074	68	8	gaining	gain	VERB
cana-3074	68	9	deep	deep	ADJ
cana-3074	68	10	and	and	CCONJ
cana-3074	68	11	relevant	relevant	ADJ
cana-3074	68	12	insights	insight	NOUN
cana-3074	68	13	,	,	PUNCT
cana-3074	68	14	thereby	thereby	ADV
cana-3074	68	15	enhancing	enhance	VERB
cana-3074	68	16	significant	significant	ADJ
cana-3074	68	17	findings	finding	NOUN
cana-3074	68	18	related	relate	VERB
cana-3074	68	19	to	to	ADP
cana-3074	68	20	geometrical	geometrical	ADJ
cana-3074	68	21	abstraction	abstraction	NOUN
cana-3074	68	22	at	at	ADP
cana-3074	68	23	each	each	DET
cana-3074	68	24	van	van	PROPN
cana-3074	68	25	hiele	hiele	PROPN
cana-3074	68	26	levels	level	NOUN
cana-3074	68	27	.	.	PUNCT
cana-3074	69	1	in	in	ADP
cana-3074	69	2	this	this	DET
cana-3074	69	3	research	research	NOUN
cana-3074	69	4	,	,	PUNCT
cana-3074	69	5	data	datum	NOUN
cana-3074	69	6	collection	collection	NOUN
cana-3074	69	7	processes	process	NOUN
cana-3074	69	8	through	through	ADP
cana-3074	69	9	steps	step	NOUN
cana-3074	69	10	;	;	PUNCT
cana-3074	69	11	1	1	X
cana-3074	69	12	.	.	X
cana-3074	69	13	selection	selection	NOUN
cana-3074	69	14	of	of	ADP
cana-3074	69	15	mathematics	mathematic	NOUN
cana-3074	69	16	undergraduates	undergraduate	NOUN
cana-3074	69	17	:	:	PUNCT
cana-3074	69	18	students	student	NOUN
cana-3074	69	19	who	who	PRON
cana-3074	69	20	completed	complete	VERB
cana-3074	69	21	the	the	DET
cana-3074	69	22	basic	basic	ADJ
cana-3074	69	23	geometry	geometry	NOUN
cana-3074	69	24	course	course	NOUN
cana-3074	69	25	were	be	AUX
cana-3074	69	26	selected	select	VERB
cana-3074	69	27	to	to	PART
cana-3074	69	28	ensure	ensure	VERB
cana-3074	69	29	relevant	relevant	ADJ
cana-3074	69	30	background	background	NOUN
cana-3074	69	31	knowledge	knowledge	NOUN
cana-3074	69	32	.	.	PUNCT
cana-3074	70	1	2	2	X
cana-3074	70	2	.	.	X
cana-3074	70	3	van	van	NOUN
cana-3074	70	4	hiele	hiele	PROPN
cana-3074	70	5	level	level	NOUN
cana-3074	70	6	categorization	categorization	NOUN
cana-3074	70	7	:	:	PUNCT
cana-3074	70	8	students	student	NOUN
cana-3074	70	9	are	be	AUX
cana-3074	70	10	categorized	categorize	VERB
cana-3074	70	11	their	their	PRON
cana-3074	70	12	geometric	geometric	ADJ
cana-3074	70	13	thinking	thinking	NOUN
cana-3074	70	14	levels	level	NOUN
cana-3074	70	15	based	base	VERB
cana-3074	70	16	on	on	ADP
cana-3074	70	17	van	van	PROPN
cana-3074	70	18	hiele	hiele	NOUN
cana-3074	70	19	.	.	PUNCT
cana-3074	71	1	3	3	X
cana-3074	71	2	.	.	NOUN
cana-3074	71	3	subject	subject	ADJ
cana-3074	71	4	selection	selection	NOUN
cana-3074	71	5	and	and	CCONJ
cana-3074	71	6	evaluation	evaluation	NOUN
cana-3074	71	7	:	:	PUNCT
cana-3074	71	8	one	one	NUM
cana-3074	71	9	student	student	NOUN
cana-3074	71	10	from	from	ADP
cana-3074	71	11	each	each	DET
cana-3074	71	12	identified	identify	VERB
cana-3074	71	13	van	van	PROPN
cana-3074	71	14	hiele	hiele	PROPN
cana-3074	71	15	level	level	NOUN
cana-3074	71	16	was	be	AUX
cana-3074	71	17	selected	select	VERB
cana-3074	71	18	for	for	ADP
cana-3074	71	19	further	further	ADJ
cana-3074	71	20	evaluation	evaluation	NOUN
cana-3074	71	21	through	through	ADP
cana-3074	71	22	the	the	DET
cana-3074	71	23	geometrical	geometrical	ADJ
cana-3074	71	24	abstraction	abstraction	NOUN
cana-3074	71	25	test	test	NOUN
cana-3074	71	26	and	and	CCONJ
cana-3074	71	27	interviews	interview	NOUN
cana-3074	71	28	.	.	PUNCT
cana-3074	72	1	4	4	X
cana-3074	72	2	.	.	X
cana-3074	72	3	data	datum	NOUN
cana-3074	72	4	triangulation	triangulation	NOUN
cana-3074	72	5	:	:	PUNCT
cana-3074	72	6	multiple	multiple	ADJ
cana-3074	72	7	data	datum	NOUN
cana-3074	72	8	sources	source	NOUN
cana-3074	72	9	were	be	AUX
cana-3074	72	10	used	use	VERB
cana-3074	72	11	to	to	PART
cana-3074	72	12	confirm	confirm	VERB
cana-3074	72	13	findings	finding	NOUN
cana-3074	72	14	and	and	CCONJ
cana-3074	72	15	enhance	enhance	VERB
cana-3074	72	16	validity	validity	NOUN
cana-3074	72	17	.	.	PUNCT
cana-3074	73	1	data	datum	NOUN
cana-3074	73	2	analysis	analysis	NOUN
cana-3074	73	3	technique	technique	NOUN
cana-3074	73	4	data	datum	NOUN
cana-3074	73	5	was	be	AUX
cana-3074	73	6	analyzed	analyze	VERB
cana-3074	73	7	using	use	VERB
cana-3074	73	8	nvivo	nvivo	PROPN
cana-3074	73	9	12	12	NUM
cana-3074	73	10	,	,	PUNCT
cana-3074	73	11	following	follow	VERB
cana-3074	73	12	the	the	DET
cana-3074	73	13	steps	step	NOUN
cana-3074	73	14	of	of	ADP
cana-3074	73	15	explanatory	explanatory	ADJ
cana-3074	73	16	sequential	sequential	ADJ
cana-3074	73	17	mixed	mixed	ADJ
cana-3074	73	18	methods	method	NOUN
cana-3074	73	19	12	12	NUM
cana-3074	73	20	;	;	PUNCT
cana-3074	73	21	1	1	NUM
cana-3074	73	22	.	.	X
cana-3074	73	23	statistical	statistical	ADJ
cana-3074	73	24	analysis	analysis	NOUN
cana-3074	73	25	:	:	PUNCT
cana-3074	73	26	quantitative	quantitative	ADJ
cana-3074	73	27	data	datum	NOUN
cana-3074	73	28	from	from	ADP
cana-3074	73	29	the	the	DET
cana-3074	73	30	van	van	PROPN
cana-3074	73	31	hiele	hiele	PROPN
cana-3074	73	32	level	level	NOUN
cana-3074	73	33	categorization	categorization	NOUN
cana-3074	73	34	was	be	AUX
cana-3074	73	35	analyzed	analyze	VERB
cana-3074	73	36	to	to	PART
cana-3074	73	37	provide	provide	VERB
cana-3074	73	38	initial	initial	ADJ
cana-3074	73	39	insights	insight	NOUN
cana-3074	73	40	into	into	ADP
cana-3074	73	41	the	the	DET
cana-3074	73	42	distribution	distribution	NOUN
cana-3074	73	43	of	of	ADP
cana-3074	73	44	van	van	PROPN
cana-3074	73	45	hiele	hiele	PROPN
cana-3074	73	46	levels	level	NOUN
cana-3074	73	47	.	.	PUNCT
cana-3074	74	1	10	10	NUM
cana-3074	74	2	piccioli	piccioli	NOUN
cana-3074	74	3	2019	2019	NUM
cana-3074	74	4	;	;	PUNCT
cana-3074	74	5	plano	plano	PROPN
cana-3074	74	6	clark	clark	PROPN
cana-3074	74	7	&	&	CCONJ
cana-3074	74	8	ivankova	ivankova	PROPN
cana-3074	74	9	2016	2016	NUM
cana-3074	74	10	11	11	NUM
cana-3074	74	11	islam	islam	PROPN
cana-3074	74	12	et	et	PROPN
cana-3074	74	13	al	al	PROPN
cana-3074	74	14	.	.	PROPN
cana-3074	74	15	2022	2022	NUM
cana-3074	74	16	12	12	NUM
cana-3074	74	17	plano	plano	PROPN
cana-3074	74	18	clark	clark	PROPN
cana-3074	74	19	&	&	CCONJ
cana-3074	74	20	ivankova	ivankova	VERB
cana-3074	74	21	2016	2016	NUM
cana-3074	74	22	communications	communication	NOUN
cana-3074	74	23	on	on	ADP
cana-3074	74	24	applied	apply	VERB
cana-3074	74	25	nonlinear	nonlinear	ADJ
cana-3074	74	26	analysis	analysis	NOUN
cana-3074	74	27	issn	issn	NOUN
cana-3074	74	28	:	:	PUNCT
cana-3074	74	29	1074	1074	NUM
cana-3074	74	30	-	-	PUNCT
cana-3074	74	31	133x	133x	NUM
cana-3074	74	32	vol	vol	NOUN
cana-3074	74	33	32	32	NUM
cana-3074	74	34	no	no	NOUN
cana-3074	74	35	.	.	PUNCT
cana-3074	75	1	5s	5s	NUM
cana-3074	75	2	(	(	PUNCT
cana-3074	75	3	2025	2025	NUM
cana-3074	75	4	)	)	PUNCT
cana-3074	75	5	272	272	NUM
cana-3074	75	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	75	7	2	2	X
cana-3074	75	8	.	.	PUNCT
cana-3074	75	9	qualitative	qualitative	ADJ
cana-3074	75	10	data	datum	NOUN
cana-3074	75	11	collection	collection	NOUN
cana-3074	75	12	:	:	PUNCT
cana-3074	75	13	based	base	VERB
cana-3074	75	14	on	on	ADP
cana-3074	75	15	quantitative	quantitative	ADJ
cana-3074	75	16	findings	finding	NOUN
cana-3074	75	17	,	,	PUNCT
cana-3074	75	18	qualitative	qualitative	ADJ
cana-3074	75	19	data	datum	NOUN
cana-3074	75	20	was	be	AUX
cana-3074	75	21	gathered	gather	VERB
cana-3074	75	22	through	through	ADP
cana-3074	75	23	the	the	DET
cana-3074	75	24	geometrical	geometrical	ADJ
cana-3074	75	25	abstraction	abstraction	NOUN
cana-3074	75	26	test	test	NOUN
cana-3074	75	27	and	and	CCONJ
cana-3074	75	28	interviews	interview	NOUN
cana-3074	75	29	.	.	PUNCT
cana-3074	76	1	3	3	X
cana-3074	76	2	.	.	X
cana-3074	76	3	thematic	thematic	ADJ
cana-3074	76	4	analysis	analysis	NOUN
cana-3074	76	5	:	:	PUNCT
cana-3074	76	6	nvivo	nvivo	ADJ
cana-3074	76	7	12	12	NUM
cana-3074	76	8	was	be	AUX
cana-3074	76	9	used	use	VERB
cana-3074	76	10	to	to	PART
cana-3074	76	11	identify	identify	VERB
cana-3074	76	12	patterns	pattern	NOUN
cana-3074	76	13	and	and	CCONJ
cana-3074	76	14	aspects	aspect	NOUN
cana-3074	76	15	of	of	ADP
cana-3074	76	16	geometrical	geometrical	ADJ
cana-3074	76	17	abstraction	abstraction	NOUN
cana-3074	76	18	in	in	ADP
cana-3074	76	19	the	the	DET
cana-3074	76	20	qualitative	qualitative	ADJ
cana-3074	76	21	data	datum	NOUN
cana-3074	76	22	.	.	PUNCT
cana-3074	77	1	4	4	X
cana-3074	77	2	.	.	X
cana-3074	77	3	interpretation	interpretation	NOUN
cana-3074	77	4	of	of	ADP
cana-3074	77	5	results	result	NOUN
cana-3074	77	6	:	:	PUNCT
cana-3074	77	7	qualitative	qualitative	ADJ
cana-3074	77	8	results	result	NOUN
cana-3074	77	9	were	be	AUX
cana-3074	77	10	interpreted	interpret	VERB
cana-3074	77	11	to	to	PART
cana-3074	77	12	provide	provide	VERB
cana-3074	77	13	a	a	DET
cana-3074	77	14	comprehensive	comprehensive	ADJ
cana-3074	77	15	understanding	understanding	NOUN
cana-3074	77	16	of	of	ADP
cana-3074	77	17	geometrical	geometrical	ADJ
cana-3074	77	18	abstraction	abstraction	NOUN
cana-3074	77	19	at	at	ADP
cana-3074	77	20	each	each	DET
cana-3074	77	21	van	van	PROPN
cana-3074	77	22	hiele	hiele	PROPN
cana-3074	77	23	level	level	NOUN
cana-3074	77	24	,	,	PUNCT
cana-3074	77	25	relating	relate	VERB
cana-3074	77	26	findings	finding	NOUN
cana-3074	77	27	to	to	ADP
cana-3074	77	28	relevant	relevant	ADJ
cana-3074	77	29	literature	literature	NOUN
cana-3074	77	30	and	and	CCONJ
cana-3074	77	31	broader	broad	ADJ
cana-3074	77	32	contexts	context	NOUN
cana-3074	77	33	result	result	VERB
cana-3074	77	34	and	and	CCONJ
cana-3074	77	35	discussion	discussion	NOUN
cana-3074	77	36	van	van	PROPN
cana-3074	77	37	hiele	hiele	PROPN
cana-3074	77	38	levels	level	NOUN
cana-3074	77	39	of	of	ADP
cana-3074	77	40	mathematics	mathematic	NOUN
cana-3074	77	41	undergraduates	undergraduate	VERB
cana-3074	77	42	a	a	DET
cana-3074	77	43	total	total	NOUN
cana-3074	77	44	of	of	ADP
cana-3074	77	45	191	191	NUM
cana-3074	77	46	subjects	subject	NOUN
cana-3074	77	47	from	from	ADP
cana-3074	77	48	mathematics	mathematics	PROPN
cana-3074	77	49	department	department	NOUN
cana-3074	77	50	of	of	ADP
cana-3074	77	51	the	the	DET
cana-3074	77	52	state	state	PROPN
cana-3074	77	53	university	university	PROPN
cana-3074	77	54	of	of	ADP
cana-3074	77	55	makassar	makassar	PROPN
cana-3074	77	56	(	(	PUNCT
cana-3074	77	57	unm	unm	PROPN
cana-3074	77	58	)	)	PUNCT
cana-3074	77	59	were	be	AUX
cana-3074	77	60	participated	participate	VERB
cana-3074	77	61	.	.	PUNCT
cana-3074	78	1	the	the	DET
cana-3074	78	2	primary	primary	ADJ
cana-3074	78	3	objective	objective	NOUN
cana-3074	78	4	was	be	AUX
cana-3074	78	5	to	to	PART
cana-3074	78	6	gather	gather	VERB
cana-3074	78	7	comprehensive	comprehensive	ADJ
cana-3074	78	8	data	datum	NOUN
cana-3074	78	9	on	on	ADP
cana-3074	78	10	the	the	DET
cana-3074	78	11	subjects	subject	NOUN
cana-3074	78	12	'	'	PART
cana-3074	78	13	van	van	PROPN
cana-3074	78	14	hiele	hiele	PROPN
cana-3074	78	15	level	level	NOUN
cana-3074	78	16	.	.	PUNCT
cana-3074	79	1	two	two	NUM
cana-3074	79	2	subjects	subject	NOUN
cana-3074	79	3	from	from	ADP
cana-3074	79	4	each	each	DET
cana-3074	79	5	level	level	NOUN
cana-3074	79	6	were	be	AUX
cana-3074	79	7	selected	select	VERB
cana-3074	79	8	based	base	VERB
cana-3074	79	9	on	on	ADP
cana-3074	79	10	test	test	NOUN
cana-3074	79	11	results	result	NOUN
cana-3074	79	12	.	.	PUNCT
cana-3074	80	1	the	the	DET
cana-3074	80	2	vhgt	vhgt	ADJ
cana-3074	80	3	results	result	NOUN
cana-3074	80	4	are	be	AUX
cana-3074	80	5	presented	present	VERB
cana-3074	80	6	in	in	ADP
cana-3074	80	7	figure	figure	NOUN
cana-3074	80	8	1	1	NUM
cana-3074	80	9	.	.	PUNCT
cana-3074	81	1	figure	figure	NOUN
cana-3074	81	2	1	1	NUM
cana-3074	81	3	.	.	PUNCT
cana-3074	82	1	van	van	PROPN
cana-3074	82	2	hiele	hiele	PROPN
cana-3074	82	3	levels	level	NOUN
cana-3074	82	4	of	of	ADP
cana-3074	82	5	mathematics	mathematic	NOUN
cana-3074	82	6	undergraduates	undergraduate	NOUN
cana-3074	82	7	at	at	ADP
cana-3074	82	8	unm	unm	PROPN
cana-3074	82	9	based	base	VERB
cana-3074	82	10	on	on	ADP
cana-3074	82	11	figure	figure	NOUN
cana-3074	82	12	50	50	NUM
cana-3074	83	1	,	,	PUNCT
cana-3074	83	2	the	the	DET
cana-3074	83	3	data	data	NOUN
cana-3074	83	4	interpretation	interpretation	NOUN
cana-3074	83	5	shows	show	VERB
cana-3074	83	6	that	that	SCONJ
cana-3074	83	7	the	the	DET
cana-3074	83	8	majority	majority	NOUN
cana-3074	83	9	of	of	ADP
cana-3074	83	10	students	student	NOUN
cana-3074	83	11	are	be	AUX
cana-3074	83	12	at	at	ADP
cana-3074	83	13	the	the	DET
cana-3074	83	14	visualization	visualization	NOUN
cana-3074	83	15	level	level	NOUN
cana-3074	83	16	(	(	PUNCT
cana-3074	83	17	39	39	NUM
cana-3074	83	18	%	%	NOUN
cana-3074	83	19	)	)	PUNCT
cana-3074	83	20	,	,	PUNCT
cana-3074	83	21	followed	follow	VERB
cana-3074	83	22	by	by	ADP
cana-3074	83	23	the	the	DET
cana-3074	83	24	analysis	analysis	NOUN
cana-3074	83	25	level	level	NOUN
cana-3074	83	26	(	(	PUNCT
cana-3074	83	27	52	52	NUM
cana-3074	83	28	%	%	NOUN
cana-3074	83	29	)	)	PUNCT
cana-3074	83	30	.	.	PUNCT
cana-3074	84	1	this	this	DET
cana-3074	84	2	finding	finding	NOUN
cana-3074	84	3	is	be	AUX
cana-3074	84	4	consistent	consistent	ADJ
cana-3074	84	5	with	with	ADP
cana-3074	84	6	putri	putri	ADJ
cana-3074	84	7	and	and	CCONJ
cana-3074	84	8	nopriana	nopriana	PROPN
cana-3074	84	9	(	(	PUNCT
cana-3074	84	10	2019	2019	NUM
cana-3074	84	11	)	)	PUNCT
cana-3074	84	12	,	,	PUNCT
cana-3074	84	13	who	who	PRON
cana-3074	84	14	also	also	ADV
cana-3074	84	15	found	find	VERB
cana-3074	84	16	that	that	SCONJ
cana-3074	84	17	most	most	ADJ
cana-3074	84	18	students	student	NOUN
cana-3074	84	19	were	be	AUX
cana-3074	84	20	at	at	ADP
cana-3074	84	21	the	the	DET
cana-3074	84	22	visualization	visualization	NOUN
cana-3074	84	23	and	and	CCONJ
cana-3074	84	24	analysis	analysis	NOUN
cana-3074	84	25	levels	level	NOUN
cana-3074	84	26	.	.	PUNCT
cana-3074	85	1	additionally	additionally	ADV
cana-3074	85	2	,	,	PUNCT
cana-3074	85	3	this	this	DET
cana-3074	85	4	study	study	NOUN
cana-3074	85	5	found	find	VERB
cana-3074	85	6	that	that	SCONJ
cana-3074	85	7	the	the	DET
cana-3074	85	8	highest	high	ADJ
cana-3074	85	9	level	level	NOUN
cana-3074	85	10	achieved	achieve	VERB
cana-3074	85	11	by	by	ADP
cana-3074	85	12	mathematics	mathematic	NOUN
cana-3074	85	13	undergraduates	undergraduate	NOUN
cana-3074	85	14	is	be	AUX
cana-3074	85	15	the	the	DET
cana-3074	85	16	rigor	rigor	NOUN
cana-3074	85	17	level	level	NOUN
cana-3074	85	18	,	,	PUNCT
cana-3074	85	19	with	with	ADP
cana-3074	85	20	3.62	3.62	NUM
cana-3074	85	21	%	%	NOUN
cana-3074	85	22	of	of	ADP
cana-3074	85	23	the	the	DET
cana-3074	85	24	total	total	NOUN
cana-3074	85	25	.	.	PUNCT
cana-3074	86	1	this	this	DET
cana-3074	86	2	finding	finding	NOUN
cana-3074	86	3	contrasts	contrast	VERB
cana-3074	86	4	with	with	ADP
cana-3074	86	5	putri	putri	ADJ
cana-3074	86	6	and	and	CCONJ
cana-3074	86	7	nopriana	nopriana	PROPN
cana-3074	86	8	(	(	PUNCT
cana-3074	86	9	2019	2019	NUM
cana-3074	86	10	)	)	PUNCT
cana-3074	86	11	,	,	PUNCT
cana-3074	86	12	who	who	PRON
cana-3074	86	13	stated	state	VERB
cana-3074	86	14	that	that	SCONJ
cana-3074	86	15	the	the	DET
cana-3074	86	16	highest	high	ADJ
cana-3074	86	17	level	level	NOUN
cana-3074	86	18	that	that	PRON
cana-3074	86	19	could	could	AUX
cana-3074	86	20	be	be	AUX
cana-3074	86	21	achieved	achieve	VERB
cana-3074	86	22	was	be	AUX
cana-3074	86	23	the	the	DET
cana-3074	86	24	analysis	analysis	NOUN
cana-3074	86	25	level	level	NOUN
cana-3074	86	26	,	,	PUNCT
cana-3074	86	27	but	but	CCONJ
cana-3074	86	28	it	it	PRON
cana-3074	86	29	aligns	align	VERB
cana-3074	86	30	with	with	ADP
cana-3074	86	31	wicaksono	wicaksono	NOUN
cana-3074	86	32	and	and	CCONJ
cana-3074	86	33	juniati	juniati	NOUN
cana-3074	86	34	(	(	PUNCT
cana-3074	86	35	2022	2022	NUM
cana-3074	86	36	)	)	PUNCT
cana-3074	86	37	,	,	PUNCT
cana-3074	86	38	who	who	PRON
cana-3074	86	39	revealed	reveal	VERB
cana-3074	86	40	that	that	SCONJ
cana-3074	86	41	mathematics	mathematic	NOUN
cana-3074	86	42	education	education	NOUN
cana-3074	86	43	students	student	NOUN
cana-3074	86	44	reached	reach	VERB
cana-3074	86	45	all	all	DET
cana-3074	86	46	van	van	PROPN
cana-3074	86	47	hiele	hiele	PROPN
cana-3074	86	48	levels	level	NOUN
cana-3074	86	49	,	,	PUNCT
cana-3074	86	50	with	with	ADP
cana-3074	86	51	the	the	DET
cana-3074	86	52	highest	high	ADJ
cana-3074	86	53	being	be	AUX
cana-3074	86	54	the	the	DET
cana-3074	86	55	rigor	rigor	NOUN
cana-3074	86	56	level	level	NOUN
cana-3074	86	57	at	at	ADP
cana-3074	86	58	0.89	0.89	NUM
cana-3074	86	59	%	%	NOUN
cana-3074	86	60	of	of	ADP
cana-3074	86	61	the	the	DET
cana-3074	86	62	total	total	NOUN
cana-3074	86	63	.	.	PUNCT
cana-3074	87	1	the	the	DET
cana-3074	87	2	distribution	distribution	NOUN
cana-3074	87	3	in	in	ADP
cana-3074	87	4	table	table	NOUN
cana-3074	87	5	2	2	NUM
cana-3074	87	6	further	far	ADV
cana-3074	87	7	involves	involve	VERB
cana-3074	87	8	selecting	select	VERB
cana-3074	87	9	two	two	NUM
cana-3074	87	10	subjects	subject	NOUN
cana-3074	87	11	from	from	ADP
cana-3074	87	12	each	each	DET
cana-3074	87	13	level	level	NOUN
cana-3074	87	14	based	base	VERB
cana-3074	87	15	on	on	ADP
cana-3074	87	16	communicative	communicative	ADJ
cana-3074	87	17	criteria	criterion	NOUN
cana-3074	87	18	and	and	CCONJ
cana-3074	87	19	material	material	NOUN
cana-3074	87	20	mastery	mastery	NOUN
cana-3074	87	21	for	for	ADP
cana-3074	87	22	geometrical	geometrical	ADJ
cana-3074	87	23	abstraction	abstraction	NOUN
cana-3074	87	24	analysis	analysis	NOUN
cana-3074	87	25	,	,	PUNCT
cana-3074	87	26	summarized	summarize	VERB
cana-3074	87	27	in	in	ADP
cana-3074	87	28	table	table	NOUN
cana-3074	87	29	table	table	NOUN
cana-3074	87	30	2	2	NUM
cana-3074	87	31	.	.	NUM
cana-3074	87	32	selected	select	VERB
cana-3074	87	33	research	research	NOUN
cana-3074	87	34	subjects	subject	NOUN
cana-3074	87	35	van	van	PROPN
cana-3074	87	36	hiele	hiele	PROPN
cana-3074	87	37	level	level	NOUN
cana-3074	87	38	selected	select	VERB
cana-3074	87	39	subjects	subject	NOUN
cana-3074	87	40	visualization	visualization	NOUN
cana-3074	87	41	ssv	ssv	NOUN
cana-3074	87	42	ssv01	ssv01	PROPN
cana-3074	87	43	analysis	analysis	NOUN
cana-3074	87	44	ssa	ssa	NOUN
cana-3074	87	45	ssa01	ssa01	VERB
cana-3074	87	46	communications	communication	NOUN
cana-3074	87	47	on	on	ADP
cana-3074	87	48	applied	apply	VERB
cana-3074	87	49	nonlinear	nonlinear	ADJ
cana-3074	87	50	analysis	analysis	NOUN
cana-3074	87	51	issn	issn	NOUN
cana-3074	87	52	:	:	PUNCT
cana-3074	87	53	1074	1074	NUM
cana-3074	87	54	-	-	PUNCT
cana-3074	87	55	133x	133x	NUM
cana-3074	87	56	vol	vol	NOUN
cana-3074	87	57	32	32	NUM
cana-3074	87	58	no	no	NOUN
cana-3074	87	59	.	.	PUNCT
cana-3074	88	1	5s	5s	NUM
cana-3074	88	2	(	(	PUNCT
cana-3074	88	3	2025	2025	NUM
cana-3074	88	4	)	)	PUNCT
cana-3074	89	1	273	273	NUM
cana-3074	89	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	89	3	informal	informal	ADJ
cana-3074	89	4	deduction	deduction	NOUN
cana-3074	89	5	sid	sid	PROPN
cana-3074	89	6	sid01	sid01	NOUN
cana-3074	89	7	formal	formal	ADJ
cana-3074	89	8	deduction	deduction	NOUN
cana-3074	89	9	sfd	sfd	PROPN
cana-3074	89	10	sfd01	sfd01	PROPN
cana-3074	89	11	rigor	rigor	NOUN
cana-3074	89	12	ssr	ssr	PROPN
cana-3074	89	13	ssr01	ssr01	PROPN
cana-3074	89	14	geometrical	geometrical	ADJ
cana-3074	89	15	abstraction	abstraction	NOUN
cana-3074	89	16	on	on	ADP
cana-3074	89	17	van	van	PROPN
cana-3074	89	18	hiele	hiele	PROPN
cana-3074	89	19	level	level	NOUN
cana-3074	89	20	based	base	VERB
cana-3074	89	21	on	on	ADP
cana-3074	89	22	the	the	DET
cana-3074	89	23	analysis	analysis	NOUN
cana-3074	89	24	of	of	ADP
cana-3074	89	25	geometrical	geometrical	ADJ
cana-3074	89	26	abstraction	abstraction	NOUN
cana-3074	89	27	test	test	NOUN
cana-3074	89	28	data	datum	NOUN
cana-3074	89	29	and	and	CCONJ
cana-3074	89	30	interviews	interview	NOUN
cana-3074	89	31	to	to	ADP
cana-3074	89	32	ten	ten	NUM
cana-3074	89	33	selected	select	VERB
cana-3074	89	34	subjects	subject	NOUN
cana-3074	89	35	who	who	PRON
cana-3074	89	36	represented	represent	VERB
cana-3074	89	37	each	each	DET
cana-3074	89	38	van	van	PROPN
cana-3074	89	39	hiele	hiele	PROPN
cana-3074	89	40	level	level	NOUN
cana-3074	89	41	,	,	PUNCT
cana-3074	89	42	geometrical	geometrical	ADJ
cana-3074	89	43	abstraction	abstraction	NOUN
cana-3074	89	44	on	on	ADP
cana-3074	89	45	van	van	PROPN
cana-3074	89	46	hiele	hiele	PROPN
cana-3074	89	47	level	level	NOUN
cana-3074	89	48	among	among	ADP
cana-3074	89	49	mathematics	mathematics	NOUN
cana-3074	89	50	undergraduates	undergraduate	NOUN
cana-3074	89	51	is	be	AUX
cana-3074	89	52	presented	present	VERB
cana-3074	89	53	in	in	ADP
cana-3074	89	54	table	table	NOUN
cana-3074	89	55	3	3	NUM
cana-3074	89	56	.	.	PUNCT
cana-3074	89	57	table	table	NOUN
cana-3074	89	58	3	3	NUM
cana-3074	89	59	.	.	PUNCT
cana-3074	90	1	geometrical	geometrical	ADJ
cana-3074	90	2	abstraction	abstraction	NOUN
cana-3074	90	3	on	on	ADP
cana-3074	90	4	van	van	PROPN
cana-3074	90	5	hiele	hiele	PROPN
cana-3074	90	6	levels	level	NOUN
cana-3074	90	7	indicator	indicator	NOUN
cana-3074	90	8	visualization	visualization	NOUN
cana-3074	90	9	analysis	analysis	NOUN
cana-3074	90	10	informal	informal	ADJ
cana-3074	90	11	deduction	deduction	NOUN
cana-3074	90	12	formal	formal	ADJ
cana-3074	90	13	deduction	deduction	NOUN
cana-3074	90	14	rigor	rigor	VERB
cana-3074	90	15	direct	direct	ADJ
cana-3074	90	16	experience	experience	NOUN
cana-3074	90	17	identifying	identify	VERB
cana-3074	90	18	geometric	geometric	ADJ
cana-3074	90	19	characteristics	characteristic	NOUN
cana-3074	90	20	of	of	ADP
cana-3074	90	21	triangle	triangle	NOUN
cana-3074	90	22	abc	abc	PROPN
cana-3074	90	23	through	through	ADP
cana-3074	90	24	visuals	visual	NOUN
cana-3074	90	25	reality	reality	NOUN
cana-3074	90	26	or	or	CCONJ
cana-3074	90	27	imagination	imagination	NOUN
cana-3074	90	28	drawing	draw	VERB
cana-3074	90	29	a	a	DET
cana-3074	90	30	new	new	ADJ
cana-3074	90	31	triangle	triangle	NOUN
cana-3074	90	32	resulting	result	VERB
cana-3074	90	33	from	from	ADP
cana-3074	90	34	manipulating	manipulate	VERB
cana-3074	90	35	coordinate	coordinate	NOUN
cana-3074	90	36	points	point	NOUN
cana-3074	90	37	manipulating	manipulate	VERB
cana-3074	90	38	triangle	triangle	NOUN
cana-3074	90	39	variants	variant	NOUN
cana-3074	90	40	mathematical	mathematical	ADJ
cana-3074	90	41	representation	representation	NOUN
cana-3074	90	42	representing	represent	VERB
cana-3074	90	43	coordinates	coordinate	NOUN
cana-3074	90	44	a	a	DET
cana-3074	90	45	,	,	PUNCT
cana-3074	90	46	b	b	NOUN
cana-3074	90	47	,	,	PUNCT
cana-3074	90	48	and	and	CCONJ
cana-3074	90	49	c	c	X
cana-3074	90	50	in	in	ADP
cana-3074	90	51	mathematical	mathematical	ADJ
cana-3074	90	52	symbols	symbol	NOUN
cana-3074	90	53	formulating	formulate	VERB
cana-3074	90	54	the	the	DET
cana-3074	90	55	side	side	NOUN
cana-3074	90	56	lengths	length	NOUN
cana-3074	90	57	of	of	ADP
cana-3074	90	58	the	the	DET
cana-3074	90	59	triangle	triangle	NOUN
cana-3074	90	60	pattern	pattern	NOUN
cana-3074	90	61	-	-	PUNCT
cana-3074	90	62	based	base	VERB
cana-3074	90	63	generalization	generalization	NOUN
cana-3074	90	64	understanding	understand	VERB
cana-3074	90	65	general	general	ADJ
cana-3074	90	66	characteristics	characteristic	NOUN
cana-3074	90	67	of	of	ADP
cana-3074	90	68	triangles	triangle	NOUN
cana-3074	90	69	mathematical	mathematical	ADJ
cana-3074	90	70	idealization	idealization	NOUN
cana-3074	90	71	idealizing	idealize	VERB
cana-3074	90	72	the	the	DET
cana-3074	90	73	shape	shape	NOUN
cana-3074	90	74	of	of	ADP
cana-3074	90	75	triangle	triangle	NOUN
cana-3074	90	76	abc	abc	PROPN
cana-3074	90	77	into	into	ADP
cana-3074	90	78	the	the	DET
cana-3074	90	79	general	general	ADJ
cana-3074	90	80	form	form	NOUN
cana-3074	90	81	of	of	ADP
cana-3074	90	82	a	a	DET
cana-3074	90	83	triangle	triangle	NOUN
cana-3074	90	84	real	real	ADJ
cana-3074	90	85	-	-	PUNCT
cana-3074	90	86	world	world	NOUN
cana-3074	90	87	relevance	relevance	NOUN
cana-3074	90	88	providing	provide	VERB
cana-3074	90	89	examples	example	NOUN
cana-3074	90	90	of	of	ADP
cana-3074	90	91	triangles	triangle	NOUN
cana-3074	90	92	in	in	ADP
cana-3074	90	93	real	real	ADJ
cana-3074	90	94	-	-	PUNCT
cana-3074	90	95	life	life	NOUN
cana-3074	90	96	situations	situation	NOUN
cana-3074	90	97	visually	visually	ADV
cana-3074	90	98	applying	apply	VERB
cana-3074	90	99	the	the	DET
cana-3074	90	100	triangle	triangle	NOUN
cana-3074	90	101	concept	concept	NOUN
cana-3074	90	102	in	in	ADP
cana-3074	90	103	real	real	ADJ
cana-3074	90	104	-	-	PUNCT
cana-3074	90	105	life	life	NOUN
cana-3074	90	106	situations	situation	NOUN
cana-3074	90	107	concept	concept	NOUN
cana-3074	90	108	manipulation	manipulation	NOUN
cana-3074	90	109	applying	apply	VERB
cana-3074	90	110	mathematical	mathematical	ADJ
cana-3074	90	111	concepts	concept	NOUN
cana-3074	90	112	to	to	PART
cana-3074	90	113	understand	understand	VERB
cana-3074	90	114	the	the	DET
cana-3074	90	115	triangle	triangle	NOUN
cana-3074	90	116	concept	concept	NOUN
cana-3074	90	117	manipulating	manipulate	VERB
cana-3074	90	118	triangle	triangle	NOUN
cana-3074	90	119	concepts	concept	NOUN
cana-3074	90	120	to	to	PART
cana-3074	90	121	understand	understand	VERB
cana-3074	90	122	other	other	ADJ
cana-3074	90	123	math	math	NOUN
cana-3074	90	124	concepts	concept	NOUN
cana-3074	90	125	integration	integration	NOUN
cana-3074	90	126	of	of	ADP
cana-3074	90	127	mathematical	mathematical	ADJ
cana-3074	90	128	concepts	concept	NOUN
cana-3074	90	129	building	build	VERB
cana-3074	90	130	relationships	relationship	NOUN
cana-3074	90	131	among	among	ADP
cana-3074	90	132	geometry	geometry	NOUN
cana-3074	90	133	,	,	PUNCT
cana-3074	90	134	trigonometry	trigonometry	NOUN
cana-3074	90	135	,	,	PUNCT
cana-3074	90	136	and	and	CCONJ
cana-3074	90	137	cartesian	cartesian	ADJ
cana-3074	90	138	coordinates	coordinate	NOUN
cana-3074	90	139	concepts	concept	NOUN
cana-3074	90	140	according	accord	VERB
cana-3074	90	141	to	to	ADP
cana-3074	90	142	mitchelmore	mitchelmore	NOUN
cana-3074	90	143	and	and	CCONJ
cana-3074	90	144	white	white	ADJ
cana-3074	90	145	(	(	PUNCT
cana-3074	90	146	2007	2007	NUM
cana-3074	90	147	)	)	PUNCT
cana-3074	90	148	,	,	PUNCT
cana-3074	90	149	empirical	empirical	ADJ
cana-3074	90	150	abstraction	abstraction	NOUN
cana-3074	90	151	is	be	AUX
cana-3074	90	152	the	the	DET
cana-3074	90	153	process	process	NOUN
cana-3074	90	154	of	of	ADP
cana-3074	90	155	understanding	understand	VERB
cana-3074	90	156	geometric	geometric	ADJ
cana-3074	90	157	concepts	concept	NOUN
cana-3074	90	158	through	through	ADP
cana-3074	90	159	identifying	identify	VERB
cana-3074	90	160	similarities	similarity	NOUN
cana-3074	90	161	among	among	ADP
cana-3074	90	162	geometric	geometric	ADJ
cana-3074	90	163	objects	object	NOUN
cana-3074	90	164	and	and	CCONJ
cana-3074	90	165	their	their	PRON
cana-3074	90	166	properties	property	NOUN
cana-3074	90	167	,	,	PUNCT
cana-3074	90	168	direct	direct	ADJ
cana-3074	90	169	experimentation	experimentation	NOUN
cana-3074	90	170	,	,	PUNCT
cana-3074	90	171	and	and	CCONJ
cana-3074	90	172	constructing	construct	VERB
cana-3074	90	173	mental	mental	ADJ
cana-3074	90	174	models	model	NOUN
cana-3074	90	175	based	base	VERB
cana-3074	90	176	on	on	ADP
cana-3074	90	177	direct	direct	ADJ
cana-3074	90	178	experience	experience	NOUN
cana-3074	90	179	.	.	PUNCT
cana-3074	91	1	in	in	ADP
cana-3074	91	2	this	this	DET
cana-3074	91	3	study	study	NOUN
cana-3074	91	4	,	,	PUNCT
cana-3074	91	5	each	each	DET
cana-3074	91	6	van	van	PROPN
cana-3074	91	7	hiele	hiele	PROPN
cana-3074	91	8	level	level	NOUN
cana-3074	91	9	involves	involve	VERB
cana-3074	91	10	empirical	empirical	ADJ
cana-3074	91	11	abstraction	abstraction	NOUN
cana-3074	91	12	,	,	PUNCT
cana-3074	91	13	including	include	VERB
cana-3074	91	14	direct	direct	ADJ
cana-3074	91	15	experience	experience	NOUN
cana-3074	91	16	,	,	PUNCT
cana-3074	91	17	reality	reality	NOUN
cana-3074	91	18	or	or	CCONJ
cana-3074	91	19	imagination	imagination	NOUN
cana-3074	91	20	,	,	PUNCT
cana-3074	91	21	mathematical	mathematical	ADJ
cana-3074	91	22	representation	representation	NOUN
cana-3074	91	23	,	,	PUNCT
cana-3074	91	24	mathematical	mathematical	ADJ
cana-3074	91	25	idealization	idealization	NOUN
cana-3074	91	26	,	,	PUNCT
cana-3074	91	27	and	and	CCONJ
cana-3074	91	28	real	real	ADJ
cana-3074	91	29	-	-	PUNCT
cana-3074	91	30	world	world	NOUN
cana-3074	91	31	relevance	relevance	NOUN
cana-3074	91	32	.	.	PUNCT
cana-3074	92	1	this	this	DET
cana-3074	92	2	finding	finding	NOUN
cana-3074	92	3	differs	differ	VERB
cana-3074	92	4	from	from	ADP
cana-3074	92	5	nurhasanah	nurhasanah	PROPN
cana-3074	92	6	et	et	PROPN
cana-3074	92	7	al	al	PROPN
cana-3074	92	8	.	.	PROPN
cana-3074	93	1	(	(	PUNCT
cana-3074	93	2	2013	2013	NUM
cana-3074	93	3	)	)	PUNCT
cana-3074	93	4	,	,	PUNCT
cana-3074	93	5	who	who	PRON
cana-3074	93	6	stated	state	VERB
cana-3074	93	7	that	that	SCONJ
cana-3074	93	8	empirical	empirical	ADJ
cana-3074	93	9	abstraction	abstraction	NOUN
cana-3074	93	10	consists	consist	VERB
cana-3074	93	11	of	of	ADP
cana-3074	93	12	two	two	NUM
cana-3074	93	13	aspects	aspect	NOUN
cana-3074	93	14	:	:	PUNCT
cana-3074	93	15	communications	communication	NOUN
cana-3074	93	16	on	on	ADP
cana-3074	93	17	applied	apply	VERB
cana-3074	93	18	nonlinear	nonlinear	ADJ
cana-3074	93	19	analysis	analysis	NOUN
cana-3074	93	20	issn	issn	NOUN
cana-3074	93	21	:	:	PUNCT
cana-3074	93	22	1074	1074	NUM
cana-3074	93	23	-	-	PUNCT
cana-3074	93	24	133x	133x	NUM
cana-3074	93	25	vol	vol	NOUN
cana-3074	93	26	32	32	NUM
cana-3074	93	27	no	no	NOUN
cana-3074	93	28	.	.	PUNCT
cana-3074	94	1	5s	5s	NUM
cana-3074	94	2	(	(	PUNCT
cana-3074	94	3	2025	2025	NUM
cana-3074	94	4	)	)	PUNCT
cana-3074	94	5	274	274	NUM
cana-3074	94	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	94	7	recognizing	recognize	VERB
cana-3074	94	8	object	object	NOUN
cana-3074	94	9	characteristics	characteristic	NOUN
cana-3074	94	10	through	through	ADP
cana-3074	94	11	direct	direct	ADJ
cana-3074	94	12	experience	experience	NOUN
cana-3074	94	13	and	and	CCONJ
cana-3074	94	14	recognizing	recognize	VERB
cana-3074	94	15	object	object	NOUN
cana-3074	94	16	characteristics	characteristic	NOUN
cana-3074	94	17	through	through	ADP
cana-3074	94	18	manipulation	manipulation	NOUN
cana-3074	94	19	or	or	CCONJ
cana-3074	94	20	imagination	imagination	NOUN
cana-3074	94	21	.	.	PUNCT
cana-3074	95	1	this	this	DET
cana-3074	95	2	study	study	NOUN
cana-3074	95	3	found	find	VERB
cana-3074	95	4	that	that	SCONJ
cana-3074	95	5	empirical	empirical	ADJ
cana-3074	95	6	abstraction	abstraction	NOUN
cana-3074	95	7	is	be	AUX
cana-3074	95	8	also	also	ADV
cana-3074	95	9	indicated	indicate	VERB
cana-3074	95	10	through	through	ADP
cana-3074	95	11	pattern	pattern	NOUN
cana-3074	95	12	-	-	PUNCT
cana-3074	95	13	based	base	VERB
cana-3074	95	14	generalization	generalization	NOUN
cana-3074	95	15	,	,	PUNCT
cana-3074	95	16	mathematical	mathematical	ADJ
cana-3074	95	17	representation	representation	NOUN
cana-3074	95	18	,	,	PUNCT
cana-3074	95	19	mathematical	mathematical	ADJ
cana-3074	95	20	idealization	idealization	NOUN
cana-3074	95	21	,	,	PUNCT
cana-3074	95	22	and	and	CCONJ
cana-3074	95	23	real	real	ADJ
cana-3074	95	24	-	-	PUNCT
cana-3074	95	25	world	world	NOUN
cana-3074	95	26	relevance	relevance	NOUN
cana-3074	95	27	visually	visually	ADV
cana-3074	95	28	.	.	PUNCT
cana-3074	96	1	furthermore	furthermore	ADV
cana-3074	96	2	,	,	PUNCT
cana-3074	96	3	theoretical	theoretical	ADJ
cana-3074	96	4	abstraction	abstraction	NOUN
cana-3074	96	5	is	be	AUX
cana-3074	96	6	the	the	DET
cana-3074	96	7	process	process	NOUN
cana-3074	96	8	of	of	ADP
cana-3074	96	9	forming	form	VERB
cana-3074	96	10	concepts	concept	NOUN
cana-3074	96	11	that	that	PRON
cana-3074	96	12	involve	involve	VERB
cana-3074	96	13	applying	apply	VERB
cana-3074	96	14	these	these	DET
cana-3074	96	15	concepts	concept	NOUN
cana-3074	96	16	within	within	ADP
cana-3074	96	17	a	a	DET
cana-3074	96	18	specific	specific	ADJ
cana-3074	96	19	theoretical	theoretical	ADJ
cana-3074	96	20	13	13	NUM
cana-3074	96	21	.	.	PUNCT
cana-3074	97	1	in	in	ADP
cana-3074	97	2	this	this	DET
cana-3074	97	3	study	study	NOUN
cana-3074	97	4	,	,	PUNCT
cana-3074	97	5	theoretical	theoretical	ADJ
cana-3074	97	6	abstraction	abstraction	NOUN
cana-3074	97	7	is	be	AUX
cana-3074	97	8	demonstrated	demonstrate	VERB
cana-3074	97	9	through	through	ADP
cana-3074	97	10	representation	representation	NOUN
cana-3074	97	11	(	(	PUNCT
cana-3074	97	12	formulating	formulate	VERB
cana-3074	97	13	a	a	DET
cana-3074	97	14	formula	formula	NOUN
cana-3074	97	15	)	)	PUNCT
cana-3074	97	16	,	,	PUNCT
cana-3074	97	17	conceptual	conceptual	ADJ
cana-3074	97	18	real	real	ADJ
cana-3074	97	19	-	-	PUNCT
cana-3074	97	20	world	world	NOUN
cana-3074	97	21	relevance	relevance	NOUN
cana-3074	97	22	,	,	PUNCT
cana-3074	97	23	manipulation	manipulation	NOUN
cana-3074	97	24	of	of	ADP
cana-3074	97	25	abstract	abstract	ADJ
cana-3074	97	26	concepts	concept	NOUN
cana-3074	97	27	,	,	PUNCT
cana-3074	97	28	and	and	CCONJ
cana-3074	97	29	integration	integration	NOUN
cana-3074	97	30	of	of	ADP
cana-3074	97	31	mathematical	mathematical	ADJ
cana-3074	97	32	concepts	concept	NOUN
cana-3074	97	33	.	.	PUNCT
cana-3074	98	1	based	base	VERB
cana-3074	98	2	on	on	ADP
cana-3074	98	3	the	the	DET
cana-3074	98	4	empirical	empirical	ADJ
cana-3074	98	5	and	and	CCONJ
cana-3074	98	6	theoretical	theoretical	ADJ
cana-3074	98	7	geometrical	geometrical	ADJ
cana-3074	98	8	abstraction	abstraction	NOUN
cana-3074	98	9	at	at	ADP
cana-3074	98	10	each	each	DET
cana-3074	98	11	van	van	PROPN
cana-3074	98	12	hiele	hiele	PROPN
cana-3074	98	13	level	level	NOUN
cana-3074	98	14	,	,	PUNCT
cana-3074	98	15	the	the	DET
cana-3074	98	16	following	following	NOUN
cana-3074	98	17	describes	describe	VERB
cana-3074	98	18	geometrical	geometrical	ADJ
cana-3074	98	19	abstraction	abstraction	NOUN
cana-3074	98	20	on	on	ADP
cana-3074	98	21	van	van	PROPN
cana-3074	98	22	hiele	hiele	PROPN
cana-3074	98	23	level	level	NOUN
cana-3074	98	24	are	be	AUX
cana-3074	98	25	follows	follow	VERB
cana-3074	98	26	:	:	PUNCT
cana-3074	98	27	visualization	visualization	NOUN
cana-3074	98	28	level	level	NOUN
cana-3074	98	29	geometrical	geometrical	ADJ
cana-3074	98	30	abstraction	abstraction	NOUN
cana-3074	98	31	at	at	ADP
cana-3074	98	32	the	the	DET
cana-3074	98	33	visualization	visualization	NOUN
cana-3074	98	34	level	level	NOUN
cana-3074	98	35	involves	involve	VERB
cana-3074	98	36	the	the	DET
cana-3074	98	37	ability	ability	NOUN
cana-3074	98	38	to	to	PART
cana-3074	98	39	understand	understand	VERB
cana-3074	98	40	,	,	PUNCT
cana-3074	98	41	imagine	imagine	ADJ
cana-3074	98	42	,	,	PUNCT
cana-3074	98	43	represent	represent	VERB
cana-3074	98	44	,	,	PUNCT
cana-3074	98	45	idealize	idealize	VERB
cana-3074	98	46	,	,	PUNCT
cana-3074	98	47	and	and	CCONJ
cana-3074	98	48	apply	apply	VERB
cana-3074	98	49	the	the	DET
cana-3074	98	50	triangle	triangle	NOUN
cana-3074	98	51	concept	concept	NOUN
cana-3074	98	52	to	to	ADP
cana-3074	98	53	real	real	ADJ
cana-3074	98	54	-	-	PUNCT
cana-3074	98	55	world	world	NOUN
cana-3074	98	56	situations	situation	NOUN
cana-3074	98	57	visually	visually	ADV
cana-3074	98	58	.	.	PUNCT
cana-3074	99	1	on	on	ADP
cana-3074	99	2	this	this	DET
cana-3074	99	3	level	level	NOUN
cana-3074	99	4	,	,	PUNCT
cana-3074	99	5	the	the	DET
cana-3074	99	6	mathematics	mathematics	NOUN
cana-3074	99	7	undergraduates	undergraduate	NOUN
cana-3074	99	8	identify	identify	VERB
cana-3074	99	9	the	the	DET
cana-3074	99	10	geometric	geometric	ADJ
cana-3074	99	11	characteristics	characteristic	NOUN
cana-3074	99	12	of	of	ADP
cana-3074	99	13	triangle	triangle	NOUN
cana-3074	99	14	abc	abc	PROPN
cana-3074	99	15	through	through	ADP
cana-3074	99	16	direct	direct	ADJ
cana-3074	99	17	experience	experience	NOUN
cana-3074	99	18	.	.	PUNCT
cana-3074	100	1	for	for	ADP
cana-3074	100	2	example	example	NOUN
cana-3074	100	3	,	,	PUNCT
cana-3074	100	4	the	the	DET
cana-3074	100	5	mathematics	mathematics	NOUN
cana-3074	100	6	undergraduates	undergraduate	NOUN
cana-3074	100	7	can	can	AUX
cana-3074	100	8	recognize	recognize	VERB
cana-3074	100	9	that	that	SCONJ
cana-3074	100	10	a	a	DET
cana-3074	100	11	triangle	triangle	NOUN
cana-3074	100	12	has	have	VERB
cana-3074	100	13	three	three	NUM
cana-3074	100	14	sides	side	NOUN
cana-3074	100	15	and	and	CCONJ
cana-3074	100	16	three	three	NUM
cana-3074	100	17	angles	angle	NOUN
cana-3074	100	18	.	.	PUNCT
cana-3074	101	1	geometrical	geometrical	ADJ
cana-3074	101	2	abstraction	abstraction	NOUN
cana-3074	101	3	at	at	ADP
cana-3074	101	4	the	the	DET
cana-3074	101	5	visualization	visualization	NOUN
cana-3074	101	6	level	level	NOUN
cana-3074	101	7	falls	fall	VERB
cana-3074	101	8	within	within	ADP
cana-3074	101	9	empirical	empirical	ADJ
cana-3074	101	10	abstraction	abstraction	NOUN
cana-3074	101	11	.	.	PUNCT
cana-3074	102	1	analysis	analysis	NOUN
cana-3074	102	2	level	level	NOUN
cana-3074	102	3	geometrical	geometrical	ADJ
cana-3074	102	4	abstraction	abstraction	NOUN
cana-3074	102	5	at	at	ADP
cana-3074	102	6	the	the	DET
cana-3074	102	7	analysis	analysis	NOUN
cana-3074	102	8	level	level	NOUN
cana-3074	102	9	includes	include	VERB
cana-3074	102	10	the	the	DET
cana-3074	102	11	ability	ability	NOUN
cana-3074	102	12	to	to	PART
cana-3074	102	13	understand	understand	VERB
cana-3074	102	14	,	,	PUNCT
cana-3074	102	15	imagine	imagine	ADJ
cana-3074	102	16	,	,	PUNCT
cana-3074	102	17	represent	represent	VERB
cana-3074	102	18	,	,	PUNCT
cana-3074	102	19	generalize	generalize	VERB
cana-3074	102	20	,	,	PUNCT
cana-3074	102	21	idealize	idealize	VERB
cana-3074	102	22	,	,	PUNCT
cana-3074	102	23	and	and	CCONJ
cana-3074	102	24	apply	apply	VERB
cana-3074	102	25	the	the	DET
cana-3074	102	26	triangle	triangle	NOUN
cana-3074	102	27	concept	concept	NOUN
cana-3074	102	28	to	to	ADP
cana-3074	102	29	real	real	ADJ
cana-3074	102	30	-	-	PUNCT
cana-3074	102	31	world	world	NOUN
cana-3074	102	32	situations	situation	NOUN
cana-3074	102	33	conceptually	conceptually	ADV
cana-3074	102	34	.	.	PUNCT
cana-3074	103	1	on	on	ADP
cana-3074	103	2	this	this	DET
cana-3074	103	3	level	level	NOUN
cana-3074	103	4	,	,	PUNCT
cana-3074	103	5	the	the	DET
cana-3074	103	6	mathematics	mathematics	NOUN
cana-3074	103	7	undergraduates	undergraduate	NOUN
cana-3074	103	8	draw	draw	VERB
cana-3074	103	9	a	a	DET
cana-3074	103	10	new	new	ADJ
cana-3074	103	11	triangle	triangle	NOUN
cana-3074	103	12	resulting	result	VERB
cana-3074	103	13	from	from	ADP
cana-3074	103	14	manipulating	manipulate	VERB
cana-3074	103	15	the	the	DET
cana-3074	103	16	positions	position	NOUN
cana-3074	103	17	of	of	ADP
cana-3074	103	18	coordinate	coordinate	NOUN
cana-3074	103	19	points	point	NOUN
cana-3074	103	20	.	.	PUNCT
cana-3074	104	1	the	the	DET
cana-3074	104	2	mathematics	mathematics	NOUN
cana-3074	104	3	undergraduates	undergraduate	NOUN
cana-3074	104	4	also	also	ADV
cana-3074	104	5	begin	begin	VERB
cana-3074	104	6	to	to	PART
cana-3074	104	7	develop	develop	VERB
cana-3074	104	8	the	the	DET
cana-3074	104	9	ability	ability	NOUN
cana-3074	104	10	to	to	PART
cana-3074	104	11	manipulate	manipulate	VERB
cana-3074	104	12	triangle	triangle	NOUN
cana-3074	104	13	variants	variant	NOUN
cana-3074	104	14	.	.	PUNCT
cana-3074	105	1	geometrical	geometrical	ADJ
cana-3074	105	2	abstraction	abstraction	NOUN
cana-3074	105	3	at	at	ADP
cana-3074	105	4	the	the	DET
cana-3074	105	5	analysis	analysis	NOUN
cana-3074	105	6	level	level	NOUN
cana-3074	105	7	involves	involve	VERB
cana-3074	105	8	both	both	CCONJ
cana-3074	105	9	empirical	empirical	ADJ
cana-3074	105	10	and	and	CCONJ
cana-3074	105	11	theoretical	theoretical	ADJ
cana-3074	105	12	abstraction	abstraction	NOUN
cana-3074	105	13	.	.	PUNCT
cana-3074	106	1	informal	informal	ADJ
cana-3074	106	2	deduction	deduction	NOUN
cana-3074	106	3	level	level	NOUN
cana-3074	106	4	geometrical	geometrical	ADJ
cana-3074	106	5	abstraction	abstraction	NOUN
cana-3074	106	6	at	at	ADP
cana-3074	106	7	the	the	DET
cana-3074	106	8	informal	informal	ADJ
cana-3074	106	9	deduction	deduction	NOUN
cana-3074	106	10	level	level	NOUN
cana-3074	106	11	involves	involve	VERB
cana-3074	106	12	the	the	DET
cana-3074	106	13	ability	ability	NOUN
cana-3074	106	14	to	to	PART
cana-3074	106	15	understand	understand	VERB
cana-3074	106	16	,	,	PUNCT
cana-3074	106	17	imagine	imagine	ADJ
cana-3074	106	18	,	,	PUNCT
cana-3074	106	19	represent	represent	VERB
cana-3074	106	20	,	,	PUNCT
cana-3074	106	21	generalize	generalize	VERB
cana-3074	106	22	,	,	PUNCT
cana-3074	106	23	idealize	idealize	VERB
cana-3074	106	24	,	,	PUNCT
cana-3074	106	25	apply	apply	VERB
cana-3074	106	26	,	,	PUNCT
cana-3074	106	27	and	and	CCONJ
cana-3074	106	28	apply	apply	VERB
cana-3074	106	29	geometric	geometric	ADJ
cana-3074	106	30	concepts	concept	NOUN
cana-3074	106	31	in	in	ADP
cana-3074	106	32	various	various	ADJ
cana-3074	106	33	contexts	contexts	NOUN
cana-3074	106	34	.	.	PUNCT
cana-3074	107	1	on	on	ADP
cana-3074	107	2	this	this	DET
cana-3074	107	3	level	level	NOUN
cana-3074	107	4	,	,	PUNCT
cana-3074	107	5	the	the	DET
cana-3074	107	6	mathematics	mathematics	NOUN
cana-3074	107	7	undergraduates	undergraduate	VERB
cana-3074	107	8	manipulate	manipulate	VERB
cana-3074	107	9	triangle	triangle	NOUN
cana-3074	107	10	variants	variant	NOUN
cana-3074	107	11	and	and	CCONJ
cana-3074	107	12	idealize	idealize	VERB
cana-3074	107	13	the	the	DET
cana-3074	107	14	shape	shape	NOUN
cana-3074	107	15	of	of	ADP
cana-3074	107	16	triangle	triangle	NOUN
cana-3074	107	17	abc	abc	PROPN
cana-3074	107	18	into	into	ADP
cana-3074	107	19	a	a	DET
cana-3074	107	20	general	general	ADJ
cana-3074	107	21	form	form	NOUN
cana-3074	107	22	visually	visually	ADV
cana-3074	107	23	.	.	PUNCT
cana-3074	108	1	the	the	DET
cana-3074	108	2	mathematics	mathematics	NOUN
cana-3074	108	3	undergraduates	undergraduate	NOUN
cana-3074	108	4	also	also	ADV
cana-3074	108	5	begin	begin	VERB
cana-3074	108	6	to	to	PART
cana-3074	108	7	form	form	VERB
cana-3074	108	8	relationships	relationship	NOUN
cana-3074	108	9	between	between	ADP
cana-3074	108	10	the	the	DET
cana-3074	108	11	lengths	length	NOUN
cana-3074	108	12	of	of	ADP
cana-3074	108	13	sides	side	NOUN
cana-3074	108	14	and	and	CCONJ
cana-3074	108	15	angles	angle	NOUN
cana-3074	108	16	of	of	ADP
cana-3074	108	17	a	a	DET
cana-3074	108	18	triangle	triangle	NOUN
cana-3074	108	19	more	more	ADV
cana-3074	108	20	formally	formally	ADV
cana-3074	108	21	.	.	PUNCT
cana-3074	109	1	geometrical	geometrical	ADJ
cana-3074	109	2	abstraction	abstraction	NOUN
cana-3074	109	3	at	at	ADP
cana-3074	109	4	the	the	DET
cana-3074	109	5	informal	informal	ADJ
cana-3074	109	6	deduction	deduction	NOUN
cana-3074	109	7	level	level	NOUN
cana-3074	109	8	involves	involve	VERB
cana-3074	109	9	both	both	CCONJ
cana-3074	109	10	empirical	empirical	ADJ
cana-3074	109	11	and	and	CCONJ
cana-3074	109	12	theoretical	theoretical	ADJ
cana-3074	109	13	abstraction	abstraction	NOUN
cana-3074	109	14	.	.	PUNCT
cana-3074	110	1	formal	formal	ADJ
cana-3074	110	2	deduction	deduction	NOUN
cana-3074	110	3	level	level	NOUN
cana-3074	110	4	geometrical	geometrical	ADJ
cana-3074	110	5	abstraction	abstraction	NOUN
cana-3074	110	6	at	at	ADP
cana-3074	110	7	the	the	DET
cana-3074	110	8	formal	formal	ADJ
cana-3074	110	9	deduction	deduction	NOUN
cana-3074	110	10	level	level	NOUN
cana-3074	110	11	involves	involve	VERB
cana-3074	110	12	the	the	DET
cana-3074	110	13	ability	ability	NOUN
cana-3074	110	14	to	to	PART
cana-3074	110	15	understand	understand	VERB
cana-3074	110	16	,	,	PUNCT
cana-3074	110	17	imagine	imagine	ADJ
cana-3074	110	18	,	,	PUNCT
cana-3074	110	19	represent	represent	VERB
cana-3074	110	20	,	,	PUNCT
cana-3074	110	21	generalize	generalize	VERB
cana-3074	110	22	,	,	PUNCT
cana-3074	110	23	idealize	idealize	VERB
cana-3074	110	24	,	,	PUNCT
cana-3074	110	25	apply	apply	VERB
cana-3074	110	26	,	,	PUNCT
cana-3074	110	27	apply	apply	VERB
cana-3074	110	28	,	,	PUNCT
cana-3074	110	29	and	and	CCONJ
cana-3074	110	30	integrate	integrate	VERB
cana-3074	110	31	geometric	geometric	ADJ
cana-3074	110	32	concepts	concept	NOUN
cana-3074	110	33	in	in	ADP
cana-3074	110	34	various	various	ADJ
cana-3074	110	35	contexts	contexts	NOUN
cana-3074	110	36	.	.	PUNCT
cana-3074	111	1	on	on	ADP
cana-3074	111	2	this	this	DET
cana-3074	111	3	level	level	NOUN
cana-3074	111	4	,	,	PUNCT
cana-3074	111	5	the	the	DET
cana-3074	111	6	mathematics	mathematics	NOUN
cana-3074	111	7	undergraduates	undergraduate	NOUN
cana-3074	111	8	demonstrate	demonstrate	VERB
cana-3074	111	9	a	a	DET
cana-3074	111	10	more	more	ADV
cana-3074	111	11	formal	formal	ADJ
cana-3074	111	12	understanding	understanding	NOUN
cana-3074	111	13	of	of	ADP
cana-3074	111	14	geometry	geometry	NOUN
cana-3074	111	15	and	and	CCONJ
cana-3074	111	16	manipulate	manipulate	VERB
cana-3074	111	17	triangle	triangle	NOUN
cana-3074	111	18	concepts	concept	NOUN
cana-3074	111	19	to	to	PART
cana-3074	111	20	understand	understand	VERB
cana-3074	111	21	other	other	ADJ
cana-3074	111	22	mathematical	mathematical	ADJ
cana-3074	111	23	concepts	concept	NOUN
cana-3074	111	24	.	.	PUNCT
cana-3074	112	1	the	the	DET
cana-3074	112	2	mathematics	mathematics	NOUN
cana-3074	112	3	undergraduates	undergraduate	NOUN
cana-3074	112	4	also	also	ADV
cana-3074	112	5	build	build	VERB
cana-3074	112	6	relationships	relationship	NOUN
cana-3074	112	7	among	among	ADP
cana-3074	112	8	various	various	ADJ
cana-3074	112	9	mathematical	mathematical	ADJ
cana-3074	112	10	concepts	concept	NOUN
cana-3074	112	11	,	,	PUNCT
cana-3074	112	12	such	such	ADJ
cana-3074	112	13	as	as	ADP
cana-3074	112	14	geometry	geometry	NOUN
cana-3074	112	15	,	,	PUNCT
cana-3074	112	16	trigonometry	trigonometry	NOUN
cana-3074	112	17	,	,	PUNCT
cana-3074	112	18	and	and	CCONJ
cana-3074	112	19	cartesian	cartesian	ADJ
cana-3074	112	20	coordinates	coordinate	NOUN
cana-3074	112	21	,	,	PUNCT
cana-3074	112	22	in	in	ADP
cana-3074	112	23	understanding	understand	VERB
cana-3074	112	24	triangle	triangle	NOUN
cana-3074	112	25	abc	abc	PROPN
cana-3074	112	26	using	use	VERB
cana-3074	112	27	a	a	DET
cana-3074	112	28	more	more	ADV
cana-3074	112	29	formal	formal	ADJ
cana-3074	112	30	and	and	CCONJ
cana-3074	112	31	in	in	ADP
cana-3074	112	32	13	13	NUM
cana-3074	112	33	mitchelmore	mitchelmore	NOUN
cana-3074	112	34	&	&	CCONJ
cana-3074	112	35	white	white	PROPN
cana-3074	112	36	2007	2007	NUM
cana-3074	112	37	communications	communication	NOUN
cana-3074	112	38	on	on	ADP
cana-3074	112	39	applied	apply	VERB
cana-3074	112	40	nonlinear	nonlinear	ADJ
cana-3074	112	41	analysis	analysis	NOUN
cana-3074	112	42	issn	issn	NOUN
cana-3074	112	43	:	:	PUNCT
cana-3074	112	44	1074	1074	NUM
cana-3074	112	45	-	-	PUNCT
cana-3074	112	46	133x	133x	NUM
cana-3074	112	47	vol	vol	NOUN
cana-3074	112	48	32	32	NUM
cana-3074	112	49	no	no	NOUN
cana-3074	112	50	.	.	PUNCT
cana-3074	113	1	5s	5s	NUM
cana-3074	113	2	(	(	PUNCT
cana-3074	113	3	2025	2025	NUM
cana-3074	113	4	)	)	PUNCT
cana-3074	114	1	275	275	NUM
cana-3074	114	2	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-3074	114	3	depth	depth	NOUN
cana-3074	114	4	understanding	understanding	NOUN
cana-3074	114	5	of	of	ADP
cana-3074	114	6	mathematical	mathematical	ADJ
cana-3074	114	7	concepts	concept	NOUN
cana-3074	114	8	.	.	PUNCT
cana-3074	115	1	geometrical	geometrical	ADJ
cana-3074	115	2	abstraction	abstraction	NOUN
cana-3074	115	3	at	at	ADP
cana-3074	115	4	the	the	DET
cana-3074	115	5	formal	formal	ADJ
cana-3074	115	6	deduction	deduction	NOUN
cana-3074	115	7	level	level	NOUN
cana-3074	115	8	involves	involve	VERB
cana-3074	115	9	both	both	CCONJ
cana-3074	115	10	empirical	empirical	ADJ
cana-3074	115	11	and	and	CCONJ
cana-3074	115	12	theoretical	theoretical	ADJ
cana-3074	115	13	abstraction	abstraction	NOUN
cana-3074	115	14	.	.	PUNCT
cana-3074	116	1	rigor	rigor	NOUN
cana-3074	116	2	level	level	NOUN
cana-3074	116	3	geometrical	geometrical	ADJ
cana-3074	116	4	abstraction	abstraction	NOUN
cana-3074	116	5	at	at	ADP
cana-3074	116	6	the	the	DET
cana-3074	116	7	rigor	rigor	NOUN
cana-3074	116	8	level	level	NOUN
cana-3074	116	9	involves	involve	VERB
cana-3074	116	10	the	the	DET
cana-3074	116	11	ability	ability	NOUN
cana-3074	116	12	to	to	PART
cana-3074	116	13	understand	understand	VERB
cana-3074	116	14	,	,	PUNCT
cana-3074	116	15	imagine	imagine	ADJ
cana-3074	116	16	,	,	PUNCT
cana-3074	116	17	represent	represent	VERB
cana-3074	116	18	,	,	PUNCT
cana-3074	116	19	formulate	formulate	ADJ
cana-3074	116	20	,	,	PUNCT
cana-3074	116	21	generalize	generalize	VERB
cana-3074	116	22	,	,	PUNCT
cana-3074	116	23	idealize	idealize	VERB
cana-3074	116	24	,	,	PUNCT
cana-3074	116	25	apply	apply	VERB
cana-3074	116	26	,	,	PUNCT
cana-3074	116	27	apply	apply	VERB
cana-3074	116	28	,	,	PUNCT
cana-3074	116	29	and	and	CCONJ
cana-3074	116	30	integrate	integrate	VERB
cana-3074	116	31	geometric	geometric	ADJ
cana-3074	116	32	concepts	concept	NOUN
cana-3074	116	33	in	in	ADP
cana-3074	116	34	various	various	ADJ
cana-3074	116	35	contexts	contexts	NOUN
cana-3074	116	36	.	.	PUNCT
cana-3074	117	1	on	on	ADP
cana-3074	117	2	this	this	DET
cana-3074	117	3	level	level	NOUN
cana-3074	117	4	,	,	PUNCT
cana-3074	117	5	the	the	DET
cana-3074	117	6	mathematics	mathematic	NOUN
cana-3074	117	7	undergraduates	undergraduate	NOUN
cana-3074	117	8	apply	apply	VERB
cana-3074	117	9	the	the	DET
cana-3074	117	10	triangle	triangle	NOUN
cana-3074	117	11	concept	concept	NOUN
cana-3074	117	12	to	to	ADP
cana-3074	117	13	real	real	ADJ
cana-3074	117	14	-	-	PUNCT
cana-3074	117	15	world	world	NOUN
cana-3074	117	16	situations	situation	NOUN
cana-3074	117	17	using	use	VERB
cana-3074	117	18	practical	practical	ADJ
cana-3074	117	19	geometric	geometric	ADJ
cana-3074	117	20	knowledge	knowledge	NOUN
cana-3074	117	21	.	.	PUNCT
cana-3074	118	1	additionally	additionally	ADV
cana-3074	118	2	,	,	PUNCT
cana-3074	118	3	the	the	DET
cana-3074	118	4	mathematics	mathematics	NOUN
cana-3074	118	5	undergraduates	undergraduate	NOUN
cana-3074	118	6	integrate	integrate	VERB
cana-3074	118	7	the	the	DET
cana-3074	118	8	mathematical	mathematical	ADJ
cana-3074	118	9	concepts	concept	NOUN
cana-3074	118	10	they	they	PRON
cana-3074	118	11	have	have	AUX
cana-3074	118	12	learned	learn	VERB
cana-3074	118	13	to	to	PART
cana-3074	118	14	build	build	VERB
cana-3074	118	15	a	a	DET
cana-3074	118	16	broader	broad	ADJ
cana-3074	118	17	understanding	understanding	NOUN
cana-3074	118	18	of	of	ADP
cana-3074	118	19	geometry	geometry	NOUN
cana-3074	118	20	.	.	PUNCT
cana-3074	119	1	geometrical	geometrical	ADJ
cana-3074	119	2	abstraction	abstraction	NOUN
cana-3074	119	3	at	at	ADP
cana-3074	119	4	the	the	DET
cana-3074	119	5	rigor	rigor	NOUN
cana-3074	119	6	level	level	NOUN
cana-3074	119	7	involves	involve	VERB
cana-3074	119	8	both	both	CCONJ
cana-3074	119	9	empirical	empirical	ADJ
cana-3074	119	10	and	and	CCONJ
cana-3074	119	11	theoretical	theoretical	ADJ
cana-3074	119	12	abstraction	abstraction	NOUN
cana-3074	119	13	.	.	PUNCT
cana-3074	120	1	moreover	moreover	ADV
cana-3074	120	2	,	,	PUNCT
cana-3074	120	3	this	this	DET
cana-3074	120	4	study	study	NOUN
cana-3074	120	5	found	find	VERB
cana-3074	120	6	a	a	DET
cana-3074	120	7	significant	significant	ADJ
cana-3074	120	8	finding	finding	NOUN
cana-3074	120	9	that	that	SCONJ
cana-3074	120	10	the	the	PRON
cana-3074	120	11	higher	high	ADJ
cana-3074	120	12	the	the	DET
cana-3074	120	13	van	van	PROPN
cana-3074	120	14	hiele	hiele	PROPN
cana-3074	120	15	level	level	NOUN
cana-3074	120	16	possessed	possess	VERB
cana-3074	120	17	by	by	ADP
cana-3074	120	18	the	the	DET
cana-3074	120	19	mathematics	mathematic	NOUN
cana-3074	120	20	undergraduates	undergraduate	NOUN
cana-3074	120	21	,	,	PUNCT
cana-3074	120	22	the	the	PRON
cana-3074	120	23	more	more	ADV
cana-3074	120	24	comprehensive	comprehensive	ADJ
cana-3074	120	25	the	the	DET
cana-3074	120	26	aspects	aspect	NOUN
cana-3074	120	27	of	of	ADP
cana-3074	120	28	geometrical	geometrical	ADJ
cana-3074	120	29	abstraction	abstraction	NOUN
cana-3074	120	30	they	they	PRON
cana-3074	120	31	can	can	AUX
cana-3074	120	32	achieve	achieve	VERB
cana-3074	120	33	.	.	PUNCT
cana-3074	121	1	this	this	PRON
cana-3074	121	2	indicates	indicate	VERB
cana-3074	121	3	a	a	DET
cana-3074	121	4	significant	significant	ADJ
cana-3074	121	5	relationship	relationship	NOUN
cana-3074	121	6	between	between	ADP
cana-3074	121	7	van	van	PROPN
cana-3074	121	8	hiele	hiele	PROPN
cana-3074	121	9	levels	level	NOUN
cana-3074	121	10	and	and	CCONJ
cana-3074	121	11	the	the	DET
cana-3074	121	12	mathematics	mathematics	NOUN
cana-3074	121	13	undergraduates	undergraduate	VERB
cana-3074	121	14	'	'	PART
cana-3074	121	15	geometrical	geometrical	ADJ
cana-3074	121	16	abstraction	abstraction	NOUN
cana-3074	121	17	.	.	PUNCT
cana-3074	122	1	conclusion	conclusion	NOUN
cana-3074	122	2	in	in	ADP
cana-3074	122	3	conclusion	conclusion	NOUN
cana-3074	122	4	,	,	PUNCT
cana-3074	122	5	the	the	DET
cana-3074	122	6	research	research	NOUN
cana-3074	122	7	conducted	conduct	VERB
cana-3074	122	8	on	on	ADP
cana-3074	122	9	mathematics	mathematic	NOUN
cana-3074	122	10	undergraduates	undergraduate	NOUN
cana-3074	122	11	at	at	ADP
cana-3074	122	12	the	the	DET
cana-3074	122	13	state	state	NOUN
cana-3074	122	14	university	university	PROPN
cana-3074	122	15	of	of	ADP
cana-3074	122	16	makassar	makassar	PROPN
cana-3074	122	17	found	find	VERB
cana-3074	122	18	several	several	ADJ
cana-3074	122	19	key	key	ADJ
cana-3074	122	20	findings	finding	NOUN
cana-3074	122	21	in	in	ADP
cana-3074	122	22	response	response	NOUN
cana-3074	122	23	to	to	ADP
cana-3074	122	24	the	the	DET
cana-3074	122	25	formulated	formulated	ADJ
cana-3074	122	26	problem	problem	NOUN
cana-3074	122	27	.	.	PUNCT
cana-3074	123	1	firstly	firstly	ADV
cana-3074	123	2	,	,	PUNCT
cana-3074	123	3	there	there	PRON
cana-3074	123	4	are	be	VERB
cana-3074	123	5	differences	difference	NOUN
cana-3074	123	6	in	in	ADP
cana-3074	123	7	the	the	DET
cana-3074	123	8	levels	level	NOUN
cana-3074	123	9	of	of	ADP
cana-3074	123	10	van	van	PROPN
cana-3074	123	11	hiele	hiele	PROPN
cana-3074	123	12	among	among	ADP
cana-3074	123	13	mathematics	mathematics	NOUN
cana-3074	123	14	undergraduates	undergraduate	NOUN
cana-3074	123	15	at	at	ADP
cana-3074	123	16	the	the	DET
cana-3074	123	17	state	state	NOUN
cana-3074	123	18	university	university	PROPN
cana-3074	123	19	of	of	ADP
cana-3074	123	20	makassar	makassar	PROPN
cana-3074	123	21	.	.	PUNCT
cana-3074	124	1	around	around	ADV
cana-3074	124	2	27.7	27.7	NUM
cana-3074	124	3	%	%	NOUN
cana-3074	124	4	of	of	ADP
cana-3074	124	5	mathematics	mathematics	NOUN
cana-3074	124	6	undergraduates	undergraduate	NOUN
cana-3074	124	7	demonstrate	demonstrate	VERB
cana-3074	124	8	visualization	visualization	NOUN
cana-3074	124	9	skills	skill	NOUN
cana-3074	124	10	,	,	PUNCT
cana-3074	124	11	whereas	whereas	SCONJ
cana-3074	124	12	37.2	37.2	NUM
cana-3074	124	13	%	%	NOUN
cana-3074	124	14	are	be	AUX
cana-3074	124	15	at	at	ADP
cana-3074	124	16	the	the	DET
cana-3074	124	17	analysis	analysis	NOUN
cana-3074	124	18	level	level	NOUN
cana-3074	124	19	.	.	PUNCT
cana-3074	125	1	however	however	ADV
cana-3074	125	2	,	,	PUNCT
cana-3074	125	3	only	only	ADV
cana-3074	125	4	a	a	DET
cana-3074	125	5	minority	minority	NOUN
cana-3074	125	6	of	of	ADP
cana-3074	125	7	undergraduates	undergraduate	NOUN
cana-3074	125	8	,	,	PUNCT
cana-3074	125	9	about	about	ADV
cana-3074	125	10	14.1	14.1	NUM
cana-3074	125	11	%	%	NOUN
cana-3074	125	12	,	,	PUNCT
cana-3074	125	13	1.0	1.0	NUM
cana-3074	125	14	%	%	NOUN
cana-3074	125	15	,	,	PUNCT
cana-3074	125	16	and	and	CCONJ
cana-3074	125	17	2.6	2.6	NUM
cana-3074	125	18	%	%	NOUN
cana-3074	125	19	respectively	respectively	ADV
cana-3074	125	20	,	,	PUNCT
cana-3074	125	21	achieve	achieve	VERB
cana-3074	125	22	the	the	DET
cana-3074	125	23	informal	informal	ADJ
cana-3074	125	24	deduction	deduction	NOUN
cana-3074	125	25	,	,	PUNCT
cana-3074	125	26	formal	formal	ADJ
cana-3074	125	27	deduction	deduction	NOUN
cana-3074	125	28	,	,	PUNCT
cana-3074	125	29	and	and	CCONJ
cana-3074	125	30	rigor	rigor	NOUN
cana-3074	125	31	levels	level	NOUN
cana-3074	125	32	.	.	PUNCT
cana-3074	126	1	secondly	secondly	ADV
cana-3074	126	2	,	,	PUNCT
cana-3074	126	3	the	the	DET
cana-3074	126	4	geometrical	geometrical	ADJ
cana-3074	126	5	abstraction	abstraction	NOUN
cana-3074	126	6	on	on	ADP
cana-3074	126	7	the	the	DET
cana-3074	126	8	visualization	visualization	NOUN
cana-3074	126	9	level	level	NOUN
cana-3074	126	10	involves	involve	VERB
cana-3074	126	11	understanding	understanding	NOUN
cana-3074	126	12	and	and	CCONJ
cana-3074	126	13	visually	visually	ADV
cana-3074	126	14	representing	represent	VERB
cana-3074	126	15	triangle	triangle	NOUN
cana-3074	126	16	concepts	concept	NOUN
cana-3074	126	17	,	,	PUNCT
cana-3074	126	18	primarily	primarily	ADV
cana-3074	126	19	based	base	VERB
cana-3074	126	20	on	on	ADP
cana-3074	126	21	empirical	empirical	ADJ
cana-3074	126	22	abstraction	abstraction	NOUN
cana-3074	126	23	.	.	PUNCT
cana-3074	127	1	on	on	ADP
cana-3074	127	2	the	the	DET
cana-3074	127	3	analysis	analysis	NOUN
cana-3074	127	4	level	level	NOUN
cana-3074	127	5	,	,	PUNCT
cana-3074	127	6	students	student	NOUN
cana-3074	127	7	generalize	generalize	VERB
cana-3074	127	8	triangle	triangle	NOUN
cana-3074	127	9	concepts	concept	NOUN
cana-3074	127	10	conceptually	conceptually	ADV
cana-3074	127	11	,	,	PUNCT
cana-3074	127	12	involving	involve	VERB
cana-3074	127	13	both	both	CCONJ
cana-3074	127	14	empirical	empirical	ADJ
cana-3074	127	15	and	and	CCONJ
cana-3074	127	16	early	early	ADJ
cana-3074	127	17	stages	stage	NOUN
cana-3074	127	18	of	of	ADP
cana-3074	127	19	theoretical	theoretical	ADJ
cana-3074	127	20	abstraction	abstraction	NOUN
cana-3074	127	21	.	.	PUNCT
cana-3074	128	1	in	in	ADP
cana-3074	128	2	addition	addition	NOUN
cana-3074	128	3	,	,	PUNCT
cana-3074	128	4	on	on	ADP
cana-3074	128	5	the	the	DET
cana-3074	128	6	informal	informal	ADJ
cana-3074	128	7	deduction	deduction	NOUN
cana-3074	128	8	level	level	NOUN
cana-3074	128	9	,	,	PUNCT
cana-3074	128	10	students	student	NOUN
cana-3074	128	11	apply	apply	VERB
cana-3074	128	12	geometric	geometric	ADJ
cana-3074	128	13	concepts	concept	NOUN
cana-3074	128	14	in	in	ADP
cana-3074	128	15	different	different	ADJ
cana-3074	128	16	contexts	contexts	NOUN
cana-3074	128	17	,	,	PUNCT
cana-3074	128	18	forming	form	VERB
cana-3074	128	19	formal	formal	ADJ
cana-3074	128	20	relationships	relationship	NOUN
cana-3074	128	21	between	between	ADP
cana-3074	128	22	sides	side	NOUN
cana-3074	128	23	and	and	CCONJ
cana-3074	128	24	angles	angle	NOUN
cana-3074	128	25	based	base	VERB
cana-3074	128	26	on	on	ADP
cana-3074	128	27	experience	experience	NOUN
cana-3074	128	28	and	and	CCONJ
cana-3074	128	29	intuitive	intuitive	ADJ
cana-3074	128	30	understanding	understanding	NOUN
cana-3074	128	31	,	,	PUNCT
cana-3074	128	32	encompassing	encompass	VERB
cana-3074	128	33	both	both	CCONJ
cana-3074	128	34	empirical	empirical	ADJ
cana-3074	128	35	and	and	CCONJ
cana-3074	128	36	deeper	deep	ADJ
cana-3074	128	37	theoretical	theoretical	ADJ
cana-3074	128	38	abstraction	abstraction	NOUN
cana-3074	128	39	.	.	PUNCT
cana-3074	129	1	furthermore	furthermore	ADV
cana-3074	129	2	,	,	PUNCT
cana-3074	129	3	formal	formal	ADJ
cana-3074	129	4	deduction	deduction	NOUN
cana-3074	129	5	involves	involve	VERB
cana-3074	129	6	integrating	integrate	VERB
cana-3074	129	7	triangle	triangle	NOUN
cana-3074	129	8	concepts	concept	NOUN
cana-3074	129	9	into	into	ADP
cana-3074	129	10	a	a	DET
cana-3074	129	11	broader	broad	ADJ
cana-3074	129	12	mathematical	mathematical	ADJ
cana-3074	129	13	context	context	NOUN
cana-3074	129	14	more	more	ADV
cana-3074	129	15	formally	formally	ADV
cana-3074	129	16	,	,	PUNCT
cana-3074	129	17	connecting	connect	VERB
cana-3074	129	18	triangles	triangle	NOUN
cana-3074	129	19	with	with	ADP
cana-3074	129	20	other	other	ADJ
cana-3074	129	21	mathematical	mathematical	ADJ
cana-3074	129	22	concepts	concept	NOUN
cana-3074	129	23	like	like	ADP
cana-3074	129	24	trigonometry	trigonometry	NOUN
cana-3074	129	25	and	and	CCONJ
cana-3074	129	26	cartesian	cartesian	ADJ
cana-3074	129	27	coordinates	coordinate	NOUN
cana-3074	129	28	.	.	PUNCT
cana-3074	130	1	this	this	DET
cana-3074	130	2	level	level	NOUN
cana-3074	130	3	consists	consist	VERB
cana-3074	130	4	of	of	ADP
cana-3074	130	5	empirical	empirical	ADJ
cana-3074	130	6	and	and	CCONJ
cana-3074	130	7	deep	deep	ADJ
cana-3074	130	8	theoretical	theoretical	ADJ
cana-3074	130	9	abstraction	abstraction	NOUN
cana-3074	130	10	.	.	PUNCT
cana-3074	131	1	finally	finally	ADV
cana-3074	131	2	,	,	PUNCT
cana-3074	131	3	at	at	ADP
cana-3074	131	4	the	the	DET
cana-3074	131	5	rigor	rigor	NOUN
cana-3074	131	6	level	level	NOUN
cana-3074	131	7	,	,	PUNCT
cana-3074	131	8	practical	practical	ADJ
cana-3074	131	9	applications	application	NOUN
cana-3074	131	10	of	of	ADP
cana-3074	131	11	triangle	triangle	NOUN
cana-3074	131	12	concepts	concept	NOUN
cana-3074	131	13	in	in	ADP
cana-3074	131	14	real	real	ADJ
cana-3074	131	15	-	-	PUNCT
cana-3074	131	16	world	world	NOUN
cana-3074	131	17	situations	situation	NOUN
cana-3074	131	18	and	and	CCONJ
cana-3074	131	19	extensive	extensive	ADJ
cana-3074	131	20	integration	integration	NOUN
cana-3074	131	21	with	with	ADP
cana-3074	131	22	other	other	ADJ
cana-3074	131	23	mathematical	mathematical	ADJ
cana-3074	131	24	concepts	concept	NOUN
cana-3074	131	25	occur	occur	VERB
cana-3074	131	26	.	.	PUNCT
cana-3074	132	1	this	this	DET
cana-3074	132	2	level	level	NOUN
cana-3074	132	3	involves	involve	VERB
cana-3074	132	4	strong	strong	ADJ
cana-3074	132	5	empirical	empirical	ADJ
cana-3074	132	6	abstraction	abstraction	NOUN
cana-3074	132	7	and	and	CCONJ
cana-3074	132	8	broad	broad	ADJ
cana-3074	132	9	theoretical	theoretical	ADJ
cana-3074	132	10	understanding	understanding	NOUN
cana-3074	132	11	moreover	moreover	ADV
cana-3074	132	12	,	,	PUNCT
cana-3074	132	13	students	student	NOUN
cana-3074	132	14	with	with	ADP
cana-3074	132	15	higher	high	ADJ
cana-3074	132	16	levels	level	NOUN
cana-3074	132	17	of	of	ADP
cana-3074	132	18	van	van	PROPN
cana-3074	132	19	hiele	hiele	PROPN
cana-3074	132	20	demonstrate	demonstrate	VERB
cana-3074	132	21	better	well	ADJ
cana-3074	132	22	abilities	ability	NOUN
cana-3074	132	23	to	to	ADP
cana-3074	132	24	abstract	abstract	ADJ
cana-3074	132	25	geometric	geometric	ADJ
cana-3074	132	26	concepts	concept	NOUN
cana-3074	132	27	,	,	PUNCT
cana-3074	132	28	indicating	indicate	VERB
cana-3074	132	29	a	a	DET
cana-3074	132	30	significant	significant	ADJ
cana-3074	132	31	relationship	relationship	NOUN
cana-3074	132	32	between	between	ADP
cana-3074	132	33	van	van	PROPN
cana-3074	132	34	hiele	hiele	PROPN
cana-3074	132	35	levels	level	NOUN
cana-3074	132	36	and	and	CCONJ
cana-3074	132	37	the	the	DET
cana-3074	132	38	aspects	aspect	NOUN
cana-3074	132	39	of	of	ADP
cana-3074	132	40	geometrical	geometrical	ADJ
cana-3074	132	41	abstraction	abstraction	NOUN
cana-3074	132	42	achieved	achieve	VERB
cana-3074	132	43	by	by	ADP
cana-3074	132	44	students	student	NOUN
cana-3074	132	45	.	.	PUNCT
cana-3074	133	1	these	these	DET
cana-3074	133	2	findings	finding	NOUN
cana-3074	133	3	suggest	suggest	VERB
cana-3074	133	4	the	the	DET
cana-3074	133	5	potential	potential	NOUN
cana-3074	133	6	for	for	ADP
cana-3074	133	7	further	further	ADJ
cana-3074	133	8	research	research	NOUN
cana-3074	133	9	activities	activity	NOUN
cana-3074	133	10	to	to	PART
cana-3074	133	11	explore	explore	VERB
cana-3074	133	12	the	the	DET
cana-3074	133	13	application	application	NOUN
cana-3074	133	14	of	of	ADP
cana-3074	133	15	van	van	PROPN
cana-3074	133	16	hiele	hiele	PROPN
cana-3074	133	17	's	's	PART
cana-3074	133	18	theory	theory	NOUN
cana-3074	133	19	in	in	ADP
cana-3074	133	20	enhancing	enhance	VERB
cana-3074	133	21	geometric	geometric	ADJ
cana-3074	133	22	understanding	understanding	NOUN
cana-3074	133	23	among	among	ADP
cana-3074	133	24	mathematics	mathematic	NOUN
cana-3074	133	25	undergraduates	undergraduate	NOUN
cana-3074	133	26	,	,	PUNCT
cana-3074	133	27	both	both	PRON
cana-3074	133	28	in	in	ADP
cana-3074	133	29	solving	solve	VERB
cana-3074	133	30	real	real	ADJ
cana-3074	133	31	-	-	PUNCT
cana-3074	133	32	life	life	NOUN
cana-3074	133	33	problems	problem	NOUN
cana-3074	133	34	and	and	CCONJ
cana-3074	133	35	advancing	advance	VERB
cana-3074	133	36	scientific	scientific	ADJ
cana-3074	133	37	knowledge	knowledge	NOUN
cana-3074	133	38	.	.	PUNCT
cana-3074	134	1	eventually	eventually	ADV
cana-3074	134	2	,	,	PUNCT
cana-3074	134	3	based	base	VERB
cana-3074	134	4	on	on	ADP
cana-3074	134	5	the	the	DET
cana-3074	134	6	findings	finding	NOUN
cana-3074	134	7	of	of	ADP
cana-3074	134	8	this	this	DET
cana-3074	134	9	research	research	NOUN
cana-3074	134	10	,	,	PUNCT
cana-3074	134	11	further	further	ADJ
cana-3074	134	12	research	research	NOUN
cana-3074	134	13	is	be	AUX
cana-3074	134	14	suggested	suggest	VERB
cana-3074	134	15	to	to	PART
cana-3074	134	16	explore	explore	VERB
cana-3074	134	17	the	the	DET
cana-3074	134	18	relationship	relationship	NOUN
cana-3074	134	19	between	between	ADP
cana-3074	134	20	van	van	PROPN
cana-3074	134	21	hiele	hiele	PROPN
cana-3074	134	22	levels	level	NOUN
cana-3074	134	23	and	and	CCONJ
cana-3074	134	24	geometrical	geometrical	ADJ
cana-3074	134	25	abstraction	abstraction	NOUN
cana-3074	134	26	,	,	PUNCT
cana-3074	134	27	other	other	ADJ
cana-3074	134	28	factors	factor	NOUN
cana-3074	134	29	influencing	influence	VERB
cana-3074	134	30	the	the	DET
cana-3074	134	31	communications	communication	NOUN
cana-3074	134	32	on	on	ADP
cana-3074	134	33	applied	apply	VERB
cana-3074	134	34	nonlinear	nonlinear	ADJ
cana-3074	134	35	analysis	analysis	NOUN
cana-3074	134	36	issn	issn	NOUN
cana-3074	134	37	:	:	PUNCT
cana-3074	134	38	1074	1074	NUM
cana-3074	134	39	-	-	PUNCT
cana-3074	134	40	133x	133x	NUM
cana-3074	134	41	vol	vol	NOUN
cana-3074	134	42	32	32	NUM
cana-3074	134	43	no	no	NOUN
cana-3074	134	44	.	.	PUNCT
cana-3074	135	1	5s	5s	NUM
cana-3074	135	2	(	(	PUNCT
cana-3074	135	3	2025	2025	NUM
cana-3074	135	4	)	)	PUNCT
cana-3074	135	5	276	276	NUM
cana-3074	135	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3074	135	7	development	development	NOUN
cana-3074	135	8	of	of	ADP
cana-3074	135	9	van	van	PROPN
cana-3074	135	10	hiele	hiele	PROPN
cana-3074	135	11	levels	level	NOUN
cana-3074	135	12	and	and	CCONJ
cana-3074	135	13	using	use	VERB
cana-3074	135	14	longitudinal	longitudinal	ADJ
cana-3074	135	15	research	research	NOUN
cana-3074	135	16	designs	design	NOUN
cana-3074	135	17	for	for	ADP
cana-3074	135	18	a	a	DET
cana-3074	135	19	deeper	deep	ADJ
cana-3074	135	20	understanding	understanding	NOUN
cana-3074	135	21	of	of	ADP
cana-3074	135	22	students	student	NOUN
cana-3074	135	23	'	'	PART
cana-3074	135	24	van	van	PROPN
cana-3074	135	25	hiele	hiele	PROPN
cana-3074	135	26	levels	level	NOUN
cana-3074	135	27	.	.	PUNCT
cana-3074	136	1	these	these	DET
cana-3074	136	2	recommendations	recommendation	NOUN
cana-3074	136	3	aim	aim	VERB
cana-3074	136	4	to	to	PART
cana-3074	136	5	enhance	enhance	VERB
cana-3074	136	6	the	the	DET
cana-3074	136	7	understanding	understanding	NOUN
cana-3074	136	8	of	of	ADP
cana-3074	136	9	geometrical	geometrical	ADJ
cana-3074	136	10	abstraction	abstraction	NOUN
cana-3074	136	11	and	and	CCONJ
cana-3074	136	12	its	its	PRON
cana-3074	136	13	implications	implication	NOUN
cana-3074	136	14	for	for	ADP
cana-3074	136	15	mathematics	mathematic	NOUN
cana-3074	136	16	education	education	NOUN
cana-3074	136	17	.	.	PUNCT
cana-3074	137	1	references	reference	NOUN
cana-3074	137	2	[	[	X
cana-3074	137	3	1	1	NUM
cana-3074	137	4	]	]	X
cana-3074	137	5	chiossi	chiossi	ADJ
cana-3074	137	6	,	,	PUNCT
cana-3074	137	7	s.	s.	PROPN
cana-3074	137	8	g.	g.	PROPN
cana-3074	137	9	(	(	PUNCT
cana-3074	137	10	2021	2021	NUM
cana-3074	137	11	)	)	PUNCT
cana-3074	137	12	.	.	PUNCT
cana-3074	138	1	vector	vector	NOUN
cana-3074	138	2	spaces	space	NOUN
cana-3074	138	3	.	.	PUNCT
cana-3074	139	1	in	in	ADP
cana-3074	139	2	s.	s.	PROPN
cana-3074	139	3	g.	g.	PROPN
cana-3074	139	4	chiossi	chiossi	PROPN
cana-3074	139	5	,	,	PUNCT
cana-3074	139	6	essential	essential	ADJ
cana-3074	139	7	mathematics	mathematic	NOUN
cana-3074	139	8	for	for	ADP
cana-3074	139	9	undergraduates	undergraduate	NOUN
cana-3074	139	10	(	(	PUNCT
cana-3074	139	11	pp	pp	ADJ
cana-3074	139	12	.	.	PUNCT
cana-3074	139	13	339–372	339–372	NUM
cana-3074	139	14	)	)	PUNCT
cana-3074	139	15	.	.	PUNCT
cana-3074	140	1	springer	springer	NOUN
cana-3074	140	2	international	international	ADJ
cana-3074	140	3	publishing	publishing	NOUN
cana-3074	140	4	.	.	PUNCT
cana-3074	141	1	https://doi.org/10.1007/978-3-030-87174-1_15	https://doi.org/10.1007/978-3-030-87174-1_15	PUNCT
cana-3074	141	2	[	[	X
cana-3074	141	3	2	2	NUM
cana-3074	141	4	]	]	X
cana-3074	141	5	ebissa	ebissa	NOUN
cana-3074	141	6	,	,	PUNCT
cana-3074	141	7	l.	l.	PROPN
cana-3074	141	8	(	(	PUNCT
cana-3074	141	9	2020	2020	NUM
cana-3074	141	10	)	)	PUNCT
cana-3074	141	11	.	.	PUNCT
cana-3074	142	1	improving	improve	VERB
cana-3074	142	2	geometric	geometric	ADJ
cana-3074	142	3	concepts	concept	NOUN
cana-3074	142	4	perceived	perceive	VERB
cana-3074	142	5	difficult	difficult	ADJ
cana-3074	142	6	to	to	ADP
cana-3074	142	7	first	first	ADJ
cana-3074	142	8	year	year	NOUN
cana-3074	142	9	linear	linear	PROPN
cana-3074	142	10	mathematics	mathematics	PROPN
cana-3074	142	11	students	student	NOUN
cana-3074	142	12	’	'	PUNCT
cana-3074	142	13	of	of	ADP
cana-3074	142	14	kemissie	kemissie	PROPN
cana-3074	142	15	college	college	PROPN
cana-3074	142	16	of	of	ADP
cana-3074	142	17	teachers	teachers	PROPN
cana-3074	142	18	education	education	NOUN
cana-3074	142	19	in	in	ADP
cana-3074	142	20	2019	2019	NUM
cana-3074	142	21	g.c	g.c	PROPN
cana-3074	142	22	.	.	PROPN
cana-3074	142	23	8(11	8(11	NUM
cana-3074	142	24	)	)	PUNCT
cana-3074	142	25	.	.	PUNCT
cana-3074	143	1	[	[	X
cana-3074	143	2	3	3	NUM
cana-3074	143	3	]	]	X
cana-3074	143	4	geometry	geometry	NOUN
cana-3074	143	5	.	.	PUNCT
cana-3074	144	1	(	(	PUNCT
cana-3074	144	2	2023	2023	NUM
cana-3074	144	3	)	)	PUNCT
cana-3074	144	4	.	.	PUNCT
cana-3074	145	1	in	in	ADP
cana-3074	145	2	oxford	oxford	PROPN
cana-3074	145	3	dictionaries	dictionary	NOUN
cana-3074	145	4	.	.	PUNCT
cana-3074	146	1	oxford	oxford	PROPN
cana-3074	146	2	university	university	PROPN
cana-3074	146	3	press	press	NOUN
cana-3074	146	4	.	.	PUNCT
cana-3074	147	1	http://www.oxforddictionaries.com/definition/geometry	http://www.oxforddictionaries.com/definition/geometry	NOUN
cana-3074	147	2	,	,	PUNCT
cana-3074	147	3	2023	2023	NUM
cana-3074	147	4	[	[	X
cana-3074	147	5	4	4	NUM
cana-3074	147	6	]	]	X
cana-3074	147	7	islam	islam	PROPN
cana-3074	147	8	,	,	PUNCT
cana-3074	147	9	m.	m.	PROPN
cana-3074	147	10	r.	r.	PROPN
cana-3074	147	11	,	,	PUNCT
cana-3074	147	12	khan	khan	PROPN
cana-3074	147	13	,	,	PUNCT
cana-3074	147	14	n.	n.	PROPN
cana-3074	147	15	a.	a.	PROPN
cana-3074	147	16	&	&	CCONJ
cana-3074	147	17	baikady	baikady	PROPN
cana-3074	147	18	,	,	PUNCT
cana-3074	147	19	r.	r.	PROPN
cana-3074	147	20	(	(	PUNCT
cana-3074	147	21	eds	eds	PROPN
cana-3074	147	22	.	.	PUNCT
cana-3074	147	23	)	)	PUNCT
cana-3074	147	24	.	.	PUNCT
cana-3074	148	1	(	(	PUNCT
cana-3074	148	2	2022	2022	NUM
cana-3074	148	3	)	)	PUNCT
cana-3074	148	4	.	.	PUNCT
cana-3074	149	1	principles	principle	NOUN
cana-3074	149	2	of	of	ADP
cana-3074	149	3	social	social	ADJ
cana-3074	149	4	research	research	NOUN
cana-3074	149	5	methodology	methodology	NOUN
cana-3074	149	6	.	.	PUNCT
cana-3074	150	1	springer	springer	NOUN
cana-3074	150	2	.	.	PUNCT
cana-3074	151	1	[	[	X
cana-3074	151	2	5	5	NUM
cana-3074	151	3	]	]	X
cana-3074	151	4	mitchelmore	mitchelmore	NOUN
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cana-3074	151	13	)	)	PUNCT
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cana-3074	152	5	.	.	PUNCT
cana-3074	153	1	mathematics	mathematic	NOUN
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cana-3074	153	5	,	,	PUNCT
cana-3074	153	6	19(2	19(2	NUM
cana-3074	153	7	)	)	PUNCT
cana-3074	153	8	,	,	PUNCT
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cana-3074	153	10	.	.	PUNCT
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cana-3074	154	1	[	[	X
cana-3074	154	2	6	6	NUM
cana-3074	154	3	]	]	PUNCT
cana-3074	154	4	naufal	naufal	NOUN
cana-3074	154	5	,	,	PUNCT
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cana-3074	154	8	,	,	PUNCT
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cana-3074	154	19	,	,	PUNCT
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cana-3074	154	21	s.	s.	PROPN
cana-3074	154	22	&	&	CCONJ
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cana-3074	154	24	,	,	PUNCT
cana-3074	154	25	h.	h.	PROPN
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cana-3074	154	27	2020	2020	NUM
cana-3074	154	28	)	)	PUNCT
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cana-3074	155	11	.	.	PUNCT
cana-3074	155	12	8(6	8(6	NUM
cana-3074	155	13	)	)	PUNCT
cana-3074	155	14	,	,	PUNCT
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cana-3074	155	16	.	.	PUNCT
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cana-3074	156	4	]	]	X
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cana-3074	156	6	,	,	PUNCT
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cana-3074	156	8	,	,	PUNCT
cana-3074	156	9	jozua	jozua	PROPN
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cana-3074	156	11	,	,	PUNCT
cana-3074	156	12	&	&	CCONJ
cana-3074	156	13	yaya	yaya	PROPN
cana-3074	156	14	s.	s.	PROPN
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cana-3074	156	16	.	.	PUNCT
cana-3074	157	1	(	(	PUNCT
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cana-3074	157	3	)	)	PUNCT
cana-3074	157	4	.	.	PUNCT
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cana-3074	158	5	geometry	geometry	NOUN
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cana-3074	158	7	gsp	gsp	PROPN
cana-3074	158	8	.	.	PUNCT
cana-3074	159	1	https://doi.org/10.13140/2.1.1452.0005	https://doi.org/10.13140/2.1.1452.0005	PROPN
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cana-3074	160	3	]	]	X
cana-3074	160	4	oecd	oecd	PROPN
cana-3074	160	5	.	.	PUNCT
cana-3074	161	1	(	(	PUNCT
cana-3074	161	2	2023	2023	NUM
cana-3074	161	3	)	)	PUNCT
cana-3074	161	4	.	.	PUNCT
cana-3074	162	1	pisa	pisa	PROPN
cana-3074	162	2	2022	2022	NUM
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cana-3074	162	4	(	(	PUNCT
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cana-3074	162	12	and	and	CCONJ
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cana-3074	162	14	in	in	ADP
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cana-3074	162	16	.	.	PUNCT
cana-3074	163	1	oecd	oecd	PROPN
cana-3074	163	2	.	.	PUNCT
cana-3074	164	1	https://doi.org/10.1787/53f23881-en	https://doi.org/10.1787/53f23881-en	PROPN
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cana-3074	164	4	]	]	PUNCT
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cana-3074	164	6	,	,	PUNCT
cana-3074	164	7	g.	g.	PROPN
cana-3074	164	8	&	&	CCONJ
cana-3074	164	9	bočková	bočková	PROPN
cana-3074	164	10	,	,	PUNCT
cana-3074	164	11	v.	v.	PROPN
cana-3074	164	12	(	(	PUNCT
cana-3074	164	13	2021	2021	NUM
cana-3074	164	14	)	)	PUNCT
cana-3074	164	15	.	.	PUNCT
cana-3074	165	1	geometric	geometric	ADJ
cana-3074	165	2	thinking	thinking	NOUN
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cana-3074	165	5	teachers	teacher	NOUN
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cana-3074	165	9	—	—	PUNCT
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cana-3074	165	15	.	.	PUNCT
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cana-3074	166	2	,	,	PUNCT
cana-3074	166	3	9(23	9(23	NOUN
cana-3074	166	4	)	)	PUNCT
cana-3074	166	5	,	,	PUNCT
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cana-3074	166	7	.	.	PUNCT
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cana-3074	168	3	]	]	X
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cana-3074	168	5	,	,	PUNCT
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cana-3074	168	7	(	(	PUNCT
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cana-3074	168	9	)	)	PUNCT
cana-3074	168	10	.	.	PUNCT
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cana-3074	170	1	research	research	NOUN
cana-3074	170	2	designs	design	NOUN
cana-3074	170	3	,	,	PUNCT
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cana-3074	170	5	perspectives	perspective	NOUN
cana-3074	170	6	,	,	PUNCT
cana-3074	170	7	and	and	CCONJ
cana-3074	170	8	food	food	NOUN
cana-3074	170	9	for	for	ADP
cana-3074	170	10	thought	thought	NOUN
cana-3074	170	11	.	.	PUNCT
cana-3074	171	1	22	22	NUM
cana-3074	171	2	,	,	PUNCT
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cana-3074	171	4	.	.	PUNCT
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cana-3074	173	1	[	[	X
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cana-3074	173	3	]	]	X
cana-3074	173	4	plano	plano	PROPN
cana-3074	173	5	clark	clark	PROPN
cana-3074	173	6	,	,	PUNCT
cana-3074	173	7	v.	v.	PROPN
cana-3074	173	8	l.	l.	PROPN
cana-3074	173	9	&	&	CCONJ
cana-3074	173	10	ivankova	ivankova	PROPN
cana-3074	173	11	,	,	PUNCT
cana-3074	173	12	n.	n.	PROPN
cana-3074	173	13	v.	v.	PROPN
cana-3074	173	14	(	(	PUNCT
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cana-3074	174	1	mixed	mixed	ADJ
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cana-3074	174	4	:	:	PUNCT
cana-3074	174	5	a	a	DET
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cana-3074	174	10	.	.	PUNCT
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cana-3074	175	2	.	.	PUNCT
cana-3074	176	1	[	[	X
cana-3074	176	2	12	12	NUM
cana-3074	176	3	]	]	X
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cana-3074	176	5	,	,	PUNCT
cana-3074	176	6	m.	m.	PROPN
cana-3074	176	7	e.	e.	PROPN
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cana-3074	176	9	(	(	PUNCT
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cana-3074	176	11	)	)	PUNCT
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cana-3074	178	8	,	,	PUNCT
cana-3074	178	9	5(3	5(3	NUM
cana-3074	178	10	)	)	PUNCT
cana-3074	178	11	,	,	PUNCT
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cana-3074	178	13	.	.	PUNCT
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cana-3074	180	2	13	13	NUM
cana-3074	180	3	]	]	X
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cana-3074	180	5	,	,	PUNCT
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cana-3074	181	9	.	.	PUNCT
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cana-3074	182	4	.	.	PUNCT
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cana-3074	183	2	14	14	NUM
cana-3074	183	3	]	]	PUNCT
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cana-3074	183	5	,	,	PUNCT
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cana-3074	183	7	,	,	PUNCT
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cana-3074	183	9	,	,	PUNCT
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cana-3074	185	6	)	)	PUNCT
cana-3074	185	7	,	,	PUNCT
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cana-3074	187	8	,	,	PUNCT
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cana-3074	187	16	y.-h	y.-h	PROPN
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cana-3074	187	22	&	&	CCONJ
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cana-3074	188	6	:	:	PUNCT
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cana-3074	191	14	&	&	CCONJ
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cana-3074	191	16	.	.	PUNCT
cana-3074	191	17	(	(	PUNCT
cana-3074	191	18	2023	2023	NUM
cana-3074	191	19	)	)	PUNCT
cana-3074	191	20	.	.	PUNCT
cana-3074	192	1	effect	effect	NOUN
cana-3074	192	2	of	of	ADP
cana-3074	192	3	two	two	NUM
cana-3074	192	4	-	-	PUNCT
cana-3074	192	5	dimensional	dimensional	ADJ
cana-3074	192	6	geometry	geometry	NOUN
cana-3074	192	7	learning	learning	NOUN
cana-3074	192	8	on	on	ADP
cana-3074	192	9	geometric	geometric	ADJ
cana-3074	192	10	thinking	thinking	NOUN
cana-3074	192	11	of	of	ADP
cana-3074	192	12	undergraduate	undergraduate	ADJ
cana-3074	192	13	students	student	NOUN
cana-3074	192	14	during	during	ADP
cana-3074	192	15	the	the	DET
cana-3074	192	16	covid-19	covid-19	PROPN
cana-3074	192	17	pandemic	pandemic	NOUN
cana-3074	192	18	.	.	PUNCT
cana-3074	193	1	journal	journal	NOUN
cana-3074	193	2	of	of	ADP
cana-3074	193	3	higher	high	ADJ
cana-3074	193	4	education	education	NOUN
cana-3074	193	5	theory	theory	NOUN
cana-3074	193	6	and	and	CCONJ
cana-3074	193	7	practice	practice	NOUN
cana-3074	193	8	,	,	PUNCT
cana-3074	193	9	23(3	23(3	NUM
cana-3074	193	10	)	)	PUNCT
cana-3074	193	11	.	.	PUNCT
cana-3074	194	1	https://doi.org/10.33423/jhetp.v23i3.5848	https://doi.org/10.33423/jhetp.v23i3.5848	PUNCT
cana-3074	195	1	[	[	X
cana-3074	195	2	17	17	NUM
cana-3074	195	3	]	]	X
cana-3074	195	4	van	van	PROPN
cana-3074	195	5	hiele	hiele	PROPN
cana-3074	195	6	,	,	PUNCT
cana-3074	195	7	p.	p.	NOUN
cana-3074	195	8	m.	m.	NOUN
cana-3074	195	9	(	(	PUNCT
cana-3074	195	10	1999	1999	NUM
cana-3074	195	11	)	)	PUNCT
cana-3074	195	12	.	.	PUNCT
cana-3074	196	1	developing	develop	VERB
cana-3074	196	2	geometric	geometric	ADJ
cana-3074	196	3	thinking	thinking	NOUN
cana-3074	196	4	through	through	ADP
cana-3074	196	5	activities	activity	NOUN
cana-3074	196	6	that	that	PRON
cana-3074	196	7	begin	begin	VERB
cana-3074	196	8	with	with	ADP
cana-3074	196	9	play	play	NOUN
cana-3074	196	10	.	.	PUNCT
cana-3074	197	1	teaching	teach	VERB
cana-3074	197	2	children	child	NOUN
cana-3074	197	3	mathematics	mathematic	NOUN
cana-3074	197	4	,	,	PUNCT
cana-3074	197	5	5(6	5(6	NUM
cana-3074	197	6	)	)	PUNCT
cana-3074	197	7	,	,	PUNCT
cana-3074	197	8	310–316	310–316	NUM
cana-3074	197	9	.	.	PUNCT
cana-3074	198	1	https://doi.org/10.5951/tcm.5.6.0310	https://doi.org/10.5951/tcm.5.6.0310	PRON
cana-3074	198	2	[	[	X
cana-3074	198	3	18	18	NUM
cana-3074	198	4	]	]	X
cana-3074	198	5	wicaksono	wicaksono	NOUN
cana-3074	198	6	,	,	PUNCT
cana-3074	198	7	a.	a.	PROPN
cana-3074	198	8	b.	b.	PROPN
cana-3074	198	9	&	&	CCONJ
cana-3074	198	10	juniati	juniati	PROPN
cana-3074	198	11	,	,	PUNCT
cana-3074	198	12	d.	d.	PROPN
cana-3074	198	13	(	(	PUNCT
cana-3074	198	14	2022	2022	NUM
cana-3074	198	15	)	)	PUNCT
cana-3074	198	16	.	.	PUNCT
cana-3074	199	1	level	level	NOUN
cana-3074	199	2	berpikir	berpikir	PROPN
cana-3074	199	3	geometris	geometris	PROPN
cana-3074	199	4	mahasiswa	mahasiswa	PROPN
cana-3074	199	5	calon	calon	PROPN
cana-3074	199	6	guru	guru	PROPN
cana-3074	199	7	matematika	matematika	PROPN
cana-3074	199	8	berdasarkan	berdasarkan	PROPN
cana-3074	199	9	teori	teori	PROPN
cana-3074	199	10	van	van	PROPN
cana-3074	199	11	hiele	hiele	PROPN
cana-3074	199	12	.	.	PUNCT
cana-3074	200	1	aksioma	aksioma	PROPN
cana-3074	200	2	:	:	PUNCT
cana-3074	200	3	jurnal	jurnal	ADJ
cana-3074	200	4	program	program	NOUN
cana-3074	200	5	studi	studi	PROPN
cana-3074	200	6	pendidikan	pendidikan	PROPN
cana-3074	200	7	matematika	matematika	PROPN
cana-3074	200	8	,	,	PUNCT
cana-3074	200	9	11(3	11(3	NUM
cana-3074	200	10	)	)	PUNCT
cana-3074	200	11	,	,	PUNCT
cana-3074	200	12	2479	2479	NUM
cana-3074	200	13	.	.	PUNCT
cana-3074	200	14	https://doi.org/10.24127/ajpm.v11i3.5491	https://doi.org/10.24127/ajpm.v11i3.5491	NUM
cana-3074	201	1	[	[	X
cana-3074	201	2	19	19	NUM
cana-3074	201	3	]	]	X
cana-3074	201	4	widada	widada	PROPN
cana-3074	201	5	,	,	PUNCT
cana-3074	201	6	w.	w.	PROPN
cana-3074	201	7	,	,	PUNCT
cana-3074	201	8	agustina	agustina	PROPN
cana-3074	201	9	,	,	PUNCT
cana-3074	201	10	a.	a.	PROPN
cana-3074	201	11	,	,	PUNCT
cana-3074	201	12	serlis	serlis	PROPN
cana-3074	201	13	,	,	PUNCT
cana-3074	201	14	s.	s.	PROPN
cana-3074	201	15	,	,	PUNCT
cana-3074	201	16	dinata	dinata	PROPN
cana-3074	201	17	,	,	PUNCT
cana-3074	201	18	b.	b.	PROPN
cana-3074	201	19	m.	m.	PROPN
cana-3074	201	20	&	&	CCONJ
cana-3074	201	21	hasari	hasari	PROPN
cana-3074	201	22	,	,	PUNCT
cana-3074	201	23	s.	s.	PROPN
cana-3074	201	24	t.	t.	PROPN
cana-3074	201	25	(	(	PUNCT
cana-3074	201	26	2019	2019	NUM
cana-3074	201	27	)	)	PUNCT
cana-3074	201	28	.	.	PUNCT
cana-3074	202	1	the	the	DET
cana-3074	202	2	abstraction	abstraction	ADJ
cana-3074	202	3	ability	ability	NOUN
cana-3074	202	4	of	of	ADP
cana-3074	202	5	students	student	NOUN
cana-3074	202	6	in	in	ADP
cana-3074	202	7	understanding	understand	VERB
cana-3074	202	8	the	the	DET
cana-3074	202	9	concept	concept	NOUN
cana-3074	202	10	of	of	ADP
cana-3074	202	11	geometry	geometry	NOUN
cana-3074	202	12	.	.	PUNCT
cana-3074	203	1	journal	journal	PROPN
cana-3074	203	2	of	of	ADP
cana-3074	203	3	physics	physics	PROPN
cana-3074	203	4	:	:	PUNCT
cana-3074	203	5	conference	conference	NOUN
cana-3074	203	6	series	series	NOUN
cana-3074	203	7	,	,	PUNCT
cana-3074	203	8	1318(1	1318(1	NUM
cana-3074	203	9	)	)	PUNCT
cana-3074	203	10	,	,	PUNCT
cana-3074	203	11	012082	012082	NUM
cana-3074	203	12	.	.	PUNCT
cana-3074	204	1	https://doi.org/10.1088/1742-6596/1318/1/012082	https://doi.org/10.1088/1742-6596/1318/1/012082	PROPN