id	sid	tid	token	lemma	pos
cana-6096	1	1	communications	communication	NOUN
cana-6096	1	2	on	on	ADP
cana-6096	1	3	applied	apply	VERB
cana-6096	1	4	nonlinear	nonlinear	ADJ
cana-6096	1	5	analysis	analysis	NOUN
cana-6096	1	6	issn	issn	NOUN
cana-6096	1	7	:	:	PUNCT
cana-6096	1	8	1074	1074	NUM
cana-6096	1	9	-	-	PUNCT
cana-6096	1	10	133x	133x	NUM
cana-6096	1	11	vol	vol	NOUN
cana-6096	1	12	32	32	NUM
cana-6096	1	13	no	no	NOUN
cana-6096	1	14	.	.	NOUN
cana-6096	1	15	3	3	NUM
cana-6096	1	16	(	(	PUNCT
cana-6096	1	17	2025	2025	NUM
cana-6096	1	18	)	)	PUNCT
cana-6096	1	19	1061	1061	NUM
cana-6096	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	1	21	a	a	DET
cana-6096	1	22	reflection	reflection	NOUN
cana-6096	1	23	on	on	ADP
cana-6096	1	24	the	the	DET
cana-6096	1	25	teaching	teaching	NOUN
cana-6096	1	26	and	and	CCONJ
cana-6096	1	27	learning	learning	NOUN
cana-6096	1	28	of	of	ADP
cana-6096	1	29	mathematics	mathematics	PROPN
cana-6096	1	30	rabah	rabah	PROPN
cana-6096	1	31	belbaki	belbaki	PROPN
cana-6096	1	32	1	1	NUM
cana-6096	1	33	,	,	PUNCT
cana-6096	1	34	ahmed	ahme	VERB
cana-6096	1	35	abbassi	abbassi	PROPN
cana-6096	1	36	2	2	NUM
cana-6096	1	37	1laboratory	1laboratory	NUM
cana-6096	1	38	of	of	ADP
cana-6096	1	39	physics	physics	NOUN
cana-6096	1	40	mathematics	mathematic	NOUN
cana-6096	1	41	and	and	CCONJ
cana-6096	1	42	applications	application	NOUN
cana-6096	1	43	,	,	PUNCT
cana-6096	1	44	ens	ens	PROPN
cana-6096	1	45	de	de	X
cana-6096	1	46	kouba	kouba	PROPN
cana-6096	1	47	,	,	PUNCT
cana-6096	1	48	16050	16050	NUM
cana-6096	1	49	algiers	algiers	PROPN
cana-6096	1	50	,	,	PUNCT
cana-6096	1	51	algeria	algeria	PROPN
cana-6096	1	52	.	.	PUNCT
cana-6096	2	1	email	email	NOUN
cana-6096	2	2	:	:	PUNCT
cana-6096	2	3	rabah.belbaki@g.ens-kouba.dz	rabah.belbaki@g.ens-kouba.dz	VERB
cana-6096	2	4	2applied	2applied	NUM
cana-6096	2	5	mathematics	mathematic	NOUN
cana-6096	2	6	and	and	CCONJ
cana-6096	2	7	physics	physics	NOUN
cana-6096	2	8	laboratory	laboratory	NOUN
cana-6096	2	9	,	,	PUNCT
cana-6096	2	10	ens	ens	PROPN
cana-6096	2	11	de	de	PROPN
cana-6096	2	12	bousaâda	bousaâda	PROPN
cana-6096	2	13	,	,	PUNCT
cana-6096	2	14	28001	28001	NUM
cana-6096	2	15	bousaâda	bousaâda	PROPN
cana-6096	2	16	,	,	PUNCT
cana-6096	2	17	algeria	algeria	PROPN
cana-6096	2	18	.	.	PUNCT
cana-6096	3	1	email	email	NOUN
cana-6096	3	2	:	:	PUNCT
cana-6096	3	3	abbasi.ahmed@ens-bousaada.dz	abbasi.ahmed@ens-bousaada.dz	PROPN
cana-6096	3	4	article	article	NOUN
cana-6096	3	5	history	history	NOUN
cana-6096	3	6	:	:	PUNCT
cana-6096	3	7	received	receive	VERB
cana-6096	3	8	:	:	PUNCT
cana-6096	3	9	19	19	NUM
cana-6096	3	10	-	-	PUNCT
cana-6096	3	11	03	03	NUM
cana-6096	3	12	-	-	PUNCT
cana-6096	3	13	2025	2025	NUM
cana-6096	3	14	revised	revise	VERB
cana-6096	3	15	:	:	PUNCT
cana-6096	3	16	24	24	NUM
cana-6096	3	17	-	-	PUNCT
cana-6096	3	18	07	07	NUM
cana-6096	3	19	-	-	PUNCT
cana-6096	3	20	2025	2025	NUM
cana-6096	3	21	accepted	accept	VERB
cana-6096	3	22	:	:	PUNCT
cana-6096	3	23	21	21	NUM
cana-6096	3	24	-	-	SYM
cana-6096	3	25	08	08	NUM
cana-6096	3	26	-	-	PUNCT
cana-6096	3	27	2025	2025	NUM
cana-6096	3	28	abstract	abstract	NOUN
cana-6096	3	29	:	:	PUNCT
cana-6096	3	30	in	in	ADP
cana-6096	3	31	this	this	DET
cana-6096	3	32	paper	paper	NOUN
cana-6096	3	33	,	,	PUNCT
cana-6096	3	34	we	we	PRON
cana-6096	3	35	approach	approach	VERB
cana-6096	3	36	the	the	DET
cana-6096	3	37	idea	idea	NOUN
cana-6096	3	38	of	of	ADP
cana-6096	3	39	meaning	meaning	NOUN
cana-6096	3	40	in	in	ADP
cana-6096	3	41	mathematics	mathematic	NOUN
cana-6096	3	42	,	,	PUNCT
cana-6096	3	43	by	by	ADP
cana-6096	3	44	reflecting	reflect	VERB
cana-6096	3	45	on	on	ADP
cana-6096	3	46	its	its	PRON
cana-6096	3	47	teaching	teaching	NOUN
cana-6096	3	48	and	and	CCONJ
cana-6096	3	49	let	let	VERB
cana-6096	3	50	the	the	DET
cana-6096	3	51	students	student	NOUN
cana-6096	3	52	learn	learn	VERB
cana-6096	3	53	it	it	PRON
cana-6096	3	54	freely	freely	ADV
cana-6096	3	55	and	and	CCONJ
cana-6096	3	56	passionately	passionately	ADV
cana-6096	3	57	,	,	PUNCT
cana-6096	3	58	the	the	DET
cana-6096	3	59	list	list	NOUN
cana-6096	3	60	is	be	AUX
cana-6096	3	61	long	long	ADJ
cana-6096	3	62	and	and	CCONJ
cana-6096	3	63	if	if	SCONJ
cana-6096	3	64	the	the	DET
cana-6096	3	65	questions	question	NOUN
cana-6096	3	66	are	be	AUX
cana-6096	3	67	precise	precise	ADJ
cana-6096	3	68	,	,	PUNCT
cana-6096	3	69	the	the	DET
cana-6096	3	70	answers	answer	NOUN
cana-6096	3	71	nonetheless	nonetheless	ADV
cana-6096	3	72	remain	remain	VERB
cana-6096	3	73	complex	complex	ADJ
cana-6096	3	74	.	.	PUNCT
cana-6096	4	1	what	what	PRON
cana-6096	4	2	is	be	AUX
cana-6096	4	3	the	the	DET
cana-6096	4	4	age	age	NOUN
cana-6096	4	5	from	from	ADP
cana-6096	4	6	which	which	PRON
cana-6096	4	7	a	a	DET
cana-6096	4	8	student	student	NOUN
cana-6096	4	9	can	can	AUX
cana-6096	4	10	assimilate	assimilate	VERB
cana-6096	4	11	certain	certain	ADJ
cana-6096	4	12	concepts	concept	NOUN
cana-6096	4	13	:	:	PUNCT
cana-6096	4	14	abstraction	abstraction	NOUN
cana-6096	4	15	,	,	PUNCT
cana-6096	4	16	literal	literal	ADJ
cana-6096	4	17	calculus	calculus	NOUN
cana-6096	4	18	,	,	PUNCT
cana-6096	4	19	demonstrations	demonstration	NOUN
cana-6096	4	20	?	?	PUNCT
cana-6096	5	1	by	by	ADP
cana-6096	5	2	the	the	DET
cana-6096	5	3	learning	learning	NOUN
cana-6096	5	4	objectives	objective	NOUN
cana-6096	5	5	of	of	ADP
cana-6096	5	6	mathematics	mathematic	NOUN
cana-6096	5	7	proper	proper	ADJ
cana-6096	5	8	is	be	AUX
cana-6096	5	9	to	to	PART
cana-6096	5	10	try	try	VERB
cana-6096	5	11	to	to	PART
cana-6096	5	12	redefine	redefine	VERB
cana-6096	5	13	the	the	DET
cana-6096	5	14	roles	role	NOUN
cana-6096	5	15	of	of	ADP
cana-6096	5	16	the	the	DET
cana-6096	5	17	teacher	teacher	NOUN
cana-6096	5	18	.	.	PUNCT
cana-6096	6	1	this	this	DET
cana-6096	6	2	"	"	PUNCT
cana-6096	6	3	role	role	NOUN
cana-6096	6	4	"	"	PUNCT
cana-6096	6	5	should	should	AUX
cana-6096	6	6	be	be	AUX
cana-6096	6	7	facilitated	facilitate	VERB
cana-6096	6	8	by	by	ADP
cana-6096	6	9	the	the	DET
cana-6096	6	10	basic	basic	ADJ
cana-6096	6	11	thinking	thinking	NOUN
cana-6096	6	12	options	option	NOUN
cana-6096	6	13	dealt	deal	VERB
cana-6096	6	14	with	with	ADP
cana-6096	6	15	and	and	CCONJ
cana-6096	6	16	preliminary	preliminary	ADJ
cana-6096	6	17	and	and	CCONJ
cana-6096	6	18	effective	effective	ADJ
cana-6096	6	19	questions	question	NOUN
cana-6096	6	20	.	.	PUNCT
cana-6096	7	1	in	in	ADP
cana-6096	7	2	short	short	ADJ
cana-6096	7	3	,	,	PUNCT
cana-6096	7	4	theorize	theorize	VERB
cana-6096	7	5	professional	professional	ADJ
cana-6096	7	6	practices	practice	NOUN
cana-6096	7	7	of	of	ADP
cana-6096	7	8	a	a	DET
cana-6096	7	9	different	different	ADJ
cana-6096	7	10	kind	kind	NOUN
cana-6096	7	11	.	.	PUNCT
cana-6096	8	1	we	we	PRON
cana-6096	8	2	are	be	AUX
cana-6096	8	3	looking	look	VERB
cana-6096	8	4	for	for	ADP
cana-6096	8	5	methods	method	NOUN
cana-6096	8	6	of	of	ADP
cana-6096	8	7	teaching	teach	VERB
cana-6096	8	8	mathematics	mathematic	NOUN
cana-6096	8	9	.	.	PUNCT
cana-6096	9	1	according	accord	VERB
cana-6096	9	2	to	to	ADP
cana-6096	9	3	the	the	DET
cana-6096	9	4	two	two	NUM
cana-6096	9	5	points	point	NOUN
cana-6096	9	6	of	of	ADP
cana-6096	9	7	view	view	NOUN
cana-6096	9	8	horizontal	horizontal	ADJ
cana-6096	9	9	,	,	PUNCT
cana-6096	9	10	vertical	vertical	ADJ
cana-6096	9	11	and	and	CCONJ
cana-6096	9	12	the	the	DET
cana-6096	9	13	horizontal	horizontal	ADJ
cana-6096	9	14	view	view	NOUN
cana-6096	9	15	it	it	PRON
cana-6096	9	16	is	be	AUX
cana-6096	9	17	based	base	VERB
cana-6096	9	18	on	on	ADP
cana-6096	9	19	reality	reality	NOUN
cana-6096	9	20	,	,	PUNCT
cana-6096	9	21	which	which	PRON
cana-6096	9	22	searches	search	VERB
cana-6096	9	23	for	for	ADP
cana-6096	9	24	mathematics	mathematic	NOUN
cana-6096	9	25	in	in	ADP
cana-6096	9	26	different	different	ADJ
cana-6096	9	27	contexts	context	NOUN
cana-6096	9	28	(	(	PUNCT
cana-6096	9	29	daily	daily	ADJ
cana-6096	9	30	,	,	PUNCT
cana-6096	9	31	physical	physical	ADJ
cana-6096	9	32	,	,	PUNCT
cana-6096	9	33	geographical	geographical	ADJ
cana-6096	9	34	,	,	PUNCT
cana-6096	9	35	economic	economic	ADJ
cana-6096	9	36	,	,	PUNCT
cana-6096	9	37	etc	etc	X
cana-6096	9	38	.	.	X
cana-6096	9	39	)	)	PUNCT
cana-6096	9	40	,	,	PUNCT
cana-6096	9	41	where	where	SCONJ
cana-6096	9	42	one	one	PRON
cana-6096	9	43	uses	use	VERB
cana-6096	9	44	the	the	DET
cana-6096	9	45	drawing	drawing	NOUN
cana-6096	9	46	,	,	PUNCT
cana-6096	9	47	constructions	construction	NOUN
cana-6096	9	48	,	,	PUNCT
cana-6096	9	49	manipulation	manipulation	NOUN
cana-6096	9	50	,	,	PUNCT
cana-6096	9	51	perceptions	perception	NOUN
cana-6096	9	52	and	and	CCONJ
cana-6096	9	53	intuition	intuition	NOUN
cana-6096	9	54	.	.	PUNCT
cana-6096	10	1	the	the	DET
cana-6096	10	2	second	second	ADJ
cana-6096	10	3	a	a	DET
cana-6096	10	4	vertical	vertical	ADJ
cana-6096	10	5	perspective	perspective	NOUN
cana-6096	10	6	is	be	AUX
cana-6096	10	7	one	one	NUM
cana-6096	10	8	that	that	PRON
cana-6096	10	9	presents	present	VERB
cana-6096	10	10	theory	theory	NOUN
cana-6096	10	11	,	,	PUNCT
cana-6096	10	12	structure	structure	NOUN
cana-6096	10	13	,	,	PUNCT
cana-6096	10	14	logic	logic	NOUN
cana-6096	10	15	,	,	PUNCT
cana-6096	10	16	conclusion	conclusion	NOUN
cana-6096	10	17	,	,	PUNCT
cana-6096	10	18	clarifications	clarification	NOUN
cana-6096	10	19	,	,	PUNCT
cana-6096	10	20	and	and	CCONJ
cana-6096	10	21	correctness	correctness	NOUN
cana-6096	10	22	.	.	PUNCT
cana-6096	11	1	we	we	PRON
cana-6096	11	2	will	will	AUX
cana-6096	11	3	focus	focus	VERB
cana-6096	11	4	primarily	primarily	ADV
cana-6096	11	5	on	on	ADP
cana-6096	11	6	two	two	NUM
cana-6096	11	7	dimensions	dimension	NOUN
cana-6096	11	8	related	relate	VERB
cana-6096	11	9	to	to	ADP
cana-6096	11	10	mathematics	mathematic	NOUN
cana-6096	11	11	education	education	NOUN
cana-6096	11	12	,	,	PUNCT
cana-6096	11	13	one	one	NUM
cana-6096	11	14	of	of	ADP
cana-6096	11	15	which	which	PRON
cana-6096	11	16	is	be	AUX
cana-6096	11	17	the	the	DET
cana-6096	11	18	problem	problem	NOUN
cana-6096	11	19	-	-	PUNCT
cana-6096	11	20	solving	solve	VERB
cana-6096	11	21	approach	approach	NOUN
cana-6096	11	22	,	,	PUNCT
cana-6096	11	23	and	and	CCONJ
cana-6096	11	24	the	the	DET
cana-6096	11	25	second	second	NOUN
cana-6096	11	26	is	be	AUX
cana-6096	11	27	the	the	DET
cana-6096	11	28	importance	importance	NOUN
cana-6096	11	29	of	of	ADP
cana-6096	11	30	using	use	VERB
cana-6096	11	31	the	the	DET
cana-6096	11	32	history	history	NOUN
cana-6096	11	33	of	of	ADP
cana-6096	11	34	mathematics	mathematic	NOUN
cana-6096	11	35	in	in	ADP
cana-6096	11	36	thinking	think	VERB
cana-6096	11	37	to	to	PART
cana-6096	11	38	design	design	VERB
cana-6096	11	39	good	good	ADJ
cana-6096	11	40	ways	way	NOUN
cana-6096	11	41	to	to	PART
cana-6096	11	42	learn	learn	VERB
cana-6096	11	43	the	the	DET
cana-6096	11	44	material	material	NOUN
cana-6096	11	45	.	.	PUNCT
cana-6096	12	1	keywords	keyword	NOUN
cana-6096	12	2	,	,	PUNCT
cana-6096	12	3	mathematics	mathematic	NOUN
cana-6096	12	4	,	,	PUNCT
cana-6096	12	5	treffers	treffer	NOUN
cana-6096	12	6	model	model	NOUN
cana-6096	12	7	,	,	PUNCT
cana-6096	12	8	problem	problem	NOUN
cana-6096	12	9	,	,	PUNCT
cana-6096	12	10	situation	situation	NOUN
cana-6096	12	11	,	,	PUNCT
cana-6096	12	12	didactics	didactics	NOUN
cana-6096	12	13	,	,	PUNCT
cana-6096	12	14	meaning	mean	VERB
cana-6096	12	15	in	in	ADP
cana-6096	12	16	mathematics	mathematic	NOUN
cana-6096	12	17	.	.	PUNCT
cana-6096	13	1	published:24/09/2025	published:24/09/2025	VERB
cana-6096	13	2	communications	communication	NOUN
cana-6096	13	3	on	on	ADP
cana-6096	13	4	applied	apply	VERB
cana-6096	13	5	nonlinear	nonlinear	ADJ
cana-6096	13	6	analysis	analysis	NOUN
cana-6096	13	7	issn	issn	NOUN
cana-6096	13	8	:	:	PUNCT
cana-6096	13	9	1074	1074	NUM
cana-6096	13	10	-	-	PUNCT
cana-6096	13	11	133x	133x	NUM
cana-6096	13	12	vol	vol	NOUN
cana-6096	13	13	32	32	NUM
cana-6096	13	14	no	no	NOUN
cana-6096	13	15	.	.	NOUN
cana-6096	13	16	3	3	NUM
cana-6096	13	17	(	(	PUNCT
cana-6096	13	18	2025	2025	NUM
cana-6096	13	19	)	)	PUNCT
cana-6096	13	20	1062	1062	NUM
cana-6096	14	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	14	2	introduction	introduction	NOUN
cana-6096	14	3	one	one	NUM
cana-6096	14	4	of	of	ADP
cana-6096	14	5	the	the	DET
cana-6096	14	6	most	most	ADV
cana-6096	14	7	remarkable	remarkable	ADJ
cana-6096	14	8	things	thing	NOUN
cana-6096	14	9	of	of	ADP
cana-6096	14	10	late	late	ADJ
cana-6096	14	11	is	be	AUX
cana-6096	14	12	the	the	DET
cana-6096	14	13	persistence	persistence	NOUN
cana-6096	14	14	of	of	ADP
cana-6096	14	15	failure	failure	NOUN
cana-6096	14	16	rates	rate	NOUN
cana-6096	14	17	in	in	ADP
cana-6096	14	18	mathematics	mathematic	NOUN
cana-6096	14	19	despite	despite	SCONJ
cana-6096	14	20	the	the	DET
cana-6096	14	21	constant	constant	ADJ
cana-6096	14	22	change	change	NOUN
cana-6096	14	23	in	in	ADP
cana-6096	14	24	curricula	curricula	NOUN
cana-6096	14	25	.	.	PUNCT
cana-6096	15	1	mathematics	mathematic	NOUN
cana-6096	15	2	has	have	AUX
cana-6096	15	3	become	become	VERB
cana-6096	15	4	a	a	DET
cana-6096	15	5	difficult	difficult	ADJ
cana-6096	15	6	and	and	CCONJ
cana-6096	15	7	dry	dry	ADJ
cana-6096	15	8	subject	subject	NOUN
cana-6096	15	9	for	for	ADP
cana-6096	15	10	our	our	PRON
cana-6096	15	11	students	student	NOUN
cana-6096	15	12	.	.	PUNCT
cana-6096	16	1	levels	level	NOUN
cana-6096	16	2	of	of	ADP
cana-6096	16	3	difficulty	difficulty	NOUN
cana-6096	16	4	in	in	ADP
cana-6096	16	5	learning	learn	VERB
cana-6096	16	6	mathematics	mathematic	NOUN
cana-6096	16	7	generally	generally	ADV
cana-6096	16	8	vary	vary	VERB
cana-6096	16	9	.	.	PUNCT
cana-6096	17	1	there	there	PRON
cana-6096	17	2	are	be	VERB
cana-6096	17	3	comprehension	comprehension	NOUN
cana-6096	17	4	difficulties	difficulty	NOUN
cana-6096	17	5	related	relate	VERB
cana-6096	17	6	to	to	ADP
cana-6096	17	7	symbols	symbol	NOUN
cana-6096	17	8	or	or	CCONJ
cana-6096	17	9	expression	expression	NOUN
cana-6096	17	10	,	,	PUNCT
cana-6096	17	11	difficulties	difficulty	NOUN
cana-6096	17	12	in	in	ADP
cana-6096	17	13	understanding	understand	VERB
cana-6096	17	14	a	a	DET
cana-6096	17	15	problem	problem	NOUN
cana-6096	17	16	,	,	PUNCT
cana-6096	17	17	the	the	DET
cana-6096	17	18	inability	inability	NOUN
cana-6096	17	19	to	to	PART
cana-6096	17	20	infer	infer	VERB
cana-6096	17	21	,	,	PUNCT
cana-6096	17	22	the	the	DET
cana-6096	17	23	inability	inability	NOUN
cana-6096	17	24	to	to	PART
cana-6096	17	25	analyze	analyze	VERB
cana-6096	17	26	the	the	DET
cana-6096	17	27	elements	element	NOUN
cana-6096	17	28	of	of	ADP
cana-6096	17	29	a	a	DET
cana-6096	17	30	problem	problem	NOUN
cana-6096	17	31	,	,	PUNCT
cana-6096	17	32	or	or	CCONJ
cana-6096	17	33	other	other	ADJ
cana-6096	17	34	difficulties	difficulty	NOUN
cana-6096	17	35	.	.	PUNCT
cana-6096	18	1	does	do	AUX
cana-6096	18	2	the	the	DET
cana-6096	18	3	problem	problem	NOUN
cana-6096	18	4	lie	lie	VERB
cana-6096	18	5	with	with	ADP
cana-6096	18	6	the	the	DET
cana-6096	18	7	subject	subject	NOUN
cana-6096	18	8	,	,	PUNCT
cana-6096	18	9	the	the	DET
cana-6096	18	10	teacher	teacher	NOUN
cana-6096	18	11	,	,	PUNCT
cana-6096	18	12	the	the	DET
cana-6096	18	13	curriculum	curriculum	NOUN
cana-6096	18	14	,	,	PUNCT
cana-6096	18	15	or	or	CCONJ
cana-6096	18	16	the	the	DET
cana-6096	18	17	students	student	NOUN
cana-6096	18	18	'	'	PART
cana-6096	18	19	negative	negative	ADJ
cana-6096	18	20	attitudes	attitude	NOUN
cana-6096	18	21	?	?	PUNCT
cana-6096	19	1	it	it	PRON
cana-6096	19	2	is	be	AUX
cana-6096	19	3	therefore	therefore	ADV
cana-6096	19	4	not	not	PART
cana-6096	19	5	unlikely	unlikely	ADJ
cana-6096	19	6	that	that	SCONJ
cana-6096	19	7	students	student	NOUN
cana-6096	19	8	view	view	VERB
cana-6096	19	9	mathematics	mathematic	NOUN
cana-6096	19	10	as	as	ADP
cana-6096	19	11	a	a	DET
cana-6096	19	12	mysterious	mysterious	ADJ
cana-6096	19	13	subject	subject	NOUN
cana-6096	19	14	and	and	CCONJ
cana-6096	19	15	a	a	DET
cana-6096	19	16	static	static	ADJ
cana-6096	19	17	part	part	NOUN
cana-6096	19	18	of	of	ADP
cana-6096	19	19	knowledge	knowledge	NOUN
cana-6096	19	20	.	.	PUNCT
cana-6096	20	1	not	not	PART
cana-6096	20	2	presenting	present	VERB
cana-6096	20	3	the	the	DET
cana-6096	20	4	motor	motor	NOUN
cana-6096	20	5	development	development	NOUN
cana-6096	20	6	nature	nature	NOUN
cana-6096	20	7	of	of	ADP
cana-6096	20	8	mathematics	mathematic	NOUN
cana-6096	20	9	deprives	deprive	VERB
cana-6096	20	10	them	they	PRON
cana-6096	20	11	of	of	ADP
cana-6096	20	12	the	the	DET
cana-6096	20	13	experience	experience	NOUN
cana-6096	20	14	of	of	ADP
cana-6096	20	15	experimentation	experimentation	NOUN
cana-6096	20	16	,	,	PUNCT
cana-6096	20	17	discovery	discovery	NOUN
cana-6096	20	18	,	,	PUNCT
cana-6096	20	19	creativity	creativity	NOUN
cana-6096	20	20	,	,	PUNCT
cana-6096	20	21	and	and	CCONJ
cana-6096	20	22	appreciation	appreciation	NOUN
cana-6096	20	23	.	.	PUNCT
cana-6096	21	1	what	what	PRON
cana-6096	21	2	's	be	AUX
cana-6096	21	3	sometimes	sometimes	ADV
cana-6096	21	4	missing	missing	ADJ
cana-6096	21	5	is	be	AUX
cana-6096	21	6	a	a	DET
cana-6096	21	7	connection	connection	NOUN
cana-6096	21	8	with	with	ADP
cana-6096	21	9	intuition	intuition	NOUN
cana-6096	21	10	and	and	CCONJ
cana-6096	21	11	imagination	imagination	NOUN
cana-6096	21	12	,	,	PUNCT
cana-6096	21	13	completing	complete	VERB
cana-6096	21	14	meaning	meaning	NOUN
cana-6096	21	15	.	.	PUNCT
cana-6096	22	1	as	as	SCONJ
cana-6096	22	2	e.	e.	PROPN
cana-6096	22	3	kant	kant	PROPN
cana-6096	22	4	said	say	VERB
cana-6096	22	5	:	:	PUNCT
cana-6096	22	6	"	"	PUNCT
cana-6096	22	7	a	a	DET
cana-6096	22	8	concept	concept	NOUN
cana-6096	22	9	without	without	ADP
cana-6096	22	10	intuition	intuition	NOUN
cana-6096	22	11	remains	remain	VERB
cana-6096	22	12	empty	empty	ADJ
cana-6096	22	13	.	.	PUNCT
cana-6096	22	14	"	"	PUNCT
cana-6096	23	1	the	the	DET
cana-6096	23	2	completion	completion	NOUN
cana-6096	23	3	of	of	ADP
cana-6096	23	4	meaning	meaning	NOUN
cana-6096	23	5	can	can	AUX
cana-6096	23	6	be	be	AUX
cana-6096	23	7	found	find	VERB
cana-6096	23	8	in	in	ADP
cana-6096	23	9	many	many	ADJ
cana-6096	23	10	places	place	NOUN
cana-6096	23	11	:	:	PUNCT
cana-6096	23	12	practical	practical	ADJ
cana-6096	23	13	problems	problem	NOUN
cana-6096	23	14	,	,	PUNCT
cana-6096	23	15	games	game	NOUN
cana-6096	23	16	,	,	PUNCT
cana-6096	23	17	etc	etc	X
cana-6096	23	18	.	.	X
cana-6096	23	19	;	;	PUNCT
cana-6096	23	20	but	but	CCONJ
cana-6096	23	21	also	also	ADV
cana-6096	23	22	,	,	PUNCT
cana-6096	23	23	in	in	ADP
cana-6096	23	24	the	the	DET
cana-6096	23	25	history	history	NOUN
cana-6096	23	26	of	of	ADP
cana-6096	23	27	matter	matter	NOUN
cana-6096	23	28	.	.	PUNCT
cana-6096	24	1	is	be	AUX
cana-6096	24	2	repetition	repetition	VERB
cana-6096	24	3	necessary	necessary	ADJ
cana-6096	24	4	?	?	PUNCT
cana-6096	25	1	is	be	AUX
cana-6096	25	2	n't	not	PART
cana-6096	25	3	too	too	ADV
cana-6096	25	4	much	much	ADJ
cana-6096	25	5	repetition	repetition	NOUN
cana-6096	25	6	proof	proof	NOUN
cana-6096	25	7	that	that	SCONJ
cana-6096	25	8	the	the	DET
cana-6096	25	9	content	content	NOUN
cana-6096	25	10	has	have	AUX
cana-6096	25	11	n't	not	PART
cana-6096	25	12	been	be	AUX
cana-6096	25	13	understood	understand	VERB
cana-6096	25	14	?	?	PUNCT
cana-6096	26	1	how	how	SCONJ
cana-6096	26	2	can	can	AUX
cana-6096	26	3	we	we	PRON
cana-6096	26	4	accustom	accustom	VERB
cana-6096	26	5	students	student	NOUN
cana-6096	26	6	to	to	ADP
cana-6096	26	7	using	use	VERB
cana-6096	26	8	rules	rule	NOUN
cana-6096	26	9	?	?	PUNCT
cana-6096	27	1	should	should	AUX
cana-6096	27	2	we	we	PRON
cana-6096	27	3	be	be	AUX
cana-6096	27	4	patient	patient	ADJ
cana-6096	27	5	and	and	CCONJ
cana-6096	27	6	go	go	VERB
cana-6096	27	7	through	through	ADP
cana-6096	27	8	a	a	DET
cana-6096	27	9	long	long	ADJ
cana-6096	27	10	process	process	NOUN
cana-6096	27	11	of	of	ADP
cana-6096	27	12	assimilating	assimilate	VERB
cana-6096	27	13	concepts	concept	NOUN
cana-6096	27	14	,	,	PUNCT
cana-6096	27	15	or	or	CCONJ
cana-6096	27	16	should	should	AUX
cana-6096	27	17	we	we	PRON
cana-6096	27	18	,	,	PUNCT
cana-6096	27	19	on	on	ADP
cana-6096	27	20	the	the	DET
cana-6096	27	21	contrary	contrary	NOUN
cana-6096	27	22	,	,	PUNCT
cana-6096	27	23	move	move	VERB
cana-6096	27	24	as	as	ADV
cana-6096	27	25	quickly	quickly	ADV
cana-6096	27	26	as	as	ADP
cana-6096	27	27	possible	possible	ADJ
cana-6096	27	28	toward	toward	ADP
cana-6096	27	29	the	the	DET
cana-6096	27	30	use	use	NOUN
cana-6096	27	31	of	of	ADP
cana-6096	27	32	rules	rule	NOUN
cana-6096	27	33	?	?	PUNCT
cana-6096	28	1	what	what	PRON
cana-6096	28	2	are	be	AUX
cana-6096	28	3	the	the	DET
cana-6096	28	4	pedagogical	pedagogical	ADJ
cana-6096	28	5	dangers	danger	NOUN
cana-6096	28	6	of	of	ADP
cana-6096	28	7	these	these	DET
cana-6096	28	8	different	different	ADJ
cana-6096	28	9	approaches	approach	NOUN
cana-6096	28	10	?	?	PUNCT
cana-6096	29	1	at	at	ADP
cana-6096	29	2	what	what	DET
cana-6096	29	3	age	age	NOUN
cana-6096	29	4	can	can	AUX
cana-6096	29	5	a	a	DET
cana-6096	29	6	student	student	NOUN
cana-6096	29	7	assimilate	assimilate	VERB
cana-6096	29	8	certain	certain	ADJ
cana-6096	29	9	concepts	concept	NOUN
cana-6096	29	10	:	:	PUNCT
cana-6096	29	11	abstraction	abstraction	NOUN
cana-6096	29	12	,	,	PUNCT
cana-6096	29	13	literal	literal	ADJ
cana-6096	29	14	calculation	calculation	NOUN
cana-6096	29	15	,	,	PUNCT
cana-6096	29	16	demonstrations	demonstration	NOUN
cana-6096	29	17	?	?	PUNCT
cana-6096	30	1	is	be	AUX
cana-6096	30	2	it	it	PRON
cana-6096	30	3	true	true	ADJ
cana-6096	30	4	that	that	SCONJ
cana-6096	30	5	if	if	SCONJ
cana-6096	30	6	we	we	PRON
cana-6096	30	7	wait	wait	VERB
cana-6096	30	8	too	too	ADV
cana-6096	30	9	long	long	ADV
cana-6096	30	10	(	(	PUNCT
cana-6096	30	11	for	for	ADP
cana-6096	30	12	example	example	NOUN
cana-6096	30	13	,	,	PUNCT
cana-6096	30	14	before	before	ADP
cana-6096	30	15	doing	do	VERB
cana-6096	30	16	demonstrations	demonstration	NOUN
cana-6096	30	17	)	)	PUNCT
cana-6096	30	18	,	,	PUNCT
cana-6096	30	19	students	student	NOUN
cana-6096	30	20	are	be	AUX
cana-6096	30	21	no	no	ADV
cana-6096	30	22	longer	long	ADV
cana-6096	30	23	"	"	PUNCT
cana-6096	30	24	open	open	ADJ
cana-6096	30	25	"	"	PUNCT
cana-6096	30	26	enough	enough	ADJ
cana-6096	30	27	to	to	PART
cana-6096	30	28	be	be	AUX
cana-6096	30	29	interested	interested	ADJ
cana-6096	30	30	in	in	ADP
cana-6096	30	31	more	more	ADJ
cana-6096	30	32	abstract	abstract	ADJ
cana-6096	30	33	reasoning	reasoning	NOUN
cana-6096	30	34	?	?	PUNCT
cana-6096	31	1	should	should	AUX
cana-6096	31	2	we	we	PRON
cana-6096	31	3	be	be	AUX
cana-6096	31	4	strict	strict	ADJ
cana-6096	31	5	with	with	ADP
cana-6096	31	6	grading	grade	VERB
cana-6096	31	7	?	?	PUNCT
cana-6096	32	1	does	do	AUX
cana-6096	32	2	rigor	rigor	VERB
cana-6096	32	3	go	go	VERB
cana-6096	32	4	further	far	ADV
cana-6096	32	5	than	than	ADP
cana-6096	32	6	complacency	complacency	NOUN
cana-6096	32	7	?	?	PUNCT
cana-6096	33	1	what	what	PRON
cana-6096	33	2	are	be	AUX
cana-6096	33	3	the	the	DET
cana-6096	33	4	origins	origin	NOUN
cana-6096	33	5	and	and	CCONJ
cana-6096	33	6	nature	nature	NOUN
cana-6096	33	7	of	of	ADP
cana-6096	33	8	certain	certain	ADJ
cana-6096	33	9	mathematical	mathematical	ADJ
cana-6096	33	10	errors	error	NOUN
cana-6096	33	11	?	?	PUNCT
cana-6096	34	1	how	how	SCONJ
cana-6096	34	2	can	can	AUX
cana-6096	34	3	mathematics	mathematics	PROPN
cana-6096	34	4	curricula	curricula	NOUN
cana-6096	34	5	be	be	AUX
cana-6096	34	6	formulated	formulate	VERB
cana-6096	34	7	so	so	ADV
cana-6096	34	8	as	as	SCONJ
cana-6096	34	9	to	to	PART
cana-6096	34	10	be	be	AUX
cana-6096	34	11	independent	independent	ADJ
cana-6096	34	12	of	of	ADP
cana-6096	34	13	the	the	DET
cana-6096	34	14	chosen	choose	VERB
cana-6096	34	15	textbooks	textbook	NOUN
cana-6096	34	16	?	?	PUNCT
cana-6096	35	1	is	be	AUX
cana-6096	35	2	a	a	DET
cana-6096	35	3	competency	competency	NOUN
cana-6096	35	4	-	-	PUNCT
cana-6096	35	5	based	base	VERB
cana-6096	35	6	formulation	formulation	NOUN
cana-6096	35	7	a	a	DET
cana-6096	35	8	solution	solution	NOUN
cana-6096	35	9	?	?	PUNCT
cana-6096	36	1	the	the	DET
cana-6096	36	2	list	list	NOUN
cana-6096	36	3	is	be	AUX
cana-6096	36	4	long	long	ADJ
cana-6096	36	5	,	,	PUNCT
cana-6096	36	6	and	and	CCONJ
cana-6096	36	7	while	while	SCONJ
cana-6096	36	8	the	the	DET
cana-6096	36	9	questions	question	NOUN
cana-6096	36	10	are	be	AUX
cana-6096	36	11	specific	specific	ADJ
cana-6096	36	12	,	,	PUNCT
cana-6096	36	13	the	the	DET
cana-6096	36	14	answers	answer	NOUN
cana-6096	36	15	remain	remain	VERB
cana-6096	36	16	complex	complex	ADJ
cana-6096	36	17	.	.	PUNCT
cana-6096	37	1	rather	rather	ADV
cana-6096	37	2	than	than	ADP
cana-6096	37	3	tackling	tackle	VERB
cana-6096	37	4	these	these	DET
cana-6096	37	5	questions	question	NOUN
cana-6096	37	6	head	head	NOUN
cana-6096	37	7	-	-	PUNCT
cana-6096	37	8	on	on	ADP
cana-6096	37	9	,	,	PUNCT
cana-6096	37	10	let	let	AUX
cana-6096	37	11	's	us	PRON
cana-6096	37	12	(	(	PUNCT
cana-6096	37	13	re	re	NOUN
cana-6096	37	14	)	)	PUNCT
cana-6096	37	15	focus	focus	VERB
cana-6096	37	16	the	the	DET
cana-6096	37	17	objectives	objective	NOUN
cana-6096	37	18	of	of	ADP
cana-6096	37	19	the	the	DET
cana-6096	37	20	mathematics	mathematic	NOUN
cana-6096	37	21	course	course	NOUN
cana-6096	37	22	and	and	CCONJ
cana-6096	37	23	thus	thus	ADV
cana-6096	37	24	(	(	PUNCT
cana-6096	37	25	re	re	NOUN
cana-6096	37	26	)	)	PUNCT
cana-6096	37	27	specify	specify	VERB
cana-6096	37	28	the	the	DET
cana-6096	37	29	teacher	teacher	NOUN
cana-6096	37	30	's	's	PART
cana-6096	37	31	role	role	NOUN
cana-6096	37	32	.	.	PUNCT
cana-6096	38	1	this	this	DET
cana-6096	38	2	"	"	PUNCT
cana-6096	38	3	detour	detour	NOUN
cana-6096	38	4	"	"	PUNCT
cana-6096	38	5	through	through	ADP
cana-6096	38	6	fundamental	fundamental	ADJ
cana-6096	38	7	concepts	concept	NOUN
cana-6096	38	8	and	and	CCONJ
cana-6096	38	9	options	option	NOUN
cana-6096	38	10	should	should	AUX
cana-6096	38	11	facilitate	facilitate	VERB
cana-6096	38	12	the	the	DET
cana-6096	38	13	effective	effective	ADJ
cana-6096	38	14	handling	handling	NOUN
cana-6096	38	15	of	of	ADP
cana-6096	38	16	the	the	DET
cana-6096	38	17	initial	initial	ADJ
cana-6096	38	18	questions	question	NOUN
cana-6096	38	19	.	.	PUNCT
cana-6096	39	1	indeed	indeed	ADV
cana-6096	39	2	,	,	PUNCT
cana-6096	39	3	examining	examine	VERB
cana-6096	39	4	each	each	DET
cana-6096	39	5	person	person	NOUN
cana-6096	39	6	's	's	PART
cana-6096	39	7	representations	representation	NOUN
cana-6096	39	8	regarding	regard	VERB
cana-6096	39	9	the	the	DET
cana-6096	39	10	teaching	teaching	NOUN
cana-6096	39	11	and	and	CCONJ
cana-6096	39	12	learning	learning	NOUN
cana-6096	39	13	of	of	ADP
cana-6096	39	14	mathematics	mathematic	NOUN
cana-6096	39	15	and	and	CCONJ
cana-6096	39	16	putting	put	VERB
cana-6096	39	17	them	they	PRON
cana-6096	39	18	into	into	ADP
cana-6096	39	19	words	word	NOUN
cana-6096	39	20	allows	allow	VERB
cana-6096	39	21	us	we	PRON
cana-6096	39	22	to	to	PART
cana-6096	39	23	go	go	VERB
cana-6096	39	24	beyond	beyond	ADP
cana-6096	39	25	the	the	DET
cana-6096	39	26	exchange	exchange	NOUN
cana-6096	39	27	of	of	ADP
cana-6096	39	28	individual	individual	ADJ
cana-6096	39	29	recipes	recipe	NOUN
cana-6096	39	30	,	,	PUNCT
cana-6096	39	31	to	to	PART
cana-6096	39	32	place	place	VERB
cana-6096	39	33	discussions	discussion	NOUN
cana-6096	39	34	on	on	ADP
cana-6096	39	35	a	a	DET
cana-6096	39	36	higher	high	ADJ
cana-6096	39	37	level	level	NOUN
cana-6096	39	38	of	of	ADP
cana-6096	39	39	reflection	reflection	NOUN
cana-6096	39	40	,	,	PUNCT
cana-6096	39	41	to	to	PART
cana-6096	39	42	distance	distance	VERB
cana-6096	39	43	ourselves	ourselves	PRON
cana-6096	39	44	from	from	ADP
cana-6096	39	45	our	our	PRON
cana-6096	39	46	own	own	ADJ
cana-6096	39	47	routines	routine	NOUN
cana-6096	39	48	in	in	ADP
cana-6096	39	49	order	order	NOUN
cana-6096	39	50	to	to	PART
cana-6096	39	51	better	well	ADV
cana-6096	39	52	understand	understand	VERB
cana-6096	39	53	their	their	PRON
cana-6096	39	54	scope	scope	NOUN
cana-6096	39	55	.	.	PUNCT
cana-6096	40	1	in	in	ADP
cana-6096	40	2	short	short	ADJ
cana-6096	40	3	,	,	PUNCT
cana-6096	40	4	theorize	theorize	VERB
cana-6096	40	5	our	our	PRON
cana-6096	40	6	professional	professional	ADJ
cana-6096	40	7	practice	practice	NOUN
cana-6096	40	8	in	in	ADP
cana-6096	40	9	order	order	NOUN
cana-6096	40	10	to	to	PART
cana-6096	40	11	increase	increase	VERB
cana-6096	40	12	our	our	PRON
cana-6096	40	13	mastery	mastery	NOUN
cana-6096	40	14	of	of	ADP
cana-6096	40	15	it	it	PRON
cana-6096	40	16	.	.	PUNCT
cana-6096	41	1	this	this	DET
cana-6096	41	2	article	article	NOUN
cana-6096	41	3	is	be	AUX
cana-6096	41	4	therefore	therefore	ADV
cana-6096	41	5	presented	present	VERB
cana-6096	41	6	as	as	ADP
cana-6096	41	7	a	a	DET
cana-6096	41	8	tool	tool	NOUN
cana-6096	41	9	to	to	PART
cana-6096	41	10	help	help	VERB
cana-6096	41	11	analyze	analyze	VERB
cana-6096	41	12	practices	practice	NOUN
cana-6096	41	13	and	and	CCONJ
cana-6096	41	14	their	their	PRON
cana-6096	41	15	evaluation	evaluation	NOUN
cana-6096	41	16	.	.	PUNCT
cana-6096	42	1	if	if	SCONJ
cana-6096	42	2	“	"	PUNCT
cana-6096	42	3	to	to	PART
cana-6096	42	4	evaluate	evaluate	VERB
cana-6096	42	5	is	be	AUX
cana-6096	42	6	to	to	PART
cana-6096	42	7	compare	compare	VERB
cana-6096	42	8	,	,	PUNCT
cana-6096	42	9	”	"	PUNCT
cana-6096	42	10	it	it	PRON
cana-6096	42	11	is	be	AUX
cana-6096	42	12	important	important	ADJ
cana-6096	42	13	to	to	PART
cana-6096	42	14	have	have	VERB
cana-6096	42	15	a	a	DET
cana-6096	42	16	reference	reference	NOUN
cana-6096	42	17	point	point	NOUN
cana-6096	42	18	,	,	PUNCT
cana-6096	42	19	allowing	allow	VERB
cana-6096	42	20	us	we	PRON
cana-6096	42	21	to	to	PART
cana-6096	42	22	compare	compare	VERB
cana-6096	42	23	“	"	PUNCT
cana-6096	42	24	what	what	PRON
cana-6096	42	25	is	be	AUX
cana-6096	42	26	done	do	VERB
cana-6096	42	27	”	"	PUNCT
cana-6096	42	28	with	with	ADP
cana-6096	42	29	the	the	DET
cana-6096	42	30	“	"	PUNCT
cana-6096	42	31	ideal	ideal	ADJ
cana-6096	42	32	principles	principle	NOUN
cana-6096	42	33	of	of	ADP
cana-6096	42	34	what	what	PRON
cana-6096	42	35	should	should	AUX
cana-6096	42	36	be	be	AUX
cana-6096	42	37	done	do	VERB
cana-6096	42	38	.	.	PUNCT
cana-6096	42	39	”	"	PUNCT
cana-6096	43	1	9	9	NUM
cana-6096	43	2	communications	communication	NOUN
cana-6096	43	3	on	on	ADP
cana-6096	43	4	applied	apply	VERB
cana-6096	43	5	nonlinear	nonlinear	ADJ
cana-6096	43	6	analysis	analysis	NOUN
cana-6096	43	7	issn	issn	NOUN
cana-6096	43	8	:	:	PUNCT
cana-6096	43	9	1074	1074	NUM
cana-6096	43	10	-	-	PUNCT
cana-6096	43	11	133x	133x	NUM
cana-6096	43	12	vol	vol	NOUN
cana-6096	43	13	32	32	NUM
cana-6096	43	14	no	no	NOUN
cana-6096	43	15	.	.	NOUN
cana-6096	43	16	3	3	NUM
cana-6096	43	17	(	(	PUNCT
cana-6096	43	18	2025	2025	NUM
cana-6096	43	19	)	)	PUNCT
cana-6096	43	20	1063	1063	NUM
cana-6096	43	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	44	1	what	what	PRON
cana-6096	44	2	mathematics	mathematic	NOUN
cana-6096	44	3	do	do	AUX
cana-6096	44	4	we	we	PRON
cana-6096	44	5	want	want	VERB
cana-6096	44	6	for	for	ADP
cana-6096	44	7	our	our	PRON
cana-6096	44	8	students	student	NOUN
cana-6096	44	9	?	?	PUNCT
cana-6096	45	1	there	there	PRON
cana-6096	45	2	is	be	VERB
cana-6096	45	3	not	not	PART
cana-6096	45	4	one	one	NUM
cana-6096	45	5	conception	conception	NOUN
cana-6096	45	6	of	of	ADP
cana-6096	45	7	mathematics	mathematic	NOUN
cana-6096	45	8	,	,	PUNCT
cana-6096	45	9	but	but	CCONJ
cana-6096	45	10	several	several	ADJ
cana-6096	45	11	.	.	PUNCT
cana-6096	46	1	indeed	indeed	ADV
cana-6096	46	2	,	,	PUNCT
cana-6096	46	3	for	for	ADP
cana-6096	46	4	some	some	DET
cana-6096	46	5	people	people	NOUN
cana-6096	46	6	,	,	PUNCT
cana-6096	46	7	mathematics	mathematics	PROPN
cana-6096	46	8	is	be	AUX
cana-6096	46	9	a	a	DET
cana-6096	46	10	purely	purely	ADV
cana-6096	46	11	gratuitous	gratuitous	ADJ
cana-6096	46	12	mind	mind	NOUN
cana-6096	46	13	game	game	NOUN
cana-6096	46	14	whose	whose	DET
cana-6096	46	15	usefulness	usefulness	NOUN
cana-6096	46	16	remains	remain	VERB
cana-6096	46	17	to	to	PART
cana-6096	46	18	be	be	AUX
cana-6096	46	19	verified	verify	VERB
cana-6096	46	20	;	;	PUNCT
cana-6096	46	21	for	for	ADP
cana-6096	46	22	others	other	NOUN
cana-6096	46	23	,	,	PUNCT
cana-6096	46	24	it	it	PRON
cana-6096	46	25	proves	prove	VERB
cana-6096	46	26	to	to	PART
cana-6096	46	27	be	be	AUX
cana-6096	46	28	a	a	DET
cana-6096	46	29	powerful	powerful	ADJ
cana-6096	46	30	language	language	NOUN
cana-6096	46	31	and	and	CCONJ
cana-6096	46	32	an	an	DET
cana-6096	46	33	instrument	instrument	NOUN
cana-6096	46	34	of	of	ADP
cana-6096	46	35	implacable	implacable	ADJ
cana-6096	46	36	logic	logic	NOUN
cana-6096	46	37	;	;	PUNCT
cana-6096	46	38	for	for	ADP
cana-6096	46	39	still	still	ADV
cana-6096	46	40	others	other	NOUN
cana-6096	46	41	,	,	PUNCT
cana-6096	46	42	it	it	PRON
cana-6096	46	43	is	be	AUX
cana-6096	46	44	reduced	reduce	VERB
cana-6096	46	45	to	to	ADP
cana-6096	46	46	a	a	DET
cana-6096	46	47	multitude	multitude	NOUN
cana-6096	46	48	of	of	ADP
cana-6096	46	49	symbols	symbol	NOUN
cana-6096	46	50	whose	whose	DET
cana-6096	46	51	learning	learning	NOUN
cana-6096	46	52	is	be	AUX
cana-6096	46	53	more	more	ADV
cana-6096	46	54	akin	akin	ADJ
cana-6096	46	55	to	to	ADP
cana-6096	46	56	a	a	DET
cana-6096	46	57	chinese	chinese	ADJ
cana-6096	46	58	puzzle	puzzle	NOUN
cana-6096	46	59	than	than	ADP
cana-6096	46	60	to	to	ADP
cana-6096	46	61	any	any	DET
cana-6096	46	62	kind	kind	NOUN
cana-6096	46	63	of	of	ADP
cana-6096	46	64	logic	logic	NOUN
cana-6096	46	65	of	of	ADP
cana-6096	46	66	thought	thought	NOUN
cana-6096	46	67	.	.	PUNCT
cana-6096	47	1	even	even	ADV
cana-6096	47	2	if	if	SCONJ
cana-6096	47	3	it	it	PRON
cana-6096	47	4	seems	seem	VERB
cana-6096	47	5	oversimplified	oversimplified	ADJ
cana-6096	47	6	,	,	PUNCT
cana-6096	47	7	even	even	ADV
cana-6096	47	8	caricatured	caricature	VERB
cana-6096	47	9	,	,	PUNCT
cana-6096	47	10	the	the	DET
cana-6096	47	11	treffers	treffer	NOUN
cana-6096	47	12	model	model	NOUN
cana-6096	47	13	has	have	AUX
cana-6096	47	14	the	the	DET
cana-6096	47	15	advantage	advantage	NOUN
cana-6096	47	16	of	of	ADP
cana-6096	47	17	the	the	DET
cana-6096	47	18	horizontal	horizontal	ADJ
cana-6096	47	19	axis	axis	NOUN
cana-6096	47	20	is	be	AUX
cana-6096	47	21	that	that	PRON
cana-6096	47	22	of	of	ADP
cana-6096	47	23	context	context	NOUN
cana-6096	47	24	,	,	PUNCT
cana-6096	47	25	of	of	ADP
cana-6096	47	26	the	the	DET
cana-6096	47	27	familiar	familiar	ADJ
cana-6096	47	28	sources	source	NOUN
cana-6096	47	29	of	of	ADP
cana-6096	47	30	mathematics	mathematic	NOUN
cana-6096	47	31	,	,	PUNCT
cana-6096	47	32	of	of	ADP
cana-6096	47	33	reality	reality	NOUN
cana-6096	47	34	,	,	PUNCT
cana-6096	47	35	of	of	ADP
cana-6096	47	36	the	the	DET
cana-6096	47	37	meaning	mean	VERB
cana-6096	47	38	external	external	ADJ
cana-6096	47	39	to	to	ADP
cana-6096	47	40	mathematics	mathematic	NOUN
cana-6096	47	41	that	that	PRON
cana-6096	47	42	encourages	encourage	VERB
cana-6096	47	43	observation	observation	NOUN
cana-6096	47	44	and	and	CCONJ
cana-6096	47	45	manipulation	manipulation	NOUN
cana-6096	47	46	(	(	PUNCT
cana-6096	47	47	material	material	NOUN
cana-6096	47	48	or	or	CCONJ
cana-6096	47	49	mental	mental	ADJ
cana-6096	47	50	)	)	PUNCT
cana-6096	47	51	,	,	PUNCT
cana-6096	47	52	the	the	DET
cana-6096	47	53	vertical	vertical	ADJ
cana-6096	47	54	axis	axis	NOUN
cana-6096	47	55	is	be	AUX
cana-6096	47	56	that	that	PRON
cana-6096	47	57	of	of	ADP
cana-6096	47	58	deductive	deductive	ADJ
cana-6096	47	59	architecture	architecture	NOUN
cana-6096	47	60	,	,	PUNCT
cana-6096	47	61	of	of	ADP
cana-6096	47	62	the	the	DET
cana-6096	47	63	sequence	sequence	NOUN
cana-6096	47	64	of	of	ADP
cana-6096	47	65	definitions	definition	NOUN
cana-6096	47	66	,	,	PUNCT
cana-6096	47	67	of	of	ADP
cana-6096	47	68	properties	property	NOUN
cana-6096	47	69	,	,	PUNCT
cana-6096	47	70	of	of	ADP
cana-6096	47	71	the	the	DET
cana-6096	47	72	meaning	mean	VERB
cana-6096	47	73	internal	internal	ADJ
cana-6096	47	74	to	to	ADP
cana-6096	47	75	mathematics	mathematic	NOUN
cana-6096	47	76	.	.	PUNCT
cana-6096	48	1	schedule	schedule	NOUN
cana-6096	48	2	1	1	NUM
cana-6096	48	3	:	:	PUNCT
cana-6096	48	4	mathematical	mathematical	ADJ
cana-6096	48	5	concepts	concept	NOUN
cana-6096	48	6	(	(	PUNCT
cana-6096	48	7	treffers	treffer	NOUN
cana-6096	48	8	model	model	NOUN
cana-6096	48	9	)	)	PUNCT
cana-6096	48	10	in	in	ADP
cana-6096	48	11	relation	relation	NOUN
cana-6096	48	12	to	to	ADP
cana-6096	48	13	their	their	PRON
cana-6096	48	14	positions	position	NOUN
cana-6096	48	15	on	on	ADP
cana-6096	48	16	these	these	DET
cana-6096	48	17	two	two	NUM
cana-6096	48	18	axes	axis	NOUN
cana-6096	48	19	,	,	PUNCT
cana-6096	48	20	three	three	NUM
cana-6096	48	21	conceptions	conception	NOUN
cana-6096	48	22	of	of	ADP
cana-6096	48	23	mathematics	mathematic	NOUN
cana-6096	48	24	emerge	emerge	VERB
cana-6096	48	25	:	:	PUNCT
cana-6096	48	26	▪	▪	X
cana-6096	48	27	a	a	DET
cana-6096	48	28	mechanistic	mechanistic	ADJ
cana-6096	48	29	concept	concept	NOUN
cana-6096	48	30	if	if	SCONJ
cana-6096	48	31	it	it	PRON
cana-6096	48	32	is	be	AUX
cana-6096	48	33	not	not	PART
cana-6096	48	34	concerned	concern	VERB
cana-6096	48	35	with	with	ADP
cana-6096	48	36	either	either	CCONJ
cana-6096	48	37	the	the	DET
cana-6096	48	38	vertical	vertical	ADJ
cana-6096	48	39	or	or	CCONJ
cana-6096	48	40	horizontal	horizontal	ADJ
cana-6096	48	41	perspective	perspective	NOUN
cana-6096	48	42	.	.	PUNCT
cana-6096	49	1	doing	do	VERB
cana-6096	49	2	mathematics	mathematics	NOUN
cana-6096	49	3	amounts	amount	NOUN
cana-6096	49	4	to	to	ADP
cana-6096	49	5	performing	perform	VERB
cana-6096	49	6	routine	routine	ADJ
cana-6096	49	7	calculations	calculation	NOUN
cana-6096	49	8	,	,	PUNCT
cana-6096	49	9	applying	apply	VERB
cana-6096	49	10	rules	rule	NOUN
cana-6096	49	11	and	and	CCONJ
cana-6096	49	12	techniques	technique	NOUN
cana-6096	49	13	without	without	ADP
cana-6096	49	14	understanding	understanding	NOUN
cana-6096	49	15	where	where	SCONJ
cana-6096	49	16	these	these	DET
cana-6096	49	17	rules	rule	NOUN
cana-6096	49	18	come	come	VERB
cana-6096	49	19	from	from	ADP
cana-6096	49	20	(	(	PUNCT
cana-6096	49	21	no	no	DET
cana-6096	49	22	vertical	vertical	ADJ
cana-6096	49	23	perspective	perspective	NOUN
cana-6096	49	24	)	)	PUNCT
cana-6096	49	25	,	,	PUNCT
cana-6096	49	26	or	or	CCONJ
cana-6096	49	27	what	what	PRON
cana-6096	49	28	problems	problem	NOUN
cana-6096	49	29	they	they	PRON
cana-6096	49	30	are	be	AUX
cana-6096	49	31	likely	likely	ADJ
cana-6096	49	32	to	to	PART
cana-6096	49	33	explain	explain	VERB
cana-6096	49	34	(	(	PUNCT
cana-6096	49	35	no	no	DET
cana-6096	49	36	horizontal	horizontal	ADJ
cana-6096	49	37	perspective	perspective	NOUN
cana-6096	49	38	)	)	PUNCT
cana-6096	49	39	.	.	PUNCT
cana-6096	50	1	▪	▪	NOUN
cana-6096	50	2	the	the	DET
cana-6096	50	3	empiricist	empiricist	NOUN
cana-6096	50	4	conception	conception	NOUN
cana-6096	50	5	when	when	SCONJ
cana-6096	50	6	the	the	DET
cana-6096	50	7	emphasis	emphasis	NOUN
cana-6096	50	8	is	be	AUX
cana-6096	50	9	on	on	ADP
cana-6096	50	10	manipulation	manipulation	NOUN
cana-6096	50	11	and	and	CCONJ
cana-6096	50	12	observation	observation	NOUN
cana-6096	50	13	without	without	ADP
cana-6096	50	14	organization	organization	NOUN
cana-6096	50	15	,	,	PUNCT
cana-6096	50	16	demonstration	demonstration	NOUN
cana-6096	50	17	,	,	PUNCT
cana-6096	50	18	or	or	CCONJ
cana-6096	50	19	justification	justification	NOUN
cana-6096	50	20	of	of	ADP
cana-6096	50	21	"	"	PUNCT
cana-6096	50	22	discoveries	discovery	NOUN
cana-6096	50	23	.	.	PUNCT
cana-6096	50	24	"	"	PUNCT
cana-6096	51	1	people	people	NOUN
cana-6096	51	2	imbued	imbue	VERB
cana-6096	51	3	with	with	ADP
cana-6096	51	4	this	this	DET
cana-6096	51	5	representation	representation	NOUN
cana-6096	51	6	of	of	ADP
cana-6096	51	7	mathematics	mathematic	NOUN
cana-6096	51	8	are	be	AUX
cana-6096	51	9	often	often	ADV
cana-6096	51	10	attracted	attract	VERB
cana-6096	51	11	to	to	ADP
cana-6096	51	12	solving	solve	VERB
cana-6096	51	13	challenges	challenge	NOUN
cana-6096	51	14	,	,	PUNCT
cana-6096	51	15	puzzles	puzzle	NOUN
cana-6096	51	16	,	,	PUNCT
cana-6096	51	17	and	and	CCONJ
cana-6096	51	18	problems	problem	NOUN
cana-6096	51	19	,	,	PUNCT
cana-6096	51	20	1	1	NUM
cana-6096	51	21	treffers	treffer	NOUN
cana-6096	51	22	,	,	PUNCT
cana-6096	51	23	a.	a.	NOUN
cana-6096	51	24	(	(	PUNCT
cana-6096	51	25	1986	1986	NUM
cana-6096	51	26	)	)	PUNCT
cana-6096	51	27	.	.	PUNCT
cana-6096	52	1	op	op	NOUN
cana-6096	52	2	.	.	PUNCT
cana-6096	53	1	cit	cit	PROPN
cana-6096	53	2	,	,	PUNCT
cana-6096	53	3	17	17	NUM
cana-6096	53	4	17	17	NUM
cana-6096	53	5	fallowing[17	fallowing[17	X
cana-6096	53	6	]	]	PUNCT
cana-6096	53	7	for	for	ADP
cana-6096	53	8	a	a	DET
cana-6096	53	9	fairly	fairly	ADV
cana-6096	53	10	easy	easy	ADJ
cana-6096	53	11	"	"	PUNCT
cana-6096	53	12	positioning	positioning	NOUN
cana-6096	53	13	"	"	PUNCT
cana-6096	53	14	in	in	ADP
cana-6096	53	15	relation	relation	NOUN
cana-6096	53	16	to	to	ADP
cana-6096	53	17	the	the	DET
cana-6096	53	18	conceptions	conception	NOUN
cana-6096	53	19	of	of	ADP
cana-6096	53	20	mathematics	mathematic	NOUN
cana-6096	53	21	.	.	PUNCT
cana-6096	54	1	this	this	DET
cana-6096	54	2	model	model	NOUN
cana-6096	54	3	proposes	propose	VERB
cana-6096	54	4	to	to	PART
cana-6096	54	5	position	position	VERB
cana-6096	54	6	oneself	oneself	PRON
cana-6096	54	7	in	in	ADP
cana-6096	54	8	relation	relation	NOUN
cana-6096	54	9	to	to	ADP
cana-6096	54	10	two	two	NUM
cana-6096	54	11	axes	axis	NOUN
cana-6096	54	12	:	:	PUNCT
cana-6096	54	13	communications	communication	NOUN
cana-6096	54	14	on	on	ADP
cana-6096	54	15	applied	apply	VERB
cana-6096	54	16	nonlinear	nonlinear	ADJ
cana-6096	54	17	analysis	analysis	NOUN
cana-6096	54	18	issn	issn	NOUN
cana-6096	54	19	:	:	PUNCT
cana-6096	54	20	1074	1074	NUM
cana-6096	54	21	-	-	PUNCT
cana-6096	54	22	133x	133x	NUM
cana-6096	54	23	vol	vol	NOUN
cana-6096	54	24	32	32	NUM
cana-6096	54	25	no	no	NOUN
cana-6096	54	26	.	.	NOUN
cana-6096	54	27	3	3	NUM
cana-6096	54	28	(	(	PUNCT
cana-6096	54	29	2025	2025	NUM
cana-6096	54	30	)	)	PUNCT
cana-6096	54	31	1064	1064	NUM
cana-6096	54	32	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	54	33	but	but	CCONJ
cana-6096	54	34	not	not	PART
cana-6096	54	35	by	by	ADP
cana-6096	54	36	justifying	justify	VERB
cana-6096	54	37	the	the	DET
cana-6096	54	38	method	method	NOUN
cana-6096	54	39	used	use	VERB
cana-6096	54	40	to	to	PART
cana-6096	54	41	achieve	achieve	VERB
cana-6096	54	42	this	this	DET
cana-6096	54	43	resolution	resolution	NOUN
cana-6096	54	44	.	.	PUNCT
cana-6096	55	1	this	this	DET
cana-6096	55	2	conception	conception	NOUN
cana-6096	55	3	of	of	ADP
cana-6096	55	4	mathematics	mathematic	NOUN
cana-6096	55	5	is	be	AUX
cana-6096	55	6	located	locate	VERB
cana-6096	55	7	at	at	ADP
cana-6096	55	8	the	the	DET
cana-6096	55	9	extreme	extreme	NOUN
cana-6096	55	10	of	of	ADP
cana-6096	55	11	the	the	DET
cana-6096	55	12	horizontal	horizontal	ADJ
cana-6096	55	13	axis	axis	NOUN
cana-6096	55	14	.	.	PUNCT
cana-6096	56	1	▪	▪	NOUN
cana-6096	56	2	finally	finally	ADV
cana-6096	56	3	,	,	PUNCT
cana-6096	56	4	a	a	DET
cana-6096	56	5	conception	conception	NOUN
cana-6096	56	6	that	that	PRON
cana-6096	56	7	overly	overly	ADV
cana-6096	56	8	favors	favor	VERB
cana-6096	56	9	the	the	DET
cana-6096	56	10	vertical	vertical	ADJ
cana-6096	56	11	axis	axis	NOUN
cana-6096	56	12	is	be	AUX
cana-6096	56	13	called	call	VERB
cana-6096	56	14	structuralist	structuralist	ADJ
cana-6096	56	15	because	because	SCONJ
cana-6096	56	16	it	it	PRON
cana-6096	56	17	emphasizes	emphasize	VERB
cana-6096	56	18	the	the	DET
cana-6096	56	19	structure	structure	NOUN
cana-6096	56	20	of	of	ADP
cana-6096	56	21	mathematics	mathematic	NOUN
cana-6096	56	22	.	.	PUNCT
cana-6096	57	1	the	the	DET
cana-6096	57	2	structuralist	structuralist	ADJ
cana-6096	57	3	views	view	VERB
cana-6096	57	4	mathematics	mathematic	NOUN
cana-6096	57	5	as	as	ADP
cana-6096	57	6	a	a	DET
cana-6096	57	7	flawless	flawless	ADJ
cana-6096	57	8	construction	construction	NOUN
cana-6096	57	9	,	,	PUNCT
cana-6096	57	10	where	where	SCONJ
cana-6096	57	11	everything	everything	PRON
cana-6096	57	12	fits	fit	VERB
cana-6096	57	13	together	together	ADV
cana-6096	57	14	logically	logically	ADV
cana-6096	57	15	.	.	PUNCT
cana-6096	58	1	the	the	DET
cana-6096	58	2	teaching	teaching	NOUN
cana-6096	58	3	of	of	ADP
cana-6096	58	4	"	"	PUNCT
cana-6096	58	5	modern	modern	ADJ
cana-6096	58	6	mathematics	mathematic	NOUN
cana-6096	58	7	"	"	PUNCT
cana-6096	58	8	contributed	contribute	VERB
cana-6096	58	9	to	to	ADP
cana-6096	58	10	the	the	DET
cana-6096	58	11	development	development	NOUN
cana-6096	58	12	of	of	ADP
cana-6096	58	13	this	this	DET
cana-6096	58	14	view	view	NOUN
cana-6096	58	15	,	,	PUNCT
cana-6096	58	16	where	where	SCONJ
cana-6096	58	17	clear	clear	ADJ
cana-6096	58	18	and	and	CCONJ
cana-6096	58	19	elegant	elegant	ADJ
cana-6096	58	20	theoretical	theoretical	ADJ
cana-6096	58	21	connections	connection	NOUN
cana-6096	58	22	were	be	AUX
cana-6096	58	23	the	the	DET
cana-6096	58	24	primary	primary	ADJ
cana-6096	58	25	concern	concern	NOUN
cana-6096	58	26	.	.	PUNCT
cana-6096	59	1	▪	▪	X
cana-6096	59	2	a	a	DET
cana-6096	59	3	realistic	realistic	ADJ
cana-6096	59	4	conception	conception	NOUN
cana-6096	59	5	of	of	ADP
cana-6096	59	6	mathematics	mathematic	NOUN
cana-6096	59	7	integrates	integrate	VERB
cana-6096	59	8	the	the	DET
cana-6096	59	9	three	three	NUM
cana-6096	59	10	previous	previous	ADJ
cana-6096	59	11	dimensions	dimension	NOUN
cana-6096	59	12	.	.	PUNCT
cana-6096	60	1	this	this	PRON
cana-6096	60	2	gives	give	VERB
cana-6096	60	3	meaning	meaning	NOUN
cana-6096	60	4	to	to	ADP
cana-6096	60	5	the	the	DET
cana-6096	60	6	mathematical	mathematical	ADJ
cana-6096	60	7	activities	activity	NOUN
cana-6096	60	8	offered	offer	VERB
cana-6096	60	9	to	to	ADP
cana-6096	60	10	students	student	NOUN
cana-6096	60	11	.	.	PUNCT
cana-6096	61	1	indeed	indeed	ADV
cana-6096	61	2	,	,	PUNCT
cana-6096	61	3	when	when	SCONJ
cana-6096	61	4	faced	face	VERB
cana-6096	61	5	with	with	ADP
cana-6096	61	6	a	a	DET
cana-6096	61	7	mathematical	mathematical	ADJ
cana-6096	61	8	tool	tool	NOUN
cana-6096	61	9	to	to	PART
cana-6096	61	10	use	use	VERB
cana-6096	61	11	(	(	PUNCT
cana-6096	61	12	mechanistic	mechanistic	ADJ
cana-6096	61	13	logic	logic	NOUN
cana-6096	61	14	)	)	PUNCT
cana-6096	61	15	,	,	PUNCT
cana-6096	61	16	the	the	DET
cana-6096	61	17	student	student	NOUN
cana-6096	61	18	has	have	VERB
cana-6096	61	19	the	the	DET
cana-6096	61	20	right	right	NOUN
cana-6096	61	21	to	to	PART
cana-6096	61	22	ask	ask	VERB
cana-6096	61	23	themselves	themselves	PRON
cana-6096	61	24	on	on	ADP
cana-6096	61	25	the	the	DET
cana-6096	61	26	one	one	NUM
cana-6096	61	27	hand	hand	NOUN
cana-6096	61	28	,	,	PUNCT
cana-6096	61	29	where	where	SCONJ
cana-6096	61	30	they	they	PRON
cana-6096	61	31	fit	fit	VERB
cana-6096	61	32	into	into	ADP
cana-6096	61	33	the	the	DET
cana-6096	61	34	mathematical	mathematical	ADJ
cana-6096	61	35	construction	construction	NOUN
cana-6096	61	36	(	(	PUNCT
cana-6096	61	37	structuralist	structuralist	ADJ
cana-6096	61	38	logic	logic	NOUN
cana-6096	61	39	)	)	PUNCT
cana-6096	61	40	,	,	PUNCT
cana-6096	61	41	on	on	ADP
cana-6096	61	42	the	the	DET
cana-6096	61	43	other	other	ADJ
cana-6096	61	44	hand	hand	NOUN
cana-6096	61	45	,	,	PUNCT
cana-6096	61	46	what	what	DET
cana-6096	61	47	context	context	NOUN
cana-6096	61	48	they	they	PRON
cana-6096	61	49	fit	fit	VERB
cana-6096	61	50	into	into	ADP
cana-6096	61	51	(	(	PUNCT
cana-6096	61	52	empiricist	empiricist	NOUN
cana-6096	61	53	logic	logic	NOUN
cana-6096	61	54	)	)	PUNCT
cana-6096	61	55	.	.	PUNCT
cana-6096	62	1	schedule	schedule	NOUN
cana-6096	62	2	2	2	NUM
cana-6096	62	3	:	:	PUNCT
cana-6096	62	4	“	"	PUNCT
cana-6096	62	5	the	the	DET
cana-6096	62	6	meaning	meaning	NOUN
cana-6096	62	7	”	"	PUNCT
cana-6096	62	8	access	access	NOUN
cana-6096	62	9	to	to	ADP
cana-6096	62	10	meaning	mean	VERB
cana-6096	62	11	access	access	NOUN
cana-6096	62	12	to	to	ADP
cana-6096	62	13	meaning	mean	VERB
cana-6096	62	14	inside	inside	ADP
cana-6096	62	15	mathematical	mathematical	ADJ
cana-6096	62	16	deductive	deductive	ADJ
cana-6096	62	17	logic	logic	NOUN
cana-6096	62	18	mechanistic	mechanistic	ADJ
cana-6096	62	19	concept	concept	NOUN
cana-6096	62	20	within	within	ADP
cana-6096	62	21	the	the	DET
cana-6096	62	22	mathematical	mathematical	ADJ
cana-6096	62	23	context	context	NOUN
cana-6096	62	24	structuralist	structuralist	ADJ
cana-6096	62	25	concept	concept	NOUN
cana-6096	62	26	empiricist	empiricist	NOUN
cana-6096	62	27	concept	concept	NOUN
cana-6096	62	28	“	"	PUNCT
cana-6096	62	29	i	i	PRON
cana-6096	62	30	know	know	VERB
cana-6096	62	31	structurally	structurally	ADV
cana-6096	62	32	why	why	SCONJ
cana-6096	62	33	i	i	PRON
cana-6096	62	34	do	do	VERB
cana-6096	62	35	it	it	PRON
cana-6096	62	36	”	"	PUNCT
cana-6096	62	37	“	"	PUNCT
cana-6096	62	38	i	i	PRON
cana-6096	62	39	do	do	AUX
cana-6096	62	40	”	"	PUNCT
cana-6096	62	41	“	"	PUNCT
cana-6096	62	42	i	i	PRON
cana-6096	62	43	know	know	VERB
cana-6096	62	44	contextually	contextually	ADV
cana-6096	62	45	why	why	SCONJ
cana-6096	62	46	i	i	PRON
cana-6096	62	47	am	be	AUX
cana-6096	62	48	doing	do	VERB
cana-6096	62	49	it	it	PRON
cana-6096	62	50	”	"	PUNCT
cana-6096	62	51	the	the	DET
cana-6096	62	52	acquisition	acquisition	NOUN
cana-6096	62	53	of	of	ADP
cana-6096	62	54	the	the	DET
cana-6096	62	55	meaning	meaning	NOUN
cana-6096	62	56	or	or	CCONJ
cana-6096	62	57	significance	significance	NOUN
cana-6096	62	58	of	of	ADP
cana-6096	62	59	a	a	DET
cana-6096	62	60	concept	concept	NOUN
cana-6096	62	61	(	(	PUNCT
cana-6096	62	62	or	or	CCONJ
cana-6096	62	63	knowledge	knowledge	NOUN
cana-6096	62	64	)	)	PUNCT
cana-6096	62	65	occurs	occur	VERB
cana-6096	62	66	through	through	ADP
cana-6096	62	67	confrontation	confrontation	NOUN
cana-6096	62	68	with	with	ADP
cana-6096	62	69	problematic	problematic	ADJ
cana-6096	62	70	situations	situation	NOUN
cana-6096	62	71	that	that	PRON
cana-6096	62	72	involve	involve	VERB
cana-6096	62	73	the	the	DET
cana-6096	62	74	concept	concept	NOUN
cana-6096	62	75	(	(	PUNCT
cana-6096	62	76	or	or	CCONJ
cana-6096	62	77	knowledge	knowledge	NOUN
cana-6096	62	78	)	)	PUNCT
cana-6096	62	79	.	.	PUNCT
cana-6096	63	1	meaning	mean	VERB
cana-6096	63	2	:	:	PUNCT
cana-6096	63	3	this	this	PRON
cana-6096	63	4	is	be	AUX
cana-6096	63	5	a	a	DET
cana-6096	63	6	relationship	relationship	NOUN
cana-6096	63	7	between	between	ADP
cana-6096	63	8	the	the	DET
cana-6096	63	9	subject	subject	NOUN
cana-6096	63	10	and	and	CCONJ
cana-6096	63	11	the	the	DET
cana-6096	63	12	situations	situation	NOUN
cana-6096	63	13	and	and	CCONJ
cana-6096	63	14	symbols	symbol	NOUN
cana-6096	63	15	that	that	PRON
cana-6096	63	16	indicate	indicate	VERB
cana-6096	63	17	the	the	DET
cana-6096	63	18	concept	concept	NOUN
cana-6096	63	19	.	.	PUNCT
cana-6096	64	1	these	these	PRON
cana-6096	64	2	are	be	AUX
cana-6096	64	3	the	the	DET
cana-6096	64	4	schemas	schema	NOUN
cana-6096	64	5	we	we	PRON
cana-6096	64	6	evoke	evoke	VERB
cana-6096	64	7	when	when	SCONJ
cana-6096	64	8	situations	situation	NOUN
cana-6096	64	9	are	be	AUX
cana-6096	64	10	presented	present	VERB
cana-6096	64	11	to	to	ADP
cana-6096	64	12	us	we	PRON
cana-6096	64	13	.	.	PUNCT
cana-6096	65	1	schema	schema	NOUN
cana-6096	65	2	:	:	PUNCT
cana-6096	65	3	the	the	DET
cana-6096	65	4	invariant	invariant	ADJ
cana-6096	65	5	organization	organization	NOUN
cana-6096	65	6	of	of	ADP
cana-6096	65	7	behavior	behavior	NOUN
cana-6096	65	8	for	for	ADP
cana-6096	65	9	a	a	DET
cana-6096	65	10	given	give	VERB
cana-6096	65	11	class	class	NOUN
cana-6096	65	12	of	of	ADP
cana-6096	65	13	problems	problem	NOUN
cana-6096	65	14	.	.	PUNCT
cana-6096	66	1	theorems	theorem	NOUN
cana-6096	66	2	in	in	ADP
cana-6096	66	3	action	action	NOUN
cana-6096	66	4	:	:	PUNCT
cana-6096	66	5	these	these	PRON
cana-6096	66	6	are	be	AUX
cana-6096	66	7	"	"	PUNCT
cana-6096	66	8	propositional	propositional	ADJ
cana-6096	66	9	"	"	PUNCT
cana-6096	66	10	invariants	invariant	NOUN
cana-6096	66	11	:	:	PUNCT
cana-6096	66	12	they	they	PRON
cana-6096	66	13	are	be	AUX
cana-6096	66	14	held	hold	VERB
cana-6096	66	15	to	to	PART
cana-6096	66	16	be	be	AUX
cana-6096	66	17	true	true	ADJ
cana-6096	66	18	in	in	ADP
cana-6096	66	19	the	the	DET
cana-6096	66	20	functioning	functioning	NOUN
cana-6096	66	21	of	of	ADP
cana-6096	66	22	the	the	DET
cana-6096	66	23	activity	activity	NOUN
cana-6096	66	24	.	.	PUNCT
cana-6096	67	1	example	example	NOUN
cana-6096	67	2	:	:	PUNCT
cana-6096	67	3	10	10	NUM
cana-6096	67	4	×	×	NOUN
cana-6096	67	5	4.7	4.7	NUM
cana-6096	67	6	=	=	SYM
cana-6096	67	7	4.70	4.70	NUM
cana-6096	67	8	(	(	PUNCT
cana-6096	67	9	"	"	PUNCT
cana-6096	67	10	when	when	SCONJ
cana-6096	67	11	we	we	PRON
cana-6096	67	12	multiply	multiply	VERB
cana-6096	67	13	a	a	DET
cana-6096	67	14	number	number	NOUN
cana-6096	67	15	by	by	ADP
cana-6096	67	16	10	10	NUM
cana-6096	67	17	,	,	PUNCT
cana-6096	67	18	we	we	PRON
cana-6096	67	19	add	add	VERB
cana-6096	67	20	0	0	NUM
cana-6096	67	21	.	.	PUNCT
cana-6096	67	22	"	"	PUNCT
cana-6096	67	23	)	)	PUNCT
cana-6096	68	1	what	what	PRON
cana-6096	68	2	is	be	AUX
cana-6096	68	3	the	the	DET
cana-6096	68	4	role	role	NOUN
cana-6096	68	5	of	of	ADP
cana-6096	68	6	the	the	DET
cana-6096	68	7	mathematics	mathematics	NOUN
cana-6096	68	8	teacher	teacher	NOUN
cana-6096	68	9	?	?	PUNCT
cana-6096	69	1	1	1	X
cana-6096	69	2	.	.	X
cana-6096	69	3	teaching	teach	VERB
cana-6096	69	4	this	this	DET
cana-6096	69	5	role	role	NOUN
cana-6096	69	6	focuses	focus	VERB
cana-6096	69	7	on	on	ADP
cana-6096	69	8	the	the	DET
cana-6096	69	9	mathematical	mathematical	ADJ
cana-6096	69	10	content	content	NOUN
cana-6096	69	11	to	to	PART
cana-6096	69	12	be	be	AUX
cana-6096	69	13	taught	teach	VERB
cana-6096	69	14	.	.	PUNCT
cana-6096	70	1	this	this	PRON
cana-6096	70	2	constitutes	constitute	VERB
cana-6096	70	3	the	the	DET
cana-6096	70	4	basic	basic	ADJ
cana-6096	70	5	material	material	NOUN
cana-6096	70	6	for	for	ADP
cana-6096	70	7	fully	fully	ADV
cana-6096	70	8	fulfilling	fulfil	VERB
cana-6096	70	9	this	this	DET
cana-6096	70	10	role	role	NOUN
cana-6096	70	11	.	.	PUNCT
cana-6096	71	1	the	the	DET
cana-6096	71	2	objective	objective	NOUN
cana-6096	71	3	is	be	AUX
cana-6096	71	4	the	the	DET
cana-6096	71	5	student	student	NOUN
cana-6096	71	6	's	's	PART
cana-6096	71	7	mastery	mastery	NOUN
cana-6096	71	8	of	of	ADP
cana-6096	71	9	the	the	DET
cana-6096	71	10	curriculum	curriculum	NOUN
cana-6096	71	11	content	content	NOUN
cana-6096	71	12	.	.	PUNCT
cana-6096	72	1	its	its	PRON
cana-6096	72	2	assessment	assessment	NOUN
cana-6096	72	3	aims	aim	VERB
cana-6096	72	4	to	to	PART
cana-6096	72	5	monitor	monitor	VERB
cana-6096	72	6	the	the	DET
cana-6096	72	7	level	level	NOUN
cana-6096	72	8	of	of	ADP
cana-6096	72	9	mastery	mastery	NOUN
cana-6096	72	10	achieved	achieve	VERB
cana-6096	72	11	by	by	ADP
cana-6096	72	12	the	the	DET
cana-6096	72	13	student	student	NOUN
cana-6096	72	14	.	.	PUNCT
cana-6096	73	1	meaning	mean	VERB
cana-6096	73	2	according	accord	VERB
cana-6096	73	3	to	to	ADP
cana-6096	73	4	vergnaud	vergnaud	VERB
cana-6096	73	5	[	[	X
cana-6096	73	6	19	19	NUM
cana-6096	73	7	]	]	PUNCT
cana-6096	73	8	.	.	PUNCT
cana-6096	74	1	communications	communication	NOUN
cana-6096	74	2	on	on	ADP
cana-6096	74	3	applied	apply	VERB
cana-6096	74	4	nonlinear	nonlinear	ADJ
cana-6096	74	5	analysis	analysis	NOUN
cana-6096	74	6	issn	issn	NOUN
cana-6096	74	7	:	:	PUNCT
cana-6096	74	8	1074	1074	NUM
cana-6096	74	9	-	-	PUNCT
cana-6096	74	10	133x	133x	NUM
cana-6096	74	11	vol	vol	NOUN
cana-6096	74	12	32	32	NUM
cana-6096	74	13	no	no	NOUN
cana-6096	74	14	.	.	NOUN
cana-6096	74	15	3	3	NUM
cana-6096	74	16	(	(	PUNCT
cana-6096	74	17	2025	2025	NUM
cana-6096	74	18	)	)	PUNCT
cana-6096	74	19	1065	1065	NUM
cana-6096	75	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	75	2	2	2	X
cana-6096	75	3	.	.	PUNCT
cana-6096	75	4	trainer	trainer	NOUN
cana-6096	75	5	this	this	DET
cana-6096	75	6	second	second	ADJ
cana-6096	75	7	role	role	NOUN
cana-6096	75	8	is	be	AUX
cana-6096	75	9	just	just	ADV
cana-6096	75	10	as	as	ADV
cana-6096	75	11	fundamental	fundamental	ADJ
cana-6096	75	12	as	as	ADP
cana-6096	75	13	the	the	DET
cana-6096	75	14	first	first	ADJ
cana-6096	75	15	.	.	PUNCT
cana-6096	76	1	it	it	PRON
cana-6096	76	2	focuses	focus	VERB
cana-6096	76	3	more	more	ADJ
cana-6096	76	4	on	on	ADP
cana-6096	76	5	the	the	DET
cana-6096	76	6	student	student	NOUN
cana-6096	76	7	as	as	ADP
cana-6096	76	8	a	a	DET
cana-6096	76	9	learner	learner	NOUN
cana-6096	76	10	of	of	ADP
cana-6096	76	11	mathematics	mathematic	NOUN
cana-6096	76	12	.	.	PUNCT
cana-6096	77	1	mathematics	mathematic	NOUN
cana-6096	77	2	is	be	AUX
cana-6096	77	3	no	no	ADV
cana-6096	77	4	longer	long	ADV
cana-6096	77	5	experienced	experience	VERB
cana-6096	77	6	as	as	ADP
cana-6096	77	7	the	the	DET
cana-6096	77	8	goal	goal	NOUN
cana-6096	77	9	of	of	ADP
cana-6096	77	10	learning	learning	NOUN
cana-6096	77	11	but	but	CCONJ
cana-6096	77	12	as	as	ADP
cana-6096	77	13	a	a	DET
cana-6096	77	14	support	support	NOUN
cana-6096	77	15	the	the	DET
cana-6096	77	16	development	development	NOUN
cana-6096	77	17	of	of	ADP
cana-6096	77	18	qualities	quality	NOUN
cana-6096	77	19	that	that	PRON
cana-6096	77	20	promote	promote	VERB
cana-6096	77	21	learning	learning	NOUN
cana-6096	77	22	.	.	PUNCT
cana-6096	78	1	the	the	DET
cana-6096	78	2	assessment	assessment	NOUN
cana-6096	78	3	implemented	implement	VERB
cana-6096	78	4	to	to	PART
cana-6096	78	5	support	support	VERB
cana-6096	78	6	this	this	DET
cana-6096	78	7	development	development	NOUN
cana-6096	78	8	is	be	AUX
cana-6096	78	9	formative	formative	ADJ
cana-6096	78	10	in	in	ADP
cana-6096	78	11	the	the	DET
cana-6096	78	12	sense	sense	NOUN
cana-6096	78	13	that	that	SCONJ
cana-6096	78	14	it	it	PRON
cana-6096	78	15	is	be	AUX
cana-6096	78	16	the	the	DET
cana-6096	78	17	progress	progress	NOUN
cana-6096	78	18	made	make	VERB
cana-6096	78	19	by	by	ADP
cana-6096	78	20	the	the	DET
cana-6096	78	21	student	student	NOUN
cana-6096	78	22	that	that	PRON
cana-6096	78	23	is	be	AUX
cana-6096	78	24	important	important	ADJ
cana-6096	78	25	.	.	PUNCT
cana-6096	79	1	these	these	DET
cana-6096	79	2	two	two	NUM
cana-6096	79	3	roles	role	NOUN
cana-6096	79	4	are	be	AUX
cana-6096	79	5	not	not	PART
cana-6096	79	6	juxtaposed	juxtapose	VERB
cana-6096	79	7	,	,	PUNCT
cana-6096	79	8	nor	nor	CCONJ
cana-6096	79	9	does	do	AUX
cana-6096	79	10	one	one	PRON
cana-6096	79	11	exclude	exclude	VERB
cana-6096	79	12	the	the	DET
cana-6096	79	13	other	other	ADJ
cana-6096	79	14	;	;	PUNCT
cana-6096	79	15	on	on	ADP
cana-6096	79	16	the	the	DET
cana-6096	79	17	contrary	contrary	NOUN
cana-6096	79	18	,	,	PUNCT
cana-6096	79	19	they	they	PRON
cana-6096	79	20	stem	stem	VERB
cana-6096	79	21	from	from	ADP
cana-6096	79	22	the	the	DET
cana-6096	79	23	same	same	ADJ
cana-6096	79	24	goal	goal	NOUN
cana-6096	79	25	:	:	PUNCT
cana-6096	79	26	"	"	PUNCT
cana-6096	79	27	the	the	DET
cana-6096	79	28	training	training	NOUN
cana-6096	79	29	of	of	ADP
cana-6096	79	30	the	the	DET
cana-6096	79	31	student	student	NOUN
cana-6096	79	32	in	in	ADP
cana-6096	79	33	mathematics	mathematic	NOUN
cana-6096	79	34	.	.	PUNCT
cana-6096	79	35	"	"	PUNCT
cana-6096	80	1	the	the	DET
cana-6096	80	2	teacher	teacher	NOUN
cana-6096	80	3	-	-	PUNCT
cana-6096	80	4	teacher	teacher	NOUN
cana-6096	80	5	and	and	CCONJ
cana-6096	80	6	the	the	DET
cana-6096	80	7	teacher	teacher	NOUN
cana-6096	80	8	-	-	PUNCT
cana-6096	80	9	trainer	trainer	NOUN
cana-6096	80	10	are	be	AUX
cana-6096	80	11	not	not	PART
cana-6096	80	12	independent	independent	ADJ
cana-6096	80	13	.	.	PUNCT
cana-6096	81	1	one	one	NUM
cana-6096	81	2	has	have	VERB
cana-6096	81	3	an	an	DET
cana-6096	81	4	impact	impact	NOUN
cana-6096	81	5	on	on	ADP
cana-6096	81	6	the	the	DET
cana-6096	81	7	other	other	ADJ
cana-6096	81	8	.	.	PUNCT
cana-6096	82	1	thus	thus	ADV
cana-6096	82	2	,	,	PUNCT
cana-6096	82	3	the	the	DET
cana-6096	82	4	following	follow	VERB
cana-6096	82	5	hypothesis	hypothesis	NOUN
cana-6096	82	6	is	be	AUX
cana-6096	82	7	strongly	strongly	ADV
cana-6096	82	8	suggested	suggest	VERB
cana-6096	82	9	:	:	PUNCT
cana-6096	82	10	the	the	DET
cana-6096	82	11	development	development	NOUN
cana-6096	82	12	of	of	ADP
cana-6096	82	13	qualities	quality	NOUN
cana-6096	82	14	specific	specific	ADJ
cana-6096	82	15	to	to	ADP
cana-6096	82	16	learning	learn	VERB
cana-6096	82	17	mathematics	mathematic	NOUN
cana-6096	82	18	will	will	AUX
cana-6096	82	19	influence	influence	VERB
cana-6096	82	20	the	the	DET
cana-6096	82	21	results	result	NOUN
cana-6096	82	22	obtained	obtain	VERB
cana-6096	82	23	during	during	ADP
cana-6096	82	24	this	this	DET
cana-6096	82	25	learning	learning	NOUN
cana-6096	82	26	.	.	PUNCT
cana-6096	83	1	in	in	ADP
cana-6096	83	2	other	other	ADJ
cana-6096	83	3	words	word	NOUN
cana-6096	83	4	,	,	PUNCT
cana-6096	83	5	it	it	PRON
cana-6096	83	6	seems	seem	VERB
cana-6096	83	7	beneficial	beneficial	ADJ
cana-6096	83	8	to	to	PART
cana-6096	83	9	pursue	pursue	VERB
cana-6096	83	10	training	training	NOUN
cana-6096	83	11	objectives	objective	NOUN
cana-6096	83	12	to	to	PART
cana-6096	83	13	better	well	ADV
cana-6096	83	14	achieve	achieve	VERB
cana-6096	83	15	teaching	teaching	NOUN
cana-6096	83	16	objectives	objective	NOUN
cana-6096	83	17	.	.	PUNCT
cana-6096	84	1	the	the	DET
cana-6096	84	2	following	follow	VERB
cana-6096	84	3	table	table	NOUN
cana-6096	84	4	summarizes	summarize	VERB
cana-6096	84	5	these	these	DET
cana-6096	84	6	two	two	NUM
cana-6096	84	7	roles	role	NOUN
cana-6096	84	8	and	and	CCONJ
cana-6096	84	9	their	their	PRON
cana-6096	84	10	main	main	ADJ
cana-6096	84	11	characteristics	characteristic	NOUN
cana-6096	84	12	.	.	PUNCT
cana-6096	85	1	schedule	schedule	NOUN
cana-6096	85	2	3	3	NUM
cana-6096	85	3	:	:	PUNCT
cana-6096	85	4	“	"	PUNCT
cana-6096	85	5	teaching	teach	VERB
cana-6096	85	6	-	-	PUNCT
cana-6096	85	7	training	training	NOUN
cana-6096	85	8	”	"	PUNCT
cana-6096	85	9	objective	objective	NOUN
cana-6096	85	10	…	…	PUNCT
cana-6096	85	11	teaching	teach	VERB
cana-6096	85	12	training	train	VERB
cana-6096	85	13	direct	direct	ADJ
cana-6096	85	14	purpose	purpose	NOUN
cana-6096	85	15	:	:	PUNCT
cana-6096	85	16	teaching	teach	VERB
cana-6096	85	17	someone	someone	PRON
cana-6096	85	18	something	something	PRON
cana-6096	85	19	training	train	VERB
cana-6096	85	20	someone	someone	PRON
cana-6096	85	21	to	to	PART
cana-6096	85	22	do	do	VERB
cana-6096	85	23	something	something	PRON
cana-6096	85	24	focused	focus	VERB
cana-6096	85	25	on	on	ADP
cana-6096	85	26	...	...	PUNCT
cana-6096	85	27	content	content	NOUN
cana-6096	85	28	mastery	mastery	NOUN
cana-6096	85	29	developing	develop	VERB
cana-6096	85	30	skills	skill	NOUN
cana-6096	85	31	logic	logic	NOUN
cana-6096	85	32	of	of	ADP
cana-6096	85	33	...	...	PUNCT
cana-6096	85	34	results	result	NOUN
cana-6096	85	35	process	process	NOUN
cana-6096	85	36	role	role	NOUN
cana-6096	85	37	teacher	teacher	NOUN
cana-6096	85	38	-	-	PUNCT
cana-6096	85	39	monitor	monitor	NOUN
cana-6096	85	40	trainer	trainer	NOUN
cana-6096	85	41	-	-	PUNCT
cana-6096	85	42	observer	observer	NOUN
cana-6096	85	43	of	of	ADP
cana-6096	85	44	assessment	assessment	NOUN
cana-6096	85	45	:	:	PUNCT
cana-6096	85	46	summative	summative	ADJ
cana-6096	85	47	and	and	CCONJ
cana-6096	85	48	certification	certification	NOUN
cana-6096	85	49	formative	formative	ADJ
cana-6096	85	50	assessment	assessment	NOUN
cana-6096	85	51	situations	situation	NOUN
cana-6096	85	52	:	:	PUNCT
cana-6096	85	53	tests	test	NOUN
cana-6096	85	54	,	,	PUNCT
cana-6096	85	55	homework	homework	NOUN
cana-6096	85	56	,	,	PUNCT
cana-6096	85	57	essays	essay	NOUN
cana-6096	85	58	classroom	classroom	NOUN
cana-6096	85	59	activities	activity	NOUN
cana-6096	85	60	,	,	PUNCT
cana-6096	85	61	resolving	resolve	VERB
cana-6096	85	62	problem	problem	NOUN
cana-6096	85	63	or	or	CCONJ
cana-6096	85	64	open	open	ADV
cana-6096	85	65	-	-	PUNCT
cana-6096	85	66	ended	end	VERB
cana-6096	85	67	situations	situation	NOUN
cana-6096	85	68	,	,	PUNCT
cana-6096	85	69	group	group	NOUN
cana-6096	85	70	work	work	NOUN
cana-6096	85	71	,	,	PUNCT
cana-6096	85	72	presentations	presentation	NOUN
cana-6096	85	73	,	,	PUNCT
cana-6096	85	74	etc	etc	X
cana-6096	85	75	.	.	X
cana-6096	85	76	summary	summary	NOUN
cana-6096	85	77	of	of	ADP
cana-6096	85	78	assessments	assessment	NOUN
cana-6096	85	79	:	:	PUNCT
cana-6096	85	80	grades	grade	NOUN
cana-6096	85	81	educational	educational	ADJ
cana-6096	85	82	interviews	interview	NOUN
cana-6096	85	83	,	,	PUNCT
cana-6096	85	84	remarks	remark	NOUN
cana-6096	85	85	,	,	PUNCT
cana-6096	85	86	comments	comment	NOUN
cana-6096	85	87	,	,	PUNCT
cana-6096	85	88	monitoring	monitoring	NOUN
cana-6096	85	89	sheets	sheet	NOUN
cana-6096	85	90	,	,	PUNCT
cana-6096	85	91	etc	etc	X
cana-6096	85	92	.	.	X
cana-6096	85	93	assessment	assessment	NOUN
cana-6096	85	94	referent	referent	NOUN
cana-6096	85	95	:	:	PUNCT
cana-6096	85	96	program	program	NOUN
cana-6096	85	97	purpose	purpose	NOUN
cana-6096	85	98	of	of	ADP
cana-6096	85	99	assessment	assessment	NOUN
cana-6096	85	100	:	:	PUNCT
cana-6096	85	101	level	level	NOUN
cana-6096	85	102	control	control	NOUN
cana-6096	85	103	state	state	NOUN
cana-6096	85	104	of	of	ADP
cana-6096	85	105	progress	progress	NOUN
cana-6096	85	106	how	how	SCONJ
cana-6096	85	107	to	to	PART
cana-6096	85	108	“	"	PUNCT
cana-6096	85	109	learn	learn	VERB
cana-6096	85	110	by	by	ADP
cana-6096	85	111	problems	problem	NOUN
cana-6096	85	112	”	"	PUNCT
cana-6096	85	113	in	in	ADP
cana-6096	85	114	mathematics	mathematic	NOUN
cana-6096	85	115	?	?	PUNCT
cana-6096	86	1	before	before	ADP
cana-6096	86	2	addressing	address	VERB
cana-6096	86	3	the	the	DET
cana-6096	86	4	issue	issue	NOUN
cana-6096	86	5	of	of	ADP
cana-6096	86	6	problem	problem	NOUN
cana-6096	86	7	-	-	PUNCT
cana-6096	86	8	based	base	VERB
cana-6096	86	9	learning	learning	NOUN
cana-6096	86	10	in	in	ADP
cana-6096	86	11	mathematics	mathematic	NOUN
cana-6096	86	12	in	in	ADP
cana-6096	86	13	more	more	ADJ
cana-6096	86	14	detail	detail	NOUN
cana-6096	86	15	,	,	PUNCT
cana-6096	86	16	it	it	PRON
cana-6096	86	17	is	be	AUX
cana-6096	86	18	important	important	ADJ
cana-6096	86	19	to	to	PART
cana-6096	86	20	introduce	introduce	VERB
cana-6096	86	21	the	the	DET
cana-6096	86	22	different	different	ADJ
cana-6096	86	23	types	type	NOUN
cana-6096	86	24	of	of	ADP
cana-6096	86	25	problems	problem	NOUN
cana-6096	86	26	encountered	encounter	VERB
cana-6096	86	27	in	in	ADP
cana-6096	86	28	mathematics	mathematic	NOUN
cana-6096	86	29	.	.	PUNCT
cana-6096	87	1	let	let	VERB
cana-6096	87	2	's	us	PRON
cana-6096	87	3	distinguish	distinguish	VERB
cana-6096	87	4	three	three	NUM
cana-6096	87	5	types	type	NOUN
cana-6096	87	6	of	of	ADP
cana-6096	87	7	problems	problem	NOUN
cana-6096	87	8	:	:	PUNCT
cana-6096	87	9	1	1	X
cana-6096	87	10	.	.	X
cana-6096	87	11	application	application	NOUN
cana-6096	87	12	problems	problem	NOUN
cana-6096	87	13	;	;	PUNCT
cana-6096	87	14	2	2	X
cana-6096	87	15	.	.	NOUN
cana-6096	87	16	problem	problem	NOUN
cana-6096	87	17	situations	situation	NOUN
cana-6096	87	18	;	;	PUNCT
cana-6096	87	19	3	3	X
cana-6096	87	20	.	.	X
cana-6096	87	21	open	open	ADJ
cana-6096	87	22	problems	problem	NOUN
cana-6096	87	23	.	.	PUNCT
cana-6096	88	1	skills	skill	NOUN
cana-6096	88	2	framework	framework	NOUN
cana-6096	89	1	[	[	X
cana-6096	89	2	12	12	NUM
cana-6096	89	3	]	]	PUNCT
cana-6096	89	4	for	for	ADP
cana-6096	89	5	a	a	DET
cana-6096	89	6	deeper	deep	ADJ
cana-6096	89	7	learning	learning	NOUN
cana-6096	89	8	process	process	NOUN
cana-6096	89	9	,	,	PUNCT
cana-6096	89	10	that	that	PRON
cana-6096	89	11	of	of	ADP
cana-6096	89	12	"	"	PUNCT
cana-6096	89	13	structuring	structure	VERB
cana-6096	89	14	one	one	NOUN
cana-6096	89	15	's	's	PART
cana-6096	89	16	thinking"[14	thinking"[14	PROPN
cana-6096	89	17	]	]	PUNCT
cana-6096	89	18	the	the	DET
cana-6096	89	19	objective	objective	NOUN
cana-6096	89	20	this	this	DET
cana-6096	89	21	time	time	NOUN
cana-6096	89	22	is	be	AUX
cana-6096	89	23	communications	communication	NOUN
cana-6096	89	24	on	on	ADP
cana-6096	89	25	applied	apply	VERB
cana-6096	89	26	nonlinear	nonlinear	ADJ
cana-6096	89	27	analysis	analysis	NOUN
cana-6096	89	28	issn	issn	NOUN
cana-6096	89	29	:	:	PUNCT
cana-6096	89	30	1074	1074	NUM
cana-6096	89	31	-	-	PUNCT
cana-6096	89	32	133x	133x	NUM
cana-6096	89	33	vol	vol	NOUN
cana-6096	89	34	32	32	NUM
cana-6096	89	35	no	no	NOUN
cana-6096	89	36	.	.	NOUN
cana-6096	89	37	3	3	NUM
cana-6096	89	38	(	(	PUNCT
cana-6096	89	39	2025	2025	NUM
cana-6096	89	40	)	)	PUNCT
cana-6096	89	41	1066	1066	NUM
cana-6096	89	42	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	89	43	➢	➢	VERB
cana-6096	89	44	the	the	DET
cana-6096	89	45	application	application	NOUN
cana-6096	89	46	problem	problem	NOUN
cana-6096	89	47	is	be	AUX
cana-6096	89	48	the	the	DET
cana-6096	89	49	"	"	PUNCT
cana-6096	89	50	classic	classic	ADJ
cana-6096	89	51	"	"	PUNCT
cana-6096	89	52	mathematics	mathematic	NOUN
cana-6096	89	53	problem	problem	NOUN
cana-6096	89	54	.	.	PUNCT
cana-6096	90	1	it	it	PRON
cana-6096	90	2	consists	consist	VERB
cana-6096	90	3	of	of	ADP
cana-6096	90	4	a	a	DET
cana-6096	90	5	statement	statement	NOUN
cana-6096	90	6	whose	whose	DET
cana-6096	90	7	purpose	purpose	NOUN
cana-6096	90	8	is	be	AUX
cana-6096	90	9	to	to	PART
cana-6096	90	10	stimulate	stimulate	VERB
cana-6096	90	11	the	the	DET
cana-6096	90	12	application	application	NOUN
cana-6096	90	13	of	of	ADP
cana-6096	90	14	techniques	technique	NOUN
cana-6096	90	15	previously	previously	ADV
cana-6096	90	16	seen	see	VERB
cana-6096	90	17	(	(	PUNCT
cana-6096	90	18	very	very	ADV
cana-6096	90	19	often	often	ADV
cana-6096	90	20	seen	see	VERB
cana-6096	90	21	just	just	ADV
cana-6096	90	22	before	before	ADV
cana-6096	90	23	)	)	PUNCT
cana-6096	90	24	.	.	PUNCT
cana-6096	91	1	it	it	PRON
cana-6096	91	2	is	be	AUX
cana-6096	91	3	rarely	rarely	ADV
cana-6096	91	4	isolated	isolate	VERB
cana-6096	91	5	but	but	CCONJ
cana-6096	91	6	rather	rather	ADV
cana-6096	91	7	is	be	AUX
cana-6096	91	8	part	part	NOUN
cana-6096	91	9	of	of	ADP
cana-6096	91	10	a	a	DET
cana-6096	91	11	series	series	NOUN
cana-6096	91	12	of	of	ADP
cana-6096	91	13	problems	problem	NOUN
cana-6096	91	14	of	of	ADP
cana-6096	91	15	increasing	increase	VERB
cana-6096	91	16	difficulty	difficulty	NOUN
cana-6096	91	17	.	.	PUNCT
cana-6096	92	1	it	it	PRON
cana-6096	92	2	is	be	AUX
cana-6096	92	3	traditionally	traditionally	ADV
cana-6096	92	4	proposed	propose	VERB
cana-6096	92	5	at	at	ADP
cana-6096	92	6	the	the	DET
cana-6096	92	7	end	end	NOUN
cana-6096	92	8	of	of	ADP
cana-6096	92	9	a	a	DET
cana-6096	92	10	learning	learning	NOUN
cana-6096	92	11	period	period	NOUN
cana-6096	92	12	.	.	PUNCT
cana-6096	93	1	old	old	ADJ
cana-6096	93	2	mathematics	mathematics	PROPN
cana-6096	93	3	textbooks	textbook	NOUN
cana-6096	93	4	were	be	AUX
cana-6096	93	5	generally	generally	ADV
cana-6096	93	6	very	very	ADV
cana-6096	93	7	fond	fond	ADJ
cana-6096	93	8	of	of	ADP
cana-6096	93	9	this	this	DET
cana-6096	93	10	type	type	NOUN
cana-6096	93	11	of	of	ADP
cana-6096	93	12	problems	problem	NOUN
cana-6096	93	13	.	.	PUNCT
cana-6096	94	1	solving	solve	VERB
cana-6096	94	2	this	this	DET
cana-6096	94	3	type	type	NOUN
cana-6096	94	4	of	of	ADP
cana-6096	94	5	problem	problem	NOUN
cana-6096	94	6	is	be	AUX
cana-6096	94	7	often	often	ADV
cana-6096	94	8	based	base	VERB
cana-6096	94	9	on	on	ADP
cana-6096	94	10	"	"	PUNCT
cana-6096	94	11	model	model	NOUN
cana-6096	94	12	practice	practice	NOUN
cana-6096	94	13	,	,	PUNCT
cana-6096	94	14	"	"	PUNCT
cana-6096	94	15	meaning	mean	VERB
cana-6096	94	16	that	that	SCONJ
cana-6096	94	17	a	a	DET
cana-6096	94	18	model	model	NOUN
cana-6096	94	19	problem	problem	NOUN
cana-6096	94	20	is	be	AUX
cana-6096	94	21	solved	solve	VERB
cana-6096	94	22	in	in	ADP
cana-6096	94	23	front	front	NOUN
cana-6096	94	24	of	of	ADP
cana-6096	94	25	the	the	DET
cana-6096	94	26	class	class	NOUN
cana-6096	94	27	and	and	CCONJ
cana-6096	94	28	then	then	ADV
cana-6096	94	29	,	,	PUNCT
cana-6096	94	30	through	through	ADP
cana-6096	94	31	imitation	imitation	NOUN
cana-6096	94	32	,	,	PUNCT
cana-6096	94	33	the	the	DET
cana-6096	94	34	student	student	NOUN
cana-6096	94	35	is	be	AUX
cana-6096	94	36	expected	expect	VERB
cana-6096	94	37	to	to	PART
cana-6096	94	38	solve	solve	VERB
cana-6096	94	39	the	the	DET
cana-6096	94	40	following	follow	VERB
cana-6096	94	41	problems	problem	NOUN
cana-6096	94	42	.	.	PUNCT
cana-6096	95	1	initially	initially	ADV
cana-6096	95	2	,	,	PUNCT
cana-6096	95	3	the	the	DET
cana-6096	95	4	numbers	number	NOUN
cana-6096	95	5	in	in	ADP
cana-6096	95	6	the	the	DET
cana-6096	95	7	statement	statement	NOUN
cana-6096	95	8	are	be	AUX
cana-6096	95	9	varied	varied	ADJ
cana-6096	95	10	without	without	ADP
cana-6096	95	11	departing	depart	VERB
cana-6096	95	12	from	from	ADP
cana-6096	95	13	the	the	DET
cana-6096	95	14	context	context	NOUN
cana-6096	95	15	.	.	PUNCT
cana-6096	96	1	the	the	DET
cana-6096	96	2	student	student	NOUN
cana-6096	96	3	's	's	PART
cana-6096	96	4	task	task	NOUN
cana-6096	96	5	is	be	AUX
cana-6096	96	6	to	to	PART
cana-6096	96	7	identify	identify	VERB
cana-6096	96	8	them	they	PRON
cana-6096	96	9	and	and	CCONJ
cana-6096	96	10	substitute	substitute	VERB
cana-6096	96	11	them	they	PRON
cana-6096	96	12	for	for	ADP
cana-6096	96	13	those	those	PRON
cana-6096	96	14	in	in	ADP
cana-6096	96	15	the	the	DET
cana-6096	96	16	proposed	propose	VERB
cana-6096	96	17	model	model	NOUN
cana-6096	96	18	.	.	PUNCT
cana-6096	97	1	then	then	ADV
cana-6096	97	2	,	,	PUNCT
cana-6096	97	3	more	more	ADV
cana-6096	97	4	significant	significant	ADJ
cana-6096	97	5	modifications	modification	NOUN
cana-6096	97	6	are	be	AUX
cana-6096	97	7	introduced	introduce	VERB
cana-6096	97	8	:	:	PUNCT
cana-6096	97	9	changes	change	NOUN
cana-6096	97	10	in	in	ADP
cana-6096	97	11	context	context	NOUN
cana-6096	97	12	,	,	PUNCT
cana-6096	97	13	introduction	introduction	NOUN
cana-6096	97	14	of	of	ADP
cana-6096	97	15	intermediate	intermediate	ADJ
cana-6096	97	16	steps	step	NOUN
cana-6096	97	17	,	,	PUNCT
cana-6096	97	18	variations	variation	NOUN
cana-6096	97	19	in	in	ADP
cana-6096	97	20	the	the	DET
cana-6096	97	21	chosen	choose	VERB
cana-6096	97	22	units	unit	NOUN
cana-6096	97	23	,	,	PUNCT
cana-6096	97	24	etc	etc	X
cana-6096	97	25	.	.	X
cana-6096	97	26	while	while	SCONJ
cana-6096	97	27	these	these	DET
cana-6096	97	28	problems	problem	NOUN
cana-6096	97	29	rightly	rightly	ADV
cana-6096	97	30	continue	continue	VERB
cana-6096	97	31	to	to	PART
cana-6096	97	32	occupy	occupy	VERB
cana-6096	97	33	a	a	DET
cana-6096	97	34	prominent	prominent	ADJ
cana-6096	97	35	place	place	NOUN
cana-6096	97	36	in	in	ADP
cana-6096	97	37	mathematics	mathematic	NOUN
cana-6096	97	38	teaching	teaching	NOUN
cana-6096	97	39	,	,	PUNCT
cana-6096	97	40	it	it	PRON
cana-6096	97	41	is	be	AUX
cana-6096	97	42	also	also	ADV
cana-6096	97	43	important	important	ADJ
cana-6096	97	44	to	to	PART
cana-6096	97	45	control	control	VERB
cana-6096	97	46	the	the	DET
cana-6096	97	47	limits	limit	NOUN
cana-6096	97	48	of	of	ADP
cana-6096	97	49	their	their	PRON
cana-6096	97	50	scope	scope	NOUN
cana-6096	97	51	.	.	PUNCT
cana-6096	98	1	"	"	PUNCT
cana-6096	98	2	when	when	SCONJ
cana-6096	98	3	using	use	VERB
cana-6096	98	4	this	this	DET
cana-6096	98	5	type	type	NOUN
cana-6096	98	6	of	of	ADP
cana-6096	98	7	problem	problem	NOUN
cana-6096	98	8	,	,	PUNCT
cana-6096	98	9	we	we	PRON
cana-6096	98	10	do	do	AUX
cana-6096	98	11	not	not	PART
cana-6096	98	12	always	always	ADV
cana-6096	98	13	pay	pay	VERB
cana-6096	98	14	sufficient	sufficient	ADJ
cana-6096	98	15	attention	attention	NOUN
cana-6096	98	16	to	to	ADP
cana-6096	98	17	the	the	DET
cana-6096	98	18	fact	fact	NOUN
cana-6096	98	19	that	that	SCONJ
cana-6096	98	20	it	it	PRON
cana-6096	98	21	is	be	AUX
cana-6096	98	22	not	not	PART
cana-6096	98	23	enough	enough	ADJ
cana-6096	98	24	for	for	SCONJ
cana-6096	98	25	a	a	DET
cana-6096	98	26	student	student	NOUN
cana-6096	98	27	to	to	PART
cana-6096	98	28	have	have	AUX
cana-6096	98	29	studied	study	VERB
cana-6096	98	30	a	a	DET
cana-6096	98	31	concept	concept	NOUN
cana-6096	98	32	(	(	PUNCT
cana-6096	98	33	that	that	PRON
cana-6096	98	34	of	of	ADP
cana-6096	98	35	division	division	NOUN
cana-6096	98	36	,	,	PUNCT
cana-6096	98	37	for	for	ADP
cana-6096	98	38	example	example	NOUN
cana-6096	98	39	)	)	PUNCT
cana-6096	98	40	and	and	CCONJ
cana-6096	98	41	to	to	PART
cana-6096	98	42	have	have	AUX
cana-6096	98	43	understood	understand	VERB
cana-6096	98	44	its	its	PRON
cana-6096	98	45	use	use	NOUN
cana-6096	98	46	in	in	ADP
cana-6096	98	47	certain	certain	ADJ
cana-6096	98	48	situations	situation	NOUN
cana-6096	98	49	,	,	PUNCT
cana-6096	98	50	for	for	SCONJ
cana-6096	98	51	them	they	PRON
cana-6096	98	52	to	to	PART
cana-6096	98	53	be	be	AUX
cana-6096	98	54	able	able	ADJ
cana-6096	98	55	to	to	PART
cana-6096	98	56	reuse	reuse	VERB
cana-6096	98	57	it	it	PRON
cana-6096	98	58	in	in	ADP
cana-6096	98	59	other	other	ADJ
cana-6096	98	60	situations	situation	NOUN
cana-6096	98	61	which	which	PRON
cana-6096	98	62	,	,	PUNCT
cana-6096	98	63	for	for	ADP
cana-6096	98	64	us	we	PRON
cana-6096	98	65	,	,	PUNCT
cana-6096	98	66	seem	seem	VERB
cana-6096	98	67	similar	similar	ADJ
cana-6096	98	68	.	.	PUNCT
cana-6096	99	1	we	we	PRON
cana-6096	99	2	will	will	AUX
cana-6096	99	3	show	show	VERB
cana-6096	99	4	,	,	PUNCT
cana-6096	99	5	(	(	PUNCT
cana-6096	99	6	…	…	PUNCT
cana-6096	99	7	)	)	PUNCT
cana-6096	99	8	,	,	PUNCT
cana-6096	99	9	that	that	SCONJ
cana-6096	99	10	the	the	DET
cana-6096	99	11	understanding	understanding	NOUN
cana-6096	99	12	of	of	ADP
cana-6096	99	13	a	a	DET
cana-6096	99	14	concept	concept	NOUN
cana-6096	99	15	takes	take	VERB
cana-6096	99	16	time	time	NOUN
cana-6096	99	17	,	,	PUNCT
cana-6096	99	18	that	that	SCONJ
cana-6096	99	19	it	it	PRON
cana-6096	99	20	takes	take	VERB
cana-6096	99	21	time	time	NOUN
cana-6096	99	22	,	,	PUNCT
cana-6096	99	23	a	a	DET
cana-6096	99	24	lot	lot	NOUN
cana-6096	99	25	of	of	ADP
cana-6096	99	26	time	time	NOUN
cana-6096	99	27	,	,	PUNCT
cana-6096	99	28	for	for	ADP
cana-6096	99	29	the	the	DET
cana-6096	99	30	different	different	ADJ
cana-6096	99	31	aspects	aspect	NOUN
cana-6096	99	32	of	of	ADP
cana-6096	99	33	the	the	DET
cana-6096	99	34	same	same	ADJ
cana-6096	99	35	concept	concept	NOUN
cana-6096	99	36	to	to	PART
cana-6096	99	37	be	be	AUX
cana-6096	99	38	appropriated	appropriate	VERB
cana-6096	99	39	by	by	ADP
cana-6096	99	40	the	the	PRON
cana-6096	99	41	in	in	ADP
cana-6096	99	42	addition	addition	NOUN
cana-6096	99	43	to	to	ADP
cana-6096	99	44	this	this	DET
cana-6096	99	45	drawback	drawback	NOUN
cana-6096	99	46	due	due	ADP
cana-6096	99	47	to	to	ADP
cana-6096	99	48	the	the	DET
cana-6096	99	49	lack	lack	NOUN
cana-6096	99	50	of	of	ADP
cana-6096	99	51	time	time	NOUN
cana-6096	99	52	-	-	PUNCT
cana-6096	99	53	based	base	VERB
cana-6096	99	54	approach	approach	NOUN
cana-6096	99	55	,	,	PUNCT
cana-6096	99	56	there	there	PRON
cana-6096	99	57	is	be	VERB
cana-6096	99	58	another	another	DET
cana-6096	99	59	criticism	criticism	NOUN
cana-6096	99	60	often	often	ADV
cana-6096	99	61	leveled	level	VERB
cana-6096	99	62	at	at	ADP
cana-6096	99	63	this	this	DET
cana-6096	99	64	type	type	NOUN
cana-6096	99	65	of	of	ADP
cana-6096	99	66	problem	problem	NOUN
cana-6096	99	67	.	.	PUNCT
cana-6096	100	1	this	this	DET
cana-6096	100	2	problem	problem	NOUN
cana-6096	100	3	-	-	PUNCT
cana-6096	100	4	solving	solve	VERB
cana-6096	100	5	approach	approach	NOUN
cana-6096	100	6	is	be	AUX
cana-6096	100	7	often	often	ADV
cana-6096	100	8	based	base	VERB
cana-6096	100	9	on	on	ADP
cana-6096	100	10	excessive	excessive	ADJ
cana-6096	100	11	mechanization	mechanization	NOUN
cana-6096	100	12	,	,	PUNCT
cana-6096	100	13	which	which	PRON
cana-6096	100	14	risks	risk	VERB
cana-6096	100	15	leading	lead	VERB
cana-6096	100	16	to	to	ADP
cana-6096	100	17	"	"	PUNCT
cana-6096	100	18	automatic	automatic	ADJ
cana-6096	100	19	"	"	PUNCT
cana-6096	100	20	phenomena	phenomenon	NOUN
cana-6096	100	21	➢	➢	VERB
cana-6096	100	22	the	the	DET
cana-6096	100	23	situation	situation	NOUN
cana-6096	100	24	problem	problem	NOUN
cana-6096	100	25	has	have	AUX
cana-6096	100	26	been	be	AUX
cana-6096	100	27	appearing	appear	VERB
cana-6096	100	28	for	for	ADP
cana-6096	100	29	several	several	ADJ
cana-6096	100	30	years	year	NOUN
cana-6096	100	31	now	now	ADV
cana-6096	100	32	in	in	ADP
cana-6096	100	33	mathematics	mathematics	NOUN
cana-6096	100	34	textbooks	textbook	NOUN
cana-6096	100	35	and	and	CCONJ
cana-6096	100	36	curricula	curricula	NOUN
cana-6096	100	37	in	in	ADP
cana-6096	100	38	the	the	DET
cana-6096	100	39	various	various	ADJ
cana-6096	100	40	countries	country	NOUN
cana-6096	100	41	where	where	SCONJ
cana-6096	100	42	mathematics	mathematic	NOUN
cana-6096	100	43	teaching	teaching	NOUN
cana-6096	100	44	has	have	AUX
cana-6096	100	45	taken	take	VERB
cana-6096	100	46	root	root	NOUN
cana-6096	100	47	.	.	PUNCT
cana-6096	101	1	it	it	PRON
cana-6096	101	2	is	be	AUX
cana-6096	101	3	a	a	DET
cana-6096	101	4	problem	problem	NOUN
cana-6096	101	5	whose	whose	DET
cana-6096	101	6	objective	objective	NOUN
cana-6096	101	7	is	be	AUX
cana-6096	101	8	the	the	DET
cana-6096	101	9	opposite	opposite	NOUN
cana-6096	101	10	of	of	ADP
cana-6096	101	11	that	that	PRON
cana-6096	101	12	of	of	ADP
cana-6096	101	13	the	the	DET
cana-6096	101	14	application	application	NOUN
cana-6096	101	15	problem	problem	NOUN
cana-6096	101	16	,	,	PUNCT
cana-6096	101	17	since	since	SCONJ
cana-6096	101	18	it	it	PRON
cana-6096	101	19	is	be	AUX
cana-6096	101	20	no	no	ADV
cana-6096	101	21	longer	long	ADV
cana-6096	101	22	a	a	DET
cana-6096	101	23	matter	matter	NOUN
cana-6096	101	24	of	of	ADP
cana-6096	101	25	exercising	exercise	VERB
cana-6096	101	26	and	and	CCONJ
cana-6096	101	27	reinforcing	reinforce	VERB
cana-6096	101	28	existing	exist	VERB
cana-6096	101	29	knowledge	knowledge	NOUN
cana-6096	101	30	,	,	PUNCT
cana-6096	101	31	but	but	CCONJ
cana-6096	101	32	rather	rather	ADV
cana-6096	101	33	of	of	ADP
cana-6096	101	34	discovering	discover	VERB
cana-6096	101	35	knowledge	knowledge	NOUN
cana-6096	101	36	from	from	ADP
cana-6096	101	37	the	the	DET
cana-6096	101	38	problem	problem	NOUN
cana-6096	101	39	,	,	PUNCT
cana-6096	101	40	of	of	ADP
cana-6096	101	41	giving	give	VERB
cana-6096	101	42	it	it	PRON
cana-6096	101	43	meaning	meaning	NOUN
cana-6096	101	44	.	.	PUNCT
cana-6096	102	1	the	the	DET
cana-6096	102	2	problem	problem	NOUN
cana-6096	102	3	situation	situation	NOUN
cana-6096	102	4	must	must	AUX
cana-6096	102	5	therefore	therefore	ADV
cana-6096	102	6	"	"	PUNCT
cana-6096	102	7	the	the	DET
cana-6096	102	8	creation	creation	NOUN
cana-6096	102	9	of	of	ADP
cana-6096	102	10	ignorance	ignorance	NOUN
cana-6096	102	11	,	,	PUNCT
cana-6096	102	12	a	a	DET
cana-6096	102	13	condition	condition	NOUN
cana-6096	102	14	for	for	ADP
cana-6096	102	15	learning	learn	VERB
cana-6096	102	16	.	.	PUNCT
cana-6096	102	17	"	"	PUNCT
cana-6096	103	1	by	by	ADP
cana-6096	103	2	its	its	PRON
cana-6096	103	3	very	very	ADJ
cana-6096	103	4	nature	nature	NOUN
cana-6096	103	5	,	,	PUNCT
cana-6096	103	6	the	the	DET
cana-6096	103	7	problem	problem	NOUN
cana-6096	103	8	situation	situation	NOUN
cana-6096	103	9	is	be	AUX
cana-6096	103	10	at	at	ADP
cana-6096	103	11	the	the	DET
cana-6096	103	12	beginning	beginning	NOUN
cana-6096	103	13	of	of	ADP
cana-6096	103	14	the	the	DET
cana-6096	103	15	learning	learning	NOUN
cana-6096	103	16	sequence	sequence	NOUN
cana-6096	103	17	.	.	PUNCT
cana-6096	104	1	we	we	PRON
cana-6096	104	2	sometimes	sometimes	ADV
cana-6096	104	3	refer	refer	VERB
cana-6096	104	4	to	to	ADP
cana-6096	104	5	it	it	PRON
cana-6096	104	6	as	as	ADP
cana-6096	104	7	a	a	DET
cana-6096	104	8	"	"	PUNCT
cana-6096	104	9	questioning	question	VERB
cana-6096	104	10	situation	situation	NOUN
cana-6096	104	11	"	"	PUNCT
cana-6096	104	12	rather	rather	ADV
cana-6096	104	13	than	than	ADP
cana-6096	104	14	a	a	DET
cana-6096	104	15	problem	problem	NOUN
cana-6096	104	16	situation	situation	NOUN
cana-6096	104	17	to	to	PART
cana-6096	104	18	emphasize	emphasize	VERB
cana-6096	104	19	the	the	DET
cana-6096	104	20	questioning	question	VERB
cana-6096	104	21	role	role	NOUN
cana-6096	104	22	played	play	VERB
cana-6096	104	23	by	by	ADP
cana-6096	104	24	the	the	DET
cana-6096	104	25	problem	problem	NOUN
cana-6096	104	26	.	.	PUNCT
cana-6096	105	1	it	it	PRON
cana-6096	105	2	is	be	AUX
cana-6096	105	3	important	important	ADJ
cana-6096	105	4	to	to	PART
cana-6096	105	5	"	"	PUNCT
cana-6096	105	6	put	put	VERB
cana-6096	105	7	the	the	DET
cana-6096	105	8	student	student	NOUN
cana-6096	105	9	in	in	ADP
cana-6096	105	10	question	question	NOUN
cana-6096	105	11	"	"	PUNCT
cana-6096	105	12	before	before	ADP
cana-6096	105	13	introducing	introduce	VERB
cana-6096	105	14	the	the	DET
cana-6096	105	15	desired	desire	VERB
cana-6096	105	16	knowledge	knowledge	NOUN
cana-6096	105	17	.	.	PUNCT
cana-6096	106	1	much	much	ADV
cana-6096	106	2	like	like	INTJ
cana-6096	106	3	in	in	ADP
cana-6096	106	4	a	a	DET
cana-6096	106	5	television	television	NOUN
cana-6096	106	6	commercial	commercial	NOUN
cana-6096	106	7	,	,	PUNCT
cana-6096	106	8	where	where	SCONJ
cana-6096	106	9	the	the	DET
cana-6096	106	10	first	first	ADJ
cana-6096	106	11	phase	phase	NOUN
cana-6096	106	12	serves	serve	VERB
cana-6096	106	13	to	to	PART
cana-6096	106	14	engage	engage	VERB
cana-6096	106	15	the	the	DET
cana-6096	106	16	viewer	viewer	NOUN
cana-6096	106	17	,	,	PUNCT
cana-6096	106	18	to	to	PART
cana-6096	106	19	put	put	VERB
cana-6096	106	20	them	they	PRON
cana-6096	106	21	in	in	ADP
cana-6096	106	22	a	a	DET
cana-6096	106	23	situation	situation	NOUN
cana-6096	106	24	of	of	ADP
cana-6096	106	25	"	"	PUNCT
cana-6096	106	26	astonishment	astonishment	ADJ
cana-6096	106	27	"	"	PUNCT
cana-6096	106	28	before	before	ADP
cana-6096	106	29	informing	inform	VERB
cana-6096	106	30	them	they	PRON
cana-6096	106	31	about	about	ADP
cana-6096	106	32	the	the	DET
cana-6096	106	33	product	product	NOUN
cana-6096	106	34	in	in	ADP
cana-6096	106	35	question	question	NOUN
cana-6096	106	36	,	,	PUNCT
cana-6096	106	37	in	in	ADP
cana-6096	106	38	class	class	NOUN
cana-6096	106	39	,	,	PUNCT
cana-6096	106	40	it	it	PRON
cana-6096	106	41	is	be	AUX
cana-6096	106	42	therefore	therefore	ADV
cana-6096	106	43	important	important	ADJ
cana-6096	106	44	to	to	PART
cana-6096	106	45	place	place	VERB
cana-6096	106	46	the	the	DET
cana-6096	106	47	student	student	NOUN
cana-6096	106	48	in	in	ADP
cana-6096	106	49	a	a	DET
cana-6096	106	50	situation	situation	NOUN
cana-6096	106	51	of	of	ADP
cana-6096	106	52	"	"	PUNCT
cana-6096	106	53	astonishment	astonishment	NOUN
cana-6096	106	54	"	"	PUNCT
cana-6096	106	55	to	to	PART
cana-6096	106	56	facilitate	facilitate	VERB
cana-6096	106	57	the	the	DET
cana-6096	106	58	assimilation	assimilation	NOUN
cana-6096	106	59	of	of	ADP
cana-6096	106	60	the	the	DET
cana-6096	106	61	information	information	NOUN
cana-6096	106	62	.	.	PUNCT
cana-6096	107	1	"	"	PUNCT
cana-6096	107	2	learning	learn	VERB
cana-6096	107	3	mathematics	mathematic	NOUN
cana-6096	107	4	,	,	PUNCT
cana-6096	107	5	in	in	ADP
cana-6096	107	6	our	our	PRON
cana-6096	107	7	opinion	opinion	NOUN
cana-6096	107	8	,	,	PUNCT
cana-6096	107	9	is	be	AUX
cana-6096	107	10	first	first	ADV
cana-6096	107	11	learning	learn	VERB
cana-6096	107	12	to	to	PART
cana-6096	107	13	be	be	AUX
cana-6096	107	14	amazed	amazed	ADJ
cana-6096	107	15	,	,	PUNCT
cana-6096	107	16	then	then	ADV
cana-6096	107	17	learning	learn	VERB
cana-6096	107	18	to	to	PART
cana-6096	107	19	ask	ask	VERB
cana-6096	107	20	questions	question	NOUN
cana-6096	107	21	.	.	PUNCT
cana-6096	107	22	"	"	PUNCT
cana-6096	108	1	for	for	ADP
cana-6096	108	2	if	if	SCONJ
cana-6096	108	3	there	there	PRON
cana-6096	108	4	are	be	VERB
cana-6096	108	5	no	no	DET
cana-6096	108	6	answers	answer	NOUN
cana-6096	108	7	where	where	SCONJ
cana-6096	108	8	there	there	PRON
cana-6096	108	9	are	be	VERB
cana-6096	108	10	no	no	DET
cana-6096	108	11	questions	question	NOUN
cana-6096	108	12	,	,	PUNCT
cana-6096	108	13	there	there	PRON
cana-6096	108	14	can	can	AUX
cana-6096	108	15	be	be	AUX
cana-6096	108	16	no	no	DET
cana-6096	108	17	questions	question	NOUN
cana-6096	108	18	[	[	X
cana-6096	108	19	2,3,4	2,3,4	NUM
cana-6096	108	20	]	]	X
cana-6096	108	21	.	.	PUNCT
cana-6096	109	1	students	student	NOUN
cana-6096	109	2	,	,	PUNCT
cana-6096	109	3	even	even	ADV
cana-6096	109	4	when	when	SCONJ
cana-6096	109	5	,	,	PUNCT
cana-6096	109	6	for	for	ADP
cana-6096	109	7	the	the	DET
cana-6096	109	8	experts	expert	NOUN
cana-6096	109	9	that	that	PRON
cana-6096	109	10	we	we	PRON
cana-6096	109	11	are	be	AUX
cana-6096	109	12	,	,	PUNCT
cana-6096	109	13	these	these	DET
cana-6096	109	14	aspects	aspect	NOUN
cana-6096	109	15	seem	seem	VERB
cana-6096	109	16	very	very	ADV
cana-6096	109	17	similar.[5	similar.[5	NOUN
cana-6096	109	18	]	]	PUNCT
cana-6096	109	19	"	"	PUNCT
cana-6096	109	20	"	"	PUNCT
cana-6096	109	21	create	create	VERB
cana-6096	109	22	the	the	DET
cana-6096	109	23	gap	gap	NOUN
cana-6096	109	24	,	,	PUNCT
cana-6096	109	25	"	"	PUNCT
cana-6096	109	26	open	open	VERB
cana-6096	109	27	a	a	DET
cana-6096	109	28	gap	gap	NOUN
cana-6096	109	29	that	that	SCONJ
cana-6096	109	30	knowledge	knowledge	NOUN
cana-6096	109	31	will	will	AUX
cana-6096	109	32	then	then	ADV
cana-6096	109	33	fill	fill	VERB
cana-6096	109	34	.	.	PUNCT
cana-6096	110	1	a.	a.	PROPN
cana-6096	110	2	mercier	mercier	PROPN
cana-6096	110	3	summarized	summarize	VERB
cana-6096	110	4	this	this	DET
cana-6096	110	5	process	process	NOUN
cana-6096	110	6	very	very	ADV
cana-6096	110	7	well	well	ADV
cana-6096	110	8	by	by	ADP
cana-6096	110	9	entitling	entitle	VERB
cana-6096	110	10	an	an	DET
cana-6096	110	11	article	article	NOUN
cana-6096	110	12	[	[	X
cana-6096	110	13	15	15	NUM
cana-6096	110	14	]	]	X
cana-6096	110	15	:	:	PUNCT
cana-6096	110	16	communications	communication	NOUN
cana-6096	110	17	on	on	ADP
cana-6096	110	18	applied	apply	VERB
cana-6096	110	19	nonlinear	nonlinear	ADJ
cana-6096	110	20	analysis	analysis	NOUN
cana-6096	110	21	issn	issn	NOUN
cana-6096	110	22	:	:	PUNCT
cana-6096	110	23	1074	1074	NUM
cana-6096	110	24	-	-	PUNCT
cana-6096	110	25	133x	133x	NUM
cana-6096	110	26	vol	vol	NOUN
cana-6096	110	27	32	32	NUM
cana-6096	111	1	no	no	NOUN
cana-6096	111	2	.	.	NOUN
cana-6096	111	3	3	3	NUM
cana-6096	111	4	(	(	PUNCT
cana-6096	111	5	2025	2025	NUM
cana-6096	111	6	)	)	PUNCT
cana-6096	111	7	1067	1067	NUM
cana-6096	111	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	111	9	didactics	didactics	NOUN
cana-6096	111	10	of	of	ADP
cana-6096	111	11	astonishment	astonishment	NOUN
cana-6096	111	12	.	.	PUNCT
cana-6096	111	13	”	"	PUNCT
cana-6096	111	14	differs	differ	VERB
cana-6096	111	15	from	from	ADP
cana-6096	111	16	the	the	DET
cana-6096	111	17	application	application	NOUN
cana-6096	111	18	problem	problem	NOUN
cana-6096	111	19	and	and	CCONJ
cana-6096	111	20	the	the	DET
cana-6096	111	21	situation	situation	NOUN
cana-6096	111	22	problem	problem	NOUN
cana-6096	111	23	in	in	ADP
cana-6096	111	24	that	that	SCONJ
cana-6096	111	25	it	it	PRON
cana-6096	111	26	does	do	AUX
cana-6096	111	27	not	not	PART
cana-6096	111	28	aim	aim	VERB
cana-6096	111	29	at	at	ADP
cana-6096	111	30	the	the	DET
cana-6096	111	31	application	application	NOUN
cana-6096	111	32	of	of	ADP
cana-6096	111	33	knowledge	knowledge	NOUN
cana-6096	111	34	or	or	CCONJ
cana-6096	111	35	the	the	DET
cana-6096	111	36	construction	construction	NOUN
cana-6096	111	37	of	of	ADP
cana-6096	111	38	knowledge	knowledge	NOUN
cana-6096	111	39	.	.	PUNCT
cana-6096	112	1	its	its	PRON
cana-6096	112	2	objective	objective	NOUN
cana-6096	112	3	is	be	AUX
cana-6096	112	4	to	to	PART
cana-6096	112	5	introduce	introduce	VERB
cana-6096	112	6	the	the	DET
cana-6096	112	7	student	student	NOUN
cana-6096	112	8	to	to	ADP
cana-6096	112	9	mathematical	mathematical	ADJ
cana-6096	112	10	research	research	NOUN
cana-6096	112	11	and	and	CCONJ
cana-6096	112	12	its	its	PRON
cana-6096	112	13	various	various	ADJ
cana-6096	112	14	strategies	strategy	NOUN
cana-6096	112	15	.	.	PUNCT
cana-6096	113	1	it	it	PRON
cana-6096	113	2	is	be	AUX
cana-6096	113	3	obvious	obvious	ADJ
cana-6096	113	4	that	that	SCONJ
cana-6096	113	5	it	it	PRON
cana-6096	113	6	is	be	AUX
cana-6096	113	7	impossible	impossible	ADJ
cana-6096	113	8	to	to	PART
cana-6096	113	9	completely	completely	ADV
cana-6096	113	10	isolate	isolate	VERB
cana-6096	113	11	a	a	DET
cana-6096	113	12	problem	problem	NOUN
cana-6096	113	13	from	from	ADP
cana-6096	113	14	the	the	DET
cana-6096	113	15	field	field	NOUN
cana-6096	113	16	of	of	ADP
cana-6096	113	17	knowledge	knowledge	NOUN
cana-6096	113	18	,	,	PUNCT
cana-6096	113	19	and	and	CCONJ
cana-6096	113	20	therefore	therefore	ADV
cana-6096	113	21	no	no	DET
cana-6096	113	22	one	one	NOUN
cana-6096	113	23	will	will	AUX
cana-6096	113	24	deny	deny	VERB
cana-6096	113	25	that	that	PRON
cana-6096	113	26	to	to	PART
cana-6096	113	27	successfully	successfully	ADV
cana-6096	113	28	complete	complete	VERB
cana-6096	113	29	an	an	DET
cana-6096	113	30	open	open	ADJ
cana-6096	113	31	problem	problem	NOUN
cana-6096	113	32	,	,	PUNCT
cana-6096	113	33	a	a	DET
cana-6096	113	34	certain	certain	ADJ
cana-6096	113	35	amount	amount	NOUN
cana-6096	113	36	of	of	ADP
cana-6096	113	37	knowledge	knowledge	NOUN
cana-6096	113	38	is	be	AUX
cana-6096	113	39	involved	involve	VERB
cana-6096	113	40	,	,	PUNCT
cana-6096	113	41	but	but	CCONJ
cana-6096	113	42	this	this	DET
cana-6096	113	43	knowledge	knowledge	NOUN
cana-6096	113	44	should	should	AUX
cana-6096	113	45	not	not	PART
cana-6096	113	46	hinder	hinder	VERB
cana-6096	113	47	the	the	DET
cana-6096	113	48	progress	progress	NOUN
cana-6096	113	49	of	of	ADP
cana-6096	113	50	the	the	DET
cana-6096	113	51	task	task	NOUN
cana-6096	113	52	in	in	ADP
cana-6096	113	53	an	an	DET
cana-6096	113	54	open	open	ADJ
cana-6096	113	55	problem	problem	NOUN
cana-6096	113	56	.	.	PUNCT
cana-6096	114	1	these	these	DET
cana-6096	114	2	sequences	sequence	NOUN
cana-6096	114	3	.	.	PUNCT
cana-6096	115	1	moreover	moreover	ADV
cana-6096	115	2	,	,	PUNCT
cana-6096	115	3	in	in	ADP
cana-6096	115	4	the	the	DET
cana-6096	115	5	textbooks	textbook	NOUN
cana-6096	115	6	used	use	VERB
cana-6096	115	7	in	in	ADP
cana-6096	115	8	french	french	PROPN
cana-6096	115	9	-	-	PUNCT
cana-6096	115	10	speaking	speak	VERB
cana-6096	115	11	switzerland	switzerland	NOUN
cana-6096	115	12	,	,	PUNCT
cana-6096	115	13	these	these	DET
cana-6096	115	14	open	open	ADJ
cana-6096	115	15	problems	problem	NOUN
cana-6096	115	16	are	be	AUX
cana-6096	115	17	offered	offer	VERB
cana-6096	115	18	in	in	ADP
cana-6096	115	19	the	the	DET
cana-6096	115	20	form	form	NOUN
cana-6096	115	21	of	of	ADP
cana-6096	115	22	mathematical	mathematical	ADJ
cana-6096	115	23	workshops	workshop	NOUN
cana-6096	115	24	alongside	alongside	ADP
cana-6096	115	25	"	"	PUNCT
cana-6096	115	26	normal	normal	ADJ
cana-6096	115	27	lessons	lesson	NOUN
cana-6096	115	28	,	,	PUNCT
cana-6096	115	29	"	"	PUNCT
cana-6096	115	30	even	even	ADV
cana-6096	115	31	though	though	SCONJ
cana-6096	115	32	the	the	DET
cana-6096	115	33	skills	skill	NOUN
cana-6096	115	34	developed	develop	VERB
cana-6096	115	35	during	during	ADP
cana-6096	115	36	these	these	DET
cana-6096	115	37	activities	activity	NOUN
cana-6096	115	38	are	be	AUX
cana-6096	115	39	obviously	obviously	ADV
cana-6096	115	40	injected	inject	VERB
cana-6096	115	41	into	into	ADP
cana-6096	115	42	the	the	DET
cana-6096	115	43	overall	overall	ADJ
cana-6096	115	44	mathematical	mathematical	ADJ
cana-6096	115	45	activity	activity	NOUN
cana-6096	115	46	.	.	PUNCT
cana-6096	116	1	"	"	PUNCT
cana-6096	116	2	the	the	DET
cana-6096	116	3	goal	goal	NOUN
cana-6096	116	4	is	be	AUX
cana-6096	116	5	to	to	PART
cana-6096	116	6	strengthen	strengthen	VERB
cana-6096	116	7	and	and	CCONJ
cana-6096	116	8	promote	promote	VERB
cana-6096	116	9	activities	activity	NOUN
cana-6096	116	10	in	in	ADP
cana-6096	116	11	which	which	PRON
cana-6096	116	12	the	the	DET
cana-6096	116	13	objectives	objective	NOUN
cana-6096	116	14	of	of	ADP
cana-6096	116	15	acquiring	acquire	VERB
cana-6096	116	16	concepts	concept	NOUN
cana-6096	116	17	give	give	VERB
cana-6096	116	18	priority	priority	NOUN
cana-6096	116	19	to	to	ADP
cana-6096	116	20	behavioral	behavioral	ADJ
cana-6096	116	21	objectives	objective	NOUN
cana-6096	116	22	,	,	PUNCT
cana-6096	116	23	such	such	ADJ
cana-6096	116	24	as	as	ADP
cana-6096	116	25	:	:	PUNCT
cana-6096	116	26	teaching	teach	VERB
cana-6096	116	27	students	student	NOUN
cana-6096	116	28	to	to	PART
cana-6096	116	29	search	search	VERB
cana-6096	116	30	for	for	ADP
cana-6096	116	31	and	and	CCONJ
cana-6096	116	32	interpret	interpret	VERB
cana-6096	116	33	data	datum	NOUN
cana-6096	116	34	,	,	PUNCT
cana-6096	116	35	extract	extract	VERB
cana-6096	116	36	relevant	relevant	ADJ
cana-6096	116	37	information	information	NOUN
cana-6096	116	38	,	,	PUNCT
cana-6096	116	39	and	and	CCONJ
cana-6096	116	40	ask	ask	VERB
cana-6096	116	41	questions	question	NOUN
cana-6096	116	42	;	;	PUNCT
cana-6096	116	43	accustoming	accustom	VERB
cana-6096	116	44	students	student	NOUN
cana-6096	116	45	to	to	ADP
cana-6096	116	46	reacting	react	VERB
cana-6096	116	47	positively	positively	ADV
cana-6096	116	48	to	to	PART
cana-6096	116	49	open	open	VERB
cana-6096	116	50	-	-	PUNCT
cana-6096	116	51	ended	end	VERB
cana-6096	116	52	or	or	CCONJ
cana-6096	116	53	momentarily	momentarily	ADV
cana-6096	116	54	difficult	difficult	ADJ
cana-6096	116	55	situations	situation	NOUN
cana-6096	116	56	;	;	PUNCT
cana-6096	116	57	valuing	value	VERB
cana-6096	116	58	the	the	DET
cana-6096	116	59	procedures	procedure	NOUN
cana-6096	116	60	students	student	NOUN
cana-6096	116	61	find	find	VERB
cana-6096	116	62	to	to	PART
cana-6096	116	63	solve	solve	VERB
cana-6096	116	64	a	a	DET
cana-6096	116	65	problem	problem	NOUN
cana-6096	116	66	;	;	PUNCT
cana-6096	116	67	encouraging	encourage	VERB
cana-6096	116	68	students	student	NOUN
cana-6096	116	69	to	to	PART
cana-6096	116	70	increasingly	increasingly	ADV
cana-6096	116	71	refer	refer	VERB
cana-6096	116	72	to	to	ADP
cana-6096	116	73	the	the	DET
cana-6096	116	74	results	result	NOUN
cana-6096	116	75	of	of	ADP
cana-6096	116	76	their	their	PRON
cana-6096	116	77	actions	action	NOUN
cana-6096	116	78	to	to	PART
cana-6096	116	79	judge	judge	VERB
cana-6096	116	80	the	the	DET
cana-6096	116	81	value	value	NOUN
cana-6096	116	82	of	of	ADP
cana-6096	116	83	the	the	DET
cana-6096	116	84	work	work	NOUN
cana-6096	116	85	accomplished	accomplish	VERB
cana-6096	116	86	;	;	PUNCT
cana-6096	116	87	the	the	DET
cana-6096	116	88	open	open	ADV
cana-6096	116	89	-	-	PUNCT
cana-6096	116	90	ended	end	VERB
cana-6096	116	91	problem	problem	NOUN
cana-6096	116	92	emphasizes	emphasize	VERB
cana-6096	116	93	the	the	DET
cana-6096	116	94	processes	process	NOUN
cana-6096	116	95	involved	involve	VERB
cana-6096	116	96	more	more	ADJ
cana-6096	116	97	than	than	ADP
cana-6096	116	98	the	the	DET
cana-6096	116	99	results	result	NOUN
cana-6096	116	100	;	;	PUNCT
cana-6096	116	101	it	it	PRON
cana-6096	116	102	encourages	encourage	VERB
cana-6096	116	103	the	the	DET
cana-6096	116	104	adoption	adoption	NOUN
cana-6096	116	105	of	of	ADP
cana-6096	116	106	a	a	DET
cana-6096	116	107	"	"	PUNCT
cana-6096	116	108	research	research	NOUN
cana-6096	116	109	attitude	attitude	NOUN
cana-6096	116	110	.	.	PUNCT
cana-6096	116	111	"	"	PUNCT
cana-6096	117	1	r.	r.	PROPN
cana-6096	117	2	charnay	charnay	PROPN
cana-6096	117	3	makes	make	VERB
cana-6096	117	4	a	a	DET
cana-6096	117	5	genuine	genuine	ADJ
cana-6096	117	6	case	case	NOUN
cana-6096	117	7	for	for	SCONJ
cana-6096	117	8	the	the	DET
cana-6096	117	9	"	"	PUNCT
cana-6096	117	10	a	a	DET
cana-6096	117	11	large	large	ADJ
cana-6096	117	12	part	part	NOUN
cana-6096	117	13	of	of	ADP
cana-6096	117	14	school	school	NOUN
cana-6096	117	15	time	time	NOUN
cana-6096	117	16	is	be	AUX
cana-6096	117	17	devoted	devote	VERB
cana-6096	117	18	to	to	ADP
cana-6096	117	19	learning	learn	VERB
cana-6096	117	20	new	new	ADJ
cana-6096	117	21	knowledge	knowledge	NOUN
cana-6096	117	22	and	and	CCONJ
cana-6096	117	23	practicing	practice	VERB
cana-6096	117	24	its	its	PRON
cana-6096	117	25	use	use	NOUN
cana-6096	117	26	.	.	PUNCT
cana-6096	118	1	is	be	AUX
cana-6096	118	2	there	there	PRON
cana-6096	118	3	time	time	NOUN
cana-6096	118	4	left	leave	VERB
cana-6096	118	5	to	to	PART
cana-6096	118	6	develop	develop	VERB
cana-6096	118	7	the	the	DET
cana-6096	118	8	pleasure	pleasure	NOUN
cana-6096	118	9	of	of	ADP
cana-6096	118	10	research	research	NOUN
cana-6096	118	11	,	,	PUNCT
cana-6096	118	12	to	to	PART
cana-6096	118	13	challenge	challenge	VERB
cana-6096	118	14	students	student	NOUN
cana-6096	118	15	with	with	ADP
cana-6096	118	16	intellectual	intellectual	ADJ
cana-6096	118	17	challenges	challenge	NOUN
cana-6096	118	18	whose	whose	DET
cana-6096	118	19	objective	objective	ADJ
cana-6096	118	20	lies	lie	VERB
cana-6096	118	21	in	in	ADP
cana-6096	118	22	the	the	DET
cana-6096	118	23	activity	activity	NOUN
cana-6096	118	24	rather	rather	ADV
cana-6096	118	25	than	than	ADP
cana-6096	118	26	its	its	PRON
cana-6096	118	27	results	result	NOUN
cana-6096	118	28	?	?	PUNCT
cana-6096	119	1	time	time	NOUN
cana-6096	119	2	,	,	PUNCT
cana-6096	119	3	too	too	ADV
cana-6096	119	4	,	,	PUNCT
cana-6096	119	5	to	to	PART
cana-6096	119	6	develop	develop	VERB
cana-6096	119	7	the	the	DET
cana-6096	119	8	attitudes	attitude	NOUN
cana-6096	119	9	and	and	CCONJ
cana-6096	119	10	skills	skill	NOUN
cana-6096	119	11	necessary	necessary	ADJ
cana-6096	119	12	for	for	ADP
cana-6096	119	13	this	this	DET
cana-6096	119	14	activity	activity	NOUN
cana-6096	119	15	,	,	PUNCT
cana-6096	119	16	time	time	NOUN
cana-6096	119	17	to	to	PART
cana-6096	119	18	try	try	VERB
cana-6096	119	19	,	,	PUNCT
cana-6096	119	20	to	to	PART
cana-6096	119	21	make	make	VERB
cana-6096	119	22	mistakes	mistake	NOUN
cana-6096	119	23	,	,	PUNCT
cana-6096	119	24	to	to	PART
cana-6096	119	25	discuss	discuss	VERB
cana-6096	119	26	a	a	DET
cana-6096	119	27	solution	solution	NOUN
cana-6096	119	28	with	with	ADP
cana-6096	119	29	others	other	NOUN
cana-6096	119	30	,	,	PUNCT
cana-6096	119	31	to	to	PART
cana-6096	119	32	try	try	VERB
cana-6096	119	33	to	to	PART
cana-6096	119	34	convince	convince	VERB
cana-6096	119	35	others	other	NOUN
cana-6096	119	36	,	,	PUNCT
cana-6096	119	37	to	to	PART
cana-6096	119	38	question	question	VERB
cana-6096	119	39	a	a	DET
cana-6096	119	40	method	method	NOUN
cana-6096	119	41	or	or	CCONJ
cana-6096	119	42	an	an	DET
cana-6096	119	43	answer	answer	NOUN
cana-6096	119	44	?	?	PUNCT
cana-6096	120	1	and	and	CCONJ
cana-6096	120	2	all	all	DET
cana-6096	120	3	this	this	PRON
cana-6096	120	4	,	,	PUNCT
cana-6096	120	5	without	without	ADP
cana-6096	120	6	the	the	DET
cana-6096	120	7	concern	concern	NOUN
cana-6096	120	8	for	for	ADP
cana-6096	120	9	learning	learn	VERB
cana-6096	120	10	concepts	concept	NOUN
cana-6096	120	11	and	and	CCONJ
cana-6096	120	12	without	without	ADP
cana-6096	120	13	the	the	DET
cana-6096	120	14	pressure	pressure	NOUN
cana-6096	120	15	of	of	ADP
cana-6096	120	16	assessment	assessment	NOUN
cana-6096	120	17	(	(	PUNCT
cana-6096	120	18	...	...	PUNCT
cana-6096	120	19	)	)	PUNCT
cana-6096	120	20	,	,	PUNCT
cana-6096	120	21	there	there	PRON
cana-6096	120	22	must	must	AUX
cana-6096	120	23	be	be	AUX
cana-6096	120	24	room	room	NOUN
cana-6096	120	25	in	in	ADP
cana-6096	120	26	school	school	NOUN
cana-6096	120	27	for	for	ADP
cana-6096	120	28	this	this	DET
cana-6096	120	29	kind	kind	NOUN
cana-6096	120	30	of	of	ADP
cana-6096	120	31	activity	activity	NOUN
cana-6096	120	32	.	.	PUNCT
cana-6096	120	33	"	"	PUNCT
cana-6096	121	1	,	,	PUNCT
cana-6096	121	2	the	the	DET
cana-6096	121	3	material	material	NOUN
cana-6096	121	4	for	for	ADP
cana-6096	121	5	mathematical	mathematical	ADJ
cana-6096	121	6	research	research	NOUN
cana-6096	121	7	,	,	PUNCT
cana-6096	121	8	is	be	AUX
cana-6096	121	9	a	a	DET
cana-6096	121	10	problem	problem	NOUN
cana-6096	121	11	with	with	ADP
cana-6096	121	12	the	the	DET
cana-6096	121	13	following	follow	VERB
cana-6096	121	14	characteristics	characteristic	NOUN
cana-6096	121	15	:	:	PUNCT
cana-6096	121	16	.	.	PUNCT
cana-6096	122	1	the	the	DET
cana-6096	122	2	open	open	ADJ
cana-6096	122	3	problem	problem	NOUN
cana-6096	122	4	[	[	X
cana-6096	122	5	8	8	NUM
cana-6096	122	6	]	]	SYM
cana-6096	122	7	➢	➢	X
cana-6096	122	8	open	open	ADV
cana-6096	122	9	-	-	PUNCT
cana-6096	122	10	ended	end	VERB
cana-6096	122	11	problem	problem	NOUN
cana-6096	122	12	and	and	CCONJ
cana-6096	122	13	the	the	DET
cana-6096	122	14	"	"	PUNCT
cana-6096	122	15	pleasure	pleasure	NOUN
cana-6096	122	16	of	of	ADP
cana-6096	122	17	research	research	NOUN
cana-6096	122	18	"	"	PUNCT
cana-6096	122	19	it	it	PRON
cana-6096	122	20	is	be	AUX
cana-6096	122	21	supposed	suppose	VERB
cana-6096	122	22	to	to	PART
cana-6096	122	23	foster	foster	VERB
cana-6096	122	24	[	[	X
cana-6096	122	25	5	5	NUM
cana-6096	122	26	]	]	PUNCT
cana-6096	122	27	the	the	DET
cana-6096	122	28	open	open	ADJ
cana-6096	122	29	problem	problem	NOUN
cana-6096	122	30	[	[	X
cana-6096	122	31	16	16	NUM
cana-6096	122	32	]	]	PUNCT
cana-6096	122	33	where	where	SCONJ
cana-6096	122	34	there	there	PRON
cana-6096	122	35	is	be	VERB
cana-6096	122	36	no	no	DET
cana-6096	122	37	astonishment	astonishment	NOUN
cana-6096	122	38	!	!	PUNCT
cana-6096	123	1	in	in	ADP
cana-6096	123	2	which	which	DET
cana-6096	123	3	case	case	NOUN
cana-6096	123	4	,	,	PUNCT
cana-6096	123	5	didactics	didactics	NOUN
cana-6096	123	6	of	of	ADP
cana-6096	123	7	mathematics	mathematic	NOUN
cana-6096	123	8	is	be	AUX
cana-6096	123	9	first	first	ADJ
cana-6096	123	10	and	and	CCONJ
cana-6096	123	11	foremost	foremost	ADV
cana-6096	123	12	this	this	DET
cana-6096	123	13	type	type	NOUN
cana-6096	123	14	of	of	ADP
cana-6096	123	15	problem	problem	NOUN
cana-6096	123	16	[	[	X
cana-6096	123	17	18	18	NUM
cana-6096	123	18	]	]	X
cana-6096	123	19	does	do	AUX
cana-6096	123	20	not	not	PART
cana-6096	123	21	intervene	intervene	VERB
cana-6096	123	22	directly	directly	ADV
cana-6096	123	23	within	within	ADP
cana-6096	123	24	a	a	DET
cana-6096	123	25	learning	learning	NOUN
cana-6096	123	26	sequence	sequence	NOUN
cana-6096	123	27	but	but	CCONJ
cana-6096	123	28	rather	rather	ADV
cana-6096	123	29	alongside	alongside	ADP
cana-6096	123	30	promote	promote	VERB
cana-6096	123	31	all	all	DET
cana-6096	123	32	forms	form	NOUN
cana-6096	123	33	of	of	ADP
cana-6096	123	34	intelligence	intelligence	NOUN
cana-6096	123	35	[	[	X
cana-6096	123	36	7	7	NUM
cana-6096	123	37	]	]	X
cana-6096	123	38	"	"	PUNCT
cana-6096	124	1	[	[	X
cana-6096	124	2	10	10	NUM
cana-6096	124	3	]	]	X
cana-6096	124	4	communications	communication	NOUN
cana-6096	124	5	on	on	ADP
cana-6096	124	6	applied	apply	VERB
cana-6096	124	7	nonlinear	nonlinear	ADJ
cana-6096	124	8	analysis	analysis	NOUN
cana-6096	124	9	issn	issn	NOUN
cana-6096	124	10	:	:	PUNCT
cana-6096	124	11	1074	1074	NUM
cana-6096	124	12	-	-	PUNCT
cana-6096	124	13	133x	133x	NUM
cana-6096	124	14	vol	vol	NOUN
cana-6096	124	15	32	32	NUM
cana-6096	124	16	no	no	NOUN
cana-6096	124	17	.	.	NOUN
cana-6096	124	18	3	3	NUM
cana-6096	124	19	(	(	PUNCT
cana-6096	124	20	2025	2025	NUM
cana-6096	124	21	)	)	PUNCT
cana-6096	124	22	1068	1068	NUM
cana-6096	124	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	125	1	the	the	DET
cana-6096	125	2	statement	statement	NOUN
cana-6096	125	3	does	do	AUX
cana-6096	125	4	not	not	PART
cana-6096	125	5	imply	imply	VERB
cana-6096	125	6	either	either	CCONJ
cana-6096	125	7	the	the	DET
cana-6096	125	8	method	method	NOUN
cana-6096	125	9	or	or	CCONJ
cana-6096	125	10	the	the	DET
cana-6096	125	11	solution	solution	NOUN
cana-6096	125	12	.	.	PUNCT
cana-6096	126	1	under	under	ADP
cana-6096	126	2	no	no	DET
cana-6096	126	3	circumstances	circumstance	NOUN
cana-6096	126	4	should	should	AUX
cana-6096	126	5	this	this	DET
cana-6096	126	6	solution	solution	NOUN
cana-6096	126	7	be	be	AUX
cana-6096	126	8	reduced	reduce	VERB
cana-6096	126	9	to	to	ADP
cana-6096	126	10	the	the	DET
cana-6096	126	11	immediate	immediate	ADJ
cana-6096	126	12	use	use	NOUN
cana-6096	126	13	or	or	CCONJ
cana-6096	126	14	application	application	NOUN
cana-6096	126	15	of	of	ADP
cana-6096	126	16	a	a	DET
cana-6096	126	17	strategy	strategy	NOUN
cana-6096	126	18	presented	present	VERB
cana-6096	126	19	in	in	ADP
cana-6096	126	20	class	class	NOUN
cana-6096	126	21	.	.	PUNCT
cana-6096	127	1	in	in	ADP
cana-6096	127	2	this	this	DET
cana-6096	127	3	sense	sense	NOUN
cana-6096	127	4	,	,	PUNCT
cana-6096	127	5	an	an	DET
cana-6096	127	6	open	open	ADJ
cana-6096	127	7	problem	problem	NOUN
cana-6096	127	8	is	be	AUX
cana-6096	127	9	always	always	ADV
cana-6096	127	10	original	original	ADJ
cana-6096	127	11	;	;	PUNCT
cana-6096	127	12	it	it	PRON
cana-6096	127	13	always	always	ADV
cana-6096	127	14	requires	require	VERB
cana-6096	127	15	a	a	DET
cana-6096	127	16	"	"	PUNCT
cana-6096	127	17	design	design	NOUN
cana-6096	127	18	"	"	PUNCT
cana-6096	127	19	phase	phase	NOUN
cana-6096	127	20	.	.	PUNCT
cana-6096	128	1	the	the	DET
cana-6096	128	2	"	"	PUNCT
cana-6096	128	3	paths	path	NOUN
cana-6096	128	4	"	"	PUNCT
cana-6096	128	5	leading	lead	VERB
cana-6096	128	6	to	to	ADP
cana-6096	128	7	the	the	DET
cana-6096	128	8	solution	solution	NOUN
cana-6096	128	9	are	be	AUX
cana-6096	128	10	multiple	multiple	ADJ
cana-6096	128	11	.	.	PUNCT
cana-6096	129	1	thus	thus	ADV
cana-6096	129	2	,	,	PUNCT
cana-6096	129	3	there	there	PRON
cana-6096	129	4	is	be	VERB
cana-6096	129	5	no	no	DET
cana-6096	129	6	single	single	ADJ
cana-6096	129	7	way	way	NOUN
cana-6096	129	8	to	to	PART
cana-6096	129	9	handle	handle	VERB
cana-6096	129	10	the	the	DET
cana-6096	129	11	situation	situation	NOUN
cana-6096	129	12	favorably	favorably	ADV
cana-6096	129	13	.	.	PUNCT
cana-6096	130	1	multiple	multiple	ADJ
cana-6096	130	2	approaches	approach	NOUN
cana-6096	130	3	are	be	AUX
cana-6096	130	4	thus	thus	ADV
cana-6096	130	5	discussed	discuss	VERB
cana-6096	130	6	and	and	CCONJ
cana-6096	130	7	emphasized	emphasize	VERB
cana-6096	130	8	;	;	PUNCT
cana-6096	130	9	a	a	DET
cana-6096	130	10	single	single	ADJ
cana-6096	130	11	approach	approach	NOUN
cana-6096	130	12	will	will	AUX
cana-6096	130	13	never	never	ADV
cana-6096	130	14	be	be	AUX
cana-6096	130	15	institutionalized	institutionalize	VERB
cana-6096	130	16	.	.	PUNCT
cana-6096	131	1	the	the	DET
cana-6096	131	2	problem	problem	NOUN
cana-6096	131	3	is	be	AUX
cana-6096	131	4	located	locate	VERB
cana-6096	131	5	in	in	ADP
cana-6096	131	6	a	a	DET
cana-6096	131	7	conceptual	conceptual	ADJ
cana-6096	131	8	field	field	NOUN
cana-6096	131	9	with	with	ADP
cana-6096	131	10	which	which	PRON
cana-6096	131	11	the	the	DET
cana-6096	131	12	students	student	NOUN
cana-6096	131	13	are	be	AUX
cana-6096	131	14	sufficiently	sufficiently	ADV
cana-6096	131	15	familiar	familiar	ADJ
cana-6096	131	16	.	.	PUNCT
cana-6096	132	1	this	this	PRON
cana-6096	132	2	allows	allow	VERB
cana-6096	132	3	them	they	PRON
cana-6096	132	4	to	to	PART
cana-6096	132	5	easily	easily	ADV
cana-6096	132	6	take	take	VERB
cana-6096	132	7	"	"	PUNCT
cana-6096	132	8	possession	possession	NOUN
cana-6096	132	9	"	"	PUNCT
cana-6096	132	10	of	of	ADP
cana-6096	132	11	the	the	DET
cana-6096	132	12	situation	situation	NOUN
cana-6096	132	13	and	and	CCONJ
cana-6096	132	14	engage	engage	VERB
cana-6096	132	15	in	in	ADP
cana-6096	132	16	testing	testing	NOUN
cana-6096	132	17	and	and	CCONJ
cana-6096	132	18	solution	solution	NOUN
cana-6096	132	19	projects	project	NOUN
cana-6096	132	20	.	.	PUNCT
cana-6096	133	1	“	"	PUNCT
cana-6096	133	2	the	the	DET
cana-6096	133	3	entrance	entrance	NOUN
cana-6096	133	4	is	be	AUX
cana-6096	133	5	wide	wide	ADJ
cana-6096	133	6	and	and	CCONJ
cana-6096	133	7	welcoming	welcome	VERB
cana-6096	133	8	enough	enough	ADV
cana-6096	133	9	to	to	PART
cana-6096	133	10	stimulate	stimulate	VERB
cana-6096	133	11	investigation	investigation	NOUN
cana-6096	133	12	”	"	PUNCT
cana-6096	133	13	the	the	DET
cana-6096	133	14	situation	situation	NOUN
cana-6096	133	15	must	must	AUX
cana-6096	133	16	be	be	AUX
cana-6096	133	17	complex	complex	ADJ
cana-6096	133	18	enough	enough	ADV
cana-6096	133	19	to	to	PART
cana-6096	133	20	encourage	encourage	VERB
cana-6096	133	21	a	a	DET
cana-6096	133	22	real	real	ADJ
cana-6096	133	23	research	research	NOUN
cana-6096	133	24	process	process	NOUN
cana-6096	133	25	,	,	PUNCT
cana-6096	133	26	where	where	SCONJ
cana-6096	133	27	exchanges	exchange	NOUN
cana-6096	133	28	between	between	ADP
cana-6096	133	29	students	student	NOUN
cana-6096	133	30	are	be	AUX
cana-6096	133	31	necessary	necessary	ADJ
cana-6096	133	32	and	and	CCONJ
cana-6096	133	33	fruitful	fruitful	ADJ
cana-6096	133	34	.	.	PUNCT
cana-6096	134	1	“	"	PUNCT
cana-6096	134	2	the	the	DET
cana-6096	134	3	exit	exit	NOUN
cana-6096	134	4	is	be	AUX
cana-6096	134	5	far	far	ADV
cana-6096	134	6	enough	enough	ADV
cana-6096	134	7	away	away	ADV
cana-6096	134	8	for	for	SCONJ
cana-6096	134	9	the	the	DET
cana-6096	134	10	stay	stay	NOUN
cana-6096	134	11	in	in	ADP
cana-6096	134	12	the	the	DET
cana-6096	134	13	research	research	NOUN
cana-6096	134	14	space	space	NOUN
cana-6096	134	15	to	to	PART
cana-6096	134	16	be	be	AUX
cana-6096	134	17	fruitful	fruitful	ADJ
cana-6096	134	18	.	.	PUNCT
cana-6096	134	19	”	"	PUNCT
cana-6096	134	20	schedule	schedule	VERB
cana-6096	134	21	4	4	NUM
cana-6096	134	22	:	:	PUNCT
cana-6096	134	23	“	"	PUNCT
cana-6096	134	24	different	different	ADJ
cana-6096	134	25	types	type	NOUN
cana-6096	134	26	of	of	ADP
cana-6096	134	27	mathematical	mathematical	ADJ
cana-6096	134	28	problems	problem	NOUN
cana-6096	134	29	”	"	PUNCT
cana-6096	134	30	the	the	DET
cana-6096	134	31	implementation	implementation	NOUN
cana-6096	134	32	of	of	ADP
cana-6096	134	33	these	these	DET
cana-6096	134	34	different	different	ADJ
cana-6096	134	35	types	type	NOUN
cana-6096	134	36	of	of	ADP
cana-6096	134	37	problems	problem	NOUN
cana-6096	134	38	in	in	ADP
cana-6096	134	39	student	student	NOUN
cana-6096	134	40	activities	activity	NOUN
cana-6096	134	41	contributes	contribute	VERB
cana-6096	134	42	to	to	ADP
cana-6096	134	43	what	what	PRON
cana-6096	134	44	some	some	PRON
cana-6096	134	45	have	have	AUX
cana-6096	134	46	called	call	VERB
cana-6096	134	47	"	"	PUNCT
cana-6096	134	48	problem	problem	NOUN
cana-6096	134	49	-	-	PUNCT
cana-6096	134	50	based	base	VERB
cana-6096	134	51	learning	learning	NOUN
cana-6096	134	52	.	.	PUNCT
cana-6096	135	1	"3	"3	NOUN
cana-6096	135	2	this	this	DET
cana-6096	135	3	concept	concept	NOUN
cana-6096	135	4	of	of	ADP
cana-6096	135	5	learning	learn	VERB
cana-6096	135	6	finds	find	VERB
cana-6096	135	7	its	its	PRON
cana-6096	135	8	place	place	NOUN
cana-6096	135	9	in	in	ADP
cana-6096	135	10	the	the	DET
cana-6096	135	11	mathematics	mathematics	NOUN
cana-6096	135	12	classroom	classroom	NOUN
cana-6096	135	13	for	for	ADP
cana-6096	135	14	two	two	NUM
cana-6096	135	15	major	major	ADJ
cana-6096	135	16	reasons	reason	NOUN
cana-6096	135	17	.	.	PUNCT
cana-6096	136	1	the	the	DET
cana-6096	136	2	first	first	ADJ
cana-6096	136	3	is	be	AUX
cana-6096	136	4	the	the	DET
cana-6096	136	5	fact	fact	NOUN
cana-6096	136	6	that	that	SCONJ
cana-6096	136	7	the	the	DET
cana-6096	136	8	fundamental	fundamental	ADJ
cana-6096	136	9	importance	importance	NOUN
cana-6096	136	10	of	of	ADP
cana-6096	136	11	the	the	DET
cana-6096	136	12	"	"	PUNCT
cana-6096	136	13	problem	problem	NOUN
cana-6096	136	14	"	"	PUNCT
cana-6096	136	15	in	in	ADP
cana-6096	136	16	learning	learn	VERB
cana-6096	136	17	mathematics	mathematic	NOUN
cana-6096	136	18	is	be	AUX
cana-6096	136	19	well	well	ADV
cana-6096	136	20	established	establish	VERB
cana-6096	136	21	:	:	PUNCT
cana-6096	136	22	every	every	DET
cana-6096	136	23	mathematical	mathematical	ADJ
cana-6096	136	24	concept	concept	NOUN
cana-6096	136	25	starts	start	VERB
cana-6096	136	26	with	with	ADP
cana-6096	136	27	a	a	DET
cana-6096	136	28	problem	problem	NOUN
cana-6096	136	29	and	and	CCONJ
cana-6096	136	30	returns	return	NOUN
cana-6096	136	31	to	to	ADP
cana-6096	136	32	it	it	PRON
cana-6096	136	33	.	.	PUNCT
cana-6096	137	1	the	the	DET
cana-6096	137	2	second	second	ADJ
cana-6096	137	3	reason	reason	NOUN
cana-6096	137	4	is	be	AUX
cana-6096	137	5	that	that	SCONJ
cana-6096	137	6	the	the	DET
cana-6096	137	7	objectives	objective	NOUN
cana-6096	137	8	of	of	ADP
cana-6096	137	9	the	the	DET
cana-6096	137	10	mathematics	mathematic	NOUN
cana-6096	137	11	course	course	NOUN
cana-6096	137	12	,	,	PUNCT
cana-6096	137	13	as	as	SCONJ
cana-6096	137	14	we	we	PRON
cana-6096	137	15	have	have	AUX
cana-6096	137	16	developed	develop	VERB
cana-6096	137	17	them	they	PRON
cana-6096	137	18	in	in	ADP
cana-6096	137	19	the	the	DET
cana-6096	137	20	previous	previous	ADJ
cana-6096	137	21	pages	page	NOUN
cana-6096	137	22	,	,	PUNCT
cana-6096	137	23	coincide	coincide	VERB
cana-6096	137	24	with	with	ADP
cana-6096	137	25	the	the	DET
cana-6096	137	26	goals	goal	NOUN
cana-6096	137	27	sought	seek	VERB
cana-6096	137	28	by	by	ADP
cana-6096	137	29	“	"	PUNCT
cana-6096	137	30	problem	problem	NOUN
cana-6096	137	31	-	-	PUNCT
cana-6096	137	32	based	base	VERB
cana-6096	137	33	learning	learning	NOUN
cana-6096	137	34	”	"	PUNCT
cana-6096	137	35	,	,	PUNCT
cana-6096	137	36	where	where	SCONJ
cana-6096	137	37	the	the	DET
cana-6096	137	38	aim	aim	NOUN
cana-6096	137	39	is	be	AUX
cana-6096	137	40	on	on	ADP
cana-6096	137	41	the	the	DET
cana-6096	137	42	one	one	NUM
cana-6096	137	43	hand	hand	NOUN
cana-6096	137	44	to	to	PART
cana-6096	137	45	master	master	VERB
cana-6096	137	46	content	content	NOUN
cana-6096	137	47	and	and	CCONJ
cana-6096	137	48	on	on	ADP
cana-6096	137	49	the	the	DET
cana-6096	137	50	other	other	ADJ
cana-6096	137	51	hand	hand	NOUN
cana-6096	137	52	to	to	PART
cana-6096	137	53	develop	develop	VERB
cana-6096	137	54	qualities	quality	NOUN
cana-6096	137	55	.	.	PUNCT
cana-6096	138	1	this	this	DET
cana-6096	138	2	duality	duality	NOUN
cana-6096	138	3	is	be	AUX
cana-6096	138	4	similar	similar	ADJ
cana-6096	138	5	to	to	ADP
cana-6096	138	6	that	that	PRON
cana-6096	138	7	mentioned	mention	VERB
cana-6096	138	8	in	in	ADP
cana-6096	138	9	the	the	DET
cana-6096	138	10	table	table	NOUN
cana-6096	138	11	.	.	PUNCT
cana-6096	139	1	comparison	comparison	NOUN
cana-6096	139	2	between	between	ADP
cana-6096	139	3	open	open	ADJ
cana-6096	139	4	situation	situation	NOUN
cana-6096	139	5	and	and	CCONJ
cana-6096	139	6	problem	problem	NOUN
cana-6096	139	7	situation	situation	NOUN
cana-6096	139	8	.	.	PUNCT
cana-6096	140	1	open	open	ADJ
cana-6096	140	2	problem	problem	NOUN
cana-6096	140	3	situation	situation	NOUN
cana-6096	140	4	-	-	PUNCT
cana-6096	140	5	problem	problem	NOUN
cana-6096	140	6	activity	activity	NOUN
cana-6096	140	7	type	type	NOUN
cana-6096	140	8	•	•	ADP
cana-6096	140	9	the	the	DET
cana-6096	140	10	student	student	NOUN
cana-6096	140	11	is	be	AUX
cana-6096	140	12	placed	place	VERB
cana-6096	140	13	in	in	ADP
cana-6096	140	14	a	a	DET
cana-6096	140	15	research	research	NOUN
cana-6096	140	16	situation	situation	NOUN
cana-6096	140	17	,	,	PUNCT
cana-6096	140	18	•	•	ADP
cana-6096	140	19	the	the	DET
cana-6096	140	20	statement	statement	NOUN
cana-6096	140	21	is	be	AUX
cana-6096	140	22	chosen	choose	VERB
cana-6096	140	23	so	so	SCONJ
cana-6096	140	24	that	that	SCONJ
cana-6096	140	25	everyone	everyone	PRON
cana-6096	140	26	can	can	AUX
cana-6096	140	27	engage	engage	VERB
cana-6096	140	28	in	in	ADP
cana-6096	140	29	the	the	DET
cana-6096	140	30	resolution	resolution	NOUN
cana-6096	140	31	.	.	PUNCT
cana-6096	141	1	communications	communication	NOUN
cana-6096	141	2	on	on	ADP
cana-6096	141	3	applied	apply	VERB
cana-6096	141	4	nonlinear	nonlinear	ADJ
cana-6096	141	5	analysis	analysis	NOUN
cana-6096	141	6	issn	issn	NOUN
cana-6096	141	7	:	:	PUNCT
cana-6096	141	8	1074	1074	NUM
cana-6096	141	9	-	-	PUNCT
cana-6096	141	10	133x	133x	NUM
cana-6096	141	11	vol	vol	NOUN
cana-6096	141	12	32	32	NUM
cana-6096	141	13	no	no	NOUN
cana-6096	141	14	.	.	NOUN
cana-6096	141	15	3	3	NUM
cana-6096	141	16	(	(	PUNCT
cana-6096	141	17	2025	2025	NUM
cana-6096	141	18	)	)	PUNCT
cana-6096	141	19	1069	1069	NUM
cana-6096	141	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	141	21	objectify	objectify	VERB
cana-6096	141	22	methodological	methodological	ADJ
cana-6096	141	23	the	the	DET
cana-6096	141	24	student	student	NOUN
cana-6096	141	25	does	do	AUX
cana-6096	141	26	not	not	PART
cana-6096	141	27	have	have	VERB
cana-6096	141	28	a	a	DET
cana-6096	141	29	problem	problem	NOUN
cana-6096	141	30	-	-	PUNCT
cana-6096	141	31	solving	solve	VERB
cana-6096	141	32	method	method	NOUN
cana-6096	141	33	that	that	PRON
cana-6096	141	34	has	have	AUX
cana-6096	141	35	been	be	AUX
cana-6096	141	36	taught	teach	VERB
cana-6096	141	37	to	to	ADP
cana-6096	141	38	them	they	PRON
cana-6096	141	39	.	.	PUNCT
cana-6096	142	1	they	they	PRON
cana-6096	142	2	must	must	AUX
cana-6096	142	3	develop	develop	VERB
cana-6096	142	4	their	their	PRON
cana-6096	142	5	own	own	ADJ
cana-6096	142	6	solutions	solution	NOUN
cana-6096	142	7	.	.	PUNCT
cana-6096	143	1	acquisition	acquisition	NOUN
cana-6096	143	2	of	of	ADP
cana-6096	143	3	new	new	ADJ
cana-6096	143	4	knowledge	knowledge	NOUN
cana-6096	143	5	the	the	DET
cana-6096	143	6	student	student	NOUN
cana-6096	143	7	can	can	AUX
cana-6096	143	8	engage	engage	VERB
cana-6096	143	9	in	in	ADP
cana-6096	143	10	the	the	DET
cana-6096	143	11	solution	solution	NOUN
cana-6096	143	12	by	by	ADP
cana-6096	143	13	drawing	draw	VERB
cana-6096	143	14	on	on	ADP
cana-6096	143	15	prior	prior	ADJ
cana-6096	143	16	knowledge	knowledge	NOUN
cana-6096	143	17	.	.	PUNCT
cana-6096	144	1	but	but	CCONJ
cana-6096	144	2	this	this	DET
cana-6096	144	3	knowledge	knowledge	NOUN
cana-6096	144	4	proves	prove	VERB
cana-6096	144	5	to	to	PART
cana-6096	144	6	be	be	AUX
cana-6096	144	7	either	either	CCONJ
cana-6096	144	8	wasteful	wasteful	ADJ
cana-6096	144	9	or	or	CCONJ
cana-6096	144	10	inappropriate	inappropriate	ADJ
cana-6096	144	11	.	.	PUNCT
cana-6096	145	1	taking	take	VERB
cana-6096	145	2	the	the	DET
cana-6096	145	3	student	student	NOUN
cana-6096	145	4	into	into	ADP
cana-6096	145	5	account	account	NOUN
cana-6096	145	6	taking	take	VERB
cana-6096	145	7	into	into	ADP
cana-6096	145	8	account	account	NOUN
cana-6096	145	9	student	student	NOUN
cana-6096	145	10	differences	difference	NOUN
cana-6096	145	11	:	:	PUNCT
cana-6096	145	12	each	each	DET
cana-6096	145	13	piece	piece	NOUN
cana-6096	145	14	of	of	ADP
cana-6096	145	15	work	work	NOUN
cana-6096	145	16	is	be	AUX
cana-6096	145	17	taken	take	VERB
cana-6096	145	18	into	into	ADP
cana-6096	145	19	account	account	NOUN
cana-6096	145	20	,	,	PUNCT
cana-6096	145	21	the	the	DET
cana-6096	145	22	diversity	diversity	NOUN
cana-6096	145	23	of	of	ADP
cana-6096	145	24	approaches	approach	NOUN
cana-6096	145	25	is	be	AUX
cana-6096	145	26	recognized	recognize	VERB
cana-6096	145	27	,	,	PUNCT
cana-6096	145	28	and	and	CCONJ
cana-6096	145	29	originality	originality	NOUN
cana-6096	145	30	is	be	AUX
cana-6096	145	31	valued	value	VERB
cana-6096	145	32	.	.	PUNCT
cana-6096	146	1	no	no	DET
cana-6096	146	2	single	single	ADJ
cana-6096	146	3	procedure	procedure	NOUN
cana-6096	146	4	is	be	AUX
cana-6096	146	5	favored	favor	VERB
cana-6096	146	6	.	.	PUNCT
cana-6096	147	1	context	context	NOUN
cana-6096	147	2	-	-	PUNCT
cana-6096	147	3	based	base	VERB
cana-6096	147	4	validation	validation	NOUN
cana-6096	147	5	is	be	AUX
cana-6096	147	6	not	not	PART
cana-6096	147	7	always	always	ADV
cana-6096	147	8	possible	possible	ADJ
cana-6096	147	9	.	.	PUNCT
cana-6096	148	1	considering	consider	VERB
cana-6096	148	2	students	student	NOUN
cana-6096	148	3	'	'	PART
cana-6096	148	4	conceptions	conception	NOUN
cana-6096	148	5	:	:	PUNCT
cana-6096	148	6	students	student	NOUN
cana-6096	148	7	must	must	AUX
cana-6096	148	8	be	be	AUX
cana-6096	148	9	able	able	ADJ
cana-6096	148	10	to	to	PART
cana-6096	148	11	verify	verify	VERB
cana-6096	148	12	for	for	ADP
cana-6096	148	13	themselves	themselves	PRON
cana-6096	148	14	whether	whether	SCONJ
cana-6096	148	15	their	their	PRON
cana-6096	148	16	knowledge	knowledge	NOUN
cana-6096	148	17	is	be	AUX
cana-6096	148	18	uneconomical	uneconomical	ADJ
cana-6096	148	19	or	or	CCONJ
cana-6096	148	20	inadequate	inadequate	ADJ
cana-6096	148	21	(	(	PUNCT
cana-6096	148	22	an	an	DET
cana-6096	148	23	obstacle	obstacle	NOUN
cana-6096	148	24	)	)	PUNCT
cana-6096	148	25	for	for	ADP
cana-6096	148	26	solving	solve	VERB
cana-6096	148	27	problems	problem	NOUN
cana-6096	148	28	.	.	PUNCT
cana-6096	149	1	the	the	DET
cana-6096	149	2	targeted	target	VERB
cana-6096	149	3	knowledge	knowledge	NOUN
cana-6096	149	4	is	be	AUX
cana-6096	149	5	the	the	DET
cana-6096	149	6	most	most	ADV
cana-6096	149	7	effective	effective	ADJ
cana-6096	149	8	solution	solution	NOUN
cana-6096	149	9	tool	tool	NOUN
cana-6096	149	10	.	.	PUNCT
cana-6096	150	1	contextual	contextual	ADJ
cana-6096	150	2	validation	validation	NOUN
cana-6096	150	3	is	be	AUX
cana-6096	150	4	necessary	necessary	ADJ
cana-6096	150	5	;	;	PUNCT
cana-6096	150	6	the	the	DET
cana-6096	150	7	importance	importance	NOUN
cana-6096	150	8	of	of	ADP
cana-6096	150	9	control	control	NOUN
cana-6096	150	10	methods	method	NOUN
cana-6096	150	11	.	.	PUNCT
cana-6096	151	1	conclusion	conclusion	NOUN
cana-6096	151	2	teacher	teacher	NOUN
cana-6096	151	3	's	's	PART
cana-6096	151	4	choice	choice	NOUN
cana-6096	151	5	:	:	PUNCT
cana-6096	151	6	•	•	PUNCT
cana-6096	151	7	research	research	NOUN
cana-6096	151	8	methods	method	NOUN
cana-6096	151	9	•	•	ADV
cana-6096	151	10	highlighting	highlight	VERB
cana-6096	151	11	the	the	DET
cana-6096	151	12	diversity	diversity	NOUN
cana-6096	151	13	of	of	ADP
cana-6096	151	14	approaches	approach	NOUN
cana-6096	151	15	institutionalization	institutionalization	NOUN
cana-6096	151	16	:	:	PUNCT
cana-6096	151	17	identification	identification	NOUN
cana-6096	151	18	of	of	ADP
cana-6096	151	19	new	new	ADJ
cana-6096	151	20	knowledge	knowledge	NOUN
cana-6096	151	21	or	or	CCONJ
cana-6096	151	22	know	know	NOUN
cana-6096	151	23	-	-	PUNCT
cana-6096	151	24	how	how	NOUN
cana-6096	151	25	.	.	PUNCT
cana-6096	152	1	contract	contract	NOUN
cana-6096	152	2	the	the	DET
cana-6096	152	3	student	student	NOUN
cana-6096	152	4	should	should	AUX
cana-6096	152	5	not	not	PART
cana-6096	152	6	be	be	AUX
cana-6096	152	7	able	able	ADJ
cana-6096	152	8	to	to	PART
cana-6096	152	9	be	be	AUX
cana-6096	152	10	guided	guide	VERB
cana-6096	152	11	by	by	ADP
cana-6096	152	12	the	the	DET
cana-6096	152	13	teacher	teacher	NOUN
cana-6096	152	14	's	's	PART
cana-6096	152	15	expectations	expectation	NOUN
cana-6096	152	16	.	.	PUNCT
cana-6096	153	1	the	the	DET
cana-6096	153	2	following	follow	VERB
cana-6096	153	3	table	table	NOUN
cana-6096	153	4	schematically	schematically	NOUN
cana-6096	153	5	shows	show	VERB
cana-6096	153	6	how	how	SCONJ
cana-6096	153	7	"	"	PUNCT
cana-6096	153	8	problem	problem	NOUN
cana-6096	153	9	-	-	PUNCT
cana-6096	153	10	based	base	VERB
cana-6096	153	11	learning	learning	NOUN
cana-6096	153	12	,	,	PUNCT
cana-6096	153	13	"	"	PUNCT
cana-6096	153	14	or	or	CCONJ
cana-6096	153	15	pbl	pbl	PROPN
cana-6096	153	16	,	,	PUNCT
cana-6096	153	17	can	can	AUX
cana-6096	153	18	be	be	AUX
cana-6096	153	19	according	accord	VERB
cana-6096	153	20	to	to	ADP
cana-6096	153	21	the	the	DET
cana-6096	153	22	learning	learning	NOUN
cana-6096	153	23	objectives	objective	NOUN
cana-6096	153	24	.	.	PUNCT
cana-6096	154	1	•	•	NUM
cana-6096	154	2	problem	problem	NOUN
cana-6096	154	3	situations	situation	NOUN
cana-6096	154	4	lead	lead	VERB
cana-6096	154	5	students	student	NOUN
cana-6096	154	6	to	to	AUX
cana-6096	154	7	self	self	NOUN
cana-6096	154	8	-	-	PUNCT
cana-6096	154	9	construct	construct	VERB
cana-6096	154	10	new	new	ADJ
cana-6096	154	11	knowledge	knowledge	NOUN
cana-6096	154	12	.	.	PUNCT
cana-6096	155	1	students	student	NOUN
cana-6096	155	2	become	become	VERB
cana-6096	155	3	aware	aware	ADJ
cana-6096	155	4	of	of	ADP
cana-6096	155	5	the	the	DET
cana-6096	155	6	limitations	limitation	NOUN
cana-6096	155	7	of	of	ADP
cana-6096	155	8	their	their	PRON
cana-6096	155	9	current	current	ADJ
cana-6096	155	10	knowledge	knowledge	NOUN
cana-6096	155	11	in	in	ADP
cana-6096	155	12	order	order	NOUN
cana-6096	155	13	to	to	PART
cana-6096	155	14	construct	construct	VERB
cana-6096	155	15	new	new	ADJ
cana-6096	155	16	knowledge	knowledge	NOUN
cana-6096	155	17	.	.	PUNCT
cana-6096	156	1	•	•	NOUN
cana-6096	156	2	reinvestment	reinvestment	NOUN
cana-6096	156	3	problems	problem	NOUN
cana-6096	156	4	allow	allow	VERB
cana-6096	156	5	students	student	NOUN
cana-6096	156	6	to	to	PART
cana-6096	156	7	reinvest	reinvest	VERB
cana-6096	156	8	previously	previously	ADV
cana-6096	156	9	acquired	acquire	VERB
cana-6096	156	10	knowledge	knowledge	NOUN
cana-6096	156	11	.	.	PUNCT
cana-6096	157	1	•	•	ADJ
cana-6096	157	2	synthesis	synthesis	NOUN
cana-6096	157	3	problems	problem	NOUN
cana-6096	157	4	,	,	PUNCT
cana-6096	157	5	often	often	ADV
cana-6096	157	6	more	more	ADV
cana-6096	157	7	complex	complex	ADJ
cana-6096	157	8	,	,	PUNCT
cana-6096	157	9	allow	allow	VERB
cana-6096	157	10	the	the	DET
cana-6096	157	11	implementation	implementation	NOUN
cana-6096	157	12	of	of	ADP
cana-6096	157	13	several	several	ADJ
cana-6096	157	14	types	type	NOUN
cana-6096	157	15	of	of	ADP
cana-6096	157	16	knowledge	knowledge	NOUN
cana-6096	157	17	.	.	PUNCT
cana-6096	158	1	•	•	ADJ
cana-6096	158	2	assessment	assessment	NOUN
cana-6096	158	3	problems	problem	NOUN
cana-6096	158	4	,	,	PUNCT
cana-6096	158	5	fairly	fairly	ADV
cana-6096	158	6	standard	standard	ADJ
cana-6096	158	7	,	,	PUNCT
cana-6096	158	8	allow	allow	VERB
cana-6096	158	9	the	the	DET
cana-6096	158	10	teacher	teacher	NOUN
cana-6096	158	11	and	and	CCONJ
cana-6096	158	12	students	student	NOUN
cana-6096	158	13	to	to	PART
cana-6096	158	14	take	take	VERB
cana-6096	158	15	stock	stock	NOUN
cana-6096	158	16	of	of	ADP
cana-6096	158	17	how	how	SCONJ
cana-6096	158	18	knowledge	knowledge	NOUN
cana-6096	158	19	is	be	AUX
cana-6096	158	20	being	be	AUX
cana-6096	158	21	mastered	master	VERB
cana-6096	158	22	.	.	PUNCT
cana-6096	159	1	•	•	NUM
cana-6096	159	2	open	open	ADJ
cana-6096	159	3	problems	problem	NOUN
cana-6096	159	4	are	be	AUX
cana-6096	159	5	designed	design	VERB
cana-6096	159	6	to	to	PART
cana-6096	159	7	place	place	VERB
cana-6096	159	8	students	student	NOUN
cana-6096	159	9	in	in	ADP
cana-6096	159	10	a	a	DET
cana-6096	159	11	research	research	NOUN
cana-6096	159	12	situation	situation	NOUN
cana-6096	159	13	.	.	PUNCT
cana-6096	160	1	this	this	DET
cana-6096	160	2	typology	typology	NOUN
cana-6096	160	3	highlights	highlight	VERB
cana-6096	160	4	the	the	DET
cana-6096	160	5	unique	unique	ADJ
cana-6096	160	6	nature	nature	NOUN
cana-6096	160	7	of	of	ADP
cana-6096	160	8	the	the	DET
cana-6096	160	9	open	open	ADV
cana-6096	160	10	-	-	PUNCT
cana-6096	160	11	ended	end	VERB
cana-6096	160	12	problem	problem	NOUN
cana-6096	160	13	.	.	PUNCT
cana-6096	161	1	the	the	DET
cana-6096	161	2	other	other	ADJ
cana-6096	161	3	types	type	NOUN
cana-6096	161	4	of	of	ADP
cana-6096	161	5	problems	problem	NOUN
cana-6096	161	6	focus	focus	VERB
cana-6096	161	7	on	on	ADP
cana-6096	161	8	the	the	DET
cana-6096	161	9	acquisition	acquisition	NOUN
cana-6096	161	10	or	or	CCONJ
cana-6096	161	11	mastery	mastery	NOUN
cana-6096	161	12	of	of	ADP
cana-6096	161	13	mathematical	mathematical	ADJ
cana-6096	161	14	concepts	concept	NOUN
cana-6096	161	15	.	.	PUNCT
cana-6096	162	1	the	the	DET
cana-6096	162	2	open	open	ADJ
cana-6096	162	3	problem	problem	NOUN
cana-6096	162	4	is	be	AUX
cana-6096	162	5	intended	intend	VERB
cana-6096	162	6	to	to	PART
cana-6096	162	7	develop	develop	VERB
cana-6096	162	8	research	research	NOUN
cana-6096	162	9	behavior	behavior	NOUN
cana-6096	162	10	and	and	CCONJ
cana-6096	162	11	methodological	methodological	ADJ
cana-6096	162	12	skills	skill	NOUN
cana-6096	162	13	.	.	PUNCT
cana-6096	163	1	above	above	ADP
cana-6096	163	2	fit	fit	VERB
cana-6096	163	3	into	into	ADP
cana-6096	163	4	it.applied	it.applie	VERB
cana-6096	163	5	in	in	ADP
cana-6096	163	6	mathematics	mathematic	NOUN
cana-6096	163	7	and	and	CCONJ
cana-6096	163	8	how	how	SCONJ
cana-6096	163	9	the	the	DET
cana-6096	163	10	three	three	NUM
cana-6096	163	11	types	type	NOUN
cana-6096	163	12	of	of	ADP
cana-6096	163	13	problems	problem	NOUN
cana-6096	163	14	mentioned	mention	VERB
cana-6096	163	15	[	[	X
cana-6096	163	16	1	1	NUM
cana-6096	163	17	]	]	PUNCT
cana-6096	163	18	communications	communication	NOUN
cana-6096	163	19	on	on	ADP
cana-6096	163	20	applied	apply	VERB
cana-6096	163	21	nonlinear	nonlinear	ADJ
cana-6096	163	22	analysis	analysis	NOUN
cana-6096	163	23	issn	issn	NOUN
cana-6096	163	24	:	:	PUNCT
cana-6096	163	25	1074	1074	NUM
cana-6096	163	26	-	-	PUNCT
cana-6096	163	27	133x	133x	NUM
cana-6096	163	28	vol	vol	NOUN
cana-6096	163	29	32	32	NUM
cana-6096	163	30	no	no	NOUN
cana-6096	163	31	.	.	NOUN
cana-6096	163	32	3	3	NUM
cana-6096	163	33	(	(	PUNCT
cana-6096	163	34	2025	2025	NUM
cana-6096	163	35	)	)	PUNCT
cana-6096	163	36	1070	1070	NUM
cana-6096	163	37	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	163	38	schedule	schedule	NOUN
cana-6096	163	39	5	5	NUM
cana-6096	163	40	:	:	PUNCT
cana-6096	163	41	”	"	PUNCT
cana-6096	164	1	the	the	DET
cana-6096	164	2	a.p	a.p	PROPN
cana-6096	164	3	.	.	PROPN
cana-6096	164	4	p	p	NOUN
cana-6096	164	5	in	in	ADP
cana-6096	164	6	mathematics	mathematic	NOUN
cana-6096	164	7	”	"	PUNCT
cana-6096	164	8	application	application	NOUN
cana-6096	164	9	1	1	NUM
cana-6096	164	10	.	.	PUNCT
cana-6096	165	1	(	(	PUNCT
cana-6096	165	2	the	the	DET
cana-6096	165	3	greatest	great	ADJ
cana-6096	165	4	product	product	NOUN
cana-6096	165	5	)	)	PUNCT
cana-6096	165	6	the	the	DET
cana-6096	165	7	number	number	NOUN
cana-6096	165	8	23	23	NUM
cana-6096	165	9	can	can	AUX
cana-6096	165	10	be	be	AUX
cana-6096	165	11	written	write	VERB
cana-6096	165	12	in	in	ADP
cana-6096	165	13	several	several	ADJ
cana-6096	165	14	ways	way	NOUN
cana-6096	165	15	as	as	ADP
cana-6096	165	16	the	the	DET
cana-6096	165	17	sum	sum	NOUN
cana-6096	165	18	of	of	ADP
cana-6096	165	19	integers	integer	NOUN
cana-6096	165	20	:	:	PUNCT
cana-6096	165	21	for	for	ADP
cana-6096	165	22	example	example	NOUN
cana-6096	165	23	:	:	PUNCT
cana-6096	165	24	23	23	NUM
cana-6096	165	25	=	=	SYM
cana-6096	165	26	11	11	NUM
cana-6096	165	27	+	+	NUM
cana-6096	165	28	5	5	NUM
cana-6096	165	29	+	+	CCONJ
cana-6096	165	30	7	7	NUM
cana-6096	165	31	.	.	X
cana-6096	165	32	find	find	VERB
cana-6096	165	33	among	among	ADP
cana-6096	165	34	these	these	DET
cana-6096	165	35	sums	sum	NOUN
cana-6096	165	36	the	the	DET
cana-6096	165	37	one	one	NUM
cana-6096	165	38	whose	whose	DET
cana-6096	165	39	product	product	NOUN
cana-6096	165	40	of	of	ADP
cana-6096	165	41	the	the	DET
cana-6096	165	42	terms	term	NOUN
cana-6096	165	43	is	be	AUX
cana-6096	165	44	maximum	maximum	ADJ
cana-6096	165	45	.	.	PUNCT
cana-6096	166	1	and	and	CCONJ
cana-6096	166	2	with	with	ADP
cana-6096	166	3	other	other	ADJ
cana-6096	166	4	numbers	number	NOUN
cana-6096	166	5	?	?	PUNCT
cana-6096	167	1	the	the	DET
cana-6096	167	2	mathematical	mathematical	ADJ
cana-6096	167	3	situation	situation	NOUN
cana-6096	167	4	study	study	NOUN
cana-6096	167	5	of	of	ADP
cana-6096	167	6	the	the	DET
cana-6096	167	7	product	product	NOUN
cana-6096	167	8	of	of	ADP
cana-6096	167	9	integers	integer	NOUN
cana-6096	167	10	with	with	ADP
cana-6096	167	11	a	a	DET
cana-6096	167	12	fixed	fixed	ADJ
cana-6096	167	13	sum	sum	NOUN
cana-6096	167	14	.	.	PUNCT
cana-6096	168	1	the	the	DET
cana-6096	168	2	solution	solution	NOUN
cana-6096	168	3	to	to	ADP
cana-6096	168	4	the	the	DET
cana-6096	168	5	problem	problem	NOUN
cana-6096	168	6	can	can	AUX
cana-6096	168	7	be	be	AUX
cana-6096	168	8	expressed	express	VERB
cana-6096	168	9	as	as	SCONJ
cana-6096	168	10	follows	follow	VERB
cana-6096	168	11	:	:	PUNCT
cana-6096	168	12	•	•	ADP
cana-6096	168	13	if	if	SCONJ
cana-6096	168	14	the	the	DET
cana-6096	168	15	number	number	NOUN
cana-6096	168	16	is	be	AUX
cana-6096	168	17	a	a	DET
cana-6096	168	18	multiple	multiple	NOUN
cana-6096	168	19	of	of	ADP
cana-6096	168	20	3	3	NUM
cana-6096	168	21	,	,	PUNCT
cana-6096	168	22	the	the	DET
cana-6096	168	23	largest	large	ADJ
cana-6096	168	24	product	product	NOUN
cana-6096	168	25	is	be	AUX
cana-6096	168	26	obtained	obtain	VERB
cana-6096	168	27	by	by	ADP
cana-6096	168	28	calculating	calculate	VERB
cana-6096	168	29	3	3	NUM
cana-6096	168	30	×	×	NOUN
cana-6096	168	31	3	3	NUM
cana-6096	168	32	×	×	NOUN
cana-6096	168	33	...	...	PUNCT
cana-6096	168	34	×	×	NOUN
cana-6096	168	35	3	3	NUM
cana-6096	168	36	(	(	PUNCT
cana-6096	168	37	decomposition	decomposition	NOUN
cana-6096	168	38	into	into	ADP
cana-6096	168	39	3	3	NUM
cana-6096	168	40	+	+	SYM
cana-6096	168	41	3	3	NUM
cana-6096	168	42	+	+	NOUN
cana-6096	168	43	...	...	PUNCT
cana-6096	169	1	+	+	NUM
cana-6096	169	2	3	3	NUM
cana-6096	169	3	;	;	PUNCT
cana-6096	169	4	for	for	ADP
cana-6096	169	5	example	example	NOUN
cana-6096	169	6	,	,	PUNCT
cana-6096	169	7	for	for	ADP
cana-6096	169	8	12	12	NUM
cana-6096	169	9	,	,	PUNCT
cana-6096	169	10	the	the	DET
cana-6096	169	11	largest	large	ADJ
cana-6096	169	12	product	product	NOUN
cana-6096	169	13	is	be	AUX
cana-6096	169	14	3	3	NUM
cana-6096	169	15	×	×	NOUN
cana-6096	169	16	3	3	NUM
cana-6096	169	17	×	×	NOUN
cana-6096	169	18	3	3	NUM
cana-6096	169	19	×	×	NOUN
cana-6096	169	20	3	3	NUM
cana-6096	169	21	=	=	SYM
cana-6096	169	22	81	81	NUM
cana-6096	169	23	)	)	PUNCT
cana-6096	169	24	•	•	NOUN
cana-6096	170	1	if	if	SCONJ
cana-6096	170	2	the	the	DET
cana-6096	170	3	remainder	remainder	NOUN
cana-6096	170	4	of	of	ADP
cana-6096	170	5	the	the	DET
cana-6096	170	6	number	number	NOUN
cana-6096	170	7	in	in	ADP
cana-6096	170	8	division	division	NOUN
cana-6096	170	9	by	by	ADP
cana-6096	170	10	3	3	NUM
cana-6096	170	11	is	be	AUX
cana-6096	170	12	1	1	NUM
cana-6096	170	13	(	(	PUNCT
cana-6096	170	14	"	"	PUNCT
cana-6096	170	15	if	if	SCONJ
cana-6096	170	16	the	the	DET
cana-6096	170	17	number	number	NOUN
cana-6096	170	18	is	be	AUX
cana-6096	170	19	equal	equal	ADJ
cana-6096	170	20	to	to	ADP
cana-6096	170	21	a	a	DET
cana-6096	170	22	multiple	multiple	NOUN
cana-6096	170	23	of	of	ADP
cana-6096	170	24	3	3	NUM
cana-6096	170	25	plus	plus	CCONJ
cana-6096	170	26	one	one	NUM
cana-6096	170	27	,	,	PUNCT
cana-6096	170	28	"	"	PUNCT
cana-6096	170	29	to	to	PART
cana-6096	170	30	use	use	VERB
cana-6096	170	31	a	a	DET
cana-6096	170	32	common	common	ADJ
cana-6096	170	33	formulation	formulation	NOUN
cana-6096	170	34	among	among	ADP
cana-6096	170	35	students	student	NOUN
cana-6096	170	36	)	)	PUNCT
cana-6096	170	37	,	,	PUNCT
cana-6096	170	38	the	the	DET
cana-6096	170	39	largest	large	ADJ
cana-6096	170	40	product	product	NOUN
cana-6096	170	41	is	be	AUX
cana-6096	170	42	obtained	obtain	VERB
cana-6096	170	43	by	by	ADP
cana-6096	170	44	calculating	calculate	VERB
cana-6096	170	45	3	3	NUM
cana-6096	170	46	×	×	NOUN
cana-6096	170	47	3	3	NUM
cana-6096	170	48	×	×	NOUN
cana-6096	170	49	...	...	PUNCT
cana-6096	171	1	×	×	NOUN
cana-6096	171	2	3	3	NUM
cana-6096	171	3	×	×	NOUN
cana-6096	171	4	4	4	NUM
cana-6096	171	5	;	;	PUNCT
cana-6096	171	6	(	(	PUNCT
cana-6096	171	7	decomposition	decomposition	NOUN
cana-6096	171	8	3	3	NUM
cana-6096	171	9	+	+	CCONJ
cana-6096	171	10	3	3	NUM
cana-6096	171	11	+	+	NOUN
cana-6096	171	12	...	...	PUNCT
cana-6096	171	13	+	+	CCONJ
cana-6096	171	14	3	3	NUM
cana-6096	171	15	+	+	SYM
cana-6096	171	16	4	4	NUM
cana-6096	171	17	,	,	PUNCT
cana-6096	171	18	the	the	DET
cana-6096	171	19	4	4	NUM
cana-6096	171	20	being	be	AUX
cana-6096	171	21	obtained	obtain	VERB
cana-6096	171	22	by	by	ADP
cana-6096	171	23	adding	add	VERB
cana-6096	171	24	the	the	DET
cana-6096	171	25	last	last	ADJ
cana-6096	171	26	3	3	NUM
cana-6096	171	27	and	and	CCONJ
cana-6096	171	28	1	1	NUM
cana-6096	171	29	;	;	PUNCT
cana-6096	171	30	for	for	ADP
cana-6096	171	31	example	example	NOUN
cana-6096	171	32	,	,	PUNCT
cana-6096	171	33	for	for	ADP
cana-6096	171	34	10	10	NUM
cana-6096	171	35	the	the	DET
cana-6096	171	36	largest	large	ADJ
cana-6096	171	37	product	product	NOUN
cana-6096	171	38	is	be	AUX
cana-6096	171	39	36	36	NUM
cana-6096	171	40	;	;	PUNCT
cana-6096	171	41	3	3	NUM
cana-6096	171	42	×	×	NOUN
cana-6096	171	43	3	3	NUM
cana-6096	171	44	×	×	NOUN
cana-6096	171	45	4	4	NUM
cana-6096	171	46	or	or	CCONJ
cana-6096	171	47	3	3	NUM
cana-6096	171	48	×	×	NOUN
cana-6096	171	49	3	3	NUM
cana-6096	171	50	×	×	NOUN
cana-6096	171	51	2	2	NUM
cana-6096	171	52	×	×	NOUN
cana-6096	171	53	2	2	NUM
cana-6096	171	54	)	)	PUNCT
cana-6096	171	55	•	•	NOUN
cana-6096	171	56	if	if	SCONJ
cana-6096	171	57	the	the	DET
cana-6096	171	58	remainder	remainder	NOUN
cana-6096	171	59	of	of	ADP
cana-6096	171	60	the	the	DET
cana-6096	171	61	number	number	NOUN
cana-6096	171	62	in	in	ADP
cana-6096	171	63	division	division	NOUN
cana-6096	171	64	by	by	ADP
cana-6096	171	65	3	3	NUM
cana-6096	171	66	is	be	AUX
cana-6096	171	67	2	2	NUM
cana-6096	171	68	(	(	PUNCT
cana-6096	171	69	"	"	PUNCT
cana-6096	171	70	if	if	SCONJ
cana-6096	171	71	the	the	DET
cana-6096	171	72	number	number	NOUN
cana-6096	171	73	is	be	AUX
cana-6096	171	74	equal	equal	ADJ
cana-6096	171	75	to	to	ADP
cana-6096	171	76	a	a	DET
cana-6096	171	77	multiple	multiple	NOUN
cana-6096	171	78	of	of	ADP
cana-6096	171	79	3	3	NUM
cana-6096	171	80	plus	plus	CCONJ
cana-6096	171	81	2	2	NUM
cana-6096	171	82	"	"	PUNCT
cana-6096	171	83	)	)	PUNCT
cana-6096	171	84	,	,	PUNCT
cana-6096	171	85	the	the	DET
cana-6096	171	86	largest	large	ADJ
cana-6096	171	87	product	product	NOUN
cana-6096	171	88	is	be	AUX
cana-6096	171	89	obtained	obtain	VERB
cana-6096	171	90	by	by	ADP
cana-6096	171	91	doing	do	VERB
cana-6096	171	92	3	3	NUM
cana-6096	171	93	×	×	NOUN
cana-6096	171	94	3	3	NUM
cana-6096	171	95	×	×	NOUN
cana-6096	171	96	...	...	PUNCT
cana-6096	171	97	×	×	NOUN
cana-6096	171	98	3	3	NUM
cana-6096	171	99	×	×	NOUN
cana-6096	171	100	2	2	NUM
cana-6096	171	101	(	(	PUNCT
cana-6096	171	102	for	for	ADP
cana-6096	171	103	example	example	NOUN
cana-6096	171	104	,	,	PUNCT
cana-6096	171	105	for	for	ADP
cana-6096	171	106	14	14	NUM
cana-6096	171	107	the	the	DET
cana-6096	171	108	largest	large	ADJ
cana-6096	171	109	product	product	NOUN
cana-6096	171	110	is	be	AUX
cana-6096	171	111	3	3	NUM
cana-6096	171	112	×	×	NOUN
cana-6096	171	113	3	3	NUM
cana-6096	171	114	×	×	NOUN
cana-6096	171	115	3	3	NUM
cana-6096	171	116	×	×	NOUN
cana-6096	171	117	3	3	NUM
cana-6096	171	118	×	×	NOUN
cana-6096	171	119	2	2	NUM
cana-6096	171	120	=	=	SYM
cana-6096	171	121	162	162	NUM
cana-6096	171	122	)	)	PUNCT
cana-6096	171	123	.	.	PUNCT
cana-6096	172	1	the	the	DET
cana-6096	172	2	proof	proof	NOUN
cana-6096	172	3	of	of	ADP
cana-6096	172	4	this	this	DET
cana-6096	172	5	solution	solution	NOUN
cana-6096	172	6	is	be	AUX
cana-6096	172	7	based	base	VERB
cana-6096	172	8	on	on	ADP
cana-6096	172	9	the	the	DET
cana-6096	172	10	following	follow	VERB
cana-6096	172	11	properties	property	NOUN
cana-6096	172	12	:	:	PUNCT
cana-6096	172	13	a.	a.	NOUN
cana-6096	172	14	if	if	SCONJ
cana-6096	172	15	0	0	NUM
cana-6096	172	16	appears	appear	VERB
cana-6096	172	17	in	in	ADP
cana-6096	172	18	the	the	DET
cana-6096	172	19	additive	additive	ADJ
cana-6096	172	20	decomposition	decomposition	NOUN
cana-6096	172	21	,	,	PUNCT
cana-6096	172	22	the	the	DET
cana-6096	172	23	product	product	NOUN
cana-6096	172	24	of	of	ADP
cana-6096	172	25	the	the	DET
cana-6096	172	26	terms	term	NOUN
cana-6096	172	27	is	be	AUX
cana-6096	172	28	zero	zero	NUM
cana-6096	172	29	.	.	PUNCT
cana-6096	173	1	b.	b.	NOUN
cana-6096	174	1	if	if	SCONJ
cana-6096	174	2	1	1	NUM
cana-6096	174	3	appears	appear	VERB
cana-6096	174	4	in	in	ADP
cana-6096	174	5	the	the	DET
cana-6096	174	6	additive	additive	ADJ
cana-6096	174	7	decomposition	decomposition	NOUN
cana-6096	174	8	,	,	PUNCT
cana-6096	174	9	the	the	DET
cana-6096	174	10	product	product	NOUN
cana-6096	174	11	of	of	ADP
cana-6096	174	12	the	the	DET
cana-6096	174	13	terms	term	NOUN
cana-6096	174	14	is	be	AUX
cana-6096	174	15	improved	improve	VERB
cana-6096	174	16	by	by	ADP
cana-6096	174	17	adding	add	VERB
cana-6096	174	18	1	1	NUM
cana-6096	174	19	to	to	ADP
cana-6096	174	20	one	one	NUM
cana-6096	174	21	of	of	ADP
cana-6096	174	22	the	the	DET
cana-6096	174	23	terms	term	NOUN
cana-6096	174	24	of	of	ADP
cana-6096	174	25	the	the	DET
cana-6096	174	26	product	product	NOUN
cana-6096	174	27	(	(	PUNCT
cana-6096	174	28	e.g.	e.g.	ADV
cana-6096	174	29	,	,	PUNCT
cana-6096	174	30	3	3	NUM
cana-6096	174	31	×	×	NOUN
cana-6096	174	32	3	3	NUM
cana-6096	174	33	×	×	NOUN
cana-6096	174	34	4	4	NUM
cana-6096	174	35	instead	instead	ADV
cana-6096	174	36	of	of	ADP
cana-6096	174	37	3	3	NUM
cana-6096	174	38	×	×	NOUN
cana-6096	174	39	3	3	NUM
cana-6096	174	40	×	×	NOUN
cana-6096	174	41	3	3	NUM
cana-6096	174	42	×	×	NOUN
cana-6096	174	43	1	1	NUM
cana-6096	174	44	)	)	PUNCT
cana-6096	174	45	.	.	PUNCT
cana-6096	175	1	communications	communication	NOUN
cana-6096	175	2	on	on	ADP
cana-6096	175	3	applied	apply	VERB
cana-6096	175	4	nonlinear	nonlinear	ADJ
cana-6096	175	5	analysis	analysis	NOUN
cana-6096	175	6	issn	issn	NOUN
cana-6096	175	7	:	:	PUNCT
cana-6096	175	8	1074	1074	NUM
cana-6096	175	9	-	-	PUNCT
cana-6096	175	10	133x	133x	NUM
cana-6096	175	11	vol	vol	NOUN
cana-6096	175	12	32	32	NUM
cana-6096	175	13	no	no	NOUN
cana-6096	175	14	.	.	NOUN
cana-6096	175	15	3	3	NUM
cana-6096	175	16	(	(	PUNCT
cana-6096	175	17	2025	2025	NUM
cana-6096	175	18	)	)	PUNCT
cana-6096	175	19	1071	1071	NUM
cana-6096	175	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	175	21	c.	c.	PROPN
cana-6096	175	22	if	if	SCONJ
cana-6096	175	23	,	,	PUNCT
cana-6096	175	24	in	in	ADP
cana-6096	175	25	an	an	DET
cana-6096	175	26	additive	additive	ADJ
cana-6096	175	27	decomposition	decomposition	NOUN
cana-6096	175	28	,	,	PUNCT
cana-6096	175	29	any	any	DET
cana-6096	175	30	number	number	NOUN
cana-6096	175	31	greater	great	ADJ
cana-6096	175	32	than	than	ADP
cana-6096	175	33	or	or	CCONJ
cana-6096	175	34	equal	equal	ADJ
cana-6096	175	35	to	to	ADP
cana-6096	175	36	5	5	NUM
cana-6096	175	37	is	be	AUX
cana-6096	175	38	decomposed	decompose	VERB
cana-6096	175	39	into	into	ADP
cana-6096	175	40	two	two	NUM
cana-6096	175	41	terms	term	NOUN
cana-6096	175	42	greater	great	ADJ
cana-6096	175	43	than	than	ADP
cana-6096	175	44	1	1	NUM
cana-6096	175	45	,	,	PUNCT
cana-6096	175	46	the	the	DET
cana-6096	175	47	product	product	NOUN
cana-6096	175	48	of	of	ADP
cana-6096	175	49	these	these	DET
cana-6096	175	50	two	two	NUM
cana-6096	175	51	terms	term	NOUN
cana-6096	175	52	will	will	AUX
cana-6096	175	53	be	be	AUX
cana-6096	175	54	greater	great	ADJ
cana-6096	175	55	than	than	ADP
cana-6096	175	56	the	the	DET
cana-6096	175	57	original	original	ADJ
cana-6096	175	58	number	number	NOUN
cana-6096	175	59	.	.	PUNCT
cana-6096	176	1	indeed	indeed	ADV
cana-6096	176	2	,	,	PUNCT
cana-6096	176	3	if	if	SCONJ
cana-6096	176	4	n	n	PRON
cana-6096	176	5	is	be	AUX
cana-6096	176	6	one	one	NUM
cana-6096	176	7	of	of	ADP
cana-6096	176	8	the	the	DET
cana-6096	176	9	numbers	number	NOUN
cana-6096	176	10	in	in	ADP
cana-6096	176	11	the	the	DET
cana-6096	176	12	decomposition	decomposition	NOUN
cana-6096	176	13	,	,	PUNCT
cana-6096	176	14	replacing	replace	VERB
cana-6096	176	15	it	it	PRON
cana-6096	176	16	with	with	ADP
cana-6096	176	17	[	[	X
cana-6096	176	18	(	(	PUNCT
cana-6096	176	19	n	n	PRON
cana-6096	176	20	2	2	NUM
cana-6096	176	21	)	)	PUNCT
cana-6096	176	22	+	+	CCONJ
cana-6096	176	23	2	2	X
cana-6096	176	24	]	]	PUNCT
cana-6096	176	25	does	do	AUX
cana-6096	176	26	not	not	PART
cana-6096	176	27	change	change	VERB
cana-6096	176	28	the	the	DET
cana-6096	176	29	sum	sum	NOUN
cana-6096	176	30	,	,	PUNCT
cana-6096	176	31	and	and	CCONJ
cana-6096	176	32	the	the	DET
cana-6096	176	33	product	product	NOUN
cana-6096	176	34	becomes	become	VERB
cana-6096	176	35	2	2	NUM
cana-6096	176	36	×	×	NOUN
cana-6096	176	37	(	(	PUNCT
cana-6096	176	38	n	n	NOUN
cana-6096	176	39	2	2	NUM
cana-6096	176	40	)	)	PUNCT
cana-6096	176	41	=	=	NOUN
cana-6096	176	42	2n	2n	NUM
cana-6096	176	43	4	4	NUM
cana-6096	176	44	=	=	SYM
cana-6096	176	45	n	n	NOUN
cana-6096	176	46	+	+	CCONJ
cana-6096	176	47	(	(	PUNCT
cana-6096	176	48	n	n	PRON
cana-6096	176	49	4	4	NUM
cana-6096	176	50	)	)	PUNCT
cana-6096	176	51	.	.	PUNCT
cana-6096	177	1	now	now	ADV
cana-6096	177	2	(	(	PUNCT
cana-6096	177	3	n	n	NOUN
cana-6096	177	4	4	4	NUM
cana-6096	177	5	)	)	PUNCT
cana-6096	177	6	is	be	AUX
cana-6096	177	7	positive	positive	ADJ
cana-6096	177	8	if	if	SCONJ
cana-6096	177	9	n	n	PRON
cana-6096	177	10	is	be	AUX
cana-6096	177	11	greater	great	ADJ
cana-6096	177	12	than	than	ADP
cana-6096	177	13	4	4	NUM
cana-6096	177	14	,	,	PUNCT
cana-6096	177	15	so	so	ADV
cana-6096	177	16	n	n	PROPN
cana-6096	177	17	+	+	CCONJ
cana-6096	177	18	(	(	PUNCT
cana-6096	177	19	n	n	PRON
cana-6096	177	20	4	4	NUM
cana-6096	177	21	)	)	PUNCT
cana-6096	177	22	is	be	AUX
cana-6096	177	23	greater	great	ADJ
cana-6096	177	24	than	than	ADP
cana-6096	177	25	n	n	CCONJ
cana-6096	177	26	,	,	PUNCT
cana-6096	177	27	if	if	SCONJ
cana-6096	177	28	n	n	PRON
cana-6096	177	29	is	be	AUX
cana-6096	177	30	greater	great	ADJ
cana-6096	177	31	than	than	ADP
cana-6096	177	32	4	4	NUM
cana-6096	177	33	.	.	PUNCT
cana-6096	178	1	any	any	DET
cana-6096	178	2	number	number	NOUN
cana-6096	178	3	n	n	CCONJ
cana-6096	178	4	greater	great	ADJ
cana-6096	178	5	than	than	ADP
cana-6096	178	6	4	4	NUM
cana-6096	178	7	(	(	PUNCT
cana-6096	178	8	greater	great	ADJ
cana-6096	178	9	than	than	ADP
cana-6096	178	10	or	or	CCONJ
cana-6096	178	11	equal	equal	ADJ
cana-6096	178	12	to	to	ADP
cana-6096	178	13	5	5	NUM
cana-6096	178	14	)	)	PUNCT
cana-6096	178	15	allows	allow	VERB
cana-6096	178	16	us	we	PRON
cana-6096	178	17	to	to	PART
cana-6096	178	18	obtain	obtain	VERB
cana-6096	178	19	a	a	DET
cana-6096	178	20	larger	large	ADJ
cana-6096	178	21	product	product	NOUN
cana-6096	178	22	if	if	SCONJ
cana-6096	178	23	we	we	PRON
cana-6096	178	24	replace	replace	VERB
cana-6096	178	25	it	it	PRON
cana-6096	178	26	with	with	ADP
cana-6096	178	27	2	2	NUM
cana-6096	178	28	×	×	NOUN
cana-6096	178	29	(	(	PUNCT
cana-6096	178	30	n	n	NOUN
cana-6096	178	31	2	2	NUM
cana-6096	178	32	)	)	PUNCT
cana-6096	178	33	.	.	PUNCT
cana-6096	179	1	by	by	ADP
cana-6096	179	2	applying	apply	VERB
cana-6096	179	3	this	this	DET
cana-6096	179	4	property	property	NOUN
cana-6096	179	5	,	,	PUNCT
cana-6096	179	6	the	the	DET
cana-6096	179	7	only	only	ADJ
cana-6096	179	8	numbers	number	NOUN
cana-6096	179	9	kept	keep	VERB
cana-6096	179	10	are	be	AUX
cana-6096	179	11	3s	3s	NUM
cana-6096	179	12	or	or	CCONJ
cana-6096	179	13	2s	2s	PROPN
cana-6096	179	14	(	(	PUNCT
cana-6096	179	15	since	since	SCONJ
cana-6096	179	16	4	4	NUM
cana-6096	179	17	=	=	SYM
cana-6096	179	18	2	2	NUM
cana-6096	179	19	×	×	NOUN
cana-6096	179	20	2	2	NUM
cana-6096	179	21	)	)	PUNCT
cana-6096	179	22	.	.	PUNCT
cana-6096	180	1	d.	d.	PROPN
cana-6096	180	2	if	if	SCONJ
cana-6096	180	3	in	in	ADP
cana-6096	180	4	a	a	DET
cana-6096	180	5	product	product	NOUN
cana-6096	180	6	we	we	PRON
cana-6096	180	7	replace	replace	VERB
cana-6096	180	8	2	2	NUM
cana-6096	180	9	×	×	NOUN
cana-6096	180	10	2	2	NUM
cana-6096	180	11	×	×	NOUN
cana-6096	180	12	2	2	NUM
cana-6096	180	13	=	=	SYM
cana-6096	180	14	8	8	NUM
cana-6096	180	15	with	with	ADP
cana-6096	180	16	3	3	NUM
cana-6096	180	17	×	×	NOUN
cana-6096	180	18	3	3	NUM
cana-6096	180	19	=	=	SYM
cana-6096	180	20	9	9	NUM
cana-6096	180	21	,	,	PUNCT
cana-6096	180	22	the	the	DET
cana-6096	180	23	product	product	NOUN
cana-6096	180	24	will	will	AUX
cana-6096	180	25	be	be	AUX
cana-6096	180	26	larger	large	ADJ
cana-6096	180	27	;	;	PUNCT
cana-6096	180	28	so	so	SCONJ
cana-6096	180	29	as	as	ADV
cana-6096	180	30	soon	soon	ADV
cana-6096	180	31	as	as	SCONJ
cana-6096	180	32	there	there	PRON
cana-6096	180	33	are	be	VERB
cana-6096	180	34	three	three	NUM
cana-6096	180	35	2s	2s	NUM
cana-6096	180	36	in	in	ADP
cana-6096	180	37	the	the	DET
cana-6096	180	38	decomposition	decomposition	NOUN
cana-6096	180	39	,	,	PUNCT
cana-6096	180	40	we	we	PRON
cana-6096	180	41	replace	replace	VERB
cana-6096	180	42	2	2	NUM
cana-6096	180	43	×	×	NOUN
cana-6096	180	44	2	2	NUM
cana-6096	180	45	×	×	NOUN
cana-6096	180	46	2	2	NUM
cana-6096	180	47	with	with	ADP
cana-6096	180	48	3	3	NUM
cana-6096	180	49	×	×	NOUN
cana-6096	180	50	3	3	NUM
cana-6096	180	51	;	;	PUNCT
cana-6096	180	52	therefore	therefore	ADV
cana-6096	180	53	,	,	PUNCT
cana-6096	180	54	only	only	ADV
cana-6096	180	55	one	one	NUM
cana-6096	180	56	or	or	CCONJ
cana-6096	180	57	two	two	NUM
cana-6096	180	58	2s	2	NOUN
cana-6096	180	59	are	be	AUX
cana-6096	180	60	retained	retain	VERB
cana-6096	180	61	among	among	ADP
cana-6096	180	62	the	the	DET
cana-6096	180	63	terms	term	NOUN
cana-6096	180	64	of	of	ADP
cana-6096	180	65	the	the	DET
cana-6096	180	66	product	product	NOUN
cana-6096	180	67	.	.	PUNCT
cana-6096	181	1	mathematical	mathematical	ADJ
cana-6096	181	2	objects	object	NOUN
cana-6096	181	3	that	that	PRON
cana-6096	181	4	can	can	AUX
cana-6096	181	5	be	be	AUX
cana-6096	181	6	worked	work	VERB
cana-6096	181	7	on	on	ADP
cana-6096	181	8	regarding	regard	VERB
cana-6096	181	9	the	the	DET
cana-6096	181	10	mathematical	mathematical	ADJ
cana-6096	181	11	objects	object	NOUN
cana-6096	181	12	worked	work	VERB
cana-6096	181	13	on	on	ADP
cana-6096	181	14	,	,	PUNCT
cana-6096	181	15	several	several	ADJ
cana-6096	181	16	are	be	AUX
cana-6096	181	17	objects	object	NOUN
cana-6096	181	18	that	that	PRON
cana-6096	181	19	can	can	AUX
cana-6096	181	20	be	be	AUX
cana-6096	181	21	considered	consider	VERB
cana-6096	181	22	acquired	acquire	VERB
cana-6096	181	23	by	by	ADP
cana-6096	181	24	the	the	DET
cana-6096	181	25	fourth	fourth	ADJ
cana-6096	181	26	grade	grade	NOUN
cana-6096	181	27	,	,	PUNCT
cana-6096	181	28	but	but	CCONJ
cana-6096	181	29	certain	certain	ADJ
cana-6096	181	30	types	type	NOUN
cana-6096	181	31	of	of	ADP
cana-6096	181	32	reasoning	reasoning	NOUN
cana-6096	181	33	make	make	VERB
cana-6096	181	34	it	it	PRON
cana-6096	181	35	possible	possible	ADJ
cana-6096	181	36	to	to	PART
cana-6096	181	37	consider	consider	VERB
cana-6096	181	38	implementing	implement	VERB
cana-6096	181	39	this	this	DET
cana-6096	181	40	situation	situation	NOUN
cana-6096	181	41	at	at	ADP
cana-6096	181	42	all	all	DET
cana-6096	181	43	levels	level	NOUN
cana-6096	181	44	of	of	ADP
cana-6096	181	45	high	high	ADJ
cana-6096	181	46	school	school	NOUN
cana-6096	181	47	,	,	PUNCT
cana-6096	181	48	and	and	CCONJ
cana-6096	181	49	even	even	ADV
cana-6096	181	50	beyond	beyond	ADP
cana-6096	181	51	.	.	PUNCT
cana-6096	182	1	primary	primary	ADJ
cana-6096	182	2	college	college	PROPN
cana-6096	182	3	high	high	ADJ
cana-6096	182	4	school	school	NOUN
cana-6096	182	5	0	0	NUM
cana-6096	182	6	absorbing	absorb	VERB
cana-6096	182	7	elements	element	NOUN
cana-6096	182	8	of	of	ADP
cana-6096	182	9	multiplication	multiplication	NOUN
cana-6096	182	10	1	1	NUM
cana-6096	182	11	neutral	neutral	ADJ
cana-6096	182	12	element	element	NOUN
cana-6096	182	13	of	of	ADP
cana-6096	182	14	multiplication	multiplication	NOUN
cana-6096	182	15	additive	additive	ADJ
cana-6096	182	16	decompositions	decomposition	NOUN
cana-6096	182	17	of	of	ADP
cana-6096	182	18	an	an	DET
cana-6096	182	19	integer	integer	NOUN
cana-6096	182	20	multiplication	multiplication	NOUN
cana-6096	182	21	tables	table	NOUN
cana-6096	182	22	associativity	associativity	NOUN
cana-6096	182	23	and	and	CCONJ
cana-6096	182	24	commutativity	commutativity	NOUN
cana-6096	182	25	of	of	ADP
cana-6096	182	26	multiplication	multiplication	NOUN
cana-6096	182	27	.	.	PUNCT
cana-6096	183	1	understanding	understanding	NOUN
cana-6096	183	2	of	of	ADP
cana-6096	183	3	the	the	DET
cana-6096	183	4	terms	term	NOUN
cana-6096	183	5	"	"	PUNCT
cana-6096	183	6	sum	sum	NOUN
cana-6096	183	7	,	,	PUNCT
cana-6096	183	8	"	"	PUNCT
cana-6096	183	9	"	"	PUNCT
cana-6096	183	10	product	product	NOUN
cana-6096	183	11	,	,	PUNCT
cana-6096	183	12	"	"	PUNCT
cana-6096	183	13	"	"	PUNCT
cana-6096	183	14	terms	term	NOUN
cana-6096	183	15	,	,	PUNCT
cana-6096	183	16	"	"	PUNCT
cana-6096	183	17	"	"	PUNCT
cana-6096	183	18	product	product	NOUN
cana-6096	183	19	of	of	ADP
cana-6096	183	20	the	the	DET
cana-6096	183	21	terms	term	NOUN
cana-6096	183	22	of	of	ADP
cana-6096	183	23	the	the	DET
cana-6096	183	24	sum	sum	NOUN
cana-6096	183	25	"	"	PUNCT
cana-6096	183	26	elementary	elementary	ADJ
cana-6096	183	27	reasoning	reasoning	NOUN
cana-6096	183	28	about	about	ADP
cana-6096	183	29	numbers	number	NOUN
cana-6096	183	30	:	:	PUNCT
cana-6096	183	31	1	1	NUM
cana-6096	183	32	×	×	NOUN
cana-6096	183	33	1	1	NUM
cana-6096	183	34	<	<	X
cana-6096	183	35	2	2	NUM
cana-6096	183	36	;	;	PUNCT
cana-6096	183	37	1	1	NUM
cana-6096	183	38	×	×	NOUN
cana-6096	183	39	1	1	NUM
cana-6096	183	40	×	×	NOUN
cana-6096	183	41	1	1	NUM
cana-6096	183	42	<	<	SYM
cana-6096	183	43	3	3	NUM
cana-6096	183	44	and	and	CCONJ
cana-6096	183	45	1	1	NUM
cana-6096	183	46	×	×	NOUN
cana-6096	183	47	2	2	NUM
cana-6096	183	48	<	<	X
cana-6096	183	49	3	3	NUM
cana-6096	183	50	;	;	PUNCT
cana-6096	183	51	2	2	NUM
cana-6096	183	52	×	×	NOUN
cana-6096	183	53	2	2	NUM
cana-6096	183	54	>	>	SYM
cana-6096	183	55	1	1	NUM
cana-6096	183	56	×	×	NOUN
cana-6096	183	57	3	3	NUM
cana-6096	183	58	return	return	NOUN
cana-6096	183	59	to	to	ADP
cana-6096	183	60	additional	additional	ADJ
cana-6096	183	61	methodological	methodological	ADJ
cana-6096	183	62	skills	skill	NOUN
cana-6096	183	63	,	,	PUNCT
cana-6096	183	64	particularly	particularly	ADV
cana-6096	183	65	:	:	PUNCT
cana-6096	183	66	reasoning	reasoning	NOUN
cana-6096	183	67	by	by	ADP
cana-6096	183	68	disjunction	disjunction	NOUN
cana-6096	183	69	of	of	ADP
cana-6096	183	70	cases	case	NOUN
cana-6096	183	71	reasoning	reason	VERB
cana-6096	183	72	by	by	ADP
cana-6096	183	73	recurrence	recurrence	NOUN
cana-6096	183	74	writing	write	VERB
cana-6096	183	75	the	the	DET
cana-6096	183	76	solution	solution	NOUN
cana-6096	183	77	to	to	ADP
cana-6096	183	78	the	the	DET
cana-6096	183	79	problem	problem	NOUN
cana-6096	183	80	posed	pose	VERB
cana-6096	183	81	interpreting	interpret	VERB
cana-6096	183	82	elementary	elementary	ADJ
cana-6096	183	83	reasoning	reasoning	NOUN
cana-6096	183	84	about	about	ADP
cana-6096	183	85	numbers	number	NOUN
cana-6096	183	86	?	?	PUNCT
cana-6096	184	1	(	(	PUNCT
cana-6096	184	2	1	1	NUM
cana-6096	184	3	×	×	NOUN
cana-6096	184	4	1	1	NUM
cana-6096	184	5	<	<	X
cana-6096	184	6	2	2	NUM
cana-6096	184	7	;	;	PUNCT
cana-6096	184	8	1	1	NUM
cana-6096	184	9	×	×	NOUN
cana-6096	184	10	1	1	NUM
cana-6096	184	11	×	×	NOUN
cana-6096	184	12	1	1	NUM
cana-6096	184	13	<	<	SYM
cana-6096	184	14	3	3	NUM
cana-6096	184	15	and	and	CCONJ
cana-6096	184	16	1	1	NUM
cana-6096	184	17	×	×	NOUN
cana-6096	184	18	2	2	NUM
cana-6096	184	19	<	<	X
cana-6096	184	20	3	3	NUM
cana-6096	184	21	;	;	PUNCT
cana-6096	184	22	2	2	NUM
cana-6096	184	23	×	×	NOUN
cana-6096	184	24	2	2	NUM
cana-6096	184	25	>	>	SYM
cana-6096	184	26	1	1	NUM
cana-6096	184	27	×	×	NOUN
cana-6096	184	28	3	3	NUM
cana-6096	184	29	)	)	PUNCT
cana-6096	184	30	in	in	ADP
cana-6096	184	31	terms	term	NOUN
cana-6096	184	32	of	of	ADP
cana-6096	184	33	the	the	DET
cana-6096	184	34	form	form	NOUN
cana-6096	184	35	of	of	ADP
cana-6096	184	36	the	the	DET
cana-6096	184	37	additive	additive	ADJ
cana-6096	184	38	decomposition	decomposition	NOUN
cana-6096	184	39	obtained	obtain	VERB
cana-6096	184	40	for	for	ADP
cana-6096	184	41	the	the	DET
cana-6096	184	42	initial	initial	ADJ
cana-6096	184	43	integer	integer	NOUN
cana-6096	184	44	.	.	PUNCT
cana-6096	185	1	euclidean	euclidean	ADJ
cana-6096	185	2	division	division	NOUN
cana-6096	185	3	by	by	ADP
cana-6096	185	4	three	three	NUM
cana-6096	185	5	,	,	PUNCT
cana-6096	185	6	more	more	ADV
cana-6096	185	7	precisely	precisely	ADV
cana-6096	185	8	,	,	PUNCT
cana-6096	185	9	remainders	remainder	NOUN
cana-6096	185	10	in	in	ADP
cana-6096	185	11	this	this	DET
cana-6096	185	12	division	division	NOUN
cana-6096	185	13	algebraic	algebraic	ADJ
cana-6096	185	14	calculus	calculus	NOUN
cana-6096	185	15	,	,	PUNCT
cana-6096	185	16	more	more	ADV
cana-6096	185	17	precisely	precisely	ADV
cana-6096	185	18	,	,	PUNCT
cana-6096	185	19	solving	solve	VERB
cana-6096	185	20	a	a	DET
cana-6096	185	21	first	first	ADJ
cana-6096	185	22	-	-	PUNCT
cana-6096	185	23	degree	degree	NOUN
cana-6096	185	24	inequality	inequality	NOUN
cana-6096	185	25	with	with	ADP
cana-6096	185	26	one	one	NUM
cana-6096	185	27	unknown	unknown	NOUN
cana-6096	185	28	,	,	PUNCT
cana-6096	185	29	and	and	CCONJ
cana-6096	185	30	interpreting	interpret	VERB
cana-6096	185	31	the	the	DET
cana-6096	185	32	solutions	solution	NOUN
cana-6096	185	33	by	by	ADP
cana-6096	185	34	returning	return	VERB
cana-6096	185	35	to	to	ADP
cana-6096	185	36	the	the	DET
cana-6096	185	37	problem	problem	NOUN
cana-6096	185	38	posed	pose	VERB
cana-6096	185	39	communications	communication	NOUN
cana-6096	185	40	on	on	ADP
cana-6096	185	41	applied	apply	VERB
cana-6096	185	42	nonlinear	nonlinear	ADJ
cana-6096	185	43	analysis	analysis	NOUN
cana-6096	185	44	issn	issn	NOUN
cana-6096	185	45	:	:	PUNCT
cana-6096	185	46	1074	1074	NUM
cana-6096	185	47	-	-	PUNCT
cana-6096	185	48	133x	133x	NUM
cana-6096	185	49	vol	vol	NOUN
cana-6096	185	50	32	32	NUM
cana-6096	185	51	no	no	NOUN
cana-6096	185	52	.	.	NOUN
cana-6096	185	53	3	3	NUM
cana-6096	185	54	(	(	PUNCT
cana-6096	185	55	2025	2025	NUM
cana-6096	185	56	)	)	PUNCT
cana-6096	185	57	1072	1072	NUM
cana-6096	185	58	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	185	59	without	without	ADP
cana-6096	185	60	calculation	calculation	NOUN
cana-6096	185	61	,	,	PUNCT
cana-6096	185	62	use	use	VERB
cana-6096	185	63	the	the	DET
cana-6096	185	64	straightedge	straightedge	NOUN
cana-6096	185	65	and	and	CCONJ
cana-6096	185	66	compass	compass	NOUN
cana-6096	185	67	to	to	PART
cana-6096	185	68	transform	transform	VERB
cana-6096	185	69	a	a	DET
cana-6096	185	70	hexagon	hexagon	NOUN
cana-6096	185	71	into	into	ADP
cana-6096	185	72	a	a	DET
cana-6096	185	73	rectangle	rectangle	NOUN
cana-6096	185	74	solutions	solution	NOUN
cana-6096	185	75	(	(	PUNCT
cana-6096	185	76	nondetailed	nondetaile	VERB
cana-6096	185	77	)	)	PUNCT
cana-6096	185	78	if	if	SCONJ
cana-6096	185	79	the	the	DET
cana-6096	185	80	hexagon	hexagon	NOUN
cana-6096	185	81	is	be	AUX
cana-6096	185	82	regular	regular	ADJ
cana-6096	185	83	,	,	PUNCT
cana-6096	185	84	we	we	PRON
cana-6096	185	85	can	can	AUX
cana-6096	185	86	consider	consider	VERB
cana-6096	185	87	the	the	DET
cana-6096	185	88	following	follow	VERB
cana-6096	185	89	transformation	transformation	NOUN
cana-6096	185	90	:	:	PUNCT
cana-6096	185	91	if	if	SCONJ
cana-6096	185	92	the	the	DET
cana-6096	185	93	hexagon	hexagon	NOUN
cana-6096	185	94	has	have	VERB
cana-6096	185	95	two	two	NUM
cana-6096	185	96	axes	axis	NOUN
cana-6096	185	97	of	of	ADP
cana-6096	185	98	symmetry	symmetry	NOUN
cana-6096	185	99	,	,	PUNCT
cana-6096	185	100	we	we	PRON
cana-6096	185	101	can	can	AUX
cana-6096	185	102	consider	consider	VERB
cana-6096	185	103	the	the	DET
cana-6096	185	104	following	follow	VERB
cana-6096	185	105	transformation	transformation	NOUN
cana-6096	185	106	:	:	PUNCT
cana-6096	185	107	i	i	PRON
cana-6096	185	108	let	let	VERB
cana-6096	185	109	abcdef	abcdef	NOUN
cana-6096	185	110	be	be	AUX
cana-6096	185	111	any	any	DET
cana-6096	185	112	hexagon	hexagon	NOUN
cana-6096	185	113	.	.	PUNCT
cana-6096	186	1	ii	ii	NOUN
cana-6096	186	2	we	we	PRON
cana-6096	186	3	draw	draw	VERB
cana-6096	186	4	the	the	DET
cana-6096	186	5	segment	segment	NOUN
cana-6096	186	6	[	[	X
cana-6096	186	7	ea	ea	X
cana-6096	186	8	]	]	X
cana-6096	186	9	(	(	PUNCT
cana-6096	186	10	we	we	PRON
cana-6096	186	11	join	join	VERB
cana-6096	186	12	two	two	NUM
cana-6096	186	13	nonconsecutive	nonconsecutive	ADJ
cana-6096	186	14	vertices	vertex	NOUN
cana-6096	186	15	of	of	ADP
cana-6096	186	16	the	the	DET
cana-6096	186	17	hexagon	hexagon	NOUN
cana-6096	186	18	)	)	PUNCT
cana-6096	186	19	,	,	PUNCT
cana-6096	186	20	the	the	DET
cana-6096	186	21	halfline	halfline	NOUN
cana-6096	186	22	[	[	X
cana-6096	186	23	de	de	X
cana-6096	186	24	)	)	PUNCT
cana-6096	186	25	.	.	PUNCT
cana-6096	187	1	we	we	PRON
cana-6096	187	2	then	then	ADV
cana-6096	187	3	draw	draw	VERB
cana-6096	187	4	the	the	DET
cana-6096	187	5	parallel	parallel	NOUN
cana-6096	187	6	to	to	ADP
cana-6096	187	7	[	[	X
cana-6096	187	8	ea	ea	X
cana-6096	187	9	]	]	X
cana-6096	187	10	passing	pass	VERB
cana-6096	187	11	through	through	ADP
cana-6096	187	12	f	f	NOUN
cana-6096	187	13	:	:	PUNCT
cana-6096	187	14	it	it	PRON
cana-6096	187	15	intersects	intersect	VERB
cana-6096	187	16	[	[	X
cana-6096	187	17	de	de	X
cana-6096	187	18	)	)	PUNCT
cana-6096	187	19	at	at	ADP
cana-6096	187	20	g.	g.	PROPN
cana-6096	187	21	we	we	PRON
cana-6096	187	22	thus	thus	ADV
cana-6096	187	23	obtain	obtain	VERB
cana-6096	187	24	the	the	DET
cana-6096	187	25	pentagon	pentagon	PROPN
cana-6096	187	26	abcdg	abcdg	PROPN
cana-6096	187	27	.	.	PUNCT
cana-6096	188	1	iii	iii	X
cana-6096	188	2	we	we	PRON
cana-6096	188	3	draw	draw	VERB
cana-6096	188	4	the	the	DET
cana-6096	188	5	segment	segment	NOUN
cana-6096	188	6	[	[	X
cana-6096	188	7	ad	ad	X
cana-6096	188	8	]	]	X
cana-6096	188	9	,	,	PUNCT
cana-6096	188	10	the	the	DET
cana-6096	188	11	half	half	ADJ
cana-6096	188	12	-	-	PUNCT
cana-6096	188	13	line	line	NOUN
cana-6096	188	14	[	[	X
cana-6096	188	15	cd	cd	PROPN
cana-6096	188	16	)	)	PUNCT
cana-6096	188	17	.	.	PUNCT
cana-6096	189	1	we	we	PRON
cana-6096	189	2	then	then	ADV
cana-6096	189	3	draw	draw	VERB
cana-6096	189	4	the	the	DET
cana-6096	189	5	parallel	parallel	NOUN
cana-6096	189	6	to	to	ADP
cana-6096	189	7	[	[	PUNCT
cana-6096	189	8	ad	ad	X
cana-6096	189	9	]	]	PUNCT
cana-6096	189	10	passing	pass	VERB
cana-6096	189	11	through	through	ADP
cana-6096	189	12	g	g	NOUN
cana-6096	189	13	:	:	PUNCT
cana-6096	189	14	it	it	PRON
cana-6096	189	15	intersects	intersect	VERB
cana-6096	189	16	[	[	X
cana-6096	189	17	cd	cd	NOUN
cana-6096	189	18	)	)	PUNCT
cana-6096	189	19	at	at	ADP
cana-6096	189	20	h.	h.	PROPN
cana-6096	189	21	we	we	PRON
cana-6096	189	22	thus	thus	ADV
cana-6096	189	23	obtain	obtain	VERB
cana-6096	189	24	the	the	DET
cana-6096	189	25	quadrilateral	quadrilateral	ADJ
cana-6096	189	26	abch	abch	NOUN
cana-6096	189	27	.	.	PUNCT
cana-6096	190	1	iv	iv	X
cana-6096	190	2	we	we	PRON
cana-6096	190	3	draw	draw	VERB
cana-6096	190	4	the	the	DET
cana-6096	190	5	segment	segment	NOUN
cana-6096	190	6	[	[	X
cana-6096	190	7	bh	bh	X
cana-6096	190	8	]	]	X
cana-6096	190	9	,	,	PUNCT
cana-6096	190	10	the	the	DET
cana-6096	190	11	half	half	ADJ
cana-6096	190	12	-	-	PUNCT
cana-6096	190	13	line	line	NOUN
cana-6096	190	14	[	[	X
cana-6096	190	15	ab	ab	X
cana-6096	190	16	)	)	PUNCT
cana-6096	190	17	.	.	PUNCT
cana-6096	191	1	we	we	PRON
cana-6096	191	2	then	then	ADV
cana-6096	191	3	draw	draw	VERB
cana-6096	191	4	the	the	DET
cana-6096	191	5	parallel	parallel	NOUN
cana-6096	191	6	to	to	ADP
cana-6096	191	7	[	[	X
cana-6096	191	8	bh	bh	X
cana-6096	191	9	]	]	X
cana-6096	191	10	passing	pass	VERB
cana-6096	191	11	through	through	ADP
cana-6096	191	12	c	c	NOUN
cana-6096	191	13	:	:	PUNCT
cana-6096	191	14	it	it	PRON
cana-6096	191	15	intersects	intersect	VERB
cana-6096	191	16	[	[	X
cana-6096	191	17	ab	ab	X
cana-6096	191	18	)	)	PUNCT
cana-6096	191	19	at	at	ADP
cana-6096	191	20	i.	i.	NOUN
cana-6096	191	21	we	we	PRON
cana-6096	191	22	thus	thus	ADV
cana-6096	191	23	obtain	obtain	VERB
cana-6096	191	24	the	the	DET
cana-6096	191	25	triangle	triangle	NOUN
cana-6096	191	26	aih	aih	PROPN
cana-6096	191	27	.	.	PUNCT
cana-6096	191	28	)	)	PUNCT
cana-6096	191	29	application	application	NOUN
cana-6096	191	30	2	2	NUM
cana-6096	191	31	.	.	PUNCT
cana-6096	192	1	(	(	PUNCT
cana-6096	192	2	areas	area	NOUN
cana-6096	192	3	without	without	ADP
cana-6096	192	4	calculation	calculation	NOUN
cana-6096	192	5	[	[	X
cana-6096	192	6	6	6	NUM
cana-6096	192	7	]	]	PUNCT
cana-6096	192	8	with	with	ADP
cana-6096	192	9	the	the	DET
cana-6096	192	10	same	same	ADJ
cana-6096	192	11	area	area	NOUN
cana-6096	192	12	.	.	PUNCT
cana-6096	193	1	communications	communication	NOUN
cana-6096	193	2	on	on	ADP
cana-6096	193	3	applied	apply	VERB
cana-6096	193	4	nonlinear	nonlinear	ADJ
cana-6096	193	5	analysis	analysis	NOUN
cana-6096	193	6	issn	issn	NOUN
cana-6096	193	7	:	:	PUNCT
cana-6096	193	8	1074	1074	NUM
cana-6096	193	9	-	-	PUNCT
cana-6096	193	10	133x	133x	NUM
cana-6096	193	11	vol	vol	NOUN
cana-6096	193	12	32	32	NUM
cana-6096	193	13	no	no	NOUN
cana-6096	193	14	.	.	NOUN
cana-6096	193	15	3	3	NUM
cana-6096	193	16	(	(	PUNCT
cana-6096	193	17	2025	2025	NUM
cana-6096	193	18	)	)	PUNCT
cana-6096	193	19	1073	1073	NUM
cana-6096	193	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	193	21	v	v	X
cana-6096	193	22	we	we	PRON
cana-6096	193	23	draw	draw	VERB
cana-6096	193	24	l	l	NOUN
cana-6096	193	25	,	,	PUNCT
cana-6096	193	26	the	the	DET
cana-6096	193	27	middle	middle	NOUN
cana-6096	193	28	of	of	ADP
cana-6096	193	29	[	[	X
cana-6096	193	30	ih	ih	X
cana-6096	193	31	]	]	PUNCT
cana-6096	193	32	.	.	PUNCT
cana-6096	194	1	we	we	PRON
cana-6096	194	2	then	then	ADV
cana-6096	194	3	draw	draw	VERB
cana-6096	194	4	the	the	DET
cana-6096	194	5	parallel	parallel	NOUN
cana-6096	194	6	to	to	ADP
cana-6096	194	7	[	[	X
cana-6096	194	8	ai	ai	VERB
cana-6096	194	9	]	]	X
cana-6096	194	10	passing	pass	VERB
cana-6096	194	11	through	through	ADP
cana-6096	194	12	l	l	NOUN
cana-6096	194	13	and	and	CCONJ
cana-6096	194	14	the	the	DET
cana-6096	194	15	parallel	parallel	NOUN
cana-6096	194	16	to	to	ADP
cana-6096	194	17	[	[	X
cana-6096	194	18	ih	ih	X
cana-6096	194	19	]	]	PUNCT
cana-6096	194	20	passing	pass	VERB
cana-6096	194	21	through	through	ADP
cana-6096	194	22	a.	a.	NOUN
cana-6096	194	23	we	we	PRON
cana-6096	194	24	obtain	obtain	VERB
cana-6096	194	25	the	the	DET
cana-6096	194	26	parallelogram	parallelogram	NOUN
cana-6096	194	27	ailm	ailm	NOUN
cana-6096	194	28	.	.	PUNCT
cana-6096	195	1	vi	vi	PROPN
cana-6096	196	1	we	we	PRON
cana-6096	196	2	draw	draw	VERB
cana-6096	196	3	the	the	DET
cana-6096	196	4	perpendicular	perpendicular	NOUN
cana-6096	196	5	to	to	ADP
cana-6096	196	6	[	[	X
cana-6096	196	7	am	am	AUX
cana-6096	196	8	]	]	X
cana-6096	196	9	passing	pass	VERB
cana-6096	196	10	through	through	ADP
cana-6096	196	11	l	l	NOUN
cana-6096	196	12	:	:	PUNCT
cana-6096	196	13	it	it	PRON
cana-6096	196	14	intersects	intersect	VERB
cana-6096	196	15	[	[	X
cana-6096	196	16	am	be	AUX
cana-6096	196	17	]	]	X
cana-6096	196	18	at	at	ADP
cana-6096	196	19	l.	l.	NOUN
cana-6096	196	20	we	we	PRON
cana-6096	196	21	draw	draw	VERB
cana-6096	196	22	the	the	DET
cana-6096	196	23	perpendicular	perpendicular	NOUN
cana-6096	196	24	to	to	ADP
cana-6096	196	25	(	(	PUNCT
cana-6096	196	26	li	li	NOUN
cana-6096	196	27	)	)	PUNCT
cana-6096	196	28	passing	pass	VERB
cana-6096	196	29	through	through	ADP
cana-6096	196	30	i	i	PRON
cana-6096	196	31	:	:	PUNCT
cana-6096	196	32	it	it	PRON
cana-6096	196	33	intersects	intersect	VERB
cana-6096	196	34	(	(	PUNCT
cana-6096	196	35	am	be	AUX
cana-6096	196	36	)	)	PUNCT
cana-6096	196	37	at	at	ADP
cana-6096	196	38	p.	p.	NOUN
cana-6096	196	39	we	we	PRON
cana-6096	196	40	obtain	obtain	VERB
cana-6096	196	41	the	the	DET
cana-6096	196	42	rectangle	rectangle	NOUN
cana-6096	196	43	opil	opil	NOUN
cana-6096	196	44	.	.	PUNCT
cana-6096	197	1	changing	change	VERB
cana-6096	197	2	one	one	PRON
cana-6096	197	3	's	's	PART
cana-6096	197	4	practices	practice	NOUN
cana-6096	197	5	?	?	PUNCT
cana-6096	198	1	under	under	ADP
cana-6096	198	2	what	what	DET
cana-6096	198	3	conditions	condition	NOUN
cana-6096	198	4	?	?	PUNCT
cana-6096	199	1	at	at	ADP
cana-6096	199	2	this	this	DET
cana-6096	199	3	point	point	NOUN
cana-6096	199	4	in	in	ADP
cana-6096	199	5	the	the	DET
cana-6096	199	6	reflection	reflection	NOUN
cana-6096	199	7	,	,	PUNCT
cana-6096	199	8	it	it	PRON
cana-6096	199	9	seems	seem	VERB
cana-6096	199	10	interesting	interesting	ADJ
cana-6096	199	11	to	to	PART
cana-6096	199	12	question	question	VERB
cana-6096	199	13	the	the	DET
cana-6096	199	14	necessity	necessity	NOUN
cana-6096	199	15	,	,	PUNCT
cana-6096	199	16	the	the	DET
cana-6096	199	17	interest	interest	NOUN
cana-6096	199	18	,	,	PUNCT
cana-6096	199	19	or	or	CCONJ
cana-6096	199	20	the	the	DET
cana-6096	199	21	need	need	NOUN
cana-6096	199	22	for	for	SCONJ
cana-6096	199	23	teachers	teacher	NOUN
cana-6096	199	24	to	to	PART
cana-6096	199	25	change	change	VERB
cana-6096	199	26	their	their	PRON
cana-6096	199	27	ways	way	NOUN
cana-6096	199	28	of	of	ADP
cana-6096	199	29	doing	do	VERB
cana-6096	199	30	things	thing	NOUN
cana-6096	199	31	.	.	PUNCT
cana-6096	200	1	this	this	DET
cana-6096	200	2	question	question	NOUN
cana-6096	200	3	is	be	AUX
cana-6096	200	4	central	central	ADJ
cana-6096	200	5	to	to	ADP
cana-6096	200	6	didactic	didactic	ADJ
cana-6096	200	7	thinking	thinking	NOUN
cana-6096	200	8	.	.	PUNCT
cana-6096	201	1	does	do	AUX
cana-6096	201	2	this	this	PRON
cana-6096	201	3	mean	mean	VERB
cana-6096	201	4	we	we	PRON
cana-6096	201	5	must	must	AUX
cana-6096	201	6	question	question	VERB
cana-6096	201	7	everything	everything	PRON
cana-6096	201	8	?	?	PUNCT
cana-6096	202	1	that	that	SCONJ
cana-6096	202	2	we	we	PRON
cana-6096	202	3	must	must	AUX
cana-6096	202	4	change	change	VERB
cana-6096	202	5	our	our	PRON
cana-6096	202	6	practices	practice	NOUN
cana-6096	202	7	from	from	ADP
cana-6096	202	8	top	top	NOUN
cana-6096	202	9	to	to	ADP
cana-6096	202	10	bottom	bottom	NOUN
cana-6096	202	11	?	?	PUNCT
cana-6096	203	1	that	that	SCONJ
cana-6096	203	2	what	what	PRON
cana-6096	203	3	is	be	AUX
cana-6096	203	4	currently	currently	ADV
cana-6096	203	5	being	be	AUX
cana-6096	203	6	done	do	VERB
cana-6096	203	7	in	in	ADP
cana-6096	203	8	our	our	PRON
cana-6096	203	9	classrooms	classroom	NOUN
cana-6096	203	10	is	be	AUX
cana-6096	203	11	derisory	derisory	ADJ
cana-6096	203	12	or	or	CCONJ
cana-6096	203	13	even	even	ADV
cana-6096	203	14	outdated	outdated	ADJ
cana-6096	203	15	?	?	PUNCT
cana-6096	204	1	these	these	DET
cana-6096	204	2	reflections	reflection	NOUN
cana-6096	204	3	are	be	AUX
cana-6096	204	4	not	not	PART
cana-6096	204	5	part	part	NOUN
cana-6096	204	6	of	of	ADP
cana-6096	204	7	a	a	DET
cana-6096	204	8	logic	logic	NOUN
cana-6096	204	9	of	of	ADP
cana-6096	204	10	radical	radical	ADJ
cana-6096	204	11	change	change	NOUN
cana-6096	204	12	but	but	CCONJ
cana-6096	204	13	rather	rather	ADV
cana-6096	204	14	a	a	DET
cana-6096	204	15	perspective	perspective	NOUN
cana-6096	204	16	of	of	ADP
cana-6096	204	17	evolution	evolution	NOUN
cana-6096	204	18	.	.	PUNCT
cana-6096	205	1	it	it	PRON
cana-6096	205	2	is	be	AUX
cana-6096	205	3	about	about	ADP
cana-6096	205	4	progressing	progress	VERB
cana-6096	205	5	in	in	ADP
cana-6096	205	6	our	our	PRON
cana-6096	205	7	professionalization	professionalization	NOUN
cana-6096	205	8	rather	rather	ADV
cana-6096	205	9	than	than	ADP
cana-6096	205	10	"	"	PUNCT
cana-6096	205	11	wanting	want	VERB
cana-6096	205	12	to	to	PART
cana-6096	205	13	do	do	VERB
cana-6096	205	14	things	thing	NOUN
cana-6096	205	15	differently	differently	ADV
cana-6096	205	16	tomorrow	tomorrow	NOUN
cana-6096	205	17	and	and	CCONJ
cana-6096	205	18	denying	deny	VERB
cana-6096	205	19	what	what	PRON
cana-6096	205	20	was	be	AUX
cana-6096	205	21	done	do	VERB
cana-6096	205	22	yesterday	yesterday	NOUN
cana-6096	205	23	.	.	PUNCT
cana-6096	205	24	"	"	PUNCT
cana-6096	206	1	according	accord	VERB
cana-6096	206	2	to	to	ADP
cana-6096	206	3	this	this	DET
cana-6096	206	4	model	model	NOUN
cana-6096	206	5	,	,	PUNCT
cana-6096	206	6	any	any	DET
cana-6096	206	7	change	change	NOUN
cana-6096	206	8	in	in	ADP
cana-6096	206	9	an	an	DET
cana-6096	206	10	individual	individual	NOUN
cana-6096	206	11	's	's	PART
cana-6096	206	12	behavior	behavior	NOUN
cana-6096	206	13	(	(	PUNCT
cana-6096	206	14	student	student	NOUN
cana-6096	206	15	,	,	PUNCT
cana-6096	206	16	teacher	teacher	NOUN
cana-6096	206	17	,	,	PUNCT
cana-6096	206	18	or	or	CCONJ
cana-6096	206	19	other	other	ADJ
cana-6096	206	20	)	)	PUNCT
cana-6096	206	21	requires	require	VERB
cana-6096	206	22	the	the	DET
cana-6096	206	23	integration	integration	NOUN
cana-6096	206	24	of	of	ADP
cana-6096	206	25	numerous	numerous	ADJ
cana-6096	206	26	learning	learning	NOUN
cana-6096	206	27	processes	process	NOUN
cana-6096	206	28	,	,	PUNCT
cana-6096	206	29	while	while	SCONJ
cana-6096	206	30	the	the	DET
cana-6096	206	31	achievement	achievement	NOUN
cana-6096	206	32	of	of	ADP
cana-6096	206	33	learning	learning	NOUN
cana-6096	206	34	requires	require	VERB
cana-6096	206	35	a	a	DET
cana-6096	206	36	change	change	NOUN
cana-6096	206	37	in	in	ADP
cana-6096	206	38	cognitive	cognitive	ADJ
cana-6096	206	39	structure	structure	NOUN
cana-6096	206	40	.	.	PUNCT
cana-6096	207	1	to	to	PART
cana-6096	207	2	summarize	summarize	VERB
cana-6096	207	3	,	,	PUNCT
cana-6096	207	4	we	we	PRON
cana-6096	207	5	will	will	AUX
cana-6096	207	6	say	say	VERB
cana-6096	207	7	that	that	PRON
cana-6096	207	8	to	to	PART
cana-6096	207	9	change	change	VERB
cana-6096	207	10	is	be	AUX
cana-6096	207	11	to	to	PART
cana-6096	207	12	learn	learn	VERB
cana-6096	207	13	,	,	PUNCT
cana-6096	207	14	and	and	CCONJ
cana-6096	207	15	to	to	PART
cana-6096	207	16	learn	learn	VERB
cana-6096	207	17	is	be	AUX
cana-6096	207	18	to	to	PART
cana-6096	207	19	change	change	VERB
cana-6096	207	20	.	.	PUNCT
cana-6096	208	1	this	this	DET
cana-6096	208	2	statement	statement	NOUN
cana-6096	208	3	is	be	AUX
cana-6096	208	4	put	put	VERB
cana-6096	208	5	into	into	ADP
cana-6096	208	6	perspective	perspective	NOUN
cana-6096	208	7	with	with	ADP
cana-6096	208	8	neuroscience	neuroscience	NOUN
cana-6096	208	9	and	and	CCONJ
cana-6096	208	10	more	more	ADV
cana-6096	208	11	specifically	specifically	ADV
cana-6096	208	12	the	the	DET
cana-6096	208	13	fact	fact	NOUN
cana-6096	208	14	that	that	SCONJ
cana-6096	208	15	following	follow	VERB
cana-6096	208	16	the	the	DET
cana-6096	208	17	vertical	vertical	ADJ
cana-6096	208	18	axis	axis	NOUN
cana-6096	208	19	,	,	PUNCT
cana-6096	208	20	the	the	DET
cana-6096	208	21	human	human	ADJ
cana-6096	208	22	brain	brain	NOUN
cana-6096	208	23	is	be	AUX
cana-6096	208	24	subdivided	subdivide	VERB
cana-6096	208	25	into	into	ADP
cana-6096	208	26	three	three	NUM
cana-6096	208	27	distinct	distinct	ADJ
cana-6096	208	28	but	but	CCONJ
cana-6096	208	29	complementary	complementary	ADJ
cana-6096	208	30	structures	structure	NOUN
cana-6096	208	31	:	:	PUNCT
cana-6096	208	32	the	the	DET
cana-6096	208	33	reptilian	reptilian	ADJ
cana-6096	208	34	brain	brain	NOUN
cana-6096	208	35	,	,	PUNCT
cana-6096	208	36	the	the	DET
cana-6096	208	37	limbic	limbic	ADJ
cana-6096	208	38	brain	brain	NOUN
cana-6096	208	39	and	and	CCONJ
cana-6096	208	40	the	the	DET
cana-6096	208	41	gray	gray	ADJ
cana-6096	208	42	matter	matter	NOUN
cana-6096	208	43	,	,	PUNCT
cana-6096	208	44	the	the	DET
cana-6096	208	45	cortex	cortex	NOUN
cana-6096	208	46	.	.	PUNCT
cana-6096	209	1	each	each	DET
cana-6096	209	2	structure	structure	NOUN
cana-6096	209	3	has	have	VERB
cana-6096	209	4	a	a	DET
cana-6096	209	5	different	different	ADJ
cana-6096	209	6	function	function	NOUN
cana-6096	209	7	.	.	PUNCT
cana-6096	210	1	“	"	PUNCT
cana-6096	210	2	these	these	DET
cana-6096	210	3	data	datum	NOUN
cana-6096	210	4	from	from	ADP
cana-6096	210	5	neuroscience	neuroscience	NOUN
cana-6096	210	6	now	now	ADV
cana-6096	210	7	allow	allow	VERB
cana-6096	210	8	us	we	PRON
cana-6096	210	9	to	to	PART
cana-6096	210	10	know	know	VERB
cana-6096	210	11	that	that	SCONJ
cana-6096	210	12	our	our	PRON
cana-6096	210	13	cognitive	cognitive	ADJ
cana-6096	210	14	activity	activity	NOUN
cana-6096	210	15	begins	begin	VERB
cana-6096	210	16	as	as	ADV
cana-6096	210	17	soon	soon	ADV
cana-6096	210	18	as	as	SCONJ
cana-6096	210	19	sensory	sensory	ADJ
cana-6096	210	20	stimuli	stimulus	NOUN
cana-6096	210	21	enter	enter	VERB
cana-6096	210	22	the	the	DET
cana-6096	210	23	reptilian	reptilian	ADJ
cana-6096	210	24	complex	complex	NOUN
cana-6096	210	25	,	,	PUNCT
cana-6096	210	26	which	which	PRON
cana-6096	210	27	processes	process	VERB
cana-6096	210	28	them	they	PRON
cana-6096	210	29	according	accord	VERB
cana-6096	210	30	to	to	ADP
cana-6096	210	31	a	a	DET
cana-6096	210	32	register	register	NOUN
cana-6096	210	33	of	of	ADP
cana-6096	210	34	security	security	NOUN
cana-6096	210	35	or	or	CCONJ
cana-6096	210	36	insecurity	insecurity	NOUN
cana-6096	210	37	,	,	PUNCT
cana-6096	210	38	that	that	ADV
cana-6096	210	39	is	is	ADV
cana-6096	210	40	,	,	PUNCT
cana-6096	210	41	by	by	ADP
cana-6096	210	42	assessing	assess	VERB
cana-6096	210	43	whether	whether	SCONJ
cana-6096	210	44	they	they	PRON
cana-6096	210	45	constitute	constitute	VERB
cana-6096	210	46	a	a	DET
cana-6096	210	47	threat	threat	NOUN
cana-6096	210	48	to	to	ADP
cana-6096	210	49	our	our	PRON
cana-6096	210	50	physical	physical	ADJ
cana-6096	210	51	or	or	CCONJ
cana-6096	210	52	psychological	psychological	ADJ
cana-6096	210	53	integrity	integrity	NOUN
cana-6096	210	54	.	.	PUNCT
cana-6096	211	1	the	the	DET
cana-6096	211	2	limbic	limbic	ADJ
cana-6096	211	3	system	system	NOUN
cana-6096	211	4	then	then	ADV
cana-6096	211	5	takes	take	VERB
cana-6096	211	6	over	over	ADP
cana-6096	211	7	and	and	CCONJ
cana-6096	211	8	apprehends	apprehend	VERB
cana-6096	211	9	the	the	DET
cana-6096	211	10	stimuli	stimulus	NOUN
cana-6096	211	11	that	that	PRON
cana-6096	211	12	reach	reach	VERB
cana-6096	211	13	it	it	PRON
cana-6096	211	14	from	from	ADP
cana-6096	211	15	a	a	DET
cana-6096	211	16	register	register	NOUN
cana-6096	211	17	of	of	ADP
cana-6096	211	18	pleasure	pleasure	NOUN
cana-6096	211	19	or	or	CCONJ
cana-6096	211	20	displeasure	displeasure	NOUN
cana-6096	211	21	,	,	PUNCT
cana-6096	211	22	searching	search	VERB
cana-6096	211	23	its	its	PRON
cana-6096	211	24	memory	memory	NOUN
cana-6096	211	25	to	to	PART
cana-6096	211	26	give	give	VERB
cana-6096	211	27	it	it	PRON
cana-6096	211	28	meaning	meaning	NOUN
cana-6096	211	29	.	.	PUNCT
cana-6096	212	1	the	the	DET
cana-6096	212	2	information	information	NOUN
cana-6096	212	3	finally	finally	ADV
cana-6096	212	4	reaches	reach	VERB
cana-6096	212	5	the	the	DET
cana-6096	212	6	cortex	cortex	NOUN
cana-6096	212	7	,	,	PUNCT
cana-6096	212	8	which	which	PRON
cana-6096	212	9	processes	process	VERB
cana-6096	212	10	it	it	PRON
cana-6096	212	11	based	base	VERB
cana-6096	212	12	on	on	ADP
cana-6096	212	13	a	a	DET
cana-6096	212	14	register	register	NOUN
cana-6096	212	15	of	of	ADP
cana-6096	212	16	adaptability	adaptability	NOUN
cana-6096	212	17	to	to	PART
cana-6096	212	18	understand	understand	VERB
cana-6096	212	19	its	its	PRON
cana-6096	212	20	meaning	meaning	NOUN
cana-6096	212	21	.	.	PUNCT
cana-6096	213	1	in	in	ADP
cana-6096	213	2	summary	summary	NOUN
cana-6096	213	3	,	,	PUNCT
cana-6096	213	4	to	to	PART
cana-6096	213	5	function	function	VERB
cana-6096	213	6	optimally	optimally	ADV
cana-6096	213	7	,	,	PUNCT
cana-6096	213	8	our	our	PRON
cana-6096	213	9	reptilian	reptilian	ADJ
cana-6096	213	10	brain	brain	NOUN
cana-6096	213	11	needs	need	VERB
cana-6096	213	12	to	to	PART
cana-6096	213	13	feel	feel	VERB
cana-6096	213	14	safe	safe	ADJ
cana-6096	213	15	,	,	PUNCT
cana-6096	213	16	and	and	CCONJ
cana-6096	213	17	our	our	PRON
cana-6096	213	18	limbic	limbic	ADJ
cana-6096	213	19	system	system	NOUN
cana-6096	213	20	must	must	AUX
cana-6096	213	21	experience	experience	VERB
cana-6096	213	22	or	or	CCONJ
cana-6096	213	23	anticipate	anticipate	VERB
cana-6096	213	24	a	a	DET
cana-6096	213	25	minimum	minimum	NOUN
cana-6096	213	26	of	of	ADP
cana-6096	213	27	pleasure	pleasure	NOUN
cana-6096	213	28	so	so	SCONJ
cana-6096	213	29	that	that	SCONJ
cana-6096	213	30	the	the	DET
cana-6096	213	31	cortex	cortex	NOUN
cana-6096	213	32	can	can	AUX
cana-6096	213	33	understand	understand	VERB
cana-6096	213	34	the	the	DET
cana-6096	213	35	information	information	NOUN
cana-6096	213	36	provided	provide	VERB
cana-6096	213	37	to	to	ADP
cana-6096	213	38	it	it	PRON
cana-6096	213	39	.	.	PUNCT
cana-6096	213	40	”	"	PUNCT
cana-6096	214	1	thus	thus	ADV
cana-6096	214	2	,	,	PUNCT
cana-6096	214	3	we	we	PRON
cana-6096	214	4	can	can	AUX
cana-6096	214	5	summarize	summarize	VERB
cana-6096	214	6	in	in	ADP
cana-6096	214	7	the	the	DET
cana-6096	214	8	following	follow	VERB
cana-6096	214	9	table	table	NOUN
cana-6096	214	10	the	the	DET
cana-6096	214	11	three	three	NUM
cana-6096	214	12	dimensions	dimension	NOUN
cana-6096	214	13	that	that	PRON
cana-6096	214	14	any	any	DET
cana-6096	214	15	change	change	NOUN
cana-6096	214	16	must	must	AUX
cana-6096	214	17	include	include	VERB
cana-6096	214	18	if	if	SCONJ
cana-6096	214	19	it	it	PRON
cana-6096	214	20	is	be	AUX
cana-6096	214	21	to	to	PART
cana-6096	214	22	be	be	AUX
cana-6096	214	23	efficient	efficient	ADJ
cana-6096	214	24	,	,	PUNCT
cana-6096	214	25	each	each	PRON
cana-6096	214	26	corresponding	correspond	VERB
cana-6096	214	27	to	to	ADP
cana-6096	214	28	a	a	DET
cana-6096	214	29	structure	structure	NOUN
cana-6096	214	30	cerebral	cerebral	NOUN
cana-6096	214	31	.	.	PUNCT
cana-6096	215	1	communications	communication	NOUN
cana-6096	215	2	on	on	ADP
cana-6096	215	3	applied	apply	VERB
cana-6096	215	4	nonlinear	nonlinear	ADJ
cana-6096	215	5	analysis	analysis	NOUN
cana-6096	215	6	issn	issn	NOUN
cana-6096	215	7	:	:	PUNCT
cana-6096	215	8	1074	1074	NUM
cana-6096	215	9	-	-	PUNCT
cana-6096	215	10	133x	133x	NUM
cana-6096	215	11	vol	vol	NOUN
cana-6096	215	12	32	32	NUM
cana-6096	215	13	no	no	NOUN
cana-6096	215	14	.	.	NOUN
cana-6096	215	15	3	3	NUM
cana-6096	215	16	(	(	PUNCT
cana-6096	215	17	2025	2025	NUM
cana-6096	215	18	)	)	PUNCT
cana-6096	215	19	1074	1074	NUM
cana-6096	215	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	215	21	schedule	schedule	NOUN
cana-6096	215	22	6:”the	6:”the	NUM
cana-6096	215	23	three	three	NUM
cana-6096	215	24	dimensions	dimension	NOUN
cana-6096	215	25	of	of	ADP
cana-6096	215	26	change	change	NOUN
cana-6096	215	27	-	-	PUNCT
cana-6096	215	28	learning	learning	NOUN
cana-6096	215	29	”	"	PUNCT
cana-6096	215	30	communications	communication	NOUN
cana-6096	215	31	on	on	ADP
cana-6096	215	32	applied	apply	VERB
cana-6096	215	33	nonlinear	nonlinear	ADJ
cana-6096	215	34	analysis	analysis	NOUN
cana-6096	215	35	issn	issn	NOUN
cana-6096	215	36	:	:	PUNCT
cana-6096	215	37	1074	1074	NUM
cana-6096	215	38	-	-	PUNCT
cana-6096	215	39	133x	133x	NUM
cana-6096	215	40	vol	vol	NOUN
cana-6096	215	41	32	32	NUM
cana-6096	215	42	no	no	NOUN
cana-6096	215	43	.	.	NOUN
cana-6096	215	44	3	3	NUM
cana-6096	215	45	(	(	PUNCT
cana-6096	215	46	2025	2025	NUM
cana-6096	215	47	)	)	PUNCT
cana-6096	215	48	1075	1075	NUM
cana-6096	215	49	https://internationalpubls.com	https://internationalpubls.com	X
cana-6096	215	50	bibliography	bibliography	NOUN
cana-6096	215	51	1astolfi	1astolfi	NUM
cana-6096	215	52	,	,	PUNCT
cana-6096	215	53	j.-p	j.-p	PROPN
cana-6096	215	54	.	.	PUNCT
cana-6096	216	1	(	(	PUNCT
cana-6096	216	2	1993	1993	NUM
cana-6096	216	3	)	)	PUNCT
cana-6096	216	4	.	.	PUNCT
cana-6096	217	1	placer	placer	NOUN
cana-6096	217	2	les	les	PROPN
cana-6096	217	3	élèves	élèves	X
cana-6096	217	4	en	en	ADP
cana-6096	217	5	situation	situation	NOUN
cana-6096	217	6	-	-	PUNCT
cana-6096	217	7	problème	problème	NOUN
cana-6096	217	8	?	?	PUNCT
cana-6096	217	9	probio	probio	NOUN
cana-6096	217	10	-	-	PUNCT
cana-6096	217	11	revue	revue	NOUN
cana-6096	217	12	,	,	PUNCT
cana-6096	217	13	16(4	16(4	NUM
cana-6096	217	14	)	)	PUNCT
cana-6096	217	15	,	,	PUNCT
cana-6096	217	16	311	311	NUM
cana-6096	217	17	-	-	SYM
cana-6096	217	18	321	321	NUM
cana-6096	217	19	.	.	PUNCT
cana-6096	218	1	2baruk	2baruk	NUM
cana-6096	218	2	,	,	PUNCT
cana-6096	218	3	s.	s.	PROPN
cana-6096	218	4	(	(	PUNCT
cana-6096	218	5	1973	1973	NUM
cana-6096	218	6	)	)	PUNCT
cana-6096	218	7	.	.	PUNCT
cana-6096	219	1	echecs	echecs	PROPN
cana-6096	219	2	et	et	PROPN
cana-6096	219	3	maths	maths	PROPN
cana-6096	219	4	.	.	PUNCT
cana-6096	220	1	paris	paris	PROPN
cana-6096	220	2	:	:	PUNCT
cana-6096	220	3	editions	edition	NOUN
cana-6096	220	4	du	du	PROPN
cana-6096	220	5	seuil	seuil	PROPN
cana-6096	220	6	(	(	PUNCT
cana-6096	220	7	coll	coll	PROPN
cana-6096	220	8	.	.	PUNCT
cana-6096	221	1	“	"	PUNCT
cana-6096	221	2	science	science	NOUN
cana-6096	221	3	ouverte	ouverte	NOUN
cana-6096	221	4	”	"	PUNCT
cana-6096	221	5	)	)	PUNCT
cana-6096	221	6	.	.	PUNCT
cana-6096	222	1	3baruk	3baruk	NUM
cana-6096	222	2	,	,	PUNCT
cana-6096	222	3	s.	s.	PROPN
cana-6096	222	4	(	(	PUNCT
cana-6096	222	5	1985	1985	NUM
cana-6096	222	6	)	)	PUNCT
cana-6096	222	7	.	.	PUNCT
cana-6096	223	1	l’âge	l’âge	PROPN
cana-6096	223	2	du	du	PROPN
cana-6096	223	3	capitaine	capitaine	PROPN
cana-6096	223	4	.	.	PUNCT
cana-6096	224	1	de	de	ADP
cana-6096	224	2	l’erreur	l’erreur	X
cana-6096	224	3	en	en	X
cana-6096	224	4	mathématiques	mathématique	NOUN
cana-6096	224	5	.	.	PUNCT
cana-6096	225	1	paris	paris	PROPN
cana-6096	225	2	:	:	PUNCT
cana-6096	225	3	editions	edition	NOUN
cana-6096	225	4	du	du	PROPN
cana-6096	225	5	seuil	seuil	PROPN
cana-6096	225	6	(	(	PUNCT
cana-6096	225	7	coll	coll	PROPN
cana-6096	225	8	.	.	PUNCT
cana-6096	226	1	“	"	PUNCT
cana-6096	226	2	science	science	NOUN
cana-6096	226	3	ouverte	ouverte	NOUN
cana-6096	226	4	”	"	PUNCT
cana-6096	226	5	)	)	PUNCT
cana-6096	226	6	.	.	PUNCT
cana-6096	227	1	4baruk	4baruk	NUM
cana-6096	227	2	,	,	PUNCT
cana-6096	227	3	s.	s.	PROPN
cana-6096	227	4	(	(	PUNCT
cana-6096	227	5	1993	1993	NUM
cana-6096	227	6	)	)	PUNCT
cana-6096	227	7	.	.	PUNCT
cana-6096	228	1	c’est	c’	ADJ
cana-6096	228	2	à	à	X
cana-6096	228	3	dire	dire	X
cana-6096	228	4	en	en	X
cana-6096	228	5	mathématiques	mathématiques	X
cana-6096	228	6	ou	ou	X
cana-6096	228	7	ailleurs	ailleurs	PROPN
cana-6096	228	8	.	.	PUNCT
cana-6096	229	1	paris	paris	PROPN
cana-6096	229	2	:	:	PUNCT
cana-6096	229	3	editions	edition	NOUN
cana-6096	229	4	du	du	PROPN
cana-6096	229	5	seuil	seuil	PROPN
cana-6096	229	6	(	(	PUNCT
cana-6096	229	7	coll	coll	PROPN
cana-6096	229	8	.	.	PUNCT
cana-6096	230	1	“	"	PUNCT
cana-6096	230	2	science	science	NOUN
cana-6096	230	3	ouverte	ouverte	NOUN
cana-6096	230	4	”	"	PUNCT
cana-6096	230	5	)	)	PUNCT
cana-6096	230	6	.	.	PUNCT
cana-6096	231	1	5	5	NUM
cana-6096	231	2	charnay	charnay	NOUN
cana-6096	231	3	,	,	PUNCT
cana-6096	231	4	r.	r.	PROPN
cana-6096	231	5	(	(	PUNCT
cana-6096	231	6	1996	1996	NUM
cana-6096	231	7	)	)	PUNCT
cana-6096	231	8	.	.	PUNCT
cana-6096	232	1	pourquoi	pourquoi	PROPN
cana-6096	232	2	des	des	X
cana-6096	232	3	mathématiques	mathématiques	X
cana-6096	232	4	à	à	X
cana-6096	232	5	l’école	l’école	PROPN
cana-6096	232	6	?	?	PUNCT
cana-6096	233	1	2	2	NUM
cana-6096	233	2	éd	éd	PROPN
cana-6096	233	3	paris	paris	PROPN
cana-6096	233	4	:	:	PUNCT
cana-6096	233	5	esf	esf	PROPN
cana-6096	233	6	(	(	PUNCT
cana-6096	233	7	coll	coll	PROPN
cana-6096	233	8	.	.	PUNCT
cana-6096	233	9	“	"	PUNCT
cana-6096	233	10	pratiques	pratiques	X
cana-6096	233	11	et	et	PROPN
cana-6096	233	12	enjeux	enjeux	PROPN
cana-6096	233	13	pédagogiques	pédagogiques	PROPN
cana-6096	233	14	”	"	PUNCT
cana-6096	233	15	)	)	PUNCT
cana-6096	233	16	.	.	PUNCT
cana-6096	234	1	6	6	NUM
cana-6096	234	2	celi	celi	PROPN
cana-6096	234	3	valentina	valentina	PROPN
cana-6096	234	4	(	(	PUNCT
cana-6096	234	5	2004	2004	NUM
cana-6096	234	6	)	)	PUNCT
cana-6096	234	7	,	,	PUNCT
cana-6096	234	8	des	des	PROPN
cana-6096	234	9	aires	aires	PROPN
cana-6096	234	10	sans	sans	PROPN
cana-6096	234	11	calcul	calcul	PROPN
cana-6096	234	12	,	,	PUNCT
cana-6096	234	13	petit	petit	NOUN
cana-6096	234	14	x	x	SYM
cana-6096	234	15	n065	n065	PROPN
cana-6096	234	16	,	,	PUNCT
cana-6096	234	17	p.	p.	NOUN
cana-6096	234	18	82	82	NUM
cana-6096	234	19	-	-	SYM
cana-6096	234	20	83	83	NUM
cana-6096	234	21	,	,	PUNCT
cana-6096	234	22	irem	irem	PROPN
cana-6096	234	23	de	de	PROPN
cana-6096	234	24	grenoble	grenoble	PROPN
cana-6096	234	25	,	,	PUNCT
cana-6096	234	26	issn	issn	PROPN
cana-6096	234	27	0759-9188.https://irem.univ-grenoble-alpes.fr/revues/petit-x/consultation/numero-65-petit-x/7	0759-9188.https://irem.univ-grenoble-alpes.fr/revues/petit-x/consultation/numero-65-petit-x/7	NUM
cana-6096	234	28	-activite	-activite	PROPN
cana-6096	234	29	-	-	PUNCT
cana-6096	234	30	des	des	PROPN
cana-6096	234	31	-	-	PUNCT
cana-6096	234	32	aires	aire	NOUN
cana-6096	234	33	-	-	PUNCT
cana-6096	234	34	sans	san	NOUN
cana-6096	234	35	-	-	PUNCT
cana-6096	234	36	calculs--514947.kjsp?rh=1550185125418	calculs--514947.kjsp?rh=1550185125418	NOUN
cana-6096	234	37	7chastellain	7chastellain	NUM
cana-6096	234	38	,	,	PUNCT
cana-6096	234	39	m.	m.	NOUN
cana-6096	234	40	,	,	PUNCT
cana-6096	234	41	jaquet	jaquet	PROPN
cana-6096	234	42	,	,	PUNCT
cana-6096	234	43	f.	f.	PROPN
cana-6096	234	44	et	et	PROPN
cana-6096	234	45	michlig	michlig	PROPN
cana-6096	234	46	,	,	PUNCT
cana-6096	234	47	y.	y.	PROPN
cana-6096	234	48	(	(	PUNCT
cana-6096	234	49	1985	1985	NUM
cana-6096	234	50	)	)	PUNCT
cana-6096	234	51	.	.	PUNCT
cana-6096	235	1	mathématique	mathématique	PROPN
cana-6096	235	2	,	,	PUNCT
cana-6096	235	3	sixième	sixième	PROPN
cana-6096	235	4	année	année	PROPN
cana-6096	235	5	,	,	PUNCT
cana-6096	235	6	méthodologie	méthodologie	NOUN
cana-6096	235	7	-	-	PUNCT
cana-6096	235	8	commentaires	commentaire	NOUN
cana-6096	235	9	.	.	PUNCT
cana-6096	236	1	office	office	NOUN
cana-6096	236	2	romand	romand	PROPN
cana-6096	236	3	des	des	PROPN
cana-6096	236	4	éditions	éditions	PROPN
cana-6096	236	5	et	et	PROPN
cana-6096	236	6	du	du	PROPN
cana-6096	236	7	matériel	matériel	PROPN
cana-6096	236	8	scolaires	scolaires	PROPN
cana-6096	236	9	.	.	PUNCT
cana-6096	237	1	extrait	extrait	ADJ
cana-6096	237	2	p.	p.	NOUN
cana-6096	237	3	30	30	NUM
cana-6096	237	4	.	.	PUNCT
cana-6096	238	1	8donnay	8donnay	PROPN
cana-6096	238	2	j.	j.	PROPN
cana-6096	238	3	&	&	CCONJ
cana-6096	238	4	cheffert	cheffert	PROPN
cana-6096	238	5	j	j	PROPN
cana-6096	238	6	-	-	PROPN
cana-6096	238	7	l.	l.	PROPN
cana-6096	238	8	(	(	PUNCT
cana-6096	238	9	1997	1997	NUM
cana-6096	238	10	)	)	PUNCT
cana-6096	238	11	.	.	PUNCT
cana-6096	239	1	l’apprentissage	l’apprentissage	NOUN
cana-6096	239	2	par	par	PROPN
cana-6096	239	3	problème	problème	X
cana-6096	239	4	(	(	PUNCT
cana-6096	239	5	a.p.p	a.p.p	ADJ
cana-6096	239	6	)	)	PUNCT
cana-6096	239	7	dans	dans	PROPN
cana-6096	239	8	la	la	PRON
cana-6096	239	9	formation	formation	PROPN
cana-6096	239	10	initiale	initiale	PROPN
cana-6096	239	11	d’enseignants	d’enseignant	NOUN
cana-6096	239	12	à	à	X
cana-6096	239	13	l’université	l’université	NOUN
cana-6096	239	14	.	.	PUNCT
cana-6096	239	15	namur	namur	PROPN
cana-6096	239	16	:	:	PUNCT
cana-6096	239	17	facultés	facultés	NOUN
cana-6096	239	18	universitaires	universitaire	NOUN
cana-6096	239	19	.	.	PUNCT
cana-6096	240	1	9emmanuel	9emmanuel	NUM
cana-6096	240	2	kant	kant	NOUN
cana-6096	240	3	,	,	PUNCT
cana-6096	240	4	(	(	PUNCT
cana-6096	240	5	trad	trad	NOUN
cana-6096	240	6	.	.	PUNCT
cana-6096	241	1	tremesaygues	tremesaygue	NOUN
cana-6096	241	2	et	et	PROPN
cana-6096	241	3	pacaud	pacaud	PROPN
cana-6096	241	4	,	,	PUNCT
cana-6096	241	5	préf	préf	PROPN
cana-6096	241	6	.	.	PUNCT
cana-6096	242	1	charles	charles	PROPN
cana-6096	242	2	serrus	serrus	PROPN
cana-6096	242	3	)	)	PUNCT
cana-6096	242	4	(	(	PUNCT
cana-6096	242	5	1975	1975	NUM
cana-6096	242	6	)	)	PUNCT
cana-6096	242	7	,	,	PUNCT
cana-6096	242	8	critique	critique	PROPN
cana-6096	242	9	de	de	X
cana-6096	242	10	la	la	X
cana-6096	242	11	raison	raison	NOUN
cana-6096	242	12	pure	pure	PROPN
cana-6096	242	13	,	,	PUNCT
cana-6096	242	14	puf	puf	PROPN
cana-6096	242	15	,	,	PUNCT
cana-6096	242	16	coll	coll	PROPN
cana-6096	242	17	.	.	PUNCT
cana-6096	242	18	«	«	PUNCT
cana-6096	243	1	bibliothèque	bibliothèque	PROPN
cana-6096	243	2	de	de	X
cana-6096	243	3	philosophie	philosophie	PROPN
cana-6096	243	4	contemporaine	contemporaine	NOUN
cana-6096	243	5	»	»	PUNCT
cana-6096	243	6	,	,	PUNCT
cana-6096	243	7	8e	8e	PROPN
cana-6096	243	8	éd	éd	PROPN
cana-6096	243	9	.	.	PROPN
cana-6096	243	10	,	,	PUNCT
cana-6096	243	11	584	584	NUM
cana-6096	243	12	p.	p.	NOUN
cana-6096	243	13	p76	p76	NOUN
cana-6096	243	14	.	.	PUNCT
cana-6096	244	1	10jonnaert	10jonnaert	NUM
cana-6096	244	2	,	,	PUNCT
cana-6096	244	3	p.	p.	NOUN
cana-6096	244	4	(	(	PUNCT
cana-6096	244	5	1994	1994	NUM
cana-6096	244	6	)	)	PUNCT
cana-6096	244	7	.	.	PUNCT
cana-6096	245	1	l’enfant	l’enfant	PROPN
cana-6096	245	2	-	-	NOUN
cana-6096	245	3	géomètre	géomètre	PROPN
cana-6096	245	4	.	.	PUNCT
cana-6096	246	1	une	une	PROPN
cana-6096	246	2	autre	autre	PROPN
cana-6096	246	3	approche	approche	PROPN
cana-6096	246	4	de	de	X
cana-6096	246	5	la	la	PROPN
cana-6096	246	6	didactique	didactique	PROPN
cana-6096	246	7	des	des	X
cana-6096	246	8	mathématiques	mathématiques	PROPN
cana-6096	246	9	à	à	X
cana-6096	246	10	l’école	l’école	ADJ
cana-6096	246	11	fondamentale	fondamentale	PROPN
cana-6096	246	12	.	.	PUNCT
cana-6096	247	1	bruxelles	bruxelle	NOUN
cana-6096	247	2	:	:	PUNCT
cana-6096	247	3	editions	edition	NOUN
cana-6096	247	4	plantyn	plantyn	NOUN
cana-6096	247	5	.	.	PUNCT
cana-6096	248	1	extrait	extrait	NOUN
cana-6096	248	2	,	,	PUNCT
cana-6096	248	3	p.	p.	NOUN
cana-6096	248	4	17	17	NUM
cana-6096	248	5	.	.	PUNCT
cana-6096	249	1	11lachaud	11lachaud	X
cana-6096	249	2	.	.	PUNCT
cana-6096	250	1	g.	g.	PROPN
cana-6096	250	2	1983	1983	NUM
cana-6096	250	3	,	,	PUNCT
cana-6096	250	4	what	what	PRON
cana-6096	250	5	we	we	PRON
cana-6096	250	6	can	can	AUX
cana-6096	250	7	get	get	VERB
cana-6096	250	8	from	from	ADP
cana-6096	250	9	history	history	NOUN
cana-6096	250	10	of	of	ADP
cana-6096	250	11	arthematic	arthematic	ADJ
cana-6096	250	12	,	,	PUNCT
cana-6096	250	13	fourth	fourth	PROPN
cana-6096	250	14	international	international	ADJ
cana-6096	250	15	congress	congress	PROPN
cana-6096	250	16	on	on	ADP
cana-6096	250	17	mathematical	mathematical	ADJ
cana-6096	250	18	education	education	NOUN
cana-6096	250	19	,	,	PUNCT
cana-6096	250	20	ed	ed	NOUN
cana-6096	250	21	.	.	PUNCT
cana-6096	251	1	zweng	zweng	PROPN
cana-6096	251	2	;	;	PUNCT
cana-6096	251	3	m.	m.	NOUN
cana-6096	251	4	and	and	CCONJ
cana-6096	251	5	others	other	NOUN
cana-6096	251	6	,	,	PUNCT
cana-6096	251	7	birkhäuser	birkhäuser	PROPN
cana-6096	251	8	boston	boston	PROPN
cana-6096	251	9	inc	inc	PROPN
cana-6096	251	10	.	.	PROPN
cana-6096	251	11	pp.449	pp.449	PROPN
cana-6096	251	12	-	-	PUNCT
cana-6096	251	13	459	459	NUM
cana-6096	251	14	.	.	PUNCT
cana-6096	251	15	12	12	NUM
cana-6096	251	16	le	le	X
cana-6096	251	17	boterf	boterf	NOUN
cana-6096	251	18	,	,	PUNCT
cana-6096	251	19	1994	1994	NUM
cana-6096	251	20	,	,	PUNCT
cana-6096	251	21	“	"	PUNCT
cana-6096	251	22	de	de	X
cana-6096	251	23	la	la	DET
cana-6096	251	24	compétence	compétence	PROPN
cana-6096	251	25	.	.	PUNCT
cana-6096	252	1	essai	essai	PROPN
cana-6096	252	2	sur	sur	PROPN
cana-6096	252	3	un	un	PROPN
cana-6096	252	4	attracteur	attracteur	PROPN
cana-6096	252	5	étrange	étrange	PROPN
cana-6096	252	6	”	"	PUNCT
cana-6096	252	7	.	.	PUNCT
cana-6096	253	1	paris	paris	PROPN
cana-6096	253	2	:	:	PUNCT
cana-6096	253	3	les	les	X
cana-6096	253	4	editions	edition	NOUN
cana-6096	253	5	d’organisation	d’organisation	PROPN
cana-6096	253	6	.	.	PUNCT
cana-6096	254	1	13	13	NUM
cana-6096	254	2	matthew	matthew	PROPN
cana-6096	254	3	lipman	lipman	PROPN
cana-6096	254	4	(	(	PUNCT
cana-6096	254	5	1995	1995	NUM
cana-6096	254	6	)	)	PUNCT
cana-6096	254	7	.	.	PUNCT
cana-6096	255	1	a	a	DET
cana-6096	255	2	l’école	l’école	PROPN
cana-6096	255	3	de	de	X
cana-6096	255	4	la	la	X
cana-6096	255	5	pensée	pensée	PROPN
cana-6096	255	6	(	(	PUNCT
cana-6096	255	7	traduit	traduit	PROPN
cana-6096	255	8	de	de	PROPN
cana-6096	255	9	l’anglais	l’anglais	PROPN
cana-6096	255	10	par	par	PROPN
cana-6096	255	11	n.	n.	PROPN
cana-6096	255	12	decostre	decostre	PROPN
cana-6096	255	13	)	)	PUNCT
cana-6096	255	14	.	.	PUNCT
cana-6096	256	1	bruxelles	bruxelle	NOUN
cana-6096	256	2	:	:	PUNCT
cana-6096	256	3	de	de	X
cana-6096	256	4	boeck	boeck	NOUN
cana-6096	256	5	.	.	PUNCT
cana-6096	257	1	14	14	NUM
cana-6096	257	2	maurice	maurice	NOUN
cana-6096	257	3	sachot	sachot	NOUN
cana-6096	257	4	(	(	PUNCT
cana-6096	257	5	1997	1997	NUM
cana-6096	257	6	)	)	PUNCT
cana-6096	257	7	.	.	PUNCT
cana-6096	258	1	“	"	PUNCT
cana-6096	258	2	disciplines	discipline	VERB
cana-6096	258	3	du	du	PROPN
cana-6096	258	4	maître	maître	PROPN
cana-6096	258	5	disciplines	discipline	NOUN
cana-6096	258	6	de	de	X
cana-6096	258	7	l’élève	l’élève	PROPN
cana-6096	258	8	:	:	PUNCT
cana-6096	258	9	contre	contre	X
cana-6096	258	10	une	une	INTJ
cana-6096	258	11	“	"	PUNCT
cana-6096	258	12	disciplinarisation	disciplinarisation	NOUN
cana-6096	258	13	”	"	PUNCT
cana-6096	258	14	du	du	NOUN
cana-6096	258	15	primaire	primaire	NOUN
cana-6096	258	16	”	"	PUNCT
cana-6096	258	17	,	,	PUNCT
cana-6096	258	18	les	les	X
cana-6096	258	19	cahiers	cahier	NOUN
cana-6096	258	20	du	du	VERB
cana-6096	258	21	cirid	cirid	VERB
cana-6096	258	22	,	,	PUNCT
cana-6096	258	23	n	n	CCONJ
cana-6096	258	24	°	°	PROPN
cana-6096	258	25	4	4	NUM
cana-6096	258	26	.	.	PUNCT
cana-6096	258	27	université	université	PROPN
cana-6096	258	28	de	de	X
cana-6096	258	29	strasbourg	strasbourg	PROPN
cana-6096	258	30	.	.	PUNCT
cana-6096	259	1	15	15	NUM
cana-6096	259	2	mercier	merci	ADJ
cana-6096	259	3	,	,	PUNCT
cana-6096	259	4	a.	a.	NOUN
cana-6096	259	5	(	(	PUNCT
cana-6096	259	6	1996	1996	NUM
cana-6096	259	7	)	)	PUNCT
cana-6096	259	8	.	.	PUNCT
cana-6096	260	1	“	"	PUNCT
cana-6096	260	2	la	la	X
cana-6096	260	3	création	création	NOUN
cana-6096	260	4	d’ignorance	d’ignorance	PROPN
cana-6096	260	5	,	,	PUNCT
cana-6096	260	6	condition	condition	NOUN
cana-6096	260	7	de	de	ADP
cana-6096	260	8	l’apprentissage	l’apprentissage	NOUN
cana-6096	260	9	”	"	PUNCT
cana-6096	260	10	,	,	PUNCT
cana-6096	260	11	revue	revue	PROPN
cana-6096	260	12	des	des	PROPN
cana-6096	260	13	sciences	sciences	PROPN
cana-6096	260	14	de	de	PROPN
cana-6096	260	15	l’éducation	l’éducation	PROPN
cana-6096	260	16	,	,	PUNCT
cana-6096	260	17	vol	vol	NOUN
cana-6096	260	18	.	.	PUNCT
cana-6096	261	1	xxii	xxii	PROPN
cana-6096	261	2	,	,	PUNCT
cana-6096	261	3	n	n	CCONJ
cana-6096	261	4	°	°	NUM
cana-6096	261	5	2	2	NUM
cana-6096	261	6	,	,	PUNCT
cana-6096	261	7	pp	pp	ADJ
cana-6096	261	8	.	.	PUNCT
cana-6096	262	1	345	345	NUM
cana-6096	262	2	-	-	SYM
cana-6096	262	3	363	363	NUM
cana-6096	262	4	.	.	PUNCT
cana-6096	263	1	16pochet	16pochet	NUM
cana-6096	263	2	,	,	PUNCT
cana-6096	263	3	b.	b.	PROPN
cana-6096	263	4	(	(	PUNCT
cana-6096	263	5	1995	1995	NUM
cana-6096	263	6	)	)	PUNCT
cana-6096	263	7	.	.	PUNCT
cana-6096	264	1	“	"	PUNCT
cana-6096	264	2	le	le	X
cana-6096	264	3	“	"	PUNCT
cana-6096	264	4	problem	problem	NOUN
cana-6096	264	5	-	-	PUNCT
cana-6096	264	6	based	base	VERB
cana-6096	264	7	learning	learning	NOUN
cana-6096	264	8	”	"	PUNCT
cana-6096	264	9	,	,	PUNCT
cana-6096	264	10	une	une	PROPN
cana-6096	264	11	révolution	révolution	PROPN
cana-6096	264	12	ou	ou	X
cana-6096	264	13	un	un	PROPN
cana-6096	264	14	progrès	progrès	PROPN
cana-6096	264	15	attendu	attendu	NOUN
cana-6096	264	16	”	"	PUNCT
cana-6096	264	17	in	in	ADP
cana-6096	264	18	revue	revue	PROPN
cana-6096	264	19	française	française	PROPN
cana-6096	264	20	de	de	X
cana-6096	264	21	pédagogie	pédagogie	PROPN
cana-6096	264	22	,	,	PUNCT
cana-6096	264	23	n	n	CCONJ
cana-6096	264	24	°	°	NOUN
cana-6096	264	25	111	111	NUM
cana-6096	264	26	,	,	PUNCT
cana-6096	264	27	p.	p.	NOUN
cana-6096	264	28	95	95	NUM
cana-6096	264	29	-	-	SYM
cana-6096	264	30	107	107	NUM
cana-6096	264	31	.	.	PUNCT
cana-6096	265	1	17treffers	17treffer	NOUN
cana-6096	265	2	,	,	PUNCT
cana-6096	265	3	a.	a.	NOUN
cana-6096	265	4	(	(	PUNCT
cana-6096	265	5	1986	1986	NUM
cana-6096	265	6	)	)	PUNCT
cana-6096	265	7	.	.	PUNCT
cana-6096	266	1	three	three	NUM
cana-6096	266	2	dimensions	dimension	NOUN
cana-6096	266	3	:	:	PUNCT
cana-6096	266	4	a	a	DET
cana-6096	266	5	model	model	NOUN
cana-6096	266	6	of	of	ADP
cana-6096	266	7	theory	theory	NOUN
cana-6096	266	8	and	and	CCONJ
cana-6096	266	9	goal	goal	NOUN
cana-6096	266	10	description	description	NOUN
cana-6096	266	11	in	in	ADP
cana-6096	266	12	mathematics	mathematics	NOUN
cana-6096	266	13	instruction	instruction	NOUN
cana-6096	266	14	,	,	PUNCT
cana-6096	266	15	the	the	DET
cana-6096	266	16	wiskobas	wiskobas	PROPN
cana-6096	266	17	project	project	NOUN
cana-6096	266	18	.	.	PUNCT
cana-6096	267	1	dordrecht	dordrecht	PROPN
cana-6096	267	2	:	:	PUNCT
cana-6096	267	3	reidel	reidel	PROPN
cana-6096	267	4	.	.	PUNCT
cana-6096	267	5	18tardif	18tardif	NUM
cana-6096	268	1	j.	j.	PROPN
cana-6096	268	2	(	(	PUNCT
cana-6096	268	3	1996	1996	NUM
cana-6096	268	4	)	)	PUNCT
cana-6096	268	5	.	.	PUNCT
cana-6096	269	1	“	"	PUNCT
cana-6096	269	2	le	le	X
cana-6096	269	3	transfert	transfert	PROPN
cana-6096	269	4	de	de	X
cana-6096	269	5	compétences	compétences	PROPN
cana-6096	269	6	analysé	analysé	PROPN
cana-6096	269	7	à	à	X
cana-6096	269	8	travers	traver	NOUN
cana-6096	269	9	la	la	PRON
cana-6096	269	10	formation	formation	NOUN
cana-6096	269	11	de	de	X
cana-6096	269	12	professionnel	professionnel	X
cana-6096	269	13	s	s	PART
cana-6096	269	14	”	"	PUNCT
cana-6096	269	15	,	,	PUNCT
cana-6096	269	16	in	in	ADP
cana-6096	269	17	meirieu	meirieu	PROPN
cana-6096	269	18	p.	p.	PROPN
cana-6096	269	19	,	,	PUNCT
cana-6096	269	20	develay	develay	ADJ
cana-6096	269	21	m.	m.	NOUN
cana-6096	269	22	,	,	PUNCT
cana-6096	269	23	durand	durand	PROPN
cana-6096	269	24	c.	c.	PROPN
cana-6096	269	25	et	et	PROPN
cana-6096	269	26	mariani	mariani	PROPN
cana-6096	269	27	y.	y.	PROPN
cana-6096	269	28	(	(	PUNCT
cana-6096	269	29	dir	dir	PROPN
cana-6096	269	30	)	)	PUNCT
cana-6096	269	31	,	,	PUNCT
cana-6096	269	32	le	le	X
cana-6096	269	33	concept	concept	PROPN
cana-6096	269	34	de	de	PROPN
cana-6096	269	35	transfert	transfert	X
cana-6096	269	36	de	de	X
cana-6096	269	37	connaissance	connaissance	PROPN
cana-6096	269	38	en	en	PROPN
cana-6096	269	39	formation	formation	NOUN
cana-6096	269	40	initiale	initiale	NOUN
cana-6096	269	41	et	et	PROPN
cana-6096	269	42	continue	continue	VERB
cana-6096	269	43	,	,	PUNCT
cana-6096	269	44	lyon	lyon	PROPN
cana-6096	269	45	,	,	PUNCT
cana-6096	269	46	crdp	crdp	PROPN
cana-6096	269	47	,	,	PUNCT
cana-6096	269	48	pp31	pp31	PROPN
cana-6096	269	49	-	-	PUNCT
cana-6096	269	50	46	46	NUM
cana-6096	269	51	.	.	PUNCT
cana-6096	270	1	19vergnaud	19vergnaud	NUM
cana-6096	270	2	g.	g.	PROPN
cana-6096	270	3	(	(	PUNCT
cana-6096	270	4	1991	1991	NUM
cana-6096	270	5	)	)	PUNCT
cana-6096	270	6	.	.	PUNCT
cana-6096	271	1	la	la	PROPN
cana-6096	271	2	théorie	théorie	PROPN
cana-6096	271	3	des	des	PROPN
cana-6096	271	4	champs	champs	PROPN
cana-6096	271	5	conceptuels	conceptuel	NOUN
cana-6096	271	6	.	.	PUNCT
cana-6096	272	1	in	in	ADP
cana-6096	272	2	recherches	recherche	NOUN
cana-6096	272	3	en	en	ADP
cana-6096	272	4	didactiques	didactique	NOUN
cana-6096	272	5	des	des	PROPN
cana-6096	272	6	mathématiques	mathématiques	PROPN
cana-6096	272	7	,	,	PUNCT
cana-6096	272	8	vol	vol	NOUN
cana-6096	272	9	10	10	NUM
cana-6096	272	10	2/3	2/3	NUM
cana-6096	272	11	,	,	PUNCT
cana-6096	272	12	pp	pp	ADJ
cana-6096	272	13	.	.	PUNCT
cana-6096	273	1	133	133	NUM
cana-6096	273	2	-	-	SYM
cana-6096	273	3	170	170	NUM
cana-6096	273	4	.	.	PUNCT