id	sid	tid	token	lemma	pos
easat-2635	1	1	edelweiss	edelweiss	PROPN
easat-2635	1	2	applied	apply	VERB
easat-2635	1	3	science	science	NOUN
easat-2635	1	4	and	and	CCONJ
easat-2635	1	5	technology	technology	NOUN
easat-2635	1	6	issn	issn	PROPN
easat-2635	1	7	:	:	PUNCT
easat-2635	1	8	2576	2576	NUM
easat-2635	1	9	-	-	SYM
easat-2635	1	10	8484	8484	NUM
easat-2635	1	11	vol	vol	NOUN
easat-2635	1	12	.	.	PROPN
easat-2635	1	13	8	8	NUM
easat-2635	1	14	,	,	PUNCT
easat-2635	1	15	no	no	INTJ
easat-2635	1	16	.	.	NOUN
easat-2635	1	17	6	6	NUM
easat-2635	1	18	,	,	PUNCT
easat-2635	1	19	2931	2931	NUM
easat-2635	1	20	-	-	SYM
easat-2635	1	21	2936	2936	NUM
easat-2635	1	22	2024	2024	NUM
easat-2635	1	23	publisher	publisher	NOUN
easat-2635	1	24	:	:	PUNCT
easat-2635	1	25	learning	learn	VERB
easat-2635	1	26	gate	gate	NOUN
easat-2635	1	27	doi	doi	PROPN
easat-2635	1	28	:	:	PUNCT
easat-2635	1	29	10.55214/25768484.v8i6.2635	10.55214/25768484.v8i6.2635	NUM
easat-2635	1	30	©	©	PROPN
easat-2635	1	31	2024	2024	NUM
easat-2635	1	32	by	by	ADP
easat-2635	1	33	the	the	DET
easat-2635	1	34	authors	author	NOUN
easat-2635	1	35	;	;	PUNCT
easat-2635	1	36	licensee	licensee	PROPN
easat-2635	1	37	learning	learning	NOUN
easat-2635	1	38	gate	gate	NOUN
easat-2635	1	39	©	©	PROPN
easat-2635	1	40	2024	2024	NUM
easat-2635	1	41	by	by	ADP
easat-2635	1	42	the	the	DET
easat-2635	1	43	authors	author	NOUN
easat-2635	1	44	;	;	PUNCT
easat-2635	1	45	licensee	licensee	PROPN
easat-2635	1	46	learning	learn	VERB
easat-2635	1	47	gate	gate	NOUN
easat-2635	1	48	*	*	PUNCT
easat-2635	1	49	correspondence	correspondence	NOUN
easat-2635	1	50	:	:	PUNCT
easat-2635	1	51	bonanis@vutcloud.onmicrosoft.com	bonanis@vutcloud.onmicrosoft.com	NUM
easat-2635	1	52	investigating	investigate	VERB
easat-2635	1	53	different	different	ADJ
easat-2635	1	54	answers	answer	NOUN
easat-2635	1	55	to	to	ADP
easat-2635	1	56	one	one	NUM
easat-2635	1	57	euclidean	euclidean	ADJ
easat-2635	1	58	geometry	geometry	NOUN
easat-2635	1	59	problem	problem	NOUN
easat-2635	1	60	:	:	PUNCT
easat-2635	1	61	a	a	DET
easat-2635	1	62	case	case	NOUN
easat-2635	1	63	study	study	NOUN
easat-2635	1	64	of	of	ADP
easat-2635	1	65	grade	grade	NOUN
easat-2635	1	66	12	12	NUM
easat-2635	1	67	mathematics	mathematic	NOUN
easat-2635	1	68	examinations	examination	NOUN
easat-2635	1	69	in	in	ADP
easat-2635	1	70	south	south	ADJ
easat-2635	1	71	african	african	ADJ
easat-2635	1	72	secondary	secondary	ADJ
easat-2635	1	73	schools	school	NOUN
easat-2635	1	74	bonani	bonani	PROPN
easat-2635	1	75	sibanda1	sibanda1	PROPN
easat-2635	1	76	*	*	PUNCT
easat-2635	1	77	,	,	PUNCT
easat-2635	1	78	ramoshweu	ramoshweu	PROPN
easat-2635	1	79	s.	s.	PROPN
easat-2635	1	80	lebelo2	lebelo2	PROPN
easat-2635	1	81	,	,	PUNCT
easat-2635	1	82	radley	radley	PROPN
easat-2635	1	83	k.	k.	PROPN
easat-2635	1	84	mahlobo3	mahlobo3	PROPN
easat-2635	2	1	1,2,3department	1,2,3department	NUM
easat-2635	2	2	of	of	ADP
easat-2635	2	3	applied	apply	VERB
easat-2635	2	4	physical	physical	ADJ
easat-2635	2	5	sciences	science	NOUN
easat-2635	2	6	,	,	PUNCT
easat-2635	2	7	vaal	vaal	NOUN
easat-2635	2	8	university	university	NOUN
easat-2635	2	9	of	of	ADP
easat-2635	2	10	technology	technology	NOUN
easat-2635	2	11	,	,	PUNCT
easat-2635	2	12	p	p	NOUN
easat-2635	2	13	/	/	SYM
easat-2635	2	14	bag	bag	NOUN
easat-2635	2	15	x021	x021	PROPN
easat-2635	2	16	,	,	PUNCT
easat-2635	2	17	vanderbijlpark	vanderbijlpark	ADJ
easat-2635	2	18	,	,	PUNCT
easat-2635	2	19	south	south	PROPN
easat-2635	2	20	africa	africa	PROPN
easat-2635	2	21	;	;	PUNCT
easat-2635	2	22	bonanis@vutcloud.onmicrosoft.com	bonanis@vutcloud.onmicrosoft.com	PROPN
easat-2635	2	23	(	(	PUNCT
easat-2635	2	24	b.s	b.s	PROPN
easat-2635	2	25	.	.	PROPN
easat-2635	2	26	)	)	PUNCT
easat-2635	3	1	lebelors@gmail.com	lebelors@gmail.com	PROPN
easat-2635	3	2	(	(	PUNCT
easat-2635	3	3	r.s.l	r.s.l	NOUN
easat-2635	3	4	.	.	PUNCT
easat-2635	3	5	)	)	PUNCT
easat-2635	4	1	mahloboradley@gmail.com	mahloboradley@gmail.com	X
easat-2635	4	2	(	(	PUNCT
easat-2635	4	3	r.k.m	r.k.m	PROPN
easat-2635	4	4	.	.	PUNCT
easat-2635	4	5	)	)	PUNCT
easat-2635	5	1	abstract	abstract	NOUN
easat-2635	5	2	:	:	PUNCT
easat-2635	5	3	this	this	DET
easat-2635	5	4	article	article	NOUN
easat-2635	5	5	investigates	investigate	VERB
easat-2635	5	6	the	the	DET
easat-2635	5	7	tendency	tendency	NOUN
easat-2635	5	8	for	for	ADP
easat-2635	5	9	distinctly	distinctly	ADV
easat-2635	5	10	different	different	ADJ
easat-2635	5	11	answers	answer	NOUN
easat-2635	5	12	to	to	ADP
easat-2635	5	13	a	a	DET
easat-2635	5	14	problem	problem	NOUN
easat-2635	5	15	in	in	ADP
easat-2635	5	16	euclidean	euclidean	ADJ
easat-2635	5	17	geometry	geometry	NOUN
easat-2635	5	18	as	as	SCONJ
easat-2635	5	19	shown	show	VERB
easat-2635	5	20	in	in	ADP
easat-2635	5	21	some	some	DET
easat-2635	5	22	grade	grade	NOUN
easat-2635	5	23	12	12	NUM
easat-2635	5	24	examination	examination	NOUN
easat-2635	5	25	memos	memo	NOUN
easat-2635	5	26	for	for	ADP
easat-2635	5	27	secondary	secondary	ADJ
easat-2635	5	28	schools	school	NOUN
easat-2635	5	29	in	in	ADP
easat-2635	5	30	south	south	PROPN
easat-2635	5	31	africa	africa	PROPN
easat-2635	5	32	.	.	PUNCT
easat-2635	6	1	the	the	DET
easat-2635	6	2	study	study	NOUN
easat-2635	6	3	is	be	AUX
easat-2635	6	4	based	base	VERB
easat-2635	6	5	on	on	ADP
easat-2635	6	6	a	a	DET
easat-2635	6	7	qualitative	qualitative	ADJ
easat-2635	6	8	analysis	analysis	NOUN
easat-2635	6	9	of	of	ADP
easat-2635	6	10	some	some	DET
easat-2635	6	11	examples	example	NOUN
easat-2635	6	12	in	in	ADP
easat-2635	6	13	the	the	DET
easat-2635	6	14	final	final	ADJ
easat-2635	6	15	grade	grade	NOUN
easat-2635	6	16	12	12	NUM
easat-2635	6	17	examinations	examination	NOUN
easat-2635	6	18	where	where	SCONJ
easat-2635	6	19	solutions	solution	NOUN
easat-2635	6	20	to	to	ADP
easat-2635	6	21	specific	specific	ADJ
easat-2635	6	22	problems	problem	NOUN
easat-2635	6	23	are	be	AUX
easat-2635	6	24	given	give	VERB
easat-2635	6	25	in	in	ADP
easat-2635	6	26	distinctly	distinctly	ADV
easat-2635	6	27	different	different	ADJ
easat-2635	6	28	forms	form	NOUN
easat-2635	6	29	.	.	PUNCT
easat-2635	7	1	both	both	DET
easat-2635	7	2	primary	primary	ADJ
easat-2635	7	3	and	and	CCONJ
easat-2635	7	4	secondary	secondary	ADJ
easat-2635	7	5	data	datum	NOUN
easat-2635	7	6	were	be	AUX
easat-2635	7	7	applied	apply	VERB
easat-2635	7	8	to	to	ADP
easat-2635	7	9	the	the	DET
easat-2635	7	10	investigation	investigation	NOUN
easat-2635	7	11	.	.	PUNCT
easat-2635	8	1	the	the	DET
easat-2635	8	2	secondary	secondary	ADJ
easat-2635	8	3	data	datum	NOUN
easat-2635	8	4	was	be	AUX
easat-2635	8	5	the	the	DET
easat-2635	8	6	literature	literature	PROPN
easat-2635	8	7	review	review	NOUN
easat-2635	8	8	of	of	ADP
easat-2635	8	9	studies	study	NOUN
easat-2635	8	10	on	on	ADP
easat-2635	8	11	the	the	DET
easat-2635	8	12	problems	problem	NOUN
easat-2635	8	13	students	student	NOUN
easat-2635	8	14	come	come	VERB
easat-2635	8	15	across	across	ADP
easat-2635	8	16	when	when	SCONJ
easat-2635	8	17	solving	solve	VERB
easat-2635	8	18	euclidean	euclidean	ADJ
easat-2635	8	19	geometry	geometry	NOUN
easat-2635	8	20	problems	problem	NOUN
easat-2635	8	21	,	,	PUNCT
easat-2635	8	22	and	and	CCONJ
easat-2635	8	23	the	the	DET
easat-2635	8	24	primary	primary	ADJ
easat-2635	8	25	data	datum	NOUN
easat-2635	8	26	was	be	AUX
easat-2635	8	27	acquired	acquire	VERB
easat-2635	8	28	from	from	ADP
easat-2635	8	29	the	the	DET
easat-2635	8	30	example	example	NOUN
easat-2635	8	31	of	of	ADP
easat-2635	8	32	a	a	DET
easat-2635	8	33	memorandum	memorandum	NOUN
easat-2635	8	34	where	where	SCONJ
easat-2635	8	35	distinctly	distinctly	ADV
easat-2635	8	36	different	different	ADJ
easat-2635	8	37	answers	answer	NOUN
easat-2635	8	38	were	be	AUX
easat-2635	8	39	given	give	VERB
easat-2635	8	40	to	to	ADP
easat-2635	8	41	the	the	DET
easat-2635	8	42	solution	solution	NOUN
easat-2635	8	43	of	of	ADP
easat-2635	8	44	a	a	DET
easat-2635	8	45	problem	problem	NOUN
easat-2635	8	46	.	.	PUNCT
easat-2635	9	1	the	the	DET
easat-2635	9	2	approach	approach	NOUN
easat-2635	9	3	to	to	ADP
easat-2635	9	4	the	the	DET
easat-2635	9	5	problem	problem	NOUN
easat-2635	9	6	-	-	PUNCT
easat-2635	9	7	solution	solution	NOUN
easat-2635	9	8	presentation	presentation	NOUN
easat-2635	9	9	using	use	VERB
easat-2635	9	10	distinctly	distinctly	ADV
easat-2635	9	11	different	different	ADJ
easat-2635	9	12	answers	answer	NOUN
easat-2635	9	13	is	be	AUX
easat-2635	9	14	appreciated	appreciate	VERB
easat-2635	9	15	as	as	SCONJ
easat-2635	9	16	it	it	PRON
easat-2635	9	17	broadens	broaden	VERB
easat-2635	9	18	the	the	DET
easat-2635	9	19	understanding	understanding	NOUN
easat-2635	9	20	of	of	ADP
easat-2635	9	21	problem	problem	NOUN
easat-2635	9	22	-	-	PUNCT
easat-2635	9	23	solving	solving	NOUN
easat-2635	9	24	.	.	PUNCT
easat-2635	10	1	however	however	ADV
easat-2635	10	2	,	,	PUNCT
easat-2635	10	3	does	do	AUX
easat-2635	10	4	this	this	DET
easat-2635	10	5	approach	approach	NOUN
easat-2635	10	6	not	not	PART
easat-2635	10	7	leave	leave	VERB
easat-2635	10	8	the	the	DET
easat-2635	10	9	markers	marker	NOUN
easat-2635	10	10	ignorant	ignorant	ADJ
easat-2635	10	11	of	of	ADP
easat-2635	10	12	other	other	ADJ
easat-2635	10	13	solution	solution	NOUN
easat-2635	10	14	options	option	NOUN
easat-2635	10	15	,	,	PUNCT
easat-2635	10	16	thus	thus	ADV
easat-2635	10	17	disadvantaging	disadvantage	VERB
easat-2635	10	18	the	the	DET
easat-2635	10	19	learners	learner	NOUN
easat-2635	10	20	and	and	CCONJ
easat-2635	10	21	denying	deny	VERB
easat-2635	10	22	them	they	PRON
easat-2635	10	23	a	a	DET
easat-2635	10	24	pass	pass	NOUN
easat-2635	10	25	?	?	PUNCT
easat-2635	10	26	.	.	PUNCT
easat-2635	11	1	keywords	keyword	NOUN
easat-2635	11	2	:	:	PUNCT
easat-2635	11	3	distinct	distinct	VERB
easat-2635	11	4	different	different	ADJ
easat-2635	11	5	answers	answer	NOUN
easat-2635	11	6	,	,	PUNCT
easat-2635	11	7	euclidean	euclidean	ADJ
easat-2635	11	8	geometry	geometry	NOUN
easat-2635	11	9	,	,	PUNCT
easat-2635	11	10	grade	grade	NOUN
easat-2635	11	11	12	12	NUM
easat-2635	11	12	examination	examination	NOUN
easat-2635	11	13	,	,	PUNCT
easat-2635	11	14	problem	problem	NOUN
easat-2635	11	15	-	-	PUNCT
easat-2635	11	16	solving	solving	NOUN
easat-2635	11	17	.	.	PUNCT
easat-2635	12	1	1	1	X
easat-2635	12	2	.	.	X
easat-2635	12	3	introduction	introduction	NOUN
easat-2635	12	4	euclidean	euclidean	NOUN
easat-2635	12	5	geometry	geometry	NOUN
easat-2635	12	6	is	be	AUX
easat-2635	12	7	a	a	DET
easat-2635	12	8	challenging	challenging	ADJ
easat-2635	12	9	subject	subject	NOUN
easat-2635	12	10	in	in	ADP
easat-2635	12	11	high	high	ADJ
easat-2635	12	12	schools	school	NOUN
easat-2635	12	13	for	for	ADP
easat-2635	12	14	both	both	DET
easat-2635	12	15	teachers	teacher	NOUN
easat-2635	12	16	and	and	CCONJ
easat-2635	12	17	students	student	NOUN
easat-2635	12	18	.	.	PUNCT
easat-2635	13	1	some	some	DET
easat-2635	13	2	people	people	NOUN
easat-2635	13	3	even	even	ADV
easat-2635	13	4	wonder	wonder	VERB
easat-2635	13	5	why	why	SCONJ
easat-2635	13	6	euclidean	euclidean	ADJ
easat-2635	13	7	geometry	geometry	NOUN
easat-2635	13	8	should	should	AUX
easat-2635	13	9	be	be	AUX
easat-2635	13	10	taught	teach	VERB
easat-2635	13	11	in	in	ADP
easat-2635	13	12	high	high	ADJ
easat-2635	13	13	schools	school	NOUN
easat-2635	13	14	instead	instead	ADV
easat-2635	13	15	of	of	ADP
easat-2635	13	16	leaving	leave	VERB
easat-2635	13	17	it	it	PRON
easat-2635	13	18	for	for	ADP
easat-2635	13	19	a	a	DET
easat-2635	13	20	few	few	ADJ
easat-2635	13	21	university	university	NOUN
easat-2635	13	22	majors	major	NOUN
easat-2635	13	23	.	.	PUNCT
easat-2635	14	1	wu	wu	PROPN
easat-2635	15	1	[	[	X
easat-2635	15	2	1	1	X
easat-2635	15	3	]	]	PUNCT
easat-2635	15	4	argues	argue	VERB
easat-2635	15	5	that	that	SCONJ
easat-2635	15	6	it	it	PRON
easat-2635	15	7	is	be	AUX
easat-2635	15	8	unjustifiable	unjustifiable	ADJ
easat-2635	15	9	to	to	PART
easat-2635	15	10	suddenly	suddenly	ADV
easat-2635	15	11	assert	assert	VERB
easat-2635	15	12	that	that	SCONJ
easat-2635	15	13	logical	logical	ADJ
easat-2635	15	14	reasoning	reasoning	NOUN
easat-2635	15	15	in	in	ADP
easat-2635	15	16	mathematics	mathematics	PROPN
easat-2635	15	17	is	be	AUX
easat-2635	15	18	too	too	ADV
easat-2635	15	19	academically	academically	ADV
easat-2635	15	20	challenging	challenging	ADJ
easat-2635	15	21	for	for	ADP
easat-2635	15	22	all	all	DET
easat-2635	15	23	high	high	ADJ
easat-2635	15	24	school	school	NOUN
easat-2635	15	25	students	student	NOUN
easat-2635	15	26	and	and	CCONJ
easat-2635	15	27	must	must	AUX
easat-2635	15	28	be	be	AUX
easat-2635	15	29	the	the	DET
easat-2635	15	30	prerogative	prerogative	NOUN
easat-2635	15	31	of	of	ADP
easat-2635	15	32	a	a	DET
easat-2635	15	33	few	few	ADJ
easat-2635	15	34	college	college	NOUN
easat-2635	15	35	students	student	NOUN
easat-2635	15	36	majoring	major	VERB
easat-2635	15	37	in	in	ADP
easat-2635	15	38	mathematics	mathematics	PROPN
easat-2635	15	39	because	because	SCONJ
easat-2635	15	40	,	,	PUNCT
easat-2635	15	41	broadly	broadly	ADV
easat-2635	15	42	speaking	speak	VERB
easat-2635	15	43	,	,	PUNCT
easat-2635	15	44	mathematics	mathematic	NOUN
easat-2635	15	45	courses	course	NOUN
easat-2635	15	46	are	be	AUX
easat-2635	15	47	particularly	particularly	ADV
easat-2635	15	48	effective	effective	ADJ
easat-2635	15	49	at	at	ADP
easat-2635	15	50	training	train	VERB
easat-2635	15	51	students	student	NOUN
easat-2635	15	52	in	in	ADP
easat-2635	15	53	logical	logical	ADJ
easat-2635	15	54	reasoning	reasoning	NOUN
easat-2635	15	55	.	.	PUNCT
easat-2635	16	1	they	they	PRON
easat-2635	16	2	learn	learn	VERB
easat-2635	16	3	to	to	PART
easat-2635	16	4	work	work	VERB
easat-2635	16	5	their	their	PRON
easat-2635	16	6	way	way	NOUN
easat-2635	16	7	through	through	ADP
easat-2635	16	8	misleading	mislead	VERB
easat-2635	16	9	tricks	trick	NOUN
easat-2635	16	10	until	until	SCONJ
easat-2635	16	11	they	they	PRON
easat-2635	16	12	get	get	VERB
easat-2635	16	13	to	to	ADP
easat-2635	16	14	the	the	DET
easat-2635	16	15	core	core	NOUN
easat-2635	16	16	of	of	ADP
easat-2635	16	17	the	the	DET
easat-2635	16	18	problem	problem	NOUN
easat-2635	16	19	.	.	PUNCT
easat-2635	17	1	they	they	PRON
easat-2635	17	2	also	also	ADV
easat-2635	17	3	learn	learn	VERB
easat-2635	17	4	how	how	SCONJ
easat-2635	17	5	to	to	PART
easat-2635	17	6	differentiate	differentiate	VERB
easat-2635	17	7	between	between	ADP
easat-2635	17	8	the	the	DET
easat-2635	17	9	truth	truth	NOUN
easat-2635	17	10	and	and	CCONJ
easat-2635	17	11	false	false	ADJ
easat-2635	17	12	information	information	NOUN
easat-2635	17	13	that	that	PRON
easat-2635	17	14	seems	seem	VERB
easat-2635	17	15	to	to	PART
easat-2635	17	16	be	be	AUX
easat-2635	17	17	true	true	ADJ
easat-2635	17	18	.	.	PUNCT
easat-2635	18	1	many	many	ADJ
easat-2635	18	2	authors	author	NOUN
easat-2635	18	3	agree	agree	VERB
easat-2635	18	4	with	with	ADP
easat-2635	18	5	wu	wu	PROPN
easat-2635	19	1	[	[	X
easat-2635	19	2	1	1	NUM
easat-2635	19	3	]	]	PUNCT
easat-2635	19	4	,	,	PUNCT
easat-2635	19	5	including	include	VERB
easat-2635	19	6	jones	jones	PROPN
easat-2635	19	7	[	[	X
easat-2635	19	8	2	2	NUM
easat-2635	19	9	]	]	PUNCT
easat-2635	19	10	who	who	PRON
easat-2635	19	11	states	state	VERB
easat-2635	19	12	that	that	SCONJ
easat-2635	19	13	geometry	geometry	NOUN
easat-2635	19	14	broadly	broadly	ADV
easat-2635	19	15	contributes	contribute	VERB
easat-2635	19	16	to	to	ADP
easat-2635	19	17	the	the	DET
easat-2635	19	18	development	development	NOUN
easat-2635	19	19	of	of	ADP
easat-2635	19	20	the	the	DET
easat-2635	19	21	skills	skill	NOUN
easat-2635	19	22	of	of	ADP
easat-2635	19	23	visualization	visualization	NOUN
easat-2635	19	24	in	in	ADP
easat-2635	19	25	students	student	NOUN
easat-2635	19	26	,	,	PUNCT
easat-2635	19	27	as	as	ADV
easat-2635	19	28	well	well	ADV
easat-2635	19	29	as	as	ADP
easat-2635	19	30	critical	critical	ADJ
easat-2635	19	31	thinking	thinking	NOUN
easat-2635	19	32	,	,	PUNCT
easat-2635	19	33	intuition	intuition	NOUN
easat-2635	19	34	,	,	PUNCT
easat-2635	19	35	perception	perception	NOUN
easat-2635	19	36	,	,	PUNCT
easat-2635	19	37	problem	problem	NOUN
easat-2635	19	38	-	-	PUNCT
easat-2635	19	39	solving	solving	NOUN
easat-2635	19	40	,	,	PUNCT
easat-2635	19	41	speculating	speculating	NOUN
easat-2635	19	42	,	,	PUNCT
easat-2635	19	43	deductive	deductive	ADJ
easat-2635	19	44	reasoning	reasoning	NOUN
easat-2635	19	45	,	,	PUNCT
easat-2635	19	46	logical	logical	ADJ
easat-2635	19	47	argument	argument	NOUN
easat-2635	19	48	,	,	PUNCT
easat-2635	19	49	and	and	CCONJ
easat-2635	19	50	proofs	proof	NOUN
easat-2635	19	51	.	.	PUNCT
easat-2635	20	1	some	some	DET
easat-2635	20	2	challenges	challenge	NOUN
easat-2635	20	3	were	be	AUX
easat-2635	20	4	found	find	VERB
easat-2635	20	5	concerning	concern	VERB
easat-2635	20	6	delivering	deliver	VERB
easat-2635	20	7	euclidean	euclidean	ADJ
easat-2635	20	8	geometry	geometry	NOUN
easat-2635	20	9	both	both	CCONJ
easat-2635	20	10	locally	locally	ADV
easat-2635	20	11	and	and	CCONJ
easat-2635	20	12	internationally	internationally	ADV
easat-2635	20	13	.	.	PUNCT
easat-2635	21	1	jones	jones	PROPN
easat-2635	22	1	[	[	X
easat-2635	22	2	2	2	NUM
easat-2635	22	3	]	]	PUNCT
easat-2635	22	4	states	state	NOUN
easat-2635	22	5	,	,	PUNCT
easat-2635	22	6	that	that	SCONJ
easat-2635	22	7	learners	learner	NOUN
easat-2635	22	8	do	do	AUX
easat-2635	22	9	not	not	PART
easat-2635	22	10	appreciate	appreciate	VERB
easat-2635	22	11	the	the	DET
easat-2635	22	12	need	need	NOUN
easat-2635	22	13	for	for	ADP
easat-2635	22	14	proof	proof	NOUN
easat-2635	22	15	,	,	PUNCT
easat-2635	22	16	and	and	CCONJ
easat-2635	22	17	they	they	PRON
easat-2635	22	18	are	be	AUX
easat-2635	22	19	unable	unable	ADJ
easat-2635	22	20	to	to	PART
easat-2635	22	21	differentiate	differentiate	VERB
easat-2635	22	22	between	between	ADP
easat-2635	22	23	the	the	DET
easat-2635	22	24	various	various	ADJ
easat-2635	22	25	forms	form	NOUN
easat-2635	22	26	of	of	ADP
easat-2635	22	27	mathematical	mathematical	ADJ
easat-2635	22	28	reasoning	reasoning	NOUN
easat-2635	22	29	such	such	ADJ
easat-2635	22	30	as	as	ADP
easat-2635	22	31	explanation	explanation	NOUN
easat-2635	22	32	,	,	PUNCT
easat-2635	22	33	argument	argument	NOUN
easat-2635	22	34	,	,	PUNCT
easat-2635	22	35	verification	verification	NOUN
easat-2635	22	36	,	,	PUNCT
easat-2635	22	37	and	and	CCONJ
easat-2635	22	38	proof	proof	NOUN
easat-2635	22	39	.	.	PUNCT
easat-2635	23	1	several	several	ADJ
easat-2635	23	2	pedagogical	pedagogical	ADJ
easat-2635	23	3	problems	problem	NOUN
easat-2635	23	4	in	in	ADP
easat-2635	23	5	the	the	DET
easat-2635	23	6	teaching	teaching	NOUN
easat-2635	23	7	of	of	ADP
easat-2635	23	8	euclidean	euclidean	ADJ
easat-2635	23	9	geometry	geometry	NOUN
easat-2635	23	10	have	have	AUX
easat-2635	23	11	been	be	AUX
easat-2635	23	12	identified	identify	VERB
easat-2635	23	13	in	in	ADP
easat-2635	23	14	several	several	ADJ
easat-2635	23	15	countries	country	NOUN
easat-2635	23	16	including	include	VERB
easat-2635	23	17	south	south	PROPN
easat-2635	23	18	africa	africa	PROPN
easat-2635	23	19	,	,	PUNCT
easat-2635	23	20	[	[	X
easat-2635	23	21	3	3	NUM
easat-2635	23	22	,	,	PUNCT
easat-2635	23	23	4	4	NUM
easat-2635	23	24	,	,	PUNCT
easat-2635	23	25	5	5	NUM
easat-2635	23	26	]	]	X
easat-2635	23	27	south	south	PROPN
easat-2635	23	28	africa	africa	PROPN
easat-2635	23	29	,	,	PUNCT
easat-2635	24	1	[	[	X
easat-2635	24	2	6	6	NUM
easat-2635	24	3	]	]	X
easat-2635	24	4	saudi	saudi	PROPN
easat-2635	24	5	arabia	arabia	PROPN
easat-2635	24	6	,	,	PUNCT
easat-2635	24	7	[	[	X
easat-2635	24	8	7	7	NUM
easat-2635	24	9	]	]	X
easat-2635	24	10	zimbabwe	zimbabwe	X
easat-2635	24	11	,	,	PUNCT
easat-2635	24	12	[	[	X
easat-2635	24	13	8	8	NUM
easat-2635	24	14	]	]	X
easat-2635	24	15	malawi	malawi	PROPN
easat-2635	24	16	.	.	PUNCT
easat-2635	25	1	in	in	ADP
easat-2635	25	2	south	south	PROPN
easat-2635	25	3	africa	africa	PROPN
easat-2635	25	4	,	,	PUNCT
easat-2635	25	5	other	other	ADJ
easat-2635	25	6	drawbacks	drawback	NOUN
easat-2635	25	7	were	be	AUX
easat-2635	25	8	also	also	ADV
easat-2635	25	9	identified	identify	VERB
easat-2635	25	10	,	,	PUNCT
easat-2635	25	11	apart	apart	ADV
easat-2635	25	12	from	from	ADP
easat-2635	25	13	pedagogical	pedagogical	ADJ
easat-2635	25	14	challenges	challenge	NOUN
easat-2635	25	15	.	.	PUNCT
easat-2635	26	1	for	for	ADP
easat-2635	26	2	example	example	NOUN
easat-2635	26	3	,	,	PUNCT
easat-2635	26	4	a	a	DET
easat-2635	26	5	study	study	NOUN
easat-2635	26	6	carried	carry	VERB
easat-2635	26	7	out	out	ADP
easat-2635	26	8	by	by	ADP
easat-2635	26	9	mthembu	mthembu	NOUN
easat-2635	27	1	[	[	X
easat-2635	27	2	9	9	NUM
easat-2635	27	3	]	]	PUNCT
easat-2635	27	4	found	find	VERB
easat-2635	27	5	that	that	SCONJ
easat-2635	27	6	some	some	DET
easat-2635	27	7	learners	learner	NOUN
easat-2635	27	8	study	study	VERB
easat-2635	27	9	mathematics	mathematic	NOUN
easat-2635	27	10	against	against	ADP
easat-2635	27	11	their	their	PRON
easat-2635	27	12	will	will	NOUN
easat-2635	27	13	because	because	SCONJ
easat-2635	27	14	their	their	PRON
easat-2635	27	15	parents	parent	NOUN
easat-2635	27	16	or	or	CCONJ
easat-2635	27	17	the	the	DET
easat-2635	27	18	school	school	NOUN
easat-2635	27	19	forces	force	VERB
easat-2635	27	20	them	they	PRON
easat-2635	27	21	to	to	PART
easat-2635	27	22	take	take	VERB
easat-2635	27	23	the	the	DET
easat-2635	27	24	subject	subject	NOUN
easat-2635	27	25	.	.	PUNCT
easat-2635	28	1	this	this	PRON
easat-2635	28	2	greatly	greatly	ADV
easat-2635	28	3	reduces	reduce	VERB
easat-2635	28	4	the	the	DET
easat-2635	28	5	learners	learner	NOUN
easat-2635	28	6	’	'	PUNCT
easat-2635	28	7	love	love	NOUN
easat-2635	28	8	of	of	ADP
easat-2635	28	9	mathematics	mathematic	NOUN
easat-2635	28	10	and	and	CCONJ
easat-2635	28	11	euclidean	euclidean	ADJ
easat-2635	28	12	geometry	geometry	NOUN
easat-2635	28	13	is	be	AUX
easat-2635	28	14	the	the	DET
easat-2635	28	15	section	section	NOUN
easat-2635	28	16	that	that	PRON
easat-2635	28	17	suffers	suffer	VERB
easat-2635	28	18	the	the	DET
easat-2635	28	19	most	most	ADJ
easat-2635	28	20	.	.	PUNCT
easat-2635	29	1	the	the	DET
easat-2635	29	2	same	same	ADJ
easat-2635	29	3	study	study	NOUN
easat-2635	29	4	also	also	ADV
easat-2635	29	5	found	find	VERB
easat-2635	29	6	that	that	SCONJ
easat-2635	29	7	the	the	DET
easat-2635	29	8	testing	testing	NOUN
easat-2635	29	9	system	system	NOUN
easat-2635	29	10	and	and	CCONJ
easat-2635	29	11	the	the	DET
easat-2635	29	12	prioritization	prioritization	NOUN
easat-2635	29	13	of	of	ADP
easat-2635	29	14	good	good	ADJ
easat-2635	29	15	results	result	NOUN
easat-2635	29	16	by	by	ADP
easat-2635	29	17	the	the	DET
easat-2635	29	18	2932	2932	NUM
easat-2635	29	19	edelweiss	edelweiss	PROPN
easat-2635	29	20	applied	apply	VERB
easat-2635	29	21	science	science	NOUN
easat-2635	29	22	and	and	CCONJ
easat-2635	29	23	technology	technology	NOUN
easat-2635	29	24	issn	issn	PROPN
easat-2635	29	25	:	:	PUNCT
easat-2635	29	26	2576	2576	NUM
easat-2635	29	27	-	-	SYM
easat-2635	29	28	8484	8484	NUM
easat-2635	29	29	vol	vol	NOUN
easat-2635	29	30	.	.	PROPN
easat-2635	29	31	8	8	NUM
easat-2635	29	32	,	,	PUNCT
easat-2635	29	33	no	no	INTJ
easat-2635	29	34	.	.	NOUN
easat-2635	29	35	6	6	NUM
easat-2635	29	36	:	:	SYM
easat-2635	29	37	2931	2931	NUM
easat-2635	29	38	-	-	SYM
easat-2635	29	39	2936	2936	NUM
easat-2635	29	40	,	,	PUNCT
easat-2635	29	41	2024	2024	NUM
easat-2635	29	42	doi	doi	NOUN
easat-2635	29	43	:	:	PUNCT
easat-2635	29	44	10.55214/25768484.v8i6.2635	10.55214/25768484.v8i6.2635	NUM
easat-2635	29	45	©	©	PROPN
easat-2635	29	46	2024	2024	NUM
easat-2635	29	47	by	by	ADP
easat-2635	29	48	the	the	DET
easat-2635	29	49	authors	author	NOUN
easat-2635	29	50	;	;	PUNCT
easat-2635	29	51	licensee	licensee	PROPN
easat-2635	29	52	learning	learn	VERB
easat-2635	29	53	gate	gate	PROPN
easat-2635	29	54	education	education	PROPN
easat-2635	29	55	department	department	PROPN
easat-2635	29	56	encouraged	encourage	VERB
easat-2635	29	57	teachers	teacher	NOUN
easat-2635	29	58	to	to	PART
easat-2635	29	59	adopt	adopt	VERB
easat-2635	29	60	teaching	teaching	NOUN
easat-2635	29	61	methods	method	NOUN
easat-2635	29	62	that	that	PRON
easat-2635	29	63	are	be	AUX
easat-2635	29	64	not	not	PART
easat-2635	29	65	ideal	ideal	ADJ
easat-2635	29	66	and	and	CCONJ
easat-2635	29	67	hence	hence	ADV
easat-2635	29	68	poor	poor	ADJ
easat-2635	29	69	results	result	NOUN
easat-2635	29	70	.	.	PUNCT
easat-2635	30	1	students	student	NOUN
easat-2635	30	2	from	from	ADP
easat-2635	30	3	very	very	ADV
easat-2635	30	4	poor	poor	ADJ
easat-2635	30	5	schools	school	NOUN
easat-2635	30	6	performed	perform	VERB
easat-2635	30	7	better	well	ADV
easat-2635	30	8	on	on	ADP
easat-2635	30	9	lower	low	ADJ
easat-2635	30	10	-	-	PUNCT
easat-2635	30	11	order	order	NOUN
easat-2635	30	12	reasoning	reasoning	NOUN
easat-2635	30	13	questions	question	NOUN
easat-2635	30	14	but	but	CCONJ
easat-2635	30	15	they	they	PRON
easat-2635	30	16	had	have	VERB
easat-2635	30	17	challenges	challenge	NOUN
easat-2635	30	18	with	with	ADP
easat-2635	30	19	questions	question	NOUN
easat-2635	30	20	that	that	PRON
easat-2635	30	21	required	require	VERB
easat-2635	30	22	logic	logic	NOUN
easat-2635	30	23	,	,	PUNCT
easat-2635	30	24	reasoning	reasoning	NOUN
easat-2635	30	25	,	,	PUNCT
easat-2635	30	26	visualization	visualization	NOUN
easat-2635	30	27	,	,	PUNCT
easat-2635	30	28	and	and	CCONJ
easat-2635	30	29	critical	critical	ADJ
easat-2635	30	30	thinking	thinking	NOUN
easat-2635	30	31	,	,	PUNCT
easat-2635	30	32	which	which	PRON
easat-2635	30	33	are	be	AUX
easat-2635	30	34	typical	typical	ADJ
easat-2635	30	35	of	of	ADP
easat-2635	30	36	the	the	DET
easat-2635	30	37	study	study	NOUN
easat-2635	30	38	of	of	ADP
easat-2635	30	39	euclidean	euclidean	ADJ
easat-2635	30	40	geometry	geometry	NOUN
easat-2635	30	41	[	[	X
easat-2635	30	42	10	10	NUM
easat-2635	30	43	]	]	PUNCT
easat-2635	30	44	.	.	PUNCT
easat-2635	31	1	from	from	ADP
easat-2635	31	2	2008	2008	NUM
easat-2635	31	3	to	to	ADP
easat-2635	31	4	2011	2011	NUM
easat-2635	31	5	euclidean	euclidean	ADJ
easat-2635	31	6	geometry	geometry	NOUN
easat-2635	31	7	in	in	ADP
easat-2635	31	8	its	its	PRON
easat-2635	31	9	traditional	traditional	ADJ
easat-2635	31	10	form	form	NOUN
easat-2635	31	11	of	of	ADP
easat-2635	31	12	theorem	theorem	ADJ
easat-2635	31	13	recognition	recognition	NOUN
easat-2635	31	14	and	and	CCONJ
easat-2635	31	15	proof	proof	ADJ
easat-2635	31	16	construction	construction	NOUN
easat-2635	31	17	was	be	AUX
easat-2635	31	18	introduced	introduce	VERB
easat-2635	31	19	as	as	ADP
easat-2635	31	20	an	an	DET
easat-2635	31	21	optional	optional	ADJ
easat-2635	31	22	course	course	NOUN
easat-2635	31	23	in	in	ADP
easat-2635	31	24	the	the	DET
easat-2635	31	25	south	south	ADJ
easat-2635	31	26	african	african	ADJ
easat-2635	31	27	grade	grade	NOUN
easat-2635	31	28	11	11	NUM
easat-2635	31	29	and	and	CCONJ
easat-2635	31	30	12	12	NUM
easat-2635	31	31	curricula	curriculum	NOUN
easat-2635	31	32	[	[	X
easat-2635	31	33	11	11	NUM
easat-2635	31	34	]	]	PUNCT
easat-2635	31	35	.	.	PUNCT
easat-2635	32	1	this	this	DET
easat-2635	32	2	decision	decision	NOUN
easat-2635	32	3	was	be	AUX
easat-2635	32	4	made	make	VERB
easat-2635	32	5	in	in	ADP
easat-2635	32	6	response	response	NOUN
easat-2635	32	7	to	to	ADP
easat-2635	32	8	a	a	DET
easat-2635	32	9	series	series	NOUN
easat-2635	32	10	of	of	ADP
easat-2635	32	11	poor	poor	ADJ
easat-2635	32	12	results	result	NOUN
easat-2635	32	13	in	in	ADP
easat-2635	32	14	the	the	DET
easat-2635	32	15	grade	grade	NOUN
easat-2635	32	16	12	12	NUM
easat-2635	32	17	mathematics	mathematic	NOUN
easat-2635	32	18	examinations	examination	NOUN
easat-2635	32	19	[	[	X
easat-2635	32	20	12	12	NUM
easat-2635	32	21	]	]	PUNCT
easat-2635	32	22	.	.	PUNCT
easat-2635	33	1	it	it	PRON
easat-2635	33	2	was	be	AUX
easat-2635	33	3	also	also	ADV
easat-2635	33	4	assumed	assume	VERB
easat-2635	33	5	that	that	SCONJ
easat-2635	33	6	teachers	teacher	NOUN
easat-2635	33	7	did	do	AUX
easat-2635	33	8	not	not	PART
easat-2635	33	9	have	have	VERB
easat-2635	33	10	the	the	DET
easat-2635	33	11	necessary	necessary	ADJ
easat-2635	33	12	depth	depth	NOUN
easat-2635	33	13	of	of	ADP
easat-2635	33	14	content	content	NOUN
easat-2635	33	15	and	and	CCONJ
easat-2635	33	16	pedagogical	pedagogical	ADJ
easat-2635	33	17	knowledge	knowledge	NOUN
easat-2635	33	18	to	to	PART
easat-2635	33	19	effectively	effectively	ADV
easat-2635	33	20	teach	teach	VERB
easat-2635	33	21	euclidean	euclidean	ADJ
easat-2635	33	22	geometry	geometry	NOUN
easat-2635	34	1	[	[	X
easat-2635	34	2	13	13	NUM
easat-2635	34	3	]	]	PUNCT
easat-2635	34	4	.	.	PUNCT
easat-2635	35	1	it	it	PRON
easat-2635	35	2	was	be	AUX
easat-2635	35	3	reinstated	reinstate	VERB
easat-2635	35	4	in	in	ADP
easat-2635	35	5	a	a	DET
easat-2635	35	6	new	new	ADJ
easat-2635	35	7	curriculum	curriculum	NOUN
easat-2635	35	8	and	and	CCONJ
easat-2635	35	9	assessment	assessment	NOUN
easat-2635	35	10	policy	policy	NOUN
easat-2635	35	11	statement	statement	NOUN
easat-2635	35	12	(	(	PUNCT
easat-2635	35	13	caps	cap	NOUN
easat-2635	35	14	)	)	PUNCT
easat-2635	35	15	in	in	ADP
easat-2635	35	16	2012	2012	NUM
easat-2635	35	17	after	after	SCONJ
easat-2635	35	18	numerous	numerous	ADJ
easat-2635	35	19	studies	study	NOUN
easat-2635	35	20	concluded	conclude	VERB
easat-2635	35	21	that	that	SCONJ
easat-2635	35	22	university	university	NOUN
easat-2635	35	23	students	student	NOUN
easat-2635	35	24	who	who	PRON
easat-2635	35	25	had	have	AUX
easat-2635	35	26	not	not	PART
easat-2635	35	27	done	do	VERB
easat-2635	35	28	euclidean	euclidean	ADJ
easat-2635	35	29	geometry	geometry	NOUN
easat-2635	35	30	at	at	ADP
easat-2635	35	31	high	high	ADJ
easat-2635	35	32	school	school	NOUN
easat-2635	35	33	were	be	AUX
easat-2635	35	34	weaker	weak	ADJ
easat-2635	35	35	in	in	ADP
easat-2635	35	36	their	their	PRON
easat-2635	35	37	mathematical	mathematical	ADJ
easat-2635	35	38	skills	skill	NOUN
easat-2635	35	39	in	in	ADP
easat-2635	35	40	comparison	comparison	NOUN
easat-2635	35	41	to	to	ADP
easat-2635	35	42	those	those	PRON
easat-2635	35	43	who	who	PRON
easat-2635	35	44	had	have	VERB
easat-2635	35	45	a	a	DET
easat-2635	35	46	geometry	geometry	NOUN
easat-2635	35	47	background	background	NOUN
easat-2635	36	1	[	[	X
easat-2635	36	2	12	12	NUM
easat-2635	36	3	]	]	PUNCT
easat-2635	36	4	.	.	PUNCT
easat-2635	37	1	several	several	ADJ
easat-2635	37	2	challenges	challenge	NOUN
easat-2635	37	3	concerning	concern	VERB
easat-2635	37	4	the	the	DET
easat-2635	37	5	teaching	teaching	NOUN
easat-2635	37	6	and	and	CCONJ
easat-2635	37	7	learning	learning	NOUN
easat-2635	37	8	of	of	ADP
easat-2635	37	9	euclidean	euclidean	ADJ
easat-2635	37	10	geometry	geometry	NOUN
easat-2635	37	11	have	have	AUX
easat-2635	37	12	been	be	AUX
easat-2635	37	13	identified	identify	VERB
easat-2635	37	14	and	and	CCONJ
easat-2635	37	15	it	it	PRON
easat-2635	37	16	is	be	AUX
easat-2635	37	17	believed	believe	VERB
easat-2635	37	18	that	that	SCONJ
easat-2635	37	19	they	they	PRON
easat-2635	37	20	play	play	VERB
easat-2635	37	21	a	a	DET
easat-2635	37	22	significant	significant	ADJ
easat-2635	37	23	role	role	NOUN
easat-2635	37	24	in	in	ADP
easat-2635	37	25	the	the	DET
easat-2635	37	26	learners	learner	NOUN
easat-2635	37	27	’	'	PUNCT
easat-2635	37	28	poor	poor	ADJ
easat-2635	37	29	performance	performance	NOUN
easat-2635	37	30	in	in	ADP
easat-2635	37	31	euclidean	euclidean	ADJ
easat-2635	37	32	geometry	geometry	NOUN
easat-2635	37	33	.	.	PUNCT
easat-2635	38	1	nothing	nothing	PRON
easat-2635	38	2	significant	significant	ADJ
easat-2635	38	3	has	have	AUX
easat-2635	38	4	been	be	AUX
easat-2635	38	5	noted	note	VERB
easat-2635	38	6	concerning	concern	VERB
easat-2635	38	7	the	the	DET
easat-2635	38	8	approach	approach	NOUN
easat-2635	38	9	to	to	ADP
easat-2635	38	10	the	the	DET
easat-2635	38	11	problem	problem	NOUN
easat-2635	38	12	solution	solution	NOUN
easat-2635	38	13	presentation	presentation	NOUN
easat-2635	38	14	using	use	VERB
easat-2635	38	15	distinctly	distinctly	ADV
easat-2635	38	16	different	different	ADJ
easat-2635	38	17	answers	answer	NOUN
easat-2635	38	18	,	,	PUNCT
easat-2635	38	19	which	which	PRON
easat-2635	38	20	might	might	AUX
easat-2635	38	21	also	also	ADV
easat-2635	38	22	affect	affect	VERB
easat-2635	38	23	learners	learner	NOUN
easat-2635	38	24	’	'	PUNCT
easat-2635	38	25	performance	performance	NOUN
easat-2635	38	26	.	.	PUNCT
easat-2635	39	1	the	the	DET
easat-2635	39	2	objective	objective	NOUN
easat-2635	39	3	of	of	ADP
easat-2635	39	4	this	this	DET
easat-2635	39	5	study	study	NOUN
easat-2635	39	6	is	be	AUX
easat-2635	39	7	to	to	PART
easat-2635	39	8	analyse	analyse	VERB
easat-2635	39	9	distinctly	distinctly	ADV
easat-2635	39	10	different	different	ADJ
easat-2635	39	11	answers	answer	NOUN
easat-2635	39	12	to	to	ADP
easat-2635	39	13	one	one	NUM
easat-2635	39	14	euclidean	euclidean	ADJ
easat-2635	39	15	geometry	geometry	NOUN
easat-2635	39	16	problem	problem	NOUN
easat-2635	39	17	and	and	CCONJ
easat-2635	39	18	to	to	PART
easat-2635	39	19	come	come	VERB
easat-2635	39	20	up	up	ADP
easat-2635	39	21	with	with	ADP
easat-2635	39	22	conclusions	conclusion	NOUN
easat-2635	39	23	that	that	PRON
easat-2635	39	24	might	might	AUX
easat-2635	39	25	help	help	VERB
easat-2635	39	26	to	to	PART
easat-2635	39	27	improve	improve	VERB
easat-2635	39	28	the	the	DET
easat-2635	39	29	approach	approach	NOUN
easat-2635	39	30	to	to	ADP
easat-2635	39	31	teaching	teach	VERB
easat-2635	39	32	this	this	DET
easat-2635	39	33	topic	topic	NOUN
easat-2635	39	34	.	.	PUNCT
easat-2635	40	1	in	in	ADP
easat-2635	40	2	most	most	ADJ
easat-2635	40	3	cases	case	NOUN
easat-2635	40	4	,	,	PUNCT
easat-2635	40	5	different	different	ADJ
easat-2635	40	6	approaches	approach	NOUN
easat-2635	40	7	to	to	ADP
easat-2635	40	8	solving	solve	VERB
easat-2635	40	9	a	a	DET
easat-2635	40	10	problem	problem	NOUN
easat-2635	40	11	are	be	AUX
easat-2635	40	12	used	use	VERB
easat-2635	40	13	,	,	PUNCT
easat-2635	40	14	and	and	CCONJ
easat-2635	40	15	the	the	DET
easat-2635	40	16	same	same	ADJ
easat-2635	40	17	answers	answer	NOUN
easat-2635	40	18	are	be	AUX
easat-2635	40	19	obtained	obtain	VERB
easat-2635	40	20	at	at	ADP
easat-2635	40	21	the	the	DET
easat-2635	40	22	end	end	NOUN
easat-2635	40	23	.	.	PUNCT
easat-2635	41	1	there	there	PRON
easat-2635	41	2	are	be	VERB
easat-2635	41	3	situations	situation	NOUN
easat-2635	41	4	whereby	whereby	SCONJ
easat-2635	41	5	the	the	DET
easat-2635	41	6	answers	answer	NOUN
easat-2635	41	7	are	be	AUX
easat-2635	41	8	not	not	PART
easat-2635	41	9	the	the	DET
easat-2635	41	10	same	same	ADJ
easat-2635	41	11	depending	depend	VERB
easat-2635	41	12	on	on	ADP
easat-2635	41	13	the	the	DET
easat-2635	41	14	question	question	NOUN
easat-2635	41	15	,	,	PUNCT
easat-2635	41	16	even	even	ADV
easat-2635	41	17	though	though	SCONJ
easat-2635	41	18	the	the	DET
easat-2635	41	19	working	working	NOUN
easat-2635	41	20	of	of	ADP
easat-2635	41	21	the	the	DET
easat-2635	41	22	problem	problem	NOUN
easat-2635	41	23	is	be	AUX
easat-2635	41	24	correct	correct	ADJ
easat-2635	41	25	.	.	PUNCT
easat-2635	42	1	the	the	DET
easat-2635	42	2	question	question	NOUN
easat-2635	42	3	is	be	AUX
easat-2635	42	4	:	:	PUNCT
easat-2635	42	5	do	do	AUX
easat-2635	42	6	examiners	examiner	NOUN
easat-2635	42	7	often	often	ADV
easat-2635	42	8	take	take	VERB
easat-2635	42	9	note	note	NOUN
easat-2635	42	10	of	of	ADP
easat-2635	42	11	all	all	DET
easat-2635	42	12	the	the	DET
easat-2635	42	13	possible	possible	ADJ
easat-2635	42	14	approaches	approach	NOUN
easat-2635	42	15	to	to	ADP
easat-2635	42	16	a	a	DET
easat-2635	42	17	solution	solution	NOUN
easat-2635	42	18	including	include	VERB
easat-2635	42	19	the	the	DET
easat-2635	42	20	ones	one	NOUN
easat-2635	42	21	leading	lead	VERB
easat-2635	42	22	to	to	ADP
easat-2635	42	23	distinctly	distinctly	ADV
easat-2635	42	24	different	different	ADJ
easat-2635	42	25	solutions	solution	NOUN
easat-2635	42	26	when	when	SCONJ
easat-2635	42	27	they	they	PRON
easat-2635	42	28	do	do	VERB
easat-2635	42	29	the	the	DET
easat-2635	42	30	memoranda	memoranda	NOUN
easat-2635	42	31	?	?	PUNCT
easat-2635	43	1	if	if	SCONJ
easat-2635	43	2	they	they	PRON
easat-2635	43	3	do	do	VERB
easat-2635	43	4	,	,	PUNCT
easat-2635	43	5	do	do	AUX
easat-2635	43	6	the	the	DET
easat-2635	43	7	markers	marker	NOUN
easat-2635	43	8	often	often	ADV
easat-2635	43	9	take	take	VERB
easat-2635	43	10	note	note	NOUN
easat-2635	43	11	of	of	ADP
easat-2635	43	12	all	all	DET
easat-2635	43	13	the	the	DET
easat-2635	43	14	possible	possible	ADJ
easat-2635	43	15	approaches	approach	NOUN
easat-2635	43	16	to	to	ADP
easat-2635	43	17	solutions	solution	NOUN
easat-2635	43	18	when	when	SCONJ
easat-2635	43	19	marking	mark	VERB
easat-2635	43	20	or	or	CCONJ
easat-2635	43	21	do	do	AUX
easat-2635	43	22	they	they	PRON
easat-2635	43	23	ignore	ignore	VERB
easat-2635	43	24	other	other	ADJ
easat-2635	43	25	approaches	approach	NOUN
easat-2635	43	26	including	include	VERB
easat-2635	43	27	the	the	DET
easat-2635	43	28	ones	one	NOUN
easat-2635	43	29	leading	lead	VERB
easat-2635	43	30	to	to	ADP
easat-2635	43	31	distinctly	distinctly	ADV
easat-2635	43	32	different	different	ADJ
easat-2635	43	33	solutions	solution	NOUN
easat-2635	43	34	?	?	PUNCT
easat-2635	44	1	or	or	CCONJ
easat-2635	44	2	do	do	AUX
easat-2635	44	3	they	they	PRON
easat-2635	44	4	just	just	ADV
easat-2635	44	5	concentrate	concentrate	VERB
easat-2635	44	6	on	on	ADP
easat-2635	44	7	the	the	DET
easat-2635	44	8	ones	one	NOUN
easat-2635	44	9	that	that	PRON
easat-2635	44	10	they	they	PRON
easat-2635	44	11	think	think	VERB
easat-2635	44	12	are	be	AUX
easat-2635	44	13	the	the	DET
easat-2635	44	14	obvious	obvious	ADJ
easat-2635	44	15	ones	one	NOUN
easat-2635	44	16	and	and	CCONJ
easat-2635	44	17	hence	hence	ADV
easat-2635	44	18	disadvantage	disadvantage	NOUN
easat-2635	44	19	students	student	NOUN
easat-2635	44	20	?	?	PUNCT
easat-2635	45	1	the	the	DET
easat-2635	45	2	authors	author	NOUN
easat-2635	45	3	decided	decide	VERB
easat-2635	45	4	to	to	PART
easat-2635	45	5	investigate	investigate	VERB
easat-2635	45	6	the	the	DET
easat-2635	45	7	tendency	tendency	NOUN
easat-2635	45	8	for	for	ADP
easat-2635	45	9	distinctly	distinctly	ADV
easat-2635	45	10	different	different	ADJ
easat-2635	45	11	answers	answer	NOUN
easat-2635	45	12	to	to	ADP
easat-2635	45	13	a	a	DET
easat-2635	45	14	problem	problem	NOUN
easat-2635	45	15	in	in	ADP
easat-2635	45	16	euclidean	euclidean	ADJ
easat-2635	45	17	geometry	geometry	NOUN
easat-2635	45	18	and	and	CCONJ
easat-2635	45	19	its	its	PRON
easat-2635	45	20	impact	impact	NOUN
easat-2635	45	21	on	on	ADP
easat-2635	45	22	learners	learner	NOUN
easat-2635	45	23	’	'	PUNCT
easat-2635	45	24	achievement	achievement	NOUN
easat-2635	45	25	.	.	PUNCT
easat-2635	46	1	this	this	PRON
easat-2635	46	2	led	lead	VERB
easat-2635	46	3	to	to	ADP
easat-2635	46	4	the	the	DET
easat-2635	46	5	following	follow	VERB
easat-2635	46	6	research	research	NOUN
easat-2635	46	7	question	question	NOUN
easat-2635	46	8	and	and	CCONJ
easat-2635	46	9	its	its	PRON
easat-2635	46	10	objective	objective	NOUN
easat-2635	46	11	respectively	respectively	ADV
easat-2635	46	12	:	:	PUNCT
easat-2635	46	13	•	•	ADP
easat-2635	46	14	what	what	PRON
easat-2635	46	15	are	be	AUX
easat-2635	46	16	the	the	DET
easat-2635	46	17	challenges	challenge	NOUN
easat-2635	46	18	associated	associate	VERB
easat-2635	46	19	with	with	ADP
easat-2635	46	20	the	the	DET
easat-2635	46	21	approach	approach	NOUN
easat-2635	46	22	to	to	ADP
easat-2635	46	23	the	the	DET
easat-2635	46	24	problem	problem	NOUN
easat-2635	46	25	solution	solution	NOUN
easat-2635	46	26	presentation	presentation	NOUN
easat-2635	46	27	using	use	VERB
easat-2635	46	28	distinctly	distinctly	ADV
easat-2635	46	29	different	different	ADJ
easat-2635	46	30	answers	answer	NOUN
easat-2635	46	31	in	in	ADP
easat-2635	46	32	euclidean	euclidean	ADJ
easat-2635	46	33	geometry	geometry	NOUN
easat-2635	46	34	?	?	PUNCT
easat-2635	47	1	with	with	ADP
easat-2635	47	2	the	the	DET
easat-2635	47	3	objective	objective	NOUN
easat-2635	47	4	:	:	PUNCT
easat-2635	47	5	•	•	ADP
easat-2635	47	6	to	to	PART
easat-2635	47	7	investigate	investigate	VERB
easat-2635	47	8	the	the	DET
easat-2635	47	9	challenges	challenge	NOUN
easat-2635	47	10	associated	associate	VERB
easat-2635	47	11	with	with	ADP
easat-2635	47	12	the	the	DET
easat-2635	47	13	tendency	tendency	NOUN
easat-2635	47	14	for	for	ADP
easat-2635	47	15	distinctly	distinctly	ADV
easat-2635	47	16	different	different	ADJ
easat-2635	47	17	answers	answer	NOUN
easat-2635	47	18	to	to	ADP
easat-2635	47	19	a	a	DET
easat-2635	47	20	problem	problem	NOUN
easat-2635	47	21	in	in	ADP
easat-2635	47	22	euclidean	euclidean	ADJ
easat-2635	47	23	geometry	geometry	NOUN
easat-2635	47	24	.	.	PUNCT
easat-2635	48	1	many	many	ADJ
easat-2635	48	2	high	high	ADJ
easat-2635	48	3	school	school	NOUN
easat-2635	48	4	learners	learner	NOUN
easat-2635	48	5	regard	regard	VERB
easat-2635	48	6	euclidean	euclidean	ADJ
easat-2635	48	7	geometry	geometry	NOUN
easat-2635	48	8	as	as	ADP
easat-2635	48	9	one	one	NUM
easat-2635	48	10	of	of	ADP
easat-2635	48	11	the	the	DET
easat-2635	48	12	most	most	ADV
easat-2635	48	13	difficult	difficult	ADJ
easat-2635	48	14	topics	topic	NOUN
easat-2635	48	15	in	in	ADP
easat-2635	48	16	mathematics	mathematic	NOUN
easat-2635	48	17	.	.	PUNCT
easat-2635	49	1	as	as	ADP
easat-2635	49	2	a	a	DET
easat-2635	49	3	result	result	NOUN
easat-2635	49	4	,	,	PUNCT
easat-2635	49	5	most	most	ADJ
easat-2635	49	6	of	of	ADP
easat-2635	49	7	them	they	PRON
easat-2635	49	8	do	do	AUX
easat-2635	49	9	not	not	PART
easat-2635	49	10	do	do	VERB
easat-2635	49	11	well	well	ADV
easat-2635	49	12	in	in	ADP
easat-2635	49	13	the	the	DET
easat-2635	49	14	final	final	ADJ
easat-2635	49	15	examinations	examination	NOUN
easat-2635	49	16	.	.	PUNCT
easat-2635	50	1	a	a	DET
easat-2635	50	2	lot	lot	NOUN
easat-2635	50	3	of	of	ADP
easat-2635	50	4	research	research	NOUN
easat-2635	50	5	has	have	AUX
easat-2635	50	6	been	be	AUX
easat-2635	50	7	done	do	VERB
easat-2635	50	8	involving	involve	VERB
easat-2635	50	9	euclidean	euclidean	ADJ
easat-2635	50	10	geometry	geometry	NOUN
easat-2635	50	11	in	in	ADP
easat-2635	50	12	many	many	ADJ
easat-2635	50	13	countries	country	NOUN
easat-2635	50	14	.	.	PUNCT
easat-2635	51	1	many	many	ADJ
easat-2635	51	2	factors	factor	NOUN
easat-2635	51	3	both	both	CCONJ
easat-2635	51	4	internal	internal	ADJ
easat-2635	51	5	and	and	CCONJ
easat-2635	51	6	external	external	ADJ
easat-2635	51	7	leading	lead	VERB
easat-2635	51	8	to	to	ADP
easat-2635	51	9	poor	poor	ADJ
easat-2635	51	10	performance	performance	NOUN
easat-2635	51	11	in	in	ADP
easat-2635	51	12	the	the	DET
easat-2635	51	13	topic	topic	NOUN
easat-2635	51	14	have	have	AUX
easat-2635	51	15	been	be	AUX
easat-2635	51	16	found	find	VERB
easat-2635	51	17	.	.	PUNCT
easat-2635	52	1	in	in	ADP
easat-2635	52	2	south	south	PROPN
easat-2635	52	3	africa	africa	PROPN
easat-2635	52	4	,	,	PUNCT
easat-2635	52	5	makhubele	makhubele	NOUN
easat-2635	52	6	[	[	X
easat-2635	52	7	14	14	NUM
easat-2635	52	8	]	]	PUNCT
easat-2635	52	9	found	find	VERB
easat-2635	52	10	a	a	DET
easat-2635	52	11	lot	lot	NOUN
easat-2635	52	12	of	of	ADP
easat-2635	52	13	misapplication	misapplication	NOUN
easat-2635	52	14	of	of	ADP
easat-2635	52	15	concepts	concept	NOUN
easat-2635	52	16	caused	cause	VERB
easat-2635	52	17	by	by	ADP
easat-2635	52	18	:	:	PUNCT
easat-2635	52	19	i	i	NOUN
easat-2635	52	20	)	)	PUNCT
easat-2635	52	21	learning	learn	VERB
easat-2635	52	22	concepts	concept	NOUN
easat-2635	52	23	without	without	ADP
easat-2635	52	24	understanding	understanding	NOUN
easat-2635	52	25	.	.	PUNCT
easat-2635	53	1	ii	ii	X
easat-2635	53	2	)	)	PUNCT
easat-2635	53	3	challenges	challenge	NOUN
easat-2635	53	4	with	with	ADP
easat-2635	53	5	understanding	understand	VERB
easat-2635	53	6	the	the	DET
easat-2635	53	7	features	feature	NOUN
easat-2635	53	8	and	and	CCONJ
easat-2635	53	9	properties	property	NOUN
easat-2635	53	10	of	of	ADP
easat-2635	53	11	shapes	shape	NOUN
easat-2635	53	12	.	.	PUNCT
easat-2635	54	1	iii	iii	X
easat-2635	54	2	)	)	PUNCT
easat-2635	54	3	difficulties	difficulty	NOUN
easat-2635	54	4	in	in	ADP
easat-2635	54	5	dealing	deal	VERB
easat-2635	54	6	with	with	ADP
easat-2635	54	7	proof	proof	ADJ
easat-2635	54	8	questions	question	NOUN
easat-2635	54	9	.	.	PUNCT
easat-2635	55	1	the	the	DET
easat-2635	55	2	above	above	ADJ
easat-2635	55	3	was	be	AUX
easat-2635	55	4	also	also	ADV
easat-2635	55	5	echoed	echo	VERB
easat-2635	55	6	by	by	ADP
easat-2635	55	7	abosede	abosede	NOUN
easat-2635	55	8	[	[	X
easat-2635	55	9	15	15	NUM
easat-2635	55	10	]	]	PUNCT
easat-2635	55	11	who	who	PRON
easat-2635	55	12	found	find	VERB
easat-2635	55	13	that	that	SCONJ
easat-2635	55	14	learners	learner	NOUN
easat-2635	55	15	had	have	VERB
easat-2635	55	16	noticeable	noticeable	ADJ
easat-2635	55	17	difficulties	difficulty	NOUN
easat-2635	55	18	in	in	ADP
easat-2635	55	19	understanding	understand	VERB
easat-2635	55	20	properties	property	NOUN
easat-2635	55	21	of	of	ADP
easat-2635	55	22	parallel	parallel	ADJ
easat-2635	55	23	lines	line	NOUN
easat-2635	55	24	,	,	PUNCT
easat-2635	55	25	congruency	congruency	NOUN
easat-2635	55	26	,	,	PUNCT
easat-2635	55	27	and	and	CCONJ
easat-2635	55	28	proofs	proof	NOUN
easat-2635	55	29	of	of	ADP
easat-2635	55	30	parallelograms	parallelogram	NOUN
easat-2635	55	31	which	which	PRON
easat-2635	55	32	eventually	eventually	ADV
easat-2635	55	33	led	lead	VERB
easat-2635	55	34	to	to	ADP
easat-2635	55	35	problems	problem	NOUN
easat-2635	55	36	in	in	ADP
easat-2635	55	37	calculating	calculate	VERB
easat-2635	55	38	the	the	DET
easat-2635	55	39	required	require	VERB
easat-2635	55	40	angles	angle	NOUN
easat-2635	55	41	.	.	PUNCT
easat-2635	56	1	ndlovu	ndlovu	PROPN
easat-2635	56	2	&	&	CCONJ
easat-2635	56	3	mji	mji	ADJ
easat-2635	57	1	[	[	X
easat-2635	57	2	16	16	NUM
easat-2635	57	3	]	]	PUNCT
easat-2635	57	4	identified	identify	VERB
easat-2635	57	5	the	the	DET
easat-2635	57	6	following	following	ADJ
easat-2635	57	7	barriers	barrier	NOUN
easat-2635	57	8	that	that	PRON
easat-2635	57	9	students	student	NOUN
easat-2635	57	10	face	face	VERB
easat-2635	57	11	in	in	ADP
easat-2635	57	12	solving	solve	VERB
easat-2635	57	13	euclidean	euclidean	ADJ
easat-2635	57	14	geometry	geometry	NOUN
easat-2635	57	15	problems	problem	NOUN
easat-2635	57	16	:	:	PUNCT
easat-2635	57	17	lack	lack	NOUN
easat-2635	57	18	of	of	ADP
easat-2635	57	19	basic	basic	ADJ
easat-2635	57	20	geometrical	geometrical	ADJ
easat-2635	57	21	knowledge	knowledge	NOUN
easat-2635	57	22	and	and	CCONJ
easat-2635	57	23	vocabulary	vocabulary	NOUN
easat-2635	57	24	,	,	PUNCT
easat-2635	57	25	use	use	NOUN
easat-2635	57	26	of	of	ADP
easat-2635	57	27	an	an	DET
easat-2635	57	28	inappropriate	inappropriate	ADJ
easat-2635	57	29	frame	frame	NOUN
easat-2635	57	30	of	of	ADP
easat-2635	57	31	reference	reference	NOUN
easat-2635	57	32	(	(	PUNCT
easat-2635	57	33	or	or	CCONJ
easat-2635	57	34	geometrical	geometrical	ADJ
easat-2635	57	35	knowledge	knowledge	NOUN
easat-2635	57	36	)	)	PUNCT
easat-2635	57	37	,	,	PUNCT
easat-2635	57	38	inability	inability	NOUN
easat-2635	57	39	to	to	PART
easat-2635	57	40	make	make	VERB
easat-2635	57	41	logical	logical	ADJ
easat-2635	57	42	deductions	deduction	NOUN
easat-2635	57	43	,	,	PUNCT
easat-2635	57	44	and	and	CCONJ
easat-2635	57	45	inability	inability	NOUN
easat-2635	57	46	to	to	PART
easat-2635	57	47	organise	organise	VERB
easat-2635	57	48	information	information	NOUN
easat-2635	57	49	in	in	ADP
easat-2635	57	50	a	a	DET
easat-2635	57	51	logical	logical	ADJ
easat-2635	57	52	chain	chain	NOUN
easat-2635	57	53	of	of	ADP
easat-2635	57	54	arguments	argument	NOUN
easat-2635	57	55	leading	lead	VERB
easat-2635	57	56	from	from	ADP
easat-2635	57	57	givens	given	NOUN
easat-2635	57	58	to	to	ADP
easat-2635	57	59	conclusions	conclusion	NOUN
easat-2635	57	60	.	.	PUNCT
easat-2635	58	1	the	the	DET
easat-2635	58	2	layout	layout	NOUN
easat-2635	58	3	of	of	ADP
easat-2635	58	4	the	the	DET
easat-2635	58	5	paper	paper	NOUN
easat-2635	58	6	is	be	AUX
easat-2635	58	7	as	as	SCONJ
easat-2635	58	8	follows	follow	VERB
easat-2635	58	9	:	:	PUNCT
easat-2635	58	10	the	the	DET
easat-2635	58	11	first	first	ADJ
easat-2635	58	12	part	part	NOUN
easat-2635	58	13	focuses	focus	VERB
easat-2635	58	14	on	on	ADP
easat-2635	58	15	the	the	DET
easat-2635	58	16	background	background	NOUN
easat-2635	58	17	of	of	ADP
easat-2635	58	18	the	the	DET
easat-2635	58	19	problem	problem	NOUN
easat-2635	58	20	to	to	PART
easat-2635	58	21	highlight	highlight	VERB
easat-2635	58	22	the	the	DET
easat-2635	58	23	challenges	challenge	NOUN
easat-2635	58	24	of	of	ADP
easat-2635	58	25	teaching	teaching	NOUN
easat-2635	58	26	and	and	CCONJ
easat-2635	58	27	learning	learn	VERB
easat-2635	58	28	euclidean	euclidean	ADJ
easat-2635	58	29	geometry	geometry	NOUN
easat-2635	58	30	in	in	ADP
easat-2635	58	31	high	high	ADJ
easat-2635	58	32	schools	school	NOUN
easat-2635	58	33	.	.	PUNCT
easat-2635	59	1	research	research	NOUN
easat-2635	59	2	questions	question	NOUN
easat-2635	59	3	are	be	AUX
easat-2635	59	4	also	also	ADV
easat-2635	59	5	given	give	VERB
easat-2635	59	6	.	.	PUNCT
easat-2635	60	1	the	the	DET
easat-2635	60	2	second	second	ADJ
easat-2635	60	3	part	part	NOUN
easat-2635	60	4	is	be	AUX
easat-2635	60	5	the	the	DET
easat-2635	60	6	literature	literature	PROPN
easat-2635	60	7	review	review	NOUN
easat-2635	60	8	.	.	PUNCT
easat-2635	61	1	the	the	DET
easat-2635	61	2	third	third	ADJ
easat-2635	61	3	part	part	NOUN
easat-2635	61	4	explains	explain	VERB
easat-2635	61	5	the	the	DET
easat-2635	61	6	research	research	NOUN
easat-2635	61	7	instrumentation	instrumentation	NOUN
easat-2635	61	8	and	and	CCONJ
easat-2635	61	9	proceedings	proceeding	NOUN
easat-2635	61	10	.	.	PUNCT
easat-2635	62	1	the	the	DET
easat-2635	62	2	fourth	fourth	ADJ
easat-2635	62	3	section	section	NOUN
easat-2635	62	4	analyses	analyse	VERB
easat-2635	62	5	data	datum	NOUN
easat-2635	62	6	gives	give	VERB
easat-2635	62	7	and	and	CCONJ
easat-2635	62	8	discusses	discuss	VERB
easat-2635	62	9	examples	example	NOUN
easat-2635	62	10	of	of	ADP
easat-2635	62	11	distinctly	distinctly	ADV
easat-2635	62	12	different	different	ADJ
easat-2635	62	13	solutions	solution	NOUN
easat-2635	62	14	found	find	VERB
easat-2635	62	15	in	in	ADP
easat-2635	62	16	one	one	NUM
easat-2635	62	17	euclidean	euclidean	ADJ
easat-2635	62	18	geometry	geometry	NOUN
easat-2635	62	19	question	question	NOUN
easat-2635	62	20	which	which	PRON
easat-2635	62	21	markers	marker	NOUN
easat-2635	62	22	might	might	AUX
easat-2635	62	23	not	not	PART
easat-2635	62	24	take	take	VERB
easat-2635	62	25	note	note	NOUN
easat-2635	62	26	of	of	ADP
easat-2635	62	27	.	.	PUNCT
easat-2635	63	1	2933	2933	NUM
easat-2635	63	2	edelweiss	edelweiss	PROPN
easat-2635	63	3	applied	apply	VERB
easat-2635	63	4	science	science	NOUN
easat-2635	63	5	and	and	CCONJ
easat-2635	63	6	technology	technology	NOUN
easat-2635	63	7	issn	issn	PROPN
easat-2635	63	8	:	:	PUNCT
easat-2635	63	9	2576	2576	NUM
easat-2635	63	10	-	-	SYM
easat-2635	63	11	8484	8484	NUM
easat-2635	63	12	vol	vol	NOUN
easat-2635	63	13	.	.	PROPN
easat-2635	63	14	8	8	NUM
easat-2635	63	15	,	,	PUNCT
easat-2635	63	16	no	no	INTJ
easat-2635	63	17	.	.	NOUN
easat-2635	64	1	6	6	NUM
easat-2635	64	2	:	:	SYM
easat-2635	64	3	2931	2931	NUM
easat-2635	64	4	-	-	SYM
easat-2635	64	5	2936	2936	NUM
easat-2635	64	6	,	,	PUNCT
easat-2635	64	7	2024	2024	NUM
easat-2635	64	8	doi	doi	NOUN
easat-2635	64	9	:	:	PUNCT
easat-2635	64	10	10.55214/25768484.v8i6.2635	10.55214/25768484.v8i6.2635	NUM
easat-2635	64	11	©	©	PROPN
easat-2635	64	12	2024	2024	NUM
easat-2635	64	13	by	by	ADP
easat-2635	64	14	the	the	DET
easat-2635	64	15	authors	author	NOUN
easat-2635	64	16	;	;	PUNCT
easat-2635	64	17	licensee	licensee	PROPN
easat-2635	64	18	learning	learning	NOUN
easat-2635	64	19	gate	gate	NOUN
easat-2635	64	20	2	2	NUM
easat-2635	64	21	.	.	PUNCT
easat-2635	64	22	methodology	methodology	NOUN
easat-2635	64	23	an	an	DET
easat-2635	64	24	interpretive	interpretive	ADJ
easat-2635	64	25	paradigm	paradigm	NOUN
easat-2635	64	26	was	be	AUX
easat-2635	64	27	followed	follow	VERB
easat-2635	64	28	.	.	PUNCT
easat-2635	65	1	a	a	DET
easat-2635	65	2	single	single	ADJ
easat-2635	65	3	case	case	NOUN
easat-2635	65	4	study	study	NOUN
easat-2635	65	5	was	be	AUX
easat-2635	65	6	used	use	VERB
easat-2635	65	7	because	because	SCONJ
easat-2635	65	8	the	the	DET
easat-2635	65	9	cases	case	NOUN
easat-2635	65	10	were	be	AUX
easat-2635	65	11	only	only	ADV
easat-2635	65	12	grade	grade	NOUN
easat-2635	65	13	12	12	NUM
easat-2635	65	14	mathematics	mathematic	NOUN
easat-2635	65	15	examination	examination	NOUN
easat-2635	65	16	memoranda	memorandum	NOUN
easat-2635	65	17	which	which	PRON
easat-2635	65	18	were	be	AUX
easat-2635	65	19	selected	select	VERB
easat-2635	65	20	and	and	CCONJ
easat-2635	65	21	analysed	analyse	VERB
easat-2635	65	22	qualitatively	qualitatively	ADV
easat-2635	65	23	.	.	PUNCT
easat-2635	66	1	the	the	DET
easat-2635	66	2	memoranda	memoranda	NOUN
easat-2635	66	3	were	be	AUX
easat-2635	66	4	selected	select	VERB
easat-2635	66	5	randomly	randomly	ADV
easat-2635	66	6	from	from	ADP
easat-2635	66	7	2012	2012	NUM
easat-2635	66	8	to	to	ADP
easat-2635	66	9	2022	2022	NUM
easat-2635	66	10	grade	grade	NOUN
easat-2635	66	11	12	12	NUM
easat-2635	66	12	mathematics	mathematic	NOUN
easat-2635	66	13	past	past	NOUN
easat-2635	66	14	examinations	examination	NOUN
easat-2635	66	15	papers	paper	NOUN
easat-2635	66	16	.	.	PUNCT
easat-2635	67	1	only	only	ADV
easat-2635	67	2	memoranda	memoranda	NOUN
easat-2635	67	3	from	from	ADP
easat-2635	67	4	2012	2012	NUM
easat-2635	67	5	to	to	ADP
easat-2635	67	6	2022	2022	NUM
easat-2635	67	7	we	we	PRON
easat-2635	67	8	chosen	choose	VERB
easat-2635	67	9	because	because	SCONJ
easat-2635	67	10	before	before	SCONJ
easat-2635	67	11	that	that	DET
easat-2635	67	12	euclidean	euclidean	ADJ
easat-2635	67	13	geometry	geometry	NOUN
easat-2635	67	14	was	be	AUX
easat-2635	67	15	optional	optional	ADJ
easat-2635	67	16	in	in	ADP
easat-2635	67	17	south	south	ADJ
easat-2635	67	18	african	african	ADJ
easat-2635	67	19	high	high	ADJ
easat-2635	67	20	schools	school	NOUN
easat-2635	67	21	.	.	PUNCT
easat-2635	68	1	an	an	DET
easat-2635	68	2	example	example	NOUN
easat-2635	68	3	from	from	ADP
easat-2635	68	4	one	one	NUM
easat-2635	68	5	previous	previous	ADJ
easat-2635	68	6	memorandum	memorandum	NOUN
easat-2635	68	7	was	be	AUX
easat-2635	68	8	given	give	VERB
easat-2635	68	9	where	where	SCONJ
easat-2635	68	10	the	the	DET
easat-2635	68	11	authors	author	NOUN
easat-2635	68	12	were	be	AUX
easat-2635	68	13	able	able	ADJ
easat-2635	68	14	to	to	PART
easat-2635	68	15	find	find	VERB
easat-2635	68	16	alternative	alternative	ADJ
easat-2635	68	17	and	and	CCONJ
easat-2635	68	18	distinct	distinct	ADJ
easat-2635	68	19	solutions	solution	NOUN
easat-2635	68	20	to	to	ADP
easat-2635	68	21	the	the	DET
easat-2635	68	22	same	same	ADJ
easat-2635	68	23	problem	problem	NOUN
easat-2635	68	24	.	.	PUNCT
easat-2635	69	1	not	not	PART
easat-2635	69	2	many	many	ADJ
easat-2635	69	3	costs	cost	NOUN
easat-2635	69	4	were	be	AUX
easat-2635	69	5	involved	involve	VERB
easat-2635	69	6	since	since	SCONJ
easat-2635	69	7	memoranda	memorandum	NOUN
easat-2635	69	8	were	be	AUX
easat-2635	69	9	selected	select	VERB
easat-2635	69	10	from	from	ADP
easat-2635	69	11	past	past	ADJ
easat-2635	69	12	examination	examination	NOUN
easat-2635	69	13	papers	paper	NOUN
easat-2635	69	14	online	online	ADV
easat-2635	69	15	.	.	PUNCT
easat-2635	70	1	the	the	DET
easat-2635	70	2	authors	author	NOUN
easat-2635	70	3	are	be	AUX
easat-2635	70	4	aware	aware	ADJ
easat-2635	70	5	that	that	SCONJ
easat-2635	70	6	the	the	DET
easat-2635	70	7	result	result	NOUN
easat-2635	70	8	can	can	AUX
easat-2635	70	9	not	not	PART
easat-2635	70	10	be	be	AUX
easat-2635	70	11	generalized	generalize	VERB
easat-2635	70	12	since	since	SCONJ
easat-2635	70	13	not	not	PART
easat-2635	70	14	all	all	DET
easat-2635	70	15	past	past	ADJ
easat-2635	70	16	examination	examination	NOUN
easat-2635	70	17	memoranda	memoranda	NOUN
easat-2635	70	18	were	be	AUX
easat-2635	70	19	analyzed	analyze	VERB
easat-2635	70	20	.	.	PUNCT
easat-2635	71	1	the	the	DET
easat-2635	71	2	analysis	analysis	NOUN
easat-2635	71	3	was	be	AUX
easat-2635	71	4	done	do	VERB
easat-2635	71	5	to	to	PART
easat-2635	71	6	check	check	VERB
easat-2635	71	7	whether	whether	SCONJ
easat-2635	71	8	all	all	DET
easat-2635	71	9	the	the	DET
easat-2635	71	10	options	option	NOUN
easat-2635	71	11	that	that	PRON
easat-2635	71	12	were	be	AUX
easat-2635	71	13	supposed	suppose	VERB
easat-2635	71	14	to	to	PART
easat-2635	71	15	be	be	AUX
easat-2635	71	16	given	give	VERB
easat-2635	71	17	for	for	ADP
easat-2635	71	18	every	every	DET
easat-2635	71	19	euclidean	euclidean	ADJ
easat-2635	71	20	geometry	geometry	NOUN
easat-2635	71	21	question	question	NOUN
easat-2635	71	22	appeared	appear	VERB
easat-2635	71	23	in	in	ADP
easat-2635	71	24	the	the	DET
easat-2635	71	25	memorandum	memorandum	NOUN
easat-2635	71	26	.	.	PUNCT
easat-2635	72	1	literature	literature	NOUN
easat-2635	72	2	was	be	AUX
easat-2635	72	3	also	also	ADV
easat-2635	72	4	carefully	carefully	ADV
easat-2635	72	5	reviewed	review	VERB
easat-2635	72	6	based	base	VERB
easat-2635	72	7	on	on	ADP
easat-2635	72	8	the	the	DET
easat-2635	72	9	problems	problem	NOUN
easat-2635	72	10	students	student	NOUN
easat-2635	72	11	come	come	VERB
easat-2635	72	12	across	across	ADP
easat-2635	72	13	with	with	ADP
easat-2635	72	14	when	when	SCONJ
easat-2635	72	15	solving	solve	VERB
easat-2635	72	16	euclidean	euclidean	ADJ
easat-2635	72	17	geometry	geometry	NOUN
easat-2635	72	18	problems	problem	NOUN
easat-2635	72	19	.	.	PUNCT
easat-2635	73	1	in	in	ADP
easat-2635	73	2	some	some	DET
easat-2635	73	3	memoranda	memoranda	NOUN
easat-2635	73	4	,	,	PUNCT
easat-2635	73	5	not	not	PART
easat-2635	73	6	all	all	DET
easat-2635	73	7	options	option	NOUN
easat-2635	73	8	were	be	AUX
easat-2635	73	9	given	give	VERB
easat-2635	73	10	.	.	PUNCT
easat-2635	74	1	figure	figure	NOUN
easat-2635	74	2	1	1	NUM
easat-2635	74	3	below	below	ADV
easat-2635	74	4	is	be	AUX
easat-2635	74	5	an	an	DET
easat-2635	74	6	example	example	NOUN
easat-2635	74	7	where	where	SCONJ
easat-2635	74	8	a	a	DET
easat-2635	74	9	grade	grade	NOUN
easat-2635	74	10	12	12	NUM
easat-2635	74	11	final	final	ADJ
easat-2635	74	12	examination	examination	NOUN
easat-2635	74	13	question	question	NOUN
easat-2635	74	14	with	with	ADP
easat-2635	74	15	different	different	ADJ
easat-2635	74	16	options	option	NOUN
easat-2635	74	17	for	for	ADP
easat-2635	74	18	a	a	DET
easat-2635	74	19	solution	solution	NOUN
easat-2635	74	20	and	and	CCONJ
easat-2635	74	21	a	a	DET
easat-2635	74	22	distinctly	distinctly	ADV
easat-2635	74	23	different	different	ADJ
easat-2635	74	24	solution	solution	NOUN
easat-2635	74	25	was	be	AUX
easat-2635	74	26	identified	identify	VERB
easat-2635	74	27	but	but	CCONJ
easat-2635	74	28	only	only	ADV
easat-2635	74	29	one	one	NUM
easat-2635	74	30	option	option	NOUN
easat-2635	74	31	was	be	AUX
easat-2635	74	32	shown	show	VERB
easat-2635	74	33	in	in	ADP
easat-2635	74	34	the	the	DET
easat-2635	74	35	memorandum	memorandum	NOUN
easat-2635	74	36	.	.	PUNCT
easat-2635	75	1	more	more	ADJ
easat-2635	75	2	options	option	NOUN
easat-2635	75	3	are	be	AUX
easat-2635	75	4	then	then	ADV
easat-2635	75	5	given	give	VERB
easat-2635	75	6	.	.	PUNCT
easat-2635	76	1	3	3	X
easat-2635	76	2	.	.	NOUN
easat-2635	76	3	results	result	NOUN
easat-2635	76	4	and	and	CCONJ
easat-2635	76	5	discussion	discussion	NOUN
easat-2635	76	6	for	for	ADP
easat-2635	76	7	the	the	DET
easat-2635	76	8	below	below	ADV
easat-2635	76	9	chosen	choose	VERB
easat-2635	76	10	euclidean	euclidean	ADJ
easat-2635	76	11	geometry	geometry	NOUN
easat-2635	76	12	item	item	NOUN
easat-2635	76	13	,	,	PUNCT
easat-2635	76	14	the	the	DET
easat-2635	76	15	examiner	examiner	NOUN
easat-2635	76	16	gave	give	VERB
easat-2635	76	17	one	one	NUM
easat-2635	76	18	answer	answer	NOUN
easat-2635	76	19	,	,	PUNCT
easat-2635	76	20	yet	yet	CCONJ
easat-2635	76	21	it	it	PRON
easat-2635	76	22	had	have	VERB
easat-2635	76	23	varied	varied	ADJ
easat-2635	76	24	approaches	approach	NOUN
easat-2635	76	25	and	and	CCONJ
easat-2635	76	26	at	at	ADV
easat-2635	76	27	least	least	ADJ
easat-2635	76	28	2	2	NUM
easat-2635	76	29	distinct	distinct	ADJ
easat-2635	76	30	solutions	solution	NOUN
easat-2635	76	31	depending	depend	VERB
easat-2635	76	32	on	on	ADP
easat-2635	76	33	the	the	DET
easat-2635	76	34	approach	approach	NOUN
easat-2635	76	35	used	use	VERB
easat-2635	76	36	to	to	PART
easat-2635	76	37	answer	answer	VERB
easat-2635	76	38	the	the	DET
easat-2635	76	39	question	question	NOUN
easat-2635	76	40	.	.	PUNCT
easat-2635	77	1	the	the	DET
easat-2635	77	2	examiner	examiner	NOUN
easat-2635	77	3	just	just	ADV
easat-2635	77	4	used	use	VERB
easat-2635	77	5	one	one	NUM
easat-2635	77	6	approach	approach	NOUN
easat-2635	77	7	and	and	CCONJ
easat-2635	77	8	got	get	VERB
easat-2635	77	9	one	one	NUM
easat-2635	77	10	answer	answer	NOUN
easat-2635	77	11	.	.	PUNCT
easat-2635	78	1	there	there	PRON
easat-2635	78	2	could	could	AUX
easat-2635	78	3	have	have	AUX
easat-2635	78	4	been	be	AUX
easat-2635	78	5	a	a	DET
easat-2635	78	6	situation	situation	NOUN
easat-2635	78	7	whereby	whereby	SCONJ
easat-2635	78	8	some	some	DET
easat-2635	78	9	students	student	NOUN
easat-2635	78	10	used	use	VERB
easat-2635	78	11	a	a	DET
easat-2635	78	12	different	different	ADJ
easat-2635	78	13	approach	approach	NOUN
easat-2635	78	14	from	from	ADP
easat-2635	78	15	what	what	PRON
easat-2635	78	16	was	be	AUX
easat-2635	78	17	shown	show	VERB
easat-2635	78	18	on	on	ADP
easat-2635	78	19	the	the	DET
easat-2635	78	20	memorandum	memorandum	NOUN
easat-2635	78	21	and	and	CCONJ
easat-2635	78	22	got	get	AUX
easat-2635	78	23	penalised	penalise	VERB
easat-2635	78	24	by	by	ADP
easat-2635	78	25	markers	marker	NOUN
easat-2635	78	26	which	which	PRON
easat-2635	78	27	disadvantaged	disadvantage	VERB
easat-2635	78	28	them	they	PRON
easat-2635	78	29	.	.	PUNCT
easat-2635	79	1	a	a	DET
easat-2635	79	2	distinct	distinct	ADJ
easat-2635	79	3	different	different	ADJ
easat-2635	79	4	answer	answer	NOUN
easat-2635	79	5	was	be	AUX
easat-2635	79	6	also	also	ADV
easat-2635	79	7	found	find	VERB
easat-2635	79	8	as	as	ADP
easat-2635	79	9	the	the	DET
easat-2635	79	10	solution	solution	NOUN
easat-2635	79	11	which	which	PRON
easat-2635	79	12	was	be	AUX
easat-2635	79	13	not	not	PART
easat-2635	79	14	presented	present	VERB
easat-2635	79	15	in	in	ADP
easat-2635	79	16	the	the	DET
easat-2635	79	17	memorandum	memorandum	NOUN
easat-2635	79	18	.	.	PUNCT
easat-2635	80	1	on	on	ADP
easat-2635	80	2	the	the	DET
easat-2635	80	3	other	other	ADJ
easat-2635	80	4	hand	hand	NOUN
easat-2635	80	5	,	,	PUNCT
easat-2635	80	6	assuming	assume	VERB
easat-2635	80	7	that	that	SCONJ
easat-2635	80	8	all	all	DET
easat-2635	80	9	the	the	DET
easat-2635	80	10	options	option	NOUN
easat-2635	80	11	were	be	AUX
easat-2635	80	12	there	there	ADV
easat-2635	80	13	on	on	ADP
easat-2635	80	14	the	the	DET
easat-2635	80	15	memorandum	memorandum	NOUN
easat-2635	80	16	,	,	PUNCT
easat-2635	80	17	were	be	AUX
easat-2635	80	18	the	the	DET
easat-2635	80	19	markers	marker	NOUN
easat-2635	80	20	going	go	VERB
easat-2635	80	21	to	to	PART
easat-2635	80	22	take	take	VERB
easat-2635	80	23	note	note	NOUN
easat-2635	80	24	of	of	ADP
easat-2635	80	25	all	all	PRON
easat-2635	80	26	of	of	ADP
easat-2635	80	27	them	they	PRON
easat-2635	80	28	or	or	CCONJ
easat-2635	80	29	they	they	PRON
easat-2635	80	30	were	be	AUX
easat-2635	80	31	still	still	ADV
easat-2635	80	32	going	go	VERB
easat-2635	80	33	to	to	PART
easat-2635	80	34	concentrate	concentrate	VERB
easat-2635	80	35	on	on	ADP
easat-2635	80	36	only	only	ADV
easat-2635	80	37	one	one	NUM
easat-2635	80	38	option	option	NOUN
easat-2635	80	39	that	that	PRON
easat-2635	80	40	they	they	PRON
easat-2635	80	41	thought	think	VERB
easat-2635	80	42	was	be	AUX
easat-2635	80	43	the	the	DET
easat-2635	80	44	most	most	ADV
easat-2635	80	45	appropriate	appropriate	ADJ
easat-2635	80	46	and	and	CCONJ
easat-2635	80	47	forget	forget	VERB
easat-2635	80	48	about	about	ADP
easat-2635	80	49	the	the	DET
easat-2635	80	50	rest	rest	NOUN
easat-2635	80	51	and	and	CCONJ
easat-2635	80	52	hence	hence	ADV
easat-2635	80	53	disadvantage	disadvantage	VERB
easat-2635	80	54	the	the	DET
easat-2635	80	55	students	student	NOUN
easat-2635	80	56	?	?	PUNCT
easat-2635	81	1	the	the	DET
easat-2635	81	2	memorandum	memorandum	NOUN
easat-2635	81	3	showed	show	VERB
easat-2635	81	4	the	the	DET
easat-2635	81	5	below	below	ADJ
easat-2635	81	6	option	option	NOUN
easat-2635	81	7	.	.	PUNCT
easat-2635	82	1	3.1	3.1	NUM
easat-2635	82	2	.	.	PUNCT
easat-2635	82	3	example	example	NOUN
easat-2635	82	4	of	of	ADP
easat-2635	82	5	the	the	DET
easat-2635	82	6	memorandum	memorandum	NOUN
easat-2635	82	7	this	this	DET
easat-2635	82	8	memorandum	memorandum	NOUN
easat-2635	82	9	was	be	AUX
easat-2635	82	10	taken	take	VERB
easat-2635	82	11	from	from	ADP
easat-2635	82	12	the	the	DET
easat-2635	82	13	education	education	NOUN
easat-2635	82	14	department	department	NOUN
easat-2635	82	15	in	in	ADP
easat-2635	82	16	south	south	PROPN
easat-2635	82	17	africa	africa	PROPN
easat-2635	82	18	.	.	PUNCT
easat-2635	83	1	(	(	PUNCT
easat-2635	83	2	5.44.1	5.44.1	NUM
easat-2635	83	3	mathematics	mathematics	NOUN
easat-2635	83	4	paper	paper	NOUN
easat-2635	83	5	2	2	NUM
easat-2635	83	6	memorandum	memorandum	NOUN
easat-2635	83	7	2021	2021	NUM
easat-2635	83	8	)	)	PUNCT
easat-2635	83	9	.	.	PUNCT
easat-2635	84	1	the	the	DET
easat-2635	84	2	memorandum	memorandum	NOUN
easat-2635	84	3	is	be	AUX
easat-2635	84	4	based	base	VERB
easat-2635	84	5	on	on	ADP
easat-2635	84	6	the	the	DET
easat-2635	84	7	question	question	NOUN
easat-2635	84	8	,	,	PUNCT
easat-2635	84	9	where	where	SCONJ
easat-2635	84	10	learners	learner	NOUN
easat-2635	84	11	had	have	VERB
easat-2635	84	12	to	to	PART
easat-2635	84	13	determine	determine	VERB
easat-2635	84	14	,	,	PUNCT
easat-2635	84	15	with	with	ADP
easat-2635	84	16	reasons	reason	NOUN
easat-2635	84	17	,	,	PUNCT
easat-2635	84	18	the	the	DET
easat-2635	84	19	size	size	NOUN
easat-2635	84	20	of	of	ADP
easat-2635	84	21	a	a	DET
easat-2635	84	22	particular	particular	ADJ
easat-2635	84	23	angle	angle	NOUN
easat-2635	84	24	in	in	ADP
easat-2635	84	25	terms	term	NOUN
easat-2635	84	26	of	of	ADP
easat-2635	84	27	a	a	DET
easat-2635	84	28	given	give	VERB
easat-2635	84	29	variable	variable	NOUN
easat-2635	84	30	.	.	PUNCT
easat-2635	85	1	the	the	DET
easat-2635	85	2	figure	figure	NOUN
easat-2635	85	3	below	below	ADV
easat-2635	85	4	was	be	AUX
easat-2635	85	5	provided	provide	VERB
easat-2635	85	6	to	to	PART
easat-2635	85	7	help	help	VERB
easat-2635	85	8	learners	learner	NOUN
easat-2635	85	9	determine	determine	VERB
easat-2635	85	10	the	the	DET
easat-2635	85	11	angle	angle	NOUN
easat-2635	85	12	,	,	PUNCT
easat-2635	85	13	and	and	CCONJ
easat-2635	85	14	from	from	ADP
easat-2635	85	15	the	the	DET
easat-2635	85	16	diagram	diagram	NOUN
easat-2635	85	17	,	,	PUNCT
easat-2635	85	18	the	the	DET
easat-2635	85	19	angle	angle	NOUN
easat-2635	85	20	is	be	AUX
easat-2635	85	21	m1	m1	PROPN
easat-2635	85	22	which	which	PRON
easat-2635	85	23	was	be	AUX
easat-2635	85	24	to	to	PART
easat-2635	85	25	be	be	AUX
easat-2635	85	26	determined	determine	VERB
easat-2635	85	27	in	in	ADP
easat-2635	85	28	terms	term	NOUN
easat-2635	85	29	x.	x.	NOUN
easat-2635	85	30	2934	2934	NUM
easat-2635	85	31	edelweiss	edelweiss	PROPN
easat-2635	85	32	applied	apply	VERB
easat-2635	85	33	science	science	NOUN
easat-2635	85	34	and	and	CCONJ
easat-2635	85	35	technology	technology	NOUN
easat-2635	85	36	issn	issn	PROPN
easat-2635	85	37	:	:	PUNCT
easat-2635	85	38	2576	2576	NUM
easat-2635	85	39	-	-	SYM
easat-2635	85	40	8484	8484	NUM
easat-2635	85	41	vol	vol	NOUN
easat-2635	85	42	.	.	PROPN
easat-2635	86	1	8	8	NUM
easat-2635	86	2	,	,	PUNCT
easat-2635	86	3	no	no	INTJ
easat-2635	86	4	.	.	NOUN
easat-2635	87	1	6	6	NUM
easat-2635	87	2	:	:	SYM
easat-2635	87	3	2931	2931	NUM
easat-2635	87	4	-	-	SYM
easat-2635	87	5	2936	2936	NUM
easat-2635	87	6	,	,	PUNCT
easat-2635	87	7	2024	2024	NUM
easat-2635	87	8	doi	doi	NOUN
easat-2635	87	9	:	:	PUNCT
easat-2635	87	10	10.55214/25768484.v8i6.2635	10.55214/25768484.v8i6.2635	NUM
easat-2635	87	11	©	©	PROPN
easat-2635	87	12	2024	2024	NUM
easat-2635	87	13	by	by	ADP
easat-2635	87	14	the	the	DET
easat-2635	87	15	authors	author	NOUN
easat-2635	87	16	;	;	PUNCT
easat-2635	87	17	licensee	licensee	PROPN
easat-2635	87	18	learning	learn	VERB
easat-2635	87	19	gate	gate	NOUN
easat-2635	87	20	figure	figure	NOUN
easat-2635	87	21	1	1	NUM
easat-2635	87	22	.	.	PUNCT
easat-2635	88	1	the	the	DET
easat-2635	88	2	geometry	geometry	NOUN
easat-2635	88	3	of	of	ADP
easat-2635	88	4	the	the	DET
easat-2635	88	5	problem	problem	NOUN
easat-2635	88	6	(	(	PUNCT
easat-2635	88	7	mathematics	mathematics	NOUN
easat-2635	88	8	paper	paper	NOUN
easat-2635	88	9	2	2	NUM
easat-2635	88	10	memorandum	memorandum	NOUN
easat-2635	88	11	2021	2021	NUM
easat-2635	88	12	)	)	PUNCT
easat-2635	88	13	.	.	PUNCT
easat-2635	89	1	this	this	PRON
easat-2635	89	2	is	be	AUX
easat-2635	89	3	an	an	DET
easat-2635	89	4	extract	extract	NOUN
easat-2635	89	5	of	of	ADP
easat-2635	89	6	the	the	DET
easat-2635	89	7	solution	solution	NOUN
easat-2635	89	8	route	route	NOUN
easat-2635	89	9	to	to	ADP
easat-2635	89	10	the	the	DET
easat-2635	89	11	first	first	ADJ
easat-2635	89	12	different	different	ADJ
easat-2635	89	13	answer	answer	NOUN
easat-2635	89	14	to	to	ADP
easat-2635	89	15	the	the	DET
easat-2635	89	16	problem	problem	NOUN
easat-2635	89	17	,	,	PUNCT
easat-2635	89	18	the	the	DET
easat-2635	89	19	actual	actual	ADJ
easat-2635	89	20	problem	problem	NOUN
easat-2635	89	21	is	be	AUX
easat-2635	89	22	:	:	PUNCT
easat-2635	89	23	determine	determine	VERB
easat-2635	89	24	,	,	PUNCT
easat-2635	89	25	giving	give	VERB
easat-2635	89	26	reasons	reason	NOUN
easat-2635	89	27	,	,	PUNCT
easat-2635	89	28	the	the	DET
easat-2635	89	29	size	size	NOUN
easat-2635	89	30	of	of	ADP
easat-2635	89	31	𝑀1̂	𝑀1̂	PROPN
easat-2635	89	32	,	,	PUNCT
easat-2635	89	33	𝑖𝑛	𝑖𝑛	DET
easat-2635	89	34	𝑡𝑒𝑟𝑚𝑠	𝑡𝑒𝑟𝑚𝑠	NOUN
easat-2635	89	35	𝑜𝑓	𝑜𝑓	ADP
easat-2635	89	36	𝑥.	𝑥.	PRON
easat-2635	89	37	(	(	PUNCT
easat-2635	89	38	mathematics	mathematic	NOUN
easat-2635	89	39	paper	paper	NOUN
easat-2635	89	40	2	2	NUM
easat-2635	89	41	memorandum	memorandum	NOUN
easat-2635	89	42	2021	2021	NUM
easat-2635	89	43	)	)	PUNCT
easat-2635	89	44	.	.	PUNCT
easat-2635	90	1	memorandum	memorandum	NOUN
easat-2635	90	2	solution	solution	NOUN
easat-2635	90	3	(	(	PUNCT
easat-2635	90	4	mathematics	mathematics	NOUN
easat-2635	90	5	paper	paper	NOUN
easat-2635	90	6	2	2	NUM
easat-2635	90	7	memorandum	memorandum	NOUN
easat-2635	90	8	2021	2021	NUM
easat-2635	90	9	):	):	PUNCT
easat-2635	91	1	𝐴1̂	𝐴1̂	PROPN
easat-2635	91	2	=	=	PUNCT
easat-2635	91	3	90	90	NUM
easat-2635	91	4	°	°	NUM
easat-2635	91	5	−	−	PROPN
easat-2635	92	1	𝑥	𝑥	PRON
easat-2635	93	1	[	[	X
easat-2635	93	2	𝑠𝑢𝑚	𝑠𝑢𝑚	NOUN
easat-2635	93	3	𝑜𝑓	𝑜𝑓	INTJ
easat-2635	93	4	∠𝑠	∠𝑠	ADP
easat-2635	93	5	𝑖𝑛∆	𝑖𝑛∆	PROPN
easat-2635	93	6	]	]	PUNCT
easat-2635	93	7	∴	∴	NOUN
easat-2635	93	8	𝑀1̂	𝑀1̂	PROPN
easat-2635	93	9	=	=	PROPN
easat-2635	93	10	180	180	NUM
easat-2635	93	11	°	°	NOUN
easat-2635	93	12	−	−	PROPN
easat-2635	93	13	2𝑥	2𝑥	NOUN
easat-2635	93	14	[	[	X
easat-2635	93	15	∠𝑎𝑡	∠𝑎𝑡	NUM
easat-2635	93	16	𝑐𝑒𝑛𝑡𝑟𝑒	𝑐𝑒𝑛𝑡𝑟𝑒	NOUN
easat-2635	93	17	=	=	SYM
easat-2635	93	18	2	2	NUM
easat-2635	93	19	×	×	NOUN
easat-2635	93	20	𝑎𝑡	𝑎𝑡	ADP
easat-2635	93	21	𝑐𝑖𝑟𝑐𝑢𝑚𝑓.	𝑐𝑖𝑟𝑐𝑢𝑚𝑓.	NOUN
easat-2635	93	22	]	]	PUNCT
easat-2635	94	1	the	the	DET
easat-2635	94	2	other	other	ADJ
easat-2635	94	3	routes	route	NOUN
easat-2635	94	4	to	to	ADP
easat-2635	94	5	the	the	DET
easat-2635	94	6	possible	possible	ADJ
easat-2635	94	7	options	option	NOUN
easat-2635	94	8	not	not	PART
easat-2635	94	9	in	in	ADP
easat-2635	94	10	the	the	DET
easat-2635	94	11	memorandum	memorandum	NOUN
easat-2635	94	12	provided	provide	VERB
easat-2635	94	13	by	by	ADP
easat-2635	94	14	the	the	DET
easat-2635	94	15	authors	author	NOUN
easat-2635	94	16	are	be	AUX
easat-2635	94	17	as	as	SCONJ
easat-2635	94	18	follows	follow	VERB
easat-2635	94	19	:	:	PUNCT
easat-2635	94	20	suppose	suppose	VERB
easat-2635	94	21	𝐺	𝐺	PROPN
easat-2635	94	22	is	be	AUX
easat-2635	94	23	the	the	DET
easat-2635	94	24	intersection	intersection	NOUN
easat-2635	94	25	point	point	NOUN
easat-2635	94	26	of	of	ADP
easat-2635	94	27	ad	ad	NOUN
easat-2635	94	28	and	and	CCONJ
easat-2635	94	29	be	be	AUX
easat-2635	94	30	.	.	PUNCT
easat-2635	95	1	𝐶	𝐶	PROPN
easat-2635	95	2	�	�	PROPN
easat-2635	95	3	̂	̂	NOUN
easat-2635	95	4	�	�	NOUN
easat-2635	95	5	𝐷	𝐷	NOUN
easat-2635	95	6	=	=	NOUN
easat-2635	95	7	90	90	NUM
easat-2635	95	8	°	°	NUM
easat-2635	95	9	(∠	(∠	PROPN
easat-2635	95	10	𝑖𝑛	𝑖𝑛	NOUN
easat-2635	95	11	𝑠𝑒𝑚𝑖	𝑠𝑒𝑚𝑖	PROPN
easat-2635	95	12	−	−	PROPN
easat-2635	95	13	𝑐𝑖𝑟𝑐𝑙𝑒	𝑐𝑖𝑟𝑐𝑙𝑒	PROPN
easat-2635	95	14	)	)	PUNCT
easat-2635	96	1	=	=	SYM
easat-2635	96	2	𝐴𝐺𝐸	𝐴𝐺𝐸	PROPN
easat-2635	96	3	(	(	PUNCT
easat-2635	96	4	𝑀𝐵	𝑀𝐵	PROPN
easat-2635	96	5	𝑓𝑟𝑜𝑚	𝑓𝑟𝑜𝑚	PROPN
easat-2635	96	6	𝑐𝑒𝑛𝑡𝑟𝑒	𝑐𝑒𝑛𝑡𝑟𝑒	NOUN
easat-2635	96	7	⊥	⊥	NUM
easat-2635	96	8	𝑐ℎ𝑜𝑟𝑑	𝑐ℎ𝑜𝑟𝑑	PROPN
easat-2635	96	9	)	)	PUNCT
easat-2635	96	10	.	.	PUNCT
easat-2635	97	1	∴	∴	PROPN
easat-2635	97	2	𝐴𝐶	𝐴𝐶	PROPN
easat-2635	97	3	∥	∥	PUNCT
easat-2635	97	4	𝐵𝐸	𝐵𝐸	PROPN
easat-2635	97	5	∴	∴	NOUN
easat-2635	97	6	𝑀1̂	𝑀1̂	NOUN
easat-2635	97	7	=	=	SYM
easat-2635	97	8	𝑥	𝑥	PROPN
easat-2635	97	9	(	(	PUNCT
easat-2635	97	10	𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑛𝑔∠𝑠	𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑛𝑔∠𝑠	NOUN
easat-2635	97	11	)	)	PUNCT
easat-2635	97	12	or	or	CCONJ
easat-2635	97	13	comparing	compare	VERB
easat-2635	97	14	∆𝑠	∆𝑠	PROPN
easat-2635	97	15	𝐴𝐶𝐷	𝐴𝐶𝐷	PROPN
easat-2635	97	16	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
easat-2635	97	17	𝐴𝐶𝐹	𝐴𝐶𝐹	PROPN
easat-2635	97	18	:	:	PUNCT
easat-2635	97	19	𝐶	𝐶	PROPN
easat-2635	97	20	�	�	PROPN
easat-2635	97	21	̂	̂	VERB
easat-2635	97	22	�	�	NOUN
easat-2635	97	23	𝐷	𝐷	NOUN
easat-2635	97	24	=	=	NOUN
easat-2635	97	25	90	90	NUM
easat-2635	97	26	°	°	X
easat-2635	97	27	=	=	PUNCT
easat-2635	97	28	𝐶	𝐶	PROPN
easat-2635	97	29	�	�	PROPN
easat-2635	97	30	̂	̂	NOUN
easat-2635	97	31	�	�	NOUN
easat-2635	97	32	𝐴	𝐴	NOUN
easat-2635	97	33	𝑎𝑛𝑑	𝑎𝑛𝑑	VERB
easat-2635	97	34	𝑥	𝑥	PROPN
easat-2635	97	35	𝑖𝑠	𝑖𝑠	NOUN
easat-2635	97	36	𝑐𝑜𝑚𝑚𝑜𝑛	𝑐𝑜𝑚𝑚𝑜𝑛	NOUN
easat-2635	97	37	∴	∴	PROPN
easat-2635	97	38	𝐴1̂	𝐴1̂	PROPN
easat-2635	97	39	=	=	SYM
easat-2635	97	40	�	�	PROPN
easat-2635	97	41	̂	̂	NOUN
easat-2635	97	42	�	�	NOUN
easat-2635	97	43	(remaining	(remaining	NOUN
easat-2635	97	44	∠𝑠	∠𝑠	VERB
easat-2635	97	45	)	)	PUNCT
easat-2635	97	46	in	in	ADP
easat-2635	97	47	∆𝐺𝑀𝐷	∆𝐺𝑀𝐷	PROPN
easat-2635	97	48	𝑀3̂	𝑀3̂	NOUN
easat-2635	97	49	=	=	PUNCT
easat-2635	97	50	180	180	NUM
easat-2635	97	51	°	°	NUM
easat-2635	97	52	−	−	PROPN
easat-2635	97	53	(	(	PUNCT
easat-2635	97	54	90	90	NUM
easat-2635	97	55	°	°	NOUN
easat-2635	97	56	+	+	CCONJ
easat-2635	97	57	�	�	PROPN
easat-2635	97	58	̂	̂	NOUN
easat-2635	97	59	�	�	NOUN
easat-2635	97	60	)	)	PUNCT
easat-2635	97	61	=	=	NOUN
easat-2635	97	62	180	180	NUM
easat-2635	97	63	°	°	NUM
easat-2635	97	64	−	−	PROPN
easat-2635	97	65	(	(	PUNCT
easat-2635	97	66	90	90	NUM
easat-2635	97	67	°	°	NOUN
easat-2635	97	68	+	+	CCONJ
easat-2635	98	1	𝐴1̂	𝐴1̂	ADJ
easat-2635	98	2	)	)	PUNCT
easat-2635	98	3	=	=	SYM
easat-2635	99	1	90	90	NUM
easat-2635	99	2	°	°	NUM
easat-2635	99	3	−	−	PROPN
easat-2635	100	1	𝐴1̂	𝐴1̂	NOUN
easat-2635	100	2	=	=	PUNCT
easat-2635	100	3	𝑥.	𝑥.	PROPN
easat-2635	100	4	but	but	CCONJ
easat-2635	100	5	𝑀3̂	𝑀3̂	NOUN
easat-2635	100	6	=	=	PUNCT
easat-2635	100	7	𝑀1̂(𝑣𝑒𝑟𝑡.	𝑀1̂(𝑣𝑒𝑟𝑡.	PROPN
easat-2635	100	8	𝑜𝑝𝑝.	𝑜𝑝𝑝.	X
easat-2635	100	9	∠𝑠	∠𝑠	X
easat-2635	100	10	)	)	PUNCT
easat-2635	100	11	∴	∴	NOUN
easat-2635	100	12	𝑀1̂	𝑀1̂	PROPN
easat-2635	101	1	=	=	PUNCT
easat-2635	101	2	𝑥.	𝑥.	PROPN
easat-2635	101	3	or	or	CCONJ
easat-2635	101	4	𝐶	𝐶	PROPN
easat-2635	101	5	�	�	PROPN
easat-2635	101	6	̂	̂	NOUN
easat-2635	101	7	�	�	NOUN
easat-2635	101	8	𝐷	𝐷	NOUN
easat-2635	101	9	=	=	NOUN
easat-2635	101	10	90	90	NUM
easat-2635	101	11	°	°	NUM
easat-2635	101	12	(∠	(∠	PROPN
easat-2635	101	13	𝑖𝑛	𝑖𝑛	NOUN
easat-2635	101	14	𝑠𝑒𝑚𝑖	𝑠𝑒𝑚𝑖	PROPN
easat-2635	101	15	−	−	PROPN
easat-2635	101	16	𝑐𝑖𝑟𝑐𝑙𝑒	𝑐𝑖𝑟𝑐𝑙𝑒	PROPN
easat-2635	101	17	)	)	PUNCT
easat-2635	101	18	=	=	SYM
easat-2635	101	19	𝐴𝐺𝐸	𝐴𝐺𝐸	PROPN
easat-2635	101	20	(	(	PUNCT
easat-2635	101	21	𝑀𝐵	𝑀𝐵	PROPN
easat-2635	101	22	𝑓𝑟𝑜𝑚	𝑓𝑟𝑜𝑚	PROPN
easat-2635	101	23	𝑐𝑒𝑛𝑡𝑟𝑒	𝑐𝑒𝑛𝑡𝑟𝑒	NOUN
easat-2635	101	24	⊥	⊥	NUM
easat-2635	101	25	𝑐ℎ𝑜𝑟𝑑	𝑐ℎ𝑜𝑟𝑑	PROPN
easat-2635	101	26	)	)	PUNCT
easat-2635	101	27	.	.	PUNCT
easat-2635	102	1	∴	∴	PROPN
easat-2635	102	2	𝐴𝐶	𝐴𝐶	PROPN
easat-2635	102	3	∥	∥	PUNCT
easat-2635	102	4	𝐵𝐸	𝐵𝐸	PROPN
easat-2635	102	5	.	.	PUNCT
easat-2635	103	1	this	this	PRON
easat-2635	103	2	implies	imply	VERB
easat-2635	103	3	𝑀1̂	𝑀1̂	PROPN
easat-2635	103	4	=	=	SYM
easat-2635	103	5	𝑀3̂(vertically	𝑀3̂(vertically	ADV
easat-2635	103	6	opposite	opposite	ADJ
easat-2635	103	7	)	)	PUNCT
easat-2635	103	8	=	=	SYM
easat-2635	103	9	𝑥	𝑥	PROPN
easat-2635	103	10	(	(	PUNCT
easat-2635	103	11	𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔	𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔	VERB
easat-2635	103	12	∠𝑠	∠𝑠	NOUN
easat-2635	103	13	)	)	PUNCT
easat-2635	103	14	different	different	ADJ
easat-2635	103	15	options	option	NOUN
easat-2635	103	16	which	which	PRON
easat-2635	103	17	include	include	VERB
easat-2635	103	18	a	a	DET
easat-2635	103	19	distinct	distinct	ADJ
easat-2635	103	20	different	different	ADJ
easat-2635	103	21	solution	solution	NOUN
easat-2635	103	22	which	which	PRON
easat-2635	103	23	did	do	AUX
easat-2635	103	24	not	not	PART
easat-2635	103	25	appear	appear	VERB
easat-2635	103	26	in	in	ADP
easat-2635	103	27	the	the	DET
easat-2635	103	28	memorandum	memorandum	NOUN
easat-2635	103	29	were	be	AUX
easat-2635	103	30	given	give	VERB
easat-2635	103	31	.	.	PUNCT
easat-2635	104	1	this	this	PRON
easat-2635	104	2	strengthens	strengthen	VERB
easat-2635	104	3	the	the	DET
easat-2635	104	4	argument	argument	NOUN
easat-2635	104	5	of	of	ADP
easat-2635	104	6	the	the	DET
easat-2635	104	7	authors	author	NOUN
easat-2635	104	8	that	that	PRON
easat-2635	104	9	giving	give	VERB
easat-2635	104	10	only	only	ADV
easat-2635	104	11	one	one	NUM
easat-2635	104	12	solution	solution	NOUN
easat-2635	104	13	where	where	SCONJ
easat-2635	104	14	there	there	PRON
easat-2635	104	15	is	be	VERB
easat-2635	104	16	a	a	DET
easat-2635	104	17	possibility	possibility	NOUN
easat-2635	104	18	of	of	ADP
easat-2635	104	19	distinct	distinct	ADJ
easat-2635	104	20	different	different	ADJ
easat-2635	104	21	solutions	solution	NOUN
easat-2635	104	22	shows	show	VERB
easat-2635	104	23	that	that	SCONJ
easat-2635	104	24	learners	learner	NOUN
easat-2635	104	25	who	who	PRON
easat-2635	104	26	gave	give	VERB
easat-2635	104	27	different	different	ADJ
easat-2635	104	28	correct	correct	ADJ
easat-2635	104	29	solution	solution	NOUN
easat-2635	104	30	with	with	ADP
easat-2635	104	31	different	different	ADJ
easat-2635	104	32	approach	approach	NOUN
easat-2635	104	33	may	may	AUX
easat-2635	104	34	be	be	AUX
easat-2635	104	35	disadvantaged	disadvantage	VERB
easat-2635	104	36	.	.	PUNCT
easat-2635	105	1	it	it	PRON
easat-2635	105	2	could	could	AUX
easat-2635	105	3	be	be	AUX
easat-2635	105	4	that	that	SCONJ
easat-2635	105	5	the	the	DET
easat-2635	105	6	examiner	examiner	NOUN
easat-2635	105	7	knew	know	VERB
easat-2635	105	8	the	the	DET
easat-2635	105	9	other	other	ADJ
easat-2635	105	10	options	option	NOUN
easat-2635	105	11	and	and	CCONJ
easat-2635	105	12	just	just	ADV
easat-2635	105	13	thought	think	VERB
easat-2635	105	14	that	that	SCONJ
easat-2635	105	15	the	the	DET
easat-2635	105	16	option	option	NOUN
easat-2635	105	17	used	use	VERB
easat-2635	105	18	in	in	ADP
easat-2635	105	19	the	the	DET
easat-2635	105	20	memorandum	memorandum	NOUN
easat-2635	105	21	was	be	AUX
easat-2635	105	22	the	the	DET
easat-2635	105	23	obvious	obvious	ADJ
easat-2635	105	24	and	and	CCONJ
easat-2635	105	25	best	good	ADJ
easat-2635	105	26	for	for	ADP
easat-2635	105	27	the	the	DET
easat-2635	105	28	learners	learner	NOUN
easat-2635	105	29	or	or	CCONJ
easat-2635	105	30	it	it	PRON
easat-2635	105	31	may	may	AUX
easat-2635	105	32	be	be	AUX
easat-2635	105	33	that	that	SCONJ
easat-2635	105	34	the	the	DET
easat-2635	105	35	examiner	examiner	NOUN
easat-2635	105	36	did	do	AUX
easat-2635	105	37	not	not	PART
easat-2635	105	38	think	think	VERB
easat-2635	105	39	about	about	ADP
easat-2635	105	40	other	other	ADJ
easat-2635	105	41	options	option	NOUN
easat-2635	105	42	.	.	PUNCT
easat-2635	106	1	learners	learner	NOUN
easat-2635	106	2	who	who	PRON
easat-2635	106	3	wrote	write	VERB
easat-2635	106	4	grade	grade	NOUN
easat-2635	106	5	12	12	NUM
easat-2635	106	6	2935	2935	NUM
easat-2635	106	7	edelweiss	edelweiss	PROPN
easat-2635	106	8	applied	apply	VERB
easat-2635	106	9	science	science	NOUN
easat-2635	106	10	and	and	CCONJ
easat-2635	106	11	technology	technology	NOUN
easat-2635	106	12	issn	issn	PROPN
easat-2635	106	13	:	:	PUNCT
easat-2635	106	14	2576	2576	NUM
easat-2635	106	15	-	-	SYM
easat-2635	106	16	8484	8484	NUM
easat-2635	106	17	vol	vol	NOUN
easat-2635	106	18	.	.	PROPN
easat-2635	106	19	8	8	NUM
easat-2635	106	20	,	,	PUNCT
easat-2635	106	21	no	no	INTJ
easat-2635	106	22	.	.	NOUN
easat-2635	107	1	6	6	NUM
easat-2635	107	2	:	:	SYM
easat-2635	107	3	2931	2931	NUM
easat-2635	107	4	-	-	SYM
easat-2635	107	5	2936	2936	NUM
easat-2635	107	6	,	,	PUNCT
easat-2635	107	7	2024	2024	NUM
easat-2635	107	8	doi	doi	NOUN
easat-2635	107	9	:	:	PUNCT
easat-2635	107	10	10.55214/25768484.v8i6.2635	10.55214/25768484.v8i6.2635	NUM
easat-2635	107	11	©	©	PROPN
easat-2635	107	12	2024	2024	NUM
easat-2635	107	13	by	by	ADP
easat-2635	107	14	the	the	DET
easat-2635	107	15	authors	author	NOUN
easat-2635	107	16	;	;	PUNCT
easat-2635	107	17	licensee	licensee	PROPN
easat-2635	107	18	learning	learn	VERB
easat-2635	107	19	gate	gate	NOUN
easat-2635	107	20	examinations	examination	NOUN
easat-2635	107	21	in	in	ADP
easat-2635	107	22	that	that	DET
easat-2635	107	23	particular	particular	ADJ
easat-2635	107	24	year	year	NOUN
easat-2635	107	25	might	might	AUX
easat-2635	107	26	have	have	AUX
easat-2635	107	27	been	be	AUX
easat-2635	107	28	disadvantaged	disadvantage	VERB
easat-2635	107	29	in	in	ADP
easat-2635	107	30	this	this	DET
easat-2635	107	31	question	question	NOUN
easat-2635	107	32	if	if	SCONJ
easat-2635	107	33	they	they	PRON
easat-2635	107	34	used	use	VERB
easat-2635	107	35	one	one	NUM
easat-2635	107	36	of	of	ADP
easat-2635	107	37	the	the	DET
easat-2635	107	38	above	above	ADJ
easat-2635	107	39	options	option	NOUN
easat-2635	107	40	which	which	PRON
easat-2635	107	41	were	be	AUX
easat-2635	107	42	not	not	PART
easat-2635	107	43	in	in	ADP
easat-2635	107	44	the	the	DET
easat-2635	107	45	memorandum	memorandum	NOUN
easat-2635	107	46	.	.	PUNCT
easat-2635	108	1	normally	normally	ADV
easat-2635	108	2	during	during	ADP
easat-2635	108	3	marking	mark	VERB
easat-2635	108	4	,	,	PUNCT
easat-2635	108	5	markers	marker	NOUN
easat-2635	108	6	have	have	VERB
easat-2635	108	7	a	a	DET
easat-2635	108	8	lot	lot	NOUN
easat-2635	108	9	of	of	ADP
easat-2635	108	10	scripts	script	NOUN
easat-2635	108	11	to	to	PART
easat-2635	108	12	mark	mark	VERB
easat-2635	108	13	so	so	SCONJ
easat-2635	108	14	they	they	PRON
easat-2635	108	15	do	do	AUX
easat-2635	108	16	not	not	PART
easat-2635	108	17	have	have	VERB
easat-2635	108	18	time	time	NOUN
easat-2635	108	19	to	to	PART
easat-2635	108	20	work	work	VERB
easat-2635	108	21	out	out	ADP
easat-2635	108	22	other	other	ADJ
easat-2635	108	23	options	option	NOUN
easat-2635	108	24	during	during	ADP
easat-2635	108	25	marking	mark	VERB
easat-2635	108	26	time	time	NOUN
easat-2635	108	27	.	.	PUNCT
easat-2635	109	1	whatever	whatever	PRON
easat-2635	109	2	is	be	AUX
easat-2635	109	3	not	not	PART
easat-2635	109	4	in	in	ADP
easat-2635	109	5	the	the	DET
easat-2635	109	6	memorandum	memorandum	NOUN
easat-2635	109	7	they	they	PRON
easat-2635	109	8	do	do	AUX
easat-2635	109	9	not	not	PART
easat-2635	109	10	consider	consider	VERB
easat-2635	109	11	it	it	PRON
easat-2635	109	12	.	.	PUNCT
easat-2635	110	1	this	this	PRON
easat-2635	110	2	could	could	AUX
easat-2635	110	3	be	be	AUX
easat-2635	110	4	one	one	NUM
easat-2635	110	5	of	of	ADP
easat-2635	110	6	the	the	DET
easat-2635	110	7	factors	factor	NOUN
easat-2635	110	8	leading	lead	VERB
easat-2635	110	9	to	to	ADP
easat-2635	110	10	underachievement	underachievement	NOUN
easat-2635	110	11	at	at	ADP
easat-2635	110	12	grade	grade	NOUN
easat-2635	110	13	12	12	NUM
easat-2635	110	14	.	.	PUNCT
easat-2635	111	1	4	4	NUM
easat-2635	111	2	.	.	X
easat-2635	111	3	conclusion	conclusion	NOUN
easat-2635	111	4	in	in	ADP
easat-2635	111	5	this	this	DET
easat-2635	111	6	article	article	NOUN
easat-2635	111	7	,	,	PUNCT
easat-2635	111	8	the	the	DET
easat-2635	111	9	authors	author	NOUN
easat-2635	111	10	investigated	investigate	VERB
easat-2635	111	11	different	different	ADJ
easat-2635	111	12	answers	answer	NOUN
easat-2635	111	13	to	to	ADP
easat-2635	111	14	one	one	NUM
easat-2635	111	15	euclidean	euclidean	ADJ
easat-2635	111	16	geometry	geometry	NOUN
easat-2635	111	17	problem	problem	NOUN
easat-2635	111	18	where	where	SCONJ
easat-2635	111	19	an	an	DET
easat-2635	111	20	example	example	NOUN
easat-2635	111	21	of	of	ADP
easat-2635	111	22	a	a	DET
easat-2635	111	23	memorandum	memorandum	NOUN
easat-2635	111	24	in	in	ADP
easat-2635	111	25	one	one	NUM
easat-2635	111	26	grade	grade	NOUN
easat-2635	111	27	12	12	NUM
easat-2635	111	28	mathematics	mathematic	NOUN
easat-2635	111	29	examination	examination	NOUN
easat-2635	111	30	was	be	AUX
easat-2635	111	31	considered	consider	VERB
easat-2635	111	32	.	.	PUNCT
easat-2635	112	1	alternative	alternative	ADJ
easat-2635	112	2	approaches	approach	NOUN
easat-2635	112	3	to	to	ADP
easat-2635	112	4	solutions	solution	NOUN
easat-2635	112	5	not	not	PART
easat-2635	112	6	given	give	VERB
easat-2635	112	7	in	in	ADP
easat-2635	112	8	the	the	DET
easat-2635	112	9	memorandum	memorandum	NOUN
easat-2635	112	10	,	,	PUNCT
easat-2635	112	11	including	include	VERB
easat-2635	112	12	the	the	DET
easat-2635	112	13	one	one	NOUN
easat-2635	112	14	for	for	ADP
easat-2635	112	15	a	a	DET
easat-2635	112	16	distinctly	distinctly	ADV
easat-2635	112	17	different	different	ADJ
easat-2635	112	18	solution	solution	NOUN
easat-2635	112	19	were	be	AUX
easat-2635	112	20	given	give	VERB
easat-2635	112	21	to	to	PART
easat-2635	112	22	show	show	VERB
easat-2635	112	23	that	that	SCONJ
easat-2635	112	24	some	some	DET
easat-2635	112	25	learners	learner	NOUN
easat-2635	112	26	might	might	AUX
easat-2635	112	27	have	have	AUX
easat-2635	112	28	been	be	AUX
easat-2635	112	29	disadvantaged	disadvantage	VERB
easat-2635	112	30	during	during	ADP
easat-2635	112	31	marking	mark	VERB
easat-2635	112	32	.	.	PUNCT
easat-2635	113	1	the	the	DET
easat-2635	113	2	approach	approach	NOUN
easat-2635	113	3	to	to	ADP
easat-2635	113	4	the	the	DET
easat-2635	113	5	problem	problem	NOUN
easat-2635	113	6	solution	solution	NOUN
easat-2635	113	7	presentation	presentation	NOUN
easat-2635	113	8	using	use	VERB
easat-2635	113	9	distinctly	distinctly	ADV
easat-2635	113	10	different	different	ADJ
easat-2635	113	11	answers	answer	NOUN
easat-2635	113	12	is	be	AUX
easat-2635	113	13	appreciated	appreciate	VERB
easat-2635	113	14	to	to	PART
easat-2635	113	15	broaden	broaden	VERB
easat-2635	113	16	the	the	DET
easat-2635	113	17	understanding	understanding	NOUN
easat-2635	113	18	of	of	ADP
easat-2635	113	19	problem	problem	NOUN
easat-2635	113	20	-	-	PUNCT
easat-2635	113	21	solving	solving	NOUN
easat-2635	113	22	but	but	CCONJ
easat-2635	113	23	the	the	DET
easat-2635	113	24	question	question	NOUN
easat-2635	113	25	is	be	AUX
easat-2635	113	26	:	:	PUNCT
easat-2635	113	27	is	be	AUX
easat-2635	113	28	this	this	DET
easat-2635	113	29	approach	approach	NOUN
easat-2635	113	30	not	not	PART
easat-2635	113	31	leading	lead	VERB
easat-2635	113	32	the	the	DET
easat-2635	113	33	markers	marker	NOUN
easat-2635	113	34	to	to	PART
easat-2635	113	35	be	be	AUX
easat-2635	113	36	ignorant	ignorant	ADJ
easat-2635	113	37	of	of	ADP
easat-2635	113	38	the	the	DET
easat-2635	113	39	other	other	ADJ
easat-2635	113	40	solution	solution	NOUN
easat-2635	113	41	options	option	NOUN
easat-2635	113	42	and	and	CCONJ
easat-2635	113	43	disadvantage	disadvantage	VERB
easat-2635	113	44	the	the	DET
easat-2635	113	45	learners	learner	NOUN
easat-2635	113	46	passing	pass	VERB
easat-2635	113	47	?	?	PUNCT
easat-2635	114	1	5	5	X
easat-2635	114	2	.	.	PUNCT
easat-2635	114	3	recommendations	recommendation	NOUN
easat-2635	114	4	the	the	DET
easat-2635	114	5	authors	author	NOUN
easat-2635	114	6	recommend	recommend	VERB
easat-2635	114	7	that	that	SCONJ
easat-2635	114	8	the	the	DET
easat-2635	114	9	grade	grade	NOUN
easat-2635	114	10	12	12	NUM
easat-2635	114	11	examiners	examiner	NOUN
easat-2635	114	12	are	be	AUX
easat-2635	114	13	supposed	suppose	VERB
easat-2635	114	14	to	to	PART
easat-2635	114	15	make	make	VERB
easat-2635	114	16	sure	sure	ADJ
easat-2635	114	17	that	that	SCONJ
easat-2635	114	18	they	they	PRON
easat-2635	114	19	include	include	VERB
easat-2635	114	20	all	all	DET
easat-2635	114	21	the	the	DET
easat-2635	114	22	possible	possible	ADJ
easat-2635	114	23	options	option	NOUN
easat-2635	114	24	when	when	SCONJ
easat-2635	114	25	making	make	VERB
easat-2635	114	26	the	the	DET
easat-2635	114	27	memoranda	memoranda	NOUN
easat-2635	114	28	so	so	SCONJ
easat-2635	114	29	that	that	SCONJ
easat-2635	114	30	during	during	ADP
easat-2635	114	31	marking	mark	VERB
easat-2635	114	32	learners	learner	NOUN
easat-2635	114	33	are	be	AUX
easat-2635	114	34	not	not	PART
easat-2635	114	35	disadvantaged	disadvantage	VERB
easat-2635	114	36	by	by	ADP
easat-2635	114	37	markers	marker	NOUN
easat-2635	114	38	.	.	PUNCT
easat-2635	115	1	another	another	DET
easat-2635	115	2	study	study	NOUN
easat-2635	115	3	on	on	ADP
easat-2635	115	4	markers	marker	NOUN
easat-2635	115	5	'	'	PART
easat-2635	115	6	perceptions	perception	NOUN
easat-2635	115	7	of	of	ADP
easat-2635	115	8	problem	problem	NOUN
easat-2635	115	9	solution	solution	NOUN
easat-2635	115	10	representation	representation	NOUN
easat-2635	115	11	using	use	VERB
easat-2635	115	12	distinct	distinct	ADJ
easat-2635	115	13	different	different	ADJ
easat-2635	115	14	solutions	solution	NOUN
easat-2635	115	15	is	be	AUX
easat-2635	115	16	needed	need	VERB
easat-2635	115	17	.	.	PUNCT
easat-2635	116	1	acknowledgement	acknowledgement	NOUN
easat-2635	116	2	:	:	PUNCT
easat-2635	116	3	the	the	DET
easat-2635	116	4	authors	author	NOUN
easat-2635	116	5	would	would	AUX
easat-2635	116	6	like	like	VERB
easat-2635	116	7	to	to	PART
easat-2635	116	8	acknowledge	acknowledge	VERB
easat-2635	116	9	the	the	DET
easat-2635	116	10	vaal	vaal	NOUN
easat-2635	116	11	university	university	NOUN
easat-2635	116	12	of	of	ADP
easat-2635	116	13	technology	technology	NOUN
easat-2635	116	14	for	for	ADP
easat-2635	116	15	providing	provide	VERB
easat-2635	116	16	facilities	facility	NOUN
easat-2635	116	17	to	to	PART
easat-2635	116	18	produce	produce	VERB
easat-2635	116	19	this	this	DET
easat-2635	116	20	work	work	NOUN
easat-2635	116	21	.	.	PUNCT
easat-2635	117	1	copyright	copyright	NOUN
easat-2635	117	2	:	:	PUNCT
easat-2635	117	3	©	©	PROPN
easat-2635	117	4	2024	2024	NUM
easat-2635	117	5	by	by	ADP
easat-2635	117	6	the	the	DET
easat-2635	117	7	authors	author	NOUN
easat-2635	117	8	.	.	PUNCT
easat-2635	118	1	this	this	DET
easat-2635	118	2	article	article	NOUN
easat-2635	118	3	is	be	AUX
easat-2635	118	4	an	an	DET
easat-2635	118	5	open	open	ADJ
easat-2635	118	6	access	access	NOUN
easat-2635	118	7	article	article	NOUN
easat-2635	118	8	distributed	distribute	VERB
easat-2635	118	9	under	under	ADP
easat-2635	118	10	the	the	DET
easat-2635	118	11	terms	term	NOUN
easat-2635	118	12	and	and	CCONJ
easat-2635	118	13	conditions	condition	NOUN
easat-2635	118	14	of	of	ADP
easat-2635	118	15	the	the	DET
easat-2635	118	16	creative	creative	ADJ
easat-2635	118	17	commons	common	NOUN
easat-2635	118	18	attribution	attribution	NOUN
easat-2635	118	19	(	(	PUNCT
easat-2635	118	20	cc	cc	NOUN
easat-2635	118	21	by	by	ADP
easat-2635	118	22	)	)	PUNCT
easat-2635	118	23	license	license	NOUN
easat-2635	118	24	(	(	PUNCT
easat-2635	118	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-2635	118	26	)	)	PUNCT
easat-2635	118	27	.	.	PUNCT
easat-2635	119	1	references	reference	NOUN
easat-2635	119	2	[	[	X
easat-2635	119	3	1	1	NUM
easat-2635	119	4	]	]	PUNCT
easat-2635	119	5	h.	h.	PROPN
easat-2635	119	6	h.wu	h.wu	PROPN
easat-2635	119	7	,	,	PUNCT
easat-2635	119	8	“	"	PUNCT
easat-2635	119	9	the	the	DET
easat-2635	119	10	role	role	NOUN
easat-2635	119	11	of	of	ADP
easat-2635	119	12	euclidean	euclidean	ADJ
easat-2635	119	13	geometry	geometry	NOUN
easat-2635	119	14	in	in	ADP
easat-2635	119	15	high	high	ADJ
easat-2635	119	16	school	school	NOUN
easat-2635	119	17	,	,	PUNCT
easat-2635	119	18	”	"	PUNCT
easat-2635	119	19	journal	journal	NOUN
easat-2635	119	20	of	of	ADP
easat-2635	119	21	mathematical	mathematical	ADJ
easat-2635	119	22	behavior	behavior	NOUN
easat-2635	119	23	.	.	PUNCT
easat-2635	120	1	vol	vol	NOUN
easat-2635	120	2	.	.	PROPN
easat-2635	121	1	15	15	NUM
easat-2635	121	2	,	,	PUNCT
easat-2635	121	3	pp	pp	ADJ
easat-2635	121	4	.	.	PUNCT
easat-2635	122	1	221	221	NUM
easat-2635	122	2	-	-	SYM
easat-2635	122	3	237	237	NUM
easat-2635	122	4	,	,	PUNCT
easat-2635	122	5	1996	1996	NUM
easat-2635	122	6	.	.	PUNCT
easat-2635	123	1	[	[	X
easat-2635	123	2	2	2	NUM
easat-2635	123	3	]	]	PUNCT
easat-2635	123	4	k.	k.	PROPN
easat-2635	123	5	jones	jones	PROPN
easat-2635	123	6	,	,	PUNCT
easat-2635	123	7	issues	issue	NOUN
easat-2635	123	8	in	in	ADP
easat-2635	123	9	the	the	DET
easat-2635	123	10	teaching	teaching	NOUN
easat-2635	123	11	and	and	CCONJ
easat-2635	123	12	learning	learning	NOUN
easat-2635	123	13	of	of	ADP
easat-2635	123	14	geometry	geometry	NOUN
easat-2635	123	15	in	in	ADP
easat-2635	123	16	:	:	PUNCT
easat-2635	123	17	linda	linda	PROPN
easat-2635	123	18	haggarty	haggarty	PROPN
easat-2635	123	19	(	(	PUNCT
easat-2635	123	20	ed	ed	NOUN
easat-2635	123	21	)	)	PUNCT
easat-2635	123	22	,	,	PUNCT
easat-2635	123	23	aspects	aspect	NOUN
easat-2635	123	24	of	of	ADP
easat-2635	123	25	teaching	teach	VERB
easat-2635	123	26	secondary	secondary	ADJ
easat-2635	123	27	mathematics	mathematic	NOUN
easat-2635	123	28	:	:	PUNCT
easat-2635	123	29	perspectives	perspective	NOUN
easat-2635	123	30	on	on	ADP
easat-2635	123	31	practice	practice	NOUN
easat-2635	123	32	,	,	PUNCT
easat-2635	123	33	london	london	PROPN
easat-2635	123	34	:	:	PUNCT
easat-2635	123	35	routledge	routledge	PROPN
easat-2635	123	36	falmer	falmer	PROPN
easat-2635	123	37	.	.	PROPN
easat-2635	123	38	chapter	chapter	NOUN
easat-2635	123	39	8	8	NUM
easat-2635	123	40	,	,	PUNCT
easat-2635	123	41	pp	pp	ADJ
easat-2635	123	42	.	.	PUNCT
easat-2635	124	1	121	121	NUM
easat-2635	124	2	-	-	SYM
easat-2635	124	3	139	139	NUM
easat-2635	124	4	,	,	PUNCT
easat-2635	124	5	2002	2002	NUM
easat-2635	124	6	.	.	PUNCT
easat-2635	125	1	[	[	X
easat-2635	125	2	3	3	NUM
easat-2635	125	3	]	]	PUNCT
easat-2635	125	4	a.	a.	NOUN
easat-2635	125	5	t.	t.	PROPN
easat-2635	125	6	simon	simon	PROPN
easat-2635	125	7	,	,	PUNCT
easat-2635	125	8	“	"	PUNCT
easat-2635	125	9	the	the	DET
easat-2635	125	10	challenges	challenge	NOUN
easat-2635	125	11	of	of	ADP
easat-2635	125	12	south	south	ADJ
easat-2635	125	13	african	african	ADJ
easat-2635	125	14	teachers	teacher	NOUN
easat-2635	125	15	in	in	ADP
easat-2635	125	16	teaching	teach	VERB
easat-2635	125	17	euclidean	euclidean	ADJ
easat-2635	125	18	geometry	geometry	NOUN
easat-2635	125	19	,	,	PUNCT
easat-2635	125	20	”	"	PUNCT
easat-2635	125	21	international	international	ADJ
easat-2635	125	22	journal	journal	NOUN
easat-2635	125	23	of	of	ADP
easat-2635	125	24	learning	learning	NOUN
easat-2635	125	25	,	,	PUNCT
easat-2635	125	26	teaching	teaching	NOUN
easat-2635	125	27	and	and	CCONJ
easat-2635	125	28	educational	educational	ADJ
easat-2635	125	29	research	research	NOUN
easat-2635	125	30	,	,	PUNCT
easat-2635	125	31	vol	vol	NOUN
easat-2635	125	32	.	.	PROPN
easat-2635	125	33	19	19	NUM
easat-2635	125	34	,	,	PUNCT
easat-2635	125	35	pp	pp	ADJ
easat-2635	125	36	.	.	PUNCT
easat-2635	125	37	297	297	NUM
easat-2635	125	38	-	-	SYM
easat-2635	125	39	312	312	NUM
easat-2635	125	40	,	,	PUNCT
easat-2635	125	41	2020	2020	NUM
easat-2635	125	42	.	.	PUNCT
easat-2635	126	1	[	[	X
easat-2635	126	2	4	4	NUM
easat-2635	126	3	]	]	PUNCT
easat-2635	126	4	a.	a.	NOUN
easat-2635	126	5	s.	s.	PROPN
easat-2635	126	6	nogiyeza	nogiyeza	PROPN
easat-2635	126	7	,	,	PUNCT
easat-2635	126	8	“	"	PUNCT
easat-2635	126	9	exploring	explore	VERB
easat-2635	126	10	grade	grade	NOUN
easat-2635	126	11	11	11	NUM
easat-2635	126	12	mathematics	mathematic	NOUN
easat-2635	126	13	teachers	teacher	NOUN
easat-2635	126	14	’	'	PUNCT
easat-2635	126	15	pedagogical	pedagogical	ADJ
easat-2635	126	16	content	content	NOUN
easat-2635	126	17	knowledge	knowledge	NOUN
easat-2635	126	18	when	when	SCONJ
easat-2635	126	19	teaching	teach	VERB
easat-2635	126	20	euclidean	euclidean	ADJ
easat-2635	126	21	geometry	geometry	NOUN
easat-2635	126	22	in	in	ADP
easat-2635	126	23	umlazi	umlazi	PROPN
easat-2635	126	24	district	district	NOUN
easat-2635	126	25	,	,	PUNCT
easat-2635	126	26	”	"	PUNCT
easat-2635	126	27	a	a	DET
easat-2635	126	28	coursework	coursework	NOUN
easat-2635	126	29	dissertation	dissertation	NOUN
easat-2635	126	30	for	for	ADP
easat-2635	126	31	the	the	DET
easat-2635	126	32	degree	degree	NOUN
easat-2635	126	33	of	of	ADP
easat-2635	126	34	master	master	NOUN
easat-2635	126	35	of	of	ADP
easat-2635	126	36	education	education	NOUN
easat-2635	126	37	,	,	PUNCT
easat-2635	126	38	university	university	NOUN
easat-2635	126	39	of	of	ADP
easat-2635	126	40	kwazulu	kwazulu	PROPN
easat-2635	126	41	-	-	PUNCT
easat-2635	126	42	natal	natal	NOUN
easat-2635	126	43	,	,	PUNCT
easat-2635	126	44	2019	2019	NUM
easat-2635	126	45	.	.	PUNCT
easat-2635	127	1	[	[	X
easat-2635	127	2	5	5	X
easat-2635	127	3	]	]	PUNCT
easat-2635	127	4	d.	d.	PROPN
easat-2635	127	5	luthuli	luthuli	PROPN
easat-2635	127	6	,	,	PUNCT
easat-2635	127	7	“	"	PUNCT
easat-2635	127	8	questions	question	NOUN
easat-2635	127	9	,	,	PUNCT
easat-2635	127	10	reflection	reflection	NOUN
easat-2635	127	11	,	,	PUNCT
easat-2635	127	12	and	and	CCONJ
easat-2635	127	13	problem	problem	NOUN
easat-2635	127	14	posing	pose	VERB
easat-2635	127	15	as	as	ADP
easat-2635	127	16	sources	source	NOUN
easat-2635	127	17	of	of	ADP
easat-2635	127	18	inquiry	inquiry	NOUN
easat-2635	127	19	in	in	ADP
easat-2635	127	20	euclidean	euclidean	ADJ
easat-2635	127	21	geometry	geometry	NOUN
easat-2635	127	22	,	,	PUNCT
easat-2635	127	23	”	"	PUNCT
easat-2635	127	24	pythagoras	pythagoras	PROPN
easat-2635	127	25	,	,	PUNCT
easat-2635	127	26	vol	vol	NOUN
easat-2635	127	27	.	.	PROPN
easat-2635	127	28	40	40	NUM
easat-2635	127	29	,	,	PUNCT
easat-2635	127	30	pp	pp	ADJ
easat-2635	127	31	.	.	PUNCT
easat-2635	128	1	17	17	NUM
easat-2635	128	2	-	-	SYM
easat-2635	128	3	27	27	NUM
easat-2635	128	4	,	,	PUNCT
easat-2635	128	5	1996	1996	NUM
easat-2635	128	6	.	.	PUNCT
easat-2635	129	1	[	[	X
easat-2635	129	2	6	6	NUM
easat-2635	129	3	]	]	PUNCT
easat-2635	129	4	m.	m.	NOUN
easat-2635	129	5	a.	a.	PROPN
easat-2635	129	6	al	al	PROPN
easat-2635	129	7	-	-	PUNCT
easat-2635	129	8	khateeb	khateeb	PROPN
easat-2635	129	9	,	,	PUNCT
easat-2635	129	10	“	"	PUNCT
easat-2635	129	11	the	the	DET
easat-2635	129	12	extent	extent	NOUN
easat-2635	129	13	of	of	ADP
easat-2635	129	14	mathematics	mathematics	PROPN
easat-2635	129	15	teachers	teacher	NOUN
easat-2635	129	16	’	'	PUNCT
easat-2635	129	17	awareness	awareness	NOUN
easat-2635	129	18	of	of	ADP
easat-2635	129	19	their	their	PRON
easat-2635	129	20	students	student	NOUN
easat-2635	129	21	’	'	PUNCT
easat-2635	129	22	misconceptions	misconception	NOUN
easat-2635	129	23	in	in	ADP
easat-2635	129	24	learning	learn	VERB
easat-2635	129	25	geometrical	geometrical	ADJ
easat-2635	129	26	concepts	concept	NOUN
easat-2635	129	27	in	in	ADP
easat-2635	129	28	the	the	DET
easat-2635	129	29	intermediate	intermediate	ADJ
easat-2635	129	30	education	education	NOUN
easat-2635	129	31	stage	stage	NOUN
easat-2635	129	32	,	,	PUNCT
easat-2635	129	33	”	"	PUNCT
easat-2635	129	34	european	european	ADJ
easat-2635	129	35	scientific	scientific	ADJ
easat-2635	129	36	journal	journal	NOUN
easat-2635	129	37	,	,	PUNCT
easat-2635	129	38	vol	vol	NOUN
easat-2635	129	39	.	.	PROPN
easat-2635	129	40	12	12	NUM
easat-2635	129	41	,	,	PUNCT
easat-2635	129	42	pp	pp	ADJ
easat-2635	129	43	.	.	PUNCT
easat-2635	129	44	357	357	NUM
easat-2635	129	45	-	-	SYM
easat-2635	129	46	372	372	NUM
easat-2635	129	47	,	,	PUNCT
easat-2635	129	48	2016	2016	NUM
easat-2635	129	49	.	.	PUNCT
easat-2635	130	1	[	[	X
easat-2635	130	2	7	7	X
easat-2635	130	3	]	]	X
easat-2635	130	4	e.	e.	PROPN
easat-2635	130	5	mukamba	mukamba	PROPN
easat-2635	130	6	and	and	CCONJ
easat-2635	130	7	c.	c.	PROPN
easat-2635	130	8	makamure	makamure	NOUN
easat-2635	130	9	,	,	PUNCT
easat-2635	130	10	“	"	PUNCT
easat-2635	130	11	integration	integration	NOUN
easat-2635	130	12	of	of	ADP
easat-2635	130	13	geogebra	geogebra	NOUN
easat-2635	130	14	in	in	ADP
easat-2635	130	15	teaching	teaching	NOUN
easat-2635	130	16	and	and	CCONJ
easat-2635	130	17	learning	learn	VERB
easat-2635	130	18	geometric	geometric	ADJ
easat-2635	130	19	transformations	transformation	NOUN
easat-2635	130	20	at	at	ADP
easat-2635	130	21	ordinary	ordinary	ADJ
easat-2635	130	22	level	level	NOUN
easat-2635	130	23	in	in	ADP
easat-2635	130	24	zimbabwe	zimbabwe	NOUN
easat-2635	130	25	,	,	PUNCT
easat-2635	130	26	”	"	PUNCT
easat-2635	130	27	contemporary	contemporary	ADJ
easat-2635	130	28	mathematics	mathematics	PROPN
easat-2635	130	29	and	and	CCONJ
easat-2635	130	30	science	science	NOUN
easat-2635	130	31	education	education	NOUN
easat-2635	130	32	,	,	PUNCT
easat-2635	130	33	vol	vol	NOUN
easat-2635	130	34	.	.	PROPN
easat-2635	130	35	1	1	NUM
easat-2635	130	36	,	,	PUNCT
easat-2635	130	37	pp	pp	ADJ
easat-2635	130	38	.	.	PUNCT
easat-2635	130	39	1	1	NUM
easat-2635	130	40	-	-	SYM
easat-2635	130	41	8	8	NUM
easat-2635	130	42	,	,	PUNCT
easat-2635	130	43	2020	2020	NUM
easat-2635	130	44	.	.	PUNCT
easat-2635	131	1	[	[	X
easat-2635	131	2	8	8	NUM
easat-2635	131	3	]	]	X
easat-2635	131	4	l.	l.	PROPN
easat-2635	131	5	mwadzaangati	mwadzaangati	PROPN
easat-2635	131	6	,	,	PUNCT
easat-2635	131	7	“	"	PUNCT
easat-2635	131	8	mathematical	mathematical	ADJ
easat-2635	131	9	knowledge	knowledge	NOUN
easat-2635	131	10	for	for	ADP
easat-2635	131	11	teaching	teach	VERB
easat-2635	131	12	geometric	geometric	ADJ
easat-2635	131	13	proof	proof	NOUN
easat-2635	131	14	:	:	PUNCT
easat-2635	131	15	learning	learn	VERB
easat-2635	131	16	from	from	ADP
easat-2635	131	17	teachers	teacher	NOUN
easat-2635	131	18	’	'	PUNCT
easat-2635	131	19	practices	practice	NOUN
easat-2635	131	20	,	,	PUNCT
easat-2635	131	21	”	"	PUNCT
easat-2635	131	22	proceedings	proceeding	NOUN
easat-2635	131	23	of	of	ADP
easat-2635	131	24	the	the	DET
easat-2635	131	25	ninth	ninth	ADJ
easat-2635	131	26	congress	congress	PROPN
easat-2635	131	27	of	of	ADP
easat-2635	131	28	the	the	DET
easat-2635	131	29	european	european	PROPN
easat-2635	131	30	society	society	PROPN
easat-2635	131	31	for	for	ADP
easat-2635	131	32	research	research	NOUN
easat-2635	131	33	in	in	ADP
easat-2635	131	34	mathematics	mathematics	PROPN
easat-2635	131	35	education	education	NOUN
easat-2635	131	36	,	,	PUNCT
easat-2635	131	37	prague	prague	PROPN
easat-2635	131	38	,	,	PUNCT
easat-2635	131	39	czech	czech	PROPN
easat-2635	131	40	republic	republic	NOUN
easat-2635	131	41	:	:	PUNCT
easat-2635	131	42	cerme-2015	cerme-2015	PROPN
easat-2635	131	43	,	,	PUNCT
easat-2635	131	44	pp	pp	ADJ
easat-2635	131	45	.	.	PUNCT
easat-2635	132	1	3308	3308	NUM
easat-2635	132	2	-	-	SYM
easat-2635	132	3	3308	3308	NUM
easat-2635	132	4	,	,	PUNCT
easat-2635	132	5	2015	2015	NUM
easat-2635	132	6	.	.	PUNCT
easat-2635	133	1	[	[	X
easat-2635	133	2	9	9	NUM
easat-2635	133	3	]	]	PUNCT
easat-2635	133	4	s.	s.	PROPN
easat-2635	133	5	g.	g.	PROPN
easat-2635	133	6	mthembu	mthembu	PROPN
easat-2635	133	7	,	,	PUNCT
easat-2635	133	8	“	"	PUNCT
easat-2635	133	9	instructional	instructional	ADJ
easat-2635	133	10	approaches	approach	NOUN
easat-2635	133	11	in	in	ADP
easat-2635	133	12	the	the	DET
easat-2635	133	13	teaching	teaching	NOUN
easat-2635	133	14	of	of	ADP
easat-2635	133	15	euclidean	euclidean	ADJ
easat-2635	133	16	geometry	geometry	NOUN
easat-2635	133	17	in	in	ADP
easat-2635	133	18	grade	grade	NOUN
easat-2635	133	19	11	11	NUM
easat-2635	133	20	,	,	PUNCT
easat-2635	133	21	”	"	PUNCT
easat-2635	133	22	a	a	DET
easat-2635	133	23	dissertation	dissertation	NOUN
easat-2635	133	24	submitted	submit	VERB
easat-2635	133	25	to	to	ADP
easat-2635	133	26	the	the	DET
easat-2635	133	27	faculty	faculty	NOUN
easat-2635	133	28	of	of	ADP
easat-2635	133	29	education	education	NOUN
easat-2635	133	30	of	of	ADP
easat-2635	133	31	university	university	NOUN
easat-2635	133	32	of	of	ADP
easat-2635	133	33	kwazulu	kwazulu	PROPN
easat-2635	133	34	-	-	PUNCT
easat-2635	133	35	natal	natal	NOUN
easat-2635	133	36	in	in	ADP
easat-2635	133	37	partial	partial	ADJ
easat-2635	133	38	fulfilment	fulfilment	NOUN
easat-2635	133	39	of	of	ADP
easat-2635	133	40	the	the	DET
easat-2635	133	41	requirement	requirement	NOUN
easat-2635	133	42	for	for	ADP
easat-2635	133	43	the	the	DET
easat-2635	133	44	degree	degree	NOUN
easat-2635	133	45	of	of	ADP
easat-2635	133	46	master	master	NOUN
easat-2635	133	47	of	of	ADP
easat-2635	133	48	education	education	NOUN
easat-2635	133	49	,	,	PUNCT
easat-2635	133	50	2007	2007	NUM
easat-2635	133	51	.	.	PUNCT
easat-2635	134	1	[	[	X
easat-2635	134	2	10	10	NUM
easat-2635	134	3	]	]	X
easat-2635	134	4	a	a	DET
easat-2635	134	5	bayaga	bayaga	NOUN
easat-2635	134	6	.	.	PUNCT
easat-2635	135	1	,	,	PUNCT
easat-2635	135	2	m.m	m.m	PROPN
easat-2635	135	3	.	.	PROPN
easat-2635	135	4	mthethwa	mthethwa	PROPN
easat-2635	135	5	,	,	PUNCT
easat-2635	135	6	m.j	m.j	PROPN
easat-2635	135	7	.	.	PROPN
easat-2635	135	8	bossé	bossé	NOUN
easat-2635	135	9	,	,	PUNCT
easat-2635	135	10	and	and	CCONJ
easat-2635	135	11	d.	d.	PROPN
easat-2635	135	12	williams	williams	PROPN
easat-2635	135	13	,	,	PUNCT
easat-2635	135	14	“	"	PUNCT
easat-2635	135	15	impacts	impact	NOUN
easat-2635	135	16	of	of	ADP
easat-2635	135	17	implementing	implement	VERB
easat-2635	135	18	geogebra	geogebra	NOUN
easat-2635	135	19	on	on	ADP
easat-2635	135	20	eleventh	eleventh	ADJ
easat-2635	135	21	grade	grade	NOUN
easat-2635	135	22	students	student	NOUN
easat-2635	135	23	,	,	PUNCT
easat-2635	135	24	”	"	PUNCT
easat-2635	135	25	south	south	ADJ
easat-2635	135	26	african	african	ADJ
easat-2635	135	27	journal	journal	NOUN
easat-2635	135	28	of	of	ADP
easat-2635	135	29	higher	high	ADJ
easat-2635	135	30	education	education	NOUN
easat-2635	135	31	,	,	PUNCT
easat-2635	135	32	vol	vol	NOUN
easat-2635	135	33	.	.	PROPN
easat-2635	136	1	33	33	NUM
easat-2635	136	2	,	,	PUNCT
easat-2635	136	3	pp	pp	ADJ
easat-2635	136	4	.	.	PUNCT
easat-2635	137	1	32‒54	32‒54	NUM
easat-2635	137	2	,	,	PUNCT
easat-2635	137	3	2019	2019	NUM
easat-2635	137	4	.	.	PUNCT
easat-2635	138	1	[	[	X
easat-2635	138	2	11	11	NUM
easat-2635	138	3	]	]	X
easat-2635	138	4	s.v	s.v	PROPN
easat-2635	138	5	.	.	PROPN
easat-2635	138	6	putten	putten	PROPN
easat-2635	138	7	and	and	CCONJ
easat-2635	138	8	s.	s.	PROPN
easat-2635	138	9	howie	howie	PROPN
easat-2635	138	10	,	,	PUNCT
easat-2635	138	11	“	"	PUNCT
easat-2635	138	12	making	make	VERB
easat-2635	138	13	euclidean	euclidean	ADJ
easat-2635	138	14	geometry	geometry	NOUN
easat-2635	138	15	compulsory	compulsory	NOUN
easat-2635	138	16	,	,	PUNCT
easat-2635	138	17	are	be	AUX
easat-2635	138	18	we	we	PRON
easat-2635	138	19	prepared	prepare	VERB
easat-2635	138	20	?	?	PUNCT
easat-2635	138	21	”	"	PUNCT
easat-2635	138	22	perspectives	perspective	NOUN
easat-2635	138	23	in	in	ADP
easat-2635	138	24	education	education	NOUN
easat-2635	138	25	perspectives	perspective	NOUN
easat-2635	138	26	in	in	ADP
easat-2635	138	27	education	education	NOUN
easat-2635	138	28	,	,	PUNCT
easat-2635	138	29	vol	vol	NOUN
easat-2635	138	30	.	.	PROPN
easat-2635	138	31	28	28	NUM
easat-2635	138	32	,	,	PUNCT
easat-2635	138	33	pp	pp	ADJ
easat-2635	138	34	.	.	PUNCT
easat-2635	139	1	22	22	NUM
easat-2635	139	2	-	-	SYM
easat-2635	139	3	31	31	NUM
easat-2635	139	4	,	,	PUNCT
easat-2635	139	5	2010	2010	NUM
easat-2635	139	6	.	.	PUNCT
easat-2635	140	1	[	[	X
easat-2635	140	2	12	12	NUM
easat-2635	140	3	]	]	X
easat-2635	140	4	e.	e.	PROPN
easat-2635	140	5	machisi	machisi	PROPN
easat-2635	140	6	,	,	PUNCT
easat-2635	140	7	“	"	PUNCT
easat-2635	140	8	grade	grade	NOUN
easat-2635	140	9	11	11	NUM
easat-2635	140	10	students	student	NOUN
easat-2635	140	11	’	'	PUNCT
easat-2635	140	12	reflections	reflection	NOUN
easat-2635	140	13	on	on	ADP
easat-2635	140	14	their	their	PRON
easat-2635	140	15	euclidean	euclidean	ADJ
easat-2635	140	16	geometry	geometry	NOUN
easat-2635	140	17	learning	learning	NOUN
easat-2635	140	18	experiences	experience	NOUN
easat-2635	140	19	,	,	PUNCT
easat-2635	140	20	”	"	PUNCT
easat-2635	140	21	eurasia	eurasia	PROPN
easat-2635	140	22	journal	journal	PROPN
easat-2635	140	23	of	of	ADP
easat-2635	140	24	mathematics	mathematics	PROPN
easat-2635	140	25	,	,	PUNCT
easat-2635	140	26	science	science	NOUN
easat-2635	140	27	and	and	CCONJ
easat-2635	140	28	technology	technology	NOUN
easat-2635	140	29	education	education	NOUN
easat-2635	140	30	,	,	PUNCT
easat-2635	140	31	vol	vol	NOUN
easat-2635	140	32	.	.	PROPN
easat-2635	140	33	17	17	NUM
easat-2635	140	34	,	,	PUNCT
easat-2635	140	35	pp	pp	ADJ
easat-2635	140	36	.	.	PUNCT
easat-2635	141	1	1	1	NUM
easat-2635	141	2	-	-	SYM
easat-2635	141	3	19	19	NUM
easat-2635	141	4	,	,	PUNCT
easat-2635	141	5	2021	2021	NUM
easat-2635	141	6	.	.	PUNCT
easat-2635	142	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-2635	142	2	2936	2936	NUM
easat-2635	142	3	edelweiss	edelweiss	PROPN
easat-2635	142	4	applied	apply	VERB
easat-2635	142	5	science	science	NOUN
easat-2635	142	6	and	and	CCONJ
easat-2635	142	7	technology	technology	NOUN
easat-2635	142	8	issn	issn	PROPN
easat-2635	142	9	:	:	PUNCT
easat-2635	142	10	2576	2576	NUM
easat-2635	142	11	-	-	SYM
easat-2635	142	12	8484	8484	NUM
easat-2635	142	13	vol	vol	NOUN
easat-2635	142	14	.	.	PROPN
easat-2635	142	15	8	8	NUM
easat-2635	142	16	,	,	PUNCT
easat-2635	142	17	no	no	INTJ
easat-2635	142	18	.	.	NOUN
easat-2635	143	1	6	6	NUM
easat-2635	143	2	:	:	SYM
easat-2635	143	3	2931	2931	NUM
easat-2635	143	4	-	-	SYM
easat-2635	143	5	2936	2936	NUM
easat-2635	143	6	,	,	PUNCT
easat-2635	143	7	2024	2024	NUM
easat-2635	143	8	doi	doi	NOUN
easat-2635	143	9	:	:	PUNCT
easat-2635	143	10	10.55214/25768484.v8i6.2635	10.55214/25768484.v8i6.2635	NUM
easat-2635	143	11	©	©	PROPN
easat-2635	143	12	2024	2024	NUM
easat-2635	143	13	by	by	ADP
easat-2635	143	14	the	the	DET
easat-2635	143	15	authors	author	NOUN
easat-2635	143	16	;	;	PUNCT
easat-2635	143	17	licensee	licensee	PROPN
easat-2635	143	18	learning	learning	NOUN
easat-2635	143	19	gate	gate	NOUN
easat-2635	144	1	[	[	X
easat-2635	144	2	13	13	NUM
easat-2635	144	3	]	]	PUNCT
easat-2635	144	4	l.	l.	PROPN
easat-2635	144	5	bowie	bowie	PROPN
easat-2635	144	6	,	,	PUNCT
easat-2635	144	7	“	"	PUNCT
easat-2635	144	8	what	what	PRON
easat-2635	144	9	is	be	AUX
easat-2635	144	10	mathematics	mathematics	NOUN
easat-2635	144	11	paper	paper	NOUN
easat-2635	144	12	3	3	NUM
easat-2635	144	13	for	for	ADP
easat-2635	144	14	?	?	PUNCT
easat-2635	145	1	marang	marang	PROPN
easat-2635	145	2	centre	centre	PROPN
easat-2635	145	3	for	for	ADP
easat-2635	145	4	mathematics	mathematic	NOUN
easat-2635	145	5	and	and	CCONJ
easat-2635	145	6	science	science	NOUN
easat-2635	145	7	education	education	NOUN
easat-2635	145	8	,	,	PUNCT
easat-2635	145	9	”	"	PUNCT
easat-2635	145	10	marang	marang	PROPN
easat-2635	145	11	news	news	PROPN
easat-2635	145	12	.	.	PUNCT
easat-2635	146	1	issue	issue	NOUN
easat-2635	146	2	5	5	NUM
easat-2635	146	3	,	,	PUNCT
easat-2635	146	4	2009	2009	NUM
easat-2635	146	5	.	.	PUNCT
easat-2635	147	1	[	[	X
easat-2635	147	2	14	14	NUM
easat-2635	147	3	]	]	X
easat-2635	147	4	y.	y.	PROPN
easat-2635	147	5	k.	k.	PROPN
easat-2635	147	6	makhubele	makhubele	PROPN
easat-2635	147	7	,	,	PUNCT
easat-2635	147	8	“	"	PUNCT
easat-2635	147	9	misconceptions	misconception	NOUN
easat-2635	147	10	and	and	CCONJ
easat-2635	147	11	resulting	result	VERB
easat-2635	147	12	errors	error	NOUN
easat-2635	147	13	displayed	display	VERB
easat-2635	147	14	by	by	ADP
easat-2635	147	15	grade	grade	NOUN
easat-2635	147	16	11	11	NUM
easat-2635	147	17	learners	learner	NOUN
easat-2635	147	18	in	in	ADP
easat-2635	147	19	the	the	DET
easat-2635	147	20	learning	learning	NOUN
easat-2635	147	21	of	of	ADP
easat-2635	147	22	geometry	geometry	NOUN
easat-2635	147	23	,	,	PUNCT
easat-2635	147	24	”	"	PUNCT
easat-2635	147	25	a	a	DET
easat-2635	147	26	dissertation	dissertation	NOUN
easat-2635	147	27	submitted	submit	VERB
easat-2635	147	28	to	to	ADP
easat-2635	147	29	the	the	DET
easat-2635	147	30	faculty	faculty	NOUN
easat-2635	147	31	of	of	ADP
easat-2635	147	32	education	education	NOUN
easat-2635	147	33	of	of	ADP
easat-2635	147	34	university	university	PROPN
easat-2635	147	35	of	of	ADP
easat-2635	147	36	johannesburg	johannesburg	PROPN
easat-2635	147	37	in	in	ADP
easat-2635	147	38	partial	partial	ADJ
easat-2635	147	39	fulfilment	fulfilment	NOUN
easat-2635	147	40	of	of	ADP
easat-2635	147	41	the	the	DET
easat-2635	147	42	requirement	requirement	NOUN
easat-2635	147	43	for	for	ADP
easat-2635	147	44	the	the	DET
easat-2635	147	45	degree	degree	NOUN
easat-2635	147	46	of	of	ADP
easat-2635	147	47	master	master	NOUN
easat-2635	147	48	of	of	ADP
easat-2635	147	49	education	education	NOUN
easat-2635	147	50	,	,	PUNCT
easat-2635	147	51	2015	2015	NUM
easat-2635	147	52	.	.	PUNCT
easat-2635	148	1	[	[	X
easat-2635	148	2	15	15	NUM
easat-2635	148	3	]	]	X
easat-2635	148	4	o.a	o.a	PROPN
easat-2635	148	5	.	.	PROPN
easat-2635	148	6	abosede	abosede	PROPN
easat-2635	148	7	,	,	PUNCT
easat-2635	148	8	“	"	PUNCT
easat-2635	148	9	the	the	DET
easat-2635	148	10	performance	performance	NOUN
easat-2635	148	11	and	and	CCONJ
easat-2635	148	12	learning	learn	VERB
easat-2635	148	13	difficulties	difficulty	NOUN
easat-2635	148	14	of	of	ADP
easat-2635	148	15	grade	grade	NOUN
easat-2635	148	16	10	10	NUM
easat-2635	148	17	learners	learner	NOUN
easat-2635	148	18	in	in	ADP
easat-2635	148	19	solving	solve	VERB
easat-2635	148	20	euclidean	euclidean	ADJ
easat-2635	148	21	geometry	geometry	NOUN
easat-2635	148	22	problems	problem	NOUN
easat-2635	148	23	in	in	ADP
easat-2635	148	24	tswane	tswane	NOUN
easat-2635	148	25	west	west	PROPN
easat-2635	148	26	district	district	PROPN
easat-2635	148	27	,	,	PUNCT
easat-2635	148	28	”	"	PUNCT
easat-2635	148	29	a	a	DET
easat-2635	148	30	dissertation	dissertation	NOUN
easat-2635	148	31	submitted	submit	VERB
easat-2635	148	32	to	to	ADP
easat-2635	148	33	the	the	DET
easat-2635	148	34	faculty	faculty	NOUN
easat-2635	148	35	of	of	ADP
easat-2635	148	36	education	education	NOUN
easat-2635	148	37	of	of	ADP
easat-2635	148	38	university	university	PROPN
easat-2635	148	39	of	of	ADP
easat-2635	148	40	south	south	PROPN
easat-2635	148	41	africa	africa	PROPN
easat-2635	148	42	in	in	ADP
easat-2635	148	43	partial	partial	ADJ
easat-2635	148	44	fulfilment	fulfilment	NOUN
easat-2635	148	45	of	of	ADP
easat-2635	148	46	the	the	DET
easat-2635	148	47	requirement	requirement	NOUN
easat-2635	148	48	for	for	ADP
easat-2635	148	49	the	the	DET
easat-2635	148	50	degree	degree	NOUN
easat-2635	148	51	of	of	ADP
easat-2635	148	52	master	master	NOUN
easat-2635	148	53	of	of	ADP
easat-2635	148	54	education	education	NOUN
easat-2635	148	55	,	,	PUNCT
easat-2635	148	56	2023	2023	NUM
easat-2635	148	57	.	.	PUNCT
easat-2635	149	1	[	[	X
easat-2635	149	2	16	16	NUM
easat-2635	149	3	]	]	PUNCT
easat-2635	149	4	m.	m.	NOUN
easat-2635	149	5	ndlovu	ndlovu	NOUN
easat-2635	149	6	and	and	CCONJ
easat-2635	149	7	a.	a.	NOUN
easat-2635	149	8	mji	mji	PROPN
easat-2635	149	9	,	,	PUNCT
easat-2635	149	10	“	"	PUNCT
easat-2635	149	11	pedagogical	pedagogical	ADJ
easat-2635	149	12	implications	implication	NOUN
easat-2635	149	13	of	of	ADP
easat-2635	149	14	students	student	NOUN
easat-2635	149	15	’	'	PUNCT
easat-2635	149	16	misconceptions	misconception	NOUN
easat-2635	149	17	about	about	ADP
easat-2635	149	18	deductive	deductive	ADJ
easat-2635	149	19	geometric	geometric	ADJ
easat-2635	149	20	proof	proof	NOUN
easat-2635	149	21	,	,	PUNCT
easat-2635	149	22	”	"	PUNCT
easat-2635	149	23	acta	acta	PROPN
easat-2635	149	24	academica	academica	PROPN
easat-2635	149	25	,	,	PUNCT
easat-2635	149	26	vol	vol	NOUN
easat-2635	149	27	.	.	PROPN
easat-2635	149	28	44	44	NUM
easat-2635	149	29	,	,	PUNCT
easat-2635	149	30	pp	pp	ADJ
easat-2635	149	31	.	.	PUNCT
easat-2635	149	32	175	175	NUM
easat-2635	149	33	-	-	SYM
easat-2635	149	34	205	205	NUM
easat-2635	149	35	,	,	PUNCT
easat-2635	149	36	2012	2012	NUM
easat-2635	149	37	.	.	PUNCT
easat-2635	150	1	[	[	X
easat-2635	150	2	17	17	NUM
easat-2635	150	3	]	]	X
easat-2635	150	4	department	department	NOUN
easat-2635	150	5	of	of	ADP
easat-2635	150	6	education	education	NOUN
easat-2635	150	7	in	in	ADP
easat-2635	150	8	south	south	PROPN
easat-2635	150	9	africa	africa	PROPN
easat-2635	150	10	.	.	PUNCT
easat-2635	151	1	mathematics	mathematics	PROPN
easat-2635	151	2	paper	paper	NOUN
easat-2635	151	3	2	2	NUM
easat-2635	151	4	memorandum	memorandum	NOUN
easat-2635	151	5	,	,	PUNCT
easat-2635	151	6	2021	2021	NUM
easat-2635	151	7	.	.	PUNCT
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easat-2635	152	2	https://www.researchgate.net/journal/acta-academica-2415-0479?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uiiwicg9zaxrpb24ioijwywdlsgvhzgvyin19	https://www.researchgate.net/journal/acta-academica-2415-0479?_tp=eyjjb250zxh0ijp7imzpcnn0ugfnzsi6inb1ymxpy2f0aw9uiiwicgfnzsi6inb1ymxpy2f0aw9uiiwicg9zaxrpb24ioijwywdlsgvhzgvyin19	NOUN