id	sid	tid	token	lemma	pos
easat-4521	1	1	edelweiss	edelweiss	PROPN
easat-4521	1	2	applied	apply	VERB
easat-4521	1	3	science	science	NOUN
easat-4521	1	4	and	and	CCONJ
easat-4521	1	5	technology	technology	NOUN
easat-4521	1	6	issn	issn	PROPN
easat-4521	1	7	:	:	PUNCT
easat-4521	1	8	2576	2576	NUM
easat-4521	1	9	-	-	SYM
easat-4521	1	10	8484	8484	NUM
easat-4521	1	11	vol	vol	NOUN
easat-4521	1	12	.	.	PROPN
easat-4521	2	1	9	9	NUM
easat-4521	2	2	,	,	PUNCT
easat-4521	2	3	no	no	INTJ
easat-4521	2	4	.	.	NOUN
easat-4521	2	5	2	2	NUM
easat-4521	2	6	,	,	PUNCT
easat-4521	2	7	555	555	NUM
easat-4521	2	8	-	-	SYM
easat-4521	2	9	566	566	NUM
easat-4521	2	10	2025	2025	NUM
easat-4521	2	11	publisher	publisher	NOUN
easat-4521	2	12	:	:	PUNCT
easat-4521	2	13	learning	learn	VERB
easat-4521	2	14	gate	gate	NOUN
easat-4521	2	15	doi	doi	PROPN
easat-4521	2	16	:	:	PUNCT
easat-4521	2	17	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	2	18	©	©	PROPN
easat-4521	2	19	2025	2025	NUM
easat-4521	2	20	by	by	ADP
easat-4521	2	21	the	the	DET
easat-4521	2	22	authors	author	NOUN
easat-4521	2	23	;	;	PUNCT
easat-4521	3	1	licensee	licensee	PROPN
easat-4521	3	2	learning	learning	NOUN
easat-4521	3	3	gate	gate	NOUN
easat-4521	3	4	©	©	PROPN
easat-4521	3	5	2025	2025	NUM
easat-4521	3	6	by	by	ADP
easat-4521	3	7	the	the	DET
easat-4521	3	8	authors	author	NOUN
easat-4521	3	9	;	;	PUNCT
easat-4521	3	10	licensee	licensee	PROPN
easat-4521	3	11	learning	learning	NOUN
easat-4521	3	12	gate	gate	NOUN
easat-4521	3	13	history	history	NOUN
easat-4521	3	14	:	:	PUNCT
easat-4521	3	15	received	receive	VERB
easat-4521	3	16	:	:	PUNCT
easat-4521	3	17	9	9	NUM
easat-4521	3	18	december	december	PROPN
easat-4521	3	19	2024	2024	NUM
easat-4521	3	20	;	;	PUNCT
easat-4521	3	21	revised	revise	VERB
easat-4521	3	22	:	:	PUNCT
easat-4521	3	23	20	20	NUM
easat-4521	3	24	january	january	NOUN
easat-4521	3	25	2025	2025	NUM
easat-4521	3	26	;	;	PUNCT
easat-4521	3	27	accepted	accept	VERB
easat-4521	3	28	:	:	PUNCT
easat-4521	3	29	22	22	NUM
easat-4521	3	30	january	january	PROPN
easat-4521	3	31	2025	2025	NUM
easat-4521	3	32	;	;	PUNCT
easat-4521	3	33	published	publish	VERB
easat-4521	3	34	:	:	PUNCT
easat-4521	3	35	31	31	NUM
easat-4521	3	36	january	january	NOUN
easat-4521	3	37	2025	2025	NUM
easat-4521	3	38	*	*	PUNCT
easat-4521	3	39	correspondence	correspondence	NOUN
easat-4521	3	40	:	:	PUNCT
easat-4521	3	41	ennylistiawati@stkippgri-bkl.ac.id	ennylistiawati@stkippgri-bkl.ac.id	NOUN
easat-4521	3	42	building	build	VERB
easat-4521	3	43	an	an	DET
easat-4521	3	44	understanding	understanding	NOUN
easat-4521	3	45	of	of	ADP
easat-4521	3	46	sketching	sketch	VERB
easat-4521	3	47	function	function	NOUN
easat-4521	3	48	derivative	derivative	ADJ
easat-4521	3	49	graphs	graph	NOUN
easat-4521	3	50	through	through	ADP
easat-4521	3	51	the	the	DET
easat-4521	3	52	apos	apos	PROPN
easat-4521	3	53	approach	approach	NOUN
easat-4521	3	54	enny	enny	NOUN
easat-4521	3	55	listiawati1	listiawati1	PROPN
easat-4521	3	56	*	*	PROPN
easat-4521	3	57	,	,	PUNCT
easat-4521	3	58	dwi	dwi	PROPN
easat-4521	3	59	juniati2	juniati2	PROPN
easat-4521	3	60	,	,	PUNCT
easat-4521	3	61	rooselyna	rooselyna	PROPN
easat-4521	3	62	ekawati3	ekawati3	PROPN
easat-4521	3	63	1,2,3mathematics	1,2,3mathematics	NUM
easat-4521	3	64	education	education	NOUN
easat-4521	3	65	,	,	PUNCT
easat-4521	3	66	faculty	faculty	NOUN
easat-4521	3	67	of	of	ADP
easat-4521	3	68	mathematics	mathematic	NOUN
easat-4521	3	69	and	and	CCONJ
easat-4521	3	70	natural	natural	ADJ
easat-4521	3	71	science	science	NOUN
easat-4521	3	72	,	,	PUNCT
easat-4521	3	73	universitas	universita	NOUN
easat-4521	3	74	negeri	negeri	PROPN
easat-4521	3	75	surabaya	surabaya	PROPN
easat-4521	3	76	,	,	PUNCT
easat-4521	3	77	surabaya	surabaya	PROPN
easat-4521	3	78	,	,	PUNCT
easat-4521	3	79	indonesia	indonesia	PROPN
easat-4521	3	80	;	;	PUNCT
easat-4521	3	81	ennylistiawati@stkippgri-bkl.ac.id	ennylistiawati@stkippgri-bkl.ac.id	NOUN
easat-4521	3	82	(	(	PUNCT
easat-4521	3	83	e.l	e.l	PROPN
easat-4521	3	84	.	.	PROPN
easat-4521	3	85	)	)	PUNCT
easat-4521	4	1	dwijuniati@unesa.ac.id	dwijuniati@unesa.ac.id	NOUN
easat-4521	4	2	(	(	PUNCT
easat-4521	4	3	d.j	d.j	PROPN
easat-4521	4	4	.	.	PROPN
easat-4521	4	5	)	)	PUNCT
easat-4521	5	1	rooselynaekawati@unesa.ac.id	rooselynaekawati@unesa.ac.id	NOUN
easat-4521	5	2	(	(	PUNCT
easat-4521	5	3	r.e	r.e	PROPN
easat-4521	5	4	.	.	PROPN
easat-4521	5	5	)	)	PUNCT
easat-4521	6	1	1department	1department	NUM
easat-4521	6	2	of	of	ADP
easat-4521	6	3	mathematics	mathematics	PROPN
easat-4521	6	4	education	education	NOUN
easat-4521	6	5	,	,	PUNCT
easat-4521	6	6	stkip	stkip	VERB
easat-4521	6	7	pgri	pgri	NOUN
easat-4521	6	8	bangkalan	bangkalan	NOUN
easat-4521	6	9	,	,	PUNCT
easat-4521	6	10	bangkalan	bangkalan	NOUN
easat-4521	6	11	,	,	PUNCT
easat-4521	6	12	indonesia	indonesia	PROPN
easat-4521	6	13	.	.	PUNCT
easat-4521	7	1	abstract	abstract	PROPN
easat-4521	7	2	:	:	PUNCT
easat-4521	7	3	the	the	DET
easat-4521	7	4	derivative	derivative	NOUN
easat-4521	7	5	of	of	ADP
easat-4521	7	6	a	a	DET
easat-4521	7	7	function	function	NOUN
easat-4521	7	8	is	be	AUX
easat-4521	7	9	a	a	DET
easat-4521	7	10	basic	basic	ADJ
easat-4521	7	11	concept	concept	NOUN
easat-4521	7	12	in	in	ADP
easat-4521	7	13	calculus	calculus	NOUN
easat-4521	7	14	with	with	ADP
easat-4521	7	15	various	various	ADJ
easat-4521	7	16	applications	application	NOUN
easat-4521	7	17	in	in	ADP
easat-4521	7	18	the	the	DET
easat-4521	7	19	stem	stem	NOUN
easat-4521	7	20	fields	field	NOUN
easat-4521	7	21	.	.	PUNCT
easat-4521	8	1	a	a	DET
easat-4521	8	2	deep	deep	ADJ
easat-4521	8	3	understanding	understanding	NOUN
easat-4521	8	4	of	of	ADP
easat-4521	8	5	this	this	DET
easat-4521	8	6	concept	concept	NOUN
easat-4521	8	7	is	be	AUX
easat-4521	8	8	essential	essential	ADJ
easat-4521	8	9	for	for	SCONJ
easat-4521	8	10	students	student	NOUN
easat-4521	8	11	to	to	PART
easat-4521	8	12	face	face	VERB
easat-4521	8	13	the	the	DET
easat-4521	8	14	challenges	challenge	NOUN
easat-4521	8	15	of	of	ADP
easat-4521	8	16	analysis	analysis	NOUN
easat-4521	8	17	,	,	PUNCT
easat-4521	8	18	optimization	optimization	NOUN
easat-4521	8	19	,	,	PUNCT
easat-4521	8	20	and	and	CCONJ
easat-4521	8	21	application	application	NOUN
easat-4521	8	22	in	in	ADP
easat-4521	8	23	science	science	NOUN
easat-4521	8	24	and	and	CCONJ
easat-4521	8	25	technology	technology	NOUN
easat-4521	8	26	inquiries	inquiry	NOUN
easat-4521	8	27	.	.	PUNCT
easat-4521	9	1	however	however	ADV
easat-4521	9	2	,	,	PUNCT
easat-4521	9	3	the	the	DET
easat-4521	9	4	understanding	understanding	NOUN
easat-4521	9	5	of	of	ADP
easat-4521	9	6	derivatives	derivative	NOUN
easat-4521	9	7	of	of	ADP
easat-4521	9	8	functions	function	NOUN
easat-4521	9	9	among	among	ADP
easat-4521	9	10	the	the	DET
easat-4521	9	11	population	population	NOUN
easat-4521	9	12	of	of	ADP
easat-4521	9	13	prospective	prospective	ADJ
easat-4521	9	14	mathematics	mathematic	NOUN
easat-4521	9	15	teachers	teacher	NOUN
easat-4521	9	16	in	in	ADP
easat-4521	9	17	indonesia	indonesia	PROPN
easat-4521	9	18	is	be	AUX
easat-4521	9	19	still	still	ADV
easat-4521	9	20	low	low	ADJ
easat-4521	9	21	,	,	PUNCT
easat-4521	9	22	specifically	specifically	ADV
easat-4521	9	23	when	when	SCONJ
easat-4521	9	24	it	it	PRON
easat-4521	9	25	comes	come	VERB
easat-4521	9	26	to	to	ADP
easat-4521	9	27	sketching	sketch	VERB
easat-4521	9	28	graphs	graph	NOUN
easat-4521	9	29	of	of	ADP
easat-4521	9	30	derivatives	derivative	NOUN
easat-4521	9	31	of	of	ADP
easat-4521	9	32	functions	function	NOUN
easat-4521	9	33	and	and	CCONJ
easat-4521	9	34	the	the	DET
easat-4521	9	35	application	application	NOUN
easat-4521	9	36	of	of	ADP
easat-4521	9	37	the	the	DET
easat-4521	9	38	concepts	concept	NOUN
easat-4521	9	39	.	.	PUNCT
easat-4521	10	1	the	the	DET
easat-4521	10	2	apos	apos	NOUN
easat-4521	10	3	(	(	PUNCT
easat-4521	10	4	action	action	NOUN
easat-4521	10	5	,	,	PUNCT
easat-4521	10	6	process	process	NOUN
easat-4521	10	7	,	,	PUNCT
easat-4521	10	8	object	object	NOUN
easat-4521	10	9	,	,	PUNCT
easat-4521	10	10	schema	schema	NOUN
easat-4521	10	11	)	)	PUNCT
easat-4521	10	12	theory	theory	NOUN
easat-4521	10	13	approach	approach	NOUN
easat-4521	10	14	seems	seem	VERB
easat-4521	10	15	to	to	PART
easat-4521	10	16	hold	hold	VERB
easat-4521	10	17	a	a	DET
easat-4521	10	18	relevant	relevant	ADJ
easat-4521	10	19	solution	solution	NOUN
easat-4521	10	20	needed	need	VERB
easat-4521	10	21	to	to	PART
easat-4521	10	22	improve	improve	VERB
easat-4521	10	23	this	this	DET
easat-4521	10	24	understanding	understanding	NOUN
easat-4521	10	25	.	.	PUNCT
easat-4521	11	1	previous	previous	ADJ
easat-4521	11	2	studies	study	NOUN
easat-4521	11	3	have	have	AUX
easat-4521	11	4	shown	show	VERB
easat-4521	11	5	that	that	SCONJ
easat-4521	11	6	most	most	ADJ
easat-4521	11	7	students	student	NOUN
easat-4521	11	8	still	still	ADV
easat-4521	11	9	have	have	VERB
easat-4521	11	10	difficulty	difficulty	NOUN
easat-4521	11	11	understanding	understand	VERB
easat-4521	11	12	the	the	DET
easat-4521	11	13	relationship	relationship	NOUN
easat-4521	11	14	between	between	ADP
easat-4521	11	15	graphs	graph	NOUN
easat-4521	11	16	and	and	CCONJ
easat-4521	11	17	derivatives	derivative	NOUN
easat-4521	11	18	of	of	ADP
easat-4521	11	19	functions	function	NOUN
easat-4521	11	20	.	.	PUNCT
easat-4521	12	1	in	in	ADP
easat-4521	12	2	the	the	DET
easat-4521	12	3	present	present	ADJ
easat-4521	12	4	study	study	NOUN
easat-4521	12	5	,	,	PUNCT
easat-4521	12	6	apos	apos	PROPN
easat-4521	12	7	theory	theory	NOUN
easat-4521	12	8	was	be	AUX
easat-4521	12	9	used	use	VERB
easat-4521	12	10	to	to	PART
easat-4521	12	11	analyze	analyze	VERB
easat-4521	12	12	the	the	DET
easat-4521	12	13	subjects	subject	NOUN
easat-4521	12	14	’	'	PUNCT
easat-4521	12	15	understanding	understanding	NOUN
easat-4521	12	16	of	of	ADP
easat-4521	12	17	the	the	DET
easat-4521	12	18	concept	concept	NOUN
easat-4521	12	19	of	of	ADP
easat-4521	12	20	derivatives	derivative	NOUN
easat-4521	12	21	,	,	PUNCT
easat-4521	12	22	especially	especially	ADV
easat-4521	12	23	related	relate	VERB
easat-4521	12	24	to	to	ADP
easat-4521	12	25	sketching	sketch	VERB
easat-4521	12	26	graphs	graph	NOUN
easat-4521	12	27	of	of	ADP
easat-4521	12	28	derivatives	derivative	NOUN
easat-4521	12	29	of	of	ADP
easat-4521	12	30	functions	function	NOUN
easat-4521	12	31	by	by	ADP
easat-4521	12	32	describing	describe	VERB
easat-4521	12	33	their	their	PRON
easat-4521	12	34	mental	mental	ADJ
easat-4521	12	35	structure	structure	NOUN
easat-4521	12	36	and	and	CCONJ
easat-4521	12	37	mechanisms	mechanism	NOUN
easat-4521	12	38	completely	completely	ADV
easat-4521	12	39	.	.	PUNCT
easat-4521	13	1	the	the	DET
easat-4521	13	2	results	result	NOUN
easat-4521	13	3	of	of	ADP
easat-4521	13	4	the	the	DET
easat-4521	13	5	study	study	NOUN
easat-4521	13	6	revealed	reveal	VERB
easat-4521	13	7	that	that	SCONJ
easat-4521	13	8	the	the	DET
easat-4521	13	9	subjects	subject	NOUN
easat-4521	13	10	'	'	PART
easat-4521	13	11	understanding	understanding	NOUN
easat-4521	13	12	had	have	AUX
easat-4521	13	13	reached	reach	VERB
easat-4521	13	14	the	the	DET
easat-4521	13	15	schema	schema	NOUN
easat-4521	13	16	stage	stage	NOUN
easat-4521	13	17	.	.	PUNCT
easat-4521	14	1	however	however	ADV
easat-4521	14	2	,	,	PUNCT
easat-4521	14	3	there	there	PRON
easat-4521	14	4	was	be	VERB
easat-4521	14	5	no	no	DET
easat-4521	14	6	mental	mental	ADJ
easat-4521	14	7	interiorization	interiorization	NOUN
easat-4521	14	8	mechanism	mechanism	NOUN
easat-4521	14	9	since	since	SCONJ
easat-4521	14	10	the	the	DET
easat-4521	14	11	subjects	subject	NOUN
easat-4521	14	12	had	have	VERB
easat-4521	14	13	difficulty	difficulty	NOUN
easat-4521	14	14	at	at	ADP
easat-4521	14	15	the	the	DET
easat-4521	14	16	process	process	NOUN
easat-4521	14	17	stage	stage	NOUN
easat-4521	14	18	.	.	PUNCT
easat-4521	15	1	consequently	consequently	ADV
easat-4521	15	2	,	,	PUNCT
easat-4521	15	3	the	the	DET
easat-4521	15	4	subjects	subject	NOUN
easat-4521	15	5	could	could	AUX
easat-4521	15	6	not	not	PART
easat-4521	15	7	explain	explain	VERB
easat-4521	15	8	the	the	DET
easat-4521	15	9	steps	step	NOUN
easat-4521	15	10	to	to	PART
easat-4521	15	11	draw	draw	VERB
easat-4521	15	12	a	a	DET
easat-4521	15	13	graph	graph	NOUN
easat-4521	15	14	of	of	ADP
easat-4521	15	15	derivatives	derivative	NOUN
easat-4521	15	16	of	of	ADP
easat-4521	15	17	functions	function	NOUN
easat-4521	15	18	from	from	ADP
easat-4521	15	19	the	the	DET
easat-4521	15	20	given	give	VERB
easat-4521	15	21	function	function	NOUN
easat-4521	15	22	graph	graph	NOUN
easat-4521	15	23	.	.	PUNCT
easat-4521	16	1	finally	finally	ADV
easat-4521	16	2	,	,	PUNCT
easat-4521	16	3	this	this	DET
easat-4521	16	4	study	study	NOUN
easat-4521	16	5	highlights	highlight	VERB
easat-4521	16	6	the	the	DET
easat-4521	16	7	importance	importance	NOUN
easat-4521	16	8	of	of	ADP
easat-4521	16	9	more	more	ADV
easat-4521	16	10	effective	effective	ADJ
easat-4521	16	11	teaching	teaching	NOUN
easat-4521	16	12	strategies	strategy	NOUN
easat-4521	16	13	to	to	PART
easat-4521	16	14	strengthen	strengthen	VERB
easat-4521	16	15	students	student	NOUN
easat-4521	16	16	'	'	PART
easat-4521	16	17	conceptual	conceptual	ADJ
easat-4521	16	18	understanding	understanding	NOUN
easat-4521	16	19	of	of	ADP
easat-4521	16	20	derivatives	derivative	NOUN
easat-4521	16	21	of	of	ADP
easat-4521	16	22	functions	function	NOUN
easat-4521	16	23	,	,	PUNCT
easat-4521	16	24	especially	especially	ADV
easat-4521	16	25	sketching	sketch	VERB
easat-4521	16	26	derivative	derivative	ADJ
easat-4521	16	27	graphs	graph	NOUN
easat-4521	16	28	.	.	PUNCT
easat-4521	17	1	keywords	keyword	NOUN
easat-4521	17	2	:	:	PUNCT
easat-4521	17	3	apos	apo	NOUN
easat-4521	17	4	,	,	PUNCT
easat-4521	17	5	derivatives	derivative	NOUN
easat-4521	17	6	,	,	PUNCT
easat-4521	17	7	graphics	graphic	NOUN
easat-4521	17	8	,	,	PUNCT
easat-4521	17	9	mathematics	mathematic	NOUN
easat-4521	17	10	.	.	PUNCT
easat-4521	18	1	1	1	X
easat-4521	18	2	.	.	X
easat-4521	18	3	introduction	introduction	NOUN
easat-4521	18	4	the	the	DET
easat-4521	18	5	derivative	derivative	NOUN
easat-4521	18	6	of	of	ADP
easat-4521	18	7	a	a	DET
easat-4521	18	8	function	function	NOUN
easat-4521	18	9	is	be	AUX
easat-4521	18	10	a	a	DET
easat-4521	18	11	fundamental	fundamental	ADJ
easat-4521	18	12	calculus	calculus	NOUN
easat-4521	18	13	concept	concept	NOUN
easat-4521	18	14	that	that	PRON
easat-4521	18	15	is	be	AUX
easat-4521	18	16	important	important	ADJ
easat-4521	18	17	in	in	ADP
easat-4521	18	18	the	the	DET
easat-4521	18	19	stem	stem	NOUN
easat-4521	18	20	disciplines	discipline	NOUN
easat-4521	18	21	[	[	X
easat-4521	18	22	1	1	NUM
easat-4521	18	23	,	,	PUNCT
easat-4521	18	24	2	2	NUM
easat-4521	18	25	]	]	PUNCT
easat-4521	18	26	.	.	PUNCT
easat-4521	19	1	the	the	DET
easat-4521	19	2	concept	concept	NOUN
easat-4521	19	3	is	be	AUX
easat-4521	19	4	used	use	VERB
easat-4521	19	5	as	as	ADP
easat-4521	19	6	a	a	DET
easat-4521	19	7	step	step	NOUN
easat-4521	19	8	in	in	ADP
easat-4521	19	9	function	function	NOUN
easat-4521	19	10	analysis	analysis	NOUN
easat-4521	19	11	,	,	PUNCT
easat-4521	19	12	optimization	optimization	NOUN
easat-4521	19	13	,	,	PUNCT
easat-4521	19	14	understanding	understand	VERB
easat-4521	19	15	changes	change	NOUN
easat-4521	19	16	in	in	ADP
easat-4521	19	17	phenomena	phenomenon	NOUN
easat-4521	19	18	,	,	PUNCT
easat-4521	19	19	and	and	CCONJ
easat-4521	19	20	practical	practical	ADJ
easat-4521	19	21	applications	application	NOUN
easat-4521	19	22	in	in	ADP
easat-4521	19	23	sciences	science	NOUN
easat-4521	19	24	,	,	PUNCT
easat-4521	19	25	economics	economic	NOUN
easat-4521	19	26	,	,	PUNCT
easat-4521	19	27	and	and	CCONJ
easat-4521	19	28	higher	high	ADJ
easat-4521	19	29	education	education	NOUN
easat-4521	19	30	[	[	X
easat-4521	19	31	3	3	NUM
easat-4521	19	32	,	,	PUNCT
easat-4521	19	33	4	4	NUM
easat-4521	19	34	]	]	PUNCT
easat-4521	19	35	.	.	PUNCT
easat-4521	20	1	however	however	ADV
easat-4521	20	2	,	,	PUNCT
easat-4521	20	3	students	student	NOUN
easat-4521	20	4	often	often	ADV
easat-4521	20	5	struggle	struggle	VERB
easat-4521	20	6	to	to	PART
easat-4521	20	7	understand	understand	VERB
easat-4521	20	8	the	the	DET
easat-4521	20	9	concept	concept	NOUN
easat-4521	20	10	of	of	ADP
easat-4521	20	11	the	the	DET
easat-4521	20	12	derivative	derivative	NOUN
easat-4521	20	13	of	of	ADP
easat-4521	20	14	a	a	DET
easat-4521	20	15	function	function	NOUN
easat-4521	20	16	[	[	X
easat-4521	20	17	5	5	NUM
easat-4521	20	18	]	]	PUNCT
easat-4521	20	19	especially	especially	ADV
easat-4521	20	20	in	in	ADP
easat-4521	20	21	chain	chain	NOUN
easat-4521	20	22	rules	rule	NOUN
easat-4521	20	23	,	,	PUNCT
easat-4521	20	24	graphs	graph	NOUN
easat-4521	20	25	,	,	PUNCT
easat-4521	20	26	and	and	CCONJ
easat-4521	20	27	derivative	derivative	ADJ
easat-4521	20	28	applications	application	NOUN
easat-4521	20	29	such	such	ADJ
easat-4521	20	30	as	as	ADP
easat-4521	20	31	optimization	optimization	NOUN
easat-4521	20	32	and	and	CCONJ
easat-4521	20	33	critical	critical	ADJ
easat-4521	20	34	point	point	NOUN
easat-4521	20	35	velocity	velocity	NOUN
easat-4521	20	36	calculations	calculation	NOUN
easat-4521	20	37	[	[	X
easat-4521	20	38	6	6	NUM
easat-4521	20	39	]	]	PUNCT
easat-4521	20	40	.	.	PUNCT
easat-4521	21	1	responding	respond	VERB
easat-4521	21	2	to	to	ADP
easat-4521	21	3	students	student	NOUN
easat-4521	21	4	’	’	PART
easat-4521	21	5	problems	problem	NOUN
easat-4521	21	6	in	in	ADP
easat-4521	21	7	understanding	understand	VERB
easat-4521	21	8	the	the	DET
easat-4521	21	9	stated	state	VERB
easat-4521	21	10	concept	concept	NOUN
easat-4521	21	11	,	,	PUNCT
easat-4521	21	12	this	this	DET
easat-4521	21	13	study	study	NOUN
easat-4521	21	14	highlights	highlight	VERB
easat-4521	21	15	the	the	DET
easat-4521	21	16	importance	importance	NOUN
easat-4521	21	17	of	of	ADP
easat-4521	21	18	the	the	DET
easat-4521	21	19	apos	apos	NOUN
easat-4521	21	20	(	(	PUNCT
easat-4521	21	21	action	action	NOUN
easat-4521	21	22	,	,	PUNCT
easat-4521	21	23	process	process	NOUN
easat-4521	21	24	,	,	PUNCT
easat-4521	21	25	object	object	NOUN
easat-4521	21	26	,	,	PUNCT
easat-4521	21	27	schema	schema	NOUN
easat-4521	21	28	)	)	PUNCT
easat-4521	21	29	method	method	NOUN
easat-4521	21	30	in	in	ADP
easat-4521	21	31	improving	improve	VERB
easat-4521	21	32	the	the	DET
easat-4521	21	33	understanding	understanding	NOUN
easat-4521	21	34	of	of	ADP
easat-4521	21	35	function	function	NOUN
easat-4521	21	36	derivatives	derivative	NOUN
easat-4521	21	37	,	,	PUNCT
easat-4521	21	38	especially	especially	ADV
easat-4521	21	39	in	in	ADP
easat-4521	21	40	the	the	DET
easat-4521	21	41	concept	concept	NOUN
easat-4521	21	42	of	of	ADP
easat-4521	21	43	sketching	sketch	VERB
easat-4521	21	44	function	function	NOUN
easat-4521	21	45	derivative	derivative	ADJ
easat-4521	21	46	graphs	graph	NOUN
easat-4521	21	47	.	.	PUNCT
easat-4521	22	1	in	in	ADP
easat-4521	22	2	apos	apos	PROPN
easat-4521	22	3	theory	theory	NOUN
easat-4521	22	4	,	,	PUNCT
easat-4521	22	5	the	the	DET
easat-4521	22	6	mental	mental	ADJ
easat-4521	22	7	structure	structure	NOUN
easat-4521	22	8	of	of	ADP
easat-4521	22	9	action	action	NOUN
easat-4521	22	10	,	,	PUNCT
easat-4521	22	11	process	process	NOUN
easat-4521	22	12	,	,	PUNCT
easat-4521	22	13	object	object	NOUN
easat-4521	22	14	,	,	PUNCT
easat-4521	22	15	and	and	CCONJ
easat-4521	22	16	schema	schema	NOUN
easat-4521	22	17	is	be	AUX
easat-4521	22	18	an	an	DET
easat-4521	22	19	individual	individual	NOUN
easat-4521	22	20	's	's	PART
easat-4521	22	21	construction	construction	NOUN
easat-4521	22	22	when	when	SCONJ
easat-4521	22	23	learning	learn	VERB
easat-4521	22	24	certain	certain	ADJ
easat-4521	22	25	mathematical	mathematical	ADJ
easat-4521	22	26	concepts	concept	NOUN
easat-4521	22	27	[	[	X
easat-4521	22	28	7	7	NUM
easat-4521	22	29	]	]	PUNCT
easat-4521	22	30	.	.	PUNCT
easat-4521	23	1	the	the	DET
easat-4521	23	2	mechanisms	mechanism	NOUN
easat-4521	23	3	for	for	ADP
easat-4521	23	4	building	build	VERB
easat-4521	23	5	mental	mental	ADJ
easat-4521	23	6	structures	structure	NOUN
easat-4521	23	7	(	(	PUNCT
easat-4521	23	8	mental	mental	ADJ
easat-4521	23	9	mechanisms	mechanism	NOUN
easat-4521	23	10	)	)	PUNCT
easat-4521	23	11	that	that	PRON
easat-4521	23	12	can	can	AUX
easat-4521	23	13	be	be	AUX
easat-4521	23	14	carried	carry	VERB
easat-4521	23	15	out	out	ADP
easat-4521	23	16	by	by	ADP
easat-4521	23	17	an	an	DET
easat-4521	23	18	individual	individual	NOUN
easat-4521	23	19	include	include	VERB
easat-4521	23	20	interiorization	interiorization	NOUN
easat-4521	23	21	,	,	PUNCT
easat-4521	23	22	encapsulation	encapsulation	NOUN
easat-4521	23	23	,	,	PUNCT
easat-4521	23	24	coordination	coordination	NOUN
easat-4521	23	25	,	,	PUNCT
easat-4521	23	26	reversal	reversal	NOUN
easat-4521	23	27	,	,	PUNCT
easat-4521	23	28	de	de	NOUN
easat-4521	23	29	-	-	NOUN
easat-4521	23	30	encapsulation	encapsulation	NOUN
easat-4521	23	31	,	,	PUNCT
easat-4521	23	32	and	and	CCONJ
easat-4521	23	33	thematization	thematization	NOUN
easat-4521	24	1	[	[	X
easat-4521	24	2	8	8	NUM
easat-4521	24	3	]	]	PUNCT
easat-4521	24	4	.	.	PUNCT
easat-4521	25	1	the	the	DET
easat-4521	25	2	theory	theory	NOUN
easat-4521	25	3	further	far	ADV
easat-4521	25	4	explains	explain	VERB
easat-4521	25	5	that	that	SCONJ
easat-4521	25	6	learning	learn	VERB
easat-4521	25	7	mathematical	mathematical	ADJ
easat-4521	25	8	concepts	concept	NOUN
easat-4521	25	9	involves	involve	VERB
easat-4521	25	10	applying	apply	VERB
easat-4521	25	11	transformations	transformation	NOUN
easat-4521	25	12	to	to	PART
easat-4521	25	13	already	already	ADV
easat-4521	25	14	constructed	construct	VERB
easat-4521	25	15	objects	object	NOUN
easat-4521	25	16	and	and	CCONJ
easat-4521	25	17	constructing	construct	VERB
easat-4521	25	18	new	new	ADJ
easat-4521	25	19	mental	mental	ADJ
easat-4521	25	20	or	or	CCONJ
easat-4521	25	21	cognitive	cognitive	ADJ
easat-4521	25	22	objects	object	NOUN
easat-4521	25	23	through	through	ADP
easat-4521	25	24	these	these	DET
easat-4521	25	25	transformations	transformation	NOUN
easat-4521	25	26	(	(	PUNCT
easat-4521	25	27	moll	moll	NOUN
easat-4521	25	28	,	,	PUNCT
easat-4521	25	29	et	et	PROPN
easat-4521	25	30	al	al	PROPN
easat-4521	25	31	,	,	PUNCT
easat-4521	25	32	2016	2016	NUM
easat-4521	25	33	)	)	PUNCT
easat-4521	25	34	.	.	PUNCT
easat-4521	26	1	thus	thus	ADV
easat-4521	26	2	,	,	PUNCT
easat-4521	26	3	it	it	PRON
easat-4521	26	4	https://orcid.org/0000-0002-0041-0515	https://orcid.org/0000-0002-0041-0515	VERB
easat-4521	26	5	mailto:ennylistiawati@stkippgri-bkl.ac.id	mailto:ennylistiawati@stkippgri-bkl.ac.id	ADJ
easat-4521	26	6	mailto:dwijuniati@unesa.ac.id	mailto:dwijuniati@unesa.ac.id	NOUN
easat-4521	26	7	mailto:rooselynaekawati@unesa.ac.id	mailto:rooselynaekawati@unesa.ac.id	VERB
easat-4521	26	8	556	556	NUM
easat-4521	26	9	edelweiss	edelweiss	PROPN
easat-4521	26	10	applied	apply	VERB
easat-4521	26	11	science	science	NOUN
easat-4521	26	12	and	and	CCONJ
easat-4521	26	13	technology	technology	NOUN
easat-4521	26	14	issn	issn	PROPN
easat-4521	26	15	:	:	PUNCT
easat-4521	26	16	2576	2576	NUM
easat-4521	26	17	-	-	SYM
easat-4521	26	18	8484	8484	NUM
easat-4521	26	19	vol	vol	NOUN
easat-4521	26	20	.	.	PROPN
easat-4521	27	1	9	9	NUM
easat-4521	27	2	,	,	PUNCT
easat-4521	27	3	no	no	INTJ
easat-4521	27	4	.	.	NOUN
easat-4521	27	5	2	2	NUM
easat-4521	27	6	:	:	PUNCT
easat-4521	27	7	555	555	NUM
easat-4521	27	8	-	-	SYM
easat-4521	27	9	566	566	NUM
easat-4521	27	10	,	,	PUNCT
easat-4521	27	11	2025	2025	NUM
easat-4521	27	12	doi	doi	NOUN
easat-4521	27	13	:	:	PUNCT
easat-4521	28	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	28	2	©	©	PROPN
easat-4521	28	3	2025	2025	NUM
easat-4521	28	4	by	by	ADP
easat-4521	28	5	the	the	DET
easat-4521	28	6	authors	author	NOUN
easat-4521	28	7	;	;	PUNCT
easat-4521	28	8	licensee	licensee	PROPN
easat-4521	28	9	learning	learn	VERB
easat-4521	28	10	gate	gate	NOUN
easat-4521	28	11	considers	consider	VERB
easat-4521	28	12	understanding	understand	VERB
easat-4521	28	13	mathematical	mathematical	ADJ
easat-4521	28	14	concepts	concept	NOUN
easat-4521	28	15	as	as	ADP
easat-4521	28	16	a	a	DET
easat-4521	28	17	gradual	gradual	ADJ
easat-4521	28	18	process	process	NOUN
easat-4521	28	19	of	of	ADP
easat-4521	28	20	building	building	NOUN
easat-4521	28	21	and	and	CCONJ
easat-4521	28	22	explaining	explain	VERB
easat-4521	28	23	relationships	relationship	NOUN
easat-4521	28	24	between	between	ADP
easat-4521	28	25	cognitive	cognitive	ADJ
easat-4521	28	26	structures	structure	NOUN
easat-4521	28	27	[	[	X
easat-4521	28	28	5	5	NUM
easat-4521	28	29	]	]	PUNCT
easat-4521	28	30	.	.	PUNCT
easat-4521	29	1	the	the	DET
easat-4521	29	2	apos	apos	PROPN
easat-4521	29	3	theory	theory	NOUN
easat-4521	29	4	has	have	AUX
easat-4521	29	5	been	be	AUX
easat-4521	29	6	used	use	VERB
easat-4521	29	7	in	in	ADP
easat-4521	29	8	previous	previous	ADJ
easat-4521	29	9	studies	study	NOUN
easat-4521	29	10	.	.	PUNCT
easat-4521	30	1	one	one	NUM
easat-4521	30	2	example	example	NOUN
easat-4521	30	3	[	[	X
easat-4521	30	4	9	9	NUM
easat-4521	30	5	]	]	PUNCT
easat-4521	30	6	studied	study	VERB
easat-4521	30	7	prospective	prospective	ADJ
easat-4521	30	8	mathematics	mathematic	NOUN
easat-4521	30	9	teachers	teacher	NOUN
easat-4521	30	10	’	’	PART
easat-4521	30	11	understanding	understanding	NOUN
easat-4521	30	12	on	on	ADP
easat-4521	30	13	integral	integral	ADJ
easat-4521	30	14	based	base	VERB
easat-4521	30	15	on	on	ADP
easat-4521	30	16	apos	apos	PROPN
easat-4521	30	17	theory	theory	NOUN
easat-4521	30	18	with	with	ADP
easat-4521	30	19	regard	regard	NOUN
easat-4521	30	20	to	to	ADP
easat-4521	30	21	gender	gender	NOUN
easat-4521	30	22	differences	difference	NOUN
easat-4521	30	23	.	.	PUNCT
easat-4521	31	1	in	in	ADP
easat-4521	31	2	the	the	DET
easat-4521	31	3	study	study	NOUN
easat-4521	31	4	,	,	PUNCT
easat-4521	31	5	the	the	DET
easat-4521	31	6	data	datum	NOUN
easat-4521	31	7	were	be	AUX
easat-4521	31	8	collected	collect	VERB
easat-4521	31	9	through	through	ADP
easat-4521	31	10	assignments	assignment	NOUN
easat-4521	31	11	on	on	ADP
easat-4521	31	12	integral	integral	ADJ
easat-4521	31	13	and	and	CCONJ
easat-4521	31	14	interviews	interview	NOUN
easat-4521	31	15	.	.	PUNCT
easat-4521	32	1	the	the	DET
easat-4521	32	2	results	result	NOUN
easat-4521	32	3	of	of	ADP
easat-4521	32	4	data	datum	NOUN
easat-4521	32	5	analysis	analysis	NOUN
easat-4521	32	6	showed	show	VERB
easat-4521	32	7	that	that	SCONJ
easat-4521	32	8	at	at	ADP
easat-4521	32	9	the	the	DET
easat-4521	32	10	actions	action	NOUN
easat-4521	32	11	stage	stage	NOUN
easat-4521	32	12	,	,	PUNCT
easat-4521	32	13	subjects	subject	NOUN
easat-4521	32	14	solved	solve	VERB
easat-4521	32	15	the	the	DET
easat-4521	32	16	integral	integral	ADJ
easat-4521	32	17	problem	problem	NOUN
easat-4521	32	18	procedurally	procedurally	ADV
easat-4521	32	19	but	but	CCONJ
easat-4521	32	20	at	at	ADP
easat-4521	32	21	the	the	DET
easat-4521	32	22	schemes	scheme	NOUN
easat-4521	32	23	stage	stage	NOUN
easat-4521	32	24	,	,	PUNCT
easat-4521	32	25	the	the	DET
easat-4521	32	26	coherence	coherence	NOUN
easat-4521	32	27	of	of	ADP
easat-4521	32	28	the	the	DET
easat-4521	32	29	two	two	NUM
easat-4521	32	30	subjects’schemes	subjects’scheme	NOUN
easat-4521	32	31	was	be	AUX
easat-4521	32	32	different	different	ADJ
easat-4521	32	33	.	.	PUNCT
easat-4521	33	1	on	on	ADP
easat-4521	33	2	the	the	DET
easat-4521	33	3	other	other	ADJ
easat-4521	33	4	hand	hand	NOUN
easat-4521	33	5	,	,	PUNCT
easat-4521	33	6	another	another	DET
easat-4521	33	7	study	study	NOUN
easat-4521	33	8	maf’ulah	maf’ulah	PROPN
easat-4521	33	9	and	and	CCONJ
easat-4521	33	10	juniati	juniati	NOUN
easat-4521	34	1	[	[	X
easat-4521	34	2	10	10	NUM
easat-4521	34	3	]	]	PUNCT
easat-4521	34	4	reports	report	VERB
easat-4521	34	5	that	that	SCONJ
easat-4521	34	6	by	by	ADP
easat-4521	34	7	using	use	VERB
easat-4521	34	8	the	the	DET
easat-4521	34	9	m	m	NOUN
easat-4521	34	10	-	-	PUNCT
easat-4521	34	11	apos	apos	NOUN
easat-4521	34	12	approach	approach	NOUN
easat-4521	34	13	method	method	NOUN
easat-4521	34	14	,	,	PUNCT
easat-4521	34	15	only	only	ADV
easat-4521	34	16	28	28	NUM
easat-4521	34	17	%	%	NOUN
easat-4521	34	18	of	of	ADP
easat-4521	34	19	the	the	DET
easat-4521	34	20	subjects	subject	NOUN
easat-4521	34	21	were	be	AUX
easat-4521	34	22	able	able	ADJ
easat-4521	34	23	to	to	PART
easat-4521	34	24	define	define	VERB
easat-4521	34	25	function	function	NOUN
easat-4521	34	26	graphs	graph	NOUN
easat-4521	34	27	,	,	PUNCT
easat-4521	34	28	while	while	SCONJ
easat-4521	34	29	62	62	NUM
easat-4521	34	30	%	%	NOUN
easat-4521	34	31	of	of	ADP
easat-4521	34	32	them	they	PRON
easat-4521	34	33	were	be	AUX
easat-4521	34	34	able	able	ADJ
easat-4521	34	35	to	to	PART
easat-4521	34	36	describe	describe	VERB
easat-4521	34	37	functions	function	NOUN
easat-4521	34	38	but	but	CCONJ
easat-4521	34	39	showed	show	VERB
easat-4521	34	40	difficulty	difficulty	NOUN
easat-4521	34	41	in	in	ADP
easat-4521	34	42	understanding	understand	VERB
easat-4521	34	43	the	the	DET
easat-4521	34	44	two	two	NUM
easat-4521	34	45	-	-	PUNCT
easat-4521	34	46	way	way	NOUN
easat-4521	34	47	relationship	relationship	NOUN
easat-4521	34	48	between	between	ADP
easat-4521	34	49	functions	function	NOUN
easat-4521	34	50	and	and	CCONJ
easat-4521	34	51	graphs	graph	NOUN
easat-4521	34	52	.	.	PUNCT
easat-4521	35	1	the	the	DET
easat-4521	35	2	apos	apos	PROPN
easat-4521	35	3	theory	theory	NOUN
easat-4521	35	4	was	be	AUX
easat-4521	35	5	also	also	ADV
easat-4521	35	6	utilized	utilize	VERB
easat-4521	35	7	to	to	PART
easat-4521	35	8	find	find	VERB
easat-4521	35	9	out	out	ADP
easat-4521	35	10	students	student	NOUN
easat-4521	35	11	'	'	PART
easat-4521	35	12	understanding	understanding	NOUN
easat-4521	35	13	when	when	SCONJ
easat-4521	35	14	sketching	sketch	VERB
easat-4521	35	15	quadratic	quadratic	ADJ
easat-4521	35	16	function	function	NOUN
easat-4521	35	17	graphs	graph	NOUN
easat-4521	35	18	,	,	PUNCT
easat-4521	35	19	and	and	CCONJ
easat-4521	35	20	the	the	DET
easat-4521	35	21	study	study	NOUN
easat-4521	35	22	shows	show	VERB
easat-4521	35	23	that	that	SCONJ
easat-4521	35	24	there	there	PRON
easat-4521	35	25	were	be	VERB
easat-4521	35	26	differences	difference	NOUN
easat-4521	35	27	in	in	ADP
easat-4521	35	28	understanding	understanding	NOUN
easat-4521	35	29	based	base	VERB
easat-4521	35	30	on	on	ADP
easat-4521	35	31	gender	gender	NOUN
easat-4521	35	32	;	;	PUNCT
easat-4521	35	33	the	the	DET
easat-4521	35	34	male	male	ADJ
easat-4521	35	35	subjects	subject	NOUN
easat-4521	35	36	directly	directly	ADV
easat-4521	35	37	sketched	sketch	VERB
easat-4521	35	38	the	the	DET
easat-4521	35	39	graphs	graph	NOUN
easat-4521	35	40	,	,	PUNCT
easat-4521	35	41	while	while	SCONJ
easat-4521	35	42	the	the	DET
easat-4521	35	43	female	female	ADJ
easat-4521	35	44	subjects	subject	NOUN
easat-4521	35	45	were	be	AUX
easat-4521	35	46	more	more	ADV
easat-4521	35	47	analytical	analytical	ADJ
easat-4521	35	48	in	in	ADP
easat-4521	35	49	using	use	VERB
easat-4521	35	50	tables	table	NOUN
easat-4521	35	51	and	and	CCONJ
easat-4521	35	52	coordinates	coordinate	NOUN
easat-4521	36	1	[	[	X
easat-4521	36	2	11	11	NUM
easat-4521	36	3	]	]	PUNCT
easat-4521	36	4	.	.	PUNCT
easat-4521	37	1	furthermore	furthermore	ADV
easat-4521	37	2	,	,	PUNCT
easat-4521	37	3	it	it	PRON
easat-4521	37	4	was	be	AUX
easat-4521	37	5	reported	report	VERB
easat-4521	37	6	that	that	SCONJ
easat-4521	37	7	the	the	DET
easat-4521	37	8	understanding	understanding	NOUN
easat-4521	37	9	of	of	ADP
easat-4521	37	10	the	the	DET
easat-4521	37	11	graph	graph	NOUN
easat-4521	37	12	of	of	ADP
easat-4521	37	13	inequality	inequality	NOUN
easat-4521	37	14	of	of	ADP
easat-4521	37	15	two	two	NUM
easat-4521	37	16	variables	variable	NOUN
easat-4521	37	17	can	can	AUX
easat-4521	37	18	be	be	AUX
easat-4521	37	19	expanded	expand	VERB
easat-4521	37	20	through	through	ADP
easat-4521	37	21	the	the	DET
easat-4521	37	22	concept	concept	NOUN
easat-4521	37	23	of	of	ADP
easat-4521	37	24	action	action	NOUN
easat-4521	37	25	,	,	PUNCT
easat-4521	37	26	process	process	NOUN
easat-4521	37	27	,	,	PUNCT
easat-4521	37	28	and	and	CCONJ
easat-4521	37	29	variation	variation	NOUN
easat-4521	37	30	to	to	PART
easat-4521	37	31	solve	solve	VERB
easat-4521	37	32	optimization	optimization	NOUN
easat-4521	37	33	problems	problem	NOUN
easat-4521	37	34	more	more	ADV
easat-4521	37	35	effectively	effectively	ADV
easat-4521	38	1	[	[	X
easat-4521	38	2	12	12	NUM
easat-4521	38	3	]	]	PUNCT
easat-4521	38	4	.	.	PUNCT
easat-4521	39	1	then	then	ADV
easat-4521	39	2	,	,	PUNCT
easat-4521	39	3	the	the	DET
easat-4521	39	4	use	use	NOUN
easat-4521	39	5	of	of	ADP
easat-4521	39	6	apos	apos	PROPN
easat-4521	39	7	shows	show	VERB
easat-4521	39	8	that	that	SCONJ
easat-4521	39	9	most	most	ADJ
easat-4521	39	10	prospective	prospective	ADJ
easat-4521	39	11	teachers	teacher	NOUN
easat-4521	39	12	were	be	AUX
easat-4521	39	13	still	still	ADV
easat-4521	39	14	at	at	ADP
easat-4521	39	15	the	the	DET
easat-4521	39	16	action	action	NOUN
easat-4521	39	17	level	level	NOUN
easat-4521	39	18	in	in	ADP
easat-4521	39	19	understanding	understand	VERB
easat-4521	39	20	the	the	DET
easat-4521	39	21	concept	concept	NOUN
easat-4521	39	22	of	of	ADP
easat-4521	39	23	quadratic	quadratic	ADJ
easat-4521	39	24	functions	function	NOUN
easat-4521	39	25	,	,	PUNCT
easat-4521	39	26	with	with	ADP
easat-4521	39	27	procedural	procedural	ADJ
easat-4521	39	28	understanding	understanding	NOUN
easat-4521	39	29	in	in	ADP
easat-4521	39	30	one	one	NUM
easat-4521	39	31	study	study	NOUN
easat-4521	39	32	mutambara	mutambara	NOUN
easat-4521	39	33	,	,	PUNCT
easat-4521	39	34	et	et	PROPN
easat-4521	39	35	al	al	PROPN
easat-4521	39	36	.	.	PUNCT
easat-4521	40	1	[	[	X
easat-4521	40	2	13	13	NUM
easat-4521	40	3	]	]	PUNCT
easat-4521	40	4	.	.	PUNCT
easat-4521	41	1	the	the	DET
easat-4521	41	2	apos	apos	PROPN
easat-4521	41	3	theory	theory	NOUN
easat-4521	41	4	has	have	AUX
easat-4521	41	5	also	also	ADV
easat-4521	41	6	been	be	AUX
easat-4521	41	7	used	use	VERB
easat-4521	41	8	by	by	ADP
easat-4521	41	9	another	another	DET
easat-4521	41	10	study	study	NOUN
easat-4521	41	11	fuentealba	fuentealba	PROPN
easat-4521	41	12	,	,	PUNCT
easat-4521	41	13	et	et	PROPN
easat-4521	41	14	al	al	PROPN
easat-4521	41	15	.	.	PUNCT
easat-4521	42	1	[	[	X
easat-4521	42	2	14	14	NUM
easat-4521	42	3	]	]	PUNCT
easat-4521	42	4	to	to	PART
easat-4521	42	5	identify	identify	VERB
easat-4521	42	6	and	and	CCONJ
easat-4521	42	7	characterize	characterize	VERB
easat-4521	42	8	the	the	DET
easat-4521	42	9	development	development	NOUN
easat-4521	42	10	of	of	ADP
easat-4521	42	11	students	student	NOUN
easat-4521	42	12	'	'	PART
easat-4521	42	13	understanding	understanding	NOUN
easat-4521	42	14	of	of	ADP
easat-4521	42	15	derivatives	derivative	NOUN
easat-4521	42	16	through	through	ADP
easat-4521	42	17	cluster	cluster	NOUN
easat-4521	42	18	analysis	analysis	NOUN
easat-4521	42	19	and	and	CCONJ
easat-4521	42	20	cognitive	cognitive	ADJ
easat-4521	42	21	levels	level	NOUN
easat-4521	42	22	.	.	PUNCT
easat-4521	43	1	another	another	DET
easat-4521	43	2	research	research	NOUN
easat-4521	43	3	report	report	NOUN
easat-4521	43	4	[	[	X
easat-4521	43	5	15	15	NUM
easat-4521	43	6	]	]	X
easat-4521	43	7	identifying	identify	VERB
easat-4521	43	8	students	student	NOUN
easat-4521	43	9	'	'	PART
easat-4521	43	10	errors	error	NOUN
easat-4521	43	11	in	in	ADP
easat-4521	43	12	solving	solve	VERB
easat-4521	43	13	cases	case	NOUN
easat-4521	43	14	of	of	ADP
easat-4521	43	15	critical	critical	ADJ
easat-4521	43	16	thinking	thinking	NOUN
easat-4521	43	17	skills	skill	NOUN
easat-4521	43	18	from	from	ADP
easat-4521	43	19	two	two	NUM
easat-4521	43	20	variables	variable	NOUN
easat-4521	43	21	of	of	ADP
easat-4521	43	22	linear	linear	ADJ
easat-4521	43	23	equation	equation	NOUN
easat-4521	43	24	based	base	VERB
easat-4521	43	25	on	on	ADP
easat-4521	43	26	the	the	DET
easat-4521	43	27	action	action	NOUN
easat-4521	43	28	-	-	PUNCT
easat-4521	43	29	process	process	NOUN
easat-4521	43	30	-	-	PUNCT
easat-4521	43	31	object	object	NOUN
easat-4521	43	32	-	-	PUNCT
easat-4521	43	33	schema	schema	NOUN
easat-4521	43	34	(	(	PUNCT
easat-4521	43	35	apos	apos	NOUN
easat-4521	43	36	)	)	PUNCT
easat-4521	43	37	theory	theory	NOUN
easat-4521	43	38	.	.	PUNCT
easat-4521	44	1	the	the	DET
easat-4521	44	2	findings	finding	NOUN
easat-4521	44	3	showed	show	VERB
easat-4521	44	4	that	that	SCONJ
easat-4521	44	5	the	the	DET
easat-4521	44	6	students	student	NOUN
easat-4521	44	7	have	have	VERB
easat-4521	44	8	low	low	ADJ
easat-4521	44	9	critical	critical	ADJ
easat-4521	44	10	thinking	thinking	NOUN
easat-4521	44	11	skills	skill	NOUN
easat-4521	44	12	;	;	PUNCT
easat-4521	44	13	therefore	therefore	ADV
easat-4521	44	14	,	,	PUNCT
easat-4521	44	15	they	they	PRON
easat-4521	44	16	could	could	AUX
easat-4521	44	17	not	not	PART
easat-4521	44	18	complete	complete	VERB
easat-4521	44	19	the	the	DET
easat-4521	44	20	task	task	NOUN
easat-4521	44	21	correctly	correctly	ADV
easat-4521	44	22	and	and	CCONJ
easat-4521	44	23	they	they	PRON
easat-4521	44	24	could	could	AUX
easat-4521	44	25	not	not	PART
easat-4521	44	26	reach	reach	VERB
easat-4521	44	27	a	a	DET
easat-4521	44	28	correct	correct	ADJ
easat-4521	44	29	schema	schema	NOUN
easat-4521	44	30	.	.	PUNCT
easat-4521	45	1	in	in	ADP
easat-4521	45	2	addition	addition	NOUN
easat-4521	45	3	,	,	PUNCT
easat-4521	45	4	a	a	DET
easat-4521	45	5	recent	recent	ADJ
easat-4521	45	6	inquiru	inquiru	NOUN
easat-4521	45	7	[	[	X
easat-4521	45	8	16	16	NUM
easat-4521	45	9	]	]	PUNCT
easat-4521	45	10	used	use	VERB
easat-4521	45	11	apos	apos	PROPN
easat-4521	45	12	theory	theory	NOUN
easat-4521	45	13	apos	apos	PROPN
easat-4521	45	14	-	-	PUNCT
easat-4521	45	15	ace	ace	NOUN
easat-4521	45	16	(	(	PUNCT
easat-4521	45	17	action	action	NOUN
easat-4521	45	18	,	,	PUNCT
easat-4521	45	19	process	process	NOUN
easat-4521	45	20	,	,	PUNCT
easat-4521	45	21	object	object	NOUN
easat-4521	45	22	,	,	PUNCT
easat-4521	45	23	and	and	CCONJ
easat-4521	45	24	schema	schema	NOUN
easat-4521	45	25	-	-	PUNCT
easat-4521	45	26	activities	activity	NOUN
easat-4521	45	27	,	,	PUNCT
easat-4521	45	28	classroom	classroom	NOUN
easat-4521	45	29	discussion	discussion	NOUN
easat-4521	45	30	,	,	PUNCT
easat-4521	45	31	and	and	CCONJ
easat-4521	45	32	exercises	exercise	NOUN
easat-4521	45	33	)	)	PUNCT
easat-4521	45	34	to	to	PART
easat-4521	45	35	explore	explore	VERB
easat-4521	45	36	the	the	DET
easat-4521	45	37	teaching	teaching	NOUN
easat-4521	45	38	and	and	CCONJ
easat-4521	45	39	learning	learning	NOUN
easat-4521	45	40	of	of	ADP
easat-4521	45	41	derivative	derivative	NOUN
easat-4521	45	42	by	by	ADP
easat-4521	45	43	giving	give	VERB
easat-4521	45	44	emphasis	emphasis	NOUN
easat-4521	45	45	on	on	ADP
easat-4521	45	46	its	its	PRON
easat-4521	45	47	graphical	graphical	ADJ
easat-4521	45	48	understanding	understanding	NOUN
easat-4521	45	49	.	.	PUNCT
easat-4521	46	1	for	for	ADP
easat-4521	46	2	this	this	DET
easat-4521	46	3	purpose	purpose	NOUN
easat-4521	46	4	,	,	PUNCT
easat-4521	46	5	a	a	DET
easat-4521	46	6	genetic	genetic	ADJ
easat-4521	46	7	decomposition	decomposition	NOUN
easat-4521	46	8	is	be	AUX
easat-4521	46	9	developed	develop	VERB
easat-4521	46	10	based	base	VERB
easat-4521	46	11	on	on	ADP
easat-4521	46	12	the	the	DET
easat-4521	46	13	outcomes	outcome	NOUN
easat-4521	46	14	of	of	ADP
easat-4521	46	15	previous	previous	ADJ
easat-4521	46	16	studies	study	NOUN
easat-4521	46	17	and	and	CCONJ
easat-4521	46	18	on	on	ADP
easat-4521	46	19	personal	personal	ADJ
easat-4521	46	20	teaching	teaching	NOUN
easat-4521	46	21	experiences	experience	NOUN
easat-4521	46	22	.	.	PUNCT
easat-4521	47	1	furthermore	furthermore	ADV
easat-4521	47	2	,	,	PUNCT
easat-4521	47	3	one	one	NUM
easat-4521	47	4	study	study	NOUN
easat-4521	47	5	[	[	X
easat-4521	47	6	17	17	NUM
easat-4521	47	7	]	]	PUNCT
easat-4521	47	8	identify	identify	VERB
easat-4521	47	9	the	the	DET
easat-4521	47	10	epistemological	epistemological	ADJ
easat-4521	47	11	obstacle	obstacle	NOUN
easat-4521	47	12	of	of	ADP
easat-4521	47	13	pre	pre	ADJ
easat-4521	47	14	-	-	ADJ
easat-4521	47	15	service	service	ADJ
easat-4521	47	16	mathematics	mathematic	NOUN
easat-4521	47	17	teachers	teacher	NOUN
easat-4521	47	18	on	on	ADP
easat-4521	47	19	the	the	DET
easat-4521	47	20	basic	basic	ADJ
easat-4521	47	21	concept	concept	NOUN
easat-4521	47	22	of	of	ADP
easat-4521	47	23	derivatives	derivative	NOUN
easat-4521	47	24	.	.	PUNCT
easat-4521	48	1	these	these	DET
easat-4521	48	2	data	datum	NOUN
easat-4521	48	3	are	be	AUX
easat-4521	48	4	then	then	ADV
easat-4521	48	5	reviewed	review	VERB
easat-4521	48	6	by	by	ADP
easat-4521	48	7	the	the	DET
easat-4521	48	8	framework	framework	NOUN
easat-4521	48	9	of	of	ADP
easat-4521	48	10	apos	apos	PROPN
easat-4521	48	11	theory	theory	NOUN
easat-4521	48	12	(	(	PUNCT
easat-4521	48	13	action	action	NOUN
easat-4521	48	14	-	-	PUNCT
easat-4521	48	15	process	process	NOUN
easat-4521	48	16	-	-	PUNCT
easat-4521	48	17	object	object	NOUN
easat-4521	48	18	-	-	PUNCT
easat-4521	48	19	schema	schema	NOUN
easat-4521	48	20	)	)	PUNCT
easat-4521	48	21	to	to	PART
easat-4521	48	22	overview	overview	VERB
easat-4521	48	23	the	the	DET
easat-4521	48	24	thinking	thinking	NOUN
easat-4521	48	25	of	of	ADP
easat-4521	48	26	processes	process	NOUN
easat-4521	48	27	experienced	experience	VERB
easat-4521	48	28	by	by	ADP
easat-4521	48	29	participants	participant	NOUN
easat-4521	48	30	in	in	ADP
easat-4521	48	31	answering	answer	VERB
easat-4521	48	32	the	the	DET
easat-4521	48	33	questions	question	NOUN
easat-4521	48	34	given	give	VERB
easat-4521	48	35	.	.	PUNCT
easat-4521	49	1	the	the	DET
easat-4521	49	2	results	result	NOUN
easat-4521	49	3	of	of	ADP
easat-4521	49	4	the	the	DET
easat-4521	49	5	study	study	NOUN
easat-4521	49	6	show	show	VERB
easat-4521	49	7	that	that	SCONJ
easat-4521	49	8	there	there	PRON
easat-4521	49	9	is	be	VERB
easat-4521	49	10	still	still	ADV
easat-4521	49	11	some	some	DET
easat-4521	49	12	learning	learn	VERB
easat-4521	49	13	obstacles	obstacle	NOUN
easat-4521	49	14	experienced	experience	VERB
easat-4521	49	15	by	by	ADP
easat-4521	49	16	participants	participant	NOUN
easat-4521	49	17	in	in	ADP
easat-4521	49	18	understanding	understand	VERB
easat-4521	49	19	the	the	DET
easat-4521	49	20	basic	basic	ADJ
easat-4521	49	21	concepts	concept	NOUN
easat-4521	49	22	of	of	ADP
easat-4521	49	23	derivatives	derivative	NOUN
easat-4521	49	24	.	.	PUNCT
easat-4521	50	1	another	another	DET
easat-4521	50	2	study	study	NOUN
easat-4521	50	3	baye	baye	PROPN
easat-4521	50	4	,	,	PUNCT
easat-4521	50	5	et	et	PROPN
easat-4521	50	6	al	al	PROPN
easat-4521	50	7	.	.	PUNCT
easat-4521	51	1	[	[	X
easat-4521	51	2	18	18	NUM
easat-4521	51	3	]	]	PUNCT
easat-4521	51	4	employed	employ	VERB
easat-4521	51	5	mixed	mixed	ADJ
easat-4521	51	6	methods	method	NOUN
easat-4521	51	7	experimental	experimental	ADJ
easat-4521	51	8	(	(	PUNCT
easat-4521	51	9	intervention	intervention	NOUN
easat-4521	51	10	)	)	PUNCT
easat-4521	51	11	design	design	NOUN
easat-4521	51	12	within	within	ADP
easat-4521	51	13	an	an	DET
easat-4521	51	14	apos	apos	NOUN
easat-4521	51	15	paradigm	paradigm	NOUN
easat-4521	51	16	.	.	PUNCT
easat-4521	52	1	the	the	DET
easat-4521	52	2	results	result	NOUN
easat-4521	52	3	of	of	ADP
easat-4521	52	4	the	the	DET
easat-4521	52	5	qualitative	qualitative	ADJ
easat-4521	52	6	data	datum	NOUN
easat-4521	52	7	analysis	analysis	NOUN
easat-4521	52	8	revealed	reveal	VERB
easat-4521	52	9	that	that	SCONJ
easat-4521	52	10	the	the	DET
easat-4521	52	11	learning	learn	VERB
easat-4521	52	12	milieu	milieu	NOUN
easat-4521	52	13	created	create	VERB
easat-4521	52	14	a	a	DET
easat-4521	52	15	positive	positive	ADJ
easat-4521	52	16	impact	impact	NOUN
easat-4521	52	17	on	on	ADP
easat-4521	52	18	students	student	NOUN
easat-4521	52	19	'	'	PART
easat-4521	52	20	understanding	understanding	NOUN
easat-4521	52	21	of	of	ADP
easat-4521	52	22	the	the	DET
easat-4521	52	23	concept	concept	NOUN
easat-4521	52	24	of	of	ADP
easat-4521	52	25	limit	limit	NOUN
easat-4521	52	26	.	.	PUNCT
easat-4521	53	1	additionally	additionally	ADV
easat-4521	53	2	,	,	PUNCT
easat-4521	53	3	students	student	NOUN
easat-4521	53	4	provided	provide	VERB
easat-4521	53	5	coherent	coherent	ADJ
easat-4521	53	6	and	and	CCONJ
easat-4521	53	7	viable	viable	ADJ
easat-4521	53	8	reasons	reason	NOUN
easat-4521	53	9	while	while	SCONJ
easat-4521	53	10	making	make	VERB
easat-4521	53	11	mental	mental	ADJ
easat-4521	53	12	constructions	construction	NOUN
easat-4521	53	13	and	and	CCONJ
easat-4521	53	14	their	their	PRON
easat-4521	53	15	coordination	coordination	NOUN
easat-4521	53	16	in	in	ADP
easat-4521	53	17	the	the	DET
easat-4521	53	18	learning	learning	NOUN
easat-4521	53	19	process	process	NOUN
easat-4521	53	20	based	base	VERB
easat-4521	53	21	on	on	ADP
easat-4521	53	22	the	the	DET
easat-4521	53	23	genetic	genetic	ADJ
easat-4521	53	24	decomposition	decomposition	NOUN
easat-4521	53	25	grounded	ground	VERB
easat-4521	53	26	in	in	ADP
easat-4521	53	27	apos	apos	NOUN
easat-4521	53	28	theory	theory	NOUN
easat-4521	53	29	.	.	PUNCT
easat-4521	54	1	thus	thus	ADV
easat-4521	54	2	,	,	PUNCT
easat-4521	54	3	the	the	DET
easat-4521	54	4	apos	apos	NOUN
easat-4521	54	5	theory	theory	NOUN
easat-4521	54	6	is	be	AUX
easat-4521	54	7	proven	prove	VERB
easat-4521	54	8	to	to	PART
easat-4521	54	9	hold	hold	VERB
easat-4521	54	10	importance	importance	NOUN
easat-4521	54	11	in	in	ADP
easat-4521	54	12	mathematics	mathematics	NOUN
easat-4521	54	13	education	education	NOUN
easat-4521	54	14	as	as	SCONJ
easat-4521	54	15	it	it	PRON
easat-4521	54	16	is	be	AUX
easat-4521	54	17	able	able	ADJ
easat-4521	54	18	to	to	PART
easat-4521	54	19	provide	provide	VERB
easat-4521	54	20	a	a	DET
easat-4521	54	21	deeper	deep	ADJ
easat-4521	54	22	framework	framework	NOUN
easat-4521	54	23	in	in	ADP
easat-4521	54	24	comprehending	comprehend	VERB
easat-4521	54	25	how	how	SCONJ
easat-4521	54	26	students	student	NOUN
easat-4521	54	27	build	build	VERB
easat-4521	54	28	mathematical	mathematical	ADJ
easat-4521	54	29	concepts	concept	NOUN
easat-4521	54	30	gradually	gradually	ADV
easat-4521	54	31	.	.	PUNCT
easat-4521	55	1	furthermore	furthermore	ADV
easat-4521	55	2	,	,	PUNCT
easat-4521	55	3	it	it	PRON
easat-4521	55	4	allows	allow	VERB
easat-4521	55	5	for	for	ADP
easat-4521	55	6	better	well	ADJ
easat-4521	55	7	analysis	analysis	NOUN
easat-4521	55	8	of	of	ADP
easat-4521	55	9	the	the	DET
easat-4521	55	10	development	development	NOUN
easat-4521	55	11	of	of	ADP
easat-4521	55	12	students	student	NOUN
easat-4521	55	13	'	'	PART
easat-4521	55	14	understanding	understanding	NOUN
easat-4521	55	15	of	of	ADP
easat-4521	55	16	mathematical	mathematical	ADJ
easat-4521	55	17	concepts	concept	NOUN
easat-4521	55	18	,	,	PUNCT
easat-4521	55	19	by	by	ADP
easat-4521	55	20	considering	consider	VERB
easat-4521	55	21	the	the	DET
easat-4521	55	22	cognitive	cognitive	ADJ
easat-4521	55	23	processes	process	NOUN
easat-4521	55	24	involved	involve	VERB
easat-4521	55	25	,	,	PUNCT
easat-4521	55	26	and	and	CCONJ
easat-4521	55	27	provides	provide	VERB
easat-4521	55	28	more	more	ADV
easat-4521	55	29	comprehensive	comprehensive	ADJ
easat-4521	55	30	insights	insight	NOUN
easat-4521	55	31	into	into	ADP
easat-4521	55	32	the	the	DET
easat-4521	55	33	effectiveness	effectiveness	NOUN
easat-4521	55	34	of	of	ADP
easat-4521	55	35	teachings	teaching	NOUN
easat-4521	55	36	of	of	ADP
easat-4521	55	37	mathematics	mathematic	NOUN
easat-4521	55	38	and	and	CCONJ
easat-4521	55	39	more	more	ADJ
easat-4521	55	40	objective	objective	ADJ
easat-4521	55	41	measurement	measurement	NOUN
easat-4521	55	42	of	of	ADP
easat-4521	55	43	learning	learn	VERB
easat-4521	55	44	outcomes	outcome	NOUN
easat-4521	55	45	.	.	PUNCT
easat-4521	56	1	this	this	DET
easat-4521	56	2	study	study	NOUN
easat-4521	56	3	introduces	introduce	VERB
easat-4521	56	4	an	an	DET
easat-4521	56	5	innovative	innovative	ADJ
easat-4521	56	6	approach	approach	NOUN
easat-4521	56	7	using	use	VERB
easat-4521	56	8	the	the	DET
easat-4521	56	9	apos	apos	NOUN
easat-4521	56	10	method	method	NOUN
easat-4521	56	11	involving	involve	VERB
easat-4521	56	12	the	the	DET
easat-4521	56	13	mental	mental	ADJ
easat-4521	56	14	structures	structure	NOUN
easat-4521	56	15	of	of	ADP
easat-4521	56	16	action	action	NOUN
easat-4521	56	17	,	,	PUNCT
easat-4521	56	18	process	process	NOUN
easat-4521	56	19	,	,	PUNCT
easat-4521	56	20	object	object	NOUN
easat-4521	56	21	,	,	PUNCT
easat-4521	56	22	and	and	CCONJ
easat-4521	56	23	schema	schema	NOUN
easat-4521	56	24	as	as	ADV
easat-4521	56	25	well	well	ADV
easat-4521	56	26	as	as	ADP
easat-4521	56	27	the	the	DET
easat-4521	56	28	mental	mental	ADJ
easat-4521	56	29	mechanisms	mechanism	NOUN
easat-4521	56	30	of	of	ADP
easat-4521	56	31	interiorization	interiorization	NOUN
easat-4521	56	32	,	,	PUNCT
easat-4521	56	33	encapsulation	encapsulation	NOUN
easat-4521	56	34	,	,	PUNCT
easat-4521	56	35	coordination	coordination	NOUN
easat-4521	56	36	,	,	PUNCT
easat-4521	56	37	de	de	NOUN
easat-4521	56	38	-	-	NOUN
easat-4521	56	39	encapsulation	encapsulation	NOUN
easat-4521	56	40	,	,	PUNCT
easat-4521	56	41	reversal	reversal	NOUN
easat-4521	56	42	,	,	PUNCT
easat-4521	56	43	and	and	CCONJ
easat-4521	56	44	thematization	thematization	NOUN
easat-4521	56	45	to	to	PART
easat-4521	56	46	see	see	VERB
easat-4521	56	47	students	student	NOUN
easat-4521	56	48	'	'	PART
easat-4521	56	49	understanding	understanding	NOUN
easat-4521	56	50	of	of	ADP
easat-4521	56	51	function	function	NOUN
easat-4521	56	52	derivatives	derivative	NOUN
easat-4521	56	53	,	,	PUNCT
easat-4521	56	54	especially	especially	ADV
easat-4521	56	55	in	in	ADP
easat-4521	56	56	sketching	sketch	VERB
easat-4521	56	57	function	function	NOUN
easat-4521	56	58	derivative	derivative	ADJ
easat-4521	56	59	graphs	graph	NOUN
easat-4521	56	60	.	.	PUNCT
easat-4521	57	1	theoretically	theoretically	ADV
easat-4521	57	2	,	,	PUNCT
easat-4521	57	3	this	this	DET
easat-4521	57	4	study	study	NOUN
easat-4521	57	5	is	be	AUX
easat-4521	57	6	expected	expect	VERB
easat-4521	57	7	to	to	PART
easat-4521	57	8	provide	provide	VERB
easat-4521	57	9	a	a	DET
easat-4521	57	10	deeper	deep	ADJ
easat-4521	57	11	outlook	outlook	NOUN
easat-4521	57	12	on	on	ADP
easat-4521	57	13	the	the	DET
easat-4521	57	14	mental	mental	ADJ
easat-4521	57	15	structure	structure	NOUN
easat-4521	57	16	and	and	CCONJ
easat-4521	57	17	mental	mental	ADJ
easat-4521	57	18	mechanisms	mechanism	NOUN
easat-4521	57	19	involved	involve	VERB
easat-4521	57	20	in	in	ADP
easat-4521	57	21	the	the	DET
easat-4521	57	22	concept	concept	NOUN
easat-4521	57	23	of	of	ADP
easat-4521	57	24	derivatives	derivative	NOUN
easat-4521	57	25	,	,	PUNCT
easat-4521	57	26	especially	especially	ADV
easat-4521	57	27	sketching	sketch	VERB
easat-4521	57	28	graphs	graph	NOUN
easat-4521	57	29	of	of	ADP
easat-4521	57	30	derivatives	derivative	NOUN
easat-4521	57	31	of	of	ADP
easat-4521	57	32	557	557	NUM
easat-4521	57	33	edelweiss	edelweiss	PROPN
easat-4521	57	34	applied	apply	VERB
easat-4521	57	35	science	science	NOUN
easat-4521	57	36	and	and	CCONJ
easat-4521	57	37	technology	technology	NOUN
easat-4521	57	38	issn	issn	PROPN
easat-4521	57	39	:	:	PUNCT
easat-4521	57	40	2576	2576	NUM
easat-4521	57	41	-	-	SYM
easat-4521	57	42	8484	8484	NUM
easat-4521	57	43	vol	vol	NOUN
easat-4521	57	44	.	.	PROPN
easat-4521	58	1	9	9	NUM
easat-4521	58	2	,	,	PUNCT
easat-4521	58	3	no	no	INTJ
easat-4521	58	4	.	.	NOUN
easat-4521	58	5	2	2	NUM
easat-4521	58	6	:	:	PUNCT
easat-4521	58	7	555	555	NUM
easat-4521	58	8	-	-	SYM
easat-4521	58	9	566	566	NUM
easat-4521	58	10	,	,	PUNCT
easat-4521	58	11	2025	2025	NUM
easat-4521	58	12	doi	doi	NOUN
easat-4521	58	13	:	:	PUNCT
easat-4521	59	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	59	2	©	©	PROPN
easat-4521	59	3	2025	2025	NUM
easat-4521	59	4	by	by	ADP
easat-4521	59	5	the	the	DET
easat-4521	59	6	authors	author	NOUN
easat-4521	59	7	;	;	PUNCT
easat-4521	59	8	licensee	licensee	PROPN
easat-4521	59	9	learning	learn	VERB
easat-4521	59	10	gate	gate	NOUN
easat-4521	59	11	functions	function	NOUN
easat-4521	59	12	.	.	PUNCT
easat-4521	60	1	by	by	ADP
easat-4521	60	2	using	use	VERB
easat-4521	60	3	the	the	DET
easat-4521	60	4	apos	apos	NOUN
easat-4521	60	5	theory	theory	NOUN
easat-4521	60	6	,	,	PUNCT
easat-4521	60	7	this	this	DET
easat-4521	60	8	study	study	NOUN
easat-4521	60	9	hopes	hope	VERB
easat-4521	60	10	to	to	PART
easat-4521	60	11	enhance	enhance	VERB
easat-4521	60	12	understanding	understanding	NOUN
easat-4521	60	13	of	of	ADP
easat-4521	60	14	how	how	SCONJ
easat-4521	60	15	students	student	NOUN
easat-4521	60	16	integrate	integrate	VERB
easat-4521	60	17	actions	action	NOUN
easat-4521	60	18	,	,	PUNCT
easat-4521	60	19	processes	process	NOUN
easat-4521	60	20	,	,	PUNCT
easat-4521	60	21	objects	object	NOUN
easat-4521	60	22	,	,	PUNCT
easat-4521	60	23	and	and	CCONJ
easat-4521	60	24	schemas	schema	NOUN
easat-4521	60	25	in	in	ADP
easat-4521	60	26	understanding	understand	VERB
easat-4521	60	27	mathematical	mathematical	ADJ
easat-4521	60	28	materials	material	NOUN
easat-4521	60	29	.	.	PUNCT
easat-4521	61	1	furthermore	furthermore	ADV
easat-4521	61	2	,	,	PUNCT
easat-4521	61	3	this	this	PRON
easat-4521	61	4	enriches	enrich	VERB
easat-4521	61	5	knowledge	knowledge	NOUN
easat-4521	61	6	about	about	ADP
easat-4521	61	7	how	how	SCONJ
easat-4521	61	8	students	student	NOUN
easat-4521	61	9	gradually	gradually	ADV
easat-4521	61	10	build	build	VERB
easat-4521	61	11	mathematical	mathematical	ADJ
easat-4521	61	12	understanding	understanding	NOUN
easat-4521	61	13	and	and	CCONJ
easat-4521	61	14	provides	provide	VERB
easat-4521	61	15	new	new	ADJ
easat-4521	61	16	insights	insight	NOUN
easat-4521	61	17	into	into	ADP
easat-4521	61	18	how	how	SCONJ
easat-4521	61	19	these	these	DET
easat-4521	61	20	mental	mental	ADJ
easat-4521	61	21	constructions	construction	NOUN
easat-4521	61	22	play	play	VERB
easat-4521	61	23	a	a	DET
easat-4521	61	24	role	role	NOUN
easat-4521	61	25	in	in	ADP
easat-4521	61	26	mathematics	mathematic	NOUN
easat-4521	61	27	learning	learning	NOUN
easat-4521	61	28	.	.	PUNCT
easat-4521	62	1	practically	practically	ADV
easat-4521	62	2	,	,	PUNCT
easat-4521	62	3	the	the	DET
easat-4521	62	4	results	result	NOUN
easat-4521	62	5	of	of	ADP
easat-4521	62	6	this	this	DET
easat-4521	62	7	study	study	NOUN
easat-4521	62	8	will	will	AUX
easat-4521	62	9	provide	provide	VERB
easat-4521	62	10	guidance	guidance	NOUN
easat-4521	62	11	for	for	SCONJ
easat-4521	62	12	educators	educator	NOUN
easat-4521	62	13	to	to	PART
easat-4521	62	14	design	design	VERB
easat-4521	62	15	more	more	ADV
easat-4521	62	16	effective	effective	ADJ
easat-4521	62	17	and	and	CCONJ
easat-4521	62	18	interactive	interactive	ADJ
easat-4521	62	19	teaching	teaching	NOUN
easat-4521	62	20	methods	method	NOUN
easat-4521	62	21	,	,	PUNCT
easat-4521	62	22	by	by	ADP
easat-4521	62	23	considering	consider	VERB
easat-4521	62	24	the	the	DET
easat-4521	62	25	steps	step	NOUN
easat-4521	62	26	that	that	PRON
easat-4521	62	27	students	student	NOUN
easat-4521	62	28	need	need	VERB
easat-4521	62	29	to	to	PART
easat-4521	62	30	master	master	VERB
easat-4521	62	31	at	at	ADP
easat-4521	62	32	each	each	DET
easat-4521	62	33	stage	stage	NOUN
easat-4521	62	34	of	of	ADP
easat-4521	62	35	apos	apos	PROPN
easat-4521	62	36	.	.	PUNCT
easat-4521	63	1	this	this	DET
easat-4521	63	2	study	study	NOUN
easat-4521	63	3	also	also	ADV
easat-4521	63	4	provides	provide	VERB
easat-4521	63	5	a	a	DET
easat-4521	63	6	basis	basis	NOUN
easat-4521	63	7	for	for	ADP
easat-4521	63	8	developing	develop	VERB
easat-4521	63	9	more	more	ADV
easat-4521	63	10	appropriate	appropriate	ADJ
easat-4521	63	11	evaluation	evaluation	NOUN
easat-4521	63	12	tools	tool	NOUN
easat-4521	63	13	to	to	PART
easat-4521	63	14	measure	measure	VERB
easat-4521	63	15	students	student	NOUN
easat-4521	63	16	'	'	PART
easat-4521	63	17	understanding	understanding	NOUN
easat-4521	63	18	of	of	ADP
easat-4521	63	19	the	the	DET
easat-4521	63	20	concept	concept	NOUN
easat-4521	63	21	of	of	ADP
easat-4521	63	22	derivatives	derivative	NOUN
easat-4521	63	23	,	,	PUNCT
easat-4521	63	24	and	and	CCONJ
easat-4521	63	25	can	can	AUX
easat-4521	63	26	be	be	AUX
easat-4521	63	27	applied	apply	VERB
easat-4521	63	28	in	in	ADP
easat-4521	63	29	a	a	DET
easat-4521	63	30	broader	broad	ADJ
easat-4521	63	31	context	context	NOUN
easat-4521	63	32	of	of	ADP
easat-4521	63	33	mathematics	mathematics	PROPN
easat-4521	63	34	learning	learning	NOUN
easat-4521	63	35	.	.	PUNCT
easat-4521	64	1	thus	thus	ADV
easat-4521	64	2	,	,	PUNCT
easat-4521	64	3	the	the	DET
easat-4521	64	4	results	result	NOUN
easat-4521	64	5	of	of	ADP
easat-4521	64	6	this	this	DET
easat-4521	64	7	study	study	NOUN
easat-4521	64	8	are	be	AUX
easat-4521	64	9	expected	expect	VERB
easat-4521	64	10	to	to	PART
easat-4521	64	11	support	support	VERB
easat-4521	64	12	the	the	DET
easat-4521	64	13	improvement	improvement	NOUN
easat-4521	64	14	of	of	ADP
easat-4521	64	15	the	the	DET
easat-4521	64	16	quality	quality	NOUN
easat-4521	64	17	of	of	ADP
easat-4521	64	18	mathematics	mathematic	NOUN
easat-4521	64	19	teaching	teaching	NOUN
easat-4521	64	20	and	and	CCONJ
easat-4521	64	21	help	help	VERB
easat-4521	64	22	create	create	VERB
easat-4521	64	23	a	a	DET
easat-4521	64	24	more	more	ADV
easat-4521	64	25	adaptive	adaptive	ADJ
easat-4521	64	26	learning	learning	NOUN
easat-4521	64	27	experience	experience	NOUN
easat-4521	64	28	for	for	ADP
easat-4521	64	29	students	student	NOUN
easat-4521	64	30	especially	especially	ADV
easat-4521	64	31	in	in	ADP
easat-4521	64	32	indonesia	indonesia	PROPN
easat-4521	64	33	.	.	PUNCT
easat-4521	65	1	2	2	X
easat-4521	65	2	.	.	X
easat-4521	65	3	research	research	NOUN
easat-4521	65	4	methodology	methodology	NOUN
easat-4521	65	5	2.1	2.1	NUM
easat-4521	65	6	.	.	PUNCT
easat-4521	66	1	design	design	VERB
easat-4521	66	2	this	this	DET
easat-4521	66	3	study	study	NOUN
easat-4521	66	4	aimed	aim	VERB
easat-4521	66	5	to	to	PART
easat-4521	66	6	describe	describe	VERB
easat-4521	66	7	the	the	DET
easat-4521	66	8	understanding	understanding	NOUN
easat-4521	66	9	of	of	ADP
easat-4521	66	10	prospective	prospective	ADJ
easat-4521	66	11	mathematics	mathematic	NOUN
easat-4521	66	12	teachers	teacher	NOUN
easat-4521	66	13	in	in	ADP
easat-4521	66	14	sketching	sketch	VERB
easat-4521	66	15	function	function	NOUN
easat-4521	66	16	derivative	derivative	ADJ
easat-4521	66	17	graphs	graph	NOUN
easat-4521	66	18	based	base	VERB
easat-4521	66	19	on	on	ADP
easat-4521	66	20	apos	apos	PROPN
easat-4521	66	21	theory	theory	NOUN
easat-4521	66	22	,	,	PUNCT
easat-4521	66	23	by	by	ADP
easat-4521	66	24	considering	consider	VERB
easat-4521	66	25	the	the	DET
easat-4521	66	26	level	level	NOUN
easat-4521	66	27	of	of	ADP
easat-4521	66	28	mathematics	mathematics	NOUN
easat-4521	66	29	anxiety	anxiety	NOUN
easat-4521	66	30	[	[	X
easat-4521	66	31	19	19	NUM
easat-4521	66	32	,	,	PUNCT
easat-4521	66	33	20	20	NUM
easat-4521	66	34	]	]	PUNCT
easat-4521	66	35	.	.	PUNCT
easat-4521	67	1	it	it	PRON
easat-4521	67	2	particularly	particularly	ADV
easat-4521	67	3	focused	focus	VERB
easat-4521	67	4	on	on	ADP
easat-4521	67	5	two	two	NUM
easat-4521	67	6	groups	group	NOUN
easat-4521	67	7	of	of	ADP
easat-4521	67	8	students	student	NOUN
easat-4521	67	9	with	with	ADP
easat-4521	67	10	low	low	ADJ
easat-4521	67	11	and	and	CCONJ
easat-4521	67	12	high	high	ADJ
easat-4521	67	13	mathematics	mathematic	NOUN
easat-4521	67	14	anxiety	anxiety	NOUN
easat-4521	67	15	.	.	PUNCT
easat-4521	68	1	through	through	ADP
easat-4521	68	2	function	function	NOUN
easat-4521	68	3	derivative	derivative	ADJ
easat-4521	68	4	tasks	task	NOUN
easat-4521	68	5	and	and	CCONJ
easat-4521	68	6	interviews	interview	NOUN
easat-4521	68	7	,	,	PUNCT
easat-4521	68	8	students	student	NOUN
easat-4521	68	9	'	'	PART
easat-4521	68	10	understanding	understanding	NOUN
easat-4521	68	11	was	be	AUX
easat-4521	68	12	explored	explore	VERB
easat-4521	68	13	in	in	ADP
easat-4521	68	14	the	the	DET
easat-4521	68	15	context	context	NOUN
easat-4521	68	16	of	of	ADP
easat-4521	68	17	sketching	sketch	VERB
easat-4521	68	18	function	function	NOUN
easat-4521	68	19	derivative	derivative	ADJ
easat-4521	68	20	graphs	graph	NOUN
easat-4521	68	21	[	[	X
easat-4521	68	22	11	11	NUM
easat-4521	68	23	,	,	PUNCT
easat-4521	68	24	21	21	NUM
easat-4521	68	25	,	,	PUNCT
easat-4521	68	26	22	22	NUM
easat-4521	68	27	]	]	PUNCT
easat-4521	68	28	.	.	PUNCT
easat-4521	69	1	furthermore	furthermore	ADV
easat-4521	69	2	,	,	PUNCT
easat-4521	69	3	the	the	DET
easat-4521	69	4	apos	apos	NOUN
easat-4521	69	5	theory	theory	NOUN
easat-4521	69	6	was	be	AUX
easat-4521	69	7	utilized	utilize	VERB
easat-4521	69	8	to	to	PART
easat-4521	69	9	test	test	VERB
easat-4521	69	10	students	student	NOUN
easat-4521	69	11	'	'	PART
easat-4521	69	12	mental	mental	ADJ
easat-4521	69	13	structures	structure	NOUN
easat-4521	69	14	,	,	PUNCT
easat-4521	69	15	including	include	VERB
easat-4521	69	16	action	action	NOUN
easat-4521	69	17	,	,	PUNCT
easat-4521	69	18	process	process	NOUN
easat-4521	69	19	,	,	PUNCT
easat-4521	69	20	object	object	NOUN
easat-4521	69	21	,	,	PUNCT
easat-4521	69	22	and	and	CCONJ
easat-4521	69	23	schema	schema	NOUN
easat-4521	69	24	as	as	ADV
easat-4521	69	25	well	well	ADV
easat-4521	69	26	as	as	ADP
easat-4521	69	27	their	their	PRON
easat-4521	69	28	mental	mental	ADJ
easat-4521	69	29	mechanisms	mechanism	NOUN
easat-4521	69	30	comprising	comprise	VERB
easat-4521	69	31	interiorization	interiorization	NOUN
easat-4521	69	32	,	,	PUNCT
easat-4521	69	33	encapsulation	encapsulation	NOUN
easat-4521	69	34	,	,	PUNCT
easat-4521	69	35	coordination	coordination	NOUN
easat-4521	69	36	,	,	PUNCT
easat-4521	69	37	de	de	NOUN
easat-4521	69	38	-	-	NOUN
easat-4521	69	39	encapsulation	encapsulation	NOUN
easat-4521	69	40	,	,	PUNCT
easat-4521	69	41	reversal	reversal	NOUN
easat-4521	69	42	,	,	PUNCT
easat-4521	69	43	and	and	CCONJ
easat-4521	69	44	thematization	thematization	NOUN
easat-4521	69	45	.	.	PUNCT
easat-4521	70	1	additionally	additionally	ADV
easat-4521	70	2	,	,	PUNCT
easat-4521	70	3	mathematics	mathematics	NOUN
easat-4521	70	4	anxiety	anxiety	NOUN
easat-4521	70	5	was	be	AUX
easat-4521	70	6	measured	measure	VERB
easat-4521	70	7	through	through	ADP
easat-4521	70	8	aspects	aspect	NOUN
easat-4521	70	9	of	of	ADP
easat-4521	70	10	learning	learning	NOUN
easat-4521	70	11	,	,	PUNCT
easat-4521	70	12	class	class	NOUN
easat-4521	70	13	participation	participation	NOUN
easat-4521	70	14	,	,	PUNCT
easat-4521	70	15	and	and	CCONJ
easat-4521	70	16	exams	exam	NOUN
easat-4521	70	17	.	.	PUNCT
easat-4521	71	1	the	the	DET
easat-4521	71	2	data	datum	NOUN
easat-4521	71	3	obtained	obtain	VERB
easat-4521	71	4	,	,	PUNCT
easat-4521	71	5	in	in	ADP
easat-4521	71	6	the	the	DET
easat-4521	71	7	form	form	NOUN
easat-4521	71	8	of	of	ADP
easat-4521	71	9	oral	oral	ADJ
easat-4521	71	10	and	and	CCONJ
easat-4521	71	11	written	write	VERB
easat-4521	71	12	descriptions	description	NOUN
easat-4521	71	13	,	,	PUNCT
easat-4521	71	14	were	be	AUX
easat-4521	71	15	analyzed	analyze	VERB
easat-4521	71	16	exploratively	exploratively	ADV
easat-4521	71	17	in	in	ADP
easat-4521	71	18	a	a	DET
easat-4521	71	19	qualitative	qualitative	ADJ
easat-4521	71	20	manner	manner	NOUN
easat-4521	71	21	,	,	PUNCT
easat-4521	71	22	emphasizing	emphasize	VERB
easat-4521	71	23	students	student	NOUN
easat-4521	71	24	'	'	PART
easat-4521	71	25	actual	actual	ADJ
easat-4521	71	26	understanding	understanding	NOUN
easat-4521	71	27	of	of	ADP
easat-4521	71	28	the	the	DET
easat-4521	71	29	concept	concept	NOUN
easat-4521	71	30	of	of	ADP
easat-4521	71	31	derivative	derivative	ADJ
easat-4521	71	32	functions	function	NOUN
easat-4521	71	33	.	.	PUNCT
easat-4521	72	1	2.2	2.2	NUM
easat-4521	72	2	.	.	PUNCT
easat-4521	73	1	research	research	NOUN
easat-4521	73	2	subject	subject	NOUN
easat-4521	73	3	this	this	DET
easat-4521	73	4	study	study	NOUN
easat-4521	73	5	involved	involve	VERB
easat-4521	73	6	26	26	NUM
easat-4521	73	7	prospective	prospective	ADJ
easat-4521	73	8	mathematics	mathematic	NOUN
easat-4521	73	9	teacher	teacher	NOUN
easat-4521	73	10	students	student	NOUN
easat-4521	73	11	with	with	ADP
easat-4521	73	12	high	high	ADJ
easat-4521	73	13	and	and	CCONJ
easat-4521	73	14	low	low	ADJ
easat-4521	73	15	levels	level	NOUN
easat-4521	73	16	of	of	ADP
easat-4521	73	17	mathematics	mathematics	NOUN
easat-4521	73	18	anxiety	anxiety	NOUN
easat-4521	73	19	consisting	consist	VERB
easat-4521	73	20	of	of	ADP
easat-4521	73	21	8	8	NUM
easat-4521	73	22	males	male	NOUN
easat-4521	73	23	and	and	CCONJ
easat-4521	73	24	18	18	NUM
easat-4521	73	25	females	female	NOUN
easat-4521	73	26	.	.	PUNCT
easat-4521	74	1	the	the	DET
easat-4521	74	2	category	category	NOUN
easat-4521	74	3	of	of	ADP
easat-4521	74	4	mathematics	mathematics	NOUN
easat-4521	74	5	anxiety	anxiety	NOUN
easat-4521	74	6	levels	level	NOUN
easat-4521	74	7	based	base	VERB
easat-4521	74	8	on	on	ADP
easat-4521	74	9	the	the	DET
easat-4521	74	10	score	score	NOUN
easat-4521	74	11	division	division	NOUN
easat-4521	74	12	was	be	AUX
easat-4521	74	13	considered	consider	VERB
easat-4521	74	14	low	low	ADJ
easat-4521	74	15	if	if	SCONJ
easat-4521	74	16	the	the	DET
easat-4521	74	17	score	score	NOUN
easat-4521	74	18	was	be	AUX
easat-4521	74	19	in	in	ADP
easat-4521	74	20	the	the	DET
easat-4521	74	21	interval	interval	NOUN
easat-4521	74	22	of	of	ADP
easat-4521	74	23	15	15	NUM
easat-4521	74	24	to	to	PART
easat-4521	74	25	37	37	NUM
easat-4521	74	26	,	,	PUNCT
easat-4521	74	27	while	while	SCONJ
easat-4521	74	28	high	high	ADJ
easat-4521	74	29	mathematics	mathematics	NOUN
easat-4521	74	30	anxiety	anxiety	NOUN
easat-4521	74	31	was	be	AUX
easat-4521	74	32	within	within	ADP
easat-4521	74	33	the	the	DET
easat-4521	74	34	range	range	NOUN
easat-4521	74	35	of	of	ADP
easat-4521	74	36	38	38	NUM
easat-4521	74	37	to	to	PART
easat-4521	74	38	60	60	NUM
easat-4521	75	1	[	[	X
easat-4521	75	2	23	23	NUM
easat-4521	75	3	]	]	PUNCT
easat-4521	75	4	.	.	PUNCT
easat-4521	76	1	from	from	ADP
easat-4521	76	2	the	the	DET
easat-4521	76	3	mathematics	mathematics	NOUN
easat-4521	76	4	anxiety	anxiety	NOUN
easat-4521	76	5	questionnaire	questionnaire	NOUN
easat-4521	76	6	[	[	X
easat-4521	76	7	24	24	NUM
easat-4521	76	8	]	]	PUNCT
easat-4521	76	9	given	give	VERB
easat-4521	76	10	to	to	ADP
easat-4521	76	11	the	the	DET
easat-4521	76	12	subjects	subject	NOUN
easat-4521	76	13	,	,	PUNCT
easat-4521	76	14	there	there	PRON
easat-4521	76	15	were	be	VERB
easat-4521	76	16	4	4	NUM
easat-4521	76	17	male	male	ADJ
easat-4521	76	18	students	student	NOUN
easat-4521	76	19	in	in	ADP
easat-4521	76	20	each	each	DET
easat-4521	76	21	category	category	NOUN
easat-4521	76	22	of	of	ADP
easat-4521	76	23	low	low	ADJ
easat-4521	76	24	and	and	CCONJ
easat-4521	76	25	high	high	ADJ
easat-4521	76	26	mathematics	mathematics	NOUN
easat-4521	76	27	anxiety	anxiety	NOUN
easat-4521	76	28	levels	level	NOUN
easat-4521	76	29	.	.	PUNCT
easat-4521	77	1	meanwhile	meanwhile	ADV
easat-4521	77	2	,	,	PUNCT
easat-4521	77	3	of	of	ADP
easat-4521	77	4	the	the	DET
easat-4521	77	5	18	18	NUM
easat-4521	77	6	female	female	ADJ
easat-4521	77	7	students	student	NOUN
easat-4521	77	8	,	,	PUNCT
easat-4521	77	9	there	there	PRON
easat-4521	77	10	were	be	VERB
easat-4521	77	11	6	6	NUM
easat-4521	77	12	students	student	NOUN
easat-4521	77	13	with	with	ADP
easat-4521	77	14	low	low	ADJ
easat-4521	77	15	mathematics	mathematic	NOUN
easat-4521	77	16	students	student	NOUN
easat-4521	77	17	and	and	CCONJ
easat-4521	77	18	12	12	NUM
easat-4521	77	19	subjects	subject	NOUN
easat-4521	77	20	with	with	ADP
easat-4521	77	21	high	high	ADJ
easat-4521	77	22	anxiety	anxiety	NOUN
easat-4521	77	23	.	.	PUNCT
easat-4521	78	1	this	this	DET
easat-4521	78	2	study	study	NOUN
easat-4521	78	3	explored	explore	VERB
easat-4521	78	4	qualitatively	qualitatively	ADV
easat-4521	78	5	how	how	SCONJ
easat-4521	78	6	mathematics	mathematic	NOUN
easat-4521	78	7	anxiety	anxiety	NOUN
easat-4521	78	8	affects	affect	VERB
easat-4521	78	9	students	student	NOUN
easat-4521	78	10	'	'	PART
easat-4521	78	11	understanding	understanding	NOUN
easat-4521	78	12	of	of	ADP
easat-4521	78	13	the	the	DET
easat-4521	78	14	concept	concept	NOUN
easat-4521	78	15	of	of	ADP
easat-4521	78	16	derivatives	derivative	NOUN
easat-4521	78	17	.	.	PUNCT
easat-4521	79	1	moreover	moreover	ADV
easat-4521	79	2	,	,	PUNCT
easat-4521	79	3	this	this	DET
easat-4521	79	4	study	study	NOUN
easat-4521	79	5	took	take	VERB
easat-4521	79	6	a	a	DET
easat-4521	79	7	female	female	ADJ
easat-4521	79	8	subject	subject	NOUN
easat-4521	79	9	with	with	ADP
easat-4521	79	10	low	low	ADJ
easat-4521	79	11	math	math	NOUN
easat-4521	79	12	anxiety	anxiety	NOUN
easat-4521	79	13	as	as	ADP
easat-4521	79	14	the	the	DET
easat-4521	79	15	sole	sole	ADJ
easat-4521	79	16	research	research	NOUN
easat-4521	79	17	subject	subject	NOUN
easat-4521	79	18	.	.	PUNCT
easat-4521	80	1	2.3	2.3	NUM
easat-4521	80	2	.	.	PUNCT
easat-4521	80	3	procedures	procedure	NOUN
easat-4521	80	4	and	and	CCONJ
easat-4521	80	5	data	datum	NOUN
easat-4521	80	6	collection	collection	NOUN
easat-4521	80	7	this	this	DET
easat-4521	80	8	study	study	NOUN
easat-4521	80	9	utilized	utilize	VERB
easat-4521	80	10	function	function	VERB
easat-4521	80	11	derivative	derivative	ADJ
easat-4521	80	12	tasks	task	NOUN
easat-4521	80	13	and	and	CCONJ
easat-4521	80	14	in	in	ADP
easat-4521	80	15	-	-	PUNCT
easat-4521	80	16	depth	depth	NOUN
easat-4521	80	17	interviews	interview	NOUN
easat-4521	80	18	as	as	ADP
easat-4521	80	19	research	research	NOUN
easat-4521	80	20	instruments	instrument	NOUN
easat-4521	80	21	with	with	ADP
easat-4521	80	22	the	the	DET
easat-4521	80	23	researchers	researcher	NOUN
easat-4521	80	24	as	as	ADP
easat-4521	80	25	data	datum	NOUN
easat-4521	80	26	collectors	collector	NOUN
easat-4521	80	27	and	and	CCONJ
easat-4521	80	28	analysts	analyst	NOUN
easat-4521	80	29	.	.	PUNCT
easat-4521	81	1	the	the	DET
easat-4521	81	2	supporting	support	VERB
easat-4521	81	3	instruments	instrument	NOUN
easat-4521	81	4	included	include	VERB
easat-4521	81	5	a	a	DET
easat-4521	81	6	math	math	NOUN
easat-4521	81	7	anxiety	anxiety	NOUN
easat-4521	81	8	questionnaire	questionnaire	NOUN
easat-4521	81	9	,	,	PUNCT
easat-4521	81	10	a	a	DET
easat-4521	81	11	math	math	NOUN
easat-4521	81	12	ability	ability	NOUN
easat-4521	81	13	test	test	NOUN
easat-4521	81	14	,	,	PUNCT
easat-4521	81	15	and	and	CCONJ
easat-4521	81	16	interview	interview	NOUN
easat-4521	81	17	guidelines	guideline	NOUN
easat-4521	81	18	[	[	X
easat-4521	81	19	4	4	NUM
easat-4521	81	20	,	,	PUNCT
easat-4521	81	21	25	25	NUM
easat-4521	81	22	]	]	PUNCT
easat-4521	81	23	.	.	PUNCT
easat-4521	82	1	the	the	DET
easat-4521	82	2	mathematics	mathematics	NOUN
easat-4521	82	3	anxiety	anxiety	NOUN
easat-4521	82	4	questionnaire	questionnaire	NOUN
easat-4521	82	5	[	[	X
easat-4521	82	6	26	26	NUM
easat-4521	82	7	]	]	PUNCT
easat-4521	82	8	and	and	CCONJ
easat-4521	82	9	mathematics	mathematics	NOUN
easat-4521	82	10	ability	ability	NOUN
easat-4521	82	11	test	test	NOUN
easat-4521	82	12	were	be	AUX
easat-4521	82	13	designed	design	VERB
easat-4521	82	14	to	to	PART
easat-4521	82	15	assess	assess	VERB
easat-4521	82	16	the	the	DET
easat-4521	82	17	subjects	subject	NOUN
easat-4521	82	18	’	'	PUNCT
easat-4521	82	19	mathematics	mathematic	NOUN
easat-4521	82	20	anxiety	anxiety	NOUN
easat-4521	82	21	and	and	CCONJ
easat-4521	82	22	mathematics	mathematic	NOUN
easat-4521	82	23	ability	ability	NOUN
easat-4521	82	24	,	,	PUNCT
easat-4521	82	25	while	while	SCONJ
easat-4521	82	26	the	the	DET
easat-4521	82	27	function	function	NOUN
easat-4521	82	28	derivative	derivative	ADJ
easat-4521	82	29	task	task	NOUN
easat-4521	82	30	based	base	VERB
easat-4521	82	31	on	on	ADP
easat-4521	82	32	apos	apos	PROPN
easat-4521	82	33	theory	theory	NOUN
easat-4521	82	34	was	be	AUX
easat-4521	82	35	used	use	VERB
easat-4521	82	36	to	to	PART
easat-4521	82	37	determine	determine	VERB
easat-4521	82	38	students	student	NOUN
easat-4521	82	39	'	'	PART
easat-4521	82	40	understanding	understanding	NOUN
easat-4521	82	41	of	of	ADP
easat-4521	82	42	function	function	NOUN
easat-4521	82	43	derivatives	derivative	NOUN
easat-4521	83	1	[	[	X
easat-4521	83	2	27	27	NUM
easat-4521	83	3	,	,	PUNCT
easat-4521	83	4	28	28	NUM
easat-4521	83	5	]	]	PUNCT
easat-4521	83	6	.	.	PUNCT
easat-4521	84	1	all	all	DET
easat-4521	84	2	instruments	instrument	NOUN
easat-4521	84	3	had	have	AUX
easat-4521	84	4	been	be	AUX
easat-4521	84	5	validated	validate	VERB
easat-4521	84	6	by	by	ADP
easat-4521	84	7	mathematics	mathematic	NOUN
easat-4521	84	8	education	education	NOUN
easat-4521	84	9	experts	expert	NOUN
easat-4521	84	10	prior	prior	ADV
easat-4521	84	11	to	to	ADP
easat-4521	84	12	being	be	AUX
easat-4521	84	13	disseminated	disseminate	VERB
easat-4521	84	14	to	to	ADP
easat-4521	84	15	the	the	DET
easat-4521	84	16	research	research	NOUN
easat-4521	84	17	subjects	subject	NOUN
easat-4521	84	18	.	.	PUNCT
easat-4521	85	1	data	datum	NOUN
easat-4521	85	2	were	be	AUX
easat-4521	85	3	collected	collect	VERB
easat-4521	85	4	through	through	ADP
easat-4521	85	5	triangulation	triangulation	NOUN
easat-4521	85	6	by	by	ADP
easat-4521	85	7	repeating	repeat	VERB
easat-4521	85	8	the	the	DET
easat-4521	85	9	function	function	NOUN
easat-4521	85	10	derivative	derivative	ADJ
easat-4521	85	11	task	task	NOUN
easat-4521	85	12	and	and	CCONJ
easat-4521	85	13	interviews	interview	NOUN
easat-4521	85	14	to	to	PART
easat-4521	85	15	ensure	ensure	VERB
easat-4521	85	16	consistency	consistency	NOUN
easat-4521	85	17	of	of	ADP
easat-4521	85	18	understanding	understanding	NOUN
easat-4521	85	19	.	.	PUNCT
easat-4521	86	1	data	datum	NOUN
easat-4521	86	2	were	be	AUX
easat-4521	86	3	also	also	ADV
easat-4521	86	4	analyzed	analyze	VERB
easat-4521	86	5	through	through	ADP
easat-4521	86	6	data	datum	NOUN
easat-4521	86	7	reduction	reduction	NOUN
easat-4521	86	8	,	,	PUNCT
easat-4521	86	9	data	data	NOUN
easat-4521	86	10	presentation	presentation	NOUN
easat-4521	86	11	,	,	PUNCT
easat-4521	86	12	and	and	CCONJ
easat-4521	86	13	conclusion	conclusion	NOUN
easat-4521	86	14	drawing	drawing	NOUN
easat-4521	86	15	,	,	PUNCT
easat-4521	86	16	then	then	ADV
easat-4521	86	17	validated	validate	VERB
easat-4521	86	18	by	by	ADP
easat-4521	86	19	the	the	DET
easat-4521	86	20	research	research	NOUN
easat-4521	86	21	supervisors	supervisor	NOUN
easat-4521	86	22	to	to	PART
easat-4521	86	23	evaluate	evaluate	VERB
easat-4521	86	24	the	the	DET
easat-4521	86	25	understanding	understanding	NOUN
easat-4521	86	26	of	of	ADP
easat-4521	86	27	function	function	NOUN
easat-4521	86	28	derivatives	derivative	NOUN
easat-4521	86	29	[	[	X
easat-4521	86	30	29	29	NUM
easat-4521	86	31	,	,	PUNCT
easat-4521	86	32	30	30	NUM
easat-4521	86	33	]	]	PUNCT
easat-4521	86	34	.	.	PUNCT
easat-4521	87	1	558	558	NUM
easat-4521	87	2	edelweiss	edelweiss	PROPN
easat-4521	87	3	applied	apply	VERB
easat-4521	87	4	science	science	NOUN
easat-4521	87	5	and	and	CCONJ
easat-4521	87	6	technology	technology	NOUN
easat-4521	87	7	issn	issn	PROPN
easat-4521	87	8	:	:	PUNCT
easat-4521	87	9	2576	2576	NUM
easat-4521	87	10	-	-	SYM
easat-4521	87	11	8484	8484	NUM
easat-4521	87	12	vol	vol	NOUN
easat-4521	87	13	.	.	PROPN
easat-4521	88	1	9	9	NUM
easat-4521	88	2	,	,	PUNCT
easat-4521	88	3	no	no	INTJ
easat-4521	88	4	.	.	NOUN
easat-4521	88	5	2	2	NUM
easat-4521	88	6	:	:	PUNCT
easat-4521	88	7	555	555	NUM
easat-4521	88	8	-	-	SYM
easat-4521	88	9	566	566	NUM
easat-4521	88	10	,	,	PUNCT
easat-4521	88	11	2025	2025	NUM
easat-4521	88	12	doi	doi	NOUN
easat-4521	88	13	:	:	PUNCT
easat-4521	89	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	89	2	©	©	PROPN
easat-4521	89	3	2025	2025	NUM
easat-4521	89	4	by	by	ADP
easat-4521	89	5	the	the	DET
easat-4521	89	6	authors	author	NOUN
easat-4521	89	7	;	;	PUNCT
easat-4521	89	8	licensee	licensee	PROPN
easat-4521	89	9	learning	learning	NOUN
easat-4521	89	10	gate	gate	VERB
easat-4521	89	11	2.4	2.4	NUM
easat-4521	89	12	.	.	PUNCT
easat-4521	90	1	operational	operational	ADJ
easat-4521	90	2	variables	variable	NOUN
easat-4521	90	3	the	the	DET
easat-4521	90	4	operational	operational	ADJ
easat-4521	90	5	variables	variable	NOUN
easat-4521	90	6	of	of	ADP
easat-4521	90	7	mental	mental	ADJ
easat-4521	90	8	structure	structure	NOUN
easat-4521	90	9	consist	consist	NOUN
easat-4521	90	10	of	of	ADP
easat-4521	90	11	several	several	ADJ
easat-4521	90	12	indicators	indicator	NOUN
easat-4521	90	13	:	:	PUNCT
easat-4521	90	14	action	action	NOUN
easat-4521	90	15	refers	refer	VERB
easat-4521	90	16	to	to	ADP
easat-4521	90	17	students	student	NOUN
easat-4521	90	18	'	'	PART
easat-4521	90	19	ability	ability	NOUN
easat-4521	90	20	to	to	PART
easat-4521	90	21	draw	draw	VERB
easat-4521	90	22	function	function	VERB
easat-4521	90	23	derivative	derivative	ADJ
easat-4521	90	24	graphs	graph	NOUN
easat-4521	90	25	.	.	PUNCT
easat-4521	91	1	process	process	NOUN
easat-4521	91	2	involves	involve	VERB
easat-4521	91	3	explaining	explain	VERB
easat-4521	91	4	the	the	DET
easat-4521	91	5	steps	step	NOUN
easat-4521	91	6	in	in	ADP
easat-4521	91	7	drawing	draw	VERB
easat-4521	91	8	function	function	NOUN
easat-4521	91	9	derivative	derivative	ADJ
easat-4521	91	10	graphs	graph	NOUN
easat-4521	91	11	.	.	PUNCT
easat-4521	92	1	objects	object	NOUN
easat-4521	92	2	include	include	VERB
easat-4521	92	3	determining	determine	VERB
easat-4521	92	4	the	the	DET
easat-4521	92	5	relationship	relationship	NOUN
easat-4521	92	6	between	between	ADP
easat-4521	92	7	function	function	VERB
easat-4521	92	8	derivative	derivative	ADJ
easat-4521	92	9	graphs	graph	NOUN
easat-4521	92	10	.	.	PUNCT
easat-4521	93	1	lastly	lastly	ADV
easat-4521	93	2	,	,	PUNCT
easat-4521	93	3	schema	schema	NOUN
easat-4521	93	4	describes	describe	VERB
easat-4521	93	5	the	the	DET
easat-4521	93	6	ability	ability	NOUN
easat-4521	93	7	to	to	PART
easat-4521	93	8	explain	explain	VERB
easat-4521	93	9	the	the	DET
easat-4521	93	10	nature	nature	NOUN
easat-4521	93	11	of	of	ADP
easat-4521	93	12	derivatives	derivative	NOUN
easat-4521	93	13	by	by	ADP
easat-4521	93	14	connecting	connect	VERB
easat-4521	93	15	relevant	relevant	ADJ
easat-4521	93	16	actions	action	NOUN
easat-4521	93	17	,	,	PUNCT
easat-4521	93	18	processes	process	NOUN
easat-4521	93	19	,	,	PUNCT
easat-4521	93	20	and	and	CCONJ
easat-4521	93	21	objects	object	NOUN
easat-4521	93	22	.	.	PUNCT
easat-4521	94	1	table	table	NOUN
easat-4521	94	2	1	1	NUM
easat-4521	94	3	.	.	PUNCT
easat-4521	94	4	operational	operational	ADJ
easat-4521	94	5	variables	variable	NOUN
easat-4521	94	6	.	.	PUNCT
easat-4521	95	1	mental	mental	ADJ
easat-4521	95	2	structure	structure	NOUN
easat-4521	95	3	indicators	indicator	NOUN
easat-4521	95	4	code	code	NOUN
easat-4521	95	5	action	action	NOUN
easat-4521	95	6	sketching	sketch	VERB
easat-4521	95	7	a	a	DET
easat-4521	95	8	graph	graph	NOUN
easat-4521	95	9	of	of	ADP
easat-4521	95	10	the	the	DET
easat-4521	95	11	derivative	derivative	NOUN
easat-4521	95	12	of	of	ADP
easat-4521	95	13	a	a	DET
easat-4521	95	14	function	function	NOUN
easat-4521	95	15	a	a	DET
easat-4521	95	16	process	process	NOUN
easat-4521	95	17	explaining	explain	VERB
easat-4521	95	18	the	the	DET
easat-4521	95	19	steps	step	NOUN
easat-4521	95	20	for	for	ADP
easat-4521	95	21	sketching	sketch	VERB
easat-4521	95	22	a	a	DET
easat-4521	95	23	function	function	NOUN
easat-4521	95	24	derivative	derivative	ADJ
easat-4521	95	25	graph	graph	NOUN
easat-4521	95	26	p	p	NOUN
easat-4521	95	27	objects	object	NOUN
easat-4521	95	28	determining	determine	VERB
easat-4521	95	29	the	the	DET
easat-4521	95	30	derivative	derivative	ADJ
easat-4521	95	31	relationship	relationship	NOUN
easat-4521	95	32	of	of	ADP
easat-4521	95	33	two	two	NUM
easat-4521	95	34	functions	function	NOUN
easat-4521	95	35	based	base	VERB
easat-4521	95	36	on	on	ADP
easat-4521	95	37	the	the	DET
easat-4521	95	38	given	give	VERB
easat-4521	95	39	graph	graph	NOUN
easat-4521	95	40	.	.	PUNCT
easat-4521	96	1	o	o	NOUN
easat-4521	96	2	scheme	scheme	NOUN
easat-4521	96	3	describing	describe	VERB
easat-4521	96	4	the	the	DET
easat-4521	96	5	properties	property	NOUN
easat-4521	96	6	of	of	ADP
easat-4521	96	7	derived	derive	VERB
easat-4521	96	8	functions	function	NOUN
easat-4521	96	9	by	by	ADP
easat-4521	96	10	relating	relate	VERB
easat-4521	96	11	actions	action	NOUN
easat-4521	96	12	,	,	PUNCT
easat-4521	96	13	processes	process	NOUN
easat-4521	96	14	,	,	PUNCT
easat-4521	96	15	objects	object	NOUN
easat-4521	96	16	,	,	PUNCT
easat-4521	96	17	and	and	CCONJ
easat-4521	96	18	other	other	ADJ
easat-4521	96	19	possible	possible	ADJ
easat-4521	96	20	schemes	scheme	NOUN
easat-4521	96	21	to	to	PART
easat-4521	96	22	be	be	AUX
easat-4521	96	23	used	use	VERB
easat-4521	96	24	in	in	ADP
easat-4521	96	25	completing	complete	VERB
easat-4521	96	26	derived	derived	ADJ
easat-4521	96	27	tasks	task	NOUN
easat-4521	96	28	.	.	PUNCT
easat-4521	97	1	s	s	VERB
easat-4521	97	2	2.5	2.5	NUM
easat-4521	97	3	.	.	PUNCT
easat-4521	98	1	research	research	NOUN
easat-4521	98	2	procedures	procedure	NOUN
easat-4521	98	3	this	this	DET
easat-4521	98	4	study	study	NOUN
easat-4521	98	5	analyzed	analyze	VERB
easat-4521	98	6	four	four	NUM
easat-4521	98	7	types	type	NOUN
easat-4521	98	8	of	of	ADP
easat-4521	98	9	data	datum	NOUN
easat-4521	98	10	obtained	obtain	VERB
easat-4521	98	11	from	from	ADP
easat-4521	98	12	the	the	DET
easat-4521	98	13	selected	select	VERB
easat-4521	98	14	subject	subject	NOUN
easat-4521	98	15	:	:	PUNCT
easat-4521	98	16	the	the	DET
easat-4521	98	17	results	result	NOUN
easat-4521	98	18	of	of	ADP
easat-4521	98	19	the	the	DET
easat-4521	98	20	mathematics	mathematics	NOUN
easat-4521	98	21	anxiety	anxiety	NOUN
easat-4521	98	22	questionnaire	questionnaire	NOUN
easat-4521	98	23	,	,	PUNCT
easat-4521	98	24	the	the	DET
easat-4521	98	25	mathematics	mathematic	NOUN
easat-4521	98	26	ability	ability	NOUN
easat-4521	98	27	test	test	NOUN
easat-4521	98	28	,	,	PUNCT
easat-4521	98	29	written	write	VERB
easat-4521	98	30	assignments	assignment	NOUN
easat-4521	98	31	,	,	PUNCT
easat-4521	98	32	and	and	CCONJ
easat-4521	98	33	task	task	NOUN
easat-4521	98	34	-	-	PUNCT
easat-4521	98	35	based	base	VERB
easat-4521	98	36	interview	interview	NOUN
easat-4521	98	37	transcripts	transcript	NOUN
easat-4521	98	38	[	[	X
easat-4521	98	39	12	12	NUM
easat-4521	98	40	]	]	PUNCT
easat-4521	98	41	.	.	PUNCT
easat-4521	99	1	the	the	DET
easat-4521	99	2	analysis	analysis	NOUN
easat-4521	99	3	used	use	VERB
easat-4521	99	4	the	the	DET
easat-4521	99	5	apos	apos	NOUN
easat-4521	99	6	theory	theory	NOUN
easat-4521	99	7	which	which	PRON
easat-4521	99	8	includes	include	VERB
easat-4521	99	9	four	four	NUM
easat-4521	99	10	stages	stage	NOUN
easat-4521	99	11	:	:	PUNCT
easat-4521	99	12	action	action	NOUN
easat-4521	99	13	(	(	PUNCT
easat-4521	99	14	concrete	concrete	ADJ
easat-4521	99	15	action	action	NOUN
easat-4521	99	16	)	)	PUNCT
easat-4521	99	17	,	,	PUNCT
easat-4521	99	18	process	process	NOUN
easat-4521	99	19	(	(	PUNCT
easat-4521	99	20	organizing	organizing	NOUN
easat-4521	99	21	actions	action	NOUN
easat-4521	99	22	)	)	PUNCT
easat-4521	99	23	,	,	PUNCT
easat-4521	99	24	object	object	NOUN
easat-4521	99	25	(	(	PUNCT
easat-4521	99	26	understanding	understand	VERB
easat-4521	99	27	mathematical	mathematical	ADJ
easat-4521	99	28	concepts	concept	NOUN
easat-4521	99	29	as	as	ADP
easat-4521	99	30	permanent	permanent	ADJ
easat-4521	99	31	entities	entity	NOUN
easat-4521	99	32	)	)	PUNCT
easat-4521	99	33	,	,	PUNCT
easat-4521	99	34	and	and	CCONJ
easat-4521	99	35	schema	schema	NOUN
easat-4521	99	36	(	(	PUNCT
easat-4521	99	37	mental	mental	ADJ
easat-4521	99	38	structures	structure	NOUN
easat-4521	99	39	that	that	PRON
easat-4521	99	40	organize	organize	VERB
easat-4521	99	41	knowledge	knowledge	NOUN
easat-4521	99	42	)	)	PUNCT
easat-4521	100	1	[	[	X
easat-4521	100	2	31	31	NUM
easat-4521	100	3	]	]	PUNCT
easat-4521	100	4	.	.	PUNCT
easat-4521	101	1	in	in	ADP
easat-4521	101	2	addition	addition	NOUN
easat-4521	101	3	,	,	PUNCT
easat-4521	101	4	the	the	DET
easat-4521	101	5	mental	mental	ADJ
easat-4521	101	6	mechanisms	mechanism	NOUN
easat-4521	101	7	based	base	VERB
easat-4521	101	8	on	on	ADP
easat-4521	101	9	apos	apos	NOUN
easat-4521	101	10	consisting	consist	VERB
easat-4521	101	11	of	of	ADP
easat-4521	101	12	interiorization	interiorization	NOUN
easat-4521	101	13	,	,	PUNCT
easat-4521	101	14	encapsulation	encapsulation	NOUN
easat-4521	101	15	,	,	PUNCT
easat-4521	101	16	de	de	NOUN
easat-4521	101	17	-	-	NOUN
easat-4521	101	18	encapsulation	encapsulation	NOUN
easat-4521	101	19	,	,	PUNCT
easat-4521	101	20	coordination	coordination	NOUN
easat-4521	101	21	,	,	PUNCT
easat-4521	101	22	reversal	reversal	NOUN
easat-4521	101	23	,	,	PUNCT
easat-4521	101	24	and	and	CCONJ
easat-4521	101	25	thematization	thematization	NOUN
easat-4521	101	26	were	be	AUX
easat-4521	101	27	also	also	ADV
easat-4521	101	28	analyzed	analyze	VERB
easat-4521	101	29	.	.	PUNCT
easat-4521	102	1	the	the	DET
easat-4521	102	2	analysis	analysis	NOUN
easat-4521	102	3	process	process	NOUN
easat-4521	102	4	followed	follow	VERB
easat-4521	102	5	the	the	DET
easat-4521	102	6	stages	stage	NOUN
easat-4521	102	7	of	of	ADP
easat-4521	102	8	miles	mile	NOUN
easat-4521	102	9	and	and	CCONJ
easat-4521	102	10	hubermanilyas	hubermanilyas	PROPN
easat-4521	102	11	,	,	PUNCT
easat-4521	102	12	et	et	PROPN
easat-4521	102	13	al	al	PROPN
easat-4521	102	14	.	.	PUNCT
easat-4521	103	1	[	[	X
easat-4521	103	2	32	32	NUM
easat-4521	103	3	]	]	SYM
easat-4521	103	4	;	;	PUNCT
easat-4521	103	5	miles	mile	NOUN
easat-4521	103	6	,	,	PUNCT
easat-4521	103	7	et	et	PROPN
easat-4521	103	8	al	al	PROPN
easat-4521	103	9	.	.	PUNCT
easat-4521	104	1	[	[	X
easat-4521	104	2	33	33	NUM
easat-4521	104	3	]	]	PUNCT
easat-4521	104	4	and	and	CCONJ
easat-4521	104	5	miles	mile	NOUN
easat-4521	104	6	and	and	CCONJ
easat-4521	104	7	huberman	huberman	NOUN
easat-4521	105	1	[	[	X
easat-4521	105	2	34	34	NUM
easat-4521	105	3	]	]	X
easat-4521	105	4	:	:	PUNCT
easat-4521	105	5	data	datum	NOUN
easat-4521	105	6	reduction	reduction	NOUN
easat-4521	105	7	,	,	PUNCT
easat-4521	105	8	data	datum	NOUN
easat-4521	105	9	presentation	presentation	NOUN
easat-4521	105	10	,	,	PUNCT
easat-4521	105	11	and	and	CCONJ
easat-4521	105	12	conclusion	conclusion	NOUN
easat-4521	105	13	.	.	PUNCT
easat-4521	106	1	relevant	relevant	ADJ
easat-4521	106	2	data	datum	NOUN
easat-4521	106	3	were	be	AUX
easat-4521	106	4	selected	select	VERB
easat-4521	106	5	,	,	PUNCT
easat-4521	106	6	simplified	simplify	VERB
easat-4521	106	7	,	,	PUNCT
easat-4521	106	8	and	and	CCONJ
easat-4521	106	9	grouped	group	VERB
easat-4521	106	10	to	to	PART
easat-4521	106	11	facilitate	facilitate	VERB
easat-4521	106	12	further	further	ADJ
easat-4521	106	13	analysis	analysis	NOUN
easat-4521	106	14	.	.	PUNCT
easat-4521	107	1	for	for	ADP
easat-4521	107	2	validity	validity	NOUN
easat-4521	107	3	,	,	PUNCT
easat-4521	107	4	triangulation	triangulation	NOUN
easat-4521	107	5	,	,	PUNCT
easat-4521	107	6	member	member	NOUN
easat-4521	107	7	checks	check	NOUN
easat-4521	107	8	,	,	PUNCT
easat-4521	107	9	and	and	CCONJ
easat-4521	107	10	proper	proper	ADJ
easat-4521	107	11	references	reference	NOUN
easat-4521	107	12	were	be	AUX
easat-4521	107	13	used	use	VERB
easat-4521	107	14	.	.	PUNCT
easat-4521	108	1	3	3	X
easat-4521	108	2	.	.	NOUN
easat-4521	108	3	results	result	NOUN
easat-4521	108	4	and	and	CCONJ
easat-4521	108	5	discussion	discussion	NOUN
easat-4521	108	6	3.1	3.1	NUM
easat-4521	108	7	.	.	PUNCT
easat-4521	108	8	results	result	VERB
easat-4521	108	9	3.1.1	3.1.1	NUM
easat-4521	108	10	.	.	PUNCT
easat-4521	109	1	action	action	NOUN
easat-4521	109	2	the	the	DET
easat-4521	109	3	apos	apos	NOUN
easat-4521	109	4	method	method	NOUN
easat-4521	109	5	at	at	ADP
easat-4521	109	6	the	the	DET
easat-4521	109	7	action	action	NOUN
easat-4521	109	8	stage	stage	NOUN
easat-4521	109	9	was	be	AUX
easat-4521	109	10	applied	apply	VERB
easat-4521	109	11	by	by	ADP
easat-4521	109	12	the	the	DET
easat-4521	109	13	subject	subject	NOUN
easat-4521	109	14	to	to	PART
easat-4521	109	15	understand	understand	VERB
easat-4521	109	16	the	the	DET
easat-4521	109	17	concept	concept	NOUN
easat-4521	109	18	of	of	ADP
easat-4521	109	19	function	function	NOUN
easat-4521	109	20	derivatives	derivative	NOUN
easat-4521	109	21	,	,	PUNCT
easat-4521	109	22	especially	especially	ADV
easat-4521	109	23	in	in	ADP
easat-4521	109	24	sketching	sketch	VERB
easat-4521	109	25	the	the	DET
easat-4521	109	26	function	function	NOUN
easat-4521	109	27	derivative	derivative	ADJ
easat-4521	109	28	graphs	graph	NOUN
easat-4521	109	29	using	use	VERB
easat-4521	109	30	the	the	DET
easat-4521	109	31	function	function	NOUN
easat-4521	109	32	derivative	derivative	ADJ
easat-4521	109	33	task	task	NOUN
easat-4521	109	34	(	(	PUNCT
easat-4521	109	35	fdt	fdt	NOUN
easat-4521	109	36	)	)	PUNCT
easat-4521	109	37	.	.	PUNCT
easat-4521	110	1	at	at	ADP
easat-4521	110	2	this	this	DET
easat-4521	110	3	stage	stage	NOUN
easat-4521	110	4	,	,	PUNCT
easat-4521	110	5	the	the	DET
easat-4521	110	6	subject	subject	NOUN
easat-4521	110	7	was	be	AUX
easat-4521	110	8	given	give	VERB
easat-4521	110	9	tasks	task	NOUN
easat-4521	110	10	related	relate	VERB
easat-4521	110	11	to	to	ADP
easat-4521	110	12	the	the	DET
easat-4521	110	13	material	material	NOUN
easat-4521	110	14	on	on	ADP
easat-4521	110	15	sketching	sketch	VERB
easat-4521	110	16	function	function	NOUN
easat-4521	110	17	derivative	derivative	ADJ
easat-4521	110	18	graphs	graph	NOUN
easat-4521	110	19	at	at	ADP
easat-4521	110	20	the	the	DET
easat-4521	110	21	action	action	NOUN
easat-4521	110	22	stage	stage	NOUN
easat-4521	110	23	using	use	VERB
easat-4521	110	24	fdt	fdt	NOUN
easat-4521	110	25	as	as	SCONJ
easat-4521	110	26	follows	follow	VERB
easat-4521	110	27	.	.	PUNCT
easat-4521	111	1	the	the	DET
easat-4521	111	2	following	follow	VERB
easat-4521	111	3	function	function	NOUN
easat-4521	111	4	graph	graph	NOUN
easat-4521	111	5	image	image	NOUN
easat-4521	111	6	′	′	NOUN
easat-4521	111	7	:	:	PUNCT
easat-4521	111	8	a.	a.	NOUN
easat-4521	111	9	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4521	111	10	)	)	PUNCT
easat-4521	111	11	=	=	SYM
easat-4521	111	12	𝑥2	𝑥2	NOUN
easat-4521	111	13	+	+	CCONJ
easat-4521	111	14	3	3	NUM
easat-4521	111	15	b.	b.	NOUN
easat-4521	111	16	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4521	111	17	)	)	PUNCT
easat-4521	111	18	=	=	SYM
easat-4521	111	19	𝑥3	𝑥3	NOUN
easat-4521	111	20	−	−	PROPN
easat-4521	112	1	𝑥	𝑥	NOUN
easat-4521	113	1	−	−	PROPN
easat-4521	113	2	4	4	NUM
easat-4521	113	3	the	the	DET
easat-4521	113	4	subject	subject	NOUN
easat-4521	113	5	was	be	AUX
easat-4521	113	6	given	give	VERB
easat-4521	113	7	an	an	DET
easat-4521	113	8	fdt	fdt	NOUN
easat-4521	113	9	to	to	PART
easat-4521	113	10	explore	explore	VERB
easat-4521	113	11	their	their	PRON
easat-4521	113	12	understanding	understanding	NOUN
easat-4521	113	13	at	at	ADP
easat-4521	113	14	the	the	DET
easat-4521	113	15	action	action	NOUN
easat-4521	113	16	stage	stage	NOUN
easat-4521	113	17	.	.	PUNCT
easat-4521	114	1	figure	figure	VERB
easat-4521	114	2	1	1	NUM
easat-4521	114	3	presents	present	NOUN
easat-4521	114	4	data	datum	NOUN
easat-4521	114	5	from	from	ADP
easat-4521	114	6	the	the	DET
easat-4521	114	7	results	result	NOUN
easat-4521	114	8	of	of	ADP
easat-4521	114	9	the	the	DET
easat-4521	114	10	subjects	subject	NOUN
easat-4521	114	11	'	'	PART
easat-4521	114	12	written	write	VERB
easat-4521	114	13	answers	answer	NOUN
easat-4521	114	14	at	at	ADP
easat-4521	114	15	the	the	DET
easat-4521	114	16	action	action	NOUN
easat-4521	114	17	stage	stage	NOUN
easat-4521	114	18	.	.	PUNCT
easat-4521	115	1	559	559	NUM
easat-4521	115	2	edelweiss	edelweiss	PROPN
easat-4521	115	3	applied	apply	VERB
easat-4521	115	4	science	science	NOUN
easat-4521	115	5	and	and	CCONJ
easat-4521	115	6	technology	technology	NOUN
easat-4521	115	7	issn	issn	PROPN
easat-4521	115	8	:	:	PUNCT
easat-4521	115	9	2576	2576	NUM
easat-4521	115	10	-	-	SYM
easat-4521	115	11	8484	8484	NUM
easat-4521	115	12	vol	vol	NOUN
easat-4521	115	13	.	.	PROPN
easat-4521	116	1	9	9	NUM
easat-4521	116	2	,	,	PUNCT
easat-4521	116	3	no	no	INTJ
easat-4521	116	4	.	.	NOUN
easat-4521	116	5	2	2	NUM
easat-4521	116	6	:	:	PUNCT
easat-4521	116	7	555	555	NUM
easat-4521	116	8	-	-	SYM
easat-4521	116	9	566	566	NUM
easat-4521	116	10	,	,	PUNCT
easat-4521	116	11	2025	2025	NUM
easat-4521	116	12	doi	doi	NOUN
easat-4521	116	13	:	:	PUNCT
easat-4521	117	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	117	2	©	©	PROPN
easat-4521	117	3	2025	2025	NUM
easat-4521	117	4	by	by	ADP
easat-4521	117	5	the	the	DET
easat-4521	117	6	authors	author	NOUN
easat-4521	117	7	;	;	PUNCT
easat-4521	117	8	licensee	licensee	PROPN
easat-4521	117	9	learning	learning	PROPN
easat-4521	117	10	gate	gate	PROPN
easat-4521	117	11	a.	a.	PROPN
easat-4521	117	12	b.	b.	PROPN
easat-4521	117	13	figure	figure	NOUN
easat-4521	117	14	1	1	NUM
easat-4521	117	15	.	.	PUNCT
easat-4521	117	16	subject	subject	ADJ
easat-4521	117	17	work	work	NOUN
easat-4521	117	18	results	result	VERB
easat-4521	117	19	action	action	NOUN
easat-4521	117	20	stage	stage	NOUN
easat-4521	117	21	.	.	PUNCT
easat-4521	118	1	the	the	DET
easat-4521	118	2	subject	subject	NOUN
easat-4521	118	3	sketched	sketch	VERB
easat-4521	118	4	the	the	DET
easat-4521	118	5	graphs	graph	NOUN
easat-4521	118	6	of	of	ADP
easat-4521	118	7	derivative	derivative	ADJ
easat-4521	118	8	functions	function	NOUN
easat-4521	118	9	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4521	118	10	)	)	PUNCT
easat-4521	118	11	=	=	SYM
easat-4521	118	12	𝑥2	𝑥2	NOUN
easat-4521	118	13	+	+	CCONJ
easat-4521	118	14	3	3	X
easat-4521	118	15	.	.	X
easat-4521	119	1	she	she	PRON
easat-4521	119	2	began	begin	VERB
easat-4521	119	3	by	by	ADP
easat-4521	119	4	determining	determine	VERB
easat-4521	119	5	the	the	DET
easat-4521	119	6	derivative	derivative	NOUN
easat-4521	119	7	of	of	ADP
easat-4521	119	8	the	the	DET
easat-4521	119	9	function	function	NOUN
easat-4521	119	10	,	,	PUNCT
easat-4521	119	11	namely	namely	ADV
easat-4521	119	12	𝑓′(𝑥	𝑓′(𝑥	PROPN
easat-4521	119	13	)	)	PUNCT
easat-4521	119	14	=	=	PUNCT
easat-4521	120	1	2𝑥.	2𝑥.	NUM
easat-4521	120	2	next	next	ADV
easat-4521	120	3	,	,	PUNCT
easat-4521	120	4	the	the	DET
easat-4521	120	5	subject	subject	NOUN
easat-4521	120	6	assumed	assume	VERB
easat-4521	120	7	𝑦	𝑦	PROPN
easat-4521	120	8	=	=	PROPN
easat-4521	120	9	2𝑥	2𝑥	NOUN
easat-4521	120	10	and	and	CCONJ
easat-4521	120	11	looked	look	VERB
easat-4521	120	12	for	for	ADP
easat-4521	120	13	some	some	DET
easat-4521	120	14	points	point	NOUN
easat-4521	120	15	(	(	PUNCT
easat-4521	120	16	𝑥	𝑥	NOUN
easat-4521	120	17	,	,	PUNCT
easat-4521	120	18	𝑦	𝑦	NOUN
easat-4521	120	19	)	)	PUNCT
easat-4521	120	20	which	which	PRON
easat-4521	120	21	corresponded	correspond	VERB
easat-4521	120	22	with	with	ADP
easat-4521	120	23	the	the	DET
easat-4521	120	24	equation	equation	NOUN
easat-4521	120	25	𝑦	𝑦	NOUN
easat-4521	120	26	=	=	PUNCT
easat-4521	121	1	2𝑥.	2𝑥.	NUM
easat-4521	121	2	from	from	ADP
easat-4521	121	3	several	several	ADJ
easat-4521	121	4	points	point	NOUN
easat-4521	121	5	obtained	obtain	VERB
easat-4521	121	6	,	,	PUNCT
easat-4521	121	7	the	the	DET
easat-4521	121	8	subject	subject	NOUN
easat-4521	121	9	sketched	sketch	VERB
easat-4521	121	10	a	a	DET
easat-4521	121	11	graph	graph	NOUN
easat-4521	121	12	by	by	ADP
easat-4521	121	13	connecting	connect	VERB
easat-4521	121	14	the	the	DET
easat-4521	121	15	points	point	NOUN
easat-4521	121	16	.	.	PUNCT
easat-4521	122	1	next	next	ADV
easat-4521	122	2	,	,	PUNCT
easat-4521	122	3	the	the	DET
easat-4521	122	4	subject	subject	NOUN
easat-4521	122	5	sketched	sketch	VERB
easat-4521	122	6	a	a	DET
easat-4521	122	7	graph	graph	NOUN
easat-4521	122	8	of	of	ADP
easat-4521	122	9	the	the	DET
easat-4521	122	10	derivative	derivative	NOUN
easat-4521	122	11	of	of	ADP
easat-4521	122	12	the	the	DET
easat-4521	122	13	function	function	NOUN
easat-4521	122	14	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4521	122	15	)	)	PUNCT
easat-4521	122	16	=	=	SYM
easat-4521	122	17	𝑥3	𝑥3	NOUN
easat-4521	122	18	−	−	PROPN
easat-4521	122	19	𝑥	𝑥	PRON
easat-4521	122	20	−	−	NOUN
easat-4521	122	21	4	4	NUM
easat-4521	122	22	by	by	ADP
easat-4521	122	23	first	first	ADV
easat-4521	122	24	determining	determine	VERB
easat-4521	122	25	the	the	DET
easat-4521	122	26	derivative	derivative	NOUN
easat-4521	122	27	of	of	ADP
easat-4521	122	28	the	the	DET
easat-4521	122	29	function	function	NOUN
easat-4521	122	30	,	,	PUNCT
easat-4521	122	31	namely	namely	ADV
easat-4521	122	32	𝑓′(𝑥	𝑓′(𝑥	PROPN
easat-4521	122	33	)	)	PUNCT
easat-4521	122	34	=	=	SYM
easat-4521	123	1	3𝑥2	3𝑥2	NUM
easat-4521	123	2	−	−	NOUN
easat-4521	123	3	1	1	NUM
easat-4521	123	4	.	.	PUNCT
easat-4521	124	1	after	after	ADP
easat-4521	124	2	that	that	PRON
easat-4521	124	3	,	,	PUNCT
easat-4521	124	4	the	the	DET
easat-4521	124	5	subject	subject	NOUN
easat-4521	124	6	determined	determine	VERB
easat-4521	124	7	the	the	DET
easat-4521	124	8	point	point	NOUN
easat-4521	124	9	where	where	SCONJ
easat-4521	124	10	the	the	DET
easat-4521	124	11	graph	graph	NOUN
easat-4521	124	12	intersected	intersect	VERB
easat-4521	124	13	the	the	DET
easat-4521	124	14	coordinate	coordinate	NOUN
easat-4521	124	15	axis	axis	NOUN
easat-4521	124	16	,	,	PUNCT
easat-4521	124	17	namely	namely	ADV
easat-4521	124	18	the	the	DET
easat-4521	124	19	point	point	NOUN
easat-4521	124	20	where	where	SCONJ
easat-4521	124	21	it	it	PRON
easat-4521	124	22	intersects	intersect	VERB
easat-4521	124	23	the	the	DET
easat-4521	124	24	coordinate	coordinate	NOUN
easat-4521	124	25	axis	axis	NOUN
easat-4521	124	26	𝑥	𝑥	PROPN
easat-4521	124	27	and	and	CCONJ
easat-4521	124	28	the	the	DET
easat-4521	124	29	point	point	NOUN
easat-4521	124	30	of	of	ADP
easat-4521	124	31	intersection	intersection	NOUN
easat-4521	124	32	with	with	ADP
easat-4521	124	33	the	the	DET
easat-4521	124	34	axis	axis	NOUN
easat-4521	124	35	𝑦.	𝑦.	PROPN
easat-4521	124	36	after	after	ADP
easat-4521	124	37	that	that	PRON
easat-4521	124	38	,	,	PUNCT
easat-4521	124	39	the	the	DET
easat-4521	124	40	subject	subject	NOUN
easat-4521	124	41	looked	look	VERB
easat-4521	124	42	for	for	ADP
easat-4521	124	43	the	the	DET
easat-4521	124	44	equation	equation	NOUN
easat-4521	124	45	of	of	ADP
easat-4521	124	46	the	the	DET
easat-4521	124	47	axis	axis	NOUN
easat-4521	124	48	of	of	ADP
easat-4521	124	49	symmetry	symmetry	NOUN
easat-4521	124	50	using	use	VERB
easat-4521	124	51	the	the	DET
easat-4521	124	52	formula	formula	NOUN
easat-4521	124	53	𝑥	𝑥	NOUN
easat-4521	124	54	=	=	PUNCT
easat-4521	124	55	−	−	PROPN
easat-4521	125	1	𝑏	𝑏	NUM
easat-4521	125	2	2𝑎	2𝑎	NUM
easat-4521	125	3	which	which	PRON
easat-4521	125	4	obtained	obtain	VERB
easat-4521	125	5	𝑥	𝑥	PROPN
easat-4521	125	6	=	=	SYM
easat-4521	125	7	0	0	NUM
easat-4521	125	8	.	.	PUNCT
easat-4521	126	1	then	then	ADV
easat-4521	126	2	,	,	PUNCT
easat-4521	126	3	the	the	DET
easat-4521	126	4	subject	subject	NOUN
easat-4521	126	5	looked	look	VERB
easat-4521	126	6	for	for	ADP
easat-4521	126	7	the	the	DET
easat-4521	126	8	minimum	minimum	ADJ
easat-4521	126	9	value	value	NOUN
easat-4521	126	10	using	use	VERB
easat-4521	126	11	the	the	DET
easat-4521	126	12	formula	formula	NOUN
easat-4521	126	13	𝑦	𝑦	NOUN
easat-4521	126	14	=	=	SYM
easat-4521	126	15	−	−	PROPN
easat-4521	126	16	𝐷	𝐷	PROPN
easat-4521	126	17	4𝑎	4𝑎	NOUN
easat-4521	126	18	which	which	PRON
easat-4521	126	19	obtained	obtain	VERB
easat-4521	126	20	𝑦	𝑦	NOUN
easat-4521	126	21	=	=	NOUN
easat-4521	126	22	−1	−1	NOUN
easat-4521	126	23	.	.	PUNCT
easat-4521	127	1	from	from	ADP
easat-4521	127	2	the	the	DET
easat-4521	127	3	equation	equation	NOUN
easat-4521	127	4	of	of	ADP
easat-4521	127	5	the	the	DET
easat-4521	127	6	axis	axis	NOUN
easat-4521	127	7	of	of	ADP
easat-4521	127	8	symmetry	symmetry	NOUN
easat-4521	127	9	and	and	CCONJ
easat-4521	127	10	the	the	DET
easat-4521	127	11	minimum	minimum	ADJ
easat-4521	127	12	value	value	NOUN
easat-4521	127	13	of	of	ADP
easat-4521	127	14	the	the	DET
easat-4521	127	15	function	function	NOUN
easat-4521	127	16	,	,	PUNCT
easat-4521	127	17	the	the	DET
easat-4521	127	18	peak	peak	NOUN
easat-4521	127	19	of	of	ADP
easat-4521	127	20	the	the	DET
easat-4521	127	21	parabola	parabola	NOUN
easat-4521	127	22	was	be	AUX
easat-4521	127	23	(	(	PUNCT
easat-4521	127	24	0	0	NUM
easat-4521	127	25	,	,	PUNCT
easat-4521	127	26	−1	−1	NOUN
easat-4521	127	27	)	)	PUNCT
easat-4521	127	28	.	.	PUNCT
easat-4521	128	1	from	from	ADP
easat-4521	128	2	this	this	DET
easat-4521	128	3	information	information	NOUN
easat-4521	128	4	,	,	PUNCT
easat-4521	128	5	the	the	DET
easat-4521	128	6	subject	subject	NOUN
easat-4521	128	7	connected	connect	VERB
easat-4521	128	8	the	the	DET
easat-4521	128	9	points	point	NOUN
easat-4521	128	10	obtained	obtain	VERB
easat-4521	128	11	,	,	PUNCT
easat-4521	128	12	namely	namely	ADV
easat-4521	128	13	the	the	DET
easat-4521	128	14	intersection	intersection	NOUN
easat-4521	128	15	points	point	VERB
easat-4521	128	16	with	with	ADP
easat-4521	128	17	the	the	DET
easat-4521	128	18	axis	axis	NOUN
easat-4521	128	19	.	.	PUNCT
easat-4521	129	1	𝑥	𝑥	X
easat-4521	129	2	,	,	PUNCT
easat-4521	129	3	the	the	DET
easat-4521	129	4	point	point	NOUN
easat-4521	129	5	of	of	ADP
easat-4521	129	6	intersection	intersection	NOUN
easat-4521	129	7	with	with	ADP
easat-4521	129	8	the	the	DET
easat-4521	129	9	y	y	NOUN
easat-4521	129	10	-	-	PUNCT
easat-4521	129	11	axis	axis	NOUN
easat-4521	129	12	,	,	PUNCT
easat-4521	129	13	and	and	CCONJ
easat-4521	129	14	the	the	DET
easat-4521	129	15	vertex	vertex	NOUN
easat-4521	129	16	of	of	ADP
easat-4521	129	17	the	the	DET
easat-4521	129	18	parabola	parabola	NOUN
easat-4521	129	19	to	to	PART
easat-4521	129	20	sketch	sketch	VERB
easat-4521	129	21	the	the	DET
easat-4521	129	22	graph	graph	NOUN
easat-4521	129	23	′(𝑥	′(𝑥	NOUN
easat-4521	129	24	)	)	PUNCT
easat-4521	129	25	=	=	SYM
easat-4521	130	1	3𝑥2	3𝑥2	NUM
easat-4521	130	2	−	−	NOUN
easat-4521	130	3	1	1	NUM
easat-4521	130	4	)	)	PUNCT
easat-4521	130	5	.	.	PUNCT
easat-4521	131	1	based	base	VERB
easat-4521	131	2	on	on	ADP
easat-4521	131	3	this	this	PRON
easat-4521	131	4	,	,	PUNCT
easat-4521	131	5	it	it	PRON
easat-4521	131	6	can	can	AUX
easat-4521	131	7	be	be	AUX
easat-4521	131	8	stated	state	VERB
easat-4521	131	9	that	that	SCONJ
easat-4521	131	10	in	in	ADP
easat-4521	131	11	order	order	NOUN
easat-4521	131	12	to	to	PART
easat-4521	131	13	sketch	sketch	VERB
easat-4521	131	14	a	a	DET
easat-4521	131	15	function	function	NOUN
easat-4521	131	16	derivative	derivative	ADJ
easat-4521	131	17	graph	graph	NOUN
easat-4521	131	18	,	,	PUNCT
easat-4521	131	19	the	the	DET
easat-4521	131	20	subject	subject	NOUN
easat-4521	131	21	needed	need	VERB
easat-4521	131	22	to	to	PART
easat-4521	131	23	first	first	ADV
easat-4521	131	24	determine	determine	VERB
easat-4521	131	25	the	the	DET
easat-4521	131	26	function	function	NOUN
easat-4521	131	27	derivative	derivative	NOUN
easat-4521	131	28	.	.	PUNCT
easat-4521	132	1	if	if	SCONJ
easat-4521	132	2	the	the	DET
easat-4521	132	3	function	function	NOUN
easat-4521	132	4	derivative	derivative	NOUN
easat-4521	132	5	was	be	AUX
easat-4521	132	6	a	a	DET
easat-4521	132	7	linear	linear	ADJ
easat-4521	132	8	function	function	NOUN
easat-4521	132	9	,	,	PUNCT
easat-4521	132	10	then	then	ADV
easat-4521	132	11	the	the	DET
easat-4521	132	12	subject	subject	NOUN
easat-4521	132	13	drew	draw	VERB
easat-4521	132	14	a	a	DET
easat-4521	132	15	function	function	NOUN
easat-4521	132	16	derivative	derivative	ADJ
easat-4521	132	17	graph	graph	NOUN
easat-4521	132	18	by	by	ADP
easat-4521	132	19	finding	find	VERB
easat-4521	132	20	several	several	ADJ
easat-4521	132	21	points	point	NOUN
easat-4521	132	22	that	that	PRON
easat-4521	132	23	were	be	AUX
easat-4521	132	24	in	in	ADP
easat-4521	132	25	accordance	accordance	NOUN
easat-4521	132	26	with	with	ADP
easat-4521	132	27	the	the	DET
easat-4521	132	28	equation	equation	NOUN
easat-4521	132	29	and	and	CCONJ
easat-4521	132	30	connecting	connect	VERB
easat-4521	132	31	the	the	DET
easat-4521	132	32	points	point	NOUN
easat-4521	132	33	obtained	obtain	VERB
easat-4521	132	34	so	so	SCONJ
easat-4521	132	35	that	that	SCONJ
easat-4521	132	36	a	a	DET
easat-4521	132	37	function	function	NOUN
easat-4521	132	38	derivative	derivative	ADJ
easat-4521	132	39	graph	graph	NOUN
easat-4521	132	40	was	be	AUX
easat-4521	132	41	formed	form	VERB
easat-4521	132	42	in	in	ADP
easat-4521	132	43	the	the	DET
easat-4521	132	44	form	form	NOUN
easat-4521	132	45	of	of	ADP
easat-4521	132	46	a	a	DET
easat-4521	132	47	straight	straight	ADJ
easat-4521	132	48	line	line	NOUN
easat-4521	132	49	.	.	PUNCT
easat-4521	133	1	furthermore	furthermore	ADV
easat-4521	133	2	,	,	PUNCT
easat-4521	133	3	if	if	SCONJ
easat-4521	133	4	the	the	DET
easat-4521	133	5	function	function	NOUN
easat-4521	133	6	derivative	derivative	NOUN
easat-4521	133	7	was	be	AUX
easat-4521	133	8	a	a	DET
easat-4521	133	9	quadratic	quadratic	ADJ
easat-4521	133	10	function	function	NOUN
easat-4521	133	11	,	,	PUNCT
easat-4521	133	12	then	then	ADV
easat-4521	133	13	the	the	DET
easat-4521	133	14	subject	subject	NOUN
easat-4521	133	15	determined	determine	VERB
easat-4521	133	16	the	the	DET
easat-4521	133	17	point	point	NOUN
easat-4521	133	18	of	of	ADP
easat-4521	133	19	intersection	intersection	NOUN
easat-4521	133	20	of	of	ADP
easat-4521	133	21	the	the	DET
easat-4521	133	22	graph	graph	NOUN
easat-4521	133	23	with	with	ADP
easat-4521	133	24	the	the	DET
easat-4521	133	25	coordinate	coordinate	NOUN
easat-4521	133	26	axis	axis	NOUN
easat-4521	133	27	,	,	PUNCT
easat-4521	133	28	namely	namely	ADV
easat-4521	133	29	determining	determine	VERB
easat-4521	133	30	the	the	DET
easat-4521	133	31	point	point	NOUN
easat-4521	133	32	of	of	ADP
easat-4521	133	33	intersection	intersection	NOUN
easat-4521	133	34	with	with	ADP
easat-4521	133	35	the	the	DET
easat-4521	133	36	coordinate	coordinate	NOUN
easat-4521	133	37	axis	axis	NOUN
easat-4521	133	38	𝑥	𝑥	PROPN
easat-4521	133	39	,	,	PUNCT
easat-4521	133	40	the	the	DET
easat-4521	133	41	point	point	NOUN
easat-4521	133	42	of	of	ADP
easat-4521	133	43	intersection	intersection	NOUN
easat-4521	133	44	with	with	ADP
easat-4521	133	45	the	the	DET
easat-4521	133	46	axis	axis	NOUN
easat-4521	133	47	𝑦	𝑦	NOUN
easat-4521	133	48	,	,	PUNCT
easat-4521	133	49	the	the	DET
easat-4521	133	50	equation	equation	NOUN
easat-4521	133	51	of	of	ADP
easat-4521	133	52	the	the	DET
easat-4521	133	53	axis	axis	NOUN
easat-4521	133	54	of	of	ADP
easat-4521	133	55	symmetry	symmetry	NOUN
easat-4521	133	56	,	,	PUNCT
easat-4521	133	57	the	the	DET
easat-4521	133	58	optimum	optimum	ADJ
easat-4521	133	59	value	value	NOUN
easat-4521	133	60	,	,	PUNCT
easat-4521	133	61	the	the	DET
easat-4521	133	62	peak	peak	NOUN
easat-4521	133	63	of	of	ADP
easat-4521	133	64	the	the	DET
easat-4521	133	65	parabola	parabola	NOUN
easat-4521	133	66	,	,	PUNCT
easat-4521	133	67	and	and	CCONJ
easat-4521	133	68	then	then	ADV
easat-4521	133	69	connecting	connect	VERB
easat-4521	133	70	the	the	DET
easat-4521	133	71	points	point	NOUN
easat-4521	133	72	obtained	obtain	VERB
easat-4521	133	73	so	so	SCONJ
easat-4521	133	74	that	that	SCONJ
easat-4521	133	75	a	a	DET
easat-4521	133	76	function	function	NOUN
easat-4521	133	77	derivative	derivative	ADJ
easat-4521	133	78	graph	graph	NOUN
easat-4521	133	79	was	be	AUX
easat-4521	133	80	formed	form	VERB
easat-4521	133	81	in	in	ADP
easat-4521	133	82	the	the	DET
easat-4521	133	83	form	form	NOUN
easat-4521	133	84	of	of	ADP
easat-4521	133	85	a	a	DET
easat-4521	133	86	parabola	parabola	NOUN
easat-4521	133	87	.	.	PUNCT
easat-4521	134	1	3.1.2	3.1.2	X
easat-4521	134	2	.	.	PUNCT
easat-4521	134	3	process	process	NOUN
easat-4521	134	4	and	and	CCONJ
easat-4521	134	5	interiorization	interiorization	NOUN
easat-4521	134	6	to	to	PART
easat-4521	134	7	find	find	VERB
easat-4521	134	8	out	out	ADP
easat-4521	134	9	the	the	DET
easat-4521	134	10	subject	subject	NOUN
easat-4521	134	11	's	's	PART
easat-4521	134	12	understanding	understanding	NOUN
easat-4521	134	13	of	of	ADP
easat-4521	134	14	the	the	DET
easat-4521	134	15	derivative	derivative	NOUN
easat-4521	134	16	of	of	ADP
easat-4521	134	17	a	a	DET
easat-4521	134	18	function	function	NOUN
easat-4521	134	19	,	,	PUNCT
easat-4521	134	20	especially	especially	ADV
easat-4521	134	21	about	about	ADP
easat-4521	134	22	sketching	sketching	NOUN
easat-4521	134	23	,	,	PUNCT
easat-4521	134	24	at	at	ADP
easat-4521	134	25	the	the	DET
easat-4521	134	26	subject	subject	NOUN
easat-4521	134	27	’s	’s	PART
easat-4521	134	28	process	process	NOUN
easat-4521	134	29	stage	stage	NOUN
easat-4521	134	30	,	,	PUNCT
easat-4521	134	31	the	the	DET
easat-4521	134	32	fdt	fdt	NOUN
easat-4521	134	33	was	be	AUX
easat-4521	134	34	given	give	VERB
easat-4521	134	35	,	,	PUNCT
easat-4521	134	36	and	and	CCONJ
easat-4521	134	37	the	the	DET
easat-4521	134	38	subject	subject	NOUN
easat-4521	134	39	’s	’s	PART
easat-4521	134	40	answer	answer	NOUN
easat-4521	134	41	can	can	AUX
easat-4521	134	42	be	be	AUX
easat-4521	134	43	seen	see	VERB
easat-4521	134	44	in	in	ADP
easat-4521	134	45	figure	figure	NOUN
easat-4521	134	46	2	2	NUM
easat-4521	134	47	as	as	SCONJ
easat-4521	134	48	follows	follow	VERB
easat-4521	134	49	.	.	PUNCT
easat-4521	135	1	for	for	ADP
easat-4521	135	2	example	example	NOUN
easat-4521	135	3	,	,	PUNCT
easat-4521	135	4	given	give	VERB
easat-4521	135	5	a	a	DET
easat-4521	135	6	function	function	NOUN
easat-4521	135	7	graph	graph	NOUN
easat-4521	135	8	𝑓	𝑓	PRON
easat-4521	135	9	:	:	PUNCT
easat-4521	135	10	𝑓′(𝑥	𝑓′(𝑥	PROPN
easat-4521	135	11	)	)	PUNCT
easat-4521	135	12	=	=	SYM
easat-4521	135	13	3𝑥2	3𝑥2	NUM
easat-4521	135	14	−	−	NOUN
easat-4521	135	15	1	1	NUM
easat-4521	135	16	intersection	intersection	NOUN
easat-4521	135	17	point	point	NOUN
easat-4521	135	18	𝑥	𝑥	PROPN
easat-4521	135	19	→	→	SYM
easat-4521	135	20	𝑦	𝑦	NOUN
easat-4521	135	21	=	=	SYM
easat-4521	135	22	0	0	PUNCT
easat-4521	135	23	𝑥	𝑥	PROPN
easat-4521	135	24	=	=	PUNCT
easat-4521	135	25	√1	√1	PROPN
easat-4521	135	26	3⁄	3⁄	NUM
easat-4521	135	27	𝑜𝑟	𝑜𝑟	ADP
easat-4521	135	28	𝑥	𝑥	NOUN
easat-4521	135	29	=	=	PUNCT
easat-4521	135	30	−√1	−√1	NOUN
easat-4521	135	31	3⁄	3⁄	NUM
easat-4521	135	32	axis	axis	NOUN
easat-4521	135	33	of	of	ADP
easat-4521	135	34	symmetry	symmetry	NOUN
easat-4521	135	35	=	=	SYM
easat-4521	135	36	0	0	NUM
easat-4521	135	37	𝑦𝑚𝑖𝑛	𝑦𝑚𝑖𝑛	NOUN
easat-4521	135	38	=	=	PRON
easat-4521	135	39	−(0	−(0	NOUN
easat-4521	135	40	−	−	PROPN
easat-4521	135	41	4.3(−1	4.3(−1	PROPN
easat-4521	135	42	)	)	PUNCT
easat-4521	135	43	)	)	PUNCT
easat-4521	135	44	12	12	NUM
easat-4521	135	45	=	=	SYM
easat-4521	135	46	−1	−1	NOUN
easat-4521	135	47	peak	peak	NOUN
easat-4521	135	48	(	(	PUNCT
easat-4521	135	49	0	0	NUM
easat-4521	135	50	,	,	PUNCT
easat-4521	135	51	−1	−1	NOUN
easat-4521	135	52	)	)	PUNCT
easat-4521	135	53	560	560	NUM
easat-4521	135	54	edelweiss	edelweiss	PROPN
easat-4521	135	55	applied	apply	VERB
easat-4521	135	56	science	science	NOUN
easat-4521	135	57	and	and	CCONJ
easat-4521	135	58	technology	technology	NOUN
easat-4521	135	59	issn	issn	PROPN
easat-4521	135	60	:	:	PUNCT
easat-4521	135	61	2576	2576	NUM
easat-4521	135	62	-	-	SYM
easat-4521	135	63	8484	8484	NUM
easat-4521	135	64	vol	vol	NOUN
easat-4521	135	65	.	.	PROPN
easat-4521	135	66	9	9	NUM
easat-4521	135	67	,	,	PUNCT
easat-4521	135	68	no	no	INTJ
easat-4521	135	69	.	.	NOUN
easat-4521	135	70	2	2	NUM
easat-4521	135	71	:	:	PUNCT
easat-4521	135	72	555	555	NUM
easat-4521	135	73	-	-	SYM
easat-4521	135	74	566	566	NUM
easat-4521	135	75	,	,	PUNCT
easat-4521	135	76	2025	2025	NUM
easat-4521	135	77	doi	doi	NOUN
easat-4521	135	78	:	:	PUNCT
easat-4521	135	79	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	135	80	©	©	PROPN
easat-4521	135	81	2025	2025	NUM
easat-4521	135	82	by	by	ADP
easat-4521	135	83	the	the	DET
easat-4521	135	84	authors	author	NOUN
easat-4521	135	85	;	;	PUNCT
easat-4521	135	86	licensee	licensee	PROPN
easat-4521	135	87	learning	learn	VERB
easat-4521	135	88	gate	gate	NOUN
easat-4521	135	89	figure	figure	NOUN
easat-4521	135	90	2	2	NUM
easat-4521	135	91	.	.	PUNCT
easat-4521	135	92	assignment	assignment	NOUN
easat-4521	135	93	of	of	ADP
easat-4521	135	94	sketching	sketch	VERB
easat-4521	135	95	a	a	DET
easat-4521	135	96	function	function	NOUN
easat-4521	135	97	derivative	derivative	ADJ
easat-4521	135	98	graph	graph	NOUN
easat-4521	135	99	.	.	PUNCT
easat-4521	136	1	explain	explain	VERB
easat-4521	136	2	how	how	SCONJ
easat-4521	136	3	to	to	PART
easat-4521	136	4	draw	draw	VERB
easat-4521	136	5	a	a	DET
easat-4521	136	6	graph	graph	NOUN
easat-4521	136	7	𝑓′	𝑓′	NUM
easat-4521	136	8	from	from	ADP
easat-4521	136	9	the	the	DET
easat-4521	136	10	graph	graph	NOUN
easat-4521	136	11	𝑓	𝑓	PROPN
easat-4521	136	12	!	!	PUNCT
easat-4521	137	1	the	the	DET
easat-4521	137	2	subject	subject	NOUN
easat-4521	137	3	was	be	AUX
easat-4521	137	4	given	give	VERB
easat-4521	137	5	the	the	DET
easat-4521	137	6	fdt	fdt	NOUN
easat-4521	137	7	to	to	PART
easat-4521	137	8	explore	explore	VERB
easat-4521	137	9	her	her	PRON
easat-4521	137	10	understanding	understanding	NOUN
easat-4521	137	11	at	at	ADP
easat-4521	137	12	the	the	DET
easat-4521	137	13	process	process	NOUN
easat-4521	137	14	stage	stage	NOUN
easat-4521	137	15	,	,	PUNCT
easat-4521	137	16	but	but	CCONJ
easat-4521	137	17	the	the	DET
easat-4521	137	18	subject	subject	NOUN
easat-4521	137	19	could	could	AUX
easat-4521	137	20	not	not	PART
easat-4521	137	21	explain	explain	VERB
easat-4521	137	22	the	the	DET
easat-4521	137	23	steps	step	NOUN
easat-4521	137	24	to	to	PART
easat-4521	137	25	draw	draw	VERB
easat-4521	137	26	a	a	DET
easat-4521	137	27	function	function	NOUN
easat-4521	137	28	derivative	derivative	ADJ
easat-4521	137	29	graph	graph	NOUN
easat-4521	137	30	from	from	ADP
easat-4521	137	31	the	the	DET
easat-4521	137	32	given	give	VERB
easat-4521	137	33	function	function	NOUN
easat-4521	137	34	graph	graph	NOUN
easat-4521	137	35	so	so	SCONJ
easat-4521	137	36	that	that	SCONJ
easat-4521	137	37	it	it	PRON
easat-4521	137	38	did	do	AUX
easat-4521	137	39	not	not	PART
easat-4521	137	40	meet	meet	VERB
easat-4521	137	41	the	the	DET
easat-4521	137	42	process	process	NOUN
easat-4521	137	43	indicator	indicator	NOUN
easat-4521	137	44	.	.	PUNCT
easat-4521	138	1	thus	thus	ADV
easat-4521	138	2	,	,	PUNCT
easat-4521	138	3	there	there	PRON
easat-4521	138	4	was	be	VERB
easat-4521	138	5	no	no	DET
easat-4521	138	6	mental	mental	ADJ
easat-4521	138	7	interiorization	interiorization	NOUN
easat-4521	138	8	mechanism	mechanism	NOUN
easat-4521	138	9	in	in	ADP
easat-4521	138	10	explaining	explain	VERB
easat-4521	138	11	the	the	DET
easat-4521	138	12	steps	step	NOUN
easat-4521	138	13	to	to	PART
easat-4521	138	14	sketch	sketch	VERB
easat-4521	138	15	a	a	DET
easat-4521	138	16	function	function	NOUN
easat-4521	138	17	derivative	derivative	ADJ
easat-4521	138	18	graph	graph	NOUN
easat-4521	138	19	from	from	ADP
easat-4521	138	20	the	the	DET
easat-4521	138	21	given	give	VERB
easat-4521	138	22	function	function	NOUN
easat-4521	138	23	graph	graph	NOUN
easat-4521	138	24	which	which	PRON
easat-4521	138	25	was	be	AUX
easat-4521	138	26	indicated	indicate	VERB
easat-4521	138	27	by	by	ADP
easat-4521	138	28	the	the	DET
easat-4521	138	29	subject	subject	NOUN
easat-4521	138	30	being	be	AUX
easat-4521	138	31	unable	unable	ADJ
easat-4521	138	32	to	to	PART
easat-4521	138	33	explain	explain	VERB
easat-4521	138	34	the	the	DET
easat-4521	138	35	steps	step	NOUN
easat-4521	138	36	to	to	PART
easat-4521	138	37	sketch	sketch	VERB
easat-4521	138	38	a	a	DET
easat-4521	138	39	function	function	NOUN
easat-4521	138	40	derivative	derivative	ADJ
easat-4521	138	41	graph	graph	NOUN
easat-4521	138	42	from	from	ADP
easat-4521	138	43	the	the	DET
easat-4521	138	44	given	give	VERB
easat-4521	138	45	function	function	NOUN
easat-4521	138	46	graph	graph	NOUN
easat-4521	138	47	.	.	PUNCT
easat-4521	139	1	3.1.3	3.1.3	NUM
easat-4521	139	2	.	.	PUNCT
easat-4521	139	3	objects	object	NOUN
easat-4521	139	4	,	,	PUNCT
easat-4521	139	5	de	de	NOUN
easat-4521	139	6	-	-	NOUN
easat-4521	139	7	encapsulation	encapsulation	NOUN
easat-4521	139	8	,	,	PUNCT
easat-4521	139	9	coordination	coordination	NOUN
easat-4521	139	10	,	,	PUNCT
easat-4521	139	11	and	and	CCONJ
easat-4521	139	12	reversal	reversal	NOUN
easat-4521	139	13	to	to	PART
easat-4521	139	14	find	find	VERB
easat-4521	139	15	out	out	ADP
easat-4521	139	16	the	the	DET
easat-4521	139	17	subject	subject	NOUN
easat-4521	139	18	's	's	PART
easat-4521	139	19	understanding	understanding	NOUN
easat-4521	139	20	of	of	ADP
easat-4521	139	21	the	the	DET
easat-4521	139	22	sketching	sketching	NOUN
easat-4521	139	23	function	function	NOUN
easat-4521	139	24	derivative	derivative	NOUN
easat-4521	139	25	at	at	ADP
easat-4521	139	26	the	the	DET
easat-4521	139	27	object	object	NOUN
easat-4521	139	28	stage	stage	NOUN
easat-4521	139	29	using	use	VERB
easat-4521	139	30	fdt	fdt	NOUN
easat-4521	139	31	,	,	PUNCT
easat-4521	139	32	the	the	DET
easat-4521	139	33	illustration	illustration	NOUN
easat-4521	139	34	was	be	AUX
easat-4521	139	35	given	give	VERB
easat-4521	139	36	in	in	ADP
easat-4521	139	37	figure	figure	NOUN
easat-4521	139	38	3	3	NUM
easat-4521	139	39	.	.	PUNCT
easat-4521	140	1	the	the	DET
easat-4521	140	2	following	follow	VERB
easat-4521	140	3	image	image	NOUN
easat-4521	140	4	shows	show	VERB
easat-4521	140	5	a	a	DET
easat-4521	140	6	graphic	graphic	ADJ
easat-4521	140	7	image	image	NOUN
easat-4521	140	8	of	of	ADP
easat-4521	140	9	four	four	NUM
easat-4521	140	10	functions	function	NOUN
easat-4521	140	11	indicated	indicate	VERB
easat-4521	140	12	by	by	ADP
easat-4521	140	13	the	the	DET
easat-4521	140	14	graph	graph	NOUN
easat-4521	140	15	𝑎	𝑎	PROPN
easat-4521	140	16	,	,	PUNCT
easat-4521	140	17	𝑏	𝑏	NOUN
easat-4521	140	18	,	,	PUNCT
easat-4521	140	19	𝑐	𝑐	PROPN
easat-4521	140	20	,	,	PUNCT
easat-4521	140	21	𝑑	𝑑	PRON
easat-4521	140	22	figure	figure	NOUN
easat-4521	140	23	3	3	NUM
easat-4521	140	24	.	.	PUNCT
easat-4521	140	25	function	function	NOUN
easat-4521	140	26	graph	graph	NOUN
easat-4521	140	27	.	.	PUNCT
easat-4521	141	1	based	base	VERB
easat-4521	141	2	on	on	ADP
easat-4521	141	3	the	the	DET
easat-4521	141	4	graph	graph	NOUN
easat-4521	141	5	,	,	PUNCT
easat-4521	141	6	how	how	SCONJ
easat-4521	141	7	is	be	AUX
easat-4521	141	8	the	the	DET
easat-4521	141	9	relationship	relationship	NOUN
easat-4521	141	10	between	between	ADP
easat-4521	141	11	the	the	DET
easat-4521	141	12	following	follow	VERB
easat-4521	141	13	functions	function	NOUN
easat-4521	141	14	?	?	PUNCT
easat-4521	141	15	:	:	PUNCT
easat-4521	141	16	a.	a.	NOUN
easat-4521	141	17	function	function	NOUN
easat-4521	141	18	𝑎	𝑎	NOUN
easat-4521	141	19	and	and	CCONJ
easat-4521	141	20	𝑏	𝑏	NOUN
easat-4521	141	21	?	?	PUNCT
easat-4521	141	22	b.	b.	PROPN
easat-4521	141	23	function	function	PROPN
easat-4521	141	24	𝑐	𝑐	PROPN
easat-4521	141	25	and	and	CCONJ
easat-4521	141	26	𝑑	𝑑	PROPN
easat-4521	141	27	?	?	PUNCT
easat-4521	141	28	c.	c.	PROPN
easat-4521	141	29	derivative	derivative	NOUN
easat-4521	141	30	of	of	ADP
easat-4521	141	31	function	function	NOUN
easat-4521	141	32	𝑎	𝑎	NOUN
easat-4521	141	33	and	and	CCONJ
easat-4521	141	34	𝑏	𝑏	NOUN
easat-4521	141	35	?	?	PUNCT
easat-4521	142	1	d.	d.	PROPN
easat-4521	142	2	derivative	derivative	NOUN
easat-4521	142	3	of	of	ADP
easat-4521	142	4	function	function	NOUN
easat-4521	142	5	𝑐	𝑐	PROPN
easat-4521	142	6	and	and	CCONJ
easat-4521	142	7	𝑑	𝑑	NOUN
easat-4521	142	8	?	?	PUNCT
easat-4521	143	1	the	the	DET
easat-4521	143	2	subject	subject	NOUN
easat-4521	143	3	was	be	AUX
easat-4521	143	4	given	give	VERB
easat-4521	143	5	fdt	fdt	NOUN
easat-4521	143	6	to	to	PART
easat-4521	143	7	explore	explore	VERB
easat-4521	143	8	her	her	PRON
easat-4521	143	9	understanding	understanding	NOUN
easat-4521	143	10	at	at	ADP
easat-4521	143	11	the	the	DET
easat-4521	143	12	object	object	NOUN
easat-4521	143	13	stage	stage	NOUN
easat-4521	143	14	.	.	PUNCT
easat-4521	144	1	figure	figure	VERB
easat-4521	144	2	4	4	NUM
easat-4521	144	3	presents	present	NOUN
easat-4521	144	4	data	datum	NOUN
easat-4521	144	5	on	on	ADP
easat-4521	144	6	the	the	DET
easat-4521	144	7	results	result	NOUN
easat-4521	144	8	of	of	ADP
easat-4521	144	9	the	the	DET
easat-4521	144	10	subjects	subject	NOUN
easat-4521	144	11	'	'	PART
easat-4521	144	12	written	write	VERB
easat-4521	144	13	answers	answer	NOUN
easat-4521	144	14	at	at	ADP
easat-4521	144	15	the	the	DET
easat-4521	144	16	object	object	NOUN
easat-4521	144	17	stage	stage	NOUN
easat-4521	144	18	.	.	PUNCT
easat-4521	145	1	561	561	NUM
easat-4521	145	2	edelweiss	edelweiss	PROPN
easat-4521	145	3	applied	apply	VERB
easat-4521	145	4	science	science	NOUN
easat-4521	145	5	and	and	CCONJ
easat-4521	145	6	technology	technology	NOUN
easat-4521	145	7	issn	issn	PROPN
easat-4521	145	8	:	:	PUNCT
easat-4521	145	9	2576	2576	NUM
easat-4521	145	10	-	-	SYM
easat-4521	145	11	8484	8484	NUM
easat-4521	145	12	vol	vol	NOUN
easat-4521	145	13	.	.	PROPN
easat-4521	146	1	9	9	NUM
easat-4521	146	2	,	,	PUNCT
easat-4521	146	3	no	no	INTJ
easat-4521	146	4	.	.	NOUN
easat-4521	146	5	2	2	NUM
easat-4521	146	6	:	:	PUNCT
easat-4521	146	7	555	555	NUM
easat-4521	146	8	-	-	SYM
easat-4521	146	9	566	566	NUM
easat-4521	146	10	,	,	PUNCT
easat-4521	146	11	2025	2025	NUM
easat-4521	146	12	doi	doi	NOUN
easat-4521	146	13	:	:	PUNCT
easat-4521	147	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	147	2	©	©	PROPN
easat-4521	147	3	2025	2025	NUM
easat-4521	147	4	by	by	ADP
easat-4521	147	5	the	the	DET
easat-4521	147	6	authors	author	NOUN
easat-4521	147	7	;	;	PUNCT
easat-4521	147	8	licensee	licensee	PROPN
easat-4521	147	9	learning	learn	VERB
easat-4521	147	10	gate	gate	NOUN
easat-4521	147	11	figure	figure	NOUN
easat-4521	147	12	4	4	NUM
easat-4521	147	13	.	.	PUNCT
easat-4521	148	1	the	the	DET
easat-4521	148	2	subject	subject	NOUN
easat-4521	148	3	’s	’s	PART
easat-4521	148	4	answer	answer	NOUN
easat-4521	148	5	.	.	PUNCT
easat-4521	149	1	after	after	ADP
easat-4521	149	2	that	that	PRON
easat-4521	149	3	,	,	PUNCT
easat-4521	149	4	the	the	DET
easat-4521	149	5	subject	subject	NOUN
easat-4521	149	6	determined	determine	VERB
easat-4521	149	7	the	the	DET
easat-4521	149	8	relationship	relationship	NOUN
easat-4521	149	9	between	between	ADP
easat-4521	149	10	the	the	DET
easat-4521	149	11	derivatives	derivative	NOUN
easat-4521	149	12	of	of	ADP
easat-4521	149	13	two	two	NUM
easat-4521	149	14	functions	function	NOUN
easat-4521	149	15	based	base	VERB
easat-4521	149	16	on	on	ADP
easat-4521	149	17	the	the	DET
easat-4521	149	18	given	give	VERB
easat-4521	149	19	graph	graph	NOUN
easat-4521	149	20	,	,	PUNCT
easat-4521	149	21	namely	namely	ADV
easat-4521	149	22	determining	determine	VERB
easat-4521	149	23	the	the	DET
easat-4521	149	24	relationship	relationship	NOUN
easat-4521	149	25	between	between	ADP
easat-4521	149	26	the	the	DET
easat-4521	149	27	functions	function	NOUN
easat-4521	149	28	𝑎	𝑎	NOUN
easat-4521	149	29	and	and	CCONJ
easat-4521	149	30	𝑏	𝑏	NOUN
easat-4521	149	31	and	and	CCONJ
easat-4521	149	32	functions	function	VERB
easat-4521	149	33	𝑐	𝑐	PROPN
easat-4521	149	34	and	and	CCONJ
easat-4521	149	35	𝑑	𝑑	PROPN
easat-4521	149	36	based	base	VERB
easat-4521	149	37	on	on	ADP
easat-4521	149	38	the	the	DET
easat-4521	149	39	graph	graph	NOUN
easat-4521	149	40	provided	provide	VERB
easat-4521	149	41	.	.	PUNCT
easat-4521	150	1	this	this	PRON
easat-4521	150	2	was	be	AUX
easat-4521	150	3	done	do	VERB
easat-4521	150	4	by	by	ADP
easat-4521	150	5	looking	look	VERB
easat-4521	150	6	at	at	ADP
easat-4521	150	7	the	the	DET
easat-4521	150	8	similarity	similarity	NOUN
easat-4521	150	9	of	of	ADP
easat-4521	150	10	the	the	DET
easat-4521	150	11	graph	graph	NOUN
easat-4521	150	12	with	with	ADP
easat-4521	150	13	her	her	PRON
easat-4521	150	14	previous	previous	ADJ
easat-4521	150	15	experience	experience	NOUN
easat-4521	150	16	of	of	ADP
easat-4521	150	17	working	work	VERB
easat-4521	150	18	on	on	ADP
easat-4521	150	19	questions	question	NOUN
easat-4521	150	20	so	so	SCONJ
easat-4521	150	21	that	that	SCONJ
easat-4521	150	22	a	a	DET
easat-4521	150	23	relationship	relationship	NOUN
easat-4521	150	24	of	of	ADP
easat-4521	150	25	𝑎	𝑎	DET
easat-4521	150	26	derivative	derivative	NOUN
easat-4521	150	27	of	of	ADP
easat-4521	150	28	𝑏	𝑏	PROPN
easat-4521	150	29	and	and	CCONJ
easat-4521	150	30	𝑐	𝑐	PROPN
easat-4521	150	31	derivative	derivative	NOUN
easat-4521	150	32	of	of	ADP
easat-4521	150	33	𝑑	𝑑	PRON
easat-4521	150	34	was	be	AUX
easat-4521	150	35	garnered	garner	VERB
easat-4521	150	36	.	.	PUNCT
easat-4521	151	1	based	base	VERB
easat-4521	151	2	on	on	ADP
easat-4521	151	3	this	this	PRON
easat-4521	151	4	,	,	PUNCT
easat-4521	151	5	it	it	PRON
easat-4521	151	6	can	can	AUX
easat-4521	151	7	be	be	AUX
easat-4521	151	8	said	say	VERB
easat-4521	151	9	that	that	SCONJ
easat-4521	151	10	the	the	DET
easat-4521	151	11	subject	subject	NOUN
easat-4521	151	12	determined	determine	VERB
easat-4521	151	13	the	the	DET
easat-4521	151	14	relationship	relationship	NOUN
easat-4521	151	15	between	between	ADP
easat-4521	151	16	the	the	DET
easat-4521	151	17	derivatives	derivative	NOUN
easat-4521	151	18	of	of	ADP
easat-4521	151	19	two	two	NUM
easat-4521	151	20	functions	function	NOUN
easat-4521	151	21	based	base	VERB
easat-4521	151	22	on	on	ADP
easat-4521	151	23	the	the	DET
easat-4521	151	24	graphs	graph	NOUN
easat-4521	151	25	given	give	VERB
easat-4521	151	26	by	by	ADP
easat-4521	151	27	using	use	VERB
easat-4521	151	28	previous	previous	ADJ
easat-4521	151	29	knowledge	knowledge	NOUN
easat-4521	151	30	,	,	PUNCT
easat-4521	151	31	namely	namely	ADV
easat-4521	151	32	by	by	ADP
easat-4521	151	33	seeing	see	VERB
easat-4521	151	34	the	the	DET
easat-4521	151	35	similarity	similarity	NOUN
easat-4521	151	36	of	of	ADP
easat-4521	151	37	the	the	DET
easat-4521	151	38	graphs	graph	NOUN
easat-4521	151	39	and	and	CCONJ
easat-4521	151	40	functions	function	NOUN
easat-4521	151	41	from	from	ADP
easat-4521	151	42	the	the	DET
easat-4521	151	43	previous	previous	ADJ
easat-4521	151	44	questions	question	NOUN
easat-4521	151	45	so	so	SCONJ
easat-4521	151	46	that	that	SCONJ
easat-4521	151	47	the	the	DET
easat-4521	151	48	subject	subject	NOUN
easat-4521	151	49	determined	determine	VERB
easat-4521	151	50	the	the	DET
easat-4521	151	51	relationship	relationship	NOUN
easat-4521	151	52	between	between	ADP
easat-4521	151	53	the	the	DET
easat-4521	151	54	function	function	NOUN
easat-4521	151	55	and	and	CCONJ
easat-4521	151	56	the	the	DET
easat-4521	151	57	parabola	parabola	NOUN
easat-4521	151	58	-	-	PUNCT
easat-4521	151	59	shaped	shape	VERB
easat-4521	151	60	graph	graph	NOUN
easat-4521	151	61	which	which	PRON
easat-4521	151	62	was	be	AUX
easat-4521	151	63	the	the	DET
easat-4521	151	64	derivative	derivative	NOUN
easat-4521	151	65	of	of	ADP
easat-4521	151	66	the	the	DET
easat-4521	151	67	function	function	NOUN
easat-4521	151	68	with	with	ADP
easat-4521	151	69	the	the	DET
easat-4521	151	70	graph	graph	NOUN
easat-4521	151	71	having	have	VERB
easat-4521	151	72	two	two	NUM
easat-4521	151	73	peak	peak	NOUN
easat-4521	151	74	points	point	NOUN
easat-4521	151	75	.	.	PUNCT
easat-4521	152	1	there	there	PRON
easat-4521	152	2	was	be	VERB
easat-4521	152	3	also	also	ADV
easat-4521	152	4	a	a	DET
easat-4521	152	5	mental	mental	ADJ
easat-4521	152	6	encapsulation	encapsulation	NOUN
easat-4521	152	7	mechanism	mechanism	NOUN
easat-4521	152	8	in	in	ADP
easat-4521	152	9	the	the	DET
easat-4521	152	10	form	form	NOUN
easat-4521	152	11	of	of	ADP
easat-4521	152	12	transforming	transform	VERB
easat-4521	152	13	the	the	DET
easat-4521	152	14	process	process	NOUN
easat-4521	152	15	of	of	ADP
easat-4521	152	16	sketching	sketch	VERB
easat-4521	152	17	a	a	DET
easat-4521	152	18	function	function	NOUN
easat-4521	152	19	derivative	derivative	ADJ
easat-4521	152	20	graph	graph	NOUN
easat-4521	152	21	into	into	ADP
easat-4521	152	22	an	an	DET
easat-4521	152	23	object	object	NOUN
easat-4521	152	24	marked	mark	VERB
easat-4521	152	25	by	by	ADP
easat-4521	152	26	the	the	DET
easat-4521	152	27	subject	subject	NOUN
easat-4521	152	28	being	be	AUX
easat-4521	152	29	able	able	ADJ
easat-4521	152	30	to	to	PART
easat-4521	152	31	determine	determine	VERB
easat-4521	152	32	the	the	DET
easat-4521	152	33	relationship	relationship	NOUN
easat-4521	152	34	of	of	ADP
easat-4521	152	35	the	the	DET
easat-4521	152	36	derivatives	derivative	NOUN
easat-4521	152	37	of	of	ADP
easat-4521	152	38	two	two	NUM
easat-4521	152	39	functions	function	NOUN
easat-4521	152	40	based	base	VERB
easat-4521	152	41	on	on	ADP
easat-4521	152	42	the	the	DET
easat-4521	152	43	given	give	VERB
easat-4521	152	44	graph	graph	NOUN
easat-4521	152	45	,	,	PUNCT
easat-4521	152	46	namely	namely	ADV
easat-4521	152	47	a	a	DET
easat-4521	152	48	function	function	NOUN
easat-4521	152	49	with	with	ADP
easat-4521	152	50	a	a	DET
easat-4521	152	51	parabolic	parabolic	ADJ
easat-4521	152	52	graph	graph	NOUN
easat-4521	152	53	was	be	AUX
easat-4521	152	54	a	a	DET
easat-4521	152	55	derivative	derivative	NOUN
easat-4521	152	56	of	of	ADP
easat-4521	152	57	a	a	DET
easat-4521	152	58	function	function	NOUN
easat-4521	152	59	with	with	ADP
easat-4521	152	60	a	a	DET
easat-4521	152	61	graph	graph	NOUN
easat-4521	152	62	that	that	PRON
easat-4521	152	63	had	have	VERB
easat-4521	152	64	two	two	NUM
easat-4521	152	65	peaks	peak	NOUN
easat-4521	152	66	.	.	PUNCT
easat-4521	153	1	the	the	DET
easat-4521	153	2	mental	mental	ADJ
easat-4521	153	3	coordination	coordination	NOUN
easat-4521	153	4	mechanism	mechanism	NOUN
easat-4521	153	5	occurred	occur	VERB
easat-4521	153	6	when	when	SCONJ
easat-4521	153	7	the	the	DET
easat-4521	153	8	the	the	DET
easat-4521	153	9	subject	subject	NOUN
easat-4521	153	10	combined	combine	VERB
easat-4521	153	11	two	two	NUM
easat-4521	153	12	processes	process	NOUN
easat-4521	153	13	,	,	PUNCT
easat-4521	153	14	namely	namely	ADV
easat-4521	153	15	the	the	DET
easat-4521	153	16	function	function	NOUN
easat-4521	153	17	graph	graph	NOUN
easat-4521	153	18	,	,	PUNCT
easat-4521	153	19	the	the	DET
easat-4521	153	20	function	function	NOUN
easat-4521	153	21	derivative	derivative	ADJ
easat-4521	153	22	graph	graph	NOUN
easat-4521	153	23	,	,	PUNCT
easat-4521	153	24	and	and	CCONJ
easat-4521	153	25	the	the	DET
easat-4521	153	26	corresponding	corresponding	ADJ
easat-4521	153	27	function	function	NOUN
easat-4521	153	28	.	.	PUNCT
easat-4521	154	1	the	the	DET
easat-4521	154	2	mental	mental	ADJ
easat-4521	154	3	reversal	reversal	NOUN
easat-4521	154	4	mechanism	mechanism	NOUN
easat-4521	154	5	also	also	ADV
easat-4521	154	6	occurred	occur	VERB
easat-4521	154	7	when	when	SCONJ
easat-4521	154	8	the	the	DET
easat-4521	154	9	subject	subject	NOUN
easat-4521	154	10	retraced	retrace	VERB
easat-4521	154	11	the	the	DET
easat-4521	154	12	function	function	NOUN
easat-4521	154	13	derivative	derivative	ADJ
easat-4521	154	14	graph	graph	NOUN
easat-4521	154	15	that	that	PRON
easat-4521	154	16	corresponded	correspond	VERB
easat-4521	154	17	to	to	ADP
easat-4521	154	18	the	the	DET
easat-4521	154	19	original	original	ADJ
easat-4521	154	20	function	function	NOUN
easat-4521	154	21	by	by	ADP
easat-4521	154	22	seeing	see	VERB
easat-4521	154	23	the	the	DET
easat-4521	154	24	similarity	similarity	NOUN
easat-4521	154	25	of	of	ADP
easat-4521	154	26	the	the	DET
easat-4521	154	27	function	function	NOUN
easat-4521	154	28	derivative	derivative	ADJ
easat-4521	154	29	graph	graph	NOUN
easat-4521	154	30	and	and	CCONJ
easat-4521	154	31	the	the	DET
easat-4521	154	32	function	function	NOUN
easat-4521	154	33	derivative	derivative	NOUN
easat-4521	154	34	in	in	ADP
easat-4521	154	35	her	her	PRON
easat-4521	154	36	previous	previous	ADJ
easat-4521	154	37	knowledge	knowledge	NOUN
easat-4521	154	38	.	.	PUNCT
easat-4521	155	1	the	the	DET
easat-4521	155	2	mental	mental	ADJ
easat-4521	155	3	de	de	ADJ
easat-4521	155	4	-	-	ADJ
easat-4521	155	5	encapsulation	encapsulation	NOUN
easat-4521	155	6	mechanism	mechanism	NOUN
easat-4521	155	7	occurred	occur	VERB
easat-4521	155	8	when	when	SCONJ
easat-4521	155	9	the	the	DET
easat-4521	155	10	subject	subject	NOUN
easat-4521	155	11	broke	break	VERB
easat-4521	155	12	down	down	ADP
easat-4521	155	13	the	the	DET
easat-4521	155	14	relationship	relationship	NOUN
easat-4521	155	15	between	between	ADP
easat-4521	155	16	the	the	DET
easat-4521	155	17	derivatives	derivative	NOUN
easat-4521	155	18	of	of	ADP
easat-4521	155	19	two	two	NUM
easat-4521	155	20	functions	function	NOUN
easat-4521	155	21	into	into	ADP
easat-4521	155	22	two	two	NUM
easat-4521	155	23	mental	mental	ADJ
easat-4521	155	24	structures	structure	NOUN
easat-4521	155	25	.	.	PUNCT
easat-4521	156	1	the	the	DET
easat-4521	156	2	process	process	NOUN
easat-4521	156	3	was	be	AUX
easat-4521	156	4	determining	determine	VERB
easat-4521	156	5	the	the	DET
easat-4521	156	6	function	function	NOUN
easat-4521	156	7	graph	graph	NOUN
easat-4521	156	8	of	of	ADP
easat-4521	156	9	the	the	DET
easat-4521	156	10	given	give	VERB
easat-4521	156	11	function	function	NOUN
easat-4521	156	12	and	and	CCONJ
easat-4521	156	13	determining	determine	VERB
easat-4521	156	14	the	the	DET
easat-4521	156	15	function	function	NOUN
easat-4521	156	16	derivative	derivative	ADJ
easat-4521	156	17	graph	graph	NOUN
easat-4521	156	18	of	of	ADP
easat-4521	156	19	the	the	DET
easat-4521	156	20	given	give	VERB
easat-4521	156	21	function	function	NOUN
easat-4521	156	22	.	.	PUNCT
easat-4521	157	1	3.1.4	3.1.4	X
easat-4521	157	2	.	.	PUNCT
easat-4521	157	3	scheme	scheme	VERB
easat-4521	157	4	the	the	DET
easat-4521	157	5	subject	subject	NOUN
easat-4521	157	6	was	be	AUX
easat-4521	157	7	given	give	VERB
easat-4521	157	8	fdt	fdt	NOUN
easat-4521	157	9	to	to	PART
easat-4521	157	10	explore	explore	VERB
easat-4521	157	11	her	her	PRON
easat-4521	157	12	understanding	understanding	NOUN
easat-4521	157	13	at	at	ADP
easat-4521	157	14	the	the	DET
easat-4521	157	15	schema	schema	NOUN
easat-4521	157	16	stage	stage	NOUN
easat-4521	157	17	.	.	PUNCT
easat-4521	158	1	she	she	PRON
easat-4521	158	2	explained	explain	VERB
easat-4521	158	3	the	the	DET
easat-4521	158	4	nature	nature	NOUN
easat-4521	158	5	of	of	ADP
easat-4521	158	6	the	the	DET
easat-4521	158	7	derivative	derivative	ADJ
easat-4521	158	8	function	function	NOUN
easat-4521	158	9	by	by	ADP
easat-4521	158	10	connecting	connect	VERB
easat-4521	158	11	actions	action	NOUN
easat-4521	158	12	,	,	PUNCT
easat-4521	158	13	processes	process	NOUN
easat-4521	158	14	,	,	PUNCT
easat-4521	158	15	objects	object	NOUN
easat-4521	158	16	,	,	PUNCT
easat-4521	158	17	and	and	CCONJ
easat-4521	158	18	other	other	ADJ
easat-4521	158	19	schemes	scheme	NOUN
easat-4521	158	20	that	that	PRON
easat-4521	158	21	could	could	AUX
easat-4521	158	22	be	be	AUX
easat-4521	158	23	used	use	VERB
easat-4521	158	24	to	to	PART
easat-4521	158	25	complete	complete	VERB
easat-4521	158	26	the	the	DET
easat-4521	158	27	derivative	derivative	ADJ
easat-4521	158	28	task	task	NOUN
easat-4521	158	29	of	of	ADP
easat-4521	158	30	sketching	sketch	VERB
easat-4521	158	31	a	a	DET
easat-4521	158	32	function	function	NOUN
easat-4521	158	33	derivative	derivative	ADJ
easat-4521	158	34	graph	graph	NOUN
easat-4521	158	35	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4521	158	36	)	)	PUNCT
easat-4521	158	37	=	=	SYM
easat-4521	158	38	𝑥2	𝑥2	NOUN
easat-4521	158	39	+	+	CCONJ
easat-4521	158	40	3	3	NUM
easat-4521	158	41	that	that	PRON
easat-4521	158	42	began	begin	VERB
easat-4521	158	43	by	by	ADP
easat-4521	158	44	determining	determine	VERB
easat-4521	158	45	the	the	DET
easat-4521	158	46	derivative	derivative	NOUN
easat-4521	158	47	of	of	ADP
easat-4521	158	48	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4521	158	49	)	)	PUNCT
easat-4521	158	50	=	=	SYM
easat-4521	158	51	𝑥2	𝑥2	NOUN
easat-4521	158	52	+	+	CCONJ
easat-4521	158	53	3	3	NUM
easat-4521	158	54	that	that	PRON
easat-4521	158	55	was	be	AUX
easat-4521	158	56	𝑓′(𝑥	𝑓′(𝑥	PROPN
easat-4521	158	57	)	)	PUNCT
easat-4521	158	58	=	=	SYM
easat-4521	159	1	2𝑥.	2𝑥.	NUM
easat-4521	159	2	furthermore	furthermore	ADV
easat-4521	159	3	,	,	PUNCT
easat-4521	159	4	the	the	DET
easat-4521	159	5	subject	subject	NOUN
easat-4521	159	6	assumed	assume	VERB
easat-4521	159	7	that	that	SCONJ
easat-4521	159	8	𝑦	𝑦	NOUN
easat-4521	159	9	=	=	X
easat-4521	159	10	2𝑥	2𝑥	NOUN
easat-4521	159	11	and	and	CCONJ
easat-4521	159	12	looked	look	VERB
easat-4521	159	13	for	for	ADP
easat-4521	159	14	some	some	DET
easat-4521	159	15	points	point	NOUN
easat-4521	159	16	(	(	PUNCT
easat-4521	159	17	𝑥	𝑥	NOUN
easat-4521	159	18	,	,	PUNCT
easat-4521	159	19	𝑦	𝑦	NOUN
easat-4521	159	20	)	)	PUNCT
easat-4521	159	21	which	which	PRON
easat-4521	159	22	satisfied	satisfy	VERB
easat-4521	159	23	the	the	DET
easat-4521	159	24	equation	equation	NOUN
easat-4521	159	25	𝑦	𝑦	NOUN
easat-4521	159	26	=	=	PUNCT
easat-4521	159	27	2𝑥.	2𝑥.	NUM
easat-4521	159	28	from	from	ADP
easat-4521	159	29	several	several	ADJ
easat-4521	159	30	points	point	NOUN
easat-4521	159	31	obtained	obtain	VERB
easat-4521	159	32	,	,	PUNCT
easat-4521	159	33	the	the	DET
easat-4521	159	34	subject	subject	NOUN
easat-4521	159	35	sketched	sketch	VERB
easat-4521	159	36	a	a	DET
easat-4521	159	37	graph	graph	NOUN
easat-4521	159	38	by	by	ADP
easat-4521	159	39	connecting	connect	VERB
easat-4521	159	40	the	the	DET
easat-4521	159	41	points	point	NOUN
easat-4521	159	42	.	.	PUNCT
easat-4521	160	1	then	then	ADV
easat-4521	160	2	,	,	PUNCT
easat-4521	160	3	the	the	DET
easat-4521	160	4	subject	subject	NOUN
easat-4521	160	5	sketched	sketch	VERB
easat-4521	160	6	a	a	DET
easat-4521	160	7	graph	graph	NOUN
easat-4521	160	8	of	of	ADP
easat-4521	160	9	the	the	DET
easat-4521	160	10	derivative	derivative	NOUN
easat-4521	160	11	of	of	ADP
easat-4521	160	12	the	the	DET
easat-4521	160	13	function	function	NOUN
easat-4521	160	14	𝑓(𝑥	𝑓(𝑥	NOUN
easat-4521	160	15	)	)	PUNCT
easat-4521	160	16	=	=	SYM
easat-4521	160	17	𝑥3	𝑥3	NOUN
easat-4521	160	18	−	−	PROPN
easat-4521	160	19	𝑥	𝑥	PRON
easat-4521	160	20	−	−	NOUN
easat-4521	160	21	4	4	NUM
easat-4521	160	22	by	by	ADP
easat-4521	160	23	first	first	ADV
easat-4521	160	24	determining	determine	VERB
easat-4521	160	25	the	the	DET
easat-4521	160	26	derivative	derivative	NOUN
easat-4521	160	27	of	of	ADP
easat-4521	160	28	the	the	DET
easat-4521	160	29	function	function	NOUN
easat-4521	160	30	,	,	PUNCT
easat-4521	160	31	namely	namely	ADV
easat-4521	160	32	𝑓′(𝑥	𝑓′(𝑥	PROPN
easat-4521	160	33	)	)	PUNCT
easat-4521	160	34	=	=	SYM
easat-4521	161	1	3𝑥2	3𝑥2	NUM
easat-4521	161	2	−	−	NOUN
easat-4521	161	3	1	1	NUM
easat-4521	161	4	.	.	PUNCT
easat-4521	162	1	the	the	DET
easat-4521	162	2	subject	subject	NOUN
easat-4521	162	3	determined	determine	VERB
easat-4521	162	4	the	the	DET
easat-4521	162	5	point	point	NOUN
easat-4521	162	6	where	where	SCONJ
easat-4521	162	7	the	the	DET
easat-4521	162	8	graph	graph	NOUN
easat-4521	162	9	intersected	intersect	VERB
easat-4521	162	10	the	the	DET
easat-4521	162	11	coordinate	coordinate	NOUN
easat-4521	162	12	axis	axis	NOUN
easat-4521	162	13	.	.	PUNCT
easat-4521	163	1	next	next	ADV
easat-4521	163	2	,	,	PUNCT
easat-4521	163	3	the	the	DET
easat-4521	163	4	subject	subject	NOUN
easat-4521	163	5	looked	look	VERB
easat-4521	163	6	for	for	ADP
easat-4521	163	7	the	the	DET
easat-4521	163	8	equation	equation	NOUN
easat-4521	163	9	of	of	ADP
easat-4521	163	10	the	the	DET
easat-4521	163	11	axis	axis	NOUN
easat-4521	163	12	of	of	ADP
easat-4521	163	13	symmetry	symmetry	NOUN
easat-4521	163	14	𝑥	𝑥	PROPN
easat-4521	163	15	=	=	PUNCT
easat-4521	164	1	−	−	PROPN
easat-4521	164	2	𝑏	𝑏	NUM
easat-4521	164	3	2𝑎	2𝑎	NUM
easat-4521	164	4	which	which	PRON
easat-4521	164	5	obtained	obtain	VERB
easat-4521	164	6	𝑥	𝑥	PROPN
easat-4521	164	7	=	=	SYM
easat-4521	164	8	0	0	NUM
easat-4521	164	9	.	.	PUNCT
easat-4521	165	1	after	after	ADP
easat-4521	165	2	that	that	PRON
easat-4521	165	3	,	,	PUNCT
easat-4521	165	4	the	the	DET
easat-4521	165	5	subject	subject	NOUN
easat-4521	165	6	looked	look	VERB
easat-4521	165	7	for	for	ADP
easat-4521	165	8	the	the	DET
easat-4521	165	9	minimum	minimum	ADJ
easat-4521	165	10	value	value	NOUN
easat-4521	165	11	using	use	VERB
easat-4521	165	12	the	the	DET
easat-4521	165	13	formula	formula	NOUN
easat-4521	165	14	𝑦	𝑦	NOUN
easat-4521	165	15	=	=	SYM
easat-4521	165	16	−	−	PROPN
easat-4521	165	17	𝐷	𝐷	PROPN
easat-4521	165	18	4𝑎	4𝑎	NOUN
easat-4521	165	19	and	and	CCONJ
easat-4521	165	20	obtained	obtain	VERB
easat-4521	165	21	𝑦	𝑦	NOUN
easat-4521	165	22	=	=	X
easat-4521	165	23	−1	−1	NOUN
easat-4521	165	24	and	and	CCONJ
easat-4521	165	25	the	the	DET
easat-4521	165	26	peak	peak	NOUN
easat-4521	165	27	of	of	ADP
easat-4521	165	28	the	the	DET
easat-4521	165	29	parabola	parabola	NOUN
easat-4521	165	30	was	be	AUX
easat-4521	165	31	(	(	PUNCT
easat-4521	165	32	0	0	NUM
easat-4521	165	33	,	,	PUNCT
easat-4521	165	34	−1	−1	NOUN
easat-4521	165	35	)	)	PUNCT
easat-4521	165	36	.	.	PUNCT
easat-4521	166	1	from	from	ADP
easat-4521	166	2	this	this	DET
easat-4521	166	3	information	information	NOUN
easat-4521	166	4	,	,	PUNCT
easat-4521	166	5	the	the	DET
easat-4521	166	6	subject	subject	NOUN
easat-4521	166	7	connected	connect	VERB
easat-4521	166	8	the	the	DET
easat-4521	166	9	points	point	NOUN
easat-4521	166	10	obtained	obtain	VERB
easat-4521	166	11	and	and	CCONJ
easat-4521	166	12	sketched	sketch	VERB
easat-4521	166	13	a	a	DET
easat-4521	166	14	graph	graph	NOUN
easat-4521	166	15	𝑓′(𝑥	𝑓′(𝑥	PROPN
easat-4521	166	16	)	)	PUNCT
easat-4521	166	17	=	=	PUNCT
easat-4521	167	1	3𝑥2	3𝑥2	NUM
easat-4521	167	2	−	−	NOUN
easat-4521	167	3	1	1	NUM
easat-4521	167	4	.	.	PUNCT
easat-4521	168	1	based	base	VERB
easat-4521	168	2	on	on	ADP
easat-4521	168	3	this	this	PRON
easat-4521	168	4	,	,	PUNCT
easat-4521	168	5	it	it	PRON
easat-4521	168	6	can	can	AUX
easat-4521	168	7	be	be	AUX
easat-4521	168	8	said	say	VERB
easat-4521	168	9	that	that	SCONJ
easat-4521	168	10	the	the	DET
easat-4521	168	11	subject	subject	NOUN
easat-4521	168	12	explains	explain	VERB
easat-4521	168	13	the	the	DET
easat-4521	168	14	nature	nature	NOUN
easat-4521	168	15	of	of	ADP
easat-4521	168	16	the	the	DET
easat-4521	168	17	function	function	NOUN
easat-4521	168	18	derivative	derivative	NOUN
easat-4521	168	19	by	by	ADP
easat-4521	168	20	connecting	connect	VERB
easat-4521	168	21	actions	action	NOUN
easat-4521	168	22	,	,	PUNCT
easat-4521	168	23	processes	process	NOUN
easat-4521	168	24	,	,	PUNCT
easat-4521	168	25	objects	object	NOUN
easat-4521	168	26	,	,	PUNCT
easat-4521	168	27	and	and	CCONJ
easat-4521	168	28	other	other	ADJ
easat-4521	168	29	schemes	scheme	NOUN
easat-4521	168	30	that	that	PRON
easat-4521	168	31	can	can	AUX
easat-4521	168	32	be	be	AUX
easat-4521	168	33	used	use	VERB
easat-4521	168	34	to	to	PART
easat-4521	168	35	complete	complete	VERB
easat-4521	168	36	the	the	DET
easat-4521	168	37	task	task	NOUN
easat-4521	168	38	of	of	ADP
easat-4521	168	39	𝑎	𝑎	PROPN
easat-4521	168	40	𝑖𝑠	𝑖𝑠	NOUN
easat-4521	168	41	𝑎	𝑎	ADP
easat-4521	168	42	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒	NOUN
easat-4521	168	43	𝑜𝑓	𝑜𝑓	ADP
easat-4521	168	44	𝑏	𝑏	PROPN
easat-4521	168	45	𝑐	𝑐	PROPN
easat-4521	168	46	𝑖𝑠	𝑖𝑠	ADJ
easat-4521	168	47	𝑎	𝑎	PRON
easat-4521	168	48	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒	NOUN
easat-4521	168	49	𝑜𝑓	𝑜𝑓	ADP
easat-4521	168	50	𝑑	𝑑	PROPN
easat-4521	168	51	562	562	NUM
easat-4521	168	52	edelweiss	edelweiss	PROPN
easat-4521	168	53	applied	apply	VERB
easat-4521	168	54	science	science	NOUN
easat-4521	168	55	and	and	CCONJ
easat-4521	168	56	technology	technology	NOUN
easat-4521	168	57	issn	issn	PROPN
easat-4521	168	58	:	:	PUNCT
easat-4521	168	59	2576	2576	NUM
easat-4521	168	60	-	-	SYM
easat-4521	168	61	8484	8484	NUM
easat-4521	168	62	vol	vol	NOUN
easat-4521	168	63	.	.	PROPN
easat-4521	169	1	9	9	NUM
easat-4521	169	2	,	,	PUNCT
easat-4521	169	3	no	no	INTJ
easat-4521	169	4	.	.	NOUN
easat-4521	169	5	2	2	NUM
easat-4521	169	6	:	:	PUNCT
easat-4521	169	7	555	555	NUM
easat-4521	169	8	-	-	SYM
easat-4521	169	9	566	566	NUM
easat-4521	169	10	,	,	PUNCT
easat-4521	169	11	2025	2025	NUM
easat-4521	169	12	doi	doi	NOUN
easat-4521	169	13	:	:	PUNCT
easat-4521	170	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	170	2	©	©	PROPN
easat-4521	170	3	2025	2025	NUM
easat-4521	170	4	by	by	ADP
easat-4521	170	5	the	the	DET
easat-4521	170	6	authors	author	NOUN
easat-4521	170	7	;	;	PUNCT
easat-4521	170	8	licensee	licensee	PROPN
easat-4521	170	9	learning	learn	VERB
easat-4521	170	10	gate	gate	NOUN
easat-4521	170	11	drawing	draw	VERB
easat-4521	170	12	a	a	DET
easat-4521	170	13	function	function	NOUN
easat-4521	170	14	derivative	derivative	ADJ
easat-4521	170	15	graph	graph	NOUN
easat-4521	170	16	using	use	VERB
easat-4521	170	17	the	the	DET
easat-4521	170	18	function	function	NOUN
easat-4521	170	19	derivative	derivative	ADJ
easat-4521	170	20	rules	rule	NOUN
easat-4521	170	21	and	and	CCONJ
easat-4521	170	22	the	the	DET
easat-4521	170	23	steps	step	NOUN
easat-4521	170	24	for	for	ADP
easat-4521	170	25	sketching	sketch	VERB
easat-4521	170	26	a	a	DET
easat-4521	170	27	function	function	NOUN
easat-4521	170	28	graph	graph	NOUN
easat-4521	170	29	,	,	PUNCT
easat-4521	170	30	namely	namely	ADV
easat-4521	170	31	determining	determine	VERB
easat-4521	170	32	the	the	DET
easat-4521	170	33	point	point	NOUN
easat-4521	170	34	of	of	ADP
easat-4521	170	35	intersection	intersection	NOUN
easat-4521	170	36	of	of	ADP
easat-4521	170	37	the	the	DET
easat-4521	170	38	graph	graph	NOUN
easat-4521	170	39	with	with	ADP
easat-4521	170	40	the	the	DET
easat-4521	170	41	coordinate	coordinate	NOUN
easat-4521	170	42	axis	axis	NOUN
easat-4521	170	43	,	,	PUNCT
easat-4521	170	44	determining	determine	VERB
easat-4521	170	45	extreme	extreme	ADJ
easat-4521	170	46	points	point	NOUN
easat-4521	170	47	and	and	CCONJ
easat-4521	170	48	determining	determine	VERB
easat-4521	170	49	other	other	ADJ
easat-4521	170	50	points	point	NOUN
easat-4521	170	51	on	on	ADP
easat-4521	170	52	the	the	DET
easat-4521	170	53	graph	graph	NOUN
easat-4521	170	54	.	.	PUNCT
easat-4521	171	1	the	the	DET
easat-4521	171	2	mental	mental	ADJ
easat-4521	171	3	mechanism	mechanism	NOUN
easat-4521	171	4	of	of	ADP
easat-4521	171	5	thematization	thematization	NOUN
easat-4521	171	6	occurred	occur	VERB
easat-4521	171	7	when	when	SCONJ
easat-4521	171	8	the	the	DET
easat-4521	171	9	subject	subject	NOUN
easat-4521	171	10	identified	identify	VERB
easat-4521	171	11	the	the	DET
easat-4521	171	12	suitability	suitability	NOUN
easat-4521	171	13	of	of	ADP
easat-4521	171	14	the	the	DET
easat-4521	171	15	function	function	NOUN
easat-4521	171	16	derivative	derivative	NOUN
easat-4521	171	17	obtained	obtain	VERB
easat-4521	171	18	with	with	ADP
easat-4521	171	19	the	the	DET
easat-4521	171	20	steps	step	NOUN
easat-4521	171	21	used	use	VERB
easat-4521	171	22	to	to	PART
easat-4521	171	23	draw	draw	VERB
easat-4521	171	24	a	a	DET
easat-4521	171	25	function	function	NOUN
easat-4521	171	26	derivative	derivative	ADJ
easat-4521	171	27	graph	graph	NOUN
easat-4521	171	28	.	.	PUNCT
easat-4521	172	1	the	the	DET
easat-4521	172	2	subject	subject	NOUN
easat-4521	172	3	's	's	PART
easat-4521	172	4	understanding	understanding	NOUN
easat-4521	172	5	of	of	ADP
easat-4521	172	6	the	the	DET
easat-4521	172	7	function	function	NOUN
easat-4521	172	8	derivative	derivative	NOUN
easat-4521	172	9	on	on	ADP
easat-4521	172	10	the	the	DET
easat-4521	172	11	topic	topic	NOUN
easat-4521	172	12	of	of	ADP
easat-4521	172	13	drawing	draw	VERB
easat-4521	172	14	a	a	DET
easat-4521	172	15	function	function	NOUN
easat-4521	172	16	derivative	derivative	ADJ
easat-4521	172	17	graph	graph	NOUN
easat-4521	172	18	based	base	VERB
easat-4521	172	19	on	on	ADP
easat-4521	172	20	the	the	DET
easat-4521	172	21	apos	apos	NOUN
easat-4521	172	22	theory	theory	NOUN
easat-4521	172	23	was	be	AUX
easat-4521	172	24	presented	present	VERB
easat-4521	172	25	in	in	ADP
easat-4521	172	26	its	its	PRON
easat-4521	172	27	entirety	entirety	NOUN
easat-4521	172	28	described	describe	VERB
easat-4521	172	29	in	in	ADP
easat-4521	172	30	the	the	DET
easat-4521	172	31	stages	stage	NOUN
easat-4521	172	32	of	of	ADP
easat-4521	172	33	the	the	DET
easat-4521	172	34	mental	mental	ADJ
easat-4521	172	35	structure	structure	NOUN
easat-4521	172	36	of	of	ADP
easat-4521	172	37	action	action	NOUN
easat-4521	172	38	,	,	PUNCT
easat-4521	172	39	process	process	NOUN
easat-4521	172	40	,	,	PUNCT
easat-4521	172	41	object	object	NOUN
easat-4521	172	42	,	,	PUNCT
easat-4521	172	43	and	and	CCONJ
easat-4521	172	44	schema	schema	NOUN
easat-4521	172	45	,	,	PUNCT
easat-4521	172	46	and	and	CCONJ
easat-4521	172	47	based	base	VERB
easat-4521	172	48	on	on	ADP
easat-4521	172	49	the	the	DET
easat-4521	172	50	mental	mental	ADJ
easat-4521	172	51	mechanisms	mechanism	NOUN
easat-4521	172	52	that	that	PRON
easat-4521	172	53	build	build	VERB
easat-4521	172	54	it	it	PRON
easat-4521	172	55	,	,	PUNCT
easat-4521	172	56	namely	namely	ADV
easat-4521	172	57	interiorization	interiorization	NOUN
easat-4521	172	58	,	,	PUNCT
easat-4521	172	59	encapsulation	encapsulation	NOUN
easat-4521	172	60	,	,	PUNCT
easat-4521	172	61	coordination	coordination	NOUN
easat-4521	172	62	,	,	PUNCT
easat-4521	172	63	reversal	reversal	NOUN
easat-4521	172	64	,	,	PUNCT
easat-4521	172	65	de	de	NOUN
easat-4521	172	66	-	-	NOUN
easat-4521	172	67	encapsulation	encapsulation	NOUN
easat-4521	172	68	,	,	PUNCT
easat-4521	172	69	and	and	CCONJ
easat-4521	172	70	thematization	thematization	NOUN
easat-4521	172	71	,	,	PUNCT
easat-4521	172	72	which	which	PRON
easat-4521	172	73	can	can	AUX
easat-4521	172	74	be	be	AUX
easat-4521	172	75	seen	see	VERB
easat-4521	172	76	in	in	ADP
easat-4521	172	77	table	table	NOUN
easat-4521	172	78	2	2	NUM
easat-4521	172	79	.	.	PUNCT
easat-4521	173	1	the	the	DET
easat-4521	173	2	subject	subject	NOUN
easat-4521	173	3	's	's	PART
easat-4521	173	4	understanding	understanding	NOUN
easat-4521	173	5	had	have	AUX
easat-4521	173	6	reached	reach	VERB
easat-4521	173	7	the	the	DET
easat-4521	173	8	schema	schema	NOUN
easat-4521	173	9	stage	stage	NOUN
easat-4521	173	10	,	,	PUNCT
easat-4521	173	11	but	but	CCONJ
easat-4521	173	12	there	there	PRON
easat-4521	173	13	was	be	VERB
easat-4521	173	14	no	no	DET
easat-4521	173	15	mental	mental	ADJ
easat-4521	173	16	mechanism	mechanism	NOUN
easat-4521	173	17	of	of	ADP
easat-4521	173	18	interiorization	interiorization	NOUN
easat-4521	173	19	as	as	SCONJ
easat-4521	173	20	she	she	PRON
easat-4521	173	21	failed	fail	VERB
easat-4521	173	22	to	to	PART
easat-4521	173	23	explain	explain	VERB
easat-4521	173	24	the	the	DET
easat-4521	173	25	steps	step	NOUN
easat-4521	173	26	for	for	ADP
easat-4521	173	27	sketching	sketch	VERB
easat-4521	173	28	a	a	DET
easat-4521	173	29	function	function	NOUN
easat-4521	173	30	derivative	derivative	ADJ
easat-4521	173	31	graph	graph	NOUN
easat-4521	173	32	from	from	ADP
easat-4521	173	33	the	the	DET
easat-4521	173	34	given	give	VERB
easat-4521	173	35	function	function	NOUN
easat-4521	173	36	graph	graph	NOUN
easat-4521	173	37	.	.	PUNCT
easat-4521	174	1	consequently	consequently	ADV
easat-4521	174	2	,	,	PUNCT
easat-4521	174	3	the	the	DET
easat-4521	174	4	subject	subject	NOUN
easat-4521	174	5	's	's	PART
easat-4521	174	6	understanding	understanding	NOUN
easat-4521	174	7	did	do	AUX
easat-4521	174	8	not	not	PART
easat-4521	174	9	reach	reach	VERB
easat-4521	174	10	the	the	DET
easat-4521	174	11	process	process	NOUN
easat-4521	174	12	stage	stage	NOUN
easat-4521	174	13	.	.	PUNCT
easat-4521	175	1	table	table	NOUN
easat-4521	175	2	2	2	NUM
easat-4521	175	3	.	.	PUNCT
easat-4521	175	4	apos	apos	PROPN
easat-4521	175	5	method	method	PROPN
easat-4521	175	6	understanding	understand	VERB
easat-4521	175	7	achievement	achievement	NOUN
easat-4521	175	8	.	.	PUNCT
easat-4521	176	1	mental	mental	ADJ
easat-4521	176	2	structure	structure	NOUN
easat-4521	176	3	/	/	SYM
easat-4521	176	4	mental	mental	ADJ
easat-4521	176	5	mechanism	mechanism	NOUN
easat-4521	176	6	indicator	indicator	NOUN
easat-4521	176	7	code	code	NOUN
easat-4521	176	8	achievement	achievement	NOUN
easat-4521	176	9	of	of	ADP
easat-4521	176	10	understanding	understand	VERB
easat-4521	176	11	action	action	NOUN
easat-4521	176	12	a	a	DET
easat-4521	176	13	sketching	sketch	VERB
easat-4521	176	14	a	a	DET
easat-4521	176	15	function	function	NOUN
easat-4521	176	16	derivative	derivative	ADJ
easat-4521	176	17	graph	graph	NOUN
easat-4521	176	18	by	by	ADP
easat-4521	176	19	first	first	ADV
easat-4521	176	20	determining	determine	VERB
easat-4521	176	21	the	the	DET
easat-4521	176	22	function	function	NOUN
easat-4521	176	23	derivative	derivative	NOUN
easat-4521	176	24	.	.	PUNCT
easat-4521	177	1	if	if	SCONJ
easat-4521	177	2	the	the	DET
easat-4521	177	3	function	function	NOUN
easat-4521	177	4	derivative	derivative	NOUN
easat-4521	177	5	was	be	AUX
easat-4521	177	6	a	a	DET
easat-4521	177	7	linear	linear	ADJ
easat-4521	177	8	function	function	NOUN
easat-4521	177	9	,	,	PUNCT
easat-4521	177	10	then	then	ADV
easat-4521	177	11	the	the	DET
easat-4521	177	12	subject	subject	NOUN
easat-4521	177	13	looked	look	VERB
easat-4521	177	14	for	for	ADP
easat-4521	177	15	several	several	ADJ
easat-4521	177	16	points	point	NOUN
easat-4521	177	17	that	that	PRON
easat-4521	177	18	satisfied	satisfy	VERB
easat-4521	177	19	the	the	DET
easat-4521	177	20	equation	equation	NOUN
easat-4521	177	21	and	and	CCONJ
easat-4521	177	22	then	then	ADV
easat-4521	177	23	connected	connect	VERB
easat-4521	177	24	the	the	DET
easat-4521	177	25	points	point	NOUN
easat-4521	177	26	obtained	obtain	VERB
easat-4521	177	27	so	so	SCONJ
easat-4521	177	28	that	that	SCONJ
easat-4521	177	29	a	a	DET
easat-4521	177	30	function	function	NOUN
easat-4521	177	31	derivative	derivative	ADJ
easat-4521	177	32	graph	graph	NOUN
easat-4521	177	33	was	be	AUX
easat-4521	177	34	formed	form	VERB
easat-4521	177	35	in	in	ADP
easat-4521	177	36	the	the	DET
easat-4521	177	37	form	form	NOUN
easat-4521	177	38	of	of	ADP
easat-4521	177	39	a	a	DET
easat-4521	177	40	straight	straight	ADJ
easat-4521	177	41	line	line	NOUN
easat-4521	177	42	.	.	PUNCT
easat-4521	178	1	if	if	SCONJ
easat-4521	178	2	the	the	DET
easat-4521	178	3	function	function	NOUN
easat-4521	178	4	derivative	derivative	NOUN
easat-4521	178	5	was	be	AUX
easat-4521	178	6	a	a	DET
easat-4521	178	7	quadratic	quadratic	ADJ
easat-4521	178	8	function	function	NOUN
easat-4521	178	9	,	,	PUNCT
easat-4521	178	10	then	then	ADV
easat-4521	178	11	the	the	DET
easat-4521	178	12	subject	subject	NOUN
easat-4521	178	13	determined	determine	VERB
easat-4521	178	14	the	the	DET
easat-4521	178	15	point	point	NOUN
easat-4521	178	16	of	of	ADP
easat-4521	178	17	intersection	intersection	NOUN
easat-4521	178	18	of	of	ADP
easat-4521	178	19	the	the	DET
easat-4521	178	20	graph	graph	NOUN
easat-4521	178	21	with	with	ADP
easat-4521	178	22	the	the	DET
easat-4521	178	23	xaxis	xaxis	NOUN
easat-4521	178	24	,	,	PUNCT
easat-4521	178	25	the	the	DET
easat-4521	178	26	point	point	NOUN
easat-4521	178	27	of	of	ADP
easat-4521	178	28	intersection	intersection	NOUN
easat-4521	178	29	with	with	ADP
easat-4521	178	30	the	the	DET
easat-4521	178	31	y	y	NOUN
easat-4521	178	32	-	-	PUNCT
easat-4521	178	33	axis	axis	NOUN
easat-4521	178	34	,	,	PUNCT
easat-4521	178	35	the	the	DET
easat-4521	178	36	equation	equation	NOUN
easat-4521	178	37	of	of	ADP
easat-4521	178	38	the	the	DET
easat-4521	178	39	axis	axis	NOUN
easat-4521	178	40	of	of	ADP
easat-4521	178	41	symmetry	symmetry	NOUN
easat-4521	178	42	,	,	PUNCT
easat-4521	178	43	the	the	DET
easat-4521	178	44	optimum	optimum	ADJ
easat-4521	178	45	value	value	NOUN
easat-4521	178	46	,	,	PUNCT
easat-4521	178	47	the	the	DET
easat-4521	178	48	peak	peak	NOUN
easat-4521	178	49	of	of	ADP
easat-4521	178	50	the	the	DET
easat-4521	178	51	parabola	parabola	NOUN
easat-4521	178	52	,	,	PUNCT
easat-4521	178	53	and	and	CCONJ
easat-4521	178	54	connected	connect	VERB
easat-4521	178	55	the	the	DET
easat-4521	178	56	points	point	NOUN
easat-4521	178	57	obtained	obtain	VERB
easat-4521	178	58	so	so	SCONJ
easat-4521	178	59	that	that	SCONJ
easat-4521	178	60	a	a	DET
easat-4521	178	61	function	function	NOUN
easat-4521	178	62	derivative	derivative	ADJ
easat-4521	178	63	graph	graph	NOUN
easat-4521	178	64	was	be	AUX
easat-4521	178	65	formed	form	VERB
easat-4521	178	66	in	in	ADP
easat-4521	178	67	the	the	DET
easat-4521	178	68	form	form	NOUN
easat-4521	178	69	of	of	ADP
easat-4521	178	70	a	a	DET
easat-4521	178	71	parabola	parabola	NOUN
easat-4521	178	72	.	.	PUNCT
easat-4521	179	1	interiorization	interiorization	NOUN
easat-4521	179	2	there	there	PRON
easat-4521	179	3	was	be	VERB
easat-4521	179	4	no	no	DET
easat-4521	179	5	mental	mental	ADJ
easat-4521	179	6	mechanism	mechanism	NOUN
easat-4521	179	7	of	of	ADP
easat-4521	179	8	interiorization	interiorization	NOUN
easat-4521	179	9	because	because	SCONJ
easat-4521	179	10	the	the	DET
easat-4521	179	11	subject	subject	NOUN
easat-4521	179	12	could	could	AUX
easat-4521	179	13	not	not	PART
easat-4521	179	14	explain	explain	VERB
easat-4521	179	15	the	the	DET
easat-4521	179	16	steps	step	NOUN
easat-4521	179	17	for	for	ADP
easat-4521	179	18	sketching	sketch	VERB
easat-4521	179	19	a	a	DET
easat-4521	179	20	function	function	NOUN
easat-4521	179	21	derivative	derivative	ADJ
easat-4521	179	22	graph	graph	NOUN
easat-4521	179	23	from	from	ADP
easat-4521	179	24	a	a	DET
easat-4521	179	25	given	give	VERB
easat-4521	179	26	function	function	NOUN
easat-4521	179	27	graph	graph	NOUN
easat-4521	179	28	.	.	PUNCT
easat-4521	180	1	process	process	NOUN
easat-4521	180	2	p	p	PROPN
easat-4521	180	3	the	the	DET
easat-4521	180	4	subject	subject	NOUN
easat-4521	180	5	could	could	AUX
easat-4521	180	6	not	not	PART
easat-4521	180	7	explain	explain	VERB
easat-4521	180	8	the	the	DET
easat-4521	180	9	steps	step	NOUN
easat-4521	180	10	for	for	ADP
easat-4521	180	11	drawing	draw	VERB
easat-4521	180	12	a	a	DET
easat-4521	180	13	function	function	NOUN
easat-4521	180	14	derivative	derivative	ADJ
easat-4521	180	15	graph	graph	NOUN
easat-4521	180	16	from	from	ADP
easat-4521	180	17	a	a	DET
easat-4521	180	18	given	give	VERB
easat-4521	180	19	function	function	NOUN
easat-4521	180	20	graph	graph	NOUN
easat-4521	180	21	.	.	PUNCT
easat-4521	181	1	encapsulation	encapsulation	NOUN
easat-4521	181	2	the	the	DET
easat-4521	181	3	subject	subject	NOUN
easat-4521	181	4	could	could	AUX
easat-4521	181	5	determine	determine	VERB
easat-4521	181	6	the	the	DET
easat-4521	181	7	relationship	relationship	NOUN
easat-4521	181	8	between	between	ADP
easat-4521	181	9	the	the	DET
easat-4521	181	10	derivatives	derivative	NOUN
easat-4521	181	11	of	of	ADP
easat-4521	181	12	two	two	NUM
easat-4521	181	13	functions	function	NOUN
easat-4521	181	14	based	base	VERB
easat-4521	181	15	on	on	ADP
easat-4521	181	16	the	the	DET
easat-4521	181	17	given	give	VERB
easat-4521	181	18	graph	graph	NOUN
easat-4521	181	19	,	,	PUNCT
easat-4521	181	20	namely	namely	ADV
easat-4521	181	21	a	a	DET
easat-4521	181	22	function	function	NOUN
easat-4521	181	23	with	with	ADP
easat-4521	181	24	a	a	DET
easat-4521	181	25	parabolic	parabolic	ADJ
easat-4521	181	26	graph	graph	NOUN
easat-4521	181	27	was	be	AUX
easat-4521	181	28	a	a	DET
easat-4521	181	29	derivative	derivative	NOUN
easat-4521	181	30	of	of	ADP
easat-4521	181	31	a	a	DET
easat-4521	181	32	function	function	NOUN
easat-4521	181	33	with	with	ADP
easat-4521	181	34	a	a	DET
easat-4521	181	35	graph	graph	NOUN
easat-4521	181	36	that	that	PRON
easat-4521	181	37	has	have	VERB
easat-4521	181	38	two	two	NUM
easat-4521	181	39	peak	peak	NOUN
easat-4521	181	40	points	point	NOUN
easat-4521	181	41	.	.	PUNCT
easat-4521	182	1	objects	object	VERB
easat-4521	182	2	o	o	PROPN
easat-4521	182	3	the	the	DET
easat-4521	182	4	subject	subject	NOUN
easat-4521	182	5	determined	determine	VERB
easat-4521	182	6	the	the	DET
easat-4521	182	7	relationship	relationship	NOUN
easat-4521	182	8	between	between	ADP
easat-4521	182	9	the	the	DET
easat-4521	182	10	derivatives	derivative	NOUN
easat-4521	182	11	of	of	ADP
easat-4521	182	12	two	two	NUM
easat-4521	182	13	functions	function	NOUN
easat-4521	182	14	based	base	VERB
easat-4521	182	15	on	on	ADP
easat-4521	182	16	the	the	DET
easat-4521	182	17	graphs	graph	NOUN
easat-4521	182	18	given	give	VERB
easat-4521	182	19	by	by	ADP
easat-4521	182	20	using	use	VERB
easat-4521	182	21	previous	previous	ADJ
easat-4521	182	22	knowledge	knowledge	NOUN
easat-4521	182	23	,	,	PUNCT
easat-4521	182	24	namely	namely	ADV
easat-4521	182	25	by	by	ADP
easat-4521	182	26	seeing	see	VERB
easat-4521	182	27	the	the	DET
easat-4521	182	28	similarity	similarity	NOUN
easat-4521	182	29	of	of	ADP
easat-4521	182	30	the	the	DET
easat-4521	182	31	graphs	graph	NOUN
easat-4521	182	32	and	and	CCONJ
easat-4521	182	33	functions	function	NOUN
easat-4521	182	34	from	from	ADP
easat-4521	182	35	the	the	DET
easat-4521	182	36	previous	previous	ADJ
easat-4521	182	37	questions	question	NOUN
easat-4521	182	38	so	so	SCONJ
easat-4521	182	39	that	that	SCONJ
easat-4521	182	40	the	the	DET
easat-4521	182	41	subject	subject	NOUN
easat-4521	182	42	determined	determine	VERB
easat-4521	182	43	the	the	DET
easat-4521	182	44	relationship	relationship	NOUN
easat-4521	182	45	between	between	ADP
easat-4521	182	46	the	the	DET
easat-4521	182	47	function	function	NOUN
easat-4521	182	48	and	and	CCONJ
easat-4521	182	49	the	the	DET
easat-4521	182	50	parabola	parabola	NOUN
easat-4521	182	51	-	-	PUNCT
easat-4521	182	52	shaped	shape	VERB
easat-4521	182	53	graph	graph	NOUN
easat-4521	182	54	which	which	PRON
easat-4521	182	55	was	be	AUX
easat-4521	182	56	the	the	DET
easat-4521	182	57	derivative	derivative	NOUN
easat-4521	182	58	of	of	ADP
easat-4521	182	59	the	the	DET
easat-4521	182	60	function	function	NOUN
easat-4521	182	61	with	with	ADP
easat-4521	182	62	the	the	DET
easat-4521	182	63	graph	graph	NOUN
easat-4521	182	64	having	have	VERB
easat-4521	182	65	two	two	NUM
easat-4521	182	66	peak	peak	NOUN
easat-4521	182	67	points	point	NOUN
easat-4521	182	68	.	.	PUNCT
easat-4521	183	1	coordination	coordination	NOUN
easat-4521	183	2	the	the	DET
easat-4521	183	3	mental	mental	ADJ
easat-4521	183	4	coordination	coordination	NOUN
easat-4521	183	5	mechanism	mechanism	NOUN
easat-4521	183	6	occurred	occur	VERB
easat-4521	183	7	when	when	SCONJ
easat-4521	183	8	the	the	DET
easat-4521	183	9	subject	subject	NOUN
easat-4521	183	10	combined	combine	VERB
easat-4521	183	11	several	several	ADJ
easat-4521	183	12	processes	process	NOUN
easat-4521	183	13	,	,	PUNCT
easat-4521	183	14	namely	namely	ADV
easat-4521	183	15	function	function	NOUN
easat-4521	183	16	graphs	graph	NOUN
easat-4521	183	17	,	,	PUNCT
easat-4521	183	18	function	function	VERB
easat-4521	183	19	derivative	derivative	ADJ
easat-4521	183	20	graphs	graph	NOUN
easat-4521	183	21	,	,	PUNCT
easat-4521	183	22	and	and	CCONJ
easat-4521	183	23	corresponding	correspond	VERB
easat-4521	183	24	functions	function	NOUN
easat-4521	183	25	.	.	PUNCT
easat-4521	184	1	reversal	reversal	VERB
easat-4521	184	2	the	the	DET
easat-4521	184	3	mental	mental	ADJ
easat-4521	184	4	reversal	reversal	NOUN
easat-4521	184	5	mechanism	mechanism	NOUN
easat-4521	184	6	occurred	occur	VERB
easat-4521	184	7	when	when	SCONJ
easat-4521	184	8	the	the	DET
easat-4521	184	9	subject	subject	NOUN
easat-4521	184	10	retraced	retrace	VERB
easat-4521	184	11	the	the	DET
easat-4521	184	12	function	function	NOUN
easat-4521	184	13	derivative	derivative	ADJ
easat-4521	184	14	graph	graph	NOUN
easat-4521	184	15	that	that	PRON
easat-4521	184	16	corresponded	correspond	VERB
easat-4521	184	17	to	to	ADP
easat-4521	184	18	the	the	DET
easat-4521	184	19	original	original	ADJ
easat-4521	184	20	function	function	NOUN
easat-4521	184	21	by	by	ADP
easat-4521	184	22	seeing	see	VERB
easat-4521	184	23	the	the	DET
easat-4521	184	24	similarity	similarity	NOUN
easat-4521	184	25	between	between	ADP
easat-4521	184	26	the	the	DET
easat-4521	184	27	function	function	NOUN
easat-4521	184	28	derivative	derivative	ADJ
easat-4521	184	29	graph	graph	NOUN
easat-4521	184	30	and	and	CCONJ
easat-4521	184	31	the	the	DET
easat-4521	184	32	function	function	NOUN
easat-4521	184	33	derivative	derivative	NOUN
easat-4521	184	34	in	in	ADP
easat-4521	184	35	her	her	PRON
easat-4521	184	36	previous	previous	ADJ
easat-4521	184	37	knowledge	knowledge	NOUN
easat-4521	184	38	.	.	PUNCT
easat-4521	185	1	de	de	NOUN
easat-4521	185	2	-	-	NOUN
easat-4521	185	3	encapsulation	encapsulation	VERB
easat-4521	185	4	the	the	DET
easat-4521	185	5	mental	mental	ADJ
easat-4521	185	6	mechanism	mechanism	NOUN
easat-4521	185	7	of	of	ADP
easat-4521	185	8	de	de	NOUN
easat-4521	185	9	-	-	NOUN
easat-4521	185	10	encapsulation	encapsulation	NOUN
easat-4521	185	11	occurred	occur	VERB
easat-4521	185	12	when	when	SCONJ
easat-4521	185	13	the	the	DET
easat-4521	185	14	subject	subject	NOUN
easat-4521	185	15	broke	break	VERB
easat-4521	185	16	down	down	ADP
easat-4521	185	17	the	the	DET
easat-4521	185	18	relationship	relationship	NOUN
easat-4521	185	19	between	between	ADP
easat-4521	185	20	the	the	DET
easat-4521	185	21	derivatives	derivative	NOUN
easat-4521	185	22	of	of	ADP
easat-4521	185	23	two	two	NUM
easat-4521	185	24	functions	function	NOUN
easat-4521	185	25	into	into	ADP
easat-4521	185	26	two	two	NUM
easat-4521	185	27	mental	mental	ADJ
easat-4521	185	28	structures	structure	NOUN
easat-4521	185	29	.	.	PUNCT
easat-4521	186	1	the	the	DET
easat-4521	186	2	process	process	NOUN
easat-4521	186	3	was	be	AUX
easat-4521	186	4	determining	determine	VERB
easat-4521	186	5	the	the	DET
easat-4521	186	6	function	function	NOUN
easat-4521	186	7	graph	graph	NOUN
easat-4521	186	8	of	of	ADP
easat-4521	186	9	a	a	DET
easat-4521	186	10	given	give	VERB
easat-4521	186	11	function	function	NOUN
easat-4521	186	12	and	and	CCONJ
easat-4521	186	13	determining	determine	VERB
easat-4521	186	14	the	the	DET
easat-4521	186	15	function	function	NOUN
easat-4521	186	16	derivative	derivative	ADJ
easat-4521	186	17	graph	graph	NOUN
easat-4521	186	18	of	of	ADP
easat-4521	186	19	a	a	DET
easat-4521	186	20	given	give	VERB
easat-4521	186	21	function	function	NOUN
easat-4521	186	22	.	.	PUNCT
easat-4521	187	1	563	563	NUM
easat-4521	187	2	edelweiss	edelweiss	PROPN
easat-4521	187	3	applied	apply	VERB
easat-4521	187	4	science	science	NOUN
easat-4521	187	5	and	and	CCONJ
easat-4521	187	6	technology	technology	NOUN
easat-4521	187	7	issn	issn	PROPN
easat-4521	187	8	:	:	PUNCT
easat-4521	187	9	2576	2576	NUM
easat-4521	187	10	-	-	SYM
easat-4521	187	11	8484	8484	NUM
easat-4521	187	12	vol	vol	NOUN
easat-4521	187	13	.	.	PROPN
easat-4521	188	1	9	9	NUM
easat-4521	188	2	,	,	PUNCT
easat-4521	188	3	no	no	INTJ
easat-4521	188	4	.	.	NOUN
easat-4521	188	5	2	2	NUM
easat-4521	188	6	:	:	PUNCT
easat-4521	188	7	555	555	NUM
easat-4521	188	8	-	-	SYM
easat-4521	188	9	566	566	NUM
easat-4521	188	10	,	,	PUNCT
easat-4521	188	11	2025	2025	NUM
easat-4521	188	12	doi	doi	NOUN
easat-4521	188	13	:	:	PUNCT
easat-4521	189	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	189	2	©	©	PROPN
easat-4521	189	3	2025	2025	NUM
easat-4521	189	4	by	by	ADP
easat-4521	189	5	the	the	DET
easat-4521	189	6	authors	author	NOUN
easat-4521	189	7	;	;	PUNCT
easat-4521	189	8	licensee	licensee	PROPN
easat-4521	189	9	learning	learn	VERB
easat-4521	189	10	gate	gate	PROPN
easat-4521	189	11	scheme	scheme	PROPN
easat-4521	189	12	s	s	VERB
easat-4521	189	13	the	the	DET
easat-4521	189	14	subject	subject	NOUN
easat-4521	189	15	explained	explain	VERB
easat-4521	189	16	the	the	DET
easat-4521	189	17	nature	nature	NOUN
easat-4521	189	18	of	of	ADP
easat-4521	189	19	the	the	DET
easat-4521	189	20	derivative	derivative	NOUN
easat-4521	189	21	of	of	ADP
easat-4521	189	22	a	a	DET
easat-4521	189	23	function	function	NOUN
easat-4521	189	24	by	by	ADP
easat-4521	189	25	connecting	connect	VERB
easat-4521	189	26	actions	action	NOUN
easat-4521	189	27	,	,	PUNCT
easat-4521	189	28	processes	process	NOUN
easat-4521	189	29	,	,	PUNCT
easat-4521	189	30	objects	object	NOUN
easat-4521	189	31	and	and	CCONJ
easat-4521	189	32	other	other	ADJ
easat-4521	189	33	schemes	scheme	NOUN
easat-4521	189	34	that	that	PRON
easat-4521	189	35	can	can	AUX
easat-4521	189	36	be	be	AUX
easat-4521	189	37	used	use	VERB
easat-4521	189	38	to	to	PART
easat-4521	189	39	complete	complete	VERB
easat-4521	189	40	the	the	DET
easat-4521	189	41	derivative	derivative	ADJ
easat-4521	189	42	task	task	NOUN
easat-4521	189	43	of	of	ADP
easat-4521	189	44	drawing	draw	VERB
easat-4521	189	45	a	a	DET
easat-4521	189	46	graph	graph	NOUN
easat-4521	189	47	of	of	ADP
easat-4521	189	48	the	the	DET
easat-4521	189	49	derivative	derivative	NOUN
easat-4521	189	50	of	of	ADP
easat-4521	189	51	a	a	DET
easat-4521	189	52	function	function	NOUN
easat-4521	189	53	using	use	VERB
easat-4521	189	54	the	the	DET
easat-4521	189	55	rules	rule	NOUN
easat-4521	189	56	of	of	ADP
easat-4521	189	57	the	the	DET
easat-4521	189	58	derivative	derivative	NOUN
easat-4521	189	59	of	of	ADP
easat-4521	189	60	a	a	DET
easat-4521	189	61	function	function	NOUN
easat-4521	189	62	and	and	CCONJ
easat-4521	189	63	the	the	DET
easat-4521	189	64	steps	step	NOUN
easat-4521	189	65	for	for	ADP
easat-4521	189	66	drawing	draw	VERB
easat-4521	189	67	a	a	DET
easat-4521	189	68	graph	graph	NOUN
easat-4521	189	69	of	of	ADP
easat-4521	189	70	a	a	DET
easat-4521	189	71	function	function	NOUN
easat-4521	189	72	,	,	PUNCT
easat-4521	189	73	namely	namely	ADV
easat-4521	189	74	determining	determine	VERB
easat-4521	189	75	the	the	DET
easat-4521	189	76	point	point	NOUN
easat-4521	189	77	of	of	ADP
easat-4521	189	78	intersection	intersection	NOUN
easat-4521	189	79	of	of	ADP
easat-4521	189	80	the	the	DET
easat-4521	189	81	graph	graph	NOUN
easat-4521	189	82	with	with	ADP
easat-4521	189	83	the	the	DET
easat-4521	189	84	coordinate	coordinate	NOUN
easat-4521	189	85	axis	axis	NOUN
easat-4521	189	86	,	,	PUNCT
easat-4521	189	87	determining	determine	VERB
easat-4521	189	88	extreme	extreme	ADJ
easat-4521	189	89	points	point	NOUN
easat-4521	189	90	and	and	CCONJ
easat-4521	189	91	determining	determine	VERB
easat-4521	189	92	other	other	ADJ
easat-4521	189	93	points	point	NOUN
easat-4521	189	94	on	on	ADP
easat-4521	189	95	the	the	DET
easat-4521	189	96	graph	graph	NOUN
easat-4521	189	97	..	..	PUNCT
easat-4521	189	98	thematization	thematization	NOUN
easat-4521	189	99	the	the	DET
easat-4521	189	100	mental	mental	ADJ
easat-4521	189	101	mechanism	mechanism	NOUN
easat-4521	189	102	of	of	ADP
easat-4521	189	103	thematization	thematization	NOUN
easat-4521	189	104	occurred	occur	VERB
easat-4521	189	105	when	when	SCONJ
easat-4521	189	106	the	the	DET
easat-4521	189	107	subject	subject	NOUN
easat-4521	189	108	identifies	identify	VERB
easat-4521	189	109	the	the	DET
easat-4521	189	110	correspondence	correspondence	NOUN
easat-4521	189	111	of	of	ADP
easat-4521	189	112	the	the	DET
easat-4521	189	113	obtained	obtain	VERB
easat-4521	189	114	function	function	NOUN
easat-4521	189	115	derivative	derivative	NOUN
easat-4521	189	116	with	with	ADP
easat-4521	189	117	the	the	DET
easat-4521	189	118	steps	step	NOUN
easat-4521	189	119	used	use	VERB
easat-4521	189	120	to	to	PART
easat-4521	189	121	draw	draw	VERB
easat-4521	189	122	the	the	DET
easat-4521	189	123	function	function	NOUN
easat-4521	189	124	derivative	derivative	ADJ
easat-4521	189	125	graph	graph	NOUN
easat-4521	189	126	.	.	PUNCT
easat-4521	190	1	4	4	X
easat-4521	190	2	.	.	X
easat-4521	190	3	discussion	discussion	NOUN
easat-4521	190	4	this	this	DET
easat-4521	190	5	study	study	NOUN
easat-4521	190	6	generated	generate	VERB
easat-4521	190	7	findings	finding	NOUN
easat-4521	190	8	on	on	ADP
easat-4521	190	9	understanding	understanding	NOUN
easat-4521	190	10	of	of	ADP
easat-4521	190	11	function	function	NOUN
easat-4521	190	12	derivatives	derivative	NOUN
easat-4521	190	13	,	,	PUNCT
easat-4521	190	14	especially	especially	ADV
easat-4521	190	15	in	in	ADP
easat-4521	190	16	sketching	sketch	VERB
easat-4521	190	17	function	function	NOUN
easat-4521	190	18	derivative	derivative	ADJ
easat-4521	190	19	graphs	graph	NOUN
easat-4521	190	20	presented	present	VERB
easat-4521	190	21	based	base	VERB
easat-4521	190	22	on	on	ADP
easat-4521	190	23	the	the	DET
easat-4521	190	24	apos	apos	NOUN
easat-4521	190	25	level	level	NOUN
easat-4521	190	26	of	of	ADP
easat-4521	190	27	understanding	understanding	NOUN
easat-4521	190	28	.	.	PUNCT
easat-4521	191	1	at	at	ADP
easat-4521	191	2	the	the	DET
easat-4521	191	3	action	action	NOUN
easat-4521	191	4	stage	stage	NOUN
easat-4521	191	5	,	,	PUNCT
easat-4521	191	6	the	the	DET
easat-4521	191	7	subject	subject	NOUN
easat-4521	191	8	sketched	sketch	VERB
easat-4521	191	9	the	the	DET
easat-4521	191	10	function	function	NOUN
easat-4521	191	11	derivative	derivative	ADJ
easat-4521	191	12	graphs	graph	NOUN
easat-4521	191	13	in	in	ADP
easat-4521	191	14	several	several	ADJ
easat-4521	191	15	stages	stage	NOUN
easat-4521	191	16	and	and	CCONJ
easat-4521	191	17	approaches	approach	NOUN
easat-4521	191	18	.	.	PUNCT
easat-4521	192	1	the	the	DET
easat-4521	192	2	first	first	ADJ
easat-4521	192	3	approach	approach	NOUN
easat-4521	192	4	focused	focus	VERB
easat-4521	192	5	on	on	ADP
easat-4521	192	6	determining	determine	VERB
easat-4521	192	7	function	function	NOUN
easat-4521	192	8	derivatives	derivative	NOUN
easat-4521	192	9	using	use	VERB
easat-4521	192	10	appropriate	appropriate	ADJ
easat-4521	192	11	derivative	derivative	ADJ
easat-4521	192	12	rules	rule	NOUN
easat-4521	192	13	,	,	PUNCT
easat-4521	192	14	while	while	SCONJ
easat-4521	192	15	the	the	DET
easat-4521	192	16	second	second	ADJ
easat-4521	192	17	approach	approach	NOUN
easat-4521	192	18	used	use	VERB
easat-4521	192	19	function	function	NOUN
easat-4521	192	20	graph	graph	NOUN
easat-4521	192	21	sketching	sketch	VERB
easat-4521	192	22	rules	rule	NOUN
easat-4521	192	23	that	that	PRON
easat-4521	192	24	were	be	AUX
easat-4521	192	25	adjusted	adjust	VERB
easat-4521	192	26	to	to	ADP
easat-4521	192	27	the	the	DET
easat-4521	192	28	function	function	NOUN
easat-4521	192	29	derivatives	derivative	NOUN
easat-4521	192	30	obtained	obtain	VERB
easat-4521	192	31	.	.	PUNCT
easat-4521	193	1	this	this	DET
easat-4521	193	2	finding	finding	NOUN
easat-4521	193	3	is	be	AUX
easat-4521	193	4	in	in	ADP
easat-4521	193	5	line	line	NOUN
easat-4521	193	6	with	with	ADP
easat-4521	193	7	a	a	DET
easat-4521	193	8	previous	previous	ADJ
easat-4521	193	9	study	study	NOUN
easat-4521	193	10	trigueros	triguero	NOUN
easat-4521	193	11	,	,	PUNCT
easat-4521	193	12	et	et	PROPN
easat-4521	193	13	al	al	PROPN
easat-4521	193	14	.	.	PUNCT
easat-4521	194	1	[	[	X
easat-4521	194	2	35	35	NUM
easat-4521	194	3	]	]	PUNCT
easat-4521	194	4	subjects	subject	NOUN
easat-4521	194	5	perform	perform	VERB
easat-4521	194	6	complex	complex	ADJ
easat-4521	194	7	analyses	analysis	NOUN
easat-4521	194	8	involved	involve	VERB
easat-4521	194	9	in	in	ADP
easat-4521	194	10	deeply	deeply	ADV
easat-4521	194	11	understanding	understand	VERB
easat-4521	194	12	the	the	DET
easat-4521	194	13	behavior	behavior	NOUN
easat-4521	194	14	of	of	ADP
easat-4521	194	15	functions	function	NOUN
easat-4521	194	16	when	when	SCONJ
easat-4521	194	17	drawing	draw	VERB
easat-4521	194	18	or	or	CCONJ
easat-4521	194	19	understanding	understand	VERB
easat-4521	194	20	their	their	PRON
easat-4521	194	21	graphs	graph	NOUN
easat-4521	194	22	.	.	PUNCT
easat-4521	195	1	understanding	understand	VERB
easat-4521	195	2	how	how	SCONJ
easat-4521	195	3	students	student	NOUN
easat-4521	195	4	use	use	VERB
easat-4521	195	5	their	their	PRON
easat-4521	195	6	knowledge	knowledge	NOUN
easat-4521	195	7	in	in	ADP
easat-4521	195	8	completing	complete	VERB
easat-4521	195	9	tasks	task	NOUN
easat-4521	195	10	provides	provide	VERB
easat-4521	195	11	information	information	NOUN
easat-4521	195	12	about	about	ADP
easat-4521	195	13	strategies	strategy	NOUN
easat-4521	195	14	that	that	PRON
easat-4521	195	15	can	can	AUX
easat-4521	195	16	be	be	AUX
easat-4521	195	17	used	use	VERB
easat-4521	195	18	when	when	SCONJ
easat-4521	195	19	teaching	teach	VERB
easat-4521	195	20	function	function	NOUN
easat-4521	195	21	derivatives	derivative	NOUN
easat-4521	195	22	to	to	ADP
easat-4521	195	23	students	student	NOUN
easat-4521	195	24	.	.	PUNCT
easat-4521	196	1	seeing	see	VERB
easat-4521	196	2	the	the	DET
easat-4521	196	3	interesting	interesting	ADJ
easat-4521	196	4	strategies	strategy	NOUN
easat-4521	196	5	used	use	VERB
easat-4521	196	6	by	by	ADP
easat-4521	196	7	students	student	NOUN
easat-4521	196	8	helps	help	VERB
easat-4521	196	9	to	to	PART
easat-4521	196	10	understand	understand	VERB
easat-4521	196	11	the	the	DET
easat-4521	196	12	difficulties	difficulty	NOUN
easat-4521	196	13	involved	involve	VERB
easat-4521	196	14	in	in	ADP
easat-4521	196	15	these	these	DET
easat-4521	196	16	interactions	interaction	NOUN
easat-4521	196	17	.	.	PUNCT
easat-4521	197	1	the	the	DET
easat-4521	197	2	importance	importance	NOUN
easat-4521	197	3	of	of	ADP
easat-4521	197	4	understanding	understand	VERB
easat-4521	197	5	the	the	DET
easat-4521	197	6	concept	concept	NOUN
easat-4521	197	7	of	of	ADP
easat-4521	197	8	function	function	NOUN
easat-4521	197	9	derivatives	derivative	NOUN
easat-4521	197	10	in	in	ADP
easat-4521	197	11	sketching	sketch	VERB
easat-4521	197	12	function	function	NOUN
easat-4521	197	13	derivative	derivative	ADJ
easat-4521	197	14	graphs	graph	NOUN
easat-4521	197	15	can	can	AUX
easat-4521	197	16	be	be	AUX
easat-4521	197	17	seen	see	VERB
easat-4521	197	18	from	from	ADP
easat-4521	197	19	the	the	DET
easat-4521	197	20	levels	level	NOUN
easat-4521	197	21	of	of	ADP
easat-4521	197	22	the	the	DET
easat-4521	197	23	apos	apos	NOUN
easat-4521	197	24	mental	mental	ADJ
easat-4521	197	25	structure	structure	NOUN
easat-4521	197	26	of	of	ADP
easat-4521	197	27	action	action	NOUN
easat-4521	197	28	,	,	PUNCT
easat-4521	197	29	process	process	NOUN
easat-4521	197	30	,	,	PUNCT
easat-4521	197	31	object	object	NOUN
easat-4521	197	32	,	,	PUNCT
easat-4521	197	33	and	and	CCONJ
easat-4521	197	34	schema	schema	NOUN
easat-4521	197	35	which	which	PRON
easat-4521	197	36	is	be	AUX
easat-4521	197	37	complemented	complement	VERB
easat-4521	197	38	by	by	ADP
easat-4521	197	39	analyzing	analyze	VERB
easat-4521	197	40	mental	mental	ADJ
easat-4521	197	41	mechanisms	mechanism	NOUN
easat-4521	197	42	coherently	coherently	ADV
easat-4521	197	43	.	.	PUNCT
easat-4521	198	1	this	this	PRON
easat-4521	198	2	can	can	AUX
easat-4521	198	3	provide	provide	VERB
easat-4521	198	4	complete	complete	ADJ
easat-4521	198	5	information	information	NOUN
easat-4521	198	6	about	about	ADP
easat-4521	198	7	understanding	understand	VERB
easat-4521	198	8	the	the	DET
easat-4521	198	9	concept	concept	NOUN
easat-4521	198	10	of	of	ADP
easat-4521	198	11	function	function	NOUN
easat-4521	198	12	derivatives	derivative	NOUN
easat-4521	198	13	.	.	PUNCT
easat-4521	199	1	in	in	ADP
easat-4521	199	2	addition	addition	NOUN
easat-4521	199	3	,	,	PUNCT
easat-4521	199	4	students	student	NOUN
easat-4521	199	5	'	'	PART
easat-4521	199	6	abstraction	abstraction	NOUN
easat-4521	199	7	abilities	ability	NOUN
easat-4521	199	8	in	in	ADP
easat-4521	199	9	learning	learn	VERB
easat-4521	199	10	mathematics	mathematic	NOUN
easat-4521	199	11	are	be	AUX
easat-4521	199	12	greatly	greatly	ADV
easat-4521	199	13	influenced	influence	VERB
easat-4521	199	14	by	by	ADP
easat-4521	199	15	the	the	DET
easat-4521	199	16	cognitive	cognitive	ADJ
easat-4521	199	17	stages	stage	NOUN
easat-4521	199	18	in	in	ADP
easat-4521	199	19	the	the	DET
easat-4521	199	20	apos	apos	NOUN
easat-4521	199	21	theory	theory	NOUN
easat-4521	199	22	(	(	PUNCT
easat-4521	199	23	action	action	NOUN
easat-4521	199	24	,	,	PUNCT
easat-4521	199	25	process	process	NOUN
easat-4521	199	26	,	,	PUNCT
easat-4521	199	27	object	object	NOUN
easat-4521	199	28	,	,	PUNCT
easat-4521	199	29	schema	schema	NOUN
easat-4521	199	30	)	)	PUNCT
easat-4521	199	31	.	.	PUNCT
easat-4521	200	1	this	this	DET
easat-4521	200	2	finding	finding	NOUN
easat-4521	200	3	reinforces	reinforce	VERB
easat-4521	200	4	the	the	DET
easat-4521	200	5	view	view	NOUN
easat-4521	200	6	that	that	SCONJ
easat-4521	200	7	understanding	understand	VERB
easat-4521	200	8	mathematical	mathematical	ADJ
easat-4521	200	9	concepts	concept	NOUN
easat-4521	200	10	involves	involve	VERB
easat-4521	200	11	the	the	DET
easat-4521	200	12	relationship	relationship	NOUN
easat-4521	200	13	between	between	ADP
easat-4521	200	14	actions	action	NOUN
easat-4521	200	15	,	,	PUNCT
easat-4521	200	16	processes	process	NOUN
easat-4521	200	17	,	,	PUNCT
easat-4521	200	18	objects	object	NOUN
easat-4521	200	19	,	,	PUNCT
easat-4521	200	20	and	and	CCONJ
easat-4521	200	21	schemes	scheme	NOUN
easat-4521	200	22	at	at	ADP
easat-4521	200	23	various	various	ADJ
easat-4521	200	24	levels	level	NOUN
easat-4521	200	25	of	of	ADP
easat-4521	200	26	cognitive	cognitive	ADJ
easat-4521	200	27	development	development	NOUN
easat-4521	200	28	.	.	PUNCT
easat-4521	201	1	in	in	ADP
easat-4521	201	2	addition	addition	NOUN
easat-4521	201	3	,	,	PUNCT
easat-4521	201	4	these	these	DET
easat-4521	201	5	findings	finding	NOUN
easat-4521	201	6	are	be	AUX
easat-4521	201	7	expected	expect	VERB
easat-4521	201	8	to	to	PART
easat-4521	201	9	help	help	VERB
easat-4521	201	10	overcome	overcome	VERB
easat-4521	201	11	students	student	NOUN
easat-4521	201	12	'	'	PART
easat-4521	201	13	difficulties	difficulty	NOUN
easat-4521	201	14	in	in	ADP
easat-4521	201	15	working	work	VERB
easat-4521	201	16	on	on	ADP
easat-4521	201	17	derivative	derivative	ADJ
easat-4521	201	18	problems	problem	NOUN
easat-4521	201	19	and	and	CCONJ
easat-4521	201	20	can	can	AUX
easat-4521	201	21	improve	improve	VERB
easat-4521	201	22	student	student	NOUN
easat-4521	201	23	achievement	achievement	NOUN
easat-4521	201	24	.	.	PUNCT
easat-4521	202	1	this	this	PRON
easat-4521	202	2	is	be	AUX
easat-4521	202	3	based	base	VERB
easat-4521	202	4	on	on	ADP
easat-4521	202	5	previous	previous	ADJ
easat-4521	202	6	research	research	NOUN
easat-4521	202	7	nga	nga	NOUN
easat-4521	202	8	,	,	PUNCT
easat-4521	202	9	et	et	PROPN
easat-4521	202	10	al	al	PROPN
easat-4521	202	11	.	.	PUNCT
easat-4521	203	1	[	[	X
easat-4521	203	2	36	36	NUM
easat-4521	203	3	]	]	PUNCT
easat-4521	203	4	which	which	PRON
easat-4521	203	5	shows	show	VERB
easat-4521	203	6	that	that	SCONJ
easat-4521	203	7	students	student	NOUN
easat-4521	203	8	who	who	PRON
easat-4521	203	9	participate	participate	VERB
easat-4521	203	10	in	in	ADP
easat-4521	203	11	learning	learn	VERB
easat-4521	203	12	activities	activity	NOUN
easat-4521	203	13	based	base	VERB
easat-4521	203	14	on	on	ADP
easat-4521	203	15	apos	apos	PROPN
easat-4521	203	16	theory	theory	NOUN
easat-4521	203	17	experience	experience	NOUN
easat-4521	203	18	increased	increase	VERB
easat-4521	203	19	academic	academic	ADJ
easat-4521	203	20	achievement	achievement	NOUN
easat-4521	203	21	and	and	CCONJ
easat-4521	203	22	attitudes	attitude	NOUN
easat-4521	203	23	.	.	PUNCT
easat-4521	204	1	in	in	ADP
easat-4521	204	2	addition	addition	NOUN
easat-4521	204	3	,	,	PUNCT
easat-4521	204	4	apos	apos	PROPN
easat-4521	204	5	theory	theory	NOUN
easat-4521	204	6	improves	improve	VERB
easat-4521	204	7	students	student	NOUN
easat-4521	204	8	'	'	PART
easat-4521	204	9	ability	ability	NOUN
easat-4521	204	10	to	to	PART
easat-4521	204	11	find	find	VERB
easat-4521	204	12	solutions	solution	NOUN
easat-4521	204	13	to	to	ADP
easat-4521	204	14	derivative	derivative	ADJ
easat-4521	204	15	problems	problem	NOUN
easat-4521	204	16	.	.	PUNCT
easat-4521	205	1	the	the	DET
easat-4521	205	2	study	study	NOUN
easat-4521	205	3	is	be	AUX
easat-4521	205	4	also	also	ADV
easat-4521	205	5	in	in	ADP
easat-4521	205	6	line	line	NOUN
easat-4521	205	7	with	with	ADP
easat-4521	205	8	one	one	NUM
easat-4521	205	9	research	research	NOUN
easat-4521	205	10	study	study	NOUN
easat-4521	205	11	fuentealba	fuentealba	PROPN
easat-4521	205	12	,	,	PUNCT
easat-4521	205	13	et	et	PROPN
easat-4521	205	14	al	al	PROPN
easat-4521	205	15	.	.	PUNCT
easat-4521	206	1	[	[	X
easat-4521	206	2	14	14	NUM
easat-4521	206	3	]	]	PUNCT
easat-4521	206	4	which	which	PRON
easat-4521	206	5	shows	show	VERB
easat-4521	206	6	that	that	SCONJ
easat-4521	206	7	students	student	NOUN
easat-4521	206	8	are	be	AUX
easat-4521	206	9	able	able	ADJ
easat-4521	206	10	to	to	PART
easat-4521	206	11	explain	explain	VERB
easat-4521	206	12	number	number	NOUN
easat-4521	206	13	sequence	sequence	NOUN
easat-4521	206	14	patterns	pattern	NOUN
easat-4521	206	15	by	by	ADP
easat-4521	206	16	connecting	connect	VERB
easat-4521	206	17	actions	action	NOUN
easat-4521	206	18	,	,	PUNCT
easat-4521	206	19	processes	process	NOUN
easat-4521	206	20	,	,	PUNCT
easat-4521	206	21	and	and	CCONJ
easat-4521	206	22	objects	object	NOUN
easat-4521	206	23	in	in	ADP
easat-4521	206	24	mathematics	mathematic	NOUN
easat-4521	206	25	learning	learning	NOUN
easat-4521	206	26	.	.	PUNCT
easat-4521	207	1	this	this	DET
easat-4521	207	2	understanding	understanding	NOUN
easat-4521	207	3	illustrates	illustrate	VERB
easat-4521	207	4	the	the	DET
easat-4521	207	5	importance	importance	NOUN
easat-4521	207	6	of	of	ADP
easat-4521	207	7	the	the	DET
easat-4521	207	8	cognitive	cognitive	ADJ
easat-4521	207	9	modeling	modeling	NOUN
easat-4521	207	10	process	process	NOUN
easat-4521	207	11	in	in	ADP
easat-4521	207	12	generalizing	generalize	VERB
easat-4521	207	13	patterns	pattern	NOUN
easat-4521	207	14	and	and	CCONJ
easat-4521	207	15	connecting	connect	VERB
easat-4521	207	16	them	they	PRON
easat-4521	207	17	to	to	ADP
easat-4521	207	18	other	other	ADJ
easat-4521	207	19	concepts	concept	NOUN
easat-4521	207	20	.	.	PUNCT
easat-4521	208	1	this	this	DET
easat-4521	208	2	approach	approach	NOUN
easat-4521	208	3	is	be	AUX
easat-4521	208	4	also	also	ADV
easat-4521	208	5	relevant	relevant	ADJ
easat-4521	208	6	in	in	ADP
easat-4521	208	7	the	the	DET
easat-4521	208	8	context	context	NOUN
easat-4521	208	9	of	of	ADP
easat-4521	208	10	learning	learn	VERB
easat-4521	208	11	derivations	derivation	NOUN
easat-4521	208	12	,	,	PUNCT
easat-4521	208	13	where	where	SCONJ
easat-4521	208	14	sketching	sketch	VERB
easat-4521	208	15	a	a	DET
easat-4521	208	16	function	function	NOUN
easat-4521	208	17	derivative	derivative	ADJ
easat-4521	208	18	graph	graph	NOUN
easat-4521	208	19	requires	require	VERB
easat-4521	208	20	strong	strong	ADJ
easat-4521	208	21	visualization	visualization	NOUN
easat-4521	208	22	skills	skill	NOUN
easat-4521	208	23	,	,	PUNCT
easat-4521	208	24	both	both	PRON
easat-4521	208	25	for	for	ADP
easat-4521	208	26	linear	linear	ADJ
easat-4521	208	27	and	and	CCONJ
easat-4521	208	28	quadratic	quadratic	ADJ
easat-4521	208	29	functions	function	NOUN
easat-4521	208	30	.	.	PUNCT
easat-4521	209	1	however	however	ADV
easat-4521	209	2	,	,	PUNCT
easat-4521	209	3	the	the	DET
easat-4521	209	4	current	current	ADJ
easat-4521	209	5	research	research	NOUN
easat-4521	209	6	’s	’s	PART
easat-4521	209	7	findings	finding	NOUN
easat-4521	209	8	show	show	VERB
easat-4521	209	9	that	that	SCONJ
easat-4521	209	10	the	the	DET
easat-4521	209	11	subject	subject	NOUN
easat-4521	209	12	had	have	VERB
easat-4521	209	13	difficulty	difficulty	NOUN
easat-4521	209	14	explaining	explain	VERB
easat-4521	209	15	how	how	SCONJ
easat-4521	209	16	to	to	PART
easat-4521	209	17	sketch	sketch	VERB
easat-4521	209	18	a	a	DET
easat-4521	209	19	function	function	NOUN
easat-4521	209	20	derivative	derivative	ADJ
easat-4521	209	21	graph	graph	NOUN
easat-4521	209	22	from	from	ADP
easat-4521	209	23	a	a	DET
easat-4521	209	24	given	give	VERB
easat-4521	209	25	function	function	NOUN
easat-4521	209	26	graph	graph	NOUN
easat-4521	209	27	so	so	SCONJ
easat-4521	209	28	that	that	SCONJ
easat-4521	209	29	there	there	PRON
easat-4521	209	30	was	be	VERB
easat-4521	209	31	no	no	DET
easat-4521	209	32	mental	mental	ADJ
easat-4521	209	33	interiorization	interiorization	NOUN
easat-4521	209	34	mechanism	mechanism	NOUN
easat-4521	209	35	that	that	PRON
easat-4521	209	36	connected	connect	VERB
easat-4521	209	37	the	the	DET
easat-4521	209	38	apos	apos	NOUN
easat-4521	209	39	action	action	NOUN
easat-4521	209	40	to	to	PART
easat-4521	209	41	process	process	VERB
easat-4521	209	42	stages	stage	NOUN
easat-4521	209	43	.	.	PUNCT
easat-4521	210	1	this	this	DET
easat-4521	210	2	study	study	NOUN
easat-4521	210	3	also	also	ADV
easat-4521	210	4	reinforces	reinforce	VERB
easat-4521	210	5	the	the	DET
easat-4521	210	6	findings	finding	NOUN
easat-4521	210	7	of	of	ADP
easat-4521	210	8	a	a	DET
easat-4521	210	9	research	research	NOUN
easat-4521	210	10	paper	paper	NOUN
easat-4521	210	11	[	[	X
easat-4521	210	12	14	14	NUM
easat-4521	210	13	]	]	PUNCT
easat-4521	210	14	regarding	regard	VERB
easat-4521	210	15	the	the	DET
easat-4521	210	16	application	application	NOUN
easat-4521	210	17	of	of	ADP
easat-4521	210	18	the	the	DET
easat-4521	210	19	apos	apos	NOUN
easat-4521	210	20	method	method	NOUN
easat-4521	210	21	in	in	ADP
easat-4521	210	22	understanding	understand	VERB
easat-4521	210	23	double	double	ADJ
easat-4521	210	24	integrals	integral	NOUN
easat-4521	210	25	,	,	PUNCT
easat-4521	210	26	which	which	PRON
easat-4521	210	27	shows	show	VERB
easat-4521	210	28	that	that	SCONJ
easat-4521	210	29	although	although	SCONJ
easat-4521	210	30	many	many	ADJ
easat-4521	210	31	students	student	NOUN
easat-4521	210	32	have	have	VERB
easat-4521	210	33	difficulty	difficulty	NOUN
easat-4521	210	34	,	,	PUNCT
easat-4521	210	35	most	most	ADV
easat-4521	210	36	succeed	succeed	VERB
easat-4521	210	37	in	in	ADP
easat-4521	210	38	achieving	achieve	VERB
easat-4521	210	39	a	a	DET
easat-4521	210	40	deeper	deep	ADJ
easat-4521	210	41	understanding	understanding	NOUN
easat-4521	210	42	of	of	ADP
easat-4521	210	43	the	the	DET
easat-4521	210	44	concept	concept	NOUN
easat-4521	210	45	.	.	PUNCT
easat-4521	211	1	in	in	ADP
easat-4521	211	2	the	the	DET
easat-4521	211	3	process	process	NOUN
easat-4521	211	4	of	of	ADP
easat-4521	211	5	sketching	sketch	VERB
easat-4521	211	6	a	a	DET
easat-4521	211	7	derivative	derivative	ADJ
easat-4521	211	8	graph	graph	NOUN
easat-4521	211	9	as	as	SCONJ
easat-4521	211	10	shown	show	VERB
easat-4521	211	11	in	in	ADP
easat-4521	211	12	the	the	DET
easat-4521	211	13	present	present	ADJ
easat-4521	211	14	study	study	NOUN
easat-4521	211	15	,	,	PUNCT
easat-4521	211	16	the	the	DET
easat-4521	211	17	subject	subject	NOUN
easat-4521	211	18	showed	show	VERB
easat-4521	211	19	recognition	recognition	NOUN
easat-4521	211	20	of	of	ADP
easat-4521	211	21	the	the	DET
easat-4521	211	22	form	form	NOUN
easat-4521	211	23	of	of	ADP
easat-4521	211	24	the	the	DET
easat-4521	211	25	derivative	derivative	ADJ
easat-4521	211	26	function	function	NOUN
easat-4521	211	27	,	,	PUNCT
easat-4521	211	28	both	both	CCONJ
easat-4521	211	29	linear	linear	ADJ
easat-4521	211	30	and	and	CCONJ
easat-4521	211	31	quadratic	quadratic	ADJ
easat-4521	211	32	,	,	PUNCT
easat-4521	211	33	explained	explain	VERB
easat-4521	211	34	the	the	DET
easat-4521	211	35	steps	step	NOUN
easat-4521	211	36	needed	need	VERB
easat-4521	211	37	to	to	PART
easat-4521	211	38	find	find	VERB
easat-4521	211	39	the	the	DET
easat-4521	211	40	intersection	intersection	NOUN
easat-4521	211	41	and	and	CCONJ
easat-4521	211	42	vertex	vertex	NOUN
easat-4521	211	43	of	of	ADP
easat-4521	211	44	a	a	DET
easat-4521	211	45	parabola	parabola	NOUN
easat-4521	211	46	,	,	PUNCT
easat-4521	211	47	and	and	CCONJ
easat-4521	211	48	determined	determine	VERB
easat-4521	211	49	the	the	DET
easat-4521	211	50	relationship	relationship	NOUN
easat-4521	211	51	of	of	ADP
easat-4521	211	52	the	the	DET
easat-4521	211	53	derivative	derivative	NOUN
easat-4521	211	54	of	of	ADP
easat-4521	211	55	two	two	NUM
easat-4521	211	56	functions	function	NOUN
easat-4521	211	57	based	base	VERB
easat-4521	211	58	on	on	ADP
easat-4521	211	59	the	the	DET
easat-4521	211	60	given	give	VERB
easat-4521	211	61	graph	graph	NOUN
easat-4521	211	62	.	.	PUNCT
easat-4521	212	1	this	this	DET
easat-4521	212	2	understanding	understanding	NOUN
easat-4521	212	3	shows	show	VERB
easat-4521	212	4	the	the	DET
easat-4521	212	5	importance	importance	NOUN
easat-4521	212	6	of	of	ADP
easat-4521	212	7	the	the	DET
easat-4521	212	8	concept	concept	NOUN
easat-4521	212	9	of	of	ADP
easat-4521	212	10	the	the	DET
easat-4521	212	11	derivative	derivative	NOUN
easat-4521	212	12	of	of	ADP
easat-4521	212	13	a	a	DET
easat-4521	212	14	function	function	NOUN
easat-4521	212	15	not	not	PART
easat-4521	212	16	only	only	ADV
easat-4521	212	17	for	for	ADP
easat-4521	212	18	problem	problem	NOUN
easat-4521	212	19	-	-	PUNCT
easat-4521	212	20	solving	solving	NOUN
easat-4521	212	21	,	,	PUNCT
easat-4521	212	22	but	but	CCONJ
easat-4521	212	23	also	also	ADV
easat-4521	212	24	for	for	ADP
easat-4521	212	25	sketching	sketching	NOUN
easat-4521	212	26	and	and	CCONJ
easat-4521	212	27	analyzing	analyze	VERB
easat-4521	212	28	the	the	DET
easat-4521	212	29	derivative	derivative	ADJ
easat-4521	212	30	graph	graph	NOUN
easat-4521	212	31	of	of	ADP
easat-4521	212	32	a	a	DET
easat-4521	212	33	function	function	NOUN
easat-4521	212	34	more	more	ADV
easat-4521	212	35	564	564	NUM
easat-4521	212	36	edelweiss	edelweiss	PROPN
easat-4521	212	37	applied	apply	VERB
easat-4521	212	38	science	science	NOUN
easat-4521	212	39	and	and	CCONJ
easat-4521	212	40	technology	technology	NOUN
easat-4521	212	41	issn	issn	PROPN
easat-4521	212	42	:	:	PUNCT
easat-4521	212	43	2576	2576	NUM
easat-4521	212	44	-	-	SYM
easat-4521	212	45	8484	8484	NUM
easat-4521	212	46	vol	vol	NOUN
easat-4521	212	47	.	.	PROPN
easat-4521	213	1	9	9	NUM
easat-4521	213	2	,	,	PUNCT
easat-4521	213	3	no	no	INTJ
easat-4521	213	4	.	.	NOUN
easat-4521	213	5	2	2	NUM
easat-4521	213	6	:	:	PUNCT
easat-4521	213	7	555	555	NUM
easat-4521	213	8	-	-	SYM
easat-4521	213	9	566	566	NUM
easat-4521	213	10	,	,	PUNCT
easat-4521	213	11	2025	2025	NUM
easat-4521	213	12	doi	doi	NOUN
easat-4521	213	13	:	:	PUNCT
easat-4521	214	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	214	2	©	©	PROPN
easat-4521	214	3	2025	2025	NUM
easat-4521	214	4	by	by	ADP
easat-4521	214	5	the	the	DET
easat-4521	214	6	authors	author	NOUN
easat-4521	214	7	;	;	PUNCT
easat-4521	214	8	licensee	licensee	PROPN
easat-4521	214	9	learning	learning	NOUN
easat-4521	214	10	gate	gate	NOUN
easat-4521	214	11	effectively	effectively	ADV
easat-4521	214	12	.	.	PUNCT
easat-4521	215	1	by	by	ADP
easat-4521	215	2	following	follow	VERB
easat-4521	215	3	clear	clear	ADJ
easat-4521	215	4	steps	step	NOUN
easat-4521	215	5	,	,	PUNCT
easat-4521	215	6	the	the	DET
easat-4521	215	7	subject	subject	NOUN
easat-4521	215	8	emphasizes	emphasize	VERB
easat-4521	215	9	that	that	SCONJ
easat-4521	215	10	a	a	DET
easat-4521	215	11	deep	deep	ADJ
easat-4521	215	12	understanding	understanding	NOUN
easat-4521	215	13	of	of	ADP
easat-4521	215	14	derivatives	derivative	NOUN
easat-4521	215	15	is	be	AUX
easat-4521	215	16	very	very	ADV
easat-4521	215	17	useful	useful	ADJ
easat-4521	215	18	in	in	ADP
easat-4521	215	19	various	various	ADJ
easat-4521	215	20	mathematical	mathematical	ADJ
easat-4521	215	21	contexts	contexts	NOUN
easat-4521	215	22	.	.	PUNCT
easat-4521	216	1	5	5	X
easat-4521	216	2	.	.	X
easat-4521	216	3	conclusion	conclusion	NOUN
easat-4521	216	4	and	and	CCONJ
easat-4521	216	5	suggestions	suggestion	NOUN
easat-4521	216	6	this	this	DET
easat-4521	216	7	study	study	NOUN
easat-4521	216	8	has	have	AUX
easat-4521	216	9	successfully	successfully	ADV
easat-4521	216	10	described	describe	VERB
easat-4521	216	11	the	the	DET
easat-4521	216	12	systematic	systematic	ADJ
easat-4521	216	13	process	process	NOUN
easat-4521	216	14	in	in	ADP
easat-4521	216	15	drawing	draw	VERB
easat-4521	216	16	function	function	NOUN
easat-4521	216	17	derivative	derivative	ADJ
easat-4521	216	18	graphs	graph	NOUN
easat-4521	216	19	with	with	ADP
easat-4521	216	20	various	various	ADJ
easat-4521	216	21	approaches	approach	NOUN
easat-4521	216	22	,	,	PUNCT
easat-4521	216	23	involving	involve	VERB
easat-4521	216	24	the	the	DET
easat-4521	216	25	use	use	NOUN
easat-4521	216	26	of	of	ADP
easat-4521	216	27	function	function	NOUN
easat-4521	216	28	derivative	derivative	ADJ
easat-4521	216	29	formulas	formula	NOUN
easat-4521	216	30	and	and	CCONJ
easat-4521	216	31	the	the	DET
easat-4521	216	32	application	application	NOUN
easat-4521	216	33	of	of	ADP
easat-4521	216	34	graph	graph	NOUN
easat-4521	216	35	drawing	draw	VERB
easat-4521	216	36	rules	rule	NOUN
easat-4521	216	37	based	base	VERB
easat-4521	216	38	on	on	ADP
easat-4521	216	39	the	the	DET
easat-4521	216	40	given	give	VERB
easat-4521	216	41	function	function	NOUN
easat-4521	216	42	.	.	PUNCT
easat-4521	217	1	this	this	DET
easat-4521	217	2	approach	approach	NOUN
easat-4521	217	3	not	not	PART
easat-4521	217	4	only	only	ADV
easat-4521	217	5	deepens	deepen	VERB
easat-4521	217	6	the	the	DET
easat-4521	217	7	understanding	understanding	NOUN
easat-4521	217	8	of	of	ADP
easat-4521	217	9	function	function	NOUN
easat-4521	217	10	derivatives	derivative	NOUN
easat-4521	217	11	but	but	CCONJ
easat-4521	217	12	also	also	ADV
easat-4521	217	13	connects	connect	VERB
easat-4521	217	14	it	it	PRON
easat-4521	217	15	with	with	ADP
easat-4521	217	16	visual	visual	ADJ
easat-4521	217	17	understanding	understanding	NOUN
easat-4521	217	18	which	which	PRON
easat-4521	217	19	is	be	AUX
easat-4521	217	20	important	important	ADJ
easat-4521	217	21	in	in	ADP
easat-4521	217	22	sketching	sketch	VERB
easat-4521	217	23	function	function	NOUN
easat-4521	217	24	derivative	derivative	ADJ
easat-4521	217	25	graphs	graph	NOUN
easat-4521	217	26	.	.	PUNCT
easat-4521	218	1	this	this	DET
easat-4521	218	2	finding	finding	NOUN
easat-4521	218	3	is	be	AUX
easat-4521	218	4	also	also	ADV
easat-4521	218	5	in	in	ADP
easat-4521	218	6	line	line	NOUN
easat-4521	218	7	with	with	ADP
easat-4521	218	8	the	the	DET
easat-4521	218	9	apos	apos	NOUN
easat-4521	218	10	theory	theory	NOUN
easat-4521	218	11	,	,	PUNCT
easat-4521	218	12	which	which	PRON
easat-4521	218	13	emphasizes	emphasize	VERB
easat-4521	218	14	the	the	DET
easat-4521	218	15	importance	importance	NOUN
easat-4521	218	16	of	of	ADP
easat-4521	218	17	the	the	DET
easat-4521	218	18	relationship	relationship	NOUN
easat-4521	218	19	between	between	ADP
easat-4521	218	20	the	the	DET
easat-4521	218	21	mental	mental	ADJ
easat-4521	218	22	structure	structure	NOUN
easat-4521	218	23	of	of	ADP
easat-4521	218	24	action	action	NOUN
easat-4521	218	25	,	,	PUNCT
easat-4521	218	26	process	process	NOUN
easat-4521	218	27	,	,	PUNCT
easat-4521	218	28	object	object	NOUN
easat-4521	218	29	,	,	PUNCT
easat-4521	218	30	and	and	CCONJ
easat-4521	218	31	schema	schema	NOUN
easat-4521	218	32	and	and	CCONJ
easat-4521	218	33	the	the	DET
easat-4521	218	34	mental	mental	ADJ
easat-4521	218	35	mechanisms	mechanism	NOUN
easat-4521	218	36	that	that	PRON
easat-4521	218	37	build	build	VERB
easat-4521	218	38	them	they	PRON
easat-4521	218	39	,	,	PUNCT
easat-4521	218	40	namely	namely	ADV
easat-4521	218	41	interiorization	interiorization	NOUN
easat-4521	218	42	,	,	PUNCT
easat-4521	218	43	encapsulation	encapsulation	NOUN
easat-4521	218	44	,	,	PUNCT
easat-4521	218	45	coordination	coordination	NOUN
easat-4521	218	46	,	,	PUNCT
easat-4521	218	47	reversal	reversal	NOUN
easat-4521	218	48	,	,	PUNCT
easat-4521	218	49	de	de	NOUN
easat-4521	218	50	-	-	NOUN
easat-4521	218	51	encapsulation	encapsulation	NOUN
easat-4521	218	52	,	,	PUNCT
easat-4521	218	53	and	and	CCONJ
easat-4521	218	54	thematization	thematization	NOUN
easat-4521	218	55	in	in	ADP
easat-4521	218	56	understanding	understand	VERB
easat-4521	218	57	the	the	DET
easat-4521	218	58	concept	concept	NOUN
easat-4521	218	59	of	of	ADP
easat-4521	218	60	derivatives	derivative	NOUN
easat-4521	218	61	.	.	PUNCT
easat-4521	219	1	the	the	DET
easat-4521	219	2	findings	finding	NOUN
easat-4521	219	3	also	also	ADV
easat-4521	219	4	show	show	VERB
easat-4521	219	5	that	that	SCONJ
easat-4521	219	6	the	the	DET
easat-4521	219	7	subject	subject	NOUN
easat-4521	219	8	's	's	PART
easat-4521	219	9	understanding	understanding	NOUN
easat-4521	219	10	reached	reach	VERB
easat-4521	219	11	the	the	DET
easat-4521	219	12	apos	apos	NOUN
easat-4521	219	13	scheme	scheme	NOUN
easat-4521	219	14	stage	stage	NOUN
easat-4521	219	15	,	,	PUNCT
easat-4521	219	16	but	but	CCONJ
easat-4521	219	17	the	the	DET
easat-4521	219	18	subject	subject	NOUN
easat-4521	219	19	had	have	VERB
easat-4521	219	20	difficulty	difficulty	NOUN
easat-4521	219	21	at	at	ADP
easat-4521	219	22	the	the	DET
easat-4521	219	23	process	process	NOUN
easat-4521	219	24	stage	stage	NOUN
easat-4521	219	25	.	.	PUNCT
easat-4521	220	1	furthermore	furthermore	ADV
easat-4521	220	2	,	,	PUNCT
easat-4521	220	3	the	the	DET
easat-4521	220	4	application	application	NOUN
easat-4521	220	5	of	of	ADP
easat-4521	220	6	the	the	DET
easat-4521	220	7	apos	apos	NOUN
easat-4521	220	8	theory	theory	NOUN
easat-4521	220	9	can	can	AUX
easat-4521	220	10	help	help	VERB
easat-4521	220	11	deepen	deepen	VERB
easat-4521	220	12	students	student	NOUN
easat-4521	220	13	'	'	PART
easat-4521	220	14	cognitive	cognitive	ADJ
easat-4521	220	15	processes	process	NOUN
easat-4521	220	16	in	in	ADP
easat-4521	220	17	understanding	understand	VERB
easat-4521	220	18	the	the	DET
easat-4521	220	19	concept	concept	NOUN
easat-4521	220	20	of	of	ADP
easat-4521	220	21	derivatives	derivative	NOUN
easat-4521	220	22	through	through	ADP
easat-4521	220	23	various	various	ADJ
easat-4521	220	24	stages	stage	NOUN
easat-4521	220	25	,	,	PUNCT
easat-4521	220	26	starting	start	VERB
easat-4521	220	27	from	from	ADP
easat-4521	220	28	action	action	NOUN
easat-4521	220	29	,	,	PUNCT
easat-4521	220	30	process	process	NOUN
easat-4521	220	31	,	,	PUNCT
easat-4521	220	32	object	object	VERB
easat-4521	220	33	,	,	PUNCT
easat-4521	220	34	to	to	ADP
easat-4521	220	35	schema	schema	NOUN
easat-4521	220	36	.	.	PUNCT
easat-4521	221	1	in	in	ADP
easat-4521	221	2	addition	addition	NOUN
easat-4521	221	3	,	,	PUNCT
easat-4521	221	4	visual	visual	ADJ
easat-4521	221	5	and	and	CCONJ
easat-4521	221	6	analytical	analytical	ADJ
easat-4521	221	7	understanding	understanding	NOUN
easat-4521	221	8	of	of	ADP
easat-4521	221	9	students	student	NOUN
easat-4521	221	10	in	in	ADP
easat-4521	221	11	sketching	sketch	VERB
easat-4521	221	12	derivative	derivative	ADJ
easat-4521	221	13	graphs	graph	NOUN
easat-4521	221	14	must	must	AUX
easat-4521	221	15	be	be	AUX
easat-4521	221	16	strengthened	strengthen	VERB
easat-4521	221	17	,	,	PUNCT
easat-4521	221	18	especially	especially	ADV
easat-4521	221	19	in	in	ADP
easat-4521	221	20	the	the	DET
easat-4521	221	21	context	context	NOUN
easat-4521	221	22	of	of	ADP
easat-4521	221	23	learning	learn	VERB
easat-4521	221	24	.	.	PUNCT
easat-4521	222	1	as	as	ADP
easat-4521	222	2	for	for	ADP
easat-4521	222	3	research	research	NOUN
easat-4521	222	4	purposes	purpose	NOUN
easat-4521	222	5	,	,	PUNCT
easat-4521	222	6	future	future	ADJ
easat-4521	222	7	studies	study	NOUN
easat-4521	222	8	need	need	VERB
easat-4521	222	9	to	to	PART
easat-4521	222	10	pay	pay	VERB
easat-4521	222	11	attention	attention	NOUN
easat-4521	222	12	to	to	ADP
easat-4521	222	13	differences	difference	NOUN
easat-4521	222	14	in	in	ADP
easat-4521	222	15	students	student	NOUN
easat-4521	222	16	'	'	PART
easat-4521	222	17	levels	level	NOUN
easat-4521	222	18	of	of	ADP
easat-4521	222	19	mathematical	mathematical	ADJ
easat-4521	222	20	anxiety	anxiety	NOUN
easat-4521	222	21	,	,	PUNCT
easat-4521	222	22	as	as	ADV
easat-4521	222	23	well	well	ADV
easat-4521	222	24	as	as	ADP
easat-4521	222	25	provide	provide	VERB
easat-4521	222	26	a	a	DET
easat-4521	222	27	deeper	deep	ADJ
easat-4521	222	28	approach	approach	NOUN
easat-4521	222	29	to	to	ADP
easat-4521	222	30	understanding	understand	VERB
easat-4521	222	31	mathematical	mathematical	ADJ
easat-4521	222	32	concepts	concept	NOUN
easat-4521	222	33	.	.	PUNCT
easat-4521	223	1	transparency	transparency	NOUN
easat-4521	223	2	:	:	PUNCT
easat-4521	223	3	the	the	DET
easat-4521	223	4	authors	author	NOUN
easat-4521	223	5	confirm	confirm	VERB
easat-4521	223	6	that	that	SCONJ
easat-4521	223	7	the	the	DET
easat-4521	223	8	manuscript	manuscript	NOUN
easat-4521	223	9	is	be	AUX
easat-4521	223	10	an	an	DET
easat-4521	223	11	honest	honest	ADJ
easat-4521	223	12	,	,	PUNCT
easat-4521	223	13	accurate	accurate	ADJ
easat-4521	223	14	,	,	PUNCT
easat-4521	223	15	and	and	CCONJ
easat-4521	223	16	transparent	transparent	ADJ
easat-4521	223	17	account	account	NOUN
easat-4521	223	18	of	of	ADP
easat-4521	223	19	the	the	DET
easat-4521	223	20	study	study	NOUN
easat-4521	223	21	;	;	PUNCT
easat-4521	223	22	that	that	SCONJ
easat-4521	223	23	no	no	DET
easat-4521	223	24	vital	vital	ADJ
easat-4521	223	25	features	feature	NOUN
easat-4521	223	26	of	of	ADP
easat-4521	223	27	the	the	DET
easat-4521	223	28	study	study	NOUN
easat-4521	223	29	have	have	AUX
easat-4521	223	30	been	be	AUX
easat-4521	223	31	omitted	omit	VERB
easat-4521	223	32	;	;	PUNCT
easat-4521	223	33	and	and	CCONJ
easat-4521	223	34	that	that	SCONJ
easat-4521	223	35	any	any	DET
easat-4521	223	36	discrepancies	discrepancy	NOUN
easat-4521	223	37	from	from	ADP
easat-4521	223	38	the	the	DET
easat-4521	223	39	study	study	NOUN
easat-4521	223	40	as	as	SCONJ
easat-4521	223	41	planned	plan	VERB
easat-4521	223	42	have	have	AUX
easat-4521	223	43	been	be	AUX
easat-4521	223	44	explained	explain	VERB
easat-4521	223	45	.	.	PUNCT
easat-4521	224	1	this	this	DET
easat-4521	224	2	study	study	NOUN
easat-4521	224	3	followed	follow	VERB
easat-4521	224	4	all	all	DET
easat-4521	224	5	ethical	ethical	ADJ
easat-4521	224	6	practices	practice	NOUN
easat-4521	224	7	during	during	ADP
easat-4521	224	8	writing	writing	NOUN
easat-4521	224	9	.	.	PUNCT
easat-4521	225	1	acknowledgement	acknowledgement	NOUN
easat-4521	225	2	:	:	PUNCT
easat-4521	225	3	we	we	PRON
easat-4521	225	4	would	would	AUX
easat-4521	225	5	like	like	VERB
easat-4521	225	6	to	to	PART
easat-4521	225	7	thank	thank	VERB
easat-4521	225	8	our	our	PRON
easat-4521	225	9	team	team	NOUN
easat-4521	225	10	from	from	ADP
easat-4521	225	11	the	the	DET
easat-4521	225	12	department	department	NOUN
easat-4521	225	13	of	of	ADP
easat-4521	225	14	mathematics	mathematics	PROPN
easat-4521	225	15	education	education	NOUN
easat-4521	225	16	,	,	PUNCT
easat-4521	225	17	faculty	faculty	NOUN
easat-4521	225	18	of	of	ADP
easat-4521	225	19	mathematics	mathematic	NOUN
easat-4521	225	20	and	and	CCONJ
easat-4521	225	21	natural	natural	ADJ
easat-4521	225	22	sciences	science	NOUN
easat-4521	225	23	,	,	PUNCT
easat-4521	225	24	universitas	universitas	PROPN
easat-4521	225	25	negeri	negeri	PROPN
easat-4521	225	26	surabaya	surabaya	PROPN
easat-4521	225	27	,	,	PUNCT
easat-4521	225	28	surabaya	surabaya	PROPN
easat-4521	225	29	,	,	PUNCT
easat-4521	225	30	indonesia	indonesia	PROPN
easat-4521	225	31	.	.	PUNCT
easat-4521	226	1	copyright	copyright	NOUN
easat-4521	226	2	:	:	PUNCT
easat-4521	227	1	©	©	PROPN
easat-4521	227	2	2024	2024	NUM
easat-4521	227	3	by	by	ADP
easat-4521	227	4	the	the	DET
easat-4521	227	5	authors	author	NOUN
easat-4521	227	6	.	.	PUNCT
easat-4521	228	1	this	this	DET
easat-4521	228	2	article	article	NOUN
easat-4521	228	3	is	be	AUX
easat-4521	228	4	an	an	DET
easat-4521	228	5	open	open	ADJ
easat-4521	228	6	access	access	NOUN
easat-4521	228	7	article	article	NOUN
easat-4521	228	8	distributed	distribute	VERB
easat-4521	228	9	under	under	ADP
easat-4521	228	10	the	the	DET
easat-4521	228	11	terms	term	NOUN
easat-4521	228	12	and	and	CCONJ
easat-4521	228	13	conditions	condition	NOUN
easat-4521	228	14	of	of	ADP
easat-4521	228	15	the	the	DET
easat-4521	228	16	creative	creative	ADJ
easat-4521	228	17	commons	common	NOUN
easat-4521	228	18	attribution	attribution	NOUN
easat-4521	228	19	(	(	PUNCT
easat-4521	228	20	cc	cc	NOUN
easat-4521	228	21	by	by	ADP
easat-4521	228	22	)	)	PUNCT
easat-4521	228	23	license	license	NOUN
easat-4521	228	24	(	(	PUNCT
easat-4521	228	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	NOUN
easat-4521	228	26	)	)	PUNCT
easat-4521	228	27	references	reference	NOUN
easat-4521	228	28	[	[	X
easat-4521	228	29	1	1	NUM
easat-4521	228	30	]	]	X
easat-4521	228	31	d.	d.	PROPN
easat-4521	228	32	fouryza	fouryza	PROPN
easat-4521	228	33	,	,	PUNCT
easat-4521	228	34	s.	s.	PROPN
easat-4521	228	35	m.	m.	PROPN
easat-4521	228	36	amin	amin	PROPN
easat-4521	228	37	,	,	PUNCT
easat-4521	228	38	and	and	CCONJ
easat-4521	228	39	r.	r.	PROPN
easat-4521	228	40	ekawati	ekawati	PROPN
easat-4521	228	41	,	,	PUNCT
easat-4521	228	42	"	"	PUNCT
easat-4521	228	43	designing	design	VERB
easat-4521	228	44	lesson	lesson	NOUN
easat-4521	228	45	plan	plan	NOUN
easat-4521	228	46	of	of	ADP
easat-4521	228	47	integer	integer	NOUN
easat-4521	228	48	number	number	NOUN
easat-4521	228	49	operation	operation	NOUN
easat-4521	228	50	based	base	VERB
easat-4521	228	51	on	on	ADP
easat-4521	228	52	fun	fun	NOUN
easat-4521	228	53	and	and	CCONJ
easat-4521	228	54	easy	easy	ADJ
easat-4521	228	55	math	math	NOUN
easat-4521	228	56	(	(	PUNCT
easat-4521	228	57	fem	fem	NOUN
easat-4521	228	58	)	)	PUNCT
easat-4521	228	59	approach	approach	NOUN
easat-4521	228	60	,	,	PUNCT
easat-4521	228	61	"	"	PUNCT
easat-4521	228	62	international	international	ADJ
easat-4521	228	63	journal	journal	NOUN
easat-4521	228	64	of	of	ADP
easat-4521	228	65	evaluation	evaluation	NOUN
easat-4521	228	66	and	and	CCONJ
easat-4521	228	67	research	research	NOUN
easat-4521	228	68	in	in	ADP
easat-4521	228	69	education	education	NOUN
easat-4521	228	70	,	,	PUNCT
easat-4521	228	71	vol	vol	NOUN
easat-4521	228	72	.	.	PROPN
easat-4521	228	73	8	8	NUM
easat-4521	228	74	,	,	PUNCT
easat-4521	228	75	no	no	INTJ
easat-4521	228	76	.	.	NOUN
easat-4521	228	77	1	1	NUM
easat-4521	228	78	,	,	PUNCT
easat-4521	228	79	pp	pp	ADJ
easat-4521	228	80	.	.	PUNCT
easat-4521	229	1	103	103	NUM
easat-4521	229	2	-	-	SYM
easat-4521	229	3	109	109	NUM
easat-4521	229	4	,	,	PUNCT
easat-4521	229	5	2019	2019	NUM
easat-4521	229	6	.	.	PUNCT
easat-4521	230	1	https://doi.org/10.11591/ijere.v8i1.15514	https://doi.org/10.11591/ijere.v8i1.15514	X
easat-4521	231	1	[	[	X
easat-4521	231	2	2	2	NUM
easat-4521	231	3	]	]	PUNCT
easat-4521	231	4	k.	k.	PROPN
easat-4521	231	5	otgonbaatar	otgonbaatar	PROPN
easat-4521	231	6	,	,	PUNCT
easat-4521	231	7	"	"	PUNCT
easat-4521	231	8	effectiveness	effectiveness	NOUN
easat-4521	231	9	of	of	ADP
easat-4521	231	10	anchoring	anchoring	NOUN
easat-4521	231	11	vignettes	vignette	NOUN
easat-4521	231	12	in	in	ADP
easat-4521	231	13	re	re	VERB
easat-4521	231	14	-	-	ADJ
easat-4521	231	15	evaluating	evaluate	VERB
easat-4521	231	16	self	self	NOUN
easat-4521	231	17	-	-	PUNCT
easat-4521	231	18	rated	rate	VERB
easat-4521	231	19	social	social	ADJ
easat-4521	231	20	and	and	CCONJ
easat-4521	231	21	emotional	emotional	ADJ
easat-4521	231	22	skills	skill	NOUN
easat-4521	231	23	in	in	ADP
easat-4521	231	24	mathematics	mathematic	NOUN
easat-4521	231	25	,	,	PUNCT
easat-4521	231	26	"	"	PUNCT
easat-4521	231	27	international	international	ADJ
easat-4521	231	28	journal	journal	NOUN
easat-4521	231	29	of	of	ADP
easat-4521	231	30	evaluation	evaluation	NOUN
easat-4521	231	31	and	and	CCONJ
easat-4521	231	32	research	research	NOUN
easat-4521	231	33	in	in	ADP
easat-4521	231	34	education	education	NOUN
easat-4521	231	35	,	,	PUNCT
easat-4521	231	36	vol	vol	NOUN
easat-4521	231	37	.	.	PROPN
easat-4521	231	38	10	10	NUM
easat-4521	231	39	,	,	PUNCT
easat-4521	231	40	no	no	INTJ
easat-4521	231	41	.	.	NOUN
easat-4521	231	42	1	1	NUM
easat-4521	231	43	,	,	PUNCT
easat-4521	231	44	pp	pp	ADJ
easat-4521	231	45	.	.	PUNCT
easat-4521	232	1	237–244	237–244	NUM
easat-4521	232	2	,	,	PUNCT
easat-4521	232	3	2021	2021	NUM
easat-4521	232	4	.	.	PUNCT
easat-4521	233	1	https://doi.org/10.11591/ijere.v10i1.20716	https://doi.org/10.11591/ijere.v10i1.20716	NOUN
easat-4521	233	2	[	[	X
easat-4521	233	3	3	3	X
easat-4521	233	4	]	]	PUNCT
easat-4521	233	5	s.	s.	PROPN
easat-4521	233	6	stewart	stewart	PROPN
easat-4521	233	7	,	,	PUNCT
easat-4521	233	8	c.	c.	PROPN
easat-4521	233	9	andrews	andrews	PROPN
easat-4521	233	10	-	-	PUNCT
easat-4521	233	11	larson	larson	PROPN
easat-4521	233	12	,	,	PUNCT
easat-4521	233	13	and	and	CCONJ
easat-4521	233	14	m.	m.	PROPN
easat-4521	233	15	zandieh	zandieh	PROPN
easat-4521	233	16	,	,	PUNCT
easat-4521	233	17	"	"	PUNCT
easat-4521	233	18	linear	linear	ADJ
easat-4521	233	19	algebra	algebra	NOUN
easat-4521	233	20	teaching	teaching	NOUN
easat-4521	233	21	and	and	CCONJ
easat-4521	233	22	learning	learning	NOUN
easat-4521	233	23	:	:	PUNCT
easat-4521	233	24	themes	theme	NOUN
easat-4521	233	25	from	from	ADP
easat-4521	233	26	recent	recent	ADJ
easat-4521	233	27	research	research	NOUN
easat-4521	233	28	and	and	CCONJ
easat-4521	233	29	evolving	evolve	VERB
easat-4521	233	30	research	research	NOUN
easat-4521	233	31	priorities	priority	NOUN
easat-4521	233	32	,	,	PUNCT
easat-4521	233	33	"	"	PUNCT
easat-4521	233	34	zdm	zdm	NOUN
easat-4521	233	35	mathematics	mathematic	NOUN
easat-4521	233	36	education	education	NOUN
easat-4521	233	37	,	,	PUNCT
easat-4521	233	38	vol	vol	NOUN
easat-4521	233	39	.	.	PROPN
easat-4521	233	40	51	51	NUM
easat-4521	233	41	,	,	PUNCT
easat-4521	233	42	pp	pp	ADJ
easat-4521	233	43	.	.	PUNCT
easat-4521	234	1	1017	1017	NUM
easat-4521	234	2	-	-	SYM
easat-4521	234	3	1030	1030	NUM
easat-4521	234	4	,	,	PUNCT
easat-4521	234	5	2019	2019	NUM
easat-4521	234	6	.	.	PUNCT
easat-4521	235	1	https://doi.org/10.1007/s11858-019-01104-1	https://doi.org/10.1007/s11858-019-01104-1	NUM
easat-4521	236	1	[	[	X
easat-4521	236	2	4	4	X
easat-4521	236	3	]	]	X
easat-4521	236	4	r.	r.	PROPN
easat-4521	236	5	martínez	martínez	PROPN
easat-4521	236	6	-	-	PUNCT
easat-4521	236	7	planell	planell	PROPN
easat-4521	236	8	,	,	PUNCT
easat-4521	236	9	m.	m.	NOUN
easat-4521	236	10	t.	t.	PROPN
easat-4521	236	11	gaisman	gaisman	PROPN
easat-4521	236	12	,	,	PUNCT
easat-4521	236	13	and	and	CCONJ
easat-4521	236	14	d.	d.	PROPN
easat-4521	236	15	mcgee	mcgee	PROPN
easat-4521	236	16	,	,	PUNCT
easat-4521	236	17	"	"	PUNCT
easat-4521	236	18	on	on	ADP
easat-4521	236	19	students	student	NOUN
easat-4521	236	20	’	’	PART
easat-4521	236	21	understanding	understanding	NOUN
easat-4521	236	22	of	of	ADP
easat-4521	236	23	the	the	DET
easat-4521	236	24	differential	differential	ADJ
easat-4521	236	25	calculus	calculus	NOUN
easat-4521	236	26	of	of	ADP
easat-4521	236	27	functions	function	NOUN
easat-4521	236	28	of	of	ADP
easat-4521	236	29	two	two	NUM
easat-4521	236	30	variables	variable	NOUN
easat-4521	236	31	,	,	PUNCT
easat-4521	236	32	"	"	PUNCT
easat-4521	236	33	the	the	DET
easat-4521	236	34	journal	journal	NOUN
easat-4521	236	35	of	of	ADP
easat-4521	236	36	mathematical	mathematical	ADJ
easat-4521	236	37	behavior	behavior	NOUN
easat-4521	236	38	,	,	PUNCT
easat-4521	236	39	vol	vol	NOUN
easat-4521	236	40	.	.	PROPN
easat-4521	236	41	38	38	NUM
easat-4521	236	42	,	,	PUNCT
easat-4521	236	43	pp	pp	ADJ
easat-4521	236	44	.	.	PUNCT
easat-4521	237	1	57	57	NUM
easat-4521	237	2	-	-	SYM
easat-4521	237	3	86	86	NUM
easat-4521	237	4	,	,	PUNCT
easat-4521	237	5	2015	2015	NUM
easat-4521	237	6	.	.	PUNCT
easat-4521	238	1	https://doi.org/10.1016/j.jmathb.2015.03.003	https://doi.org/10.1016/j.jmathb.2015.03.003	NUM
easat-4521	238	2	[	[	X
easat-4521	238	3	5	5	NUM
easat-4521	238	4	]	]	PUNCT
easat-4521	238	5	c.	c.	PROPN
easat-4521	238	6	fuentealba	fuentealba	PROPN
easat-4521	238	7	,	,	PUNCT
easat-4521	238	8	g.	g.	PROPN
easat-4521	238	9	sánchez	sánchez	PROPN
easat-4521	238	10	-	-	PUNCT
easat-4521	238	11	matamoros	matamoros	PROPN
easat-4521	238	12	,	,	PUNCT
easat-4521	238	13	e.	e.	PROPN
easat-4521	238	14	badillo	badillo	PROPN
easat-4521	238	15	,	,	PUNCT
easat-4521	238	16	and	and	CCONJ
easat-4521	238	17	m.	m.	NOUN
easat-4521	238	18	trigueros	trigueros	PROPN
easat-4521	238	19	,	,	PUNCT
easat-4521	238	20	"	"	PUNCT
easat-4521	238	21	thematization	thematization	NOUN
easat-4521	238	22	of	of	ADP
easat-4521	238	23	derivative	derivative	ADJ
easat-4521	238	24	schema	schema	NOUN
easat-4521	238	25	in	in	ADP
easat-4521	238	26	university	university	NOUN
easat-4521	238	27	students	student	NOUN
easat-4521	238	28	:	:	PUNCT
easat-4521	238	29	nuances	nuance	NOUN
easat-4521	238	30	in	in	ADP
easat-4521	238	31	constructing	construct	VERB
easat-4521	238	32	relations	relation	NOUN
easat-4521	238	33	between	between	ADP
easat-4521	238	34	a	a	DET
easat-4521	238	35	function	function	NOUN
easat-4521	238	36	's	's	PART
easat-4521	238	37	successive	successive	ADJ
easat-4521	238	38	derivatives	derivative	NOUN
easat-4521	238	39	,	,	PUNCT
easat-4521	238	40	"	"	PUNCT
easat-4521	238	41	international	international	ADJ
easat-4521	238	42	journal	journal	NOUN
easat-4521	238	43	of	of	ADP
easat-4521	238	44	mathematical	mathematical	ADJ
easat-4521	238	45	education	education	NOUN
easat-4521	238	46	in	in	ADP
easat-4521	238	47	science	science	NOUN
easat-4521	238	48	and	and	CCONJ
easat-4521	238	49	technology	technology	NOUN
easat-4521	238	50	,	,	PUNCT
easat-4521	238	51	vol	vol	NOUN
easat-4521	238	52	.	.	PROPN
easat-4521	238	53	48	48	NUM
easat-4521	238	54	,	,	PUNCT
easat-4521	238	55	no	no	INTJ
easat-4521	238	56	.	.	NOUN
easat-4521	238	57	3	3	NUM
easat-4521	238	58	,	,	PUNCT
easat-4521	238	59	pp	pp	ADJ
easat-4521	238	60	.	.	PUNCT
easat-4521	239	1	374	374	NUM
easat-4521	239	2	-	-	SYM
easat-4521	239	3	392	392	NUM
easat-4521	239	4	,	,	PUNCT
easat-4521	239	5	2017	2017	NUM
easat-4521	239	6	.	.	PUNCT
easat-4521	240	1	[	[	X
easat-4521	240	2	6	6	NUM
easat-4521	240	3	]	]	PUNCT
easat-4521	240	4	d.	d.	NOUN
easat-4521	240	5	brijlall	brijlall	PROPN
easat-4521	240	6	and	and	CCONJ
easat-4521	240	7	z.	z.	PROPN
easat-4521	240	8	ndlovu	ndlovu	PROPN
easat-4521	240	9	,	,	PUNCT
easat-4521	240	10	"	"	PUNCT
easat-4521	240	11	high	high	ADJ
easat-4521	240	12	school	school	NOUN
easat-4521	240	13	learners	learner	NOUN
easat-4521	240	14	'	'	PART
easat-4521	240	15	mental	mental	ADJ
easat-4521	240	16	construction	construction	NOUN
easat-4521	240	17	during	during	ADP
easat-4521	240	18	solving	solve	VERB
easat-4521	240	19	optimisation	optimisation	NOUN
easat-4521	240	20	problems	problem	NOUN
easat-4521	240	21	in	in	ADP
easat-4521	240	22	calculus	calculus	NOUN
easat-4521	240	23	:	:	PUNCT
easat-4521	240	24	a	a	DET
easat-4521	240	25	south	south	ADJ
easat-4521	240	26	african	african	ADJ
easat-4521	240	27	case	case	NOUN
easat-4521	240	28	study	study	NOUN
easat-4521	240	29	,	,	PUNCT
easat-4521	240	30	"	"	PUNCT
easat-4521	240	31	south	south	ADJ
easat-4521	240	32	african	african	ADJ
easat-4521	240	33	journal	journal	NOUN
easat-4521	240	34	of	of	ADP
easat-4521	240	35	education	education	NOUN
easat-4521	240	36	,	,	PUNCT
easat-4521	240	37	vol	vol	NOUN
easat-4521	240	38	.	.	PROPN
easat-4521	241	1	33	33	NUM
easat-4521	241	2	,	,	PUNCT
easat-4521	241	3	no	no	INTJ
easat-4521	241	4	.	.	NOUN
easat-4521	241	5	2	2	NUM
easat-4521	241	6	,	,	PUNCT
easat-4521	241	7	pp	pp	ADJ
easat-4521	241	8	.	.	PUNCT
easat-4521	242	1	1	1	NUM
easat-4521	242	2	-	-	SYM
easat-4521	242	3	18	18	NUM
easat-4521	242	4	,	,	PUNCT
easat-4521	242	5	2013	2013	NUM
easat-4521	242	6	.	.	PUNCT
easat-4521	243	1	https://doi.org/10.15700/saje.v33n2a679	https://doi.org/10.15700/saje.v33n2a679	PROPN
easat-4521	243	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-4521	243	3	)	)	PUNCT
easat-4521	244	1	https://doi.org/10.11591/ijere.v8i1.15514	https://doi.org/10.11591/ijere.v8i1.15514	X
easat-4521	244	2	https://doi.org/10.11591/ijere.v10i1.20716	https://doi.org/10.11591/ijere.v10i1.20716	NUM
easat-4521	244	3	https://doi.org/10.1007/s11858-019-01104-1	https://doi.org/10.1007/s11858-019-01104-1	NUM
easat-4521	244	4	https://doi.org/10.1016/j.jmathb.2015.03.003	https://doi.org/10.1016/j.jmathb.2015.03.003	NUM
easat-4521	244	5	https://doi.org/10.15700/saje.v33n2a679	https://doi.org/10.15700/saje.v33n2a679	PROPN
easat-4521	244	6	565	565	NUM
easat-4521	244	7	edelweiss	edelweiss	PROPN
easat-4521	244	8	applied	apply	VERB
easat-4521	244	9	science	science	NOUN
easat-4521	244	10	and	and	CCONJ
easat-4521	244	11	technology	technology	NOUN
easat-4521	244	12	issn	issn	PROPN
easat-4521	244	13	:	:	PUNCT
easat-4521	244	14	2576	2576	NUM
easat-4521	244	15	-	-	SYM
easat-4521	244	16	8484	8484	NUM
easat-4521	244	17	vol	vol	NOUN
easat-4521	244	18	.	.	PROPN
easat-4521	245	1	9	9	NUM
easat-4521	245	2	,	,	PUNCT
easat-4521	245	3	no	no	INTJ
easat-4521	245	4	.	.	NOUN
easat-4521	245	5	2	2	NUM
easat-4521	245	6	:	:	PUNCT
easat-4521	245	7	555	555	NUM
easat-4521	245	8	-	-	SYM
easat-4521	245	9	566	566	NUM
easat-4521	245	10	,	,	PUNCT
easat-4521	245	11	2025	2025	NUM
easat-4521	245	12	doi	doi	NOUN
easat-4521	245	13	:	:	PUNCT
easat-4521	246	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	246	2	©	©	PROPN
easat-4521	246	3	2025	2025	NUM
easat-4521	246	4	by	by	ADP
easat-4521	246	5	the	the	DET
easat-4521	246	6	authors	author	NOUN
easat-4521	246	7	;	;	PUNCT
easat-4521	246	8	licensee	licensee	PROPN
easat-4521	246	9	learning	learning	NOUN
easat-4521	246	10	gate	gate	NOUN
easat-4521	246	11	[	[	X
easat-4521	246	12	7	7	NUM
easat-4521	246	13	]	]	PUNCT
easat-4521	246	14	a.	a.	NOUN
easat-4521	246	15	oktaç	oktaç	NOUN
easat-4521	246	16	,	,	PUNCT
easat-4521	246	17	"	"	PUNCT
easat-4521	246	18	mental	mental	ADJ
easat-4521	246	19	constructions	construction	NOUN
easat-4521	246	20	in	in	ADP
easat-4521	246	21	linear	linear	PROPN
easat-4521	246	22	algebra	algebra	NOUN
easat-4521	246	23	,	,	PUNCT
easat-4521	246	24	"	"	PUNCT
easat-4521	246	25	zdm	zdm	NOUN
easat-4521	246	26	,	,	PUNCT
easat-4521	246	27	vol	vol	NOUN
easat-4521	246	28	.	.	PROPN
easat-4521	246	29	51	51	NUM
easat-4521	246	30	,	,	PUNCT
easat-4521	246	31	no	no	INTJ
easat-4521	246	32	.	.	NOUN
easat-4521	246	33	7	7	NUM
easat-4521	246	34	,	,	PUNCT
easat-4521	246	35	pp	pp	ADJ
easat-4521	246	36	.	.	PUNCT
easat-4521	246	37	1043	1043	NUM
easat-4521	246	38	-	-	SYM
easat-4521	246	39	1054	1054	NUM
easat-4521	246	40	,	,	PUNCT
easat-4521	246	41	2019	2019	NUM
easat-4521	246	42	.	.	PUNCT
easat-4521	247	1	https://doi.org/10.1007/s11858-019-01037-9	https://doi.org/10.1007/s11858-019-01037-9	VERB
easat-4521	248	1	[	[	X
easat-4521	248	2	8	8	NUM
easat-4521	248	3	]	]	X
easat-4521	248	4	i.	i.	PROPN
easat-4521	248	5	arnon	arnon	PROPN
easat-4521	248	6	,	,	PUNCT
easat-4521	248	7	j.	j.	PROPN
easat-4521	248	8	cottrill	cottrill	PROPN
easat-4521	248	9	,	,	PUNCT
easat-4521	248	10	and	and	CCONJ
easat-4521	248	11	e.	e.	PROPN
easat-4521	248	12	dubinsky	dubinsky	PROPN
easat-4521	248	13	,	,	PUNCT
easat-4521	248	14	"	"	PUNCT
easat-4521	248	15	apos	apos	NOUN
easat-4521	248	16	theory	theory	NOUN
easat-4521	248	17	,	,	PUNCT
easat-4521	248	18	"	"	PUNCT
easat-4521	248	19	2014	2014	NUM
easat-4521	248	20	.	.	PUNCT
easat-4521	249	1	[	[	X
easat-4521	249	2	9	9	NUM
easat-4521	249	3	]	]	X
easat-4521	249	4	e.	e.	PROPN
easat-4521	249	5	l.	l.	PROPN
easat-4521	249	6	langi	langi	PROPN
easat-4521	249	7	and	and	CCONJ
easat-4521	249	8	d.	d.	PROPN
easat-4521	249	9	juniati	juniati	PROPN
easat-4521	249	10	,	,	PUNCT
easat-4521	249	11	"	"	PUNCT
easat-4521	249	12	students	student	NOUN
easat-4521	249	13	as	as	ADP
easat-4521	249	14	prospective	prospective	ADJ
easat-4521	249	15	teachers	teacher	NOUN
easat-4521	249	16	’	’	PART
easat-4521	249	17	understanding	understanding	NOUN
easat-4521	249	18	of	of	ADP
easat-4521	249	19	integral	integral	ADJ
easat-4521	249	20	based	base	VERB
easat-4521	249	21	on	on	ADP
easat-4521	249	22	the	the	DET
easat-4521	249	23	apos	apos	NOUN
easat-4521	249	24	theory	theory	NOUN
easat-4521	249	25	in	in	ADP
easat-4521	249	26	terms	term	NOUN
easat-4521	249	27	of	of	ADP
easat-4521	249	28	gender	gender	NOUN
easat-4521	249	29	difference	difference	NOUN
easat-4521	249	30	,	,	PUNCT
easat-4521	249	31	"	"	PUNCT
easat-4521	249	32	journal	journal	NOUN
easat-4521	249	33	of	of	ADP
easat-4521	249	34	higher	high	ADJ
easat-4521	249	35	education	education	NOUN
easat-4521	249	36	theory	theory	NOUN
easat-4521	249	37	and	and	CCONJ
easat-4521	249	38	practice	practice	NOUN
easat-4521	249	39	,	,	PUNCT
easat-4521	249	40	vol	vol	NOUN
easat-4521	249	41	.	.	PROPN
easat-4521	249	42	23	23	NUM
easat-4521	249	43	,	,	PUNCT
easat-4521	249	44	no	no	INTJ
easat-4521	249	45	.	.	NOUN
easat-4521	249	46	4	4	NUM
easat-4521	249	47	,	,	PUNCT
easat-4521	249	48	pp	pp	ADJ
easat-4521	249	49	.	.	PUNCT
easat-4521	249	50	169	169	NUM
easat-4521	249	51	-	-	SYM
easat-4521	249	52	185	185	NUM
easat-4521	249	53	,	,	PUNCT
easat-4521	249	54	2023	2023	NUM
easat-4521	249	55	.	.	PUNCT
easat-4521	249	56	https://doi.org/10.33423/jhetp.v23i4.5897	https://doi.org/10.33423/jhetp.v23i4.5897	NUM
easat-4521	250	1	[	[	X
easat-4521	250	2	10	10	NUM
easat-4521	250	3	]	]	X
easat-4521	250	4	s.	s.	PROPN
easat-4521	250	5	maf’ulah	maf’ulah	PROPN
easat-4521	250	6	and	and	CCONJ
easat-4521	250	7	d.	d.	PROPN
easat-4521	250	8	juniati	juniati	PROPN
easat-4521	250	9	,	,	PUNCT
easat-4521	250	10	"	"	PUNCT
easat-4521	250	11	students	student	NOUN
easat-4521	250	12	’	'	PUNCT
easat-4521	250	13	strategies	strategy	NOUN
easat-4521	250	14	to	to	PART
easat-4521	250	15	solve	solve	VERB
easat-4521	250	16	reversible	reversible	ADJ
easat-4521	250	17	problems	problem	NOUN
easat-4521	250	18	of	of	ADP
easat-4521	250	19	function	function	NOUN
easat-4521	250	20	:	:	PUNCT
easat-4521	250	21	the	the	DET
easat-4521	250	22	part	part	NOUN
easat-4521	250	23	of	of	ADP
easat-4521	250	24	reversible	reversible	ADJ
easat-4521	250	25	thinking	thinking	NOUN
easat-4521	250	26	,	,	PUNCT
easat-4521	250	27	"	"	PUNCT
easat-4521	250	28	in	in	ADP
easat-4521	250	29	journal	journal	NOUN
easat-4521	250	30	of	of	ADP
easat-4521	250	31	physics	physics	PROPN
easat-4521	250	32	:	:	PUNCT
easat-4521	250	33	conference	conference	NOUN
easat-4521	250	34	series	series	NOUN
easat-4521	250	35	.	.	PUNCT
easat-4521	251	1	https://doi.org/10.1088/1742-6596/1417/1/012051	https://doi.org/10.1088/1742-6596/1417/1/012051	PROPN
easat-4521	251	2	,	,	PUNCT
easat-4521	251	3	2019	2019	NUM
easat-4521	251	4	,	,	PUNCT
easat-4521	251	5	vol	vol	NOUN
easat-4521	251	6	.	.	NOUN
easat-4521	251	7	1417	1417	NUM
easat-4521	251	8	,	,	PUNCT
easat-4521	251	9	no	no	INTJ
easat-4521	251	10	.	.	NOUN
easat-4521	251	11	1	1	NUM
easat-4521	251	12	:	:	PUNCT
easat-4521	251	13	iop	iop	NOUN
easat-4521	251	14	publishing	publishing	NOUN
easat-4521	251	15	,	,	PUNCT
easat-4521	251	16	p.	p.	NOUN
easat-4521	251	17	012051	012051	NUM
easat-4521	251	18	.	.	PUNCT
easat-4521	252	1	[	[	X
easat-4521	252	2	11	11	NUM
easat-4521	252	3	]	]	X
easat-4521	252	4	e.	e.	PROPN
easat-4521	252	5	listiawati	listiawati	PROPN
easat-4521	252	6	and	and	CCONJ
easat-4521	252	7	d.	d.	PROPN
easat-4521	252	8	juniati	juniati	PROPN
easat-4521	252	9	,	,	PUNCT
easat-4521	252	10	"	"	PUNCT
easat-4521	252	11	an	an	DET
easat-4521	252	12	apos	apos	NOUN
easat-4521	252	13	analysis	analysis	NOUN
easat-4521	252	14	of	of	ADP
easat-4521	252	15	student	student	NOUN
easat-4521	252	16	’s	’s	PART
easat-4521	252	17	understanding	understanding	NOUN
easat-4521	252	18	of	of	ADP
easat-4521	252	19	quadratic	quadratic	ADJ
easat-4521	252	20	function	function	NOUN
easat-4521	252	21	graph	graph	NOUN
easat-4521	252	22	,	,	PUNCT
easat-4521	252	23	"	"	PUNCT
easat-4521	252	24	in	in	ADP
easat-4521	252	25	journal	journal	NOUN
easat-4521	252	26	of	of	ADP
easat-4521	252	27	physics	physics	PROPN
easat-4521	252	28	:	:	PUNCT
easat-4521	252	29	conference	conference	NOUN
easat-4521	252	30	series	series	NOUN
easat-4521	252	31	.	.	PUNCT
easat-4521	253	1	https://doi.org/10.1088/1742-6596/1747/1/012028	https://doi.org/10.1088/1742-6596/1747/1/012028	PROPN
easat-4521	253	2	,	,	PUNCT
easat-4521	253	3	2021	2021	NUM
easat-4521	253	4	,	,	PUNCT
easat-4521	253	5	vol	vol	NOUN
easat-4521	253	6	.	.	PROPN
easat-4521	253	7	1747	1747	NUM
easat-4521	253	8	,	,	PUNCT
easat-4521	253	9	no	no	INTJ
easat-4521	253	10	.	.	NOUN
easat-4521	253	11	1	1	NUM
easat-4521	253	12	:	:	PUNCT
easat-4521	253	13	iop	iop	NOUN
easat-4521	253	14	publishing	publishing	NOUN
easat-4521	253	15	,	,	PUNCT
easat-4521	253	16	p.	p.	NOUN
easat-4521	253	17	012028	012028	NUM
easat-4521	253	18	.	.	PUNCT
easat-4521	254	1	[	[	X
easat-4521	254	2	12	12	NUM
easat-4521	254	3	]	]	PUNCT
easat-4521	254	4	k.	k.	PROPN
easat-4521	254	5	moon	moon	PROPN
easat-4521	254	6	,	,	PUNCT
easat-4521	254	7	"	"	PUNCT
easat-4521	254	8	graphs	graph	NOUN
easat-4521	254	9	of	of	ADP
easat-4521	254	10	two	two	NUM
easat-4521	254	11	variable	variable	ADJ
easat-4521	254	12	inequalities	inequality	NOUN
easat-4521	254	13	:	:	PUNCT
easat-4521	254	14	alternate	alternate	ADJ
easat-4521	254	15	approaches	approach	NOUN
easat-4521	254	16	to	to	ADP
easat-4521	254	17	the	the	DET
easat-4521	254	18	solution	solution	NOUN
easat-4521	254	19	test	test	NOUN
easat-4521	254	20	,	,	PUNCT
easat-4521	254	21	"	"	PUNCT
easat-4521	254	22	the	the	DET
easat-4521	254	23	mathematics	mathematic	NOUN
easat-4521	254	24	enthusiast	enthusiast	NOUN
easat-4521	254	25	,	,	PUNCT
easat-4521	254	26	vol	vol	NOUN
easat-4521	254	27	.	.	PROPN
easat-4521	254	28	16	16	NUM
easat-4521	254	29	,	,	PUNCT
easat-4521	254	30	no	no	INTJ
easat-4521	254	31	.	.	NOUN
easat-4521	254	32	1	1	NUM
easat-4521	254	33	,	,	PUNCT
easat-4521	254	34	pp	pp	ADJ
easat-4521	254	35	.	.	PUNCT
easat-4521	255	1	107	107	NUM
easat-4521	255	2	-	-	SYM
easat-4521	255	3	126	126	NUM
easat-4521	255	4	,	,	PUNCT
easat-4521	255	5	2019	2019	NUM
easat-4521	255	6	.	.	PUNCT
easat-4521	256	1	https://doi.org/10.54870/1551-3440.1452	https://doi.org/10.54870/1551-3440.1452	NOUN
easat-4521	257	1	[	[	X
easat-4521	257	2	13	13	NUM
easat-4521	257	3	]	]	PUNCT
easat-4521	257	4	l.	l.	PROPN
easat-4521	257	5	h.	h.	PROPN
easat-4521	257	6	n.	n.	PROPN
easat-4521	257	7	mutambara	mutambara	PROPN
easat-4521	257	8	,	,	PUNCT
easat-4521	257	9	j.	j.	PROPN
easat-4521	257	10	tendere	tendere	ADV
easat-4521	257	11	,	,	PUNCT
easat-4521	257	12	and	and	CCONJ
easat-4521	257	13	c.	c.	PROPN
easat-4521	257	14	j.	j.	PROPN
easat-4521	257	15	chagwiza	chagwiza	PROPN
easat-4521	257	16	,	,	PUNCT
easat-4521	257	17	"	"	PUNCT
easat-4521	257	18	exploring	explore	VERB
easat-4521	257	19	the	the	DET
easat-4521	257	20	conceptual	conceptual	ADJ
easat-4521	257	21	understanding	understanding	NOUN
easat-4521	257	22	of	of	ADP
easat-4521	257	23	the	the	DET
easat-4521	257	24	quadratic	quadratic	ADJ
easat-4521	257	25	function	function	NOUN
easat-4521	257	26	concept	concept	NOUN
easat-4521	257	27	in	in	ADP
easat-4521	257	28	teachers	teacher	NOUN
easat-4521	257	29	’	'	PUNCT
easat-4521	257	30	colleges	college	NOUN
easat-4521	257	31	in	in	ADP
easat-4521	257	32	zimbabwe	zimbabwe	NOUN
easat-4521	257	33	,	,	PUNCT
easat-4521	257	34	"	"	PUNCT
easat-4521	257	35	eurasia	eurasia	PROPN
easat-4521	257	36	journal	journal	PROPN
easat-4521	257	37	of	of	ADP
easat-4521	257	38	mathematics	mathematics	PROPN
easat-4521	257	39	,	,	PUNCT
easat-4521	257	40	science	science	NOUN
easat-4521	257	41	and	and	CCONJ
easat-4521	257	42	technology	technology	NOUN
easat-4521	257	43	education	education	NOUN
easat-4521	257	44	,	,	PUNCT
easat-4521	257	45	vol	vol	NOUN
easat-4521	257	46	.	.	PROPN
easat-4521	257	47	16	16	NUM
easat-4521	257	48	,	,	PUNCT
easat-4521	257	49	no	no	INTJ
easat-4521	257	50	.	.	NOUN
easat-4521	257	51	2	2	NUM
easat-4521	257	52	,	,	PUNCT
easat-4521	257	53	pp	pp	ADJ
easat-4521	257	54	.	.	PUNCT
easat-4521	258	1	1–17	1–17	NOUN
easat-4521	258	2	,	,	PUNCT
easat-4521	258	3	2020	2020	NUM
easat-4521	258	4	.	.	PUNCT
easat-4521	259	1	https://doi.org/10.29333/ejmste/112617	https://doi.org/10.29333/ejmste/112617	PROPN
easat-4521	259	2	[	[	X
easat-4521	259	3	14	14	NUM
easat-4521	259	4	]	]	X
easat-4521	259	5	c.	c.	PROPN
easat-4521	259	6	fuentealba	fuentealba	PROPN
easat-4521	259	7	,	,	PUNCT
easat-4521	259	8	e.	e.	PROPN
easat-4521	259	9	badillo	badillo	PROPN
easat-4521	259	10	,	,	PUNCT
easat-4521	259	11	g.	g.	PROPN
easat-4521	259	12	sánchez	sánchez	PROPN
easat-4521	259	13	-	-	PUNCT
easat-4521	259	14	matamoros	matamoros	PROPN
easat-4521	259	15	,	,	PUNCT
easat-4521	259	16	and	and	CCONJ
easat-4521	259	17	a.	a.	NOUN
easat-4521	259	18	cárcamo	cárcamo	PROPN
easat-4521	259	19	,	,	PUNCT
easat-4521	259	20	"	"	PUNCT
easat-4521	259	21	the	the	DET
easat-4521	259	22	understanding	understanding	NOUN
easat-4521	259	23	of	of	ADP
easat-4521	259	24	the	the	DET
easat-4521	259	25	derivative	derivative	ADJ
easat-4521	259	26	concept	concept	NOUN
easat-4521	259	27	in	in	ADP
easat-4521	259	28	higher	high	ADJ
easat-4521	259	29	education	education	NOUN
easat-4521	259	30	,	,	PUNCT
easat-4521	259	31	"	"	PUNCT
easat-4521	259	32	eurasia	eurasia	PROPN
easat-4521	259	33	journal	journal	PROPN
easat-4521	259	34	of	of	ADP
easat-4521	259	35	mathematics	mathematics	PROPN
easat-4521	259	36	,	,	PUNCT
easat-4521	259	37	science	science	NOUN
easat-4521	259	38	and	and	CCONJ
easat-4521	259	39	technology	technology	NOUN
easat-4521	259	40	education	education	NOUN
easat-4521	259	41	,	,	PUNCT
easat-4521	259	42	vol	vol	NOUN
easat-4521	259	43	.	.	PROPN
easat-4521	259	44	15	15	NUM
easat-4521	259	45	,	,	PUNCT
easat-4521	259	46	no	no	INTJ
easat-4521	259	47	.	.	NOUN
easat-4521	259	48	2	2	NUM
easat-4521	259	49	,	,	PUNCT
easat-4521	259	50	p.	p.	NOUN
easat-4521	259	51	em1662	em1662	NOUN
easat-4521	259	52	,	,	PUNCT
easat-4521	259	53	2018	2018	NUM
easat-4521	259	54	.	.	PUNCT
easat-4521	260	1	https://doi.org/10.29333/ejmste/100640	https://doi.org/10.29333/ejmste/100640	PUNCT
easat-4521	261	1	[	[	X
easat-4521	261	2	15	15	NUM
easat-4521	261	3	]	]	PUNCT
easat-4521	261	4	k.	k.	PROPN
easat-4521	261	5	umam	umam	PROPN
easat-4521	261	6	and	and	CCONJ
easat-4521	261	7	a.	a.	PROPN
easat-4521	261	8	d.	d.	PROPN
easat-4521	261	9	susandi	susandi	PROPN
easat-4521	261	10	,	,	PUNCT
easat-4521	261	11	"	"	PUNCT
easat-4521	261	12	critical	critical	ADJ
easat-4521	261	13	thinking	thinking	NOUN
easat-4521	261	14	skills	skill	NOUN
easat-4521	261	15	:	:	PUNCT
easat-4521	261	16	error	error	NOUN
easat-4521	261	17	identifications	identification	NOUN
easat-4521	261	18	on	on	ADP
easat-4521	261	19	students	student	NOUN
easat-4521	261	20	’	'	PUNCT
easat-4521	261	21	with	with	ADP
easat-4521	261	22	apos	apos	PROPN
easat-4521	261	23	theory	theory	NOUN
easat-4521	261	24	,	,	PUNCT
easat-4521	261	25	"	"	PUNCT
easat-4521	261	26	international	international	ADJ
easat-4521	261	27	journal	journal	NOUN
easat-4521	261	28	of	of	ADP
easat-4521	261	29	evaluation	evaluation	NOUN
easat-4521	261	30	and	and	CCONJ
easat-4521	261	31	research	research	NOUN
easat-4521	261	32	in	in	ADP
easat-4521	261	33	education	education	NOUN
easat-4521	261	34	,	,	PUNCT
easat-4521	261	35	vol	vol	NOUN
easat-4521	261	36	.	.	PROPN
easat-4521	261	37	11	11	NUM
easat-4521	261	38	,	,	PUNCT
easat-4521	261	39	no	no	INTJ
easat-4521	261	40	.	.	NOUN
easat-4521	261	41	1	1	NUM
easat-4521	261	42	,	,	PUNCT
easat-4521	261	43	pp	pp	ADJ
easat-4521	261	44	.	.	PUNCT
easat-4521	262	1	182	182	NUM
easat-4521	262	2	-	-	SYM
easat-4521	262	3	192	192	NUM
easat-4521	262	4	,	,	PUNCT
easat-4521	262	5	2022	2022	NUM
easat-4521	262	6	.	.	PUNCT
easat-4521	263	1	https://doi.org/10.11591/ijere.v11i1.21171	https://doi.org/10.11591/ijere.v11i1.21171	X
easat-4521	264	1	[	[	X
easat-4521	264	2	16	16	NUM
easat-4521	264	3	]	]	PUNCT
easat-4521	264	4	v.	v.	PROPN
easat-4521	264	5	borji	borji	PROPN
easat-4521	264	6	,	,	PUNCT
easat-4521	264	7	h.	h.	PROPN
easat-4521	264	8	alamolhodaei	alamolhodaei	PROPN
easat-4521	264	9	,	,	PUNCT
easat-4521	264	10	and	and	CCONJ
easat-4521	264	11	f.	f.	PROPN
easat-4521	264	12	radmehr	radmehr	PROPN
easat-4521	264	13	,	,	PUNCT
easat-4521	264	14	"	"	PUNCT
easat-4521	264	15	application	application	NOUN
easat-4521	264	16	of	of	ADP
easat-4521	264	17	the	the	DET
easat-4521	264	18	apos	apos	NOUN
easat-4521	264	19	-	-	PUNCT
easat-4521	264	20	ace	ace	NOUN
easat-4521	264	21	theory	theory	NOUN
easat-4521	264	22	to	to	PART
easat-4521	264	23	improve	improve	VERB
easat-4521	264	24	students	student	NOUN
easat-4521	264	25	’	'	PUNCT
easat-4521	264	26	graphical	graphical	ADJ
easat-4521	264	27	understanding	understanding	NOUN
easat-4521	264	28	of	of	ADP
easat-4521	264	29	derivative	derivative	NOUN
easat-4521	264	30	,	,	PUNCT
easat-4521	264	31	"	"	PUNCT
easat-4521	264	32	eurasia	eurasia	PROPN
easat-4521	264	33	journal	journal	PROPN
easat-4521	264	34	of	of	ADP
easat-4521	264	35	mathematics	mathematics	PROPN
easat-4521	264	36	,	,	PUNCT
easat-4521	264	37	science	science	NOUN
easat-4521	264	38	and	and	CCONJ
easat-4521	264	39	technology	technology	NOUN
easat-4521	264	40	education	education	NOUN
easat-4521	264	41	,	,	PUNCT
easat-4521	264	42	vol	vol	NOUN
easat-4521	264	43	.	.	PROPN
easat-4521	264	44	14	14	NUM
easat-4521	264	45	,	,	PUNCT
easat-4521	264	46	no	no	INTJ
easat-4521	264	47	.	.	NOUN
easat-4521	264	48	7	7	NUM
easat-4521	264	49	,	,	PUNCT
easat-4521	264	50	pp	pp	ADJ
easat-4521	264	51	.	.	PUNCT
easat-4521	264	52	29472967	29472967	NUM
easat-4521	264	53	,	,	PUNCT
easat-4521	264	54	2018	2018	NUM
easat-4521	264	55	.	.	PUNCT
easat-4521	265	1	https://doi.org/10.29333/ejmste/91451	https://doi.org/10.29333/ejmste/91451	PROPN
easat-4521	266	1	[	[	X
easat-4521	266	2	17	17	NUM
easat-4521	266	3	]	]	PUNCT
easat-4521	266	4	a.	a.	NOUN
easat-4521	266	5	prihandhika	prihandhika	NOUN
easat-4521	266	6	,	,	PUNCT
easat-4521	266	7	s.	s.	PROPN
easat-4521	266	8	prabawanto	prabawanto	PROPN
easat-4521	266	9	,	,	PUNCT
easat-4521	266	10	t.	t.	PROPN
easat-4521	266	11	turmudi	turmudi	PROPN
easat-4521	266	12	,	,	PUNCT
easat-4521	266	13	and	and	CCONJ
easat-4521	266	14	d.	d.	PROPN
easat-4521	266	15	suryadi	suryadi	PROPN
easat-4521	266	16	,	,	PUNCT
easat-4521	266	17	"	"	PUNCT
easat-4521	266	18	epistemological	epistemological	ADJ
easat-4521	266	19	obstacles	obstacle	NOUN
easat-4521	266	20	:	:	PUNCT
easat-4521	266	21	an	an	DET
easat-4521	266	22	overview	overview	NOUN
easat-4521	266	23	of	of	ADP
easat-4521	266	24	thinking	thinking	NOUN
easat-4521	266	25	process	process	NOUN
easat-4521	266	26	on	on	ADP
easat-4521	266	27	derivative	derivative	ADJ
easat-4521	266	28	concepts	concept	NOUN
easat-4521	266	29	by	by	ADP
easat-4521	266	30	apos	apos	NOUN
easat-4521	266	31	theory	theory	NOUN
easat-4521	266	32	and	and	CCONJ
easat-4521	266	33	clinical	clinical	ADJ
easat-4521	266	34	interview	interview	NOUN
easat-4521	266	35	,	,	PUNCT
easat-4521	266	36	"	"	PUNCT
easat-4521	266	37	journal	journal	NOUN
easat-4521	266	38	of	of	ADP
easat-4521	266	39	physics	physics	PROPN
easat-4521	266	40	:	:	PUNCT
easat-4521	266	41	conference	conference	NOUN
easat-4521	266	42	series	series	NOUN
easat-4521	266	43	,	,	PUNCT
easat-4521	266	44	vol	vol	NOUN
easat-4521	266	45	.	.	PROPN
easat-4521	266	46	1521	1521	NUM
easat-4521	266	47	,	,	PUNCT
easat-4521	266	48	no	no	INTJ
easat-4521	266	49	.	.	NOUN
easat-4521	266	50	3	3	NUM
easat-4521	266	51	,	,	PUNCT
easat-4521	266	52	2020	2020	NUM
easat-4521	266	53	.	.	PUNCT
easat-4521	266	54	https://doi.org/10.1088/1742-6596/1521/3/032028	https://doi.org/10.1088/1742-6596/1521/3/032028	X
easat-4521	267	1	[	[	X
easat-4521	267	2	18	18	NUM
easat-4521	267	3	]	]	PUNCT
easat-4521	267	4	m.	m.	NOUN
easat-4521	267	5	g.	g.	PROPN
easat-4521	267	6	baye	baye	PROPN
easat-4521	267	7	,	,	PUNCT
easat-4521	267	8	m.	m.	NOUN
easat-4521	267	9	a.	a.	NOUN
easat-4521	267	10	ayele	ayele	PROPN
easat-4521	267	11	,	,	PUNCT
easat-4521	267	12	and	and	CCONJ
easat-4521	267	13	t.	t.	PROPN
easat-4521	267	14	e.	e.	PROPN
easat-4521	267	15	wondimuneh	wondimuneh	PROPN
easat-4521	267	16	,	,	PUNCT
easat-4521	267	17	"	"	PUNCT
easat-4521	267	18	implementing	implement	VERB
easat-4521	267	19	geogebra	geogebra	NOUN
easat-4521	267	20	integrated	integrate	VERB
easat-4521	267	21	with	with	ADP
easat-4521	267	22	multi	multi	ADJ
easat-4521	267	23	-	-	ADJ
easat-4521	267	24	teaching	teaching	ADJ
easat-4521	267	25	approaches	approach	NOUN
easat-4521	267	26	guided	guide	VERB
easat-4521	267	27	by	by	ADP
easat-4521	267	28	the	the	DET
easat-4521	267	29	apos	apos	PROPN
easat-4521	267	30	theory	theory	NOUN
easat-4521	267	31	to	to	PART
easat-4521	267	32	enhance	enhance	VERB
easat-4521	267	33	students	student	NOUN
easat-4521	267	34	’	'	PUNCT
easat-4521	267	35	conceptual	conceptual	ADJ
easat-4521	267	36	understanding	understanding	NOUN
easat-4521	267	37	of	of	ADP
easat-4521	267	38	limit	limit	NOUN
easat-4521	267	39	in	in	ADP
easat-4521	267	40	ethiopian	ethiopian	ADJ
easat-4521	267	41	universities	university	NOUN
easat-4521	267	42	,	,	PUNCT
easat-4521	267	43	"	"	PUNCT
easat-4521	267	44	heliyon	heliyon	NOUN
easat-4521	267	45	,	,	PUNCT
easat-4521	267	46	vol	vol	NOUN
easat-4521	267	47	.	.	PROPN
easat-4521	267	48	7	7	NUM
easat-4521	267	49	,	,	PUNCT
easat-4521	267	50	no	no	INTJ
easat-4521	267	51	.	.	NOUN
easat-4521	267	52	5	5	NUM
easat-4521	267	53	,	,	PUNCT
easat-4521	267	54	p.	p.	NOUN
easat-4521	267	55	e07012	e07012	PROPN
easat-4521	267	56	,	,	PUNCT
easat-4521	267	57	2021	2021	NUM
easat-4521	267	58	.	.	PUNCT
easat-4521	268	1	https://doi.org/10.1016/j.heliyon.2021.e07012	https://doi.org/10.1016/j.heliyon.2021.e07012	X
easat-4521	269	1	[	[	X
easat-4521	269	2	19	19	NUM
easat-4521	269	3	]	]	PUNCT
easat-4521	269	4	a.	a.	PROPN
easat-4521	269	5	devine	devine	PROPN
easat-4521	269	6	,	,	PUNCT
easat-4521	269	7	k.	k.	PROPN
easat-4521	269	8	fawcett	fawcett	PROPN
easat-4521	269	9	,	,	PUNCT
easat-4521	269	10	d.	d.	PROPN
easat-4521	269	11	szűcs	szűcs	PROPN
easat-4521	269	12	,	,	PUNCT
easat-4521	269	13	and	and	CCONJ
easat-4521	269	14	a.	a.	NOUN
easat-4521	269	15	dowker	dowker	PROPN
easat-4521	269	16	,	,	PUNCT
easat-4521	269	17	"	"	PUNCT
easat-4521	269	18	gender	gender	NOUN
easat-4521	269	19	differences	difference	NOUN
easat-4521	269	20	in	in	ADP
easat-4521	269	21	mathematics	mathematics	NOUN
easat-4521	269	22	anxiety	anxiety	NOUN
easat-4521	269	23	and	and	CCONJ
easat-4521	269	24	the	the	DET
easat-4521	269	25	relation	relation	NOUN
easat-4521	269	26	to	to	ADP
easat-4521	269	27	mathematics	mathematics	NOUN
easat-4521	269	28	performance	performance	NOUN
easat-4521	269	29	while	while	SCONJ
easat-4521	269	30	controlling	control	VERB
easat-4521	269	31	for	for	ADP
easat-4521	269	32	test	test	NOUN
easat-4521	269	33	anxiety	anxiety	NOUN
easat-4521	269	34	,	,	PUNCT
easat-4521	269	35	"	"	PUNCT
easat-4521	269	36	behavioral	behavioral	ADJ
easat-4521	269	37	and	and	CCONJ
easat-4521	269	38	brain	brain	NOUN
easat-4521	269	39	functions	function	NOUN
easat-4521	269	40	,	,	PUNCT
easat-4521	269	41	vol	vol	NOUN
easat-4521	269	42	.	.	PROPN
easat-4521	269	43	8	8	NUM
easat-4521	269	44	,	,	PUNCT
easat-4521	269	45	pp	pp	ADJ
easat-4521	269	46	.	.	PUNCT
easat-4521	270	1	1	1	NUM
easat-4521	270	2	-	-	SYM
easat-4521	270	3	9	9	NUM
easat-4521	270	4	,	,	PUNCT
easat-4521	270	5	2012	2012	NUM
easat-4521	270	6	.	.	PUNCT
easat-4521	271	1	https://doi.org/10.1186/1744-9081-8-33	https://doi.org/10.1186/1744-9081-8-33	X
easat-4521	272	1	[	[	X
easat-4521	272	2	20	20	NUM
easat-4521	272	3	]	]	PUNCT
easat-4521	272	4	m.-l	m.-l	PROPN
easat-4521	272	5	.	.	PUNCT
easat-4521	273	1	parmentier	parmentier	NOUN
easat-4521	273	2	,	,	PUNCT
easat-4521	273	3	k.	k.	PROPN
easat-4521	273	4	weiss	weiss	PROPN
easat-4521	273	5	,	,	PUNCT
easat-4521	273	6	a.	a.	PROPN
easat-4521	273	7	aroua	aroua	PROPN
easat-4521	273	8	,	,	PUNCT
easat-4521	273	9	c.	c.	NOUN
easat-4521	273	10	betry	betry	NOUN
easat-4521	273	11	,	,	PUNCT
easat-4521	273	12	m.	m.	NOUN
easat-4521	273	13	rivière	rivière	PROPN
easat-4521	273	14	,	,	PUNCT
easat-4521	273	15	and	and	CCONJ
easat-4521	273	16	o.	o.	PROPN
easat-4521	273	17	navarro	navarro	PROPN
easat-4521	273	18	,	,	PUNCT
easat-4521	273	19	"	"	PUNCT
easat-4521	273	20	the	the	DET
easat-4521	273	21	influence	influence	NOUN
easat-4521	273	22	of	of	ADP
easat-4521	273	23	environmental	environmental	ADJ
easat-4521	273	24	crisis	crisis	NOUN
easat-4521	273	25	perception	perception	NOUN
easat-4521	273	26	and	and	CCONJ
easat-4521	273	27	trait	trait	NOUN
easat-4521	273	28	anxiety	anxiety	NOUN
easat-4521	273	29	on	on	ADP
easat-4521	273	30	the	the	DET
easat-4521	273	31	level	level	NOUN
easat-4521	273	32	of	of	ADP
easat-4521	273	33	eco	eco	PROPN
easat-4521	273	34	-	-	PUNCT
easat-4521	273	35	worry	worry	NOUN
easat-4521	273	36	and	and	CCONJ
easat-4521	273	37	climate	climate	NOUN
easat-4521	273	38	anxiety	anxiety	NOUN
easat-4521	273	39	,	,	PUNCT
easat-4521	273	40	"	"	PUNCT
easat-4521	273	41	journal	journal	NOUN
easat-4521	273	42	of	of	ADP
easat-4521	273	43	anxiety	anxiety	NOUN
easat-4521	273	44	disorders	disorder	NOUN
easat-4521	273	45	,	,	PUNCT
easat-4521	273	46	vol	vol	NOUN
easat-4521	273	47	.	.	PROPN
easat-4521	274	1	101	101	NUM
easat-4521	274	2	,	,	PUNCT
easat-4521	274	3	p.	p.	NOUN
easat-4521	274	4	102799	102799	NUM
easat-4521	274	5	,	,	PUNCT
easat-4521	274	6	2024	2024	NUM
easat-4521	274	7	.	.	PUNCT
easat-4521	275	1	https://doi.org/10.1016/j.janxdis.2023.102799	https://doi.org/10.1016/j.janxdis.2023.102799	PROPN
easat-4521	275	2	[	[	X
easat-4521	275	3	21	21	NUM
easat-4521	275	4	]	]	X
easat-4521	275	5	e.	e.	PROPN
easat-4521	275	6	commodari	commodari	PROPN
easat-4521	275	7	and	and	CCONJ
easat-4521	275	8	v.	v.	ADP
easat-4521	275	9	l.	l.	PROPN
easat-4521	275	10	la	la	PROPN
easat-4521	275	11	rosa	rosa	PROPN
easat-4521	275	12	,	,	PUNCT
easat-4521	275	13	"	"	PUNCT
easat-4521	275	14	general	general	ADJ
easat-4521	275	15	academic	academic	ADJ
easat-4521	275	16	anxiety	anxiety	NOUN
easat-4521	275	17	and	and	CCONJ
easat-4521	275	18	math	math	NOUN
easat-4521	275	19	anxiety	anxiety	NOUN
easat-4521	275	20	in	in	ADP
easat-4521	275	21	primary	primary	ADJ
easat-4521	275	22	school	school	NOUN
easat-4521	275	23	.	.	PUNCT
easat-4521	276	1	the	the	DET
easat-4521	276	2	impact	impact	NOUN
easat-4521	276	3	of	of	ADP
easat-4521	276	4	math	math	NOUN
easat-4521	276	5	anxiety	anxiety	NOUN
easat-4521	276	6	on	on	ADP
easat-4521	276	7	calculation	calculation	NOUN
easat-4521	276	8	skills	skill	NOUN
easat-4521	276	9	,	,	PUNCT
easat-4521	276	10	"	"	PUNCT
easat-4521	276	11	acta	acta	PROPN
easat-4521	276	12	psychologica	psychologica	PROPN
easat-4521	276	13	,	,	PUNCT
easat-4521	276	14	vol	vol	NOUN
easat-4521	276	15	.	.	NOUN
easat-4521	276	16	220	220	NUM
easat-4521	276	17	,	,	PUNCT
easat-4521	276	18	p.	p.	NOUN
easat-4521	276	19	103413	103413	NUM
easat-4521	276	20	,	,	PUNCT
easat-4521	276	21	2021	2021	NUM
easat-4521	276	22	.	.	PUNCT
easat-4521	277	1	https://doi.org/10.1016/j.actpsy.2021.103413	https://doi.org/10.1016/j.actpsy.2021.103413	PROPN
easat-4521	277	2	[	[	X
easat-4521	277	3	22	22	NUM
easat-4521	277	4	]	]	PUNCT
easat-4521	277	5	v.	v.	X
easat-4521	277	6	gashaj	gashaj	PROPN
easat-4521	277	7	,	,	PUNCT
easat-4521	277	8	q.	q.	PROPN
easat-4521	277	9	thaqi	thaqi	PROPN
easat-4521	277	10	,	,	PUNCT
easat-4521	277	11	f.	f.	PROPN
easat-4521	277	12	w.	w.	PROPN
easat-4521	277	13	mast	mast	PROPN
easat-4521	277	14	,	,	PUNCT
easat-4521	277	15	and	and	CCONJ
easat-4521	277	16	c.	c.	PROPN
easat-4521	277	17	m.	m.	PROPN
easat-4521	277	18	roebers	roeber	NOUN
easat-4521	277	19	,	,	PUNCT
easat-4521	277	20	"	"	PUNCT
easat-4521	277	21	foundations	foundation	NOUN
easat-4521	277	22	for	for	ADP
easat-4521	277	23	future	future	ADJ
easat-4521	277	24	math	math	NOUN
easat-4521	277	25	achievement	achievement	NOUN
easat-4521	277	26	:	:	PUNCT
easat-4521	277	27	early	early	ADJ
easat-4521	277	28	numeracy	numeracy	NOUN
easat-4521	277	29	,	,	PUNCT
easat-4521	277	30	home	home	NOUN
easat-4521	277	31	learning	learn	VERB
easat-4521	277	32	environment	environment	NOUN
easat-4521	277	33	,	,	PUNCT
easat-4521	277	34	and	and	CCONJ
easat-4521	277	35	the	the	DET
easat-4521	277	36	absence	absence	NOUN
easat-4521	277	37	of	of	ADP
easat-4521	277	38	math	math	NOUN
easat-4521	277	39	anxiety	anxiety	NOUN
easat-4521	277	40	,	,	PUNCT
easat-4521	277	41	"	"	PUNCT
easat-4521	277	42	trends	trend	NOUN
easat-4521	277	43	in	in	ADP
easat-4521	277	44	neuroscience	neuroscience	NOUN
easat-4521	277	45	and	and	CCONJ
easat-4521	277	46	education	education	NOUN
easat-4521	277	47	,	,	PUNCT
easat-4521	277	48	vol	vol	NOUN
easat-4521	277	49	.	.	PROPN
easat-4521	277	50	33	33	NUM
easat-4521	277	51	,	,	PUNCT
easat-4521	277	52	p.	p.	NOUN
easat-4521	277	53	100217	100217	NUM
easat-4521	277	54	,	,	PUNCT
easat-4521	277	55	2023	2023	NUM
easat-4521	277	56	.	.	PUNCT
easat-4521	278	1	https://doi.org/10.1016/j.tine.2023.100217	https://doi.org/10.1016/j.tine.2023.100217	NOUN
easat-4521	279	1	[	[	X
easat-4521	279	2	23	23	NUM
easat-4521	279	3	]	]	X
easat-4521	279	4	r.	r.	PROPN
easat-4521	279	5	wahyuni	wahyuni	PROPN
easat-4521	279	6	,	,	PUNCT
easat-4521	279	7	d.	d.	PROPN
easat-4521	279	8	juniati	juniati	PROPN
easat-4521	279	9	,	,	PUNCT
easat-4521	279	10	and	and	CCONJ
easat-4521	279	11	p.	p.	NOUN
easat-4521	279	12	wijayanti	wijayanti	PROPN
easat-4521	279	13	,	,	PUNCT
easat-4521	279	14	"	"	PUNCT
easat-4521	279	15	how	how	SCONJ
easat-4521	279	16	do	do	AUX
easat-4521	279	17	math	math	NOUN
easat-4521	279	18	anxiety	anxiety	NOUN
easat-4521	279	19	and	and	CCONJ
easat-4521	279	20	self	self	NOUN
easat-4521	279	21	-	-	PUNCT
easat-4521	279	22	confidence	confidence	NOUN
easat-4521	279	23	affect	affect	VERB
easat-4521	279	24	mathematical	mathematical	ADJ
easat-4521	279	25	problem	problem	NOUN
easat-4521	279	26	solving	solve	VERB
easat-4521	279	27	?	?	PUNCT
easat-4521	279	28	,	,	PUNCT
easat-4521	279	29	"	"	PUNCT
easat-4521	279	30	tem	tem	PROPN
easat-4521	279	31	journal	journal	NOUN
easat-4521	279	32	,	,	PUNCT
easat-4521	279	33	vol	vol	NOUN
easat-4521	279	34	.	.	PROPN
easat-4521	279	35	13	13	NUM
easat-4521	279	36	,	,	PUNCT
easat-4521	279	37	no	no	INTJ
easat-4521	279	38	.	.	NOUN
easat-4521	279	39	1	1	NUM
easat-4521	279	40	,	,	PUNCT
easat-4521	279	41	pp	pp	ADJ
easat-4521	279	42	.	.	PUNCT
easat-4521	280	1	550–560	550–560	NUM
easat-4521	280	2	,	,	PUNCT
easat-4521	280	3	2024	2024	NUM
easat-4521	280	4	.	.	PUNCT
easat-4521	281	1	https://doi.org/10.18421/tem131-58	https://doi.org/10.18421/tem131-58	NOUN
easat-4521	282	1	[	[	X
easat-4521	282	2	24	24	NUM
easat-4521	282	3	]	]	PUNCT
easat-4521	282	4	d.	d.	PROPN
easat-4521	282	5	juniati	juniati	PROPN
easat-4521	282	6	and	and	CCONJ
easat-4521	282	7	i.	i.	PROPN
easat-4521	282	8	k.	k.	PROPN
easat-4521	282	9	budayasa	budayasa	PROPN
easat-4521	282	10	,	,	PUNCT
easat-4521	282	11	"	"	PUNCT
easat-4521	282	12	working	work	VERB
easat-4521	282	13	memory	memory	NOUN
easat-4521	282	14	capacity	capacity	NOUN
easat-4521	282	15	and	and	CCONJ
easat-4521	282	16	mathematics	mathematics	NOUN
easat-4521	282	17	anxiety	anxiety	NOUN
easat-4521	282	18	of	of	ADP
easat-4521	282	19	mathematics	mathematic	NOUN
easat-4521	282	20	undergraduate	undergraduate	NOUN
easat-4521	282	21	students	student	NOUN
easat-4521	282	22	and	and	CCONJ
easat-4521	282	23	its	its	PRON
easat-4521	282	24	effect	effect	NOUN
easat-4521	282	25	on	on	ADP
easat-4521	282	26	mathematics	mathematic	NOUN
easat-4521	282	27	achievement	achievement	NOUN
easat-4521	282	28	,	,	PUNCT
easat-4521	282	29	"	"	PUNCT
easat-4521	282	30	journal	journal	NOUN
easat-4521	282	31	for	for	ADP
easat-4521	282	32	the	the	DET
easat-4521	282	33	education	education	NOUN
easat-4521	282	34	of	of	ADP
easat-4521	282	35	gifted	gifted	ADJ
easat-4521	282	36	young	young	ADJ
easat-4521	282	37	scientists	scientist	NOUN
easat-4521	282	38	,	,	PUNCT
easat-4521	282	39	vol	vol	NOUN
easat-4521	282	40	.	.	PROPN
easat-4521	282	41	8	8	NUM
easat-4521	282	42	,	,	PUNCT
easat-4521	282	43	no	no	INTJ
easat-4521	282	44	.	.	NOUN
easat-4521	282	45	1	1	NUM
easat-4521	282	46	,	,	PUNCT
easat-4521	282	47	pp	pp	ADJ
easat-4521	282	48	.	.	PUNCT
easat-4521	283	1	271	271	NUM
easat-4521	283	2	-	-	SYM
easat-4521	283	3	290	290	NUM
easat-4521	283	4	,	,	PUNCT
easat-4521	283	5	2020	2020	NUM
easat-4521	283	6	.	.	PUNCT
easat-4521	284	1	https://doi.org/10.17478/jegys.653518	https://doi.org/10.17478/jegys.653518	PROPN
easat-4521	285	1	[	[	X
easat-4521	285	2	25	25	NUM
easat-4521	285	3	]	]	PUNCT
easat-4521	285	4	l.	l.	PROPN
easat-4521	285	5	r.	r.	PROPN
easat-4521	285	6	pino	pino	PROPN
easat-4521	285	7	-	-	PUNCT
easat-4521	285	8	fan	fan	PROPN
easat-4521	285	9	,	,	PUNCT
easat-4521	285	10	v.	v.	ADP
easat-4521	285	11	font	font	NOUN
easat-4521	285	12	,	,	PUNCT
easat-4521	285	13	w.	w.	PROPN
easat-4521	285	14	gordillo	gordillo	PROPN
easat-4521	285	15	,	,	PUNCT
easat-4521	285	16	v.	v.	CCONJ
easat-4521	285	17	larios	lario	NOUN
easat-4521	285	18	,	,	PUNCT
easat-4521	285	19	and	and	CCONJ
easat-4521	285	20	a.	a.	NOUN
easat-4521	285	21	breda	breda	PROPN
easat-4521	285	22	,	,	PUNCT
easat-4521	285	23	"	"	PUNCT
easat-4521	285	24	analysis	analysis	NOUN
easat-4521	285	25	of	of	ADP
easat-4521	285	26	the	the	DET
easat-4521	285	27	meanings	meaning	NOUN
easat-4521	285	28	of	of	ADP
easat-4521	285	29	the	the	DET
easat-4521	285	30	antiderivative	antiderivative	ADJ
easat-4521	285	31	used	use	VERB
easat-4521	285	32	by	by	ADP
easat-4521	285	33	students	student	NOUN
easat-4521	285	34	of	of	ADP
easat-4521	285	35	the	the	DET
easat-4521	285	36	first	first	ADJ
easat-4521	285	37	engineering	engineering	NOUN
easat-4521	285	38	courses	course	NOUN
easat-4521	285	39	,	,	PUNCT
easat-4521	285	40	"	"	PUNCT
easat-4521	285	41	international	international	ADJ
easat-4521	285	42	journal	journal	NOUN
easat-4521	285	43	of	of	ADP
easat-4521	285	44	science	science	NOUN
easat-4521	285	45	and	and	CCONJ
easat-4521	285	46	mathematics	mathematic	NOUN
easat-4521	285	47	education	education	NOUN
easat-4521	285	48	,	,	PUNCT
easat-4521	285	49	vol	vol	NOUN
easat-4521	285	50	.	.	PROPN
easat-4521	285	51	16	16	NUM
easat-4521	285	52	,	,	PUNCT
easat-4521	285	53	pp	pp	ADJ
easat-4521	285	54	.	.	PUNCT
easat-4521	285	55	10911113	10911113	NUM
easat-4521	285	56	,	,	PUNCT
easat-4521	285	57	2018	2018	NUM
easat-4521	285	58	.	.	PUNCT
easat-4521	286	1	pino	pino	NOUN
easat-4521	286	2	-	-	PUNCT
easat-4521	286	3	fan	fan	PROPN
easat-4521	286	4	,	,	PUNCT
easat-4521	286	5	l.	l.	PROPN
easat-4521	286	6	r.	r.	PROPN
easat-4521	286	7	,	,	PUNCT
easat-4521	286	8	font	font	NOUN
easat-4521	286	9	,	,	PUNCT
easat-4521	286	10	v.	v.	ADV
easat-4521	286	11	,	,	PUNCT
easat-4521	286	12	gordillo	gordillo	PROPN
easat-4521	286	13	,	,	PUNCT
easat-4521	286	14	w.	w.	PROPN
easat-4521	286	15	,	,	PUNCT
easat-4521	286	16	larios	larios	PROPN
easat-4521	286	17	,	,	PUNCT
easat-4521	286	18	v.	v.	ADV
easat-4521	286	19	,	,	PUNCT
easat-4521	286	20	&	&	CCONJ
easat-4521	286	21	breda	breda	PROPN
easat-4521	286	22	,	,	PUNCT
easat-4521	286	23	a.	a.	NOUN
easat-4521	286	24	(	(	PUNCT
easat-4521	286	25	2018	2018	NUM
easat-4521	286	26	)	)	PUNCT
easat-4521	286	27	.	.	PUNCT
easat-4521	287	1	analysis	analysis	NOUN
easat-4521	287	2	of	of	ADP
easat-4521	287	3	the	the	DET
easat-4521	287	4	meanings	meaning	NOUN
easat-4521	287	5	of	of	ADP
easat-4521	287	6	the	the	DET
easat-4521	287	7	antiderivative	antiderivative	ADJ
easat-4521	287	8	used	use	VERB
easat-4521	287	9	by	by	ADP
easat-4521	287	10	students	student	NOUN
easat-4521	287	11	of	of	ADP
easat-4521	287	12	the	the	DET
easat-4521	287	13	first	first	ADJ
easat-4521	287	14	engineering	engineering	NOUN
easat-4521	287	15	courses	course	NOUN
easat-4521	287	16	.	.	PUNCT
easat-4521	288	1	international	international	ADJ
easat-4521	288	2	journal	journal	PROPN
easat-4521	288	3	of	of	ADP
easat-4521	288	4	science	science	NOUN
easat-4521	288	5	and	and	CCONJ
easat-4521	288	6	mathematics	mathematic	NOUN
easat-4521	288	7	education	education	NOUN
easat-4521	288	8	,	,	PUNCT
easat-4521	288	9	16(6	16(6	NUM
easat-4521	288	10	)	)	PUNCT
easat-4521	288	11	,	,	PUNCT
easat-4521	288	12	1091–1113	1091–1113	NUM
easat-4521	288	13	.	.	PUNCT
easat-4521	289	1	https://doi.org/10.1007/s10763-017-9826-2	https://doi.org/10.1007/s10763-017-9826-2	NUM
easat-4521	290	1	[	[	X
easat-4521	290	2	26	26	NUM
easat-4521	290	3	]	]	X
easat-4521	290	4	r.	r.	PROPN
easat-4521	290	5	wahyuni	wahyuni	PROPN
easat-4521	290	6	,	,	PUNCT
easat-4521	290	7	d.	d.	PROPN
easat-4521	290	8	juniati	juniati	PROPN
easat-4521	290	9	,	,	PUNCT
easat-4521	290	10	and	and	CCONJ
easat-4521	290	11	p.	p.	NOUN
easat-4521	290	12	wijayanti	wijayanti	PROPN
easat-4521	290	13	,	,	PUNCT
easat-4521	290	14	"	"	PUNCT
easat-4521	290	15	mathematics	mathematics	NOUN
easat-4521	290	16	anxiety	anxiety	NOUN
easat-4521	290	17	of	of	ADP
easat-4521	290	18	junior	junior	ADJ
easat-4521	290	19	high	high	ADJ
easat-4521	290	20	school	school	NOUN
easat-4521	290	21	students	student	NOUN
easat-4521	290	22	in	in	ADP
easat-4521	290	23	solving	solve	VERB
easat-4521	290	24	geometry	geometry	NOUN
easat-4521	290	25	problems	problem	NOUN
easat-4521	290	26	,	,	PUNCT
easat-4521	290	27	"	"	PUNCT
easat-4521	290	28	prospects	prospect	NOUN
easat-4521	290	29	of	of	ADP
easat-4521	290	30	science	science	NOUN
easat-4521	290	31	and	and	CCONJ
easat-4521	290	32	education	education	NOUN
easat-4521	290	33	,	,	PUNCT
easat-4521	290	34	vol	vol	NOUN
easat-4521	290	35	.	.	PROPN
easat-4521	290	36	71	71	NUM
easat-4521	290	37	,	,	PUNCT
easat-4521	290	38	no	no	INTJ
easat-4521	290	39	.	.	NOUN
easat-4521	290	40	5	5	NUM
easat-4521	290	41	,	,	PUNCT
easat-4521	290	42	pp	pp	ADJ
easat-4521	290	43	.	.	PUNCT
easat-4521	291	1	452–463	452–463	NUM
easat-4521	291	2	,	,	PUNCT
easat-4521	291	3	2024b	2024b	NUM
easat-4521	291	4	.	.	PUNCT
easat-4521	292	1	https://doi.org/10.32744/pse.2024.5.26	https://doi.org/10.32744/pse.2024.5.26	PROPN
easat-4521	293	1	[	[	PUNCT
easat-4521	293	2	27	27	NUM
easat-4521	293	3	]	]	PUNCT
easat-4521	293	4	a.	a.	NOUN
easat-4521	293	5	maharaj	maharaj	PROPN
easat-4521	293	6	,	,	PUNCT
easat-4521	293	7	"	"	PUNCT
easat-4521	293	8	an	an	DET
easat-4521	293	9	apos	apos	NOUN
easat-4521	293	10	analysis	analysis	NOUN
easat-4521	293	11	of	of	ADP
easat-4521	293	12	natural	natural	ADJ
easat-4521	293	13	science	science	NOUN
easat-4521	293	14	students	student	NOUN
easat-4521	293	15	'	'	PART
easat-4521	293	16	understanding	understanding	NOUN
easat-4521	293	17	of	of	ADP
easat-4521	293	18	derivatives	derivative	NOUN
easat-4521	293	19	,	,	PUNCT
easat-4521	293	20	"	"	PUNCT
easat-4521	293	21	south	south	ADJ
easat-4521	293	22	african	african	ADJ
easat-4521	293	23	journal	journal	NOUN
easat-4521	293	24	of	of	ADP
easat-4521	293	25	education	education	NOUN
easat-4521	293	26	,	,	PUNCT
easat-4521	293	27	vol	vol	NOUN
easat-4521	293	28	.	.	PROPN
easat-4521	293	29	33	33	NUM
easat-4521	293	30	,	,	PUNCT
easat-4521	293	31	no	no	INTJ
easat-4521	293	32	.	.	NOUN
easat-4521	293	33	1	1	NUM
easat-4521	293	34	,	,	PUNCT
easat-4521	293	35	pp	pp	ADJ
easat-4521	293	36	.	.	PUNCT
easat-4521	294	1	1	1	NUM
easat-4521	294	2	-	-	SYM
easat-4521	294	3	19	19	NUM
easat-4521	294	4	,	,	PUNCT
easat-4521	294	5	2013	2013	NUM
easat-4521	294	6	.	.	PUNCT
easat-4521	295	1	https://doi.org/10.15700/saje.v33n1a458	https://doi.org/10.15700/saje.v33n1a458	ADJ
easat-4521	295	2	https://doi.org/10.1007/s11858-019-01037-9	https://doi.org/10.1007/s11858-019-01037-9	NOUN
easat-4521	295	3	https://doi.org/10.33423/jhetp.v23i4.5897	https://doi.org/10.33423/jhetp.v23i4.5897	NUM
easat-4521	296	1	https://doi.org/10.1088/1742-6596/1417/1/012051	https://doi.org/10.1088/1742-6596/1417/1/012051	PROPN
easat-4521	296	2	https://doi.org/10.1088/1742-6596/1747/1/012028	https://doi.org/10.1088/1742-6596/1747/1/012028	PROPN
easat-4521	296	3	https://doi.org/10.54870/1551-3440.1452	https://doi.org/10.54870/1551-3440.1452	VERB
easat-4521	296	4	https://doi.org/10.29333/ejmste/112617	https://doi.org/10.29333/ejmste/112617	PROPN
easat-4521	296	5	https://doi.org/10.29333/ejmste/100640	https://doi.org/10.29333/ejmste/100640	PROPN
easat-4521	296	6	https://doi.org/10.11591/ijere.v11i1.21171	https://doi.org/10.11591/ijere.v11i1.21171	X
easat-4521	296	7	https://doi.org/10.29333/ejmste/91451	https://doi.org/10.29333/ejmste/91451	ADV
easat-4521	296	8	https://doi.org/10.1088/1742-6596/1521/3/032028	https://doi.org/10.1088/1742-6596/1521/3/032028	PROPN
easat-4521	296	9	https://doi.org/10.1016/j.heliyon.2021.e07012	https://doi.org/10.1016/j.heliyon.2021.e07012	ADP
easat-4521	296	10	https://doi.org/10.1186/1744-9081-8-33	https://doi.org/10.1186/1744-9081-8-33	PROPN
easat-4521	296	11	https://doi.org/10.1016/j.janxdis.2023.102799	https://doi.org/10.1016/j.janxdis.2023.102799	PROPN
easat-4521	296	12	https://doi.org/10.1016/j.actpsy.2021.103413	https://doi.org/10.1016/j.actpsy.2021.103413	PROPN
easat-4521	296	13	https://doi.org/10.1016/j.tine.2023.100217	https://doi.org/10.1016/j.tine.2023.100217	PROPN
easat-4521	296	14	https://doi.org/10.18421/tem131-58	https://doi.org/10.18421/tem131-58	PROPN
easat-4521	296	15	https://doi.org/10.17478/jegys.653518	https://doi.org/10.17478/jegys.653518	NOUN
easat-4521	296	16	https://doi.org/10.1007/s10763-017-9826-2	https://doi.org/10.1007/s10763-017-9826-2	NUM
easat-4521	297	1	https://doi.org/10.32744/pse.2024.5.26	https://doi.org/10.32744/pse.2024.5.26	PROPN
easat-4521	297	2	https://doi.org/10.15700/saje.v33n1a458	https://doi.org/10.15700/saje.v33n1a458	PROPN
easat-4521	297	3	566	566	NUM
easat-4521	297	4	edelweiss	edelweiss	PROPN
easat-4521	297	5	applied	apply	VERB
easat-4521	297	6	science	science	NOUN
easat-4521	297	7	and	and	CCONJ
easat-4521	297	8	technology	technology	NOUN
easat-4521	297	9	issn	issn	PROPN
easat-4521	297	10	:	:	PUNCT
easat-4521	297	11	2576	2576	NUM
easat-4521	297	12	-	-	SYM
easat-4521	297	13	8484	8484	NUM
easat-4521	297	14	vol	vol	NOUN
easat-4521	297	15	.	.	PROPN
easat-4521	298	1	9	9	NUM
easat-4521	298	2	,	,	PUNCT
easat-4521	298	3	no	no	INTJ
easat-4521	298	4	.	.	NOUN
easat-4521	298	5	2	2	NUM
easat-4521	298	6	:	:	PUNCT
easat-4521	298	7	555	555	NUM
easat-4521	298	8	-	-	SYM
easat-4521	298	9	566	566	NUM
easat-4521	298	10	,	,	PUNCT
easat-4521	298	11	2025	2025	NUM
easat-4521	298	12	doi	doi	NOUN
easat-4521	298	13	:	:	PUNCT
easat-4521	299	1	10.55214/25768484.v9i2.4521	10.55214/25768484.v9i2.4521	NUM
easat-4521	299	2	©	©	PROPN
easat-4521	299	3	2025	2025	NUM
easat-4521	299	4	by	by	ADP
easat-4521	299	5	the	the	DET
easat-4521	299	6	authors	author	NOUN
easat-4521	299	7	;	;	PUNCT
easat-4521	299	8	licensee	licensee	PROPN
easat-4521	299	9	learning	learning	NOUN
easat-4521	299	10	gate	gate	NOUN
easat-4521	299	11	[	[	X
easat-4521	299	12	28	28	NUM
easat-4521	299	13	]	]	X
easat-4521	299	14	j.	j.	PROPN
easat-4521	299	15	segarra	segarra	PROPN
easat-4521	299	16	and	and	CCONJ
easat-4521	299	17	a.	a.	PROPN
easat-4521	299	18	cabrera	cabrera	PROPN
easat-4521	299	19	-	-	PUNCT
easat-4521	299	20	martínez	martínez	PROPN
easat-4521	299	21	,	,	PUNCT
easat-4521	299	22	"	"	PUNCT
easat-4521	299	23	does	do	AUX
easat-4521	299	24	the	the	DET
easat-4521	299	25	use	use	NOUN
easat-4521	299	26	of	of	ADP
easat-4521	299	27	the	the	DET
easat-4521	299	28	calculator	calculator	NOUN
easat-4521	299	29	reduce	reduce	VERB
easat-4521	299	30	anxiety	anxiety	NOUN
easat-4521	299	31	in	in	ADP
easat-4521	299	32	the	the	DET
easat-4521	299	33	study	study	NOUN
easat-4521	299	34	of	of	ADP
easat-4521	299	35	differential	differential	ADJ
easat-4521	299	36	and	and	CCONJ
easat-4521	299	37	integral	integral	ADJ
easat-4521	299	38	calculus	calculus	NOUN
easat-4521	299	39	?	?	PUNCT
easat-4521	299	40	,	,	PUNCT
easat-4521	299	41	"	"	PUNCT
easat-4521	299	42	european	european	ADJ
easat-4521	299	43	journal	journal	PROPN
easat-4521	299	44	of	of	ADP
easat-4521	299	45	science	science	NOUN
easat-4521	299	46	and	and	CCONJ
easat-4521	299	47	mathematics	mathematic	NOUN
easat-4521	299	48	education	education	NOUN
easat-4521	299	49	,	,	PUNCT
easat-4521	299	50	vol	vol	NOUN
easat-4521	299	51	.	.	PROPN
easat-4521	299	52	12	12	NUM
easat-4521	299	53	,	,	PUNCT
easat-4521	299	54	no	no	INTJ
easat-4521	299	55	.	.	NOUN
easat-4521	299	56	1	1	NUM
easat-4521	299	57	,	,	PUNCT
easat-4521	299	58	pp	pp	ADJ
easat-4521	299	59	.	.	PUNCT
easat-4521	300	1	97	97	NUM
easat-4521	300	2	-	-	SYM
easat-4521	300	3	111	111	NUM
easat-4521	300	4	,	,	PUNCT
easat-4521	300	5	2024	2024	NUM
easat-4521	300	6	.	.	PUNCT
easat-4521	301	1	https://doi.org/10.30935/scimath/13867	https://doi.org/10.30935/scimath/13867	PRON
easat-4521	301	2	[	[	X
easat-4521	301	3	29	29	NUM
easat-4521	301	4	]	]	PUNCT
easat-4521	301	5	l.	l.	PROPN
easat-4521	301	6	abdelhaq	abdelhaq	PROPN
easat-4521	301	7	,	,	PUNCT
easat-4521	301	8	s.	s.	PROPN
easat-4521	301	9	m.	m.	PROPN
easat-4521	301	10	syam	syam	PROPN
easat-4521	301	11	,	,	PUNCT
easat-4521	301	12	and	and	CCONJ
easat-4521	301	13	m.	m.	PROPN
easat-4521	301	14	i.	i.	PROPN
easat-4521	301	15	syam	syam	PROPN
easat-4521	301	16	,	,	PUNCT
easat-4521	301	17	"	"	PUNCT
easat-4521	301	18	an	an	DET
easat-4521	301	19	efficient	efficient	ADJ
easat-4521	301	20	numerical	numerical	ADJ
easat-4521	301	21	method	method	NOUN
easat-4521	301	22	for	for	ADP
easat-4521	301	23	two	two	NUM
easat-4521	301	24	-	-	PUNCT
easat-4521	301	25	dimensional	dimensional	ADJ
easat-4521	301	26	fractional	fractional	ADJ
easat-4521	301	27	integrodifferential	integrodifferential	ADJ
easat-4521	301	28	equations	equation	NOUN
easat-4521	301	29	with	with	ADP
easat-4521	301	30	modified	modified	ADJ
easat-4521	301	31	atangana	atangana	PROPN
easat-4521	301	32	–	–	PUNCT
easat-4521	301	33	baleanu	baleanu	ADJ
easat-4521	301	34	fractional	fractional	ADJ
easat-4521	301	35	derivative	derivative	NOUN
easat-4521	301	36	using	use	VERB
easat-4521	301	37	operational	operational	ADJ
easat-4521	301	38	matrix	matrix	NOUN
easat-4521	301	39	approach	approach	NOUN
easat-4521	301	40	,	,	PUNCT
easat-4521	301	41	"	"	PUNCT
easat-4521	301	42	partial	partial	ADJ
easat-4521	301	43	differential	differential	NOUN
easat-4521	301	44	equations	equation	NOUN
easat-4521	301	45	in	in	ADP
easat-4521	301	46	applied	applied	ADJ
easat-4521	301	47	mathematics	mathematic	NOUN
easat-4521	301	48	,	,	PUNCT
easat-4521	301	49	vol	vol	NOUN
easat-4521	301	50	.	.	PROPN
easat-4521	301	51	11	11	NUM
easat-4521	301	52	,	,	PUNCT
easat-4521	301	53	p.	p.	NOUN
easat-4521	301	54	100824	100824	NUM
easat-4521	301	55	,	,	PUNCT
easat-4521	301	56	2024	2024	NUM
easat-4521	301	57	.	.	PUNCT
easat-4521	302	1	https://doi.org/10.1016/j.padiff.2024.100824	https://doi.org/10.1016/j.padiff.2024.100824	NOUN
easat-4521	302	2	[	[	X
easat-4521	302	3	30	30	NUM
easat-4521	302	4	]	]	PUNCT
easat-4521	302	5	m.	m.	NOUN
easat-4521	302	6	e.	e.	PROPN
easat-4521	302	7	aydin	aydin	PROPN
easat-4521	302	8	,	,	PUNCT
easat-4521	302	9	"	"	PUNCT
easat-4521	302	10	effect	effect	NOUN
easat-4521	302	11	of	of	ADP
easat-4521	302	12	local	local	ADJ
easat-4521	302	13	fractional	fractional	ADJ
easat-4521	302	14	derivatives	derivative	NOUN
easat-4521	302	15	on	on	ADP
easat-4521	302	16	riemann	riemann	PROPN
easat-4521	302	17	curvature	curvature	PROPN
easat-4521	302	18	tensor	tensor	NOUN
easat-4521	302	19	,	,	PUNCT
easat-4521	302	20	"	"	PUNCT
easat-4521	302	21	examples	example	NOUN
easat-4521	302	22	and	and	CCONJ
easat-4521	302	23	counterexamples	counterexample	NOUN
easat-4521	302	24	,	,	PUNCT
easat-4521	302	25	vol	vol	NOUN
easat-4521	302	26	.	.	PROPN
easat-4521	302	27	5	5	NUM
easat-4521	302	28	,	,	PUNCT
easat-4521	302	29	p.	p.	NOUN
easat-4521	302	30	100134	100134	NUM
easat-4521	302	31	,	,	PUNCT
easat-4521	302	32	2024	2024	NUM
easat-4521	302	33	.	.	PUNCT
easat-4521	303	1	https://doi.org/10.1016/j.exco.2023.100134	https://doi.org/10.1016/j.exco.2023.100134	VERB
easat-4521	303	2	[	[	X
easat-4521	303	3	31	31	NUM
easat-4521	303	4	]	]	X
easat-4521	303	5	e.	e.	PROPN
easat-4521	303	6	listiawati	listiawati	PROPN
easat-4521	303	7	,	,	PUNCT
easat-4521	303	8	d.	d.	PROPN
easat-4521	303	9	juniati	juniati	PROPN
easat-4521	303	10	,	,	PUNCT
easat-4521	303	11	and	and	CCONJ
easat-4521	303	12	r.	r.	PROPN
easat-4521	303	13	ekawati	ekawati	PROPN
easat-4521	303	14	,	,	PUNCT
easat-4521	303	15	"	"	PUNCT
easat-4521	303	16	mathematics	mathematic	NOUN
easat-4521	303	17	pre	pre	ADJ
easat-4521	303	18	-	-	ADJ
easat-4521	303	19	service	service	ADJ
easat-4521	303	20	teachers	teacher	NOUN
easat-4521	303	21	’	’	PART
easat-4521	303	22	understanding	understanding	NOUN
easat-4521	303	23	of	of	ADP
easat-4521	303	24	derivative	derivative	ADJ
easat-4521	303	25	concepts	concept	NOUN
easat-4521	303	26	using	use	VERB
easat-4521	303	27	apos	apos	PROPN
easat-4521	303	28	theory	theory	NOUN
easat-4521	303	29	related	relate	VERB
easat-4521	303	30	to	to	ADP
easat-4521	303	31	mathematic	mathematic	ADJ
easat-4521	303	32	anxiety	anxiety	NOUN
easat-4521	303	33	:	:	PUNCT
easat-4521	303	34	a	a	DET
easat-4521	303	35	case	case	NOUN
easat-4521	303	36	study	study	NOUN
easat-4521	303	37	,	,	PUNCT
easat-4521	303	38	"	"	PUNCT
easat-4521	303	39	in	in	ADP
easat-4521	303	40	aip	aip	PROPN
easat-4521	303	41	conference	conference	NOUN
easat-4521	303	42	proceedings	proceeding	NOUN
easat-4521	303	43	,	,	PUNCT
easat-4521	303	44	2023	2023	NUM
easat-4521	303	45	,	,	PUNCT
easat-4521	303	46	vol	vol	NOUN
easat-4521	303	47	.	.	NOUN
easat-4521	303	48	2733	2733	NUM
easat-4521	303	49	,	,	PUNCT
easat-4521	303	50	no	no	INTJ
easat-4521	303	51	.	.	NOUN
easat-4521	303	52	1	1	NUM
easat-4521	303	53	:	:	PUNCT
easat-4521	303	54	aip	aip	PROPN
easat-4521	303	55	publishing	publishing	NOUN
easat-4521	303	56	.	.	PUNCT
easat-4521	304	1	[	[	X
easat-4521	304	2	32	32	NUM
easat-4521	304	3	]	]	PUNCT
easat-4521	304	4	m.	m.	NOUN
easat-4521	304	5	ilyas	ilyas	PROPN
easat-4521	304	6	,	,	PUNCT
easat-4521	304	7	m.	m.	PROPN
easat-4521	304	8	r.	r.	PROPN
easat-4521	304	9	ma’rufi	ma’rufi	PROPN
easat-4521	304	10	,	,	PUNCT
easat-4521	304	11	f.	f.	PROPN
easat-4521	304	12	fitriani	fitriani	PROPN
easat-4521	304	13	,	,	PUNCT
easat-4521	304	14	and	and	CCONJ
easat-4521	304	15	s.	s.	PROPN
easat-4521	304	16	salwah	salwah	PROPN
easat-4521	304	17	,	,	PUNCT
easat-4521	304	18	"	"	PUNCT
easat-4521	304	19	analysis	analysis	NOUN
easat-4521	304	20	of	of	ADP
easat-4521	304	21	senior	senior	ADJ
easat-4521	304	22	high	high	ADJ
easat-4521	304	23	school	school	NOUN
easat-4521	304	24	students	student	NOUN
easat-4521	304	25	’	’	PART
easat-4521	304	26	emotional	emotional	ADJ
easat-4521	304	27	intelligence	intelligence	NOUN
easat-4521	304	28	in	in	ADP
easat-4521	304	29	cooperative	cooperative	ADJ
easat-4521	304	30	based	base	VERB
easat-4521	304	31	mathematics	mathematic	NOUN
easat-4521	304	32	learning	learning	NOUN
easat-4521	304	33	,	,	PUNCT
easat-4521	304	34	"	"	PUNCT
easat-4521	304	35	in	in	ADP
easat-4521	304	36	journal	journal	NOUN
easat-4521	304	37	of	of	ADP
easat-4521	304	38	physics	physics	PROPN
easat-4521	304	39	:	:	PUNCT
easat-4521	304	40	conference	conference	NOUN
easat-4521	304	41	series	series	NOUN
easat-4521	304	42	.	.	PUNCT
easat-4521	305	1	https://doi.org/10.1088/17426596/1088/1/012082	https://doi.org/10.1088/17426596/1088/1/012082	PROPN
easat-4521	305	2	,	,	PUNCT
easat-4521	305	3	2018	2018	NUM
easat-4521	305	4	,	,	PUNCT
easat-4521	305	5	vol	vol	NOUN
easat-4521	305	6	.	.	PROPN
easat-4521	305	7	1088	1088	NUM
easat-4521	305	8	,	,	PUNCT
easat-4521	305	9	no	no	INTJ
easat-4521	305	10	.	.	NOUN
easat-4521	305	11	1	1	NUM
easat-4521	305	12	:	:	PUNCT
easat-4521	305	13	iop	iop	NOUN
easat-4521	305	14	publishing	publishing	NOUN
easat-4521	305	15	,	,	PUNCT
easat-4521	305	16	p.	p.	NOUN
easat-4521	305	17	012082	012082	NUM
easat-4521	305	18	.	.	PUNCT
easat-4521	306	1	[	[	X
easat-4521	306	2	33	33	NUM
easat-4521	306	3	]	]	PUNCT
easat-4521	306	4	b.	b.	PROPN
easat-4521	306	5	miles	miles	PROPN
easat-4521	306	6	,	,	PUNCT
easat-4521	306	7	c.	c.	PROPN
easat-4521	306	8	r.	r.	PROPN
easat-4521	306	9	stokes	stokes	PROPN
easat-4521	306	10	,	,	PUNCT
easat-4521	306	11	a.	a.	NOUN
easat-4521	306	12	vieli	vieli	NOUN
easat-4521	306	13	,	,	PUNCT
easat-4521	306	14	and	and	CCONJ
easat-4521	306	15	n.	n.	PROPN
easat-4521	306	16	j.	j.	PROPN
easat-4521	306	17	cox	cox	PROPN
easat-4521	306	18	,	,	PUNCT
easat-4521	306	19	"	"	PUNCT
easat-4521	306	20	rapid	rapid	ADJ
easat-4521	306	21	,	,	PUNCT
easat-4521	306	22	climate	climate	NOUN
easat-4521	306	23	-	-	PUNCT
easat-4521	306	24	driven	drive	VERB
easat-4521	306	25	changes	change	NOUN
easat-4521	306	26	in	in	ADP
easat-4521	306	27	outlet	outlet	NOUN
easat-4521	306	28	glaciers	glacier	NOUN
easat-4521	306	29	on	on	ADP
easat-4521	306	30	the	the	DET
easat-4521	306	31	pacific	pacific	PROPN
easat-4521	306	32	coast	coast	PROPN
easat-4521	306	33	of	of	ADP
easat-4521	306	34	east	east	PROPN
easat-4521	306	35	antarctica	antarctica	PROPN
easat-4521	306	36	,	,	PUNCT
easat-4521	306	37	"	"	PUNCT
easat-4521	306	38	nature	nature	NOUN
easat-4521	306	39	,	,	PUNCT
easat-4521	306	40	vol	vol	NOUN
easat-4521	306	41	.	.	PROPN
easat-4521	306	42	500	500	NUM
easat-4521	306	43	,	,	PUNCT
easat-4521	306	44	no	no	INTJ
easat-4521	306	45	.	.	NOUN
easat-4521	306	46	7464	7464	NUM
easat-4521	306	47	,	,	PUNCT
easat-4521	306	48	pp	pp	ADJ
easat-4521	306	49	.	.	PUNCT
easat-4521	307	1	563	563	NUM
easat-4521	307	2	-	-	SYM
easat-4521	307	3	566	566	NUM
easat-4521	307	4	,	,	PUNCT
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easat-4521	307	6	.	.	PUNCT
easat-4521	308	1	https://doi.org/10.1038/nature12382	https://doi.org/10.1038/nature12382	NOUN
easat-4521	308	2	[	[	X
easat-4521	308	3	34	34	NUM
easat-4521	308	4	]	]	X
easat-4521	308	5	m.	m.	PROPN
easat-4521	308	6	b.	b.	PROPN
easat-4521	308	7	miles	miles	PROPN
easat-4521	308	8	and	and	CCONJ
easat-4521	308	9	a.	a.	NOUN
easat-4521	308	10	m.	m.	PROPN
easat-4521	308	11	huberman	huberman	PROPN
easat-4521	308	12	,	,	PUNCT
easat-4521	308	13	qualitative	qualitative	ADJ
easat-4521	308	14	data	datum	NOUN
easat-4521	308	15	analysis	analysis	NOUN
easat-4521	308	16	:	:	PUNCT
easat-4521	308	17	an	an	DET
easat-4521	308	18	expanded	expand	VERB
easat-4521	308	19	sourcebook	sourcebook	NOUN
easat-4521	308	20	(	(	PUNCT
easat-4521	308	21	sage	sage	NOUN
easat-4521	308	22	)	)	PUNCT
easat-4521	308	23	.	.	PUNCT
easat-4521	309	1	thousand	thousand	NUM
easat-4521	309	2	oaks	oak	NOUN
easat-4521	309	3	,	,	PUNCT
easat-4521	309	4	ca	ca	NOUN
easat-4521	309	5	,	,	PUNCT
easat-4521	309	6	1994	1994	NUM
easat-4521	309	7	.	.	PUNCT
easat-4521	310	1	[	[	X
easat-4521	310	2	35	35	NUM
easat-4521	310	3	]	]	X
easat-4521	310	4	e.	e.	PROPN
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easat-4521	310	6	et	et	PROPN
easat-4521	310	7	al	al	PROPN
easat-4521	310	8	.	.	PROPN
easat-4521	310	9	,	,	PUNCT
easat-4521	310	10	"	"	PUNCT
easat-4521	310	11	exploring	explore	VERB
easat-4521	310	12	the	the	DET
easat-4521	310	13	bioactive	bioactive	ADJ
easat-4521	310	14	potential	potential	NOUN
easat-4521	310	15	of	of	ADP
easat-4521	310	16	algae	algae	NOUN
easat-4521	310	17	residue	residue	NOUN
easat-4521	310	18	extract	extract	NOUN
easat-4521	310	19	via	via	ADP
easat-4521	310	20	subcritical	subcritical	ADJ
easat-4521	310	21	water	water	NOUN
easat-4521	310	22	extraction	extraction	NOUN
easat-4521	310	23	:	:	PUNCT
easat-4521	310	24	insights	insight	NOUN
easat-4521	310	25	into	into	ADP
easat-4521	310	26	chemical	chemical	ADJ
easat-4521	310	27	composition	composition	NOUN
easat-4521	310	28	and	and	CCONJ
easat-4521	310	29	biological	biological	ADJ
easat-4521	310	30	activity	activity	NOUN
easat-4521	310	31	,	,	PUNCT
easat-4521	310	32	"	"	PUNCT
easat-4521	310	33	food	food	NOUN
easat-4521	310	34	chemistry	chemistry	NOUN
easat-4521	310	35	,	,	PUNCT
easat-4521	310	36	vol	vol	NOUN
easat-4521	310	37	.	.	PUNCT
easat-4521	311	1	458	458	NUM
easat-4521	311	2	,	,	PUNCT
easat-4521	311	3	p.	p.	NOUN
easat-4521	311	4	140310	140310	NUM
easat-4521	311	5	,	,	PUNCT
easat-4521	311	6	2024	2024	NUM
easat-4521	311	7	.	.	PUNCT
easat-4521	312	1	https://doi.org/10.1016/j.foodchem.2024.140310	https://doi.org/10.1016/j.foodchem.2024.140310	PROPN
easat-4521	312	2	[	[	X
easat-4521	312	3	36	36	NUM
easat-4521	312	4	]	]	X
easat-4521	312	5	n.	n.	NOUN
easat-4521	312	6	t.	t.	PROPN
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easat-4521	312	8	,	,	PUNCT
easat-4521	312	9	t.	t.	PROPN
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easat-4521	312	11	dung	dung	PROPN
easat-4521	312	12	,	,	PUNCT
easat-4521	312	13	t.-t	t.-t	NOUN
easat-4521	312	14	.	.	PUNCT
easat-4521	313	1	nguyen	nguyen	PROPN
easat-4521	313	2	,	,	PUNCT
easat-4521	313	3	d.	d.	PROPN
easat-4521	313	4	h.	h.	PROPN
easat-4521	313	5	tong	tong	PROPN
easat-4521	313	6	,	,	PUNCT
easat-4521	313	7	t.	t.	PROPN
easat-4521	313	8	q.	q.	PROPN
easat-4521	313	9	van	van	PROPN
easat-4521	313	10	,	,	PUNCT
easat-4521	313	11	and	and	CCONJ
easat-4521	313	12	b.	b.	PROPN
easat-4521	313	13	p.	p.	NOUN
easat-4521	313	14	uyen	uyen	NOUN
easat-4521	313	15	,	,	PUNCT
easat-4521	313	16	"	"	PUNCT
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easat-4521	313	20	teaching	teach	VERB
easat-4521	313	21	derivatives	derivative	NOUN
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easat-4521	313	23	vietnamese	vietnamese	ADJ
easat-4521	313	24	high	high	ADJ
easat-4521	313	25	schools	school	NOUN
easat-4521	313	26	using	use	VERB
easat-4521	313	27	apos	apos	PROPN
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easat-4521	313	29	and	and	CCONJ
easat-4521	313	30	ace	ace	NOUN
easat-4521	313	31	learning	learn	VERB
easat-4521	313	32	cycle	cycle	NOUN
easat-4521	313	33	,	,	PUNCT
easat-4521	313	34	"	"	PUNCT
easat-4521	313	35	european	european	ADJ
easat-4521	313	36	journal	journal	NOUN
easat-4521	313	37	of	of	ADP
easat-4521	313	38	educational	educational	ADJ
easat-4521	313	39	research	research	NOUN
easat-4521	313	40	,	,	PUNCT
easat-4521	313	41	vol	vol	NOUN
easat-4521	313	42	.	.	PROPN
easat-4521	313	43	12	12	NUM
easat-4521	313	44	,	,	PUNCT
easat-4521	313	45	no	no	INTJ
easat-4521	313	46	.	.	NOUN
easat-4521	313	47	1	1	NUM
easat-4521	313	48	,	,	PUNCT
easat-4521	313	49	pp	pp	ADJ
easat-4521	313	50	.	.	PUNCT
easat-4521	314	1	507–523	507–523	NUM
easat-4521	314	2	,	,	PUNCT
easat-4521	314	3	2023	2023	NUM
easat-4521	314	4	.	.	PUNCT
easat-4521	315	1	https://doi.org/10.12973/eu-jer.12.1.507	https://doi.org/10.12973/eu-jer.12.1.507	PROPN
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easat-4521	315	4	https://doi.org/10.1016/j.exco.2023.100134	https://doi.org/10.1016/j.exco.2023.100134	PROPN
easat-4521	315	5	https://doi.org/10.1088/1742-6596/1088/1/012082	https://doi.org/10.1088/1742-6596/1088/1/012082	PROPN
easat-4521	315	6	https://doi.org/10.1088/1742-6596/1088/1/012082	https://doi.org/10.1088/1742-6596/1088/1/012082	PROPN
easat-4521	315	7	https://doi.org/10.1038/nature12382	https://doi.org/10.1038/nature12382	VERB
easat-4521	315	8	https://doi.org/10.1016/j.foodchem.2024.140310	https://doi.org/10.1016/j.foodchem.2024.140310	PROPN
easat-4521	315	9	https://doi.org/10.12973/eu-jer.12.1.507	https://doi.org/10.12973/eu-jer.12.1.507	PROPN