id	sid	tid	token	lemma	pos
flr-49	1	1	frontline	frontline	NOUN
flr-49	1	2	learning	learn	VERB
flr-49	1	3	research	research	NOUN
flr-49	1	4	1	1	NUM
flr-49	1	5	(	(	PUNCT
flr-49	1	6	2013	2013	NUM
flr-49	1	7	)	)	PUNCT
flr-49	1	8	81	81	NUM
flr-49	1	9	96	96	NUM
flr-49	1	10	issn	issn	VERB
flr-49	1	11	2295	2295	NUM
flr-49	1	12	-	-	SYM
flr-49	1	13	3159	3159	NUM
flr-49	1	14	corresponding	corresponding	ADJ
flr-49	1	15	author	author	NOUN
flr-49	1	16	:	:	PUNCT
flr-49	1	17	kerry	kerry	PROPN
flr-49	1	18	lee	lee	PROPN
flr-49	1	19	,	,	PUNCT
flr-49	1	20	national	national	PROPN
flr-49	1	21	institute	institute	PROPN
flr-49	1	22	of	of	ADP
flr-49	1	23	education	education	PROPN
flr-49	1	24	,	,	PUNCT
flr-49	1	25	1	1	NUM
flr-49	1	26	nanyang	nanyang	PROPN
flr-49	1	27	walk	walk	PROPN
flr-49	1	28	,	,	PUNCT
flr-49	1	29	singapore	singapore	PROPN
flr-49	1	30	637616	637616	NUM
flr-49	1	31	,	,	PUNCT
flr-49	1	32	kerry.lee@nie.edu.sg	kerry.lee@nie.edu.sg	PROPN
flr-49	1	33	,	,	PUNCT
flr-49	1	34	t	t	PROPN
flr-49	1	35	+65	+65	PROPN
flr-49	1	36	6219	6219	NUM
flr-49	1	37	3888	3888	NUM
flr-49	1	38	,	,	PUNCT
flr-49	1	39	f	f	PROPN
flr-49	1	40	+65	+65	PROPN
flr-49	1	41	6896	6896	NUM
flr-49	1	42	9845	9845	NUM
flr-49	2	1	http://dx.doi.org/10.14786/flr.v1i1.49	http://dx.doi.org/10.14786/flr.v1i1.49	PROPN
flr-49	2	2	81	81	NUM
flr-49	3	1	|	|	ADV
flr-49	3	2	f	f	NOUN
flr-49	3	3	l	l	NOUN
flr-49	3	4	r	r	NOUN
flr-49	3	5	longer	long	ADV
flr-49	3	6	bars	bar	NOUN
flr-49	3	7	for	for	ADP
flr-49	3	8	bigger	big	ADJ
flr-49	3	9	numbers	number	NOUN
flr-49	3	10	?	?	PUNCT
flr-49	4	1	children	child	NOUN
flr-49	4	2	’s	’s	PART
flr-49	4	3	usage	usage	NOUN
flr-49	4	4	and	and	CCONJ
flr-49	4	5	understanding	understanding	NOUN
flr-49	4	6	of	of	ADP
flr-49	4	7	graphical	graphical	ADJ
flr-49	4	8	representations	representation	NOUN
flr-49	4	9	of	of	ADP
flr-49	4	10	algebraic	algebraic	ADJ
flr-49	4	11	problems	problem	NOUN
flr-49	4	12	kerry	kerry	PROPN
flr-49	4	13	lee	lee	PROPN
flr-49	4	14	,	,	PUNCT
flr-49	4	15	kiat	kiat	PROPN
flr-49	4	16	hui	hui	PROPN
flr-49	4	17	khng	khng	PROPN
flr-49	4	18	,	,	PUNCT
flr-49	4	19	swee	swee	PROPN
flr-49	4	20	fong	fong	PROPN
flr-49	4	21	ng	ng	PROPN
flr-49	4	22	,	,	PUNCT
flr-49	4	23	jeremy	jeremy	PROPN
flr-49	4	24	ng	ng	PROPN
flr-49	4	25	lan	lan	PROPN
flr-49	4	26	kong	kong	PROPN
flr-49	4	27	national	national	PROPN
flr-49	4	28	institute	institute	PROPN
flr-49	4	29	of	of	ADP
flr-49	4	30	education	education	PROPN
flr-49	4	31	,	,	PUNCT
flr-49	4	32	nanyang	nanyang	PROPN
flr-49	4	33	technological	technological	PROPN
flr-49	4	34	university	university	NOUN
flr-49	4	35	,	,	PUNCT
flr-49	4	36	singapore	singapore	PROPN
flr-49	4	37	article	article	NOUN
flr-49	4	38	received	receive	VERB
flr-49	4	39	7	7	NUM
flr-49	4	40	june	june	PROPN
flr-49	4	41	2013	2013	NUM
flr-49	4	42	/	/	PUNCT
flr-49	4	43	revised	revise	VERB
flr-49	4	44	19	19	NUM
flr-49	4	45	july	july	PROPN
flr-49	4	46	2013	2013	NUM
flr-49	4	47	/	/	PUNCT
flr-49	4	48	accepted	accept	VERB
flr-49	4	49	16	16	NUM
flr-49	4	50	august	august	PROPN
flr-49	4	51	2013	2013	NUM
flr-49	4	52	/	/	SYM
flr-49	4	53	available	available	ADJ
flr-49	4	54	online	online	ADJ
flr-49	4	55	27	27	NUM
flr-49	4	56	august	august	PROPN
flr-49	4	57	2013	2013	NUM
flr-49	4	58	abstract	abstract	NOUN
flr-49	4	59	in	in	ADP
flr-49	4	60	singapore	singapore	PROPN
flr-49	4	61	,	,	PUNCT
flr-49	4	62	primary	primary	ADJ
flr-49	4	63	school	school	NOUN
flr-49	4	64	students	student	NOUN
flr-49	4	65	are	be	AUX
flr-49	4	66	taught	teach	VERB
flr-49	4	67	to	to	PART
flr-49	4	68	use	use	VERB
flr-49	4	69	bar	bar	NOUN
flr-49	4	70	diagrams	diagram	NOUN
flr-49	4	71	to	to	PART
flr-49	4	72	represent	represent	VERB
flr-49	4	73	known	known	ADJ
flr-49	4	74	and	and	CCONJ
flr-49	4	75	unknown	unknown	ADJ
flr-49	4	76	values	value	NOUN
flr-49	4	77	in	in	ADP
flr-49	4	78	algebraic	algebraic	ADJ
flr-49	4	79	word	word	NOUN
flr-49	4	80	problems	problem	NOUN
flr-49	4	81	.	.	PUNCT
flr-49	5	1	however	however	ADV
flr-49	5	2	,	,	PUNCT
flr-49	5	3	little	little	ADJ
flr-49	5	4	is	be	AUX
flr-49	5	5	known	know	VERB
flr-49	5	6	about	about	ADP
flr-49	5	7	students	student	NOUN
flr-49	5	8	’	’	PART
flr-49	5	9	understanding	understanding	NOUN
flr-49	5	10	of	of	ADP
flr-49	5	11	these	these	DET
flr-49	5	12	graphical	graphical	ADJ
flr-49	5	13	representations	representation	NOUN
flr-49	5	14	.	.	PUNCT
flr-49	6	1	we	we	PRON
flr-49	6	2	investigated	investigate	VERB
flr-49	6	3	whether	whether	SCONJ
flr-49	6	4	students	student	NOUN
flr-49	6	5	use	use	VERB
flr-49	6	6	and	and	CCONJ
flr-49	6	7	think	think	VERB
flr-49	6	8	of	of	ADP
flr-49	6	9	the	the	DET
flr-49	6	10	bar	bar	NOUN
flr-49	6	11	diagrams	diagram	NOUN
flr-49	6	12	in	in	ADP
flr-49	6	13	a	a	DET
flr-49	6	14	concrete	concrete	NOUN
flr-49	6	15	or	or	CCONJ
flr-49	6	16	a	a	DET
flr-49	6	17	more	more	ADV
flr-49	6	18	abstract	abstract	ADJ
flr-49	6	19	fashion	fashion	NOUN
flr-49	6	20	.	.	PUNCT
flr-49	7	1	we	we	PRON
flr-49	7	2	also	also	ADV
flr-49	7	3	examined	examine	VERB
flr-49	7	4	whether	whether	SCONJ
flr-49	7	5	usage	usage	NOUN
flr-49	7	6	and	and	CCONJ
flr-49	7	7	understanding	understanding	NOUN
flr-49	7	8	varied	varied	ADJ
flr-49	7	9	with	with	ADP
flr-49	7	10	grade	grade	NOUN
flr-49	7	11	.	.	PUNCT
flr-49	8	1	secondary	secondary	ADJ
flr-49	8	2	2	2	NUM
flr-49	8	3	(	(	PUNCT
flr-49	8	4	n	n	NOUN
flr-49	8	5	=	=	SYM
flr-49	8	6	68	68	NUM
flr-49	8	7	,	,	PUNCT
flr-49	8	8	mage	mage	NOUN
flr-49	8	9	=	=	NOUN
flr-49	8	10	13.9	13.9	NUM
flr-49	8	11	years	year	NOUN
flr-49	8	12	)	)	PUNCT
flr-49	8	13	and	and	CCONJ
flr-49	8	14	primary	primary	ADJ
flr-49	8	15	5	5	NUM
flr-49	8	16	students	student	NOUN
flr-49	8	17	(	(	PUNCT
flr-49	8	18	n	n	NOUN
flr-49	8	19	=	=	SYM
flr-49	8	20	110	110	NUM
flr-49	8	21	,	,	PUNCT
flr-49	8	22	mage	mage	NOUN
flr-49	8	23	=	=	NOUN
flr-49	8	24	11.1	11.1	NUM
flr-49	8	25	years	year	NOUN
flr-49	8	26	)	)	PUNCT
flr-49	8	27	were	be	AUX
flr-49	8	28	administered	administer	VERB
flr-49	8	29	a	a	DET
flr-49	8	30	production	production	NOUN
flr-49	8	31	task	task	NOUN
flr-49	8	32	in	in	ADP
flr-49	8	33	which	which	PRON
flr-49	8	34	they	they	PRON
flr-49	8	35	drew	draw	VERB
flr-49	8	36	bar	bar	NOUN
flr-49	8	37	diagrams	diagram	NOUN
flr-49	8	38	of	of	ADP
flr-49	8	39	algebraic	algebraic	ADJ
flr-49	8	40	word	word	NOUN
flr-49	8	41	problems	problem	NOUN
flr-49	8	42	with	with	ADP
flr-49	8	43	operands	operand	NOUN
flr-49	8	44	of	of	ADP
flr-49	8	45	varying	vary	VERB
flr-49	8	46	magnitude	magnitude	NOUN
flr-49	8	47	.	.	PUNCT
flr-49	9	1	in	in	ADP
flr-49	9	2	the	the	DET
flr-49	9	3	validation	validation	NOUN
flr-49	9	4	task	task	NOUN
flr-49	9	5	,	,	PUNCT
flr-49	9	6	they	they	PRON
flr-49	9	7	were	be	AUX
flr-49	9	8	presented	present	VERB
flr-49	9	9	with	with	ADP
flr-49	9	10	different	different	ADJ
flr-49	9	11	bar	bar	NOUN
flr-49	9	12	diagrams	diagram	NOUN
flr-49	9	13	for	for	ADP
flr-49	9	14	the	the	DET
flr-49	9	15	same	same	ADJ
flr-49	9	16	word	word	NOUN
flr-49	9	17	problems	problem	NOUN
flr-49	9	18	and	and	CCONJ
flr-49	9	19	were	be	AUX
flr-49	9	20	asked	ask	VERB
flr-49	9	21	to	to	PART
flr-49	9	22	ascertain	ascertain	VERB
flr-49	9	23	,	,	PUNCT
flr-49	9	24	and	and	CCONJ
flr-49	9	25	give	give	VERB
flr-49	9	26	explanations	explanation	NOUN
flr-49	9	27	regarding	regard	VERB
flr-49	9	28	the	the	DET
flr-49	9	29	accuracy	accuracy	NOUN
flr-49	9	30	of	of	ADP
flr-49	9	31	the	the	DET
flr-49	9	32	diagrams	diagram	NOUN
flr-49	9	33	.	.	PUNCT
flr-49	10	1	the	the	DET
flr-49	10	2	küchemann	küchemann	PROPN
flr-49	10	3	algebra	algebra	PROPN
flr-49	10	4	test	test	NOUN
flr-49	10	5	was	be	AUX
flr-49	10	6	administered	administer	VERB
flr-49	10	7	to	to	ADP
flr-49	10	8	the	the	DET
flr-49	10	9	secondary	secondary	ADJ
flr-49	10	10	2	2	NUM
flr-49	10	11	students	student	NOUN
flr-49	10	12	.	.	PUNCT
flr-49	11	1	students	student	NOUN
flr-49	11	2	from	from	ADP
flr-49	11	3	both	both	DET
flr-49	11	4	grades	grade	NOUN
flr-49	11	5	drew	draw	VERB
flr-49	11	6	longer	long	ADJ
flr-49	11	7	bars	bar	NOUN
flr-49	11	8	to	to	PART
flr-49	11	9	represent	represent	VERB
flr-49	11	10	larger	large	ADJ
flr-49	11	11	numbers	number	NOUN
flr-49	11	12	.	.	PUNCT
flr-49	12	1	in	in	ADP
flr-49	12	2	contrast	contrast	NOUN
flr-49	12	3	,	,	PUNCT
flr-49	12	4	findings	finding	NOUN
flr-49	12	5	from	from	ADP
flr-49	12	6	the	the	DET
flr-49	12	7	validation	validation	NOUN
flr-49	12	8	task	task	NOUN
flr-49	12	9	showed	show	VERB
flr-49	12	10	a	a	DET
flr-49	12	11	more	more	ADV
flr-49	12	12	abstract	abstract	ADJ
flr-49	12	13	appreciation	appreciation	NOUN
flr-49	12	14	for	for	ADP
flr-49	12	15	how	how	SCONJ
flr-49	12	16	the	the	DET
flr-49	12	17	bar	bar	NOUN
flr-49	12	18	diagrams	diagram	NOUN
flr-49	12	19	can	can	AUX
flr-49	12	20	be	be	AUX
flr-49	12	21	used	use	VERB
flr-49	12	22	.	.	PUNCT
flr-49	13	1	primary	primary	ADJ
flr-49	13	2	5	5	NUM
flr-49	13	3	students	student	NOUN
flr-49	13	4	who	who	PRON
flr-49	13	5	showed	show	VERB
flr-49	13	6	more	more	ADJ
flr-49	13	7	abstract	abstract	ADJ
flr-49	13	8	appreciations	appreciation	NOUN
flr-49	13	9	in	in	ADP
flr-49	13	10	the	the	DET
flr-49	13	11	validation	validation	NOUN
flr-49	13	12	task	task	NOUN
flr-49	13	13	were	be	AUX
flr-49	13	14	less	less	ADV
flr-49	13	15	likely	likely	ADJ
flr-49	13	16	to	to	PART
flr-49	13	17	use	use	VERB
flr-49	13	18	the	the	DET
flr-49	13	19	bar	bar	NOUN
flr-49	13	20	diagrams	diagram	NOUN
flr-49	13	21	in	in	ADP
flr-49	13	22	a	a	DET
flr-49	13	23	concrete	concrete	ADJ
flr-49	13	24	fashion	fashion	NOUN
flr-49	13	25	in	in	ADP
flr-49	13	26	the	the	DET
flr-49	13	27	production	production	NOUN
flr-49	13	28	task	task	NOUN
flr-49	13	29	.	.	PUNCT
flr-49	14	1	performance	performance	NOUN
flr-49	14	2	on	on	ADP
flr-49	14	3	the	the	DET
flr-49	14	4	küchemann	küchemann	PROPN
flr-49	14	5	algebra	algebra	PROPN
flr-49	14	6	test	test	NOUN
flr-49	14	7	was	be	AUX
flr-49	14	8	unrelated	unrelated	ADJ
flr-49	14	9	to	to	ADP
flr-49	14	10	performance	performance	NOUN
flr-49	14	11	on	on	ADP
flr-49	14	12	the	the	DET
flr-49	14	13	production	production	NOUN
flr-49	14	14	task	task	NOUN
flr-49	14	15	or	or	CCONJ
flr-49	14	16	the	the	DET
flr-49	14	17	validation	validation	NOUN
flr-49	14	18	task	task	NOUN
flr-49	14	19	.	.	PUNCT
flr-49	15	1	the	the	DET
flr-49	15	2	findings	finding	NOUN
flr-49	15	3	are	be	AUX
flr-49	15	4	discussed	discuss	VERB
flr-49	15	5	in	in	ADP
flr-49	15	6	terms	term	NOUN
flr-49	15	7	of	of	ADP
flr-49	15	8	a	a	DET
flr-49	15	9	production	production	NOUN
flr-49	15	10	deficit	deficit	NOUN
flr-49	15	11	,	,	PUNCT
flr-49	15	12	with	with	ADP
flr-49	15	13	students	student	NOUN
flr-49	15	14	exhibiting	exhibit	VERB
flr-49	15	15	a	a	DET
flr-49	15	16	more	more	ADV
flr-49	15	17	sophisticated	sophisticated	ADJ
flr-49	15	18	understanding	understanding	NOUN
flr-49	15	19	of	of	ADP
flr-49	15	20	bar	bar	NOUN
flr-49	15	21	diagrams	diagram	NOUN
flr-49	15	22	than	than	SCONJ
flr-49	15	23	is	be	AUX
flr-49	15	24	demonstrated	demonstrate	VERB
flr-49	15	25	by	by	ADP
flr-49	15	26	their	their	PRON
flr-49	15	27	usage	usage	NOUN
flr-49	15	28	.	.	PUNCT
flr-49	16	1	keywords	keyword	NOUN
flr-49	16	2	:	:	PUNCT
flr-49	16	3	algebra	algebra	NOUN
flr-49	16	4	;	;	PUNCT
flr-49	16	5	pre	pre	ADJ
flr-49	16	6	-	-	NOUN
flr-49	16	7	algebra	algebra	ADJ
flr-49	16	8	;	;	PUNCT
flr-49	16	9	graphical	graphical	ADJ
flr-49	16	10	representation	representation	NOUN
flr-49	16	11	;	;	PUNCT
flr-49	16	12	mathematical	mathematical	ADJ
flr-49	16	13	understanding	understanding	NOUN
flr-49	16	14	k.	k.	PROPN
flr-49	16	15	lee	lee	PROPN
flr-49	16	16	et	et	PROPN
flr-49	16	17	al	al	PROPN
flr-49	16	18	.	.	PROPN
flr-49	16	19	82	82	NUM
flr-49	17	1	|	|	NOUN
flr-49	17	2	f	f	NOUN
flr-49	17	3	l	l	NOUN
flr-49	17	4	r	r	NOUN
flr-49	17	5	1	1	NUM
flr-49	17	6	.	.	PUNCT
flr-49	18	1	introduction	introduction	NOUN
flr-49	18	2	singapore	singapore	PROPN
flr-49	18	3	has	have	AUX
flr-49	18	4	performed	perform	VERB
flr-49	18	5	well	well	ADV
flr-49	18	6	in	in	ADP
flr-49	18	7	recent	recent	ADJ
flr-49	18	8	international	international	ADJ
flr-49	18	9	tests	test	NOUN
flr-49	18	10	of	of	ADP
flr-49	18	11	mathematics	mathematic	NOUN
flr-49	18	12	(	(	PUNCT
flr-49	18	13	mullis	mullis	PROPN
flr-49	18	14	,	,	PUNCT
flr-49	18	15	martin	martin	PROPN
flr-49	18	16	,	,	PUNCT
flr-49	18	17	gonzalez	gonzalez	PROPN
flr-49	18	18	,	,	PUNCT
flr-49	18	19	&	&	CCONJ
flr-49	18	20	chrostowski	chrostowski	PROPN
flr-49	18	21	,	,	PUNCT
flr-49	18	22	2004	2004	NUM
flr-49	18	23	;	;	PUNCT
flr-49	18	24	oecd	oecd	PROPN
flr-49	18	25	,	,	PUNCT
flr-49	18	26	2010	2010	NUM
flr-49	18	27	)	)	PUNCT
flr-49	18	28	.	.	PUNCT
flr-49	19	1	perhaps	perhaps	ADV
flr-49	19	2	because	because	SCONJ
flr-49	19	3	of	of	ADP
flr-49	19	4	this	this	PRON
flr-49	19	5	,	,	PUNCT
flr-49	19	6	there	there	PRON
flr-49	19	7	has	have	AUX
flr-49	19	8	been	be	AUX
flr-49	19	9	much	much	ADJ
flr-49	19	10	interest	interest	NOUN
flr-49	19	11	in	in	ADP
flr-49	19	12	the	the	DET
flr-49	19	13	singapore	singapore	PROPN
flr-49	19	14	mathematics	mathematics	PROPN
flr-49	19	15	curriculum	curriculum	PROPN
flr-49	19	16	,	,	PUNCT
flr-49	19	17	with	with	SCONJ
flr-49	19	18	some	some	DET
flr-49	19	19	schools	school	NOUN
flr-49	19	20	in	in	ADP
flr-49	19	21	other	other	ADJ
flr-49	19	22	countries	country	NOUN
flr-49	19	23	having	having	AUX
flr-49	19	24	been	be	AUX
flr-49	19	25	reported	report	VERB
flr-49	19	26	to	to	PART
flr-49	19	27	have	have	AUX
flr-49	19	28	adopted	adopt	VERB
flr-49	19	29	her	her	PRON
flr-49	19	30	curriculum	curriculum	NOUN
flr-49	19	31	(	(	PUNCT
flr-49	19	32	e.g.	e.g.	ADV
flr-49	19	33	,	,	PUNCT
flr-49	19	34	hu	hu	PROPN
flr-49	19	35	,	,	PUNCT
flr-49	19	36	2010	2010	NUM
flr-49	19	37	)	)	PUNCT
flr-49	19	38	.	.	PUNCT
flr-49	20	1	the	the	DET
flr-49	20	2	wisdom	wisdom	NOUN
flr-49	20	3	of	of	ADP
flr-49	20	4	such	such	ADJ
flr-49	20	5	cross	cross	ADJ
flr-49	20	6	-	-	ADJ
flr-49	20	7	country	country	ADJ
flr-49	20	8	adoption	adoption	NOUN
flr-49	20	9	aside	aside	ADV
flr-49	20	10	,	,	PUNCT
flr-49	20	11	one	one	NUM
flr-49	20	12	peculiar	peculiar	ADJ
flr-49	20	13	feature	feature	NOUN
flr-49	20	14	of	of	ADP
flr-49	20	15	the	the	DET
flr-49	20	16	singapore	singapore	PROPN
flr-49	20	17	curriculum	curriculum	NOUN
flr-49	20	18	is	be	AUX
flr-49	20	19	that	that	SCONJ
flr-49	20	20	algebraic	algebraic	ADJ
flr-49	20	21	thinking	thinking	NOUN
flr-49	20	22	is	be	AUX
flr-49	20	23	introduced	introduce	VERB
flr-49	20	24	early	early	ADV
flr-49	20	25	.	.	PUNCT
flr-49	21	1	unlike	unlike	ADP
flr-49	21	2	many	many	ADJ
flr-49	21	3	countries	country	NOUN
flr-49	21	4	where	where	SCONJ
flr-49	21	5	algebra	algebra	NOUN
flr-49	21	6	is	be	AUX
flr-49	21	7	introduced	introduce	VERB
flr-49	21	8	in	in	ADP
flr-49	21	9	the	the	DET
flr-49	21	10	secondary	secondary	ADJ
flr-49	21	11	or	or	CCONJ
flr-49	21	12	high	high	ADJ
flr-49	21	13	school	school	NOUN
flr-49	21	14	years	year	NOUN
flr-49	21	15	,	,	PUNCT
flr-49	21	16	mathematical	mathematical	ADJ
flr-49	21	17	problems	problem	NOUN
flr-49	21	18	with	with	ADP
flr-49	21	19	an	an	DET
flr-49	21	20	algebraic	algebraic	ADJ
flr-49	21	21	structure	structure	NOUN
flr-49	21	22	are	be	AUX
flr-49	21	23	taught	teach	VERB
flr-49	21	24	in	in	ADP
flr-49	21	25	the	the	DET
flr-49	21	26	senior	senior	ADJ
flr-49	21	27	primary	primary	ADJ
flr-49	21	28	years	year	NOUN
flr-49	21	29	(	(	PUNCT
flr-49	21	30	grades	grade	NOUN
flr-49	21	31	4	4	NUM
flr-49	21	32	–	–	PUNCT
flr-49	21	33	6	6	NUM
flr-49	21	34	)	)	PUNCT
flr-49	21	35	.	.	PUNCT
flr-49	22	1	algebra	algebra	NOUN
flr-49	22	2	is	be	AUX
flr-49	22	3	recognised	recognise	VERB
flr-49	22	4	widely	widely	ADV
flr-49	22	5	as	as	ADP
flr-49	22	6	an	an	DET
flr-49	22	7	important	important	ADJ
flr-49	22	8	pillar	pillar	NOUN
flr-49	22	9	for	for	ADP
flr-49	22	10	both	both	CCONJ
flr-49	22	11	academic	academic	ADJ
flr-49	22	12	and	and	CCONJ
flr-49	22	13	economic	economic	ADJ
flr-49	22	14	success	success	NOUN
flr-49	22	15	(	(	PUNCT
flr-49	22	16	national	national	ADJ
flr-49	22	17	council	council	NOUN
flr-49	22	18	for	for	ADP
flr-49	22	19	teachers	teacher	NOUN
flr-49	22	20	of	of	ADP
flr-49	22	21	mathematics	mathematic	NOUN
flr-49	22	22	,	,	PUNCT
flr-49	22	23	2000	2000	NUM
flr-49	22	24	;	;	PUNCT
flr-49	22	25	national	national	ADJ
flr-49	22	26	mathematics	mathematics	PROPN
flr-49	22	27	advisory	advisory	ADJ
flr-49	22	28	panel	panel	NOUN
flr-49	22	29	,	,	PUNCT
flr-49	22	30	2008	2008	NUM
flr-49	22	31	)	)	PUNCT
flr-49	22	32	.	.	PUNCT
flr-49	23	1	primary	primary	ADJ
flr-49	23	2	school	school	NOUN
flr-49	23	3	children	child	NOUN
flr-49	23	4	have	have	AUX
flr-49	23	5	been	be	AUX
flr-49	23	6	shown	show	VERB
flr-49	23	7	capable	capable	ADJ
flr-49	23	8	of	of	ADP
flr-49	23	9	exhibiting	exhibit	VERB
flr-49	23	10	algebraic	algebraic	ADJ
flr-49	23	11	thinking	thinking	NOUN
flr-49	23	12	(	(	PUNCT
flr-49	23	13	e.g.	e.g.	ADV
flr-49	23	14	carpenter	carpenter	NOUN
flr-49	23	15	&	&	CCONJ
flr-49	23	16	levi	levi	PROPN
flr-49	23	17	,	,	PUNCT
flr-49	23	18	2000	2000	NUM
flr-49	23	19	;	;	PUNCT
flr-49	23	20	carraher	carraher	NOUN
flr-49	23	21	,	,	PUNCT
flr-49	23	22	schliemann	schliemann	NOUN
flr-49	23	23	,	,	PUNCT
flr-49	23	24	brizuela	brizuela	PROPN
flr-49	23	25	,	,	PUNCT
flr-49	23	26	&	&	CCONJ
flr-49	23	27	earnest	earnest	ADJ
flr-49	23	28	,	,	PUNCT
flr-49	23	29	2006	2006	NUM
flr-49	23	30	;	;	PUNCT
flr-49	23	31	ng	ng	PROPN
flr-49	23	32	&	&	CCONJ
flr-49	23	33	lee	lee	PROPN
flr-49	23	34	,	,	PUNCT
flr-49	23	35	2009	2009	NUM
flr-49	23	36	;	;	PUNCT
flr-49	23	37	swafford	swafford	PROPN
flr-49	23	38	&	&	CCONJ
flr-49	23	39	langrall	langrall	PROPN
flr-49	23	40	,	,	PUNCT
flr-49	23	41	2000	2000	NUM
flr-49	23	42	;	;	PUNCT
flr-49	23	43	warren	warren	PROPN
flr-49	23	44	&	&	CCONJ
flr-49	23	45	cooper	cooper	PROPN
flr-49	23	46	,	,	PUNCT
flr-49	23	47	2005	2005	NUM
flr-49	23	48	;	;	PUNCT
flr-49	23	49	warren	warren	PROPN
flr-49	23	50	&	&	CCONJ
flr-49	23	51	cooper	cooper	PROPN
flr-49	23	52	,	,	PUNCT
flr-49	23	53	2009	2009	NUM
flr-49	23	54	)	)	PUNCT
flr-49	23	55	.	.	PUNCT
flr-49	24	1	however	however	ADV
flr-49	24	2	,	,	PUNCT
flr-49	24	3	whether	whether	SCONJ
flr-49	24	4	this	this	DET
flr-49	24	5	understanding	understanding	NOUN
flr-49	24	6	is	be	AUX
flr-49	24	7	similar	similar	ADJ
flr-49	24	8	to	to	ADP
flr-49	24	9	that	that	PRON
flr-49	24	10	of	of	ADP
flr-49	24	11	older	old	ADJ
flr-49	24	12	students	student	NOUN
flr-49	24	13	has	have	AUX
flr-49	24	14	not	not	PART
flr-49	24	15	been	be	AUX
flr-49	24	16	studied	study	VERB
flr-49	24	17	widely	widely	ADV
flr-49	24	18	.	.	PUNCT
flr-49	25	1	certainly	certainly	ADV
flr-49	25	2	,	,	PUNCT
flr-49	25	3	algebra	algebra	PROPN
flr-49	25	4	can	can	AUX
flr-49	25	5	be	be	AUX
flr-49	25	6	difficult	difficult	ADJ
flr-49	25	7	;	;	PUNCT
flr-49	25	8	even	even	ADV
flr-49	25	9	for	for	ADP
flr-49	25	10	college	college	NOUN
flr-49	25	11	students	student	NOUN
flr-49	25	12	.	.	PUNCT
flr-49	26	1	some	some	PRON
flr-49	26	2	of	of	ADP
flr-49	26	3	the	the	DET
flr-49	26	4	documented	document	VERB
flr-49	26	5	difficulties	difficulty	NOUN
flr-49	26	6	include	include	VERB
flr-49	26	7	intrusion	intrusion	NOUN
flr-49	26	8	of	of	ADP
flr-49	26	9	arithmetic	arithmetic	ADJ
flr-49	26	10	reasoning	reasoning	NOUN
flr-49	26	11	(	(	PUNCT
flr-49	26	12	e.g.	e.g.	ADV
flr-49	26	13	khng	khng	PROPN
flr-49	26	14	&	&	CCONJ
flr-49	26	15	lee	lee	PROPN
flr-49	26	16	,	,	PUNCT
flr-49	26	17	2009	2009	NUM
flr-49	26	18	;	;	PUNCT
flr-49	26	19	ng	ng	PROPN
flr-49	26	20	,	,	PUNCT
flr-49	26	21	2003	2003	NUM
flr-49	26	22	;	;	PUNCT
flr-49	26	23	stacey	stacey	PROPN
flr-49	26	24	&	&	CCONJ
flr-49	26	25	macgregor	macgregor	PROPN
flr-49	26	26	,	,	PUNCT
flr-49	26	27	1999	1999	NUM
flr-49	26	28	)	)	PUNCT
flr-49	26	29	,	,	PUNCT
flr-49	26	30	difficulties	difficulty	NOUN
flr-49	26	31	translating	translate	VERB
flr-49	26	32	word	word	NOUN
flr-49	26	33	problems	problem	NOUN
flr-49	26	34	to	to	ADP
flr-49	26	35	equations	equation	NOUN
flr-49	26	36	(	(	PUNCT
flr-49	26	37	e.g.	e.g.	ADV
flr-49	26	38	capraro	capraro	NOUN
flr-49	26	39	&	&	CCONJ
flr-49	26	40	joffrion	joffrion	PROPN
flr-49	26	41	,	,	PUNCT
flr-49	26	42	2006	2006	NUM
flr-49	26	43	;	;	PUNCT
flr-49	26	44	duru	duru	PROPN
flr-49	26	45	,	,	PUNCT
flr-49	26	46	2011	2011	NUM
flr-49	26	47	;	;	PUNCT
flr-49	26	48	hefferman	hefferman	NOUN
flr-49	26	49	&	&	CCONJ
flr-49	26	50	koedinger	koedinger	PROPN
flr-49	26	51	,	,	PUNCT
flr-49	26	52	1997	1997	NUM
flr-49	26	53	)	)	PUNCT
flr-49	26	54	,	,	PUNCT
flr-49	26	55	problems	problem	NOUN
flr-49	26	56	with	with	ADP
flr-49	26	57	the	the	DET
flr-49	26	58	concept	concept	NOUN
flr-49	26	59	of	of	ADP
flr-49	26	60	equivalence	equivalence	NOUN
flr-49	26	61	(	(	PUNCT
flr-49	26	62	e.g.	e.g.	ADV
flr-49	26	63	hunter	hunter	NOUN
flr-49	26	64	,	,	PUNCT
flr-49	26	65	2007	2007	NUM
flr-49	26	66	;	;	PUNCT
flr-49	26	67	kieran	kieran	PROPN
flr-49	26	68	,	,	PUNCT
flr-49	26	69	1981	1981	NUM
flr-49	26	70	;	;	PUNCT
flr-49	26	71	knuth	knuth	PROPN
flr-49	26	72	,	,	PUNCT
flr-49	26	73	stephens	stephens	PROPN
flr-49	26	74	,	,	PUNCT
flr-49	26	75	mcneil	mcneil	PROPN
flr-49	26	76	,	,	PUNCT
flr-49	26	77	&	&	CCONJ
flr-49	26	78	alibali	alibali	VERB
flr-49	26	79	,	,	PUNCT
flr-49	26	80	2006	2006	NUM
flr-49	26	81	;	;	PUNCT
flr-49	26	82	steinberg	steinberg	PROPN
flr-49	26	83	,	,	PUNCT
flr-49	26	84	sleeman	sleeman	NOUN
flr-49	26	85	,	,	PUNCT
flr-49	26	86	&	&	CCONJ
flr-49	26	87	ktorza	ktorza	PROPN
flr-49	26	88	,	,	PUNCT
flr-49	26	89	1991	1991	NUM
flr-49	26	90	)	)	PUNCT
flr-49	26	91	and	and	CCONJ
flr-49	26	92	poor	poor	ADJ
flr-49	26	93	understanding	understanding	NOUN
flr-49	26	94	of	of	ADP
flr-49	26	95	the	the	DET
flr-49	26	96	concept	concept	NOUN
flr-49	26	97	of	of	ADP
flr-49	26	98	variables	variable	NOUN
flr-49	26	99	(	(	PUNCT
flr-49	26	100	e.g.	e.g.	ADV
flr-49	26	101	küchemann	küchemann	PROPN
flr-49	26	102	,	,	PUNCT
flr-49	26	103	1978	1978	NUM
flr-49	26	104	)	)	PUNCT
flr-49	26	105	.	.	PUNCT
flr-49	27	1	in	in	ADP
flr-49	27	2	this	this	DET
flr-49	27	3	study	study	NOUN
flr-49	27	4	,	,	PUNCT
flr-49	27	5	we	we	PRON
flr-49	27	6	focused	focus	VERB
flr-49	27	7	on	on	ADP
flr-49	27	8	an	an	DET
flr-49	27	9	important	important	ADJ
flr-49	27	10	pedagogical	pedagogical	ADJ
flr-49	27	11	device	device	NOUN
flr-49	27	12	for	for	ADP
flr-49	27	13	providing	provide	VERB
flr-49	27	14	children	child	NOUN
flr-49	27	15	with	with	ADP
flr-49	27	16	earlier	early	ADJ
flr-49	27	17	access	access	NOUN
flr-49	27	18	to	to	ADP
flr-49	27	19	algebraic	algebraic	ADJ
flr-49	27	20	problems	problem	NOUN
flr-49	27	21	.	.	PUNCT
flr-49	28	1	in	in	ADP
flr-49	28	2	the	the	DET
flr-49	28	3	latter	latter	ADJ
flr-49	28	4	part	part	NOUN
flr-49	28	5	of	of	ADP
flr-49	28	6	primary	primary	ADJ
flr-49	28	7	4	4	NUM
flr-49	28	8	(	(	PUNCT
flr-49	28	9	grade	grade	NOUN
flr-49	28	10	4	4	NUM
flr-49	28	11	,	,	PUNCT
flr-49	28	12	~10	~10	ADJ
flr-49	28	13	years	year	NOUN
flr-49	28	14	old	old	ADJ
flr-49	28	15	)	)	PUNCT
flr-49	28	16	,	,	PUNCT
flr-49	28	17	children	child	NOUN
flr-49	28	18	in	in	ADP
flr-49	28	19	singapore	singapore	PROPN
flr-49	28	20	are	be	AUX
flr-49	28	21	introduced	introduce	VERB
flr-49	28	22	to	to	ADP
flr-49	28	23	algebraic	algebraic	ADJ
flr-49	28	24	or	or	CCONJ
flr-49	28	25	start	start	VERB
flr-49	28	26	-	-	PUNCT
flr-49	28	27	unknown	unknown	ADJ
flr-49	28	28	word	word	NOUN
flr-49	28	29	problems	problem	NOUN
flr-49	28	30	.	.	PUNCT
flr-49	29	1	instead	instead	ADV
flr-49	29	2	of	of	ADP
flr-49	29	3	symbolic	symbolic	ADJ
flr-49	29	4	algebra	algebra	NOUN
flr-49	29	5	,	,	PUNCT
flr-49	29	6	children	child	NOUN
flr-49	29	7	are	be	AUX
flr-49	29	8	taught	teach	VERB
flr-49	29	9	a	a	DET
flr-49	29	10	graphical	graphical	ADJ
flr-49	29	11	heuristic	heuristic	NOUN
flr-49	29	12	in	in	ADP
flr-49	29	13	which	which	PRON
flr-49	29	14	they	they	PRON
flr-49	29	15	draw	draw	VERB
flr-49	29	16	bar	bar	NOUN
flr-49	29	17	diagrams	diagram	NOUN
flr-49	29	18	to	to	PART
flr-49	29	19	represent	represent	VERB
flr-49	29	20	known	known	ADJ
flr-49	29	21	and	and	CCONJ
flr-49	29	22	unknown	unknown	ADJ
flr-49	29	23	quantities	quantity	NOUN
flr-49	29	24	(	(	PUNCT
flr-49	29	25	ng	ng	PROPN
flr-49	29	26	&	&	CCONJ
flr-49	29	27	lee	lee	PROPN
flr-49	29	28	,	,	PUNCT
flr-49	29	29	2005	2005	NUM
flr-49	29	30	)	)	PUNCT
flr-49	29	31	.	.	PUNCT
flr-49	30	1	we	we	PRON
flr-49	30	2	examined	examine	VERB
flr-49	30	3	children	child	NOUN
flr-49	30	4	’s	’s	PART
flr-49	30	5	usage	usage	NOUN
flr-49	30	6	and	and	CCONJ
flr-49	30	7	understanding	understanding	NOUN
flr-49	30	8	of	of	ADP
flr-49	30	9	this	this	DET
flr-49	30	10	heuristic	heuristic	NOUN
flr-49	30	11	.	.	PUNCT
flr-49	31	1	1.1	1.1	NUM
flr-49	31	2	an	an	DET
flr-49	31	3	early	early	ADJ
flr-49	31	4	start	start	NOUN
flr-49	31	5	to	to	ADP
flr-49	31	6	learning	learn	VERB
flr-49	31	7	algebra	algebra	NOUN
flr-49	31	8	this	this	DET
flr-49	31	9	graphical	graphical	ADJ
flr-49	31	10	heuristic	heuristic	NOUN
flr-49	31	11	,	,	PUNCT
flr-49	31	12	also	also	ADV
flr-49	31	13	called	call	VERB
flr-49	31	14	the	the	DET
flr-49	31	15	model	model	NOUN
flr-49	31	16	method	method	NOUN
flr-49	31	17	,	,	PUNCT
flr-49	31	18	provides	provide	VERB
flr-49	31	19	students	student	NOUN
flr-49	31	20	with	with	ADP
flr-49	31	21	access	access	NOUN
flr-49	31	22	to	to	ADP
flr-49	31	23	problems	problem	NOUN
flr-49	31	24	that	that	PRON
flr-49	31	25	would	would	AUX
flr-49	31	26	otherwise	otherwise	ADV
flr-49	31	27	require	require	VERB
flr-49	31	28	symbolic	symbolic	ADJ
flr-49	31	29	algebra	algebra	NOUN
flr-49	31	30	.	.	PUNCT
flr-49	32	1	three	three	NUM
flr-49	32	2	different	different	ADJ
flr-49	32	3	types	type	NOUN
flr-49	32	4	of	of	ADP
flr-49	32	5	graphical	graphical	ADJ
flr-49	32	6	models	model	NOUN
flr-49	32	7	are	be	AUX
flr-49	32	8	commonly	commonly	ADV
flr-49	32	9	taught	teach	VERB
flr-49	32	10	:	:	PUNCT
flr-49	32	11	(	(	PUNCT
flr-49	32	12	a	a	X
flr-49	32	13	)	)	PUNCT
flr-49	32	14	part	part	NOUN
flr-49	32	15	-	-	PUNCT
flr-49	32	16	whole	whole	NOUN
flr-49	32	17	,	,	PUNCT
flr-49	32	18	(	(	PUNCT
flr-49	32	19	b	b	X
flr-49	32	20	)	)	PUNCT
flr-49	32	21	comparison	comparison	NOUN
flr-49	32	22	,	,	PUNCT
flr-49	32	23	and	and	CCONJ
flr-49	32	24	(	(	PUNCT
flr-49	32	25	c	c	NOUN
flr-49	32	26	)	)	PUNCT
flr-49	32	27	multiplication	multiplication	NOUN
flr-49	32	28	and	and	CCONJ
flr-49	32	29	division	division	NOUN
flr-49	32	30	models	model	NOUN
flr-49	32	31	(	(	PUNCT
flr-49	32	32	ng	ng	PROPN
flr-49	32	33	&	&	CCONJ
flr-49	32	34	lee	lee	PROPN
flr-49	32	35	,	,	PUNCT
flr-49	32	36	2009	2009	NUM
flr-49	32	37	)	)	PUNCT
flr-49	32	38	.	.	PUNCT
flr-49	33	1	to	to	PART
flr-49	33	2	illustrate	illustrate	VERB
flr-49	33	3	its	its	PRON
flr-49	33	4	operation	operation	NOUN
flr-49	33	5	,	,	PUNCT
flr-49	33	6	take	take	VERB
flr-49	33	7	for	for	ADP
flr-49	33	8	example	example	NOUN
flr-49	33	9	a	a	DET
flr-49	33	10	simple	simple	ADJ
flr-49	33	11	question	question	NOUN
flr-49	33	12	.	.	PUNCT
flr-49	34	1	mary	mary	PROPN
flr-49	34	2	and	and	CCONJ
flr-49	34	3	john	john	PROPN
flr-49	34	4	have	have	VERB
flr-49	34	5	6	6	NUM
flr-49	34	6	marbles	marble	NOUN
flr-49	34	7	altogether	altogether	ADV
flr-49	34	8	.	.	PUNCT
flr-49	35	1	john	john	PROPN
flr-49	35	2	has	have	VERB
flr-49	35	3	2	2	NUM
flr-49	35	4	more	more	ADJ
flr-49	35	5	marbles	marble	NOUN
flr-49	35	6	than	than	ADP
flr-49	35	7	mary	mary	PROPN
flr-49	35	8	.	.	PUNCT
flr-49	36	1	how	how	SCONJ
flr-49	36	2	many	many	ADJ
flr-49	36	3	marbles	marble	NOUN
flr-49	36	4	does	do	AUX
flr-49	36	5	mary	mary	PROPN
flr-49	36	6	have	have	VERB
flr-49	36	7	?	?	PUNCT
flr-49	37	1	figure	figure	NOUN
flr-49	37	2	1	1	NUM
flr-49	37	3	shows	show	VERB
flr-49	37	4	the	the	DET
flr-49	37	5	graphical	graphical	ADJ
flr-49	37	6	and	and	CCONJ
flr-49	37	7	letter	letter	NOUN
flr-49	37	8	symbolic	symbolic	ADJ
flr-49	37	9	approach	approach	NOUN
flr-49	37	10	to	to	ADP
flr-49	37	11	the	the	DET
flr-49	37	12	problem	problem	NOUN
flr-49	37	13	.	.	PUNCT
flr-49	38	1	in	in	ADP
flr-49	38	2	the	the	DET
flr-49	38	3	graphical	graphical	ADJ
flr-49	38	4	approach	approach	NOUN
flr-49	38	5	,	,	PUNCT
flr-49	38	6	students	student	NOUN
flr-49	38	7	draw	draw	VERB
flr-49	38	8	rectangular	rectangular	ADJ
flr-49	38	9	bars	bar	NOUN
flr-49	38	10	to	to	PART
flr-49	38	11	represent	represent	VERB
flr-49	38	12	the	the	DET
flr-49	38	13	number	number	NOUN
flr-49	38	14	of	of	ADP
flr-49	38	15	marbles	marble	NOUN
flr-49	38	16	carried	carry	VERB
flr-49	38	17	by	by	ADP
flr-49	38	18	mary	mary	PROPN
flr-49	38	19	and	and	CCONJ
flr-49	38	20	john	john	PROPN
flr-49	38	21	.	.	PUNCT
flr-49	39	1	the	the	DET
flr-49	39	2	difference	difference	NOUN
flr-49	39	3	between	between	ADP
flr-49	39	4	the	the	DET
flr-49	39	5	two	two	NUM
flr-49	39	6	quantities	quantity	NOUN
flr-49	39	7	is	be	AUX
flr-49	39	8	shown	show	VERB
flr-49	39	9	by	by	ADP
flr-49	39	10	drawing	draw	VERB
flr-49	39	11	one	one	NUM
flr-49	39	12	bar	bar	NOUN
flr-49	39	13	longer	long	ADV
flr-49	39	14	than	than	ADP
flr-49	39	15	the	the	DET
flr-49	39	16	other	other	ADJ
flr-49	39	17	.	.	PUNCT
flr-49	40	1	because	because	SCONJ
flr-49	40	2	the	the	DET
flr-49	40	3	quantitative	quantitative	ADJ
flr-49	40	4	difference	difference	NOUN
flr-49	40	5	is	be	AUX
flr-49	40	6	specified	specify	VERB
flr-49	40	7	in	in	ADP
flr-49	40	8	the	the	DET
flr-49	40	9	question	question	NOUN
flr-49	40	10	,	,	PUNCT
flr-49	40	11	john	john	PROPN
flr-49	40	12	’s	’s	PART
flr-49	40	13	bar	bar	NOUN
flr-49	40	14	is	be	AUX
flr-49	40	15	drawn	draw	VERB
flr-49	40	16	longer	long	ADV
flr-49	40	17	and	and	CCONJ
flr-49	40	18	the	the	DET
flr-49	40	19	quantity	quantity	NOUN
flr-49	40	20	represented	represent	VERB
flr-49	40	21	by	by	ADP
flr-49	40	22	the	the	DET
flr-49	40	23	difference	difference	NOUN
flr-49	40	24	in	in	ADP
flr-49	40	25	length	length	NOUN
flr-49	40	26	-the	-the	DET
flr-49	40	27	difference	difference	NOUN
flr-49	40	28	unit	unit	NOUN
flr-49	40	29	-is	-i	VERB
flr-49	40	30	labelled	label	VERB
flr-49	40	31	as	as	ADP
flr-49	40	32	2	2	NUM
flr-49	40	33	.	.	PUNCT
flr-49	40	34	with	with	ADP
flr-49	40	35	this	this	DET
flr-49	40	36	graphical	graphical	ADJ
flr-49	40	37	representation	representation	NOUN
flr-49	40	38	,	,	PUNCT
flr-49	40	39	children	child	NOUN
flr-49	40	40	typically	typically	ADV
flr-49	40	41	proceed	proceed	VERB
flr-49	40	42	with	with	ADP
flr-49	40	43	a	a	DET
flr-49	40	44	variety	variety	NOUN
flr-49	40	45	of	of	ADP
flr-49	40	46	arithmetic	arithmetic	ADJ
flr-49	40	47	strategies	strategy	NOUN
flr-49	40	48	,	,	PUNCT
flr-49	40	49	such	such	ADJ
flr-49	40	50	as	as	ADP
flr-49	40	51	unwinding	unwind	VERB
flr-49	40	52	or	or	CCONJ
flr-49	40	53	guess	guess	NOUN
flr-49	40	54	-	-	PUNCT
flr-49	40	55	and	and	CCONJ
flr-49	40	56	-	-	PUNCT
flr-49	40	57	check	check	NOUN
flr-49	40	58	(	(	PUNCT
flr-49	40	59	nathan	nathan	PROPN
flr-49	40	60	&	&	CCONJ
flr-49	40	61	koedinger	koedinger	PROPN
flr-49	40	62	,	,	PUNCT
flr-49	40	63	2000	2000	NUM
flr-49	40	64	)	)	PUNCT
flr-49	40	65	,	,	PUNCT
flr-49	40	66	to	to	PART
flr-49	40	67	arrive	arrive	VERB
flr-49	40	68	at	at	ADP
flr-49	40	69	the	the	DET
flr-49	40	70	solution	solution	NOUN
flr-49	40	71	.	.	PUNCT
flr-49	41	1	k.	k.	PROPN
flr-49	41	2	lee	lee	PROPN
flr-49	41	3	et	et	PROPN
flr-49	41	4	al	al	PROPN
flr-49	41	5	.	.	PROPN
flr-49	41	6	83	83	NUM
flr-49	42	1	|	|	CCONJ
flr-49	42	2	f	f	NOUN
flr-49	42	3	l	l	NOUN
flr-49	42	4	r	r	NOUN
flr-49	42	5	(	(	PUNCT
flr-49	42	6	a	a	NOUN
flr-49	42	7	)	)	PUNCT
flr-49	42	8	solution	solution	NOUN
flr-49	42	9	by	by	ADP
flr-49	42	10	the	the	DET
flr-49	42	11	model	model	NOUN
flr-49	42	12	method	method	NOUN
flr-49	42	13	(	(	PUNCT
flr-49	42	14	b	b	NOUN
flr-49	42	15	)	)	PUNCT
flr-49	42	16	solution	solution	NOUN
flr-49	42	17	by	by	ADP
flr-49	42	18	letter	letter	NOUN
flr-49	42	19	-	-	PUNCT
flr-49	42	20	symbolic	symbolic	ADJ
flr-49	42	21	algebra	algebra	NOUN
flr-49	42	22	6	6	NUM
flr-49	42	23	–	–	SYM
flr-49	42	24	2	2	NUM
flr-49	42	25	=	=	SYM
flr-49	42	26	4	4	NUM
flr-49	42	27	2	2	NUM
flr-49	42	28	units	unit	NOUN
flr-49	42	29	=	=	NOUN
flr-49	42	30	4	4	NUM
flr-49	42	31	1	1	NUM
flr-49	42	32	unit	unit	NOUN
flr-49	42	33	=	=	SYM
flr-49	42	34	2	2	NUM
flr-49	42	35	mary	mary	PROPN
flr-49	42	36	has	have	VERB
flr-49	42	37	2	2	NUM
flr-49	42	38	marbles	marble	NOUN
flr-49	42	39	.	.	PUNCT
flr-49	43	1	let	let	VERB
flr-49	43	2	the	the	DET
flr-49	43	3	number	number	NOUN
flr-49	43	4	of	of	ADP
flr-49	43	5	marbles	marble	NOUN
flr-49	43	6	mary	mary	PROPN
flr-49	43	7	has	have	AUX
flr-49	43	8	be	be	VERB
flr-49	43	9	x.	x.	NOUN
flr-49	43	10	john	john	PROPN
flr-49	43	11	has	have	VERB
flr-49	43	12	x	x	SYM
flr-49	43	13	+	+	CCONJ
flr-49	43	14	2	2	NUM
flr-49	43	15	number	number	NOUN
flr-49	43	16	of	of	ADP
flr-49	43	17	marbles	marble	NOUN
flr-49	43	18	.	.	PUNCT
flr-49	44	1	x	x	PUNCT
flr-49	45	1	+	+	PUNCT
flr-49	45	2	x	x	SYM
flr-49	45	3	+	+	NUM
flr-49	45	4	2	2	NUM
flr-49	45	5	=	=	SYM
flr-49	45	6	6	6	NUM
flr-49	45	7	2x	2x	NUM
flr-49	45	8	=	=	SYM
flr-49	45	9	4	4	NUM
flr-49	45	10	x	x	SYM
flr-49	45	11	=	=	SYM
flr-49	45	12	2	2	NUM
flr-49	45	13	mary	mary	PROPN
flr-49	45	14	has	have	VERB
flr-49	45	15	2	2	NUM
flr-49	45	16	marbles	marble	NOUN
flr-49	45	17	.	.	PUNCT
flr-49	46	1	figure	figure	NOUN
flr-49	46	2	1	1	NUM
flr-49	46	3	.	.	PUNCT
flr-49	46	4	model	model	NOUN
flr-49	46	5	method	method	NOUN
flr-49	46	6	and	and	CCONJ
flr-49	46	7	the	the	DET
flr-49	46	8	symbolic	symbolic	ADJ
flr-49	46	9	algebra	algebra	NOUN
flr-49	46	10	approach	approach	NOUN
flr-49	46	11	to	to	ADP
flr-49	46	12	the	the	DET
flr-49	46	13	question	question	NOUN
flr-49	46	14	“	"	PUNCT
flr-49	46	15	mary	mary	PROPN
flr-49	46	16	and	and	CCONJ
flr-49	46	17	john	john	PROPN
flr-49	46	18	have	have	VERB
flr-49	46	19	6	6	NUM
flr-49	46	20	marbles	marble	NOUN
flr-49	46	21	altogether	altogether	ADV
flr-49	46	22	.	.	PUNCT
flr-49	47	1	john	john	PROPN
flr-49	47	2	has	have	VERB
flr-49	47	3	2	2	NUM
flr-49	47	4	more	more	ADJ
flr-49	47	5	marbles	marble	NOUN
flr-49	47	6	than	than	ADP
flr-49	47	7	mary	mary	PROPN
flr-49	47	8	.	.	PUNCT
flr-49	48	1	how	how	SCONJ
flr-49	48	2	many	many	ADJ
flr-49	48	3	marbles	marble	NOUN
flr-49	48	4	does	do	AUX
flr-49	48	5	mary	mary	PROPN
flr-49	48	6	have	have	VERB
flr-49	48	7	?	?	PUNCT
flr-49	48	8	”	"	PUNCT
flr-49	49	1	the	the	DET
flr-49	49	2	bar	bar	NOUN
flr-49	49	3	labelled	label	VERB
flr-49	49	4	“	"	PUNCT
flr-49	49	5	2	2	NUM
flr-49	49	6	”	"	PUNCT
flr-49	49	7	in	in	ADP
flr-49	49	8	(	(	PUNCT
flr-49	49	9	a	a	PRON
flr-49	49	10	)	)	PUNCT
flr-49	49	11	represents	represent	VERB
flr-49	49	12	the	the	DET
flr-49	49	13	difference	difference	NOUN
flr-49	49	14	unit	unit	NOUN
flr-49	49	15	.	.	PUNCT
flr-49	50	1	formal	formal	ADJ
flr-49	50	2	algebraic	algebraic	ADJ
flr-49	50	3	notations	notation	NOUN
flr-49	50	4	in	in	ADP
flr-49	50	5	the	the	DET
flr-49	50	6	form	form	NOUN
flr-49	50	7	of	of	ADP
flr-49	50	8	letter	letter	NOUN
flr-49	50	9	symbols	symbol	NOUN
flr-49	50	10	and	and	CCONJ
flr-49	50	11	related	related	ADJ
flr-49	50	12	expressions	expression	NOUN
flr-49	50	13	were	be	AUX
flr-49	50	14	not	not	PART
flr-49	50	15	introduced	introduce	VERB
flr-49	50	16	till	till	SCONJ
flr-49	50	17	some	some	DET
flr-49	50	18	time	time	NOUN
flr-49	50	19	into	into	ADP
flr-49	50	20	grade	grade	NOUN
flr-49	50	21	6	6	NUM
flr-49	50	22	.	.	PUNCT
flr-49	51	1	although	although	SCONJ
flr-49	51	2	both	both	CCONJ
flr-49	51	3	the	the	DET
flr-49	51	4	model	model	NOUN
flr-49	51	5	method	method	NOUN
flr-49	51	6	and	and	CCONJ
flr-49	51	7	symbolic	symbolic	ADJ
flr-49	51	8	algebra	algebra	NOUN
flr-49	51	9	require	require	VERB
flr-49	51	10	students	student	NOUN
flr-49	51	11	to	to	PART
flr-49	51	12	translate	translate	VERB
flr-49	51	13	information	information	NOUN
flr-49	51	14	in	in	ADP
flr-49	51	15	a	a	DET
flr-49	51	16	word	word	NOUN
flr-49	51	17	problem	problem	NOUN
flr-49	51	18	to	to	ADP
flr-49	51	19	an	an	DET
flr-49	51	20	alternative	alternative	ADJ
flr-49	51	21	representation	representation	NOUN
flr-49	51	22	,	,	PUNCT
flr-49	51	23	there	there	PRON
flr-49	51	24	are	be	VERB
flr-49	51	25	some	some	DET
flr-49	51	26	fundamental	fundamental	ADJ
flr-49	51	27	differences	difference	NOUN
flr-49	51	28	.	.	PUNCT
flr-49	52	1	symbolic	symbolic	ADJ
flr-49	52	2	algebra	algebra	PROPN
flr-49	52	3	requires	require	VERB
flr-49	52	4	students	student	NOUN
flr-49	52	5	to	to	PART
flr-49	52	6	work	work	VERB
flr-49	52	7	directly	directly	ADV
flr-49	52	8	with	with	ADP
flr-49	52	9	unknown	unknown	ADJ
flr-49	52	10	quantities	quantity	NOUN
flr-49	52	11	.	.	PUNCT
flr-49	53	1	an	an	DET
flr-49	53	2	equation	equation	NOUN
flr-49	53	3	comprising	comprise	VERB
flr-49	53	4	both	both	CCONJ
flr-49	53	5	known	known	ADJ
flr-49	53	6	and	and	CCONJ
flr-49	53	7	unknown	unknown	ADJ
flr-49	53	8	values	value	NOUN
flr-49	53	9	is	be	AUX
flr-49	53	10	formed	form	VERB
flr-49	53	11	using	use	VERB
flr-49	53	12	forward	forward	ADV
flr-49	53	13	operations	operation	NOUN
flr-49	53	14	and	and	CCONJ
flr-49	53	15	the	the	DET
flr-49	53	16	unknown	unknown	NOUN
flr-49	53	17	is	be	AUX
flr-49	53	18	solved	solve	VERB
flr-49	53	19	by	by	ADP
flr-49	53	20	constructing	construct	VERB
flr-49	53	21	a	a	DET
flr-49	53	22	series	series	NOUN
flr-49	53	23	of	of	ADP
flr-49	53	24	equivalent	equivalent	ADJ
flr-49	53	25	expressions	expression	NOUN
flr-49	53	26	.	.	PUNCT
flr-49	54	1	students	student	NOUN
flr-49	54	2	operate	operate	VERB
flr-49	54	3	on	on	ADP
flr-49	54	4	the	the	DET
flr-49	54	5	equation	equation	NOUN
flr-49	54	6	in	in	ADP
flr-49	54	7	a	a	DET
flr-49	54	8	way	way	NOUN
flr-49	54	9	that	that	PRON
flr-49	54	10	maintains	maintain	VERB
flr-49	54	11	symmetric	symmetric	ADJ
flr-49	54	12	equivalence	equivalence	NOUN
flr-49	54	13	across	across	ADP
flr-49	54	14	the	the	DET
flr-49	54	15	two	two	NUM
flr-49	54	16	sides	side	NOUN
flr-49	54	17	of	of	ADP
flr-49	54	18	the	the	DET
flr-49	54	19	equals	equal	NOUN
flr-49	54	20	sign	sign	NOUN
flr-49	54	21	.	.	PUNCT
flr-49	55	1	in	in	ADP
flr-49	55	2	contrast	contrast	NOUN
flr-49	55	3	,	,	PUNCT
flr-49	55	4	the	the	DET
flr-49	55	5	graphical	graphical	ADJ
flr-49	55	6	approach	approach	NOUN
flr-49	55	7	can	can	AUX
flr-49	55	8	trace	trace	VERB
flr-49	55	9	its	its	PRON
flr-49	55	10	roots	root	NOUN
flr-49	55	11	to	to	ADP
flr-49	55	12	pedagogical	pedagogical	ADJ
flr-49	55	13	tools	tool	NOUN
flr-49	55	14	used	use	VERB
flr-49	55	15	in	in	ADP
flr-49	55	16	the	the	DET
flr-49	55	17	early	early	ADJ
flr-49	55	18	primary	primary	ADJ
flr-49	55	19	school	school	NOUN
flr-49	55	20	years	year	NOUN
flr-49	55	21	.	.	PUNCT
flr-49	56	1	beginning	begin	VERB
flr-49	56	2	in	in	ADP
flr-49	56	3	lower	low	ADJ
flr-49	56	4	primary	primary	ADJ
flr-49	56	5	,	,	PUNCT
flr-49	56	6	familiar	familiar	ADJ
flr-49	56	7	objects	object	NOUN
flr-49	56	8	and	and	CCONJ
flr-49	56	9	pictures	picture	NOUN
flr-49	56	10	(	(	PUNCT
flr-49	56	11	e.g.	e.g.	ADV
flr-49	56	12	,	,	PUNCT
flr-49	56	13	pictures	picture	NOUN
flr-49	56	14	of	of	ADP
flr-49	56	15	bears	bear	NOUN
flr-49	56	16	and	and	CCONJ
flr-49	56	17	dolls	doll	NOUN
flr-49	56	18	)	)	PUNCT
flr-49	56	19	are	be	AUX
flr-49	56	20	used	use	VERB
flr-49	56	21	to	to	PART
flr-49	56	22	depict	depict	VERB
flr-49	56	23	known	know	VERB
flr-49	56	24	quantities	quantity	NOUN
flr-49	56	25	as	as	ADP
flr-49	56	26	an	an	DET
flr-49	56	27	aid	aid	NOUN
flr-49	56	28	to	to	ADP
flr-49	56	29	understanding	understand	VERB
flr-49	56	30	arithmetic	arithmetic	ADJ
flr-49	56	31	word	word	NOUN
flr-49	56	32	problems	problem	NOUN
flr-49	56	33	.	.	PUNCT
flr-49	57	1	with	with	ADP
flr-49	57	2	the	the	DET
flr-49	57	3	graphical	graphical	ADJ
flr-49	57	4	approach	approach	NOUN
flr-49	57	5	,	,	PUNCT
flr-49	57	6	a	a	DET
flr-49	57	7	standardized	standardized	ADJ
flr-49	57	8	representational	representational	ADJ
flr-49	57	9	tool	tool	NOUN
flr-49	57	10	is	be	AUX
flr-49	57	11	used	use	VERB
flr-49	57	12	to	to	PART
flr-49	57	13	represent	represent	VERB
flr-49	57	14	both	both	CCONJ
flr-49	57	15	known	known	ADJ
flr-49	57	16	and	and	CCONJ
flr-49	57	17	unknown	unknown	ADJ
flr-49	57	18	quantities	quantity	NOUN
flr-49	57	19	.	.	PUNCT
flr-49	58	1	of	of	ADP
flr-49	58	2	course	course	ADV
flr-49	58	3	,	,	PUNCT
flr-49	58	4	unknown	unknown	ADJ
flr-49	58	5	quantities	quantity	NOUN
flr-49	58	6	can	can	AUX
flr-49	58	7	not	not	PART
flr-49	58	8	be	be	AUX
flr-49	58	9	depicted	depict	VERB
flr-49	58	10	exactly	exactly	ADV
flr-49	58	11	.	.	PUNCT
flr-49	59	1	instead	instead	ADV
flr-49	59	2	,	,	PUNCT
flr-49	59	3	children	child	NOUN
flr-49	59	4	are	be	AUX
flr-49	59	5	taught	teach	VERB
flr-49	59	6	to	to	PART
flr-49	59	7	draw	draw	VERB
flr-49	59	8	a	a	DET
flr-49	59	9	diagram	diagram	NOUN
flr-49	59	10	with	with	ADP
flr-49	59	11	the	the	DET
flr-49	59	12	unknown	unknown	ADJ
flr-49	59	13	quantities	quantity	NOUN
flr-49	59	14	depicted	depict	VERB
flr-49	59	15	by	by	ADP
flr-49	59	16	bars	bar	NOUN
flr-49	59	17	of	of	ADP
flr-49	59	18	arbitrary	arbitrary	ADJ
flr-49	59	19	length	length	NOUN
flr-49	59	20	,	,	PUNCT
flr-49	59	21	which	which	PRON
flr-49	59	22	are	be	AUX
flr-49	59	23	constrained	constrain	VERB
flr-49	59	24	by	by	ADP
flr-49	59	25	the	the	DET
flr-49	59	26	given	give	VERB
flr-49	59	27	quantities	quantity	NOUN
flr-49	59	28	and	and	CCONJ
flr-49	59	29	their	their	PRON
flr-49	59	30	quantitative	quantitative	ADJ
flr-49	59	31	relations	relation	NOUN
flr-49	59	32	.	.	PUNCT
flr-49	60	1	computation	computation	NOUN
flr-49	60	2	of	of	ADP
flr-49	60	3	solution	solution	NOUN
flr-49	60	4	is	be	AUX
flr-49	60	5	effected	effect	VERB
flr-49	60	6	using	use	VERB
flr-49	60	7	arithmetic	arithmetic	ADJ
flr-49	60	8	procedures	procedure	NOUN
flr-49	60	9	in	in	ADP
flr-49	60	10	which	which	PRON
flr-49	60	11	students	student	NOUN
flr-49	60	12	work	work	VERB
flr-49	60	13	only	only	ADV
flr-49	60	14	with	with	ADP
flr-49	60	15	known	know	VERB
flr-49	60	16	quantities	quantity	NOUN
flr-49	60	17	.	.	PUNCT
flr-49	61	1	in	in	ADP
flr-49	61	2	other	other	ADJ
flr-49	61	3	words	word	NOUN
flr-49	61	4	,	,	PUNCT
flr-49	61	5	the	the	DET
flr-49	61	6	unknown	unknown	NOUN
flr-49	61	7	is	be	AUX
flr-49	61	8	solved	solve	VERB
flr-49	61	9	by	by	ADP
flr-49	61	10	the	the	DET
flr-49	61	11	direct	direct	ADJ
flr-49	61	12	application	application	NOUN
flr-49	61	13	of	of	ADP
flr-49	61	14	arithmetic	arithmetic	ADJ
flr-49	61	15	operations	operation	NOUN
flr-49	61	16	on	on	ADP
flr-49	61	17	known	known	ADJ
flr-49	61	18	values	value	NOUN
flr-49	61	19	(	(	PUNCT
flr-49	61	20	e.g.	e.g.	ADV
flr-49	61	21	,	,	PUNCT
flr-49	61	22	backward	backward	ADJ
flr-49	61	23	operations	operation	NOUN
flr-49	61	24	such	such	ADJ
flr-49	61	25	as	as	ADP
flr-49	61	26	unwinding	unwind	VERB
flr-49	61	27	)	)	PUNCT
flr-49	61	28	.	.	PUNCT
flr-49	62	1	unlike	unlike	ADP
flr-49	62	2	symbolic	symbolic	ADJ
flr-49	62	3	algebra	algebra	NOUN
flr-49	62	4	,	,	PUNCT
flr-49	62	5	with	with	ADP
flr-49	62	6	the	the	DET
flr-49	62	7	graphical	graphical	ADJ
flr-49	62	8	approach	approach	NOUN
flr-49	62	9	,	,	PUNCT
flr-49	62	10	the	the	DET
flr-49	62	11	equals	equal	NOUN
flr-49	62	12	sign	sign	NOUN
flr-49	62	13	is	be	AUX
flr-49	62	14	generally	generally	ADV
flr-49	62	15	used	use	VERB
flr-49	62	16	as	as	ADP
flr-49	62	17	a	a	DET
flr-49	62	18	directive	directive	NOUN
flr-49	62	19	to	to	PART
flr-49	62	20	calculate	calculate	VERB
flr-49	62	21	instead	instead	ADV
flr-49	62	22	of	of	ADP
flr-49	62	23	representing	represent	VERB
flr-49	62	24	equality	equality	NOUN
flr-49	62	25	(	(	PUNCT
flr-49	62	26	see	see	VERB
flr-49	62	27	khng	khng	PROPN
flr-49	62	28	&	&	CCONJ
flr-49	62	29	lee	lee	PROPN
flr-49	62	30	,	,	PUNCT
flr-49	62	31	2009	2009	NUM
flr-49	62	32	,	,	PUNCT
flr-49	62	33	for	for	ADP
flr-49	62	34	more	more	ADJ
flr-49	62	35	details	detail	NOUN
flr-49	62	36	)	)	PUNCT
flr-49	62	37	.	.	PUNCT
flr-49	63	1	some	some	DET
flr-49	63	2	recent	recent	ADJ
flr-49	63	3	works	work	NOUN
flr-49	63	4	on	on	ADP
flr-49	63	5	the	the	DET
flr-49	63	6	use	use	NOUN
flr-49	63	7	of	of	ADP
flr-49	63	8	the	the	DET
flr-49	63	9	model	model	NOUN
flr-49	63	10	method	method	NOUN
flr-49	63	11	were	be	AUX
flr-49	63	12	motivated	motivate	VERB
flr-49	63	13	by	by	ADP
flr-49	63	14	parents	parent	NOUN
flr-49	63	15	’	'	PUNCT
flr-49	63	16	and	and	CCONJ
flr-49	63	17	teachers	teacher	NOUN
flr-49	63	18	’	'	PUNCT
flr-49	63	19	concerns	concern	VERB
flr-49	63	20	that	that	SCONJ
flr-49	63	21	the	the	DET
flr-49	63	22	model	model	NOUN
flr-49	63	23	method	method	NOUN
flr-49	63	24	may	may	AUX
flr-49	63	25	confuse	confuse	VERB
flr-49	63	26	students	student	NOUN
flr-49	63	27	when	when	SCONJ
flr-49	63	28	it	it	PRON
flr-49	63	29	comes	come	VERB
flr-49	63	30	time	time	NOUN
flr-49	63	31	for	for	SCONJ
flr-49	63	32	them	they	PRON
flr-49	63	33	to	to	PART
flr-49	63	34	learn	learn	VERB
flr-49	63	35	letter	letter	NOUN
flr-49	63	36	symbolic	symbolic	ADJ
flr-49	63	37	algebra	algebra	PROPN
flr-49	63	38	,	,	PUNCT
flr-49	63	39	with	with	ADP
flr-49	63	40	some	some	DET
flr-49	63	41	concerned	concerned	ADJ
flr-49	63	42	that	that	SCONJ
flr-49	63	43	the	the	DET
flr-49	63	44	two	two	NUM
flr-49	63	45	approaches	approach	NOUN
flr-49	63	46	may	may	AUX
flr-49	63	47	draw	draw	VERB
flr-49	63	48	on	on	ADP
flr-49	63	49	different	different	ADJ
flr-49	63	50	cognitive	cognitive	ADJ
flr-49	63	51	processes	process	NOUN
flr-49	63	52	(	(	PUNCT
flr-49	63	53	e.g.	e.g.	ADV
flr-49	63	54	,	,	PUNCT
flr-49	63	55	kwokwc	kwokwc	NOUN
flr-49	63	56	,	,	PUNCT
flr-49	63	57	2011	2011	NUM
flr-49	63	58	;	;	PUNCT
flr-49	63	59	lim	lim	PROPN
flr-49	63	60	,	,	PUNCT
flr-49	63	61	2007	2007	NUM
flr-49	63	62	)	)	PUNCT
flr-49	63	63	.	.	PUNCT
flr-49	64	1	the	the	DET
flr-49	64	2	model	model	NOUN
flr-49	64	3	method	method	NOUN
flr-49	64	4	is	be	AUX
flr-49	64	5	taught	teach	VERB
flr-49	64	6	system	system	NOUN
flr-49	64	7	-	-	PUNCT
flr-49	64	8	wide	wide	ADJ
flr-49	64	9	and	and	CCONJ
flr-49	64	10	has	have	AUX
flr-49	64	11	been	be	AUX
flr-49	64	12	part	part	NOUN
flr-49	64	13	of	of	ADP
flr-49	64	14	the	the	DET
flr-49	64	15	national	national	ADJ
flr-49	64	16	curriculum	curriculum	NOUN
flr-49	64	17	in	in	ADP
flr-49	64	18	singapore	singapore	PROPN
flr-49	64	19	for	for	ADP
flr-49	64	20	over	over	ADP
flr-49	64	21	a	a	PRON
flr-49	64	22	decade	decade	NOUN
flr-49	64	23	.	.	PUNCT
flr-49	65	1	for	for	ADP
flr-49	65	2	this	this	DET
flr-49	65	3	reason	reason	NOUN
flr-49	65	4	,	,	PUNCT
flr-49	65	5	it	it	PRON
flr-49	65	6	is	be	AUX
flr-49	65	7	difficult	difficult	ADJ
flr-49	65	8	to	to	PART
flr-49	65	9	evaluate	evaluate	VERB
flr-49	65	10	these	these	DET
flr-49	65	11	claims	claim	NOUN
flr-49	65	12	using	use	VERB
flr-49	65	13	standard	standard	ADJ
flr-49	65	14	programme	programme	NOUN
flr-49	65	15	evaluation	evaluation	NOUN
flr-49	65	16	methodology	methodology	NOUN
flr-49	65	17	.	.	PUNCT
flr-49	66	1	in	in	ADP
flr-49	66	2	two	two	NUM
flr-49	66	3	recent	recent	ADJ
flr-49	66	4	studies	study	NOUN
flr-49	66	5	,	,	PUNCT
flr-49	66	6	lee	lee	PROPN
flr-49	66	7	and	and	CCONJ
flr-49	66	8	his	his	PRON
flr-49	66	9	colleagues	colleague	NOUN
flr-49	66	10	used	use	VERB
flr-49	66	11	functional	functional	ADJ
flr-49	66	12	magnetic	magnetic	ADJ
flr-49	66	13	resonance	resonance	NOUN
flr-49	66	14	imaging	imaging	NOUN
flr-49	66	15	techniques	technique	NOUN
flr-49	66	16	to	to	PART
flr-49	66	17	examine	examine	VERB
flr-49	66	18	the	the	DET
flr-49	66	19	cognitive	cognitive	ADJ
flr-49	66	20	underpinnings	underpinning	NOUN
flr-49	66	21	of	of	ADP
flr-49	66	22	these	these	DET
flr-49	66	23	two	two	NUM
flr-49	66	24	approaches	approach	NOUN
flr-49	66	25	(	(	PUNCT
flr-49	66	26	lee	lee	PROPN
flr-49	66	27	et	et	PROPN
flr-49	66	28	al	al	PROPN
flr-49	66	29	.	.	PROPN
flr-49	66	30	,	,	PUNCT
flr-49	66	31	2007	2007	NUM
flr-49	66	32	;	;	PUNCT
flr-49	66	33	lee	lee	PROPN
flr-49	66	34	et	et	PROPN
flr-49	66	35	al	al	PROPN
flr-49	66	36	.	.	PROPN
flr-49	66	37	,	,	PUNCT
flr-49	66	38	2010	2010	NUM
flr-49	66	39	)	)	PUNCT
flr-49	66	40	.	.	PUNCT
flr-49	67	1	the	the	DET
flr-49	67	2	findings	finding	NOUN
flr-49	67	3	showed	show	VERB
flr-49	67	4	substantial	substantial	ADJ
flr-49	67	5	overlap	overlap	NOUN
flr-49	67	6	between	between	ADP
flr-49	67	7	the	the	DET
flr-49	67	8	two	two	NUM
flr-49	67	9	approaches	approach	NOUN
flr-49	67	10	,	,	PUNCT
flr-49	67	11	but	but	CCONJ
flr-49	67	12	symbolic	symbolic	ADJ
flr-49	67	13	algebra	algebra	NOUN
flr-49	67	14	activated	activate	VERB
flr-49	67	15	more	more	ADV
flr-49	67	16	strongly	strongly	ADV
flr-49	67	17	areas	area	NOUN
flr-49	67	18	associated	associate	VERB
flr-49	67	19	with	with	ADP
flr-49	67	20	attention	attention	NOUN
flr-49	67	21	and	and	CCONJ
flr-49	67	22	working	working	NOUN
flr-49	67	23	memory	memory	NOUN
flr-49	67	24	engagement	engagement	NOUN
flr-49	67	25	.	.	PUNCT
flr-49	68	1	these	these	DET
flr-49	68	2	findings	finding	NOUN
flr-49	68	3	suggest	suggest	VERB
flr-49	68	4	that	that	SCONJ
flr-49	68	5	symbolic	symbolic	ADJ
flr-49	68	6	algebra	algebra	NOUN
flr-49	68	7	is	be	AUX
flr-49	68	8	more	more	ADV
flr-49	68	9	demanding	demanding	ADJ
flr-49	68	10	of	of	ADP
flr-49	68	11	cognitive	cognitive	ADJ
flr-49	68	12	resources	resource	NOUN
flr-49	68	13	than	than	ADP
flr-49	68	14	the	the	DET
flr-49	68	15	model	model	NOUN
flr-49	68	16	method	method	NOUN
flr-49	68	17	.	.	PUNCT
flr-49	69	1	from	from	ADP
flr-49	69	2	a	a	DET
flr-49	69	3	pedagogical	pedagogical	ADJ
flr-49	69	4	viewpoint	viewpoint	NOUN
flr-49	69	5	,	,	PUNCT
flr-49	69	6	introducing	introduce	VERB
flr-49	69	7	the	the	DET
flr-49	69	8	model	model	NOUN
flr-49	69	9	method	method	NOUN
flr-49	69	10	prior	prior	ADV
flr-49	69	11	to	to	ADP
flr-49	69	12	symbolic	symbolic	ADJ
flr-49	69	13	algebra	algebra	NOUN
flr-49	69	14	can	can	AUX
flr-49	69	15	thus	thus	ADV
flr-49	69	16	be	be	AUX
flr-49	69	17	interpreted	interpret	VERB
flr-49	69	18	as	as	ADP
flr-49	69	19	being	be	AUX
flr-49	69	20	consistent	consistent	ADJ
flr-49	69	21	with	with	ADP
flr-49	69	22	their	their	PRON
flr-49	69	23	respective	respective	ADJ
flr-49	69	24	cognitive	cognitive	ADJ
flr-49	69	25	demands	demand	NOUN
flr-49	69	26	.	.	PUNCT
flr-49	70	1	k.	k.	PROPN
flr-49	70	2	lee	lee	PROPN
flr-49	70	3	et	et	PROPN
flr-49	70	4	al	al	PROPN
flr-49	70	5	.	.	PROPN
flr-49	70	6	84	84	NUM
flr-49	71	1	|	|	ADV
flr-49	71	2	f	f	NOUN
flr-49	71	3	l	l	NOUN
flr-49	71	4	r	r	NOUN
flr-49	71	5	1.2	1.2	NUM
flr-49	71	6	the	the	DET
flr-49	71	7	model	model	NOUN
flr-49	71	8	method	method	NOUN
flr-49	71	9	,	,	PUNCT
flr-49	71	10	letter	letter	NOUN
flr-49	71	11	symbols	symbol	NOUN
flr-49	71	12	,	,	PUNCT
flr-49	71	13	and	and	CCONJ
flr-49	71	14	variables	variable	NOUN
flr-49	71	15	regarding	regard	VERB
flr-49	71	16	the	the	DET
flr-49	71	17	cognitive	cognitive	ADJ
flr-49	71	18	factors	factor	NOUN
flr-49	71	19	that	that	PRON
flr-49	71	20	influence	influence	VERB
flr-49	71	21	children	child	NOUN
flr-49	71	22	’s	’s	PART
flr-49	71	23	success	success	NOUN
flr-49	71	24	in	in	ADP
flr-49	71	25	algebra	algebra	NOUN
flr-49	71	26	,	,	PUNCT
flr-49	71	27	there	there	PRON
flr-49	71	28	has	have	AUX
flr-49	71	29	been	be	AUX
flr-49	71	30	a	a	DET
flr-49	71	31	number	number	NOUN
flr-49	71	32	of	of	ADP
flr-49	71	33	recent	recent	ADJ
flr-49	71	34	studies	study	NOUN
flr-49	71	35	on	on	ADP
flr-49	71	36	both	both	DET
flr-49	71	37	domain	domain	NOUN
flr-49	71	38	-	-	PUNCT
flr-49	71	39	general	general	ADJ
flr-49	71	40	and	and	CCONJ
flr-49	71	41	domain	domain	NOUN
flr-49	71	42	-	-	PUNCT
flr-49	71	43	specific	specific	ADJ
flr-49	71	44	correlates	correlate	NOUN
flr-49	71	45	of	of	ADP
flr-49	71	46	algebraic	algebraic	ADJ
flr-49	71	47	performance	performance	NOUN
flr-49	71	48	(	(	PUNCT
flr-49	71	49	e.g.	e.g.	ADV
flr-49	71	50	,	,	PUNCT
flr-49	71	51	fuchs	fuchs	PROPN
flr-49	71	52	et	et	PROPN
flr-49	71	53	al	al	PROPN
flr-49	71	54	.	.	PROPN
flr-49	71	55	,	,	PUNCT
flr-49	71	56	2012	2012	NUM
flr-49	71	57	;	;	PUNCT
flr-49	71	58	lee	lee	PROPN
flr-49	71	59	,	,	PUNCT
flr-49	71	60	ng	ng	PROPN
flr-49	71	61	,	,	PUNCT
flr-49	71	62	bull	bull	NOUN
flr-49	71	63	,	,	PUNCT
flr-49	71	64	pe	pe	X
flr-49	71	65	,	,	PUNCT
flr-49	71	66	&	&	CCONJ
flr-49	71	67	ho	ho	PROPN
flr-49	71	68	,	,	PUNCT
flr-49	71	69	2011	2011	NUM
flr-49	71	70	;	;	PUNCT
flr-49	71	71	tolar	tolar	PROPN
flr-49	71	72	,	,	PUNCT
flr-49	71	73	lederberg	lederberg	PROPN
flr-49	71	74	,	,	PUNCT
flr-49	71	75	&	&	CCONJ
flr-49	71	76	fletcher	fletcher	PROPN
flr-49	71	77	,	,	PUNCT
flr-49	71	78	2009	2009	NUM
flr-49	71	79	;	;	PUNCT
flr-49	71	80	wei	wei	PROPN
flr-49	71	81	,	,	PUNCT
flr-49	71	82	yuan	yuan	PROPN
flr-49	71	83	,	,	PUNCT
flr-49	71	84	chen	chen	PROPN
flr-49	71	85	,	,	PUNCT
flr-49	71	86	&	&	CCONJ
flr-49	71	87	zhou	zhou	PROPN
flr-49	71	88	,	,	PUNCT
flr-49	71	89	2012	2012	NUM
flr-49	71	90	)	)	PUNCT
flr-49	71	91	.	.	PUNCT
flr-49	72	1	on	on	ADP
flr-49	72	2	the	the	DET
flr-49	72	3	specific	specific	ADJ
flr-49	72	4	influence	influence	NOUN
flr-49	72	5	of	of	ADP
flr-49	72	6	using	use	VERB
flr-49	72	7	diagrams	diagram	NOUN
flr-49	72	8	,	,	PUNCT
flr-49	72	9	there	there	PRON
flr-49	72	10	is	be	VERB
flr-49	72	11	a	a	DET
flr-49	72	12	large	large	ADJ
flr-49	72	13	body	body	NOUN
flr-49	72	14	of	of	ADP
flr-49	72	15	research	research	NOUN
flr-49	72	16	that	that	PRON
flr-49	72	17	examined	examine	VERB
flr-49	72	18	whether	whether	SCONJ
flr-49	72	19	students	student	NOUN
flr-49	72	20	learn	learn	VERB
flr-49	72	21	better	well	ADV
flr-49	72	22	when	when	SCONJ
flr-49	72	23	text	text	NOUN
flr-49	72	24	is	be	AUX
flr-49	72	25	accompanied	accompany	VERB
flr-49	72	26	by	by	ADP
flr-49	72	27	diagrams	diagram	NOUN
flr-49	72	28	(	(	PUNCT
flr-49	72	29	mayer	mayer	PROPN
flr-49	72	30	,	,	PUNCT
flr-49	72	31	1989	1989	NUM
flr-49	72	32	,	,	PUNCT
flr-49	72	33	2002	2002	NUM
flr-49	72	34	)	)	PUNCT
flr-49	72	35	or	or	CCONJ
flr-49	72	36	when	when	SCONJ
flr-49	72	37	students	student	NOUN
flr-49	72	38	generate	generate	VERB
flr-49	72	39	the	the	DET
flr-49	72	40	diagrams	diagram	NOUN
flr-49	72	41	themselves	themselves	PRON
flr-49	72	42	(	(	PUNCT
flr-49	72	43	meter	meter	NOUN
flr-49	72	44	&	&	CCONJ
flr-49	72	45	garner	garner	PROPN
flr-49	72	46	,	,	PUNCT
flr-49	72	47	2005	2005	NUM
flr-49	72	48	)	)	PUNCT
flr-49	72	49	.	.	PUNCT
flr-49	73	1	of	of	ADP
flr-49	73	2	particular	particular	ADJ
flr-49	73	3	relevance	relevance	NOUN
flr-49	73	4	are	be	AUX
flr-49	73	5	a	a	DET
flr-49	73	6	number	number	NOUN
flr-49	73	7	of	of	ADP
flr-49	73	8	studies	study	NOUN
flr-49	73	9	conducted	conduct	VERB
flr-49	73	10	by	by	ADP
flr-49	73	11	koedinger	koedinger	NOUN
flr-49	73	12	and	and	CCONJ
flr-49	73	13	his	his	PRON
flr-49	73	14	colleagues	colleague	NOUN
flr-49	73	15	.	.	PUNCT
flr-49	74	1	they	they	PRON
flr-49	74	2	investigated	investigate	VERB
flr-49	74	3	the	the	DET
flr-49	74	4	use	use	NOUN
flr-49	74	5	of	of	ADP
flr-49	74	6	“	"	PUNCT
flr-49	74	7	picture	picture	NOUN
flr-49	74	8	algebra	algebra	NOUN
flr-49	74	9	”	"	PUNCT
flr-49	74	10	,	,	PUNCT
flr-49	74	11	a	a	DET
flr-49	74	12	strategy	strategy	NOUN
flr-49	74	13	similar	similar	ADJ
flr-49	74	14	to	to	ADP
flr-49	74	15	the	the	DET
flr-49	74	16	model	model	NOUN
flr-49	74	17	method	method	NOUN
flr-49	74	18	.	.	PUNCT
flr-49	75	1	they	they	PRON
flr-49	75	2	found	find	VERB
flr-49	75	3	that	that	SCONJ
flr-49	75	4	by	by	ADP
flr-49	75	5	using	use	VERB
flr-49	75	6	this	this	DET
flr-49	75	7	strategy	strategy	NOUN
flr-49	75	8	,	,	PUNCT
flr-49	75	9	even	even	ADV
flr-49	75	10	students	student	NOUN
flr-49	75	11	in	in	ADP
flr-49	75	12	grade	grade	NOUN
flr-49	75	13	6	6	NUM
flr-49	75	14	were	be	AUX
flr-49	75	15	successful	successful	ADJ
flr-49	75	16	in	in	ADP
flr-49	75	17	solving	solve	VERB
flr-49	75	18	algebraic	algebraic	ADJ
flr-49	75	19	problems	problem	NOUN
flr-49	75	20	that	that	PRON
flr-49	75	21	are	be	AUX
flr-49	75	22	known	know	VERB
flr-49	75	23	to	to	PART
flr-49	75	24	be	be	AUX
flr-49	75	25	challenging	challenge	VERB
flr-49	75	26	for	for	ADP
flr-49	75	27	older	old	ADJ
flr-49	75	28	students	student	NOUN
flr-49	75	29	(	(	PUNCT
flr-49	75	30	koedinger	koedinger	NOUN
flr-49	75	31	&	&	CCONJ
flr-49	75	32	terao	terao	PROPN
flr-49	75	33	,	,	PUNCT
flr-49	75	34	2002	2002	NUM
flr-49	75	35	)	)	PUNCT
flr-49	75	36	.	.	PUNCT
flr-49	76	1	the	the	DET
flr-49	76	2	strategy	strategy	NOUN
flr-49	76	3	was	be	AUX
flr-49	76	4	also	also	ADV
flr-49	76	5	found	find	VERB
flr-49	76	6	to	to	PART
flr-49	76	7	be	be	AUX
flr-49	76	8	effective	effective	ADJ
flr-49	76	9	for	for	ADP
flr-49	76	10	lower	low	ADJ
flr-49	76	11	achieving	achieve	VERB
flr-49	76	12	pre	pre	ADJ
flr-49	76	13	-	-	ADJ
flr-49	76	14	algebra	algebra	ADJ
flr-49	76	15	students	student	NOUN
flr-49	76	16	(	(	PUNCT
flr-49	76	17	booth	booth	NOUN
flr-49	76	18	&	&	CCONJ
flr-49	76	19	koedinger	koedinger	PROPN
flr-49	76	20	,	,	PUNCT
flr-49	76	21	2010	2010	NUM
flr-49	76	22	)	)	PUNCT
flr-49	76	23	.	.	PUNCT
flr-49	77	1	although	although	SCONJ
flr-49	77	2	we	we	PRON
flr-49	77	3	now	now	ADV
flr-49	77	4	have	have	VERB
flr-49	77	5	some	some	DET
flr-49	77	6	information	information	NOUN
flr-49	77	7	on	on	ADP
flr-49	77	8	the	the	DET
flr-49	77	9	efficacy	efficacy	NOUN
flr-49	77	10	of	of	ADP
flr-49	77	11	the	the	DET
flr-49	77	12	model	model	NOUN
flr-49	77	13	method	method	NOUN
flr-49	77	14	and	and	CCONJ
flr-49	77	15	some	some	PRON
flr-49	77	16	of	of	ADP
flr-49	77	17	the	the	DET
flr-49	77	18	contexts	context	NOUN
flr-49	77	19	in	in	ADP
flr-49	77	20	which	which	PRON
flr-49	77	21	they	they	PRON
flr-49	77	22	are	be	AUX
flr-49	77	23	more	more	ADV
flr-49	77	24	likely	likely	ADJ
flr-49	77	25	to	to	PART
flr-49	77	26	be	be	AUX
flr-49	77	27	efficacious	efficacious	ADJ
flr-49	77	28	,	,	PUNCT
flr-49	77	29	an	an	DET
flr-49	77	30	important	important	ADJ
flr-49	77	31	issue	issue	NOUN
flr-49	77	32	on	on	ADP
flr-49	77	33	which	which	PRON
flr-49	77	34	we	we	PRON
flr-49	77	35	know	know	VERB
flr-49	77	36	little	little	ADJ
flr-49	77	37	is	be	AUX
flr-49	77	38	how	how	SCONJ
flr-49	77	39	students	student	NOUN
flr-49	77	40	understand	understand	VERB
flr-49	77	41	or	or	CCONJ
flr-49	77	42	perceive	perceive	VERB
flr-49	77	43	these	these	DET
flr-49	77	44	graphical	graphical	ADJ
flr-49	77	45	representations	representation	NOUN
flr-49	77	46	.	.	PUNCT
flr-49	78	1	compared	compare	VERB
flr-49	78	2	to	to	ADP
flr-49	78	3	pedagogical	pedagogical	ADJ
flr-49	78	4	practices	practice	NOUN
flr-49	78	5	in	in	ADP
flr-49	78	6	earlier	early	ADJ
flr-49	78	7	grades	grade	NOUN
flr-49	78	8	in	in	ADP
flr-49	78	9	which	which	PRON
flr-49	78	10	familiar	familiar	ADJ
flr-49	78	11	objects	object	NOUN
flr-49	78	12	are	be	AUX
flr-49	78	13	used	use	VERB
flr-49	78	14	to	to	PART
flr-49	78	15	depict	depict	VERB
flr-49	78	16	operands	operand	NOUN
flr-49	78	17	in	in	ADP
flr-49	78	18	arithmetic	arithmetic	ADJ
flr-49	78	19	in	in	ADP
flr-49	78	20	a	a	DET
flr-49	78	21	one	one	NUM
flr-49	78	22	-	-	PUNCT
flr-49	78	23	to	to	ADP
flr-49	78	24	-	-	PUNCT
flr-49	78	25	one	one	NUM
flr-49	78	26	manner	manner	NOUN
flr-49	78	27	,	,	PUNCT
flr-49	78	28	the	the	DET
flr-49	78	29	model	model	NOUN
flr-49	78	30	method	method	NOUN
flr-49	78	31	involves	involve	VERB
flr-49	78	32	a	a	DET
flr-49	78	33	greater	great	ADJ
flr-49	78	34	degree	degree	NOUN
flr-49	78	35	of	of	ADP
flr-49	78	36	abstraction	abstraction	NOUN
flr-49	78	37	.	.	PUNCT
flr-49	79	1	instead	instead	ADV
flr-49	79	2	of	of	ADP
flr-49	79	3	familiar	familiar	ADJ
flr-49	79	4	and	and	CCONJ
flr-49	79	5	discrete	discrete	ADJ
flr-49	79	6	objects	object	NOUN
flr-49	79	7	(	(	PUNCT
flr-49	79	8	e.g.	e.g.	ADV
flr-49	79	9	,	,	PUNCT
flr-49	79	10	bears	bear	NOUN
flr-49	79	11	or	or	CCONJ
flr-49	79	12	dolls	doll	NOUN
flr-49	79	13	)	)	PUNCT
flr-49	79	14	,	,	PUNCT
flr-49	79	15	bars	bar	NOUN
flr-49	79	16	of	of	ADP
flr-49	79	17	different	different	ADJ
flr-49	79	18	lengths	length	NOUN
flr-49	79	19	are	be	AUX
flr-49	79	20	used	use	VERB
flr-49	79	21	.	.	PUNCT
flr-49	80	1	nonetheless	nonetheless	ADV
flr-49	80	2	,	,	PUNCT
flr-49	80	3	given	give	VERB
flr-49	80	4	students	student	NOUN
flr-49	80	5	’	'	PUNCT
flr-49	80	6	earlier	early	ADJ
flr-49	80	7	experiences	experience	NOUN
flr-49	80	8	,	,	PUNCT
flr-49	80	9	it	it	PRON
flr-49	80	10	is	be	AUX
flr-49	80	11	possible	possible	ADJ
flr-49	80	12	that	that	SCONJ
flr-49	80	13	they	they	PRON
flr-49	80	14	retain	retain	VERB
flr-49	80	15	a	a	DET
flr-49	80	16	concrete	concrete	ADJ
flr-49	80	17	way	way	NOUN
flr-49	80	18	of	of	ADP
flr-49	80	19	thinking	think	VERB
flr-49	80	20	about	about	ADP
flr-49	80	21	the	the	DET
flr-49	80	22	bars	bar	NOUN
flr-49	80	23	,	,	PUNCT
flr-49	80	24	such	such	ADJ
flr-49	80	25	that	that	SCONJ
flr-49	80	26	a	a	DET
flr-49	80	27	bar	bar	NOUN
flr-49	80	28	of	of	ADP
flr-49	80	29	a	a	DET
flr-49	80	30	certain	certain	ADJ
flr-49	80	31	length	length	NOUN
flr-49	80	32	is	be	AUX
flr-49	80	33	deemed	deem	VERB
flr-49	80	34	capable	capable	ADJ
flr-49	80	35	of	of	ADP
flr-49	80	36	holding	hold	VERB
flr-49	80	37	,	,	PUNCT
flr-49	80	38	say	say	INTJ
flr-49	80	39	,	,	PUNCT
flr-49	80	40	ten	ten	NUM
flr-49	80	41	bears	bear	NOUN
flr-49	80	42	and	and	CCONJ
flr-49	80	43	ten	ten	NUM
flr-49	80	44	bears	bear	NOUN
flr-49	80	45	alone	alone	ADV
flr-49	80	46	.	.	PUNCT
flr-49	81	1	in	in	ADP
flr-49	81	2	teaching	teach	VERB
flr-49	81	3	the	the	DET
flr-49	81	4	model	model	NOUN
flr-49	81	5	method	method	NOUN
flr-49	81	6	,	,	PUNCT
flr-49	81	7	teachers	teacher	NOUN
flr-49	81	8	generally	generally	ADV
flr-49	81	9	ask	ask	VERB
flr-49	81	10	children	child	NOUN
flr-49	81	11	to	to	PART
flr-49	81	12	use	use	VERB
flr-49	81	13	relatively	relatively	ADV
flr-49	81	14	longer	long	ADJ
flr-49	81	15	bars	bar	NOUN
flr-49	81	16	for	for	ADP
flr-49	81	17	bigger	big	ADJ
flr-49	81	18	numbers	number	NOUN
flr-49	81	19	(	(	PUNCT
flr-49	81	20	ng	ng	PROPN
flr-49	81	21	&	&	CCONJ
flr-49	81	22	lee	lee	PROPN
flr-49	81	23	,	,	PUNCT
flr-49	81	24	2009	2009	NUM
flr-49	81	25	)	)	PUNCT
flr-49	81	26	.	.	PUNCT
flr-49	82	1	more	more	ADV
flr-49	82	2	important	important	ADJ
flr-49	82	3	than	than	ADP
flr-49	82	4	absolute	absolute	ADJ
flr-49	82	5	length	length	NOUN
flr-49	82	6	is	be	AUX
flr-49	82	7	that	that	SCONJ
flr-49	82	8	,	,	PUNCT
flr-49	82	9	within	within	ADP
flr-49	82	10	a	a	DET
flr-49	82	11	problem	problem	NOUN
flr-49	82	12	,	,	PUNCT
flr-49	82	13	children	child	NOUN
flr-49	82	14	are	be	AUX
flr-49	82	15	taught	teach	VERB
flr-49	82	16	that	that	SCONJ
flr-49	82	17	the	the	DET
flr-49	82	18	lengths	length	NOUN
flr-49	82	19	of	of	ADP
flr-49	82	20	the	the	DET
flr-49	82	21	bars	bar	NOUN
flr-49	82	22	should	should	AUX
flr-49	82	23	preserve	preserve	VERB
flr-49	82	24	the	the	DET
flr-49	82	25	quantitative	quantitative	ADJ
flr-49	82	26	relations	relation	NOUN
flr-49	82	27	between	between	ADP
flr-49	82	28	the	the	DET
flr-49	82	29	protagonists	protagonist	NOUN
flr-49	82	30	.	.	PUNCT
flr-49	83	1	this	this	PRON
flr-49	83	2	is	be	AUX
flr-49	83	3	especially	especially	ADV
flr-49	83	4	when	when	SCONJ
flr-49	83	5	more	more	ADJ
flr-49	83	6	than	than	ADP
flr-49	83	7	two	two	NUM
flr-49	83	8	protagonists	protagonist	NOUN
flr-49	83	9	are	be	AUX
flr-49	83	10	involved	involve	VERB
flr-49	83	11	in	in	ADP
flr-49	83	12	a	a	DET
flr-49	83	13	problem	problem	NOUN
flr-49	83	14	.	.	PUNCT
flr-49	84	1	how	how	SCONJ
flr-49	84	2	students	student	NOUN
flr-49	84	3	understand	understand	VERB
flr-49	84	4	these	these	DET
flr-49	84	5	graphical	graphical	ADJ
flr-49	84	6	representations	representation	NOUN
flr-49	84	7	is	be	AUX
flr-49	84	8	important	important	ADJ
flr-49	84	9	because	because	SCONJ
flr-49	84	10	when	when	SCONJ
flr-49	84	11	they	they	PRON
flr-49	84	12	learn	learn	VERB
flr-49	84	13	symbolic	symbolic	ADJ
flr-49	84	14	algebra	algebra	NOUN
flr-49	84	15	,	,	PUNCT
flr-49	84	16	a	a	DET
flr-49	84	17	concept	concept	NOUN
flr-49	84	18	that	that	SCONJ
flr-49	84	19	they	they	PRON
flr-49	84	20	should	should	AUX
flr-49	84	21	understand	understand	VERB
flr-49	84	22	is	be	AUX
flr-49	84	23	that	that	DET
flr-49	84	24	letter	letter	NOUN
flr-49	84	25	symbols	symbol	NOUN
flr-49	84	26	(	(	PUNCT
flr-49	84	27	e.g.	e.g.	ADV
flr-49	84	28	,	,	PUNCT
flr-49	84	29	x	x	SYM
flr-49	84	30	and	and	CCONJ
flr-49	84	31	y	y	PROPN
flr-49	84	32	)	)	PUNCT
flr-49	84	33	denote	denote	NOUN
flr-49	84	34	variables	variable	NOUN
flr-49	84	35	.	.	PUNCT
flr-49	85	1	although	although	SCONJ
flr-49	85	2	the	the	DET
flr-49	85	3	model	model	NOUN
flr-49	85	4	method	method	NOUN
flr-49	85	5	gives	give	VERB
flr-49	85	6	children	child	NOUN
flr-49	85	7	earlier	early	ADJ
flr-49	85	8	access	access	NOUN
flr-49	85	9	to	to	ADP
flr-49	85	10	algebraic	algebraic	ADJ
flr-49	85	11	questions	question	NOUN
flr-49	85	12	without	without	ADP
flr-49	85	13	the	the	DET
flr-49	85	14	use	use	NOUN
flr-49	85	15	of	of	ADP
flr-49	85	16	letter	letter	NOUN
flr-49	85	17	symbols	symbol	NOUN
flr-49	85	18	,	,	PUNCT
flr-49	85	19	the	the	DET
flr-49	85	20	bars	bar	NOUN
flr-49	85	21	that	that	PRON
flr-49	85	22	are	be	AUX
flr-49	85	23	used	use	VERB
flr-49	85	24	to	to	PART
flr-49	85	25	depict	depict	VERB
flr-49	85	26	quantities	quantity	NOUN
flr-49	85	27	play	play	VERB
flr-49	85	28	a	a	DET
flr-49	85	29	similar	similar	ADJ
flr-49	85	30	role	role	NOUN
flr-49	85	31	as	as	SCONJ
flr-49	85	32	do	do	AUX
flr-49	85	33	letter	letter	VERB
flr-49	85	34	symbols	symbol	NOUN
flr-49	85	35	in	in	ADP
flr-49	85	36	algebraic	algebraic	ADJ
flr-49	85	37	equations	equation	NOUN
flr-49	85	38	.	.	PUNCT
flr-49	86	1	both	both	PRON
flr-49	86	2	serve	serve	VERB
flr-49	86	3	to	to	PART
flr-49	86	4	depict	depict	VERB
flr-49	86	5	relations	relation	NOUN
flr-49	86	6	between	between	ADP
flr-49	86	7	known	known	ADJ
flr-49	86	8	and	and	CCONJ
flr-49	86	9	unknown	unknown	ADJ
flr-49	86	10	quantities	quantity	NOUN
flr-49	86	11	.	.	PUNCT
flr-49	87	1	if	if	SCONJ
flr-49	87	2	children	child	NOUN
flr-49	87	3	regard	regard	VERB
flr-49	87	4	the	the	DET
flr-49	87	5	bar	bar	NOUN
flr-49	87	6	diagrams	diagram	NOUN
flr-49	87	7	in	in	ADP
flr-49	87	8	a	a	DET
flr-49	87	9	concrete	concrete	ADJ
flr-49	87	10	manner	manner	NOUN
flr-49	87	11	,	,	PUNCT
flr-49	87	12	one	one	NUM
flr-49	87	13	potential	potential	ADJ
flr-49	87	14	drawback	drawback	NOUN
flr-49	87	15	is	be	AUX
flr-49	87	16	that	that	SCONJ
flr-49	87	17	they	they	PRON
flr-49	87	18	may	may	AUX
flr-49	87	19	over	over	ADV
flr-49	87	20	-	-	PUNCT
flr-49	87	21	generalise	generalise	VERB
flr-49	87	22	and	and	CCONJ
flr-49	87	23	regard	regard	VERB
flr-49	87	24	x	x	PUNCT
flr-49	87	25	and	and	CCONJ
flr-49	87	26	y	y	PROPN
flr-49	87	27	as	as	ADP
flr-49	87	28	depicting	depict	VERB
flr-49	87	29	unknown	unknown	ADJ
flr-49	87	30	constants	constant	NOUN
flr-49	87	31	.	.	PUNCT
flr-49	88	1	a	a	DET
flr-49	88	2	related	related	ADJ
flr-49	88	3	concern	concern	NOUN
flr-49	88	4	was	be	AUX
flr-49	88	5	raised	raise	VERB
flr-49	88	6	by	by	ADP
flr-49	88	7	dede	dede	NOUN
flr-49	88	8	(	(	PUNCT
flr-49	88	9	2004	2004	NUM
flr-49	88	10	)	)	PUNCT
flr-49	88	11	,	,	PUNCT
flr-49	88	12	who	who	PRON
flr-49	88	13	argued	argue	VERB
flr-49	88	14	that	that	SCONJ
flr-49	88	15	the	the	DET
flr-49	88	16	preponderance	preponderance	NOUN
flr-49	88	17	of	of	ADP
flr-49	88	18	questions	question	NOUN
flr-49	88	19	that	that	PRON
flr-49	88	20	use	use	VERB
flr-49	88	21	letter	letter	NOUN
flr-49	88	22	-	-	PUNCT
flr-49	88	23	symbols	symbol	NOUN
flr-49	88	24	to	to	PART
flr-49	88	25	represent	represent	VERB
flr-49	88	26	unknowns	unknown	NOUN
flr-49	88	27	could	could	AUX
flr-49	88	28	result	result	VERB
flr-49	88	29	in	in	ADP
flr-49	88	30	students	student	NOUN
flr-49	88	31	developing	develop	VERB
flr-49	88	32	a	a	DET
flr-49	88	33	restricted	restricted	ADJ
flr-49	88	34	view	view	NOUN
flr-49	88	35	of	of	ADP
flr-49	88	36	the	the	DET
flr-49	88	37	roles	role	NOUN
flr-49	88	38	and	and	CCONJ
flr-49	88	39	functions	function	NOUN
flr-49	88	40	of	of	ADP
flr-49	88	41	variables	variable	NOUN
flr-49	88	42	.	.	PUNCT
flr-49	89	1	the	the	DET
flr-49	89	2	concept	concept	NOUN
flr-49	89	3	of	of	ADP
flr-49	89	4	a	a	DET
flr-49	89	5	variable	variable	NOUN
flr-49	89	6	is	be	AUX
flr-49	89	7	important	important	ADJ
flr-49	89	8	in	in	ADP
flr-49	89	9	algebra	algebra	NOUN
flr-49	89	10	,	,	PUNCT
flr-49	89	11	but	but	CCONJ
flr-49	89	12	it	it	PRON
flr-49	89	13	is	be	AUX
flr-49	89	14	also	also	ADV
flr-49	89	15	difficult	difficult	ADJ
flr-49	89	16	,	,	PUNCT
flr-49	89	17	perhaps	perhaps	ADV
flr-49	89	18	because	because	SCONJ
flr-49	89	19	it	it	PRON
flr-49	89	20	has	have	VERB
flr-49	89	21	different	different	ADJ
flr-49	89	22	meanings	meaning	NOUN
flr-49	89	23	or	or	CCONJ
flr-49	89	24	usages	usage	NOUN
flr-49	89	25	.	.	PUNCT
flr-49	90	1	usiskin	usiskin	X
flr-49	90	2	(	(	PUNCT
flr-49	90	3	1988	1988	NUM
flr-49	90	4	)	)	PUNCT
flr-49	90	5	argued	argue	VERB
flr-49	90	6	that	that	SCONJ
flr-49	90	7	variables	variable	NOUN
flr-49	90	8	are	be	AUX
flr-49	90	9	used	use	VERB
flr-49	90	10	in	in	ADP
flr-49	90	11	different	different	ADJ
flr-49	90	12	ways	way	NOUN
flr-49	90	13	:	:	PUNCT
flr-49	90	14	(	(	PUNCT
flr-49	90	15	a	a	X
flr-49	90	16	)	)	PUNCT
flr-49	90	17	as	as	ADP
flr-49	90	18	an	an	DET
flr-49	90	19	unknown	unknown	ADJ
flr-49	90	20	or	or	CCONJ
flr-49	90	21	a	a	DET
flr-49	90	22	constant	constant	ADJ
flr-49	90	23	,	,	PUNCT
flr-49	90	24	(	(	PUNCT
flr-49	90	25	b	b	X
flr-49	90	26	)	)	PUNCT
flr-49	90	27	a	a	DET
flr-49	90	28	pattern	pattern	NOUN
flr-49	90	29	generalizer	generalizer	NOUN
flr-49	90	30	,	,	PUNCT
flr-49	90	31	(	(	PUNCT
flr-49	90	32	c	c	X
flr-49	90	33	)	)	PUNCT
flr-49	90	34	an	an	DET
flr-49	90	35	argument	argument	NOUN
flr-49	90	36	or	or	CCONJ
flr-49	90	37	parameter	parameter	NOUN
flr-49	90	38	,	,	PUNCT
flr-49	90	39	or	or	CCONJ
flr-49	90	40	(	(	PUNCT
flr-49	90	41	d	d	X
flr-49	90	42	)	)	PUNCT
flr-49	90	43	an	an	DET
flr-49	90	44	arbitrary	arbitrary	ADJ
flr-49	90	45	mark	mark	NOUN
flr-49	90	46	on	on	ADP
flr-49	90	47	paper	paper	NOUN
flr-49	90	48	.	.	PUNCT
flr-49	91	1	when	when	SCONJ
flr-49	91	2	students	student	NOUN
flr-49	91	3	are	be	AUX
flr-49	91	4	first	first	ADV
flr-49	91	5	introduced	introduce	VERB
flr-49	91	6	to	to	PART
flr-49	91	7	letter	letter	VERB
flr-49	91	8	symbols	symbol	NOUN
flr-49	91	9	,	,	PUNCT
flr-49	91	10	they	they	PRON
flr-49	91	11	typically	typically	ADV
flr-49	91	12	encounter	encounter	VERB
flr-49	91	13	them	they	PRON
flr-49	91	14	as	as	ADP
flr-49	91	15	unknowns	unknown	NOUN
flr-49	91	16	in	in	ADP
flr-49	91	17	solve	solve	NOUN
flr-49	91	18	-	-	PUNCT
flr-49	91	19	for	for	ADP
flr-49	91	20	-	-	PUNCT
flr-49	91	21	x	x	NOUN
flr-49	91	22	questions	question	NOUN
flr-49	91	23	,	,	PUNCT
flr-49	91	24	where	where	SCONJ
flr-49	91	25	students	student	NOUN
flr-49	91	26	are	be	AUX
flr-49	91	27	asked	ask	VERB
flr-49	91	28	to	to	PART
flr-49	91	29	find	find	VERB
flr-49	91	30	a	a	DET
flr-49	91	31	solution	solution	NOUN
flr-49	91	32	for	for	ADP
flr-49	91	33	the	the	DET
flr-49	91	34	letter	letter	NOUN
flr-49	91	35	symbols	symbol	NOUN
flr-49	91	36	(	(	PUNCT
flr-49	91	37	e.g.	e.g.	ADV
flr-49	91	38	,	,	PUNCT
flr-49	91	39	x	x	PUNCT
flr-49	92	1	+	+	PUNCT
flr-49	92	2	y	y	PROPN
flr-49	92	3	=	=	SYM
flr-49	92	4	47	47	NUM
flr-49	92	5	,	,	PUNCT
flr-49	92	6	x	x	PUNCT
flr-49	92	7	+	+	NOUN
flr-49	92	8	13	13	NUM
flr-49	92	9	=	=	NOUN
flr-49	92	10	y.	y.	NOUN
flr-49	92	11	what	what	PRON
flr-49	92	12	is	be	AUX
flr-49	92	13	the	the	DET
flr-49	92	14	value	value	NOUN
flr-49	92	15	of	of	ADP
flr-49	92	16	x	x	PRON
flr-49	92	17	?	?	PUNCT
flr-49	92	18	)	)	PUNCT
flr-49	92	19	.	.	PUNCT
flr-49	93	1	as	as	SCONJ
flr-49	93	2	dede	dede	NOUN
flr-49	93	3	(	(	PUNCT
flr-49	93	4	2004	2004	NUM
flr-49	93	5	)	)	PUNCT
flr-49	93	6	argued	argue	VERB
flr-49	93	7	,	,	PUNCT
flr-49	93	8	one	one	NUM
flr-49	93	9	concern	concern	NOUN
flr-49	93	10	is	be	AUX
flr-49	93	11	that	that	SCONJ
flr-49	93	12	given	give	VERB
flr-49	93	13	the	the	DET
flr-49	93	14	preponderance	preponderance	NOUN
flr-49	93	15	of	of	ADP
flr-49	93	16	experiences	experience	NOUN
flr-49	93	17	with	with	ADP
flr-49	93	18	this	this	DET
flr-49	93	19	usage	usage	NOUN
flr-49	93	20	of	of	ADP
flr-49	93	21	letter	letter	NOUN
flr-49	93	22	symbols	symbol	NOUN
flr-49	93	23	,	,	PUNCT
flr-49	93	24	children	child	NOUN
flr-49	93	25	come	come	VERB
flr-49	93	26	to	to	PART
flr-49	93	27	take	take	VERB
flr-49	93	28	this	this	PRON
flr-49	93	29	as	as	ADP
flr-49	93	30	the	the	DET
flr-49	93	31	norm	norm	NOUN
flr-49	93	32	and	and	CCONJ
flr-49	93	33	neglect	neglect	NOUN
flr-49	93	34	to	to	PART
flr-49	93	35	entertain	entertain	VERB
flr-49	93	36	other	other	ADJ
flr-49	93	37	ways	way	NOUN
flr-49	93	38	in	in	ADP
flr-49	93	39	which	which	PRON
flr-49	93	40	variables	variable	NOUN
flr-49	93	41	are	be	AUX
flr-49	93	42	used	use	VERB
flr-49	93	43	.	.	PUNCT
flr-49	94	1	indeed	indeed	ADV
flr-49	94	2	,	,	PUNCT
flr-49	94	3	when	when	SCONJ
flr-49	94	4	asked	ask	VERB
flr-49	94	5	to	to	PART
flr-49	94	6	simplify	simplify	VERB
flr-49	94	7	algebraic	algebraic	ADJ
flr-49	94	8	expressions	expression	NOUN
flr-49	94	9	(	(	PUNCT
flr-49	94	10	e.g.	e.g.	ADV
flr-49	94	11	,	,	PUNCT
flr-49	94	12	3x	3x	PROPN
flr-49	94	13	+	+	CCONJ
flr-49	94	14	5x	5x	NUM
flr-49	94	15	24	24	NUM
flr-49	94	16	)	)	PUNCT
flr-49	94	17	,	,	PUNCT
flr-49	94	18	children	child	NOUN
flr-49	94	19	tended	tend	VERB
flr-49	94	20	to	to	PART
flr-49	94	21	find	find	VERB
flr-49	94	22	a	a	DET
flr-49	94	23	solution	solution	NOUN
flr-49	94	24	for	for	ADP
flr-49	94	25	x	x	SYM
flr-49	94	26	instead	instead	ADV
flr-49	94	27	(	(	PUNCT
flr-49	94	28	philipp	philipp	PROPN
flr-49	94	29	,	,	PUNCT
flr-49	94	30	1992	1992	NUM
flr-49	94	31	)	)	PUNCT
flr-49	94	32	.	.	PUNCT
flr-49	95	1	a	a	DET
flr-49	95	2	similar	similar	ADJ
flr-49	95	3	difficulty	difficulty	NOUN
flr-49	95	4	was	be	AUX
flr-49	95	5	reported	report	VERB
flr-49	95	6	by	by	ADP
flr-49	95	7	akgün	akgün	NOUN
flr-49	95	8	and	and	CCONJ
flr-49	95	9	özdemir	özdemir	NOUN
flr-49	95	10	(	(	PUNCT
flr-49	95	11	2006	2006	NUM
flr-49	95	12	)	)	PUNCT
flr-49	95	13	.	.	PUNCT
flr-49	96	1	in	in	ADP
flr-49	96	2	their	their	PRON
flr-49	96	3	study	study	NOUN
flr-49	96	4	,	,	PUNCT
flr-49	96	5	students	student	NOUN
flr-49	96	6	presented	present	VERB
flr-49	96	7	with	with	ADP
flr-49	96	8	x	x	PROPN
flr-49	97	1	+	+	NUM
flr-49	97	2	2	2	NUM
flr-49	97	3	=	=	SYM
flr-49	97	4	2	2	NUM
flr-49	97	5	+	+	CCONJ
flr-49	97	6	x	x	PRON
flr-49	97	7	attempted	attempt	VERB
flr-49	97	8	to	to	PART
flr-49	97	9	solve	solve	VERB
flr-49	97	10	for	for	ADP
flr-49	97	11	x	x	PUNCT
flr-49	97	12	when	when	SCONJ
flr-49	97	13	they	they	PRON
flr-49	97	14	were	be	AUX
flr-49	97	15	told	tell	VERB
flr-49	97	16	to	to	PART
flr-49	97	17	report	report	VERB
flr-49	97	18	all	all	DET
flr-49	97	19	the	the	DET
flr-49	97	20	values	value	NOUN
flr-49	97	21	that	that	PRON
flr-49	97	22	x	x	PRON
flr-49	97	23	can	can	AUX
flr-49	97	24	assume	assume	VERB
flr-49	97	25	.	.	PUNCT
flr-49	98	1	kuchëmann	kuchëmann	PROPN
flr-49	98	2	(	(	PUNCT
flr-49	98	3	1978	1978	NUM
flr-49	98	4	)	)	PUNCT
flr-49	98	5	investigated	investigate	VERB
flr-49	98	6	students	student	NOUN
flr-49	98	7	’	’	PART
flr-49	98	8	understanding	understanding	NOUN
flr-49	98	9	of	of	ADP
flr-49	98	10	the	the	DET
flr-49	98	11	use	use	NOUN
flr-49	98	12	of	of	ADP
flr-49	98	13	letter	letter	NOUN
flr-49	98	14	symbols	symbol	NOUN
flr-49	98	15	and	and	CCONJ
flr-49	98	16	found	find	VERB
flr-49	98	17	most	most	ADJ
flr-49	98	18	secondary	secondary	ADJ
flr-49	98	19	school	school	NOUN
flr-49	98	20	students	student	NOUN
flr-49	98	21	treated	treat	VERB
flr-49	98	22	them	they	PRON
flr-49	98	23	as	as	ADP
flr-49	98	24	concrete	concrete	ADJ
flr-49	98	25	placeholders	placeholder	NOUN
flr-49	98	26	or	or	CCONJ
flr-49	98	27	“	"	PUNCT
flr-49	98	28	shorthand	shorthand	NOUN
flr-49	98	29	names	name	NOUN
flr-49	98	30	”	"	PUNCT
flr-49	98	31	(	(	PUNCT
flr-49	98	32	macgregor	macgregor	PROPN
flr-49	98	33	&	&	CCONJ
flr-49	98	34	stacey	stacey	PROPN
flr-49	98	35	,	,	PUNCT
flr-49	98	36	1997	1997	NUM
flr-49	98	37	)	)	PUNCT
flr-49	98	38	(	(	PUNCT
flr-49	98	39	e.g.	e.g.	ADV
flr-49	98	40	,	,	PUNCT
flr-49	98	41	p	p	NOUN
flr-49	98	42	in	in	ADP
flr-49	98	43	3p	3p	NUM
flr-49	98	44	as	as	ADP
flr-49	98	45	pears	pear	NOUN
flr-49	98	46	instead	instead	ADV
flr-49	98	47	of	of	ADP
flr-49	98	48	number	number	NOUN
flr-49	98	49	of	of	ADP
flr-49	98	50	pears	pear	NOUN
flr-49	98	51	)	)	PUNCT
flr-49	98	52	.	.	PUNCT
flr-49	99	1	only	only	ADV
flr-49	99	2	a	a	DET
flr-49	99	3	small	small	ADJ
flr-49	99	4	number	number	NOUN
flr-49	99	5	of	of	ADP
flr-49	99	6	students	student	NOUN
flr-49	99	7	displayed	display	VERB
flr-49	99	8	an	an	DET
flr-49	99	9	understanding	understanding	NOUN
flr-49	99	10	of	of	ADP
flr-49	99	11	letters	letter	NOUN
flr-49	99	12	as	as	ADP
flr-49	99	13	representing	represent	VERB
flr-49	99	14	specific	specific	ADJ
flr-49	99	15	unknowns	unknown	NOUN
flr-49	99	16	.	.	PUNCT
flr-49	100	1	an	an	DET
flr-49	100	2	even	even	ADV
flr-49	100	3	smaller	small	ADJ
flr-49	100	4	number	number	NOUN
flr-49	100	5	considered	consider	VERB
flr-49	100	6	the	the	DET
flr-49	100	7	letters	letter	NOUN
flr-49	100	8	to	to	PART
flr-49	100	9	be	be	AUX
flr-49	100	10	generalized	generalized	ADJ
flr-49	100	11	numbers	number	NOUN
flr-49	100	12	.	.	PUNCT
flr-49	101	1	k.	k.	PROPN
flr-49	101	2	lee	lee	PROPN
flr-49	101	3	et	et	PROPN
flr-49	101	4	al	al	PROPN
flr-49	101	5	.	.	PROPN
flr-49	101	6	85	85	NUM
flr-49	102	1	|	|	ADV
flr-49	102	2	f	f	NOUN
flr-49	102	3	l	l	NOUN
flr-49	102	4	r	r	NOUN
flr-49	102	5	1.3	1.3	NUM
flr-49	102	6	the	the	DET
flr-49	102	7	present	present	ADJ
flr-49	102	8	study	study	NOUN
flr-49	102	9	to	to	PART
flr-49	102	10	understand	understand	VERB
flr-49	102	11	better	well	ADJ
flr-49	102	12	the	the	DET
flr-49	102	13	utility	utility	NOUN
flr-49	102	14	of	of	ADP
flr-49	102	15	teaching	teach	VERB
flr-49	102	16	the	the	DET
flr-49	102	17	method	method	NOUN
flr-49	102	18	model	model	NOUN
flr-49	102	19	,	,	PUNCT
flr-49	102	20	we	we	PRON
flr-49	102	21	focused	focus	VERB
flr-49	102	22	on	on	ADP
flr-49	102	23	students	student	NOUN
flr-49	102	24	’	’	PART
flr-49	102	25	understanding	understanding	NOUN
flr-49	102	26	of	of	ADP
flr-49	102	27	these	these	DET
flr-49	102	28	graphical	graphical	ADJ
flr-49	102	29	representations	representation	NOUN
flr-49	102	30	.	.	PUNCT
flr-49	103	1	specifically	specifically	ADV
flr-49	103	2	,	,	PUNCT
flr-49	103	3	we	we	PRON
flr-49	103	4	investigated	investigate	VERB
flr-49	103	5	whether	whether	SCONJ
flr-49	103	6	students	student	NOUN
flr-49	103	7	use	use	VERB
flr-49	103	8	and	and	CCONJ
flr-49	103	9	think	think	VERB
flr-49	103	10	of	of	ADP
flr-49	103	11	the	the	DET
flr-49	103	12	bar	bar	NOUN
flr-49	103	13	diagrams	diagram	NOUN
flr-49	103	14	in	in	ADP
flr-49	103	15	a	a	DET
flr-49	103	16	concrete	concrete	NOUN
flr-49	103	17	or	or	CCONJ
flr-49	103	18	a	a	DET
flr-49	103	19	more	more	ADV
flr-49	103	20	abstract	abstract	ADJ
flr-49	103	21	fashion	fashion	NOUN
flr-49	103	22	.	.	PUNCT
flr-49	104	1	we	we	PRON
flr-49	104	2	asked	ask	VERB
flr-49	104	3	children	child	NOUN
flr-49	104	4	to	to	PART
flr-49	104	5	perform	perform	VERB
flr-49	104	6	two	two	NUM
flr-49	104	7	tasks	task	NOUN
flr-49	104	8	.	.	PUNCT
flr-49	105	1	in	in	ADP
flr-49	105	2	the	the	DET
flr-49	105	3	production	production	NOUN
flr-49	105	4	task	task	NOUN
flr-49	105	5	,	,	PUNCT
flr-49	105	6	we	we	PRON
flr-49	105	7	examined	examine	VERB
flr-49	105	8	how	how	SCONJ
flr-49	105	9	they	they	PRON
flr-49	105	10	drew	draw	VERB
flr-49	105	11	model	model	NOUN
flr-49	105	12	representations	representation	NOUN
flr-49	105	13	for	for	ADP
flr-49	105	14	algebraic	algebraic	ADJ
flr-49	105	15	word	word	NOUN
flr-49	105	16	problems	problem	NOUN
flr-49	105	17	with	with	ADP
flr-49	105	18	operands	operand	NOUN
flr-49	105	19	of	of	ADP
flr-49	105	20	varying	vary	VERB
flr-49	105	21	quantities	quantity	NOUN
flr-49	105	22	.	.	PUNCT
flr-49	106	1	we	we	PRON
flr-49	106	2	defined	define	VERB
flr-49	106	3	concrete	concrete	ADJ
flr-49	106	4	usage	usage	NOUN
flr-49	106	5	as	as	ADP
flr-49	106	6	varying	vary	VERB
flr-49	106	7	the	the	DET
flr-49	106	8	length	length	NOUN
flr-49	106	9	of	of	ADP
flr-49	106	10	bars	bar	NOUN
flr-49	106	11	across	across	ADP
flr-49	106	12	questions	question	NOUN
flr-49	106	13	in	in	ADP
flr-49	106	14	accordance	accordance	NOUN
flr-49	106	15	to	to	ADP
flr-49	106	16	the	the	DET
flr-49	106	17	magnitude	magnitude	NOUN
flr-49	106	18	of	of	ADP
flr-49	106	19	operands	operand	NOUN
flr-49	106	20	.	.	PUNCT
flr-49	107	1	abstract	abstract	ADJ
flr-49	107	2	usage	usage	NOUN
flr-49	107	3	was	be	AUX
flr-49	107	4	indicated	indicate	VERB
flr-49	107	5	by	by	ADP
flr-49	107	6	the	the	DET
flr-49	107	7	lack	lack	NOUN
flr-49	107	8	of	of	ADP
flr-49	107	9	a	a	DET
flr-49	107	10	consistent	consistent	ADJ
flr-49	107	11	relation	relation	NOUN
flr-49	107	12	between	between	ADP
flr-49	107	13	the	the	DET
flr-49	107	14	length	length	NOUN
flr-49	107	15	of	of	ADP
flr-49	107	16	the	the	DET
flr-49	107	17	bars	bar	NOUN
flr-49	107	18	and	and	CCONJ
flr-49	107	19	the	the	DET
flr-49	107	20	magnitude	magnitude	NOUN
flr-49	107	21	of	of	ADP
flr-49	107	22	operands	operand	NOUN
flr-49	107	23	.	.	PUNCT
flr-49	108	1	we	we	PRON
flr-49	108	2	also	also	ADV
flr-49	108	3	manipulated	manipulate	VERB
flr-49	108	4	the	the	DET
flr-49	108	5	sequence	sequence	NOUN
flr-49	108	6	in	in	ADP
flr-49	108	7	which	which	PRON
flr-49	108	8	increases	increase	VERB
flr-49	108	9	in	in	ADP
flr-49	108	10	the	the	DET
flr-49	108	11	magnitude	magnitude	NOUN
flr-49	108	12	of	of	ADP
flr-49	108	13	operands	operand	NOUN
flr-49	108	14	were	be	AUX
flr-49	108	15	presented	present	VERB
flr-49	108	16	.	.	PUNCT
flr-49	109	1	because	because	SCONJ
flr-49	109	2	a	a	DET
flr-49	109	3	sequential	sequential	ADJ
flr-49	109	4	increase	increase	NOUN
flr-49	109	5	may	may	AUX
flr-49	109	6	overly	overly	ADV
flr-49	109	7	focus	focus	VERB
flr-49	109	8	the	the	DET
flr-49	109	9	children	child	NOUN
flr-49	109	10	’s	’s	PART
flr-49	109	11	attention	attention	NOUN
flr-49	109	12	on	on	ADP
flr-49	109	13	changes	change	NOUN
flr-49	109	14	in	in	ADP
flr-49	109	15	magnitude	magnitude	NOUN
flr-49	109	16	and	and	CCONJ
flr-49	109	17	attenuate	attenuate	VERB
flr-49	109	18	any	any	DET
flr-49	109	19	tendency	tendency	NOUN
flr-49	109	20	to	to	PART
flr-49	109	21	adopt	adopt	VERB
flr-49	109	22	a	a	DET
flr-49	109	23	more	more	ADV
flr-49	109	24	abstract	abstract	ADJ
flr-49	109	25	strategy	strategy	NOUN
flr-49	109	26	,	,	PUNCT
flr-49	109	27	we	we	PRON
flr-49	109	28	also	also	ADV
flr-49	109	29	presented	present	VERB
flr-49	109	30	the	the	DET
flr-49	109	31	increases	increase	NOUN
flr-49	109	32	in	in	ADP
flr-49	109	33	a	a	DET
flr-49	109	34	random	random	ADJ
flr-49	109	35	sequence	sequence	NOUN
flr-49	109	36	.	.	PUNCT
flr-49	110	1	in	in	ADP
flr-49	110	2	the	the	DET
flr-49	110	3	validation	validation	NOUN
flr-49	110	4	task	task	NOUN
flr-49	110	5	,	,	PUNCT
flr-49	110	6	we	we	PRON
flr-49	110	7	assessed	assess	VERB
flr-49	110	8	the	the	DET
flr-49	110	9	same	same	ADJ
flr-49	110	10	children	child	NOUN
flr-49	110	11	’s	’s	PART
flr-49	110	12	understanding	understanding	NOUN
flr-49	110	13	by	by	ADP
flr-49	110	14	asking	ask	VERB
flr-49	110	15	them	they	PRON
flr-49	110	16	to	to	PART
flr-49	110	17	judge	judge	VERB
flr-49	110	18	and	and	CCONJ
flr-49	110	19	explain	explain	VERB
flr-49	110	20	whether	whether	SCONJ
flr-49	110	21	several	several	ADJ
flr-49	110	22	presented	present	VERB
flr-49	110	23	graphical	graphical	ADJ
flr-49	110	24	representations	representation	NOUN
flr-49	110	25	were	be	AUX
flr-49	110	26	drawn	draw	VERB
flr-49	110	27	correctly	correctly	ADV
flr-49	110	28	.	.	PUNCT
flr-49	111	1	the	the	DET
flr-49	111	2	representations	representation	NOUN
flr-49	111	3	contained	contain	VERB
flr-49	111	4	drawings	drawing	NOUN
flr-49	111	5	that	that	PRON
flr-49	111	6	fall	fall	VERB
flr-49	111	7	into	into	ADP
flr-49	111	8	either	either	CCONJ
flr-49	111	9	the	the	DET
flr-49	111	10	concrete	concrete	ADJ
flr-49	111	11	or	or	CCONJ
flr-49	111	12	abstract	abstract	ADJ
flr-49	111	13	pattern	pattern	NOUN
flr-49	111	14	as	as	ADV
flr-49	111	15	defined	define	VERB
flr-49	111	16	above	above	ADV
flr-49	111	17	.	.	PUNCT
flr-49	112	1	children	child	NOUN
flr-49	112	2	with	with	ADP
flr-49	112	3	more	more	ADV
flr-49	112	4	sophisticated	sophisticated	ADJ
flr-49	112	5	understanding	understanding	NOUN
flr-49	112	6	were	be	AUX
flr-49	112	7	expected	expect	VERB
flr-49	112	8	to	to	PART
flr-49	112	9	know	know	VERB
flr-49	112	10	that	that	SCONJ
flr-49	112	11	though	though	SCONJ
flr-49	112	12	bars	bar	NOUN
flr-49	112	13	of	of	ADP
flr-49	112	14	particular	particular	ADJ
flr-49	112	15	lengths	length	NOUN
flr-49	112	16	depict	depict	VERB
flr-49	112	17	unknown	unknown	ADJ
flr-49	112	18	constants	constant	NOUN
flr-49	112	19	within	within	ADP
flr-49	112	20	the	the	DET
flr-49	112	21	context	context	NOUN
flr-49	112	22	of	of	ADP
flr-49	112	23	each	each	DET
flr-49	112	24	question	question	NOUN
flr-49	112	25	,	,	PUNCT
flr-49	112	26	across	across	ADP
flr-49	112	27	questions	question	NOUN
flr-49	112	28	,	,	PUNCT
flr-49	112	29	the	the	DET
flr-49	112	30	same	same	ADJ
flr-49	112	31	bars	bar	NOUN
flr-49	112	32	can	can	AUX
flr-49	112	33	be	be	AUX
flr-49	112	34	used	use	VERB
flr-49	112	35	to	to	PART
flr-49	112	36	depict	depict	VERB
flr-49	112	37	different	different	ADJ
flr-49	112	38	quantities	quantity	NOUN
flr-49	112	39	.	.	PUNCT
flr-49	113	1	in	in	ADP
flr-49	113	2	fact	fact	NOUN
flr-49	113	3	,	,	PUNCT
flr-49	113	4	it	it	PRON
flr-49	113	5	is	be	AUX
flr-49	113	6	when	when	SCONJ
flr-49	113	7	letter	letter	NOUN
flr-49	113	8	symbols	symbol	NOUN
flr-49	113	9	are	be	AUX
flr-49	113	10	considered	consider	VERB
flr-49	113	11	in	in	ADP
flr-49	113	12	this	this	DET
flr-49	113	13	sense	sense	NOUN
flr-49	113	14	that	that	SCONJ
flr-49	113	15	they	they	PRON
flr-49	113	16	are	be	AUX
flr-49	113	17	considered	consider	VERB
flr-49	113	18	variables	variable	NOUN
flr-49	113	19	.	.	PUNCT
flr-49	114	1	we	we	PRON
flr-49	114	2	tested	test	VERB
flr-49	114	3	primary	primary	ADJ
flr-49	114	4	5	5	NUM
flr-49	114	5	(	(	PUNCT
flr-49	114	6	grade	grade	NOUN
flr-49	114	7	5	5	NUM
flr-49	114	8	)	)	PUNCT
flr-49	114	9	children	child	NOUN
flr-49	114	10	who	who	PRON
flr-49	114	11	have	have	AUX
flr-49	114	12	not	not	PART
flr-49	114	13	been	be	AUX
flr-49	114	14	taught	teach	VERB
flr-49	114	15	symbolic	symbolic	ADJ
flr-49	114	16	algebra	algebra	NOUN
flr-49	114	17	and	and	CCONJ
flr-49	114	18	secondary	secondary	ADJ
flr-49	114	19	2	2	NUM
flr-49	114	20	(	(	PUNCT
flr-49	114	21	grade	grade	NOUN
flr-49	114	22	8)	8)	NUM
flr-49	114	23	children	child	NOUN
flr-49	114	24	who	who	PRON
flr-49	114	25	have	have	AUX
flr-49	114	26	been	be	AUX
flr-49	114	27	taught	teach	VERB
flr-49	114	28	both	both	CCONJ
flr-49	114	29	the	the	DET
flr-49	114	30	model	model	NOUN
flr-49	114	31	method	method	NOUN
flr-49	114	32	and	and	CCONJ
flr-49	114	33	symbolic	symbolic	ADJ
flr-49	114	34	algebra	algebra	NOUN
flr-49	114	35	.	.	PUNCT
flr-49	115	1	the	the	DET
flr-49	115	2	primary	primary	ADJ
flr-49	115	3	school	school	NOUN
flr-49	115	4	children	child	NOUN
flr-49	115	5	would	would	AUX
flr-49	115	6	have	have	AUX
flr-49	115	7	used	use	VERB
flr-49	115	8	the	the	DET
flr-49	115	9	model	model	NOUN
flr-49	115	10	method	method	NOUN
flr-49	115	11	for	for	ADP
flr-49	115	12	a	a	DET
flr-49	115	13	year	year	NOUN
flr-49	115	14	,	,	PUNCT
flr-49	115	15	whereas	whereas	SCONJ
flr-49	115	16	the	the	DET
flr-49	115	17	secondary	secondary	ADJ
flr-49	115	18	school	school	NOUN
flr-49	115	19	children	child	NOUN
flr-49	115	20	would	would	AUX
flr-49	115	21	have	have	AUX
flr-49	115	22	been	be	AUX
flr-49	115	23	introduced	introduce	VERB
flr-49	115	24	to	to	ADP
flr-49	115	25	symbolic	symbolic	ADJ
flr-49	115	26	algebra	algebra	NOUN
flr-49	115	27	some	some	DET
flr-49	115	28	time	time	NOUN
flr-49	115	29	during	during	ADP
flr-49	115	30	since	since	SCONJ
flr-49	115	31	primary	primary	ADJ
flr-49	115	32	6	6	NUM
flr-49	115	33	.	.	PUNCT
flr-49	116	1	in	in	ADP
flr-49	116	2	an	an	DET
flr-49	116	3	interview	interview	NOUN
flr-49	116	4	study	study	NOUN
flr-49	116	5	conducted	conduct	VERB
flr-49	116	6	with	with	ADP
flr-49	116	7	ten	ten	NUM
flr-49	116	8	primary	primary	ADJ
flr-49	116	9	5	5	NUM
flr-49	116	10	students	student	NOUN
flr-49	116	11	,	,	PUNCT
flr-49	116	12	most	most	ADJ
flr-49	116	13	of	of	ADP
flr-49	116	14	the	the	DET
flr-49	116	15	children	child	NOUN
flr-49	116	16	showed	show	VERB
flr-49	116	17	some	some	DET
flr-49	116	18	abstract	abstract	ADJ
flr-49	116	19	understanding	understanding	NOUN
flr-49	116	20	of	of	ADP
flr-49	116	21	how	how	SCONJ
flr-49	116	22	the	the	DET
flr-49	116	23	bar	bar	NOUN
flr-49	116	24	diagrams	diagram	NOUN
flr-49	116	25	should	should	AUX
flr-49	116	26	be	be	AUX
flr-49	116	27	used	use	VERB
flr-49	116	28	(	(	PUNCT
flr-49	116	29	ng	ng	PROPN
flr-49	116	30	&	&	CCONJ
flr-49	116	31	lee	lee	PROPN
flr-49	116	32	,	,	PUNCT
flr-49	116	33	2008	2008	NUM
flr-49	116	34	)	)	PUNCT
flr-49	116	35	.	.	PUNCT
flr-49	117	1	typical	typical	ADJ
flr-49	117	2	of	of	ADP
flr-49	117	3	their	their	PRON
flr-49	117	4	responses	response	NOUN
flr-49	117	5	was	be	AUX
flr-49	117	6	statements	statement	NOUN
flr-49	117	7	suggesting	suggest	VERB
flr-49	117	8	that	that	SCONJ
flr-49	117	9	the	the	DET
flr-49	117	10	absolute	absolute	ADJ
flr-49	117	11	size	size	NOUN
flr-49	117	12	of	of	ADP
flr-49	117	13	the	the	DET
flr-49	117	14	bars	bar	NOUN
flr-49	117	15	do	do	AUX
flr-49	117	16	not	not	PART
flr-49	117	17	matter	matter	VERB
flr-49	117	18	.	.	PUNCT
flr-49	118	1	with	with	ADP
flr-49	118	2	their	their	PRON
flr-49	118	3	added	add	VERB
flr-49	118	4	experience	experience	NOUN
flr-49	118	5	with	with	ADP
flr-49	118	6	algebraic	algebraic	ADJ
flr-49	118	7	problems	problem	NOUN
flr-49	118	8	,	,	PUNCT
flr-49	118	9	we	we	PRON
flr-49	118	10	expected	expect	VERB
flr-49	118	11	the	the	DET
flr-49	118	12	secondary	secondary	ADJ
flr-49	118	13	school	school	NOUN
flr-49	118	14	children	child	NOUN
flr-49	118	15	to	to	PART
flr-49	118	16	display	display	VERB
flr-49	118	17	more	more	ADJ
flr-49	118	18	abstract	abstract	ADJ
flr-49	118	19	usage	usage	NOUN
flr-49	118	20	and	and	CCONJ
flr-49	118	21	awareness	awareness	NOUN
flr-49	118	22	.	.	PUNCT
flr-49	119	1	to	to	PART
flr-49	119	2	examine	examine	VERB
flr-49	119	3	how	how	SCONJ
flr-49	119	4	our	our	PRON
flr-49	119	5	measures	measure	NOUN
flr-49	119	6	of	of	ADP
flr-49	119	7	children	child	NOUN
flr-49	119	8	’s	’s	PART
flr-49	119	9	understanding	understanding	NOUN
flr-49	119	10	were	be	AUX
flr-49	119	11	related	relate	VERB
flr-49	119	12	to	to	ADP
flr-49	119	13	other	other	ADJ
flr-49	119	14	tests	test	NOUN
flr-49	119	15	of	of	ADP
flr-49	119	16	algebraic	algebraic	ADJ
flr-49	119	17	understanding	understanding	NOUN
flr-49	119	18	,	,	PUNCT
flr-49	119	19	we	we	PRON
flr-49	119	20	administered	administer	VERB
flr-49	119	21	the	the	DET
flr-49	119	22	küchemann	küchemann	PROPN
flr-49	119	23	algebra	algebra	PROPN
flr-49	119	24	test	test	NOUN
flr-49	119	25	(	(	PUNCT
flr-49	119	26	brown	brown	PROPN
flr-49	119	27	,	,	PUNCT
flr-49	119	28	hart	hart	PROPN
flr-49	119	29	,	,	PUNCT
flr-49	119	30	&	&	CCONJ
flr-49	119	31	kuchemann	kuchemann	PROPN
flr-49	119	32	,	,	PUNCT
flr-49	119	33	1985	1985	NUM
flr-49	119	34	)	)	PUNCT
flr-49	119	35	to	to	ADP
flr-49	119	36	the	the	DET
flr-49	119	37	secondary	secondary	ADJ
flr-49	119	38	school	school	NOUN
flr-49	119	39	children	child	NOUN
flr-49	119	40	.	.	PUNCT
flr-49	120	1	this	this	PRON
flr-49	120	2	is	be	AUX
flr-49	120	3	a	a	DET
flr-49	120	4	standardized	standardized	ADJ
flr-49	120	5	measure	measure	NOUN
flr-49	120	6	that	that	PRON
flr-49	120	7	gauges	gauge	VERB
flr-49	120	8	children	child	NOUN
flr-49	120	9	’s	’s	PART
flr-49	120	10	understanding	understanding	NOUN
flr-49	120	11	of	of	ADP
flr-49	120	12	variables	variable	NOUN
flr-49	120	13	expressed	express	VERB
flr-49	120	14	in	in	ADP
flr-49	120	15	the	the	DET
flr-49	120	16	letter	letter	NOUN
flr-49	120	17	symbolic	symbolic	ADJ
flr-49	120	18	format	format	NOUN
flr-49	120	19	.	.	PUNCT
flr-49	121	1	it	it	PRON
flr-49	121	2	was	be	AUX
flr-49	121	3	given	give	VERB
flr-49	121	4	only	only	ADV
flr-49	121	5	to	to	ADP
flr-49	121	6	secondary	secondary	ADJ
flr-49	121	7	school	school	NOUN
flr-49	121	8	children	child	NOUN
flr-49	121	9	as	as	SCONJ
flr-49	121	10	the	the	DET
flr-49	121	11	primary	primary	ADJ
flr-49	121	12	school	school	NOUN
flr-49	121	13	children	child	NOUN
flr-49	121	14	have	have	AUX
flr-49	121	15	not	not	PART
flr-49	121	16	been	be	AUX
flr-49	121	17	exposed	expose	VERB
flr-49	121	18	to	to	ADP
flr-49	121	19	letter	letter	VERB
flr-49	121	20	symbols	symbol	NOUN
flr-49	121	21	.	.	PUNCT
flr-49	122	1	2	2	X
flr-49	122	2	.	.	X
flr-49	122	3	method	method	VERB
flr-49	122	4	2.1	2.1	NUM
flr-49	122	5	participants	participant	NOUN
flr-49	122	6	and	and	CCONJ
flr-49	122	7	design	design	VERB
flr-49	122	8	the	the	DET
flr-49	122	9	experiment	experiment	NOUN
flr-49	122	10	was	be	AUX
flr-49	122	11	based	base	VERB
flr-49	122	12	on	on	ADP
flr-49	122	13	a	a	DET
flr-49	122	14	4	4	NUM
flr-49	122	15	(	(	PUNCT
flr-49	122	16	magnitude	magnitude	NOUN
flr-49	122	17	band	band	NOUN
flr-49	122	18	:	:	PUNCT
flr-49	122	19	one	one	NUM
flr-49	122	20	,	,	PUNCT
flr-49	122	21	tens	ten	NOUN
flr-49	122	22	,	,	PUNCT
flr-49	122	23	hundreds	hundred	NOUN
flr-49	122	24	,	,	PUNCT
flr-49	122	25	versus	versus	ADP
flr-49	122	26	thousands	thousand	NOUN
flr-49	122	27	)	)	PUNCT
flr-49	122	28	×	×	NOUN
flr-49	122	29	2	2	NUM
flr-49	122	30	(	(	PUNCT
flr-49	122	31	question	question	NOUN
flr-49	122	32	sequence	sequence	NOUN
flr-49	122	33	:	:	PUNCT
flr-49	122	34	increasing	increase	VERB
flr-49	122	35	value	value	NOUN
flr-49	122	36	versus	versus	ADP
flr-49	122	37	randomised	randomised	ADJ
flr-49	122	38	)	)	PUNCT
flr-49	122	39	×	×	NOUN
flr-49	122	40	2	2	NUM
flr-49	122	41	(	(	PUNCT
flr-49	122	42	grade	grade	NOUN
flr-49	122	43	:	:	PUNCT
flr-49	122	44	primary	primary	ADJ
flr-49	122	45	5	5	NUM
flr-49	122	46	versus	versus	ADP
flr-49	122	47	secondary	secondary	ADJ
flr-49	122	48	2	2	NUM
flr-49	122	49	)	)	PUNCT
flr-49	122	50	full	full	ADJ
flr-49	122	51	factorial	factorial	ADJ
flr-49	122	52	split	split	NOUN
flr-49	122	53	-	-	PUNCT
flr-49	122	54	plot	plot	NOUN
flr-49	122	55	design	design	NOUN
flr-49	122	56	.	.	PUNCT
flr-49	123	1	magnitude	magnitude	NOUN
flr-49	123	2	band	band	NOUN
flr-49	123	3	served	serve	VERB
flr-49	123	4	as	as	ADP
flr-49	123	5	the	the	DET
flr-49	123	6	only	only	ADJ
flr-49	123	7	within	within	ADP
flr-49	123	8	-	-	PUNCT
flr-49	123	9	subject	subject	NOUN
flr-49	123	10	variable	variable	NOUN
flr-49	123	11	.	.	PUNCT
flr-49	124	1	a	a	DET
flr-49	124	2	total	total	NOUN
flr-49	124	3	of	of	ADP
flr-49	124	4	68	68	NUM
flr-49	124	5	secondary	secondary	ADJ
flr-49	124	6	2	2	NUM
flr-49	124	7	students	student	NOUN
flr-49	124	8	(	(	PUNCT
flr-49	124	9	mage	mage	NOUN
flr-49	124	10	=	=	NOUN
flr-49	124	11	13.9	13.9	NUM
flr-49	124	12	,	,	PUNCT
flr-49	124	13	sd	sd	ADP
flr-49	124	14	=	=	NOUN
flr-49	124	15	0.45	0.45	NUM
flr-49	124	16	)	)	PUNCT
flr-49	124	17	and	and	CCONJ
flr-49	124	18	110	110	NUM
flr-49	124	19	primary	primary	ADJ
flr-49	124	20	5	5	NUM
flr-49	124	21	students	student	NOUN
flr-49	124	22	(	(	PUNCT
flr-49	124	23	mage	mage	NOUN
flr-49	124	24	=	=	NOUN
flr-49	124	25	11.1	11.1	NUM
flr-49	124	26	,	,	PUNCT
flr-49	124	27	sd	sd	ADP
flr-49	124	28	=	=	SYM
flr-49	124	29	0.60	0.60	NUM
flr-49	124	30	)	)	PUNCT
flr-49	124	31	from	from	ADP
flr-49	124	32	5	5	NUM
flr-49	124	33	schools	school	NOUN
flr-49	124	34	(	(	PUNCT
flr-49	124	35	2	2	NUM
flr-49	124	36	secondary	secondary	ADJ
flr-49	124	37	and	and	CCONJ
flr-49	124	38	3	3	NUM
flr-49	124	39	primary	primary	NOUN
flr-49	124	40	)	)	PUNCT
flr-49	124	41	of	of	ADP
flr-49	124	42	mixed	mixed	ADJ
flr-49	124	43	abilities	ability	NOUN
flr-49	124	44	and	and	CCONJ
flr-49	124	45	social	social	ADJ
flr-49	124	46	economic	economic	ADJ
flr-49	124	47	status	status	NOUN
flr-49	124	48	participated	participate	VERB
flr-49	124	49	in	in	ADP
flr-49	124	50	the	the	DET
flr-49	124	51	study	study	NOUN
flr-49	124	52	.	.	PUNCT
flr-49	125	1	all	all	DET
flr-49	125	2	schools	school	NOUN
flr-49	125	3	were	be	AUX
flr-49	125	4	government	government	NOUN
flr-49	125	5	funded	fund	VERB
flr-49	125	6	,	,	PUNCT
flr-49	125	7	located	locate	VERB
flr-49	125	8	in	in	ADP
flr-49	125	9	the	the	DET
flr-49	125	10	western	western	ADJ
flr-49	125	11	region	region	NOUN
flr-49	125	12	of	of	ADP
flr-49	125	13	singapore	singapore	PROPN
flr-49	125	14	,	,	PUNCT
flr-49	125	15	and	and	CCONJ
flr-49	125	16	followed	follow	VERB
flr-49	125	17	the	the	DET
flr-49	125	18	national	national	ADJ
flr-49	125	19	mathematics	mathematics	PROPN
flr-49	125	20	curriculum	curriculum	NOUN
flr-49	125	21	.	.	PUNCT
flr-49	126	1	all	all	DET
flr-49	126	2	children	child	NOUN
flr-49	126	3	participated	participate	VERB
flr-49	126	4	with	with	ADP
flr-49	126	5	parental	parental	ADJ
flr-49	126	6	consent	consent	NOUN
flr-49	126	7	.	.	PUNCT
flr-49	127	1	2.2	2.2	NUM
flr-49	127	2	task	task	NOUN
flr-49	127	3	and	and	CCONJ
flr-49	127	4	materials	material	NOUN
flr-49	127	5	we	we	PRON
flr-49	127	6	designed	design	VERB
flr-49	127	7	a	a	DET
flr-49	127	8	web	web	NOUN
flr-49	127	9	-	-	PUNCT
flr-49	127	10	based	base	VERB
flr-49	127	11	program	program	NOUN
flr-49	127	12	comprising	comprise	VERB
flr-49	127	13	a	a	DET
flr-49	127	14	production	production	NOUN
flr-49	127	15	task	task	NOUN
flr-49	127	16	followed	follow	VERB
flr-49	127	17	by	by	ADP
flr-49	127	18	a	a	DET
flr-49	127	19	validation	validation	NOUN
flr-49	127	20	task	task	NOUN
flr-49	127	21	.	.	PUNCT
flr-49	128	1	participants	participant	NOUN
flr-49	128	2	’	'	PUNCT
flr-49	128	3	inputs	input	NOUN
flr-49	128	4	on	on	ADP
flr-49	128	5	the	the	DET
flr-49	128	6	computer	computer	NOUN
flr-49	128	7	interface	interface	NOUN
flr-49	128	8	were	be	AUX
flr-49	128	9	logged	log	VERB
flr-49	128	10	on	on	ADP
flr-49	128	11	a	a	DET
flr-49	128	12	server	server	NOUN
flr-49	128	13	.	.	PUNCT
flr-49	129	1	in	in	ADP
flr-49	129	2	addition	addition	NOUN
flr-49	129	3	,	,	PUNCT
flr-49	129	4	the	the	DET
flr-49	129	5	secondary	secondary	ADJ
flr-49	129	6	2	2	NUM
flr-49	129	7	students	student	NOUN
flr-49	129	8	were	be	AUX
flr-49	129	9	administered	administer	VERB
flr-49	129	10	the	the	DET
flr-49	129	11	küchemann	küchemann	PROPN
flr-49	129	12	algebra	algebra	PROPN
flr-49	129	13	test	test	NOUN
flr-49	129	14	(	(	PUNCT
flr-49	129	15	brown	brown	PROPN
flr-49	129	16	et	et	PROPN
flr-49	129	17	al	al	PROPN
flr-49	129	18	.	.	PROPN
flr-49	129	19	,	,	PUNCT
flr-49	129	20	1985	1985	NUM
flr-49	129	21	)	)	PUNCT
flr-49	129	22	.	.	PUNCT
flr-49	130	1	k.	k.	PROPN
flr-49	130	2	lee	lee	PROPN
flr-49	130	3	et	et	PROPN
flr-49	130	4	al	al	PROPN
flr-49	130	5	.	.	PROPN
flr-49	130	6	86	86	NUM
flr-49	131	1	|	|	ADV
flr-49	131	2	f	f	NOUN
flr-49	131	3	l	l	NOUN
flr-49	131	4	r	r	NOUN
flr-49	131	5	2.2.1	2.2.1	NUM
flr-49	131	6	production	production	NOUN
flr-49	131	7	task	task	NOUN
flr-49	131	8	the	the	DET
flr-49	131	9	children	child	NOUN
flr-49	131	10	were	be	AUX
flr-49	131	11	presented	present	VERB
flr-49	131	12	with	with	ADP
flr-49	131	13	algebra	algebra	NOUN
flr-49	131	14	word	word	NOUN
flr-49	131	15	problems	problem	NOUN
flr-49	131	16	on	on	ADP
flr-49	131	17	the	the	DET
flr-49	131	18	computer	computer	NOUN
flr-49	131	19	screen	screen	NOUN
flr-49	131	20	and	and	CCONJ
flr-49	131	21	were	be	AUX
flr-49	131	22	asked	ask	VERB
flr-49	131	23	to	to	PART
flr-49	131	24	draw	draw	VERB
flr-49	131	25	model	model	NOUN
flr-49	131	26	diagrams	diagram	NOUN
flr-49	131	27	for	for	ADP
flr-49	131	28	these	these	DET
flr-49	131	29	problems	problem	NOUN
flr-49	131	30	using	use	VERB
flr-49	131	31	the	the	DET
flr-49	131	32	graphical	graphical	ADJ
flr-49	131	33	tools	tool	NOUN
flr-49	131	34	provided	provide	VERB
flr-49	131	35	onscreen	onscreen	ADJ
flr-49	131	36	.	.	PUNCT
flr-49	132	1	a	a	DET
flr-49	132	2	computerized	computerized	ADJ
flr-49	132	3	interface	interface	NOUN
flr-49	132	4	provided	provide	VERB
flr-49	132	5	a	a	DET
flr-49	132	6	standardized	standardized	ADJ
flr-49	132	7	interface	interface	NOUN
flr-49	132	8	both	both	PRON
flr-49	132	9	for	for	ADP
flr-49	132	10	problem	problem	NOUN
flr-49	132	11	administration	administration	NOUN
flr-49	132	12	and	and	CCONJ
flr-49	132	13	data	datum	NOUN
flr-49	132	14	collection	collection	NOUN
flr-49	132	15	.	.	PUNCT
flr-49	133	1	the	the	DET
flr-49	133	2	children	child	NOUN
flr-49	133	3	started	start	VERB
flr-49	133	4	with	with	ADP
flr-49	133	5	an	an	DET
flr-49	133	6	online	online	ADJ
flr-49	133	7	palette	palette	NOUN
flr-49	133	8	that	that	PRON
flr-49	133	9	contained	contain	VERB
flr-49	133	10	a	a	DET
flr-49	133	11	variety	variety	NOUN
flr-49	133	12	of	of	ADP
flr-49	133	13	specially	specially	ADV
flr-49	133	14	designed	design	VERB
flr-49	133	15	drawing	drawing	NOUN
flr-49	133	16	and	and	CCONJ
flr-49	133	17	labelling	labelling	NOUN
flr-49	133	18	tools	tool	NOUN
flr-49	133	19	.	.	PUNCT
flr-49	134	1	the	the	DET
flr-49	134	2	children	child	NOUN
flr-49	134	3	viewed	view	VERB
flr-49	134	4	and	and	CCONJ
flr-49	134	5	worked	work	VERB
flr-49	134	6	on	on	ADP
flr-49	134	7	one	one	NUM
flr-49	134	8	problem	problem	NOUN
flr-49	134	9	at	at	ADP
flr-49	134	10	a	a	DET
flr-49	134	11	time	time	NOUN
flr-49	134	12	.	.	PUNCT
flr-49	135	1	they	they	PRON
flr-49	135	2	were	be	AUX
flr-49	135	3	not	not	PART
flr-49	135	4	required	require	VERB
flr-49	135	5	to	to	PART
flr-49	135	6	solve	solve	VERB
flr-49	135	7	the	the	DET
flr-49	135	8	problem	problem	NOUN
flr-49	135	9	,	,	PUNCT
flr-49	135	10	just	just	ADV
flr-49	135	11	to	to	PART
flr-49	135	12	draw	draw	VERB
flr-49	135	13	the	the	DET
flr-49	135	14	bar	bar	NOUN
flr-49	135	15	diagrams	diagram	NOUN
flr-49	135	16	in	in	ADP
flr-49	135	17	the	the	DET
flr-49	135	18	same	same	ADJ
flr-49	135	19	format	format	NOUN
flr-49	135	20	that	that	PRON
flr-49	135	21	they	they	PRON
flr-49	135	22	would	would	AUX
flr-49	135	23	with	with	ADP
flr-49	135	24	pen	pen	NOUN
flr-49	135	25	and	and	CCONJ
flr-49	135	26	paper	paper	NOUN
flr-49	135	27	.	.	PUNCT
flr-49	136	1	there	there	PRON
flr-49	136	2	was	be	VERB
flr-49	136	3	no	no	DET
flr-49	136	4	limit	limit	NOUN
flr-49	136	5	to	to	ADP
flr-49	136	6	the	the	DET
flr-49	136	7	size	size	NOUN
flr-49	136	8	of	of	ADP
flr-49	136	9	the	the	DET
flr-49	136	10	bars	bar	NOUN
flr-49	136	11	that	that	PRON
flr-49	136	12	could	could	AUX
flr-49	136	13	be	be	AUX
flr-49	136	14	drawn	draw	VERB
flr-49	136	15	.	.	PUNCT
flr-49	137	1	each	each	DET
flr-49	137	2	child	child	NOUN
flr-49	137	3	completed	complete	VERB
flr-49	137	4	12	12	NUM
flr-49	137	5	problems	problem	NOUN
flr-49	137	6	.	.	PUNCT
flr-49	138	1	all	all	DET
flr-49	138	2	the	the	DET
flr-49	138	3	problems	problem	NOUN
flr-49	138	4	were	be	AUX
flr-49	138	5	of	of	ADP
flr-49	138	6	the	the	DET
flr-49	138	7	same	same	ADJ
flr-49	138	8	structure	structure	NOUN
flr-49	138	9	,	,	PUNCT
flr-49	138	10	but	but	CCONJ
flr-49	138	11	varied	varied	ADJ
flr-49	138	12	in	in	ADP
flr-49	138	13	the	the	DET
flr-49	138	14	name	name	NOUN
flr-49	138	15	of	of	ADP
flr-49	138	16	the	the	DET
flr-49	138	17	protagonists	protagonist	NOUN
flr-49	138	18	and	and	CCONJ
flr-49	138	19	referents	referent	NOUN
flr-49	138	20	(	(	PUNCT
flr-49	138	21	e.g.	e.g.	ADV
flr-49	138	22	,	,	PUNCT
flr-49	138	23	mary	mary	PROPN
flr-49	138	24	versus	versus	ADP
flr-49	138	25	jane	jane	PROPN
flr-49	138	26	,	,	PUNCT
flr-49	138	27	marbles	marble	NOUN
flr-49	138	28	versus	versus	ADP
flr-49	138	29	cupcakes	cupcake	NOUN
flr-49	138	30	)	)	PUNCT
flr-49	138	31	.	.	PUNCT
flr-49	139	1	the	the	DET
flr-49	139	2	specific	specific	ADJ
flr-49	139	3	magnitude	magnitude	NOUN
flr-49	139	4	band	band	NOUN
flr-49	139	5	in	in	ADP
flr-49	139	6	each	each	DET
flr-49	139	7	problem	problem	NOUN
flr-49	139	8	varied	varied	ADJ
flr-49	139	9	across	across	ADP
flr-49	139	10	four	four	NUM
flr-49	139	11	scales	scale	NOUN
flr-49	139	12	:	:	PUNCT
flr-49	139	13	ones	one	NOUN
flr-49	139	14	,	,	PUNCT
flr-49	139	15	tens	ten	NOUN
flr-49	139	16	,	,	PUNCT
flr-49	139	17	hundreds	hundred	NOUN
flr-49	139	18	,	,	PUNCT
flr-49	139	19	and	and	CCONJ
flr-49	139	20	thousands	thousand	NOUN
flr-49	139	21	.	.	PUNCT
flr-49	140	1	three	three	NUM
flr-49	140	2	problems	problem	NOUN
flr-49	140	3	were	be	AUX
flr-49	140	4	given	give	VERB
flr-49	140	5	within	within	ADP
flr-49	140	6	each	each	DET
flr-49	140	7	scale	scale	NOUN
flr-49	140	8	.	.	PUNCT
flr-49	141	1	the	the	DET
flr-49	141	2	size	size	NOUN
flr-49	141	3	of	of	ADP
flr-49	141	4	the	the	DET
flr-49	141	5	operand	operand	NOUN
flr-49	141	6	relating	relate	VERB
flr-49	141	7	to	to	ADP
flr-49	141	8	the	the	DET
flr-49	141	9	difference	difference	NOUN
flr-49	141	10	unit	unit	NOUN
flr-49	141	11	-our	-our	ADP
flr-49	141	12	dependent	dependent	ADJ
flr-49	141	13	measure	measure	NOUN
flr-49	141	14	of	of	ADP
flr-49	141	15	interest	interest	NOUN
flr-49	141	16	-in	-in	ADP
flr-49	141	17	these	these	DET
flr-49	141	18	three	three	NUM
flr-49	141	19	problems	problem	NOUN
flr-49	141	20	was	be	AUX
flr-49	141	21	drawn	draw	VERB
flr-49	141	22	from	from	ADP
flr-49	141	23	the	the	DET
flr-49	141	24	smaller	small	ADJ
flr-49	141	25	,	,	PUNCT
flr-49	141	26	medium	medium	ADJ
flr-49	141	27	,	,	PUNCT
flr-49	141	28	and	and	CCONJ
flr-49	141	29	larger	large	ADJ
flr-49	141	30	range	range	NOUN
flr-49	141	31	of	of	ADP
flr-49	141	32	each	each	DET
flr-49	141	33	magnitude	magnitude	NOUN
flr-49	141	34	band	band	NOUN
flr-49	141	35	;	;	PUNCT
flr-49	141	36	with	with	ADP
flr-49	141	37	one	one	NUM
flr-49	141	38	question	question	NOUN
flr-49	141	39	from	from	ADP
flr-49	141	40	each	each	DET
flr-49	141	41	range	range	NOUN
flr-49	141	42	.	.	PUNCT
flr-49	142	1	in	in	ADP
flr-49	142	2	figure	figure	NOUN
flr-49	142	3	1a	1a	NOUN
flr-49	142	4	,	,	PUNCT
flr-49	142	5	for	for	ADP
flr-49	142	6	example	example	NOUN
flr-49	142	7	,	,	PUNCT
flr-49	142	8	we	we	PRON
flr-49	142	9	depicted	depict	VERB
flr-49	142	10	a	a	DET
flr-49	142	11	question	question	NOUN
flr-49	142	12	with	with	ADP
flr-49	142	13	a	a	DET
flr-49	142	14	small	small	ADJ
flr-49	142	15	difference	difference	NOUN
flr-49	142	16	unit	unit	NOUN
flr-49	142	17	(	(	PUNCT
flr-49	142	18	“	"	PUNCT
flr-49	142	19	2	2	NUM
flr-49	142	20	”	"	PUNCT
flr-49	142	21	)	)	PUNCT
flr-49	142	22	from	from	ADP
flr-49	142	23	the	the	DET
flr-49	142	24	magnitude	magnitude	NOUN
flr-49	142	25	band	band	NOUN
flr-49	142	26	of	of	ADP
flr-49	142	27	“	"	PUNCT
flr-49	142	28	ones	one	NOUN
flr-49	142	29	”	"	PUNCT
flr-49	142	30	.	.	PUNCT
flr-49	143	1	a	a	DET
flr-49	143	2	question	question	NOUN
flr-49	143	3	with	with	ADP
flr-49	143	4	a	a	DET
flr-49	143	5	large	large	ADJ
flr-49	143	6	difference	difference	NOUN
flr-49	143	7	-	-	PUNCT
flr-49	143	8	unit	unit	NOUN
flr-49	143	9	operand	operand	NOUN
flr-49	143	10	(	(	PUNCT
flr-49	143	11	e.g.	e.g.	ADV
flr-49	143	12	,	,	PUNCT
flr-49	143	13	7	7	NUM
flr-49	143	14	)	)	PUNCT
flr-49	143	15	,	,	PUNCT
flr-49	143	16	still	still	ADV
flr-49	143	17	from	from	ADP
flr-49	143	18	the	the	DET
flr-49	143	19	magnitude	magnitude	NOUN
flr-49	143	20	band	band	NOUN
flr-49	143	21	of	of	ADP
flr-49	143	22	ones	one	NOUN
flr-49	143	23	,	,	PUNCT
flr-49	143	24	would	would	AUX
flr-49	143	25	read	read	VERB
flr-49	143	26	something	something	PRON
flr-49	143	27	like	like	ADP
flr-49	143	28	“	"	PUNCT
flr-49	143	29	mary	mary	PROPN
flr-49	143	30	and	and	CCONJ
flr-49	143	31	john	john	PROPN
flr-49	143	32	have	have	VERB
flr-49	143	33	9	9	NUM
flr-49	143	34	marbles	marble	NOUN
flr-49	143	35	altogether	altogether	ADV
flr-49	143	36	.	.	PUNCT
flr-49	144	1	john	john	PROPN
flr-49	144	2	has	have	VERB
flr-49	144	3	7	7	NUM
flr-49	144	4	more	more	ADJ
flr-49	144	5	marbles	marble	NOUN
flr-49	144	6	than	than	ADP
flr-49	144	7	mary	mary	PROPN
flr-49	144	8	…	…	PUNCT
flr-49	144	9	”	"	PUNCT
flr-49	144	10	a	a	DET
flr-49	144	11	question	question	NOUN
flr-49	144	12	with	with	ADP
flr-49	144	13	a	a	DET
flr-49	144	14	large	large	ADJ
flr-49	144	15	difference	difference	NOUN
flr-49	144	16	unit	unit	NOUN
flr-49	144	17	(	(	PUNCT
flr-49	144	18	e.g.	e.g.	ADV
flr-49	144	19	,	,	PUNCT
flr-49	144	20	70	70	NUM
flr-49	144	21	)	)	PUNCT
flr-49	144	22	from	from	ADP
flr-49	144	23	the	the	DET
flr-49	144	24	magnitude	magnitude	NOUN
flr-49	144	25	band	band	NOUN
flr-49	144	26	of	of	ADP
flr-49	144	27	tens	ten	NOUN
flr-49	144	28	would	would	AUX
flr-49	144	29	have	have	AUX
flr-49	144	30	been	be	AUX
flr-49	144	31	presented	present	VERB
flr-49	144	32	as	as	SCONJ
flr-49	144	33	“	"	PUNCT
flr-49	144	34	john	john	PROPN
flr-49	144	35	has	have	VERB
flr-49	144	36	70	70	NUM
flr-49	144	37	more	more	ADJ
flr-49	144	38	marbles	marble	NOUN
flr-49	144	39	than	than	ADP
flr-49	144	40	mary	mary	PROPN
flr-49	144	41	…	…	PUNCT
flr-49	144	42	”	"	PUNCT
flr-49	144	43	to	to	PART
flr-49	144	44	reduce	reduce	VERB
flr-49	144	45	stimuli	stimulus	NOUN
flr-49	144	46	specific	specific	ADJ
flr-49	144	47	effects	effect	NOUN
flr-49	144	48	,	,	PUNCT
flr-49	144	49	we	we	PRON
flr-49	144	50	developed	develop	VERB
flr-49	144	51	two	two	NUM
flr-49	144	52	parallel	parallel	ADJ
flr-49	144	53	sets	set	NOUN
flr-49	144	54	of	of	ADP
flr-49	144	55	problems	problem	NOUN
flr-49	144	56	that	that	PRON
flr-49	144	57	were	be	AUX
flr-49	144	58	identical	identical	ADJ
flr-49	144	59	in	in	ADP
flr-49	144	60	structure	structure	NOUN
flr-49	144	61	and	and	CCONJ
flr-49	144	62	differed	differ	VERB
flr-49	144	63	only	only	ADV
flr-49	144	64	in	in	ADP
flr-49	144	65	specific	specific	ADJ
flr-49	144	66	quantities	quantity	NOUN
flr-49	144	67	.	.	PUNCT
flr-49	145	1	in	in	ADP
flr-49	145	2	both	both	DET
flr-49	145	3	sets	set	NOUN
flr-49	145	4	,	,	PUNCT
flr-49	145	5	questions	question	NOUN
flr-49	145	6	were	be	AUX
flr-49	145	7	administered	administer	VERB
flr-49	145	8	either	either	CCONJ
flr-49	145	9	in	in	ADP
flr-49	145	10	randomized	randomized	ADJ
flr-49	145	11	order	order	NOUN
flr-49	145	12	or	or	CCONJ
flr-49	145	13	in	in	ADP
flr-49	145	14	accordance	accordance	NOUN
flr-49	145	15	to	to	ADP
flr-49	145	16	the	the	DET
flr-49	145	17	magnitude	magnitude	NOUN
flr-49	145	18	of	of	ADP
flr-49	145	19	the	the	DET
flr-49	145	20	difference	difference	NOUN
flr-49	145	21	-	-	PUNCT
flr-49	145	22	unit	unit	NOUN
flr-49	145	23	operands	operand	NOUN
flr-49	145	24	.	.	PUNCT
flr-49	146	1	the	the	DET
flr-49	146	2	children	child	NOUN
flr-49	146	3	’s	’s	PART
flr-49	146	4	drawings	drawing	NOUN
flr-49	146	5	were	be	AUX
flr-49	146	6	recorded	record	VERB
flr-49	146	7	by	by	ADP
flr-49	146	8	the	the	DET
flr-49	146	9	computer	computer	NOUN
flr-49	146	10	program	program	NOUN
flr-49	146	11	,	,	PUNCT
flr-49	146	12	which	which	PRON
flr-49	146	13	also	also	ADV
flr-49	146	14	logged	log	VERB
flr-49	146	15	the	the	DET
flr-49	146	16	pixel	pixel	PROPN
flr-49	146	17	length	length	NOUN
flr-49	146	18	of	of	ADP
flr-49	146	19	the	the	DET
flr-49	146	20	bar	bar	NOUN
flr-49	146	21	diagrams	diagram	NOUN
flr-49	146	22	.	.	PUNCT
flr-49	147	1	the	the	DET
flr-49	147	2	pixel	pixel	PROPN
flr-49	147	3	length	length	NOUN
flr-49	147	4	of	of	ADP
flr-49	147	5	the	the	DET
flr-49	147	6	difference	difference	NOUN
flr-49	147	7	unit	unit	NOUN
flr-49	147	8	or	or	CCONJ
flr-49	147	9	the	the	DET
flr-49	147	10	section	section	NOUN
flr-49	147	11	of	of	ADP
flr-49	147	12	the	the	DET
flr-49	147	13	bar	bar	NOUN
flr-49	147	14	that	that	PRON
flr-49	147	15	represents	represent	VERB
flr-49	147	16	the	the	DET
flr-49	147	17	difference	difference	NOUN
flr-49	147	18	between	between	ADP
flr-49	147	19	the	the	DET
flr-49	147	20	two	two	NUM
flr-49	147	21	protagonists	protagonist	NOUN
flr-49	147	22	(	(	PUNCT
flr-49	147	23	see	see	VERB
flr-49	147	24	figure	figure	NOUN
flr-49	147	25	1a	1a	NOUN
flr-49	147	26	)	)	PUNCT
flr-49	147	27	was	be	AUX
flr-49	147	28	used	use	VERB
flr-49	147	29	as	as	ADP
flr-49	147	30	the	the	DET
flr-49	147	31	dependent	dependent	ADJ
flr-49	147	32	variable	variable	NOUN
flr-49	147	33	.	.	PUNCT
flr-49	148	1	of	of	ADP
flr-49	148	2	particular	particular	ADJ
flr-49	148	3	interest	interest	NOUN
flr-49	148	4	was	be	AUX
flr-49	148	5	whether	whether	SCONJ
flr-49	148	6	students	student	NOUN
flr-49	148	7	varied	vary	VERB
flr-49	148	8	the	the	DET
flr-49	148	9	length	length	NOUN
flr-49	148	10	of	of	ADP
flr-49	148	11	the	the	DET
flr-49	148	12	difference	difference	NOUN
flr-49	148	13	unit	unit	NOUN
flr-49	148	14	across	across	ADP
flr-49	148	15	magnitude	magnitude	NOUN
flr-49	148	16	bands	band	NOUN
flr-49	148	17	.	.	PUNCT
flr-49	149	1	that	that	PRON
flr-49	149	2	is	be	AUX
flr-49	149	3	,	,	PUNCT
flr-49	149	4	did	do	AUX
flr-49	149	5	they	they	PRON
flr-49	149	6	draw	draw	VERB
flr-49	149	7	bars	bar	NOUN
flr-49	149	8	that	that	PRON
flr-49	149	9	were	be	AUX
flr-49	149	10	much	much	ADV
flr-49	149	11	longer	long	ADJ
flr-49	149	12	to	to	PART
flr-49	149	13	represent	represent	VERB
flr-49	149	14	“	"	PUNCT
flr-49	149	15	john	john	PROPN
flr-49	149	16	has	have	VERB
flr-49	149	17	70	70	NUM
flr-49	149	18	more	more	ADJ
flr-49	149	19	marbles	marble	NOUN
flr-49	149	20	”	"	PUNCT
flr-49	149	21	as	as	SCONJ
flr-49	149	22	compared	compare	VERB
flr-49	149	23	to	to	ADP
flr-49	149	24	“	"	PUNCT
flr-49	149	25	john	john	PROPN
flr-49	149	26	has	have	VERB
flr-49	149	27	7	7	NUM
flr-49	149	28	more	more	ADJ
flr-49	149	29	marbles	marble	NOUN
flr-49	149	30	”	"	PUNCT
flr-49	149	31	?	?	PUNCT
flr-49	150	1	because	because	SCONJ
flr-49	150	2	we	we	PRON
flr-49	150	3	did	do	AUX
flr-49	150	4	not	not	PART
flr-49	150	5	impose	impose	VERB
flr-49	150	6	an	an	DET
flr-49	150	7	upper	upper	ADJ
flr-49	150	8	limit	limit	NOUN
flr-49	150	9	on	on	ADP
flr-49	150	10	the	the	DET
flr-49	150	11	length	length	NOUN
flr-49	150	12	of	of	ADP
flr-49	150	13	the	the	DET
flr-49	150	14	bar	bar	NOUN
flr-49	150	15	,	,	PUNCT
flr-49	150	16	there	there	PRON
flr-49	150	17	was	be	VERB
flr-49	150	18	also	also	ADV
flr-49	150	19	no	no	DET
flr-49	150	20	upper	upper	ADJ
flr-49	150	21	cap	cap	NOUN
flr-49	150	22	on	on	ADP
flr-49	150	23	the	the	DET
flr-49	150	24	range	range	NOUN
flr-49	150	25	for	for	ADP
flr-49	150	26	the	the	DET
flr-49	150	27	dependent	dependent	ADJ
flr-49	150	28	variable	variable	NOUN
flr-49	150	29	.	.	PUNCT
flr-49	151	1	in	in	ADP
flr-49	151	2	table	table	NOUN
flr-49	151	3	1	1	NUM
flr-49	151	4	,	,	PUNCT
flr-49	151	5	we	we	PRON
flr-49	151	6	provided	provide	VERB
flr-49	151	7	both	both	CCONJ
flr-49	151	8	the	the	DET
flr-49	151	9	confidence	confidence	NOUN
flr-49	151	10	intervals	interval	NOUN
flr-49	151	11	and	and	CCONJ
flr-49	151	12	the	the	DET
flr-49	151	13	range	range	NOUN
flr-49	151	14	from	from	ADP
flr-49	151	15	the	the	DET
flr-49	151	16	observed	observe	VERB
flr-49	151	17	data	datum	NOUN
flr-49	151	18	.	.	PUNCT
flr-49	152	1	2.2.2	2.2.2	NUM
flr-49	152	2	validation	validation	NOUN
flr-49	152	3	task	task	NOUN
flr-49	152	4	participants	participant	NOUN
flr-49	152	5	were	be	AUX
flr-49	152	6	presented	present	VERB
flr-49	152	7	with	with	ADP
flr-49	152	8	two	two	NUM
flr-49	152	9	sets	set	NOUN
flr-49	152	10	of	of	ADP
flr-49	152	11	3	3	NUM
flr-49	152	12	questions	question	NOUN
flr-49	152	13	.	.	PUNCT
flr-49	153	1	for	for	ADP
flr-49	153	2	the	the	DET
flr-49	153	3	first	first	ADJ
flr-49	153	4	set	set	NOUN
flr-49	153	5	of	of	ADP
flr-49	153	6	validation	validation	NOUN
flr-49	153	7	questions	question	NOUN
flr-49	153	8	,	,	PUNCT
flr-49	153	9	each	each	DET
flr-49	153	10	question	question	NOUN
flr-49	153	11	comprised	comprise	VERB
flr-49	153	12	a	a	DET
flr-49	153	13	word	word	NOUN
flr-49	153	14	problem	problem	NOUN
flr-49	153	15	followed	follow	VERB
flr-49	153	16	by	by	ADP
flr-49	153	17	two	two	NUM
flr-49	153	18	model	model	NOUN
flr-49	153	19	diagrams	diagram	NOUN
flr-49	153	20	differing	differ	VERB
flr-49	153	21	in	in	ADP
flr-49	153	22	whether	whether	SCONJ
flr-49	153	23	proportionality	proportionality	NOUN
flr-49	153	24	in	in	ADP
flr-49	153	25	the	the	DET
flr-49	153	26	length	length	NOUN
flr-49	153	27	of	of	ADP
flr-49	153	28	the	the	DET
flr-49	153	29	bars	bar	NOUN
flr-49	153	30	was	be	AUX
flr-49	153	31	maintained	maintain	VERB
flr-49	153	32	,	,	PUNCT
flr-49	153	33	across	across	ADP
flr-49	153	34	questions	question	NOUN
flr-49	153	35	.	.	PUNCT
flr-49	154	1	in	in	ADP
flr-49	154	2	one	one	NUM
flr-49	154	3	diagram	diagram	NOUN
flr-49	154	4	,	,	PUNCT
flr-49	154	5	the	the	DET
flr-49	154	6	bars	bar	NOUN
flr-49	154	7	were	be	AUX
flr-49	154	8	drawn	draw	VERB
flr-49	154	9	with	with	ADP
flr-49	154	10	longer	long	ADJ
flr-49	154	11	bars	bar	NOUN
flr-49	154	12	for	for	ADP
flr-49	154	13	larger	large	ADJ
flr-49	154	14	numbers	number	NOUN
flr-49	154	15	.	.	PUNCT
flr-49	155	1	in	in	ADP
flr-49	155	2	the	the	DET
flr-49	155	3	other	other	ADJ
flr-49	155	4	,	,	PUNCT
flr-49	155	5	proportionality	proportionality	NOUN
flr-49	155	6	was	be	AUX
flr-49	155	7	not	not	PART
flr-49	155	8	maintained	maintain	VERB
flr-49	155	9	.	.	PUNCT
flr-49	156	1	in	in	ADP
flr-49	156	2	other	other	ADJ
flr-49	156	3	words	word	NOUN
flr-49	156	4	,	,	PUNCT
flr-49	156	5	the	the	DET
flr-49	156	6	diagrams	diagram	NOUN
flr-49	156	7	differed	differ	VERB
flr-49	156	8	in	in	ADP
flr-49	156	9	whether	whether	SCONJ
flr-49	156	10	the	the	DET
flr-49	156	11	bars	bar	NOUN
flr-49	156	12	were	be	AUX
flr-49	156	13	drawn	draw	VERB
flr-49	156	14	in	in	ADP
flr-49	156	15	a	a	DET
flr-49	156	16	more	more	ADV
flr-49	156	17	concrete	concrete	ADJ
flr-49	156	18	or	or	CCONJ
flr-49	156	19	abstract	abstract	ADJ
flr-49	156	20	manner	manner	NOUN
flr-49	156	21	.	.	PUNCT
flr-49	157	1	participants	participant	NOUN
flr-49	157	2	were	be	AUX
flr-49	157	3	asked	ask	VERB
flr-49	157	4	to	to	PART
flr-49	157	5	choose	choose	VERB
flr-49	157	6	which	which	DET
flr-49	157	7	diagram	diagram	NOUN
flr-49	157	8	(	(	PUNCT
flr-49	157	9	one	one	NUM
flr-49	157	10	or	or	CCONJ
flr-49	157	11	the	the	DET
flr-49	157	12	other	other	ADJ
flr-49	157	13	,	,	PUNCT
flr-49	157	14	or	or	CCONJ
flr-49	157	15	both	both	PRON
flr-49	157	16	)	)	PUNCT
flr-49	157	17	was	be	AUX
flr-49	157	18	correct	correct	ADJ
flr-49	157	19	.	.	PUNCT
flr-49	158	1	they	they	PRON
flr-49	158	2	were	be	AUX
flr-49	158	3	also	also	ADV
flr-49	158	4	asked	ask	VERB
flr-49	158	5	to	to	PART
flr-49	158	6	explain	explain	VERB
flr-49	158	7	their	their	PRON
flr-49	158	8	selection	selection	NOUN
flr-49	158	9	by	by	ADP
flr-49	158	10	selecting	select	VERB
flr-49	158	11	a	a	DET
flr-49	158	12	response	response	NOUN
flr-49	158	13	from	from	ADP
flr-49	158	14	four	four	NUM
flr-49	158	15	multiple	multiple	ADJ
flr-49	158	16	choice	choice	NOUN
flr-49	158	17	options	option	NOUN
flr-49	158	18	(	(	PUNCT
flr-49	158	19	see	see	VERB
flr-49	158	20	appendix	appendix	NOUN
flr-49	158	21	a	a	PRON
flr-49	158	22	)	)	PUNCT
flr-49	158	23	.	.	PUNCT
flr-49	159	1	for	for	ADP
flr-49	159	2	the	the	DET
flr-49	159	3	second	second	ADJ
flr-49	159	4	set	set	NOUN
flr-49	159	5	of	of	ADP
flr-49	159	6	questions	question	NOUN
flr-49	159	7	,	,	PUNCT
flr-49	159	8	each	each	DET
flr-49	159	9	question	question	NOUN
flr-49	159	10	contained	contain	VERB
flr-49	159	11	two	two	NUM
flr-49	159	12	word	word	NOUN
flr-49	159	13	problems	problem	NOUN
flr-49	159	14	,	,	PUNCT
flr-49	159	15	each	each	PRON
flr-49	159	16	accompanied	accompany	VERB
flr-49	159	17	by	by	ADP
flr-49	159	18	two	two	NUM
flr-49	159	19	diagrams	diagram	NOUN
flr-49	159	20	,	,	PUNCT
flr-49	159	21	said	say	VERB
flr-49	159	22	to	to	PART
flr-49	159	23	be	be	AUX
flr-49	159	24	drawn	draw	VERB
flr-49	159	25	by	by	ADP
flr-49	159	26	student	student	NOUN
flr-49	159	27	a	a	NOUN
flr-49	159	28	and	and	CCONJ
flr-49	159	29	student	student	NOUN
flr-49	159	30	b	b	PROPN
flr-49	159	31	respectively	respectively	ADV
flr-49	159	32	.	.	PUNCT
flr-49	160	1	the	the	DET
flr-49	160	2	two	two	NUM
flr-49	160	3	word	word	NOUN
flr-49	160	4	problems	problem	NOUN
flr-49	160	5	in	in	ADP
flr-49	160	6	each	each	DET
flr-49	160	7	question	question	NOUN
flr-49	160	8	were	be	AUX
flr-49	160	9	structurally	structurally	ADV
flr-49	160	10	equivalent	equivalent	ADJ
flr-49	160	11	,	,	PUNCT
flr-49	160	12	differing	differ	VERB
flr-49	160	13	only	only	ADV
flr-49	160	14	in	in	ADP
flr-49	160	15	the	the	DET
flr-49	160	16	magnitude	magnitude	NOUN
flr-49	160	17	of	of	ADP
flr-49	160	18	the	the	DET
flr-49	160	19	operands	operand	NOUN
flr-49	160	20	.	.	PUNCT
flr-49	161	1	student	student	NOUN
flr-49	161	2	a	a	DET
flr-49	161	3	’s	’s	NOUN
flr-49	161	4	diagrams	diagram	NOUN
flr-49	161	5	demonstrated	demonstrate	VERB
flr-49	161	6	a	a	DET
flr-49	161	7	more	more	ADV
flr-49	161	8	abstract	abstract	ADJ
flr-49	161	9	usage	usage	NOUN
flr-49	161	10	of	of	ADP
flr-49	161	11	the	the	DET
flr-49	161	12	bars	bar	NOUN
flr-49	161	13	:	:	PUNCT
flr-49	161	14	the	the	DET
flr-49	161	15	size	size	NOUN
flr-49	161	16	of	of	ADP
flr-49	161	17	the	the	DET
flr-49	161	18	bars	bar	NOUN
flr-49	161	19	were	be	AUX
flr-49	161	20	identical	identical	ADJ
flr-49	161	21	for	for	ADP
flr-49	161	22	operands	operand	NOUN
flr-49	161	23	of	of	ADP
flr-49	161	24	different	different	ADJ
flr-49	161	25	sizes	size	NOUN
flr-49	161	26	.	.	PUNCT
flr-49	162	1	student	student	PROPN
flr-49	162	2	b	b	PROPN
flr-49	162	3	’s	’s	PART
flr-49	162	4	diagrams	diagram	NOUN
flr-49	162	5	demonstrated	demonstrate	VERB
flr-49	162	6	a	a	DET
flr-49	162	7	more	more	ADV
flr-49	162	8	concrete	concrete	ADJ
flr-49	162	9	usage	usage	NOUN
flr-49	162	10	:	:	PUNCT
flr-49	162	11	the	the	DET
flr-49	162	12	size	size	NOUN
flr-49	162	13	of	of	ADP
flr-49	162	14	the	the	DET
flr-49	162	15	bars	bar	NOUN
flr-49	162	16	differed	differ	VERB
flr-49	162	17	in	in	ADP
flr-49	162	18	accordance	accordance	NOUN
flr-49	162	19	to	to	ADP
flr-49	162	20	changes	change	NOUN
flr-49	162	21	in	in	ADP
flr-49	162	22	the	the	DET
flr-49	162	23	size	size	NOUN
flr-49	162	24	of	of	ADP
flr-49	162	25	the	the	DET
flr-49	162	26	operands	operand	NOUN
flr-49	162	27	.	.	PUNCT
flr-49	163	1	participants	participant	NOUN
flr-49	163	2	were	be	AUX
flr-49	163	3	asked	ask	VERB
flr-49	163	4	to	to	PART
flr-49	163	5	indicate	indicate	VERB
flr-49	163	6	if	if	SCONJ
flr-49	163	7	the	the	DET
flr-49	163	8	two	two	NUM
flr-49	163	9	students	student	NOUN
flr-49	163	10	were	be	AUX
flr-49	163	11	correct	correct	ADJ
flr-49	163	12	.	.	PUNCT
flr-49	164	1	a	a	DET
flr-49	164	2	maximum	maximum	NOUN
flr-49	164	3	of	of	ADP
flr-49	164	4	9	9	NUM
flr-49	164	5	marks	mark	NOUN
flr-49	164	6	could	could	AUX
flr-49	164	7	be	be	AUX
flr-49	164	8	obtained	obtain	VERB
flr-49	164	9	in	in	ADP
flr-49	164	10	the	the	DET
flr-49	164	11	validation	validation	NOUN
flr-49	164	12	task	task	NOUN
flr-49	164	13	(	(	PUNCT
flr-49	164	14	see	see	VERB
flr-49	164	15	appendix	appendix	VERB
flr-49	164	16	a	a	PRON
flr-49	164	17	for	for	ADP
flr-49	164	18	scoring	scoring	NOUN
flr-49	164	19	criteria	criterion	NOUN
flr-49	164	20	)	)	PUNCT
flr-49	164	21	with	with	ADP
flr-49	164	22	higher	high	ADJ
flr-49	164	23	marks	mark	NOUN
flr-49	164	24	indicating	indicate	VERB
flr-49	164	25	a	a	DET
flr-49	164	26	more	more	ADV
flr-49	164	27	abstract	abstract	ADJ
flr-49	164	28	understanding	understanding	NOUN
flr-49	164	29	of	of	ADP
flr-49	164	30	the	the	DET
flr-49	164	31	bar	bar	NOUN
flr-49	164	32	diagrams	diagram	NOUN
flr-49	164	33	.	.	PUNCT
flr-49	165	1	k.	k.	PROPN
flr-49	165	2	lee	lee	PROPN
flr-49	165	3	et	et	PROPN
flr-49	165	4	al	al	PROPN
flr-49	165	5	.	.	PROPN
flr-49	165	6	87	87	NUM
flr-49	166	1	|	|	ADV
flr-49	166	2	f	f	NOUN
flr-49	166	3	l	l	NOUN
flr-49	166	4	r	r	NOUN
flr-49	166	5	2.2.3	2.2.3	NUM
flr-49	166	6	küchemann	küchemann	NOUN
flr-49	166	7	algebra	algebra	NOUN
flr-49	166	8	test	test	NOUN
flr-49	166	9	the	the	DET
flr-49	166	10	küchemann	küchemann	PROPN
flr-49	166	11	algebra	algebra	PROPN
flr-49	166	12	test	test	NOUN
flr-49	166	13	from	from	ADP
flr-49	166	14	the	the	DET
flr-49	166	15	chelsea	chelsea	PROPN
flr-49	166	16	diagnostic	diagnostic	ADJ
flr-49	166	17	mathematics	mathematic	NOUN
flr-49	166	18	tests	test	NOUN
flr-49	166	19	(	(	PUNCT
flr-49	166	20	brown	brown	NOUN
flr-49	166	21	et	et	PROPN
flr-49	166	22	al	al	PROPN
flr-49	166	23	.	.	PROPN
flr-49	166	24	,	,	PUNCT
flr-49	166	25	1985	1985	NUM
flr-49	166	26	)	)	PUNCT
flr-49	166	27	is	be	AUX
flr-49	166	28	a	a	DET
flr-49	166	29	standardized	standardized	ADJ
flr-49	166	30	measure	measure	NOUN
flr-49	166	31	of	of	ADP
flr-49	166	32	how	how	SCONJ
flr-49	166	33	children	child	NOUN
flr-49	166	34	interpret	interpret	VERB
flr-49	166	35	letter	letter	NOUN
flr-49	166	36	symbols	symbol	NOUN
flr-49	166	37	used	use	VERB
flr-49	166	38	in	in	ADP
flr-49	166	39	algebra	algebra	NOUN
flr-49	166	40	.	.	PUNCT
flr-49	167	1	up	up	ADP
flr-49	167	2	to	to	PART
flr-49	167	3	six	six	NUM
flr-49	167	4	different	different	ADJ
flr-49	167	5	common	common	ADJ
flr-49	167	6	interpretations	interpretation	NOUN
flr-49	167	7	have	have	AUX
flr-49	167	8	been	be	AUX
flr-49	167	9	identified	identify	VERB
flr-49	167	10	in	in	ADP
flr-49	167	11	the	the	DET
flr-49	167	12	literature	literature	NOUN
flr-49	167	13	:	:	PUNCT
flr-49	167	14	(	(	PUNCT
flr-49	167	15	i	i	NOUN
flr-49	167	16	)	)	PUNCT
flr-49	167	17	letter	letter	NOUN
flr-49	167	18	numerically	numerically	ADV
flr-49	167	19	evaluated	evaluate	VERB
flr-49	167	20	,	,	PUNCT
flr-49	167	21	(	(	PUNCT
flr-49	167	22	ii	ii	NOUN
flr-49	167	23	)	)	PUNCT
flr-49	167	24	letter	letter	NOUN
flr-49	167	25	not	not	PART
flr-49	167	26	used	use	VERB
flr-49	167	27	or	or	CCONJ
flr-49	167	28	ignored	ignore	VERB
flr-49	167	29	,	,	PUNCT
flr-49	167	30	(	(	PUNCT
flr-49	167	31	iii	iii	NOUN
flr-49	167	32	)	)	PUNCT
flr-49	167	33	letter	letter	NOUN
flr-49	167	34	used	use	VERB
flr-49	167	35	as	as	ADP
flr-49	167	36	an	an	DET
flr-49	167	37	object	object	NOUN
flr-49	167	38	or	or	CCONJ
flr-49	167	39	abbreviation	abbreviation	NOUN
flr-49	167	40	,	,	PUNCT
flr-49	167	41	(	(	PUNCT
flr-49	167	42	iv	iv	X
flr-49	167	43	)	)	PUNCT
flr-49	167	44	letter	letter	NOUN
flr-49	167	45	used	use	VERB
flr-49	167	46	as	as	ADP
flr-49	167	47	a	a	DET
flr-49	167	48	specific	specific	ADJ
flr-49	167	49	unknown	unknown	NOUN
flr-49	167	50	,	,	PUNCT
flr-49	167	51	(	(	PUNCT
flr-49	167	52	v	v	NOUN
flr-49	167	53	)	)	PUNCT
flr-49	167	54	letter	letter	NOUN
flr-49	167	55	used	use	VERB
flr-49	167	56	as	as	ADP
flr-49	167	57	a	a	DET
flr-49	167	58	generalised	generalised	ADJ
flr-49	167	59	number	number	NOUN
flr-49	167	60	,	,	PUNCT
flr-49	167	61	(	(	PUNCT
flr-49	167	62	vi	vi	NOUN
flr-49	167	63	)	)	PUNCT
flr-49	167	64	letter	letter	NOUN
flr-49	167	65	used	use	VERB
flr-49	167	66	as	as	ADP
flr-49	167	67	a	a	DET
flr-49	167	68	variable	variable	NOUN
flr-49	167	69	.	.	PUNCT
flr-49	168	1	the	the	DET
flr-49	168	2	test	test	NOUN
flr-49	168	3	places	place	VERB
flr-49	168	4	children	child	NOUN
flr-49	168	5	on	on	ADP
flr-49	168	6	one	one	NUM
flr-49	168	7	of	of	ADP
flr-49	168	8	four	four	NUM
flr-49	168	9	levels	level	NOUN
flr-49	168	10	of	of	ADP
flr-49	168	11	understanding	understanding	NOUN
flr-49	168	12	based	base	VERB
flr-49	168	13	on	on	ADP
flr-49	168	14	the	the	DET
flr-49	168	15	type	type	NOUN
flr-49	168	16	and	and	CCONJ
flr-49	168	17	complexity	complexity	NOUN
flr-49	168	18	of	of	ADP
flr-49	168	19	their	their	PRON
flr-49	168	20	interpretations	interpretation	NOUN
flr-49	168	21	.	.	PUNCT
flr-49	169	1	for	for	ADP
flr-49	169	2	example	example	NOUN
flr-49	169	3	,	,	PUNCT
flr-49	169	4	a	a	DET
flr-49	169	5	student	student	NOUN
flr-49	169	6	using	use	VERB
flr-49	169	7	any	any	PRON
flr-49	169	8	of	of	ADP
flr-49	169	9	the	the	DET
flr-49	169	10	first	first	ADJ
flr-49	169	11	three	three	NUM
flr-49	169	12	interpretations	interpretation	NOUN
flr-49	169	13	and	and	CCONJ
flr-49	169	14	can	can	AUX
flr-49	169	15	only	only	ADV
flr-49	169	16	answer	answer	VERB
flr-49	169	17	very	very	ADV
flr-49	169	18	simple	simple	ADJ
flr-49	169	19	questions	question	NOUN
flr-49	169	20	is	be	AUX
flr-49	169	21	classified	classify	VERB
flr-49	169	22	as	as	ADP
flr-49	169	23	level	level	NOUN
flr-49	169	24	1	1	NUM
flr-49	169	25	.	.	PUNCT
flr-49	170	1	a	a	DET
flr-49	170	2	student	student	NOUN
flr-49	170	3	using	use	VERB
flr-49	170	4	the	the	DET
flr-49	170	5	same	same	ADJ
flr-49	170	6	interpretations	interpretation	NOUN
flr-49	170	7	,	,	PUNCT
flr-49	170	8	but	but	CCONJ
flr-49	170	9	who	who	PRON
flr-49	170	10	is	be	AUX
flr-49	170	11	able	able	ADJ
flr-49	170	12	to	to	PART
flr-49	170	13	answer	answer	VERB
flr-49	170	14	more	more	ADV
flr-49	170	15	structurally	structurally	ADV
flr-49	170	16	complex	complex	ADJ
flr-49	170	17	questions	question	NOUN
flr-49	170	18	is	be	AUX
flr-49	170	19	classified	classify	VERB
flr-49	170	20	as	as	ADP
flr-49	170	21	level	level	NOUN
flr-49	170	22	2	2	NUM
flr-49	170	23	.	.	PUNCT
flr-49	170	24	understanding	understand	VERB
flr-49	170	25	letter	letter	NOUN
flr-49	170	26	symbols	symbol	NOUN
flr-49	170	27	as	as	ADP
flr-49	170	28	referring	refer	VERB
flr-49	170	29	to	to	ADP
flr-49	170	30	specific	specific	ADJ
flr-49	170	31	unknowns	unknown	NOUN
flr-49	170	32	qualifies	qualify	VERB
flr-49	170	33	classification	classification	NOUN
flr-49	170	34	at	at	ADP
flr-49	170	35	level	level	NOUN
flr-49	170	36	3	3	NUM
flr-49	170	37	.	.	PUNCT
flr-49	171	1	this	this	PRON
flr-49	171	2	is	be	AUX
flr-49	171	3	deemed	deem	VERB
flr-49	171	4	a	a	DET
flr-49	171	5	basic	basic	ADJ
flr-49	171	6	level	level	NOUN
flr-49	171	7	of	of	ADP
flr-49	171	8	understanding	understanding	NOUN
flr-49	171	9	required	require	VERB
flr-49	171	10	for	for	ADP
flr-49	171	11	symbolic	symbolic	ADJ
flr-49	171	12	algebra	algebra	NOUN
flr-49	171	13	.	.	PUNCT
flr-49	172	1	level	level	NOUN
flr-49	172	2	4	4	NUM
flr-49	172	3	requires	require	VERB
flr-49	172	4	students	student	NOUN
flr-49	172	5	to	to	PART
flr-49	172	6	demonstrate	demonstrate	VERB
flr-49	172	7	an	an	DET
flr-49	172	8	understanding	understanding	NOUN
flr-49	172	9	of	of	ADP
flr-49	172	10	letter	letter	NOUN
flr-49	172	11	symbols	symbol	NOUN
flr-49	172	12	as	as	ADP
flr-49	172	13	generalised	generalised	ADJ
flr-49	172	14	numbers	number	NOUN
flr-49	172	15	.	.	PUNCT
flr-49	173	1	of	of	ADP
flr-49	173	2	interest	interest	NOUN
flr-49	173	3	was	be	AUX
flr-49	173	4	whether	whether	SCONJ
flr-49	173	5	secondary	secondary	ADJ
flr-49	173	6	2	2	NUM
flr-49	173	7	students	student	NOUN
flr-49	173	8	’	'	PUNCT
flr-49	173	9	attainment	attainment	NOUN
flr-49	173	10	on	on	ADP
flr-49	173	11	the	the	DET
flr-49	173	12	küchemann	küchemann	PROPN
flr-49	173	13	test	test	NOUN
flr-49	173	14	correlated	correlate	VERB
flr-49	173	15	with	with	ADP
flr-49	173	16	their	their	PRON
flr-49	173	17	performance	performance	NOUN
flr-49	173	18	on	on	ADP
flr-49	173	19	the	the	DET
flr-49	173	20	production	production	NOUN
flr-49	173	21	task	task	NOUN
flr-49	173	22	.	.	PUNCT
flr-49	174	1	that	that	PRON
flr-49	174	2	is	be	AUX
flr-49	174	3	,	,	PUNCT
flr-49	174	4	did	do	VERB
flr-49	174	5	students	student	NOUN
flr-49	174	6	with	with	ADP
flr-49	174	7	higher	high	ADJ
flr-49	174	8	scores	score	NOUN
flr-49	174	9	on	on	ADP
flr-49	174	10	the	the	DET
flr-49	174	11	küchemann	küchemann	PROPN
flr-49	174	12	test	test	NOUN
flr-49	174	13	show	show	VERB
flr-49	174	14	less	less	ADJ
flr-49	174	15	tendency	tendency	NOUN
flr-49	174	16	to	to	PART
flr-49	174	17	adjust	adjust	VERB
flr-49	174	18	the	the	DET
flr-49	174	19	length	length	NOUN
flr-49	174	20	of	of	ADP
flr-49	174	21	the	the	DET
flr-49	174	22	bars	bar	NOUN
flr-49	174	23	in	in	ADP
flr-49	174	24	accordance	accordance	NOUN
flr-49	174	25	to	to	ADP
flr-49	174	26	the	the	DET
flr-49	174	27	magnitude	magnitude	NOUN
flr-49	174	28	of	of	ADP
flr-49	174	29	the	the	DET
flr-49	174	30	operands	operand	NOUN
flr-49	174	31	?	?	PUNCT
flr-49	175	1	2.3	2.3	NUM
flr-49	175	2	procedure	procedure	NOUN
flr-49	175	3	for	for	ADP
flr-49	175	4	the	the	DET
flr-49	175	5	computerised	computerised	ADJ
flr-49	175	6	tasks	task	NOUN
flr-49	175	7	,	,	PUNCT
flr-49	175	8	participants	participant	NOUN
flr-49	175	9	from	from	ADP
flr-49	175	10	the	the	DET
flr-49	175	11	same	same	ADJ
flr-49	175	12	school	school	NOUN
flr-49	175	13	were	be	AUX
flr-49	175	14	tested	test	VERB
flr-49	175	15	together	together	ADV
flr-49	175	16	in	in	ADP
flr-49	175	17	a	a	DET
flr-49	175	18	single	single	ADJ
flr-49	175	19	group	group	NOUN
flr-49	175	20	session	session	NOUN
flr-49	175	21	in	in	ADP
flr-49	175	22	their	their	PRON
flr-49	175	23	school	school	NOUN
flr-49	175	24	computer	computer	NOUN
flr-49	175	25	laboratories	laboratory	NOUN
flr-49	175	26	.	.	PUNCT
flr-49	176	1	the	the	DET
flr-49	176	2	secondary	secondary	ADJ
flr-49	176	3	2	2	NUM
flr-49	176	4	students	student	NOUN
flr-49	176	5	completed	complete	VERB
flr-49	176	6	the	the	DET
flr-49	176	7	küchemann	küchemann	PROPN
flr-49	176	8	algebra	algebra	PROPN
flr-49	176	9	test	test	NOUN
flr-49	176	10	in	in	ADP
flr-49	176	11	an	an	DET
flr-49	176	12	additional	additional	ADJ
flr-49	176	13	session	session	NOUN
flr-49	176	14	in	in	ADP
flr-49	176	15	a	a	DET
flr-49	176	16	classroom	classroom	NOUN
flr-49	176	17	.	.	PUNCT
flr-49	177	1	3	3	X
flr-49	177	2	.	.	NOUN
flr-49	177	3	results	result	NOUN
flr-49	177	4	to	to	PART
flr-49	177	5	examine	examine	VERB
flr-49	177	6	whether	whether	SCONJ
flr-49	177	7	children	child	NOUN
flr-49	177	8	’s	’s	PART
flr-49	177	9	performances	performance	NOUN
flr-49	177	10	on	on	ADP
flr-49	177	11	the	the	DET
flr-49	177	12	production	production	NOUN
flr-49	177	13	task	task	NOUN
flr-49	177	14	differed	differ	VERB
flr-49	177	15	across	across	ADP
flr-49	177	16	the	the	DET
flr-49	177	17	various	various	ADJ
flr-49	177	18	experimental	experimental	ADJ
flr-49	177	19	conditions	condition	NOUN
flr-49	177	20	,	,	PUNCT
flr-49	177	21	we	we	PRON
flr-49	177	22	subjected	subject	VERB
flr-49	177	23	the	the	DET
flr-49	177	24	data	datum	NOUN
flr-49	177	25	to	to	ADP
flr-49	177	26	a	a	DET
flr-49	177	27	4	4	NUM
flr-49	177	28	(	(	PUNCT
flr-49	177	29	magnitude	magnitude	NOUN
flr-49	177	30	band	band	NOUN
flr-49	177	31	:	:	PUNCT
flr-49	177	32	ones	one	NOUN
flr-49	177	33	,	,	PUNCT
flr-49	177	34	tens	ten	NOUN
flr-49	177	35	,	,	PUNCT
flr-49	177	36	hundreds	hundred	NOUN
flr-49	177	37	,	,	PUNCT
flr-49	177	38	versus	versus	ADP
flr-49	177	39	thousands	thousand	NOUN
flr-49	177	40	)	)	PUNCT
flr-49	177	41	×	×	NOUN
flr-49	177	42	2	2	NUM
flr-49	177	43	(	(	PUNCT
flr-49	177	44	question	question	NOUN
flr-49	177	45	sequence	sequence	NOUN
flr-49	177	46	:	:	PUNCT
flr-49	177	47	increasing	increase	VERB
flr-49	177	48	value	value	NOUN
flr-49	177	49	versus	versus	ADP
flr-49	177	50	randomised	randomised	ADJ
flr-49	177	51	)	)	PUNCT
flr-49	177	52	×	×	NOUN
flr-49	177	53	2	2	NUM
flr-49	177	54	(	(	PUNCT
flr-49	177	55	grade	grade	NOUN
flr-49	177	56	:	:	PUNCT
flr-49	177	57	primary	primary	ADJ
flr-49	177	58	5	5	NUM
flr-49	177	59	versus	versus	ADP
flr-49	177	60	secondary	secondary	ADJ
flr-49	177	61	2	2	NUM
flr-49	177	62	)	)	PUNCT
flr-49	177	63	repeated	repeat	VERB
flr-49	177	64	measures	measure	NOUN
flr-49	177	65	multivariate	multivariate	VERB
flr-49	177	66	analysis	analysis	NOUN
flr-49	177	67	of	of	ADP
flr-49	177	68	variance	variance	NOUN
flr-49	177	69	.	.	PUNCT
flr-49	178	1	pixel	pixel	PROPN
flr-49	178	2	length	length	NOUN
flr-49	178	3	of	of	ADP
flr-49	178	4	the	the	DET
flr-49	178	5	difference	difference	NOUN
flr-49	178	6	unit	unit	NOUN
flr-49	178	7	drawn	draw	VERB
flr-49	178	8	for	for	ADP
flr-49	178	9	questions	question	NOUN
flr-49	178	10	with	with	ADP
flr-49	178	11	smaller	small	ADJ
flr-49	178	12	,	,	PUNCT
flr-49	178	13	medium	medium	ADJ
flr-49	178	14	,	,	PUNCT
flr-49	178	15	versus	versus	ADP
flr-49	178	16	larger	large	ADJ
flr-49	178	17	operands	operand	NOUN
flr-49	178	18	within	within	ADP
flr-49	178	19	each	each	DET
flr-49	178	20	magnitude	magnitude	NOUN
flr-49	178	21	band	band	NOUN
flr-49	178	22	served	serve	VERB
flr-49	178	23	as	as	ADP
flr-49	178	24	the	the	DET
flr-49	178	25	dependent	dependent	ADJ
flr-49	178	26	measures	measure	NOUN
flr-49	178	27	.	.	PUNCT
flr-49	179	1	in	in	ADP
flr-49	179	2	addition	addition	NOUN
flr-49	179	3	to	to	ADP
flr-49	179	4	the	the	DET
flr-49	179	5	main	main	ADJ
flr-49	179	6	independent	independent	ADJ
flr-49	179	7	variables	variable	NOUN
flr-49	179	8	,	,	PUNCT
flr-49	179	9	we	we	PRON
flr-49	179	10	entered	enter	VERB
flr-49	179	11	which	which	PRON
flr-49	179	12	of	of	ADP
flr-49	179	13	the	the	DET
flr-49	179	14	two	two	NUM
flr-49	179	15	parallel	parallel	ADJ
flr-49	179	16	forms	form	NOUN
flr-49	179	17	children	child	NOUN
flr-49	179	18	were	be	AUX
flr-49	179	19	administered	administer	VERB
flr-49	179	20	to	to	PART
flr-49	179	21	take	take	VERB
flr-49	179	22	account	account	NOUN
flr-49	179	23	of	of	ADP
flr-49	179	24	potential	potential	ADJ
flr-49	179	25	differences	difference	NOUN
flr-49	179	26	in	in	ADP
flr-49	179	27	performance	performance	NOUN
flr-49	179	28	across	across	ADP
flr-49	179	29	the	the	DET
flr-49	179	30	two	two	NUM
flr-49	179	31	forms	form	NOUN
flr-49	179	32	.	.	PUNCT
flr-49	180	1	descriptive	descriptive	ADJ
flr-49	180	2	statistics	statistic	NOUN
flr-49	180	3	can	can	AUX
flr-49	180	4	be	be	AUX
flr-49	180	5	found	find	VERB
flr-49	180	6	in	in	ADP
flr-49	180	7	table	table	NOUN
flr-49	180	8	1	1	NUM
flr-49	180	9	.	.	PUNCT
flr-49	181	1	k.	k.	PROPN
flr-49	181	2	lee	lee	PROPN
flr-49	181	3	et	et	PROPN
flr-49	181	4	al	al	PROPN
flr-49	181	5	.	.	PROPN
flr-49	181	6	88	88	NUM
flr-49	182	1	|	|	CCONJ
flr-49	182	2	f	f	NOUN
flr-49	182	3	l	l	NOUN
flr-49	182	4	r	r	NOUN
flr-49	182	5	table	table	NOUN
flr-49	182	6	1	1	NUM
flr-49	182	7	mean	mean	NOUN
flr-49	182	8	pixel	pixel	PROPN
flr-49	182	9	length	length	NOUN
flr-49	182	10	,	,	PUNCT
flr-49	182	11	standard	standard	ADJ
flr-49	182	12	deviation	deviation	NOUN
flr-49	182	13	,	,	PUNCT
flr-49	182	14	and	and	CCONJ
flr-49	182	15	confidence	confidence	NOUN
flr-49	182	16	intervals	interval	NOUN
flr-49	182	17	for	for	ADP
flr-49	182	18	the	the	DET
flr-49	182	19	production	production	NOUN
flr-49	182	20	task	task	NOUN
flr-49	182	21	size	size	NOUN
flr-49	182	22	of	of	ADP
flr-49	182	23	difference	difference	NOUN
flr-49	182	24	unit	unit	NOUN
flr-49	182	25	operand	operand	NOUN
flr-49	182	26	small	small	ADJ
flr-49	182	27	medium	medium	ADJ
flr-49	182	28	large	large	ADJ
flr-49	182	29	order	order	NOUN
flr-49	182	30	of	of	ADP
flr-49	182	31	presentation/	presentation/	NUM
flr-49	182	32	magnitude	magnitude	NOUN
flr-49	182	33	band	band	NOUN
flr-49	182	34	m	m	PROPN
flr-49	182	35	sd	sd	ADP
flr-49	182	36	95	95	NUM
flr-49	182	37	%	%	NOUN
flr-49	182	38	ci	ci	NOUN
flr-49	182	39	m	m	VERB
flr-49	182	40	sd	sd	ADP
flr-49	182	41	95	95	NUM
flr-49	182	42	%	%	NOUN
flr-49	182	43	ci	ci	NOUN
flr-49	182	44	m	m	VERB
flr-49	182	45	sd	sd	ADP
flr-49	182	46	95	95	NUM
flr-49	182	47	%	%	NOUN
flr-49	182	48	ci	ci	NOUN
flr-49	182	49	primary	primary	ADJ
flr-49	182	50	5	5	NUM
flr-49	182	51	increasing	increase	VERB
flr-49	182	52	(	(	PUNCT
flr-49	182	53	n	n	NOUN
flr-49	182	54	=	=	SYM
flr-49	182	55	55	55	NUM
flr-49	182	56	)	)	PUNCT
flr-49	182	57	ones	one	NOUN
flr-49	182	58	33	33	NUM
flr-49	182	59	(	(	PUNCT
flr-49	182	60	19	19	NUM
flr-49	182	61	)	)	PUNCT
flr-49	183	1	[	[	X
flr-49	183	2	28	28	NUM
flr-49	183	3	,	,	PUNCT
flr-49	183	4	38	38	NUM
flr-49	183	5	]	]	SYM
flr-49	183	6	51	51	NUM
flr-49	183	7	(	(	PUNCT
flr-49	183	8	29	29	NUM
flr-49	183	9	)	)	PUNCT
flr-49	184	1	[	[	X
flr-49	184	2	43	43	NUM
flr-49	184	3	,	,	PUNCT
flr-49	184	4	59	59	NUM
flr-49	184	5	]	]	SYM
flr-49	184	6	111	111	NUM
flr-49	184	7	(	(	PUNCT
flr-49	184	8	56	56	NUM
flr-49	184	9	)	)	PUNCT
flr-49	185	1	[	[	X
flr-49	185	2	95	95	NUM
flr-49	185	3	,	,	PUNCT
flr-49	185	4	127	127	NUM
flr-49	185	5	]	]	PUNCT
flr-49	185	6	tens	tens	SYM
flr-49	185	7	44	44	NUM
flr-49	185	8	(	(	PUNCT
flr-49	185	9	25	25	NUM
flr-49	185	10	)	)	PUNCT
flr-49	186	1	[	[	X
flr-49	186	2	38	38	NUM
flr-49	186	3	,	,	PUNCT
flr-49	186	4	51	51	NUM
flr-49	186	5	]	]	SYM
flr-49	186	6	57	57	NUM
flr-49	186	7	(	(	PUNCT
flr-49	186	8	29	29	NUM
flr-49	186	9	)	)	PUNCT
flr-49	187	1	[	[	X
flr-49	187	2	49	49	NUM
flr-49	187	3	,	,	PUNCT
flr-49	187	4	65	65	NUM
flr-49	187	5	]	]	SYM
flr-49	187	6	116	116	NUM
flr-49	187	7	(	(	PUNCT
flr-49	187	8	59	59	NUM
flr-49	187	9	)	)	PUNCT
flr-49	188	1	[	[	X
flr-49	188	2	100	100	NUM
flr-49	188	3	,	,	PUNCT
flr-49	188	4	132	132	NUM
flr-49	188	5	]	]	PUNCT
flr-49	188	6	hundreds	hundred	NOUN
flr-49	188	7	50	50	NUM
flr-49	188	8	(	(	PUNCT
flr-49	188	9	28	28	NUM
flr-49	188	10	)	)	PUNCT
flr-49	189	1	[	[	X
flr-49	189	2	42	42	NUM
flr-49	189	3	,	,	PUNCT
flr-49	189	4	57	57	NUM
flr-49	189	5	]	]	SYM
flr-49	189	6	60	60	NUM
flr-49	189	7	(	(	PUNCT
flr-49	189	8	28	28	NUM
flr-49	189	9	)	)	PUNCT
flr-49	190	1	[	[	X
flr-49	190	2	52	52	NUM
flr-49	190	3	,	,	PUNCT
flr-49	190	4	68	68	NUM
flr-49	190	5	]	]	SYM
flr-49	190	6	122	122	NUM
flr-49	190	7	(	(	PUNCT
flr-49	190	8	68	68	NUM
flr-49	190	9	)	)	PUNCT
flr-49	191	1	[	[	X
flr-49	191	2	103	103	NUM
flr-49	191	3	,	,	PUNCT
flr-49	191	4	140	140	NUM
flr-49	191	5	]	]	PUNCT
flr-49	191	6	thousands	thousand	NOUN
flr-49	191	7	54	54	NUM
flr-49	191	8	(	(	PUNCT
flr-49	191	9	35	35	NUM
flr-49	191	10	)	)	PUNCT
flr-49	191	11	[	[	X
flr-49	191	12	44	44	NUM
flr-49	191	13	,	,	PUNCT
flr-49	191	14	63	63	NUM
flr-49	191	15	]	]	SYM
flr-49	191	16	59	59	NUM
flr-49	191	17	(	(	PUNCT
flr-49	191	18	27	27	NUM
flr-49	191	19	)	)	PUNCT
flr-49	192	1	[	[	X
flr-49	192	2	52	52	NUM
flr-49	192	3	,	,	PUNCT
flr-49	192	4	66	66	NUM
flr-49	192	5	]	]	SYM
flr-49	192	6	106	106	NUM
flr-49	192	7	(	(	PUNCT
flr-49	192	8	62	62	NUM
flr-49	192	9	)	)	PUNCT
flr-49	193	1	[	[	X
flr-49	193	2	89	89	NUM
flr-49	193	3	,	,	PUNCT
flr-49	193	4	123	123	NUM
flr-49	193	5	]	]	PUNCT
flr-49	193	6	randomized	randomize	VERB
flr-49	193	7	(	(	PUNCT
flr-49	193	8	n	n	NOUN
flr-49	193	9	=	=	SYM
flr-49	193	10	55	55	NUM
flr-49	193	11	)	)	PUNCT
flr-49	193	12	ones	one	NOUN
flr-49	193	13	35	35	NUM
flr-49	193	14	(	(	PUNCT
flr-49	193	15	22	22	NUM
flr-49	193	16	)	)	PUNCT
flr-49	194	1	[	[	X
flr-49	194	2	29	29	NUM
flr-49	194	3	,	,	PUNCT
flr-49	194	4	41	41	NUM
flr-49	194	5	]	]	SYM
flr-49	194	6	53	53	NUM
flr-49	194	7	(	(	PUNCT
flr-49	194	8	34	34	NUM
flr-49	194	9	)	)	PUNCT
flr-49	195	1	[	[	X
flr-49	195	2	44	44	NUM
flr-49	195	3	,	,	PUNCT
flr-49	195	4	62	62	NUM
flr-49	195	5	]	]	SYM
flr-49	195	6	74	74	NUM
flr-49	195	7	(	(	PUNCT
flr-49	195	8	54	54	NUM
flr-49	195	9	)	)	PUNCT
flr-49	196	1	[	[	X
flr-49	196	2	59	59	NUM
flr-49	196	3	,	,	PUNCT
flr-49	196	4	88	88	NUM
flr-49	196	5	]	]	PUNCT
flr-49	196	6	tens	ten	NOUN
flr-49	196	7	39	39	NUM
flr-49	196	8	(	(	PUNCT
flr-49	196	9	22	22	NUM
flr-49	196	10	)	)	PUNCT
flr-49	197	1	[	[	X
flr-49	197	2	33	33	NUM
flr-49	197	3	,	,	PUNCT
flr-49	197	4	46	46	NUM
flr-49	197	5	]	]	SYM
flr-49	197	6	54	54	NUM
flr-49	197	7	(	(	PUNCT
flr-49	197	8	26	26	NUM
flr-49	197	9	)	)	PUNCT
flr-49	198	1	[	[	X
flr-49	198	2	47	47	NUM
flr-49	198	3	,	,	PUNCT
flr-49	198	4	61	61	NUM
flr-49	198	5	]	]	SYM
flr-49	198	6	104	104	NUM
flr-49	198	7	(	(	PUNCT
flr-49	198	8	53	53	NUM
flr-49	198	9	)	)	PUNCT
flr-49	199	1	[	[	X
flr-49	199	2	89	89	NUM
flr-49	199	3	,	,	PUNCT
flr-49	199	4	118	118	NUM
flr-49	199	5	]	]	PUNCT
flr-49	199	6	hundreds	hundred	NOUN
flr-49	199	7	48	48	NUM
flr-49	199	8	(	(	PUNCT
flr-49	199	9	26	26	NUM
flr-49	199	10	)	)	PUNCT
flr-49	200	1	[	[	X
flr-49	200	2	41	41	NUM
flr-49	200	3	,	,	PUNCT
flr-49	200	4	55	55	NUM
flr-49	200	5	]	]	SYM
flr-49	200	6	54	54	NUM
flr-49	200	7	(	(	PUNCT
flr-49	200	8	23	23	NUM
flr-49	200	9	)	)	PUNCT
flr-49	201	1	[	[	X
flr-49	201	2	48	48	NUM
flr-49	201	3	,	,	PUNCT
flr-49	201	4	61	61	NUM
flr-49	201	5	]	]	SYM
flr-49	201	6	101	101	NUM
flr-49	201	7	(	(	PUNCT
flr-49	201	8	77	77	NUM
flr-49	201	9	)	)	PUNCT
flr-49	202	1	[	[	X
flr-49	202	2	80	80	NUM
flr-49	202	3	,	,	PUNCT
flr-49	202	4	122	122	NUM
flr-49	202	5	]	]	SYM
flr-49	202	6	thousands	thousand	NOUN
flr-49	202	7	59	59	NUM
flr-49	202	8	(	(	PUNCT
flr-49	202	9	37	37	NUM
flr-49	202	10	)	)	PUNCT
flr-49	203	1	[	[	X
flr-49	203	2	49	49	NUM
flr-49	203	3	,	,	PUNCT
flr-49	203	4	69	69	NUM
flr-49	203	5	]	]	SYM
flr-49	203	6	65	65	NUM
flr-49	203	7	(	(	PUNCT
flr-49	203	8	35	35	NUM
flr-49	203	9	)	)	PUNCT
flr-49	204	1	[	[	X
flr-49	204	2	55	55	NUM
flr-49	204	3	,	,	PUNCT
flr-49	204	4	74	74	NUM
flr-49	204	5	]	]	SYM
flr-49	204	6	123	123	NUM
flr-49	204	7	(	(	PUNCT
flr-49	204	8	63	63	NUM
flr-49	204	9	)	)	PUNCT
flr-49	205	1	[	[	X
flr-49	205	2	106	106	NUM
flr-49	205	3	,	,	PUNCT
flr-49	205	4	140	140	NUM
flr-49	205	5	]	]	PUNCT
flr-49	205	6	secondary	secondary	ADJ
flr-49	205	7	2	2	NUM
flr-49	205	8	increasing	increase	VERB
flr-49	205	9	(	(	PUNCT
flr-49	205	10	n	n	NOUN
flr-49	205	11	=	=	SYM
flr-49	205	12	36	36	NUM
flr-49	205	13	)	)	PUNCT
flr-49	205	14	ones	one	NOUN
flr-49	205	15	36	36	NUM
flr-49	205	16	(	(	PUNCT
flr-49	205	17	16	16	NUM
flr-49	205	18	)	)	PUNCT
flr-49	206	1	[	[	X
flr-49	206	2	31	31	NUM
flr-49	206	3	,	,	PUNCT
flr-49	206	4	42	42	NUM
flr-49	206	5	]	]	SYM
flr-49	206	6	59	59	NUM
flr-49	206	7	(	(	PUNCT
flr-49	206	8	26	26	NUM
flr-49	206	9	)	)	PUNCT
flr-49	207	1	[	[	X
flr-49	207	2	50	50	NUM
flr-49	207	3	,	,	PUNCT
flr-49	207	4	67	67	NUM
flr-49	207	5	]	]	SYM
flr-49	207	6	133	133	NUM
flr-49	207	7	(	(	PUNCT
flr-49	207	8	57	57	NUM
flr-49	207	9	)	)	PUNCT
flr-49	208	1	[	[	X
flr-49	208	2	114	114	NUM
flr-49	208	3	,	,	PUNCT
flr-49	208	4	153	153	NUM
flr-49	208	5	]	]	SYM
flr-49	208	6	tens	tens	NUM
flr-49	208	7	47	47	NUM
flr-49	208	8	(	(	PUNCT
flr-49	208	9	28	28	NUM
flr-49	208	10	)	)	PUNCT
flr-49	208	11	[	[	X
flr-49	208	12	38	38	NUM
flr-49	208	13	,	,	PUNCT
flr-49	208	14	56	56	NUM
flr-49	208	15	]	]	SYM
flr-49	208	16	61	61	NUM
flr-49	208	17	(	(	PUNCT
flr-49	208	18	25	25	NUM
flr-49	208	19	)	)	PUNCT
flr-49	209	1	[	[	X
flr-49	209	2	53	53	NUM
flr-49	209	3	,	,	PUNCT
flr-49	209	4	70	70	NUM
flr-49	209	5	]	]	SYM
flr-49	209	6	124	124	NUM
flr-49	209	7	(	(	PUNCT
flr-49	209	8	51	51	NUM
flr-49	209	9	)	)	PUNCT
flr-49	210	1	[	[	X
flr-49	210	2	106	106	NUM
flr-49	210	3	,	,	PUNCT
flr-49	210	4	142	142	NUM
flr-49	210	5	]	]	PUNCT
flr-49	210	6	hundreds	hundred	NOUN
flr-49	210	7	53	53	NUM
flr-49	210	8	(	(	PUNCT
flr-49	210	9	29	29	NUM
flr-49	210	10	)	)	PUNCT
flr-49	211	1	[	[	X
flr-49	211	2	43	43	NUM
flr-49	211	3	,	,	PUNCT
flr-49	211	4	63	63	NUM
flr-49	211	5	]	]	SYM
flr-49	211	6	69	69	NUM
flr-49	211	7	(	(	PUNCT
flr-49	211	8	30	30	NUM
flr-49	211	9	)	)	PUNCT
flr-49	212	1	[	[	X
flr-49	212	2	58	58	NUM
flr-49	212	3	,	,	PUNCT
flr-49	212	4	79	79	NUM
flr-49	212	5	]	]	SYM
flr-49	212	6	121	121	NUM
flr-49	212	7	(	(	PUNCT
flr-49	212	8	53	53	NUM
flr-49	212	9	)	)	PUNCT
flr-49	213	1	[	[	X
flr-49	213	2	103	103	NUM
flr-49	213	3	,	,	PUNCT
flr-49	213	4	138	138	NUM
flr-49	213	5	]	]	PUNCT
flr-49	213	6	thousands	thousand	NOUN
flr-49	213	7	59	59	NUM
flr-49	213	8	(	(	PUNCT
flr-49	213	9	32	32	NUM
flr-49	213	10	)	)	PUNCT
flr-49	214	1	[	[	X
flr-49	214	2	48	48	NUM
flr-49	214	3	,	,	PUNCT
flr-49	214	4	70	70	NUM
flr-49	214	5	]	]	SYM
flr-49	214	6	74	74	NUM
flr-49	214	7	(	(	PUNCT
flr-49	214	8	29	29	NUM
flr-49	214	9	)	)	PUNCT
flr-49	215	1	[	[	X
flr-49	215	2	64	64	NUM
flr-49	215	3	,	,	PUNCT
flr-49	215	4	84	84	NUM
flr-49	215	5	]	]	SYM
flr-49	215	6	125	125	NUM
flr-49	215	7	(	(	PUNCT
flr-49	215	8	48	48	NUM
flr-49	215	9	)	)	PUNCT
flr-49	216	1	[	[	X
flr-49	216	2	109	109	NUM
flr-49	216	3	,	,	PUNCT
flr-49	216	4	141	141	NUM
flr-49	216	5	]	]	PUNCT
flr-49	216	6	randomized	randomize	VERB
flr-49	216	7	(	(	PUNCT
flr-49	216	8	n	n	NOUN
flr-49	216	9	=	=	SYM
flr-49	216	10	32	32	NUM
flr-49	216	11	)	)	PUNCT
flr-49	216	12	ones	one	NOUN
flr-49	216	13	36	36	NUM
flr-49	216	14	(	(	PUNCT
flr-49	216	15	18	18	NUM
flr-49	216	16	)	)	PUNCT
flr-49	217	1	[	[	X
flr-49	217	2	30	30	NUM
flr-49	217	3	,	,	PUNCT
flr-49	217	4	43	43	NUM
flr-49	217	5	]	]	SYM
flr-49	217	6	59	59	NUM
flr-49	217	7	(	(	PUNCT
flr-49	217	8	29	29	NUM
flr-49	217	9	)	)	PUNCT
flr-49	218	1	[	[	X
flr-49	218	2	49	49	NUM
flr-49	218	3	,	,	PUNCT
flr-49	218	4	70	70	NUM
flr-49	218	5	]	]	SYM
flr-49	218	6	111	111	NUM
flr-49	218	7	(	(	PUNCT
flr-49	218	8	70	70	NUM
flr-49	218	9	)	)	PUNCT
flr-49	219	1	[	[	X
flr-49	219	2	85	85	NUM
flr-49	219	3	,	,	PUNCT
flr-49	219	4	136	136	NUM
flr-49	219	5	]	]	PUNCT
flr-49	219	6	tens	ten	NOUN
flr-49	219	7	52	52	NUM
flr-49	219	8	(	(	PUNCT
flr-49	219	9	25	25	NUM
flr-49	219	10	)	)	PUNCT
flr-49	220	1	[	[	X
flr-49	220	2	43	43	NUM
flr-49	220	3	,	,	PUNCT
flr-49	220	4	61	61	NUM
flr-49	220	5	]	]	SYM
flr-49	220	6	65	65	NUM
flr-49	220	7	(	(	PUNCT
flr-49	220	8	25	25	NUM
flr-49	220	9	)	)	PUNCT
flr-49	221	1	[	[	X
flr-49	221	2	56	56	NUM
flr-49	221	3	,	,	PUNCT
flr-49	221	4	74	74	NUM
flr-49	221	5	]	]	SYM
flr-49	221	6	138	138	NUM
flr-49	221	7	(	(	PUNCT
flr-49	221	8	73	73	NUM
flr-49	221	9	)	)	PUNCT
flr-49	222	1	[	[	X
flr-49	222	2	111	111	NUM
flr-49	222	3	,	,	PUNCT
flr-49	222	4	164	164	NUM
flr-49	222	5	]	]	SYM
flr-49	222	6	hundreds	hundred	NOUN
flr-49	222	7	53	53	NUM
flr-49	222	8	(	(	PUNCT
flr-49	222	9	24	24	NUM
flr-49	222	10	)	)	PUNCT
flr-49	222	11	[	[	X
flr-49	222	12	45	45	NUM
flr-49	222	13	,	,	PUNCT
flr-49	222	14	62	62	NUM
flr-49	222	15	]	]	SYM
flr-49	222	16	72	72	NUM
flr-49	222	17	(	(	PUNCT
flr-49	222	18	27	27	NUM
flr-49	222	19	)	)	PUNCT
flr-49	223	1	[	[	X
flr-49	223	2	62	62	NUM
flr-49	223	3	,	,	PUNCT
flr-49	223	4	82	82	NUM
flr-49	223	5	]	]	SYM
flr-49	223	6	134	134	NUM
flr-49	223	7	(	(	PUNCT
flr-49	223	8	84	84	NUM
flr-49	223	9	)	)	PUNCT
flr-49	224	1	[	[	X
flr-49	224	2	103	103	NUM
flr-49	224	3	,	,	PUNCT
flr-49	224	4	164	164	NUM
flr-49	224	5	]	]	SYM
flr-49	224	6	thousands	thousand	NOUN
flr-49	224	7	70	70	NUM
flr-49	224	8	(	(	PUNCT
flr-49	224	9	38	38	NUM
flr-49	224	10	)	)	PUNCT
flr-49	224	11	[	[	X
flr-49	224	12	56	56	NUM
flr-49	224	13	,	,	PUNCT
flr-49	224	14	84	84	NUM
flr-49	224	15	]	]	SYM
flr-49	224	16	81	81	NUM
flr-49	224	17	(	(	PUNCT
flr-49	224	18	39	39	NUM
flr-49	224	19	)	)	PUNCT
flr-49	225	1	[	[	X
flr-49	225	2	67	67	NUM
flr-49	225	3	,	,	PUNCT
flr-49	225	4	95	95	NUM
flr-49	225	5	]	]	SYM
flr-49	225	6	150	150	NUM
flr-49	225	7	(	(	PUNCT
flr-49	225	8	71	71	NUM
flr-49	225	9	)	)	PUNCT
flr-49	226	1	[	[	X
flr-49	226	2	125	125	NUM
flr-49	226	3	,	,	PUNCT
flr-49	226	4	176	176	NUM
flr-49	226	5	]	]	PUNCT
flr-49	226	6	notes	note	NOUN
flr-49	226	7	.	.	PUNCT
flr-49	227	1	1	1	X
flr-49	227	2	.	.	X
flr-49	227	3	m	m	VERB
flr-49	227	4	and	and	CCONJ
flr-49	227	5	sd	sd	ADP
flr-49	227	6	refers	refer	VERB
flr-49	227	7	to	to	ADP
flr-49	227	8	the	the	DET
flr-49	227	9	means	mean	NOUN
flr-49	227	10	and	and	CCONJ
flr-49	227	11	standard	standard	ADJ
flr-49	227	12	deviations	deviation	NOUN
flr-49	227	13	of	of	ADP
flr-49	227	14	the	the	DET
flr-49	227	15	bars	bar	NOUN
flr-49	227	16	drawn	draw	VERB
flr-49	227	17	for	for	ADP
flr-49	227	18	the	the	DET
flr-49	227	19	difference	difference	NOUN
flr-49	227	20	unit	unit	NOUN
flr-49	227	21	(	(	PUNCT
flr-49	227	22	du	du	PROPN
flr-49	227	23	)	)	PUNCT
flr-49	227	24	.	.	PUNCT
flr-49	228	1	2	2	NUM
flr-49	228	2	.	.	NUM
flr-49	228	3	95	95	NUM
flr-49	228	4	%	%	NOUN
flr-49	228	5	ci	ci	NOUN
flr-49	228	6	refers	refer	VERB
flr-49	228	7	to	to	ADP
flr-49	228	8	the	the	DET
flr-49	228	9	95	95	NUM
flr-49	228	10	%	%	NOUN
flr-49	228	11	confidence	confidence	NOUN
flr-49	228	12	interval	interval	NOUN
flr-49	228	13	.	.	PUNCT
flr-49	229	1	it	it	PRON
flr-49	229	2	is	be	AUX
flr-49	229	3	calculated	calculate	VERB
flr-49	229	4	from	from	ADP
flr-49	229	5	the	the	DET
flr-49	229	6	sample	sample	NOUN
flr-49	229	7	mean	mean	VERB
flr-49	229	8	and	and	CCONJ
flr-49	229	9	is	be	AUX
flr-49	229	10	used	use	VERB
flr-49	229	11	as	as	ADP
flr-49	229	12	an	an	DET
flr-49	229	13	indication	indication	NOUN
flr-49	229	14	of	of	ADP
flr-49	229	15	the	the	DET
flr-49	229	16	precision	precision	NOUN
flr-49	229	17	of	of	ADP
flr-49	229	18	the	the	DET
flr-49	229	19	estimate	estimate	NOUN
flr-49	229	20	.	.	PUNCT
flr-49	230	1	typically	typically	ADV
flr-49	230	2	,	,	PUNCT
flr-49	230	3	the	the	DET
flr-49	230	4	narrower	narrow	ADJ
flr-49	230	5	is	be	AUX
flr-49	230	6	the	the	DET
flr-49	230	7	range	range	NOUN
flr-49	230	8	,	,	PUNCT
flr-49	230	9	the	the	PRON
flr-49	230	10	more	more	ADV
flr-49	230	11	precise	precise	ADJ
flr-49	230	12	the	the	DET
flr-49	230	13	estimate	estimate	NOUN
flr-49	230	14	.	.	PUNCT
flr-49	231	1	3	3	X
flr-49	231	2	.	.	X
flr-49	231	3	values	value	NOUN
flr-49	231	4	for	for	ADP
flr-49	231	5	the	the	DET
flr-49	231	6	m	m	NOUN
flr-49	231	7	,	,	PUNCT
flr-49	231	8	sd	sd	NOUN
flr-49	231	9	and	and	CCONJ
flr-49	231	10	the	the	DET
flr-49	231	11	95	95	NUM
flr-49	231	12	%	%	NOUN
flr-49	231	13	ci	ci	NOUN
flr-49	231	14	are	be	AUX
flr-49	231	15	rounded	rounded	ADJ
flr-49	231	16	to	to	ADP
flr-49	231	17	the	the	DET
flr-49	231	18	nearest	near	ADJ
flr-49	231	19	pixel	pixel	PROPN
flr-49	231	20	unit	unit	NOUN
flr-49	231	21	.	.	PUNCT
flr-49	232	1	4	4	X
flr-49	232	2	.	.	X
flr-49	232	3	values	value	NOUN
flr-49	232	4	for	for	ADP
flr-49	232	5	the	the	DET
flr-49	232	6	du	du	PROPN
flr-49	232	7	range	range	NOUN
flr-49	232	8	from	from	ADP
flr-49	232	9	5	5	NUM
flr-49	232	10	to	to	ADP
flr-49	232	11	356	356	NUM
flr-49	232	12	.	.	PUNCT
flr-49	233	1	length	length	NOUN
flr-49	233	2	of	of	ADP
flr-49	233	3	the	the	DET
flr-49	233	4	difference	difference	NOUN
flr-49	233	5	unit	unit	NOUN
flr-49	233	6	drawn	draw	VERB
flr-49	233	7	by	by	ADP
flr-49	233	8	the	the	DET
flr-49	233	9	students	student	NOUN
flr-49	233	10	was	be	AUX
flr-49	233	11	affected	affect	VERB
flr-49	233	12	by	by	ADP
flr-49	233	13	magnitude	magnitude	NOUN
flr-49	233	14	band	band	NOUN
flr-49	233	15	,	,	PUNCT
flr-49	233	16	f(9	f(9	PROPN
flr-49	233	17	,	,	PUNCT
flr-49	233	18	150	150	NUM
flr-49	233	19	)	)	PUNCT
flr-49	233	20	=	=	SYM
flr-49	233	21	12.85	12.85	NUM
flr-49	233	22	,	,	PUNCT
flr-49	233	23	p	p	X
flr-49	233	24	<	<	X
flr-49	233	25	.001	.001	NUM
flr-49	233	26	,	,	PUNCT
flr-49	233	27	ηp	ηp	ADV
flr-49	233	28	2	2	NUM
flr-49	233	29	=	=	SYM
flr-49	233	30	.44	.44	NUM
flr-49	233	31	.	.	PUNCT
flr-49	234	1	as	as	SCONJ
flr-49	234	2	can	can	AUX
flr-49	234	3	be	be	AUX
flr-49	234	4	noted	note	VERB
flr-49	234	5	in	in	ADP
flr-49	234	6	both	both	DET
flr-49	234	7	table	table	NOUN
flr-49	234	8	1	1	NUM
flr-49	234	9	and	and	CCONJ
flr-49	234	10	figure	figure	NOUN
flr-49	234	11	2	2	NUM
flr-49	234	12	,	,	PUNCT
flr-49	234	13	children	child	NOUN
flr-49	234	14	generally	generally	ADV
flr-49	234	15	drew	draw	VERB
flr-49	234	16	longer	long	ADJ
flr-49	234	17	bars	bar	NOUN
flr-49	234	18	for	for	ADP
flr-49	234	19	larger	large	ADJ
flr-49	234	20	operands	operand	NOUN
flr-49	234	21	.	.	PUNCT
flr-49	235	1	however	however	ADV
flr-49	235	2	,	,	PUNCT
flr-49	235	3	this	this	PRON
flr-49	235	4	was	be	AUX
flr-49	235	5	qualified	qualify	VERB
flr-49	235	6	by	by	ADP
flr-49	235	7	an	an	DET
flr-49	235	8	interaction	interaction	NOUN
flr-49	235	9	with	with	ADP
flr-49	235	10	question	question	NOUN
flr-49	235	11	sequence	sequence	NOUN
flr-49	235	12	,	,	PUNCT
flr-49	235	13	f(9	f(9	PROPN
flr-49	235	14	,	,	PUNCT
flr-49	235	15	150	150	NUM
flr-49	235	16	)	)	PUNCT
flr-49	235	17	=	=	SYM
flr-49	236	1	4.13	4.13	NUM
flr-49	236	2	,	,	PUNCT
flr-49	236	3	p	p	X
flr-49	236	4	<	<	X
flr-49	236	5	.01	.01	NUM
flr-49	236	6	,	,	PUNCT
flr-49	236	7	ηp	ηp	ADV
flr-49	236	8	2	2	NUM
flr-49	236	9	=	=	SYM
flr-49	236	10	.20	.20	NUM
flr-49	236	11	.	.	PUNCT
flr-49	237	1	univariate	univariate	ADJ
flr-49	237	2	tests	test	NOUN
flr-49	237	3	showed	show	VERB
flr-49	237	4	that	that	SCONJ
flr-49	237	5	the	the	DET
flr-49	237	6	interaction	interaction	NOUN
flr-49	237	7	effect	effect	NOUN
flr-49	237	8	was	be	AUX
flr-49	237	9	not	not	PART
flr-49	237	10	significant	significant	ADJ
flr-49	237	11	for	for	ADP
flr-49	237	12	either	either	CCONJ
flr-49	237	13	the	the	DET
flr-49	237	14	smaller	small	ADJ
flr-49	237	15	or	or	CCONJ
flr-49	237	16	medium	medium	ADJ
flr-49	237	17	sized	sized	ADJ
flr-49	237	18	operands	operand	NOUN
flr-49	237	19	.	.	PUNCT
flr-49	238	1	for	for	ADP
flr-49	238	2	these	these	DET
flr-49	238	3	operands	operand	NOUN
flr-49	238	4	,	,	PUNCT
flr-49	238	5	there	there	PRON
flr-49	238	6	were	be	VERB
flr-49	238	7	significant	significant	ADJ
flr-49	238	8	and	and	CCONJ
flr-49	238	9	strong	strong	ADJ
flr-49	238	10	linear	linear	ADJ
flr-49	238	11	trends	trend	NOUN
flr-49	238	12	across	across	ADP
flr-49	238	13	the	the	DET
flr-49	238	14	four	four	NUM
flr-49	238	15	magnitude	magnitude	NOUN
flr-49	238	16	bands	band	NOUN
flr-49	238	17	,	,	PUNCT
flr-49	238	18	.39	.39	NUM
flr-49	238	19	>	>	X
flr-49	238	20	ηp	ηp	ADP
flr-49	238	21	2	2	NUM
flr-49	238	22	>	>	SYM
flr-49	238	23	.14	.14	NUM
flr-49	238	24	,	,	PUNCT
flr-49	238	25	regardless	regardless	ADV
flr-49	238	26	of	of	ADP
flr-49	238	27	sequence	sequence	NOUN
flr-49	238	28	of	of	ADP
flr-49	238	29	presentation	presentation	NOUN
flr-49	238	30	.	.	PUNCT
flr-49	239	1	in	in	ADP
flr-49	239	2	other	other	ADJ
flr-49	239	3	words	word	NOUN
flr-49	239	4	,	,	PUNCT
flr-49	239	5	children	child	NOUN
flr-49	239	6	uniformly	uniformly	ADV
flr-49	239	7	used	use	VERB
flr-49	239	8	longer	long	ADJ
flr-49	239	9	bars	bar	NOUN
flr-49	239	10	for	for	ADP
flr-49	239	11	small	small	ADJ
flr-49	239	12	and	and	CCONJ
flr-49	239	13	medium	medium	ADJ
flr-49	239	14	sized	sized	ADJ
flr-49	239	15	operands	operand	NOUN
flr-49	239	16	,	,	PUNCT
flr-49	239	17	regardless	regardless	ADV
flr-49	239	18	of	of	ADP
flr-49	239	19	magnitude	magnitude	NOUN
flr-49	239	20	band	band	NOUN
flr-49	239	21	.	.	PUNCT
flr-49	240	1	for	for	ADP
flr-49	240	2	large	large	ADJ
flr-49	240	3	operands	operand	NOUN
flr-49	240	4	,	,	PUNCT
flr-49	240	5	a	a	DET
flr-49	240	6	strong	strong	ADJ
flr-49	240	7	linear	linear	NOUN
flr-49	240	8	and	and	CCONJ
flr-49	240	9	increasing	increase	VERB
flr-49	240	10	trend	trend	NOUN
flr-49	240	11	across	across	ADP
flr-49	240	12	the	the	DET
flr-49	240	13	four	four	NUM
flr-49	240	14	magnitude	magnitude	NOUN
flr-49	240	15	bands	band	NOUN
flr-49	240	16	was	be	AUX
flr-49	240	17	found	find	VERB
flr-49	240	18	when	when	SCONJ
flr-49	240	19	question	question	NOUN
flr-49	240	20	sequence	sequence	NOUN
flr-49	240	21	was	be	AUX
flr-49	240	22	randomised	randomise	VERB
flr-49	240	23	,	,	PUNCT
flr-49	240	24	f(1	f(1	PROPN
flr-49	240	25	,	,	PUNCT
flr-49	240	26	80	80	NUM
flr-49	240	27	)	)	PUNCT
flr-49	241	1	=	=	SYM
flr-49	241	2	61.93	61.93	NUM
flr-49	241	3	,	,	PUNCT
flr-49	241	4	p	p	X
flr-49	241	5	<	<	X
flr-49	241	6	.01	.01	NUM
flr-49	241	7	,	,	PUNCT
flr-49	241	8	ηp	ηp	ADV
flr-49	241	9	2	2	NUM
flr-49	241	10	=	=	SYM
flr-49	241	11	.44	.44	NUM
flr-49	241	12	.	.	PUNCT
flr-49	242	1	there	there	PRON
flr-49	242	2	were	be	VERB
flr-49	242	3	no	no	DET
flr-49	242	4	differences	difference	NOUN
flr-49	242	5	in	in	ADP
flr-49	242	6	the	the	DET
flr-49	242	7	length	length	NOUN
flr-49	242	8	of	of	ADP
flr-49	242	9	the	the	DET
flr-49	242	10	bars	bar	NOUN
flr-49	242	11	,	,	PUNCT
flr-49	242	12	across	across	ADP
flr-49	242	13	the	the	DET
flr-49	242	14	four	four	NUM
flr-49	242	15	magnitude	magnitude	NOUN
flr-49	242	16	bands	band	NOUN
flr-49	242	17	,	,	PUNCT
flr-49	242	18	when	when	SCONJ
flr-49	242	19	questions	question	NOUN
flr-49	242	20	with	with	ADP
flr-49	242	21	large	large	ADJ
flr-49	242	22	operand	operand	NOUN
flr-49	242	23	sizes	size	NOUN
flr-49	242	24	were	be	AUX
flr-49	242	25	presented	present	VERB
flr-49	242	26	as	as	ADP
flr-49	242	27	part	part	NOUN
flr-49	242	28	of	of	ADP
flr-49	242	29	a	a	DET
flr-49	242	30	sequence	sequence	NOUN
flr-49	242	31	in	in	ADP
flr-49	242	32	which	which	PRON
flr-49	242	33	the	the	DET
flr-49	242	34	size	size	NOUN
flr-49	242	35	of	of	ADP
flr-49	242	36	operands	operand	NOUN
flr-49	242	37	was	be	AUX
flr-49	242	38	ordered	order	VERB
flr-49	242	39	(	(	PUNCT
flr-49	242	40	see	see	VERB
flr-49	242	41	figure	figure	NOUN
flr-49	242	42	2	2	NUM
flr-49	242	43	)	)	PUNCT
flr-49	242	44	.	.	PUNCT
flr-49	243	1	k.	k.	PROPN
flr-49	243	2	lee	lee	PROPN
flr-49	243	3	et	et	PROPN
flr-49	243	4	al	al	PROPN
flr-49	243	5	.	.	PROPN
flr-49	243	6	89	89	NUM
flr-49	244	1	|	|	CCONJ
flr-49	244	2	f	f	NOUN
flr-49	244	3	l	l	NOUN
flr-49	244	4	r	r	NOUN
flr-49	244	5	figure	figure	NOUN
flr-49	244	6	2	2	NUM
flr-49	244	7	.	.	PUNCT
flr-49	244	8	mean	mean	ADJ
flr-49	244	9	performance	performance	NOUN
flr-49	244	10	on	on	ADP
flr-49	244	11	the	the	DET
flr-49	244	12	production	production	NOUN
flr-49	244	13	task	task	NOUN
flr-49	244	14	by	by	ADP
flr-49	244	15	magnitude	magnitude	NOUN
flr-49	244	16	band	band	NOUN
flr-49	244	17	and	and	CCONJ
flr-49	244	18	order	order	NOUN
flr-49	244	19	of	of	ADP
flr-49	244	20	question	question	NOUN
flr-49	244	21	presentation	presentation	NOUN
flr-49	244	22	for	for	ADP
flr-49	244	23	smaller	small	ADJ
flr-49	244	24	,	,	PUNCT
flr-49	244	25	medium	medium	ADJ
flr-49	244	26	and	and	CCONJ
flr-49	244	27	larger	large	ADJ
flr-49	244	28	numbers	number	NOUN
flr-49	244	29	within	within	ADP
flr-49	244	30	each	each	DET
flr-49	244	31	band	band	NOUN
flr-49	244	32	.	.	PUNCT
flr-49	245	1	although	although	SCONJ
flr-49	245	2	there	there	PRON
flr-49	245	3	was	be	VERB
flr-49	245	4	a	a	DET
flr-49	245	5	significant	significant	ADJ
flr-49	245	6	main	main	ADJ
flr-49	245	7	effect	effect	NOUN
flr-49	245	8	associated	associate	VERB
flr-49	245	9	with	with	ADP
flr-49	245	10	grade	grade	NOUN
flr-49	245	11	,	,	PUNCT
flr-49	245	12	f(3	f(3	PROPN
flr-49	245	13	,	,	PUNCT
flr-49	245	14	156	156	NUM
flr-49	245	15	)	)	PUNCT
flr-49	245	16	=	=	NOUN
flr-49	245	17	4.05	4.05	NUM
flr-49	245	18	,	,	PUNCT
flr-49	245	19	p	p	X
flr-49	245	20	<	<	X
flr-49	245	21	.01	.01	NUM
flr-49	245	22	,	,	PUNCT
flr-49	245	23	ηp	ηp	ADV
flr-49	245	24	2	2	NUM
flr-49	245	25	=	=	SYM
flr-49	245	26	.07	.07	NUM
flr-49	245	27	,	,	PUNCT
flr-49	245	28	with	with	ADP
flr-49	245	29	the	the	DET
flr-49	245	30	older	old	ADJ
flr-49	245	31	children	child	NOUN
flr-49	245	32	drawing	draw	VERB
flr-49	245	33	longer	long	ADJ
flr-49	245	34	bars	bar	NOUN
flr-49	245	35	,	,	PUNCT
flr-49	245	36	it	it	PRON
flr-49	245	37	did	do	AUX
flr-49	245	38	not	not	PART
flr-49	245	39	enter	enter	VERB
flr-49	245	40	into	into	ADP
flr-49	245	41	interaction	interaction	NOUN
flr-49	245	42	with	with	ADP
flr-49	245	43	other	other	ADJ
flr-49	245	44	variables	variable	NOUN
flr-49	245	45	.	.	PUNCT
flr-49	246	1	for	for	ADP
flr-49	246	2	secondary	secondary	ADJ
flr-49	246	3	2	2	NUM
flr-49	246	4	students	student	NOUN
flr-49	246	5	,	,	PUNCT
flr-49	246	6	we	we	PRON
flr-49	246	7	also	also	ADV
flr-49	246	8	tested	test	VERB
flr-49	246	9	the	the	DET
flr-49	246	10	relation	relation	NOUN
flr-49	246	11	between	between	ADP
flr-49	246	12	their	their	PRON
flr-49	246	13	performance	performance	NOUN
flr-49	246	14	on	on	ADP
flr-49	246	15	the	the	DET
flr-49	246	16	production	production	NOUN
flr-49	246	17	task	task	NOUN
flr-49	246	18	and	and	CCONJ
flr-49	246	19	the	the	DET
flr-49	246	20	küchemann	küchemann	PROPN
flr-49	246	21	algebra	algebra	PROPN
flr-49	246	22	test	test	NOUN
flr-49	246	23	.	.	PUNCT
flr-49	247	1	as	as	SCONJ
flr-49	247	2	there	there	PRON
flr-49	247	3	were	be	VERB
flr-49	247	4	only	only	ADV
flr-49	247	5	2	2	NUM
flr-49	247	6	children	child	NOUN
flr-49	247	7	in	in	ADP
flr-49	247	8	the	the	DET
flr-49	247	9	küchemann	küchemann	PROPN
flr-49	247	10	level	level	NOUN
flr-49	247	11	1	1	NUM
flr-49	247	12	category	category	NOUN
flr-49	247	13	,	,	PUNCT
flr-49	247	14	levels	level	NOUN
flr-49	247	15	1	1	NUM
flr-49	247	16	and	and	CCONJ
flr-49	247	17	2	2	NUM
flr-49	247	18	were	be	AUX
flr-49	247	19	combined	combine	VERB
flr-49	247	20	.	.	PUNCT
flr-49	248	1	approximately	approximately	ADV
flr-49	248	2	22	22	NUM
flr-49	248	3	%	%	NOUN
flr-49	248	4	of	of	ADP
flr-49	248	5	the	the	DET
flr-49	248	6	students	student	NOUN
flr-49	248	7	attained	attain	VERB
flr-49	248	8	level	level	NOUN
flr-49	248	9	1	1	NUM
flr-49	248	10	–	–	SYM
flr-49	248	11	2	2	NUM
flr-49	248	12	,	,	PUNCT
flr-49	248	13	40	40	NUM
flr-49	248	14	%	%	NOUN
flr-49	248	15	level	level	NOUN
flr-49	248	16	3	3	NUM
flr-49	248	17	,	,	PUNCT
flr-49	248	18	and	and	CCONJ
flr-49	248	19	38	38	NUM
flr-49	248	20	%	%	NOUN
flr-49	248	21	level	level	NOUN
flr-49	248	22	4	4	NUM
flr-49	248	23	.	.	PUNCT
flr-49	249	1	a	a	DET
flr-49	249	2	4	4	NUM
flr-49	249	3	(	(	PUNCT
flr-49	249	4	magnitude	magnitude	NOUN
flr-49	249	5	:	:	PUNCT
flr-49	249	6	ones	one	NOUN
flr-49	249	7	,	,	PUNCT
flr-49	249	8	tens	ten	NOUN
flr-49	249	9	,	,	PUNCT
flr-49	249	10	hundreds	hundred	NOUN
flr-49	249	11	,	,	PUNCT
flr-49	249	12	vs.	vs.	X
flr-49	249	13	thousands	thousand	NOUN
flr-49	249	14	)	)	PUNCT
flr-49	249	15	×	×	NOUN
flr-49	249	16	3	3	NUM
flr-49	249	17	(	(	PUNCT
flr-49	249	18	küchemann	küchemann	PROPN
flr-49	249	19	:	:	PUNCT
flr-49	249	20	level	level	NOUN
flr-49	249	21	1	1	NUM
flr-49	249	22	–	–	SYM
flr-49	249	23	2	2	NUM
flr-49	249	24	,	,	PUNCT
flr-49	249	25	level	level	NOUN
flr-49	249	26	3	3	NUM
flr-49	249	27	vs.	vs.	ADP
flr-49	249	28	level	level	NOUN
flr-49	249	29	4	4	NUM
flr-49	249	30	)	)	PUNCT
flr-49	249	31	repeated	repeat	VERB
flr-49	249	32	measures	measure	NOUN
flr-49	249	33	analysis	analysis	NOUN
flr-49	249	34	of	of	ADP
flr-49	249	35	variance	variance	NOUN
flr-49	249	36	showed	show	VERB
flr-49	249	37	no	no	DET
flr-49	249	38	significant	significant	ADJ
flr-49	249	39	interaction	interaction	NOUN
flr-49	249	40	between	between	ADP
flr-49	249	41	magnitude	magnitude	NOUN
flr-49	249	42	band	band	NOUN
flr-49	249	43	and	and	CCONJ
flr-49	249	44	level	level	NOUN
flr-49	249	45	of	of	ADP
flr-49	249	46	algebraic	algebraic	ADJ
flr-49	249	47	understanding	understanding	NOUN
flr-49	249	48	on	on	ADP
flr-49	249	49	the	the	DET
flr-49	249	50	length	length	NOUN
flr-49	249	51	of	of	ADP
flr-49	249	52	the	the	DET
flr-49	249	53	difference	difference	NOUN
flr-49	249	54	unit	unit	NOUN
flr-49	249	55	drawn	draw	VERB
flr-49	249	56	by	by	ADP
flr-49	249	57	the	the	DET
flr-49	249	58	children	child	NOUN
flr-49	249	59	.	.	PUNCT
flr-49	250	1	children	child	NOUN
flr-49	250	2	with	with	ADP
flr-49	250	3	more	more	ADV
flr-49	250	4	advanced	advanced	ADJ
flr-49	250	5	understanding	understanding	NOUN
flr-49	250	6	of	of	ADP
flr-49	250	7	the	the	DET
flr-49	250	8	use	use	NOUN
flr-49	250	9	of	of	ADP
flr-49	250	10	letters	letter	NOUN
flr-49	250	11	in	in	ADP
flr-49	250	12	algebra	algebra	NOUN
flr-49	250	13	adjusted	adjust	VERB
flr-49	250	14	the	the	DET
flr-49	250	15	length	length	NOUN
flr-49	250	16	of	of	ADP
flr-49	250	17	bars	bar	NOUN
flr-49	250	18	according	accord	VERB
flr-49	250	19	to	to	ADP
flr-49	250	20	magnitude	magnitude	NOUN
flr-49	250	21	in	in	ADP
flr-49	250	22	a	a	DET
flr-49	250	23	similar	similar	ADJ
flr-49	250	24	manner	manner	NOUN
flr-49	250	25	as	as	SCONJ
flr-49	250	26	did	do	VERB
flr-49	250	27	students	student	NOUN
flr-49	250	28	with	with	ADP
flr-49	250	29	a	a	DET
flr-49	250	30	more	more	ADV
flr-49	250	31	basic	basic	ADJ
flr-49	250	32	level	level	NOUN
flr-49	250	33	of	of	ADP
flr-49	250	34	algebraic	algebraic	ADJ
flr-49	250	35	understanding	understanding	NOUN
flr-49	250	36	.	.	PUNCT
flr-49	251	1	the	the	DET
flr-49	251	2	students	student	NOUN
flr-49	251	3	performed	perform	VERB
flr-49	251	4	well	well	ADV
flr-49	251	5	on	on	ADP
flr-49	251	6	the	the	DET
flr-49	251	7	validation	validation	NOUN
flr-49	251	8	task	task	NOUN
flr-49	251	9	with	with	ADP
flr-49	251	10	62	62	NUM
flr-49	251	11	%	%	NOUN
flr-49	251	12	scoring	scoring	NOUN
flr-49	251	13	the	the	DET
flr-49	251	14	maximum	maximum	ADJ
flr-49	251	15	nine	nine	NUM
flr-49	251	16	marks	mark	NOUN
flr-49	251	17	.	.	PUNCT
flr-49	252	1	oneway	oneway	ADJ
flr-49	252	2	analysis	analysis	NOUN
flr-49	252	3	of	of	ADP
flr-49	252	4	variance	variance	NOUN
flr-49	252	5	indicated	indicate	VERB
flr-49	252	6	that	that	SCONJ
flr-49	252	7	there	there	PRON
flr-49	252	8	were	be	VERB
flr-49	252	9	no	no	DET
flr-49	252	10	significant	significant	ADJ
flr-49	252	11	age	age	NOUN
flr-49	252	12	differences	difference	NOUN
flr-49	252	13	in	in	ADP
flr-49	252	14	performance	performance	NOUN
flr-49	252	15	on	on	ADP
flr-49	252	16	the	the	DET
flr-49	252	17	validation	validation	NOUN
flr-49	252	18	task	task	NOUN
flr-49	252	19	.	.	PUNCT
flr-49	253	1	amongst	amongst	ADP
flr-49	253	2	the	the	DET
flr-49	253	3	secondary	secondary	ADJ
flr-49	253	4	2	2	NUM
flr-49	253	5	students	student	NOUN
flr-49	253	6	,	,	PUNCT
flr-49	253	7	performances	performance	NOUN
flr-49	253	8	also	also	ADV
flr-49	253	9	did	do	AUX
flr-49	253	10	not	not	PART
flr-49	253	11	differ	differ	VERB
flr-49	253	12	across	across	ADP
flr-49	253	13	levels	level	NOUN
flr-49	253	14	of	of	ADP
flr-49	253	15	understanding	understanding	NOUN
flr-49	253	16	on	on	ADP
flr-49	253	17	the	the	DET
flr-49	253	18	küchemann	küchemann	PROPN
flr-49	253	19	algebra	algebra	PROPN
flr-49	253	20	test	test	NOUN
flr-49	253	21	.	.	PUNCT
flr-49	254	1	we	we	PRON
flr-49	254	2	also	also	ADV
flr-49	254	3	examined	examine	VERB
flr-49	254	4	whether	whether	SCONJ
flr-49	254	5	performance	performance	NOUN
flr-49	254	6	on	on	ADP
flr-49	254	7	the	the	DET
flr-49	254	8	production	production	NOUN
flr-49	254	9	task	task	NOUN
flr-49	254	10	was	be	AUX
flr-49	254	11	related	relate	VERB
flr-49	254	12	to	to	ADP
flr-49	254	13	performance	performance	NOUN
flr-49	254	14	on	on	ADP
flr-49	254	15	the	the	DET
flr-49	254	16	validation	validation	NOUN
flr-49	254	17	task	task	NOUN
flr-49	254	18	.	.	PUNCT
flr-49	255	1	performance	performance	NOUN
flr-49	255	2	on	on	ADP
flr-49	255	3	the	the	DET
flr-49	255	4	production	production	NOUN
flr-49	255	5	task	task	NOUN
flr-49	255	6	,	,	PUNCT
flr-49	255	7	relative	relative	ADJ
flr-49	255	8	to	to	ADP
flr-49	255	9	magnitude	magnitude	NOUN
flr-49	255	10	band	band	NOUN
flr-49	255	11	,	,	PUNCT
flr-49	255	12	was	be	AUX
flr-49	255	13	indexed	index	VERB
flr-49	255	14	by	by	ADP
flr-49	255	15	a	a	DET
flr-49	255	16	performance	performance	NOUN
flr-49	255	17	coefficient	coefficient	NOUN
flr-49	255	18	.	.	PUNCT
flr-49	256	1	this	this	PRON
flr-49	256	2	was	be	AUX
flr-49	256	3	derived	derive	VERB
flr-49	256	4	for	for	ADP
flr-49	256	5	each	each	DET
flr-49	256	6	individual	individual	NOUN
flr-49	256	7	by	by	ADP
flr-49	256	8	fitting	fit	VERB
flr-49	256	9	a	a	DET
flr-49	256	10	line	line	NOUN
flr-49	256	11	of	of	ADP
flr-49	256	12	best	good	ADJ
flr-49	256	13	fit	fit	ADJ
flr-49	256	14	using	use	VERB
flr-49	256	15	the	the	DET
flr-49	256	16	length	length	NOUN
flr-49	256	17	of	of	ADP
flr-49	256	18	their	their	PRON
flr-49	256	19	bar	bar	NOUN
flr-49	256	20	diagrams	diagram	NOUN
flr-49	256	21	and	and	CCONJ
flr-49	256	22	the	the	DET
flr-49	256	23	four	four	NUM
flr-49	256	24	magnitude	magnitude	NOUN
flr-49	256	25	conditions	condition	NOUN
flr-49	256	26	as	as	ADP
flr-49	256	27	the	the	DET
flr-49	256	28	two	two	NUM
flr-49	256	29	axes	axis	NOUN
flr-49	256	30	.	.	PUNCT
flr-49	257	1	a	a	DET
flr-49	257	2	larger	large	ADJ
flr-49	257	3	performance	performance	NOUN
flr-49	257	4	coefficient	coefficient	NOUN
flr-49	257	5	indicates	indicate	VERB
flr-49	257	6	a	a	DET
flr-49	257	7	greater	great	ADJ
flr-49	257	8	propensity	propensity	NOUN
flr-49	257	9	to	to	PART
flr-49	257	10	adjust	adjust	VERB
flr-49	257	11	the	the	DET
flr-49	257	12	length	length	NOUN
flr-49	257	13	of	of	ADP
flr-49	257	14	the	the	DET
flr-49	257	15	bars	bar	NOUN
flr-49	257	16	according	accord	VERB
flr-49	257	17	to	to	ADP
flr-49	257	18	magnitude	magnitude	NOUN
flr-49	257	19	band	band	NOUN
flr-49	257	20	.	.	PUNCT
flr-49	258	1	there	there	PRON
flr-49	258	2	was	be	VERB
flr-49	258	3	a	a	DET
flr-49	258	4	small	small	ADJ
flr-49	258	5	but	but	CCONJ
flr-49	258	6	significant	significant	ADJ
flr-49	258	7	correlation	correlation	NOUN
flr-49	258	8	between	between	ADP
flr-49	258	9	the	the	DET
flr-49	258	10	performance	performance	NOUN
flr-49	258	11	coefficient	coefficient	NOUN
flr-49	258	12	and	and	CCONJ
flr-49	258	13	the	the	DET
flr-49	258	14	validation	validation	NOUN
flr-49	258	15	task	task	NOUN
flr-49	258	16	score	score	NOUN
flr-49	258	17	but	but	CCONJ
flr-49	258	18	only	only	ADV
flr-49	258	19	for	for	ADP
flr-49	258	20	the	the	DET
flr-49	258	21	younger	young	ADJ
flr-49	258	22	age	age	NOUN
flr-49	258	23	group	group	NOUN
flr-49	258	24	(	(	PUNCT
flr-49	258	25	r	r	NOUN
flr-49	258	26	=	=	NOUN
flr-49	258	27	0.26	0.26	NUM
flr-49	258	28	,	,	PUNCT
flr-49	258	29	p	p	X
flr-49	258	30	<	<	X
flr-49	258	31	.007	.007	NUM
flr-49	258	32	)	)	PUNCT
flr-49	258	33	.	.	PUNCT
flr-49	259	1	primary	primary	ADJ
flr-49	259	2	5	5	NUM
flr-49	259	3	students	student	NOUN
flr-49	259	4	with	with	ADP
flr-49	259	5	a	a	DET
flr-49	259	6	higher	high	ADJ
flr-49	259	7	score	score	NOUN
flr-49	259	8	on	on	ADP
flr-49	259	9	the	the	DET
flr-49	259	10	validation	validation	NOUN
flr-49	259	11	task	task	NOUN
flr-49	259	12	were	be	AUX
flr-49	259	13	less	less	ADV
flr-49	259	14	likely	likely	ADJ
flr-49	259	15	to	to	PART
flr-49	259	16	adjust	adjust	VERB
flr-49	259	17	the	the	DET
flr-49	259	18	length	length	NOUN
flr-49	259	19	of	of	ADP
flr-49	259	20	the	the	DET
flr-49	259	21	bars	bar	NOUN
flr-49	259	22	according	accord	VERB
flr-49	259	23	to	to	ADP
flr-49	259	24	the	the	DET
flr-49	259	25	magnitude	magnitude	NOUN
flr-49	259	26	of	of	ADP
flr-49	259	27	the	the	DET
flr-49	259	28	operands	operand	NOUN
flr-49	259	29	.	.	PUNCT
flr-49	260	1	4	4	X
flr-49	260	2	.	.	X
flr-49	260	3	discussion	discussion	NOUN
flr-49	260	4	findings	finding	NOUN
flr-49	260	5	from	from	ADP
flr-49	260	6	the	the	DET
flr-49	260	7	production	production	NOUN
flr-49	260	8	task	task	NOUN
flr-49	260	9	showed	show	VERB
flr-49	260	10	that	that	SCONJ
flr-49	260	11	children	child	NOUN
flr-49	260	12	drew	draw	VERB
flr-49	260	13	longer	long	ADJ
flr-49	260	14	bars	bar	NOUN
flr-49	260	15	when	when	SCONJ
flr-49	260	16	the	the	DET
flr-49	260	17	magnitude	magnitude	NOUN
flr-49	260	18	of	of	ADP
flr-49	260	19	the	the	DET
flr-49	260	20	operands	operand	NOUN
flr-49	260	21	increased	increase	VERB
flr-49	260	22	.	.	PUNCT
flr-49	261	1	the	the	DET
flr-49	261	2	only	only	ADJ
flr-49	261	3	condition	condition	NOUN
flr-49	261	4	in	in	ADP
flr-49	261	5	which	which	PRON
flr-49	261	6	children	child	NOUN
flr-49	261	7	did	do	AUX
flr-49	261	8	not	not	PART
flr-49	261	9	do	do	VERB
flr-49	261	10	this	this	PRON
flr-49	261	11	was	be	AUX
flr-49	261	12	when	when	SCONJ
flr-49	261	13	they	they	PRON
flr-49	261	14	were	be	AUX
flr-49	261	15	presented	present	VERB
flr-49	261	16	with	with	ADP
flr-49	261	17	larger	large	ADJ
flr-49	261	18	numbers	number	NOUN
flr-49	261	19	,	,	PUNCT
flr-49	261	20	and	and	CCONJ
flr-49	261	21	only	only	ADV
flr-49	261	22	when	when	SCONJ
flr-49	261	23	questions	question	NOUN
flr-49	261	24	were	be	AUX
flr-49	261	25	presented	present	VERB
flr-49	261	26	in	in	ADP
flr-49	261	27	order	order	NOUN
flr-49	261	28	of	of	ADP
flr-49	261	29	operand	operand	NOUN
flr-49	261	30	magnitude	magnitude	NOUN
flr-49	261	31	.	.	PUNCT
flr-49	262	1	these	these	DET
flr-49	262	2	findings	finding	NOUN
flr-49	262	3	k.	k.	PROPN
flr-49	262	4	lee	lee	PROPN
flr-49	262	5	et	et	PROPN
flr-49	262	6	al	al	PROPN
flr-49	262	7	.	.	PROPN
flr-49	263	1	90	90	NUM
flr-49	264	1	|	|	NOUN
flr-49	264	2	f	f	NOUN
flr-49	264	3	l	l	NOUN
flr-49	264	4	r	r	NOUN
flr-49	264	5	suggest	suggest	VERB
flr-49	264	6	that	that	SCONJ
flr-49	264	7	the	the	DET
flr-49	264	8	children	child	NOUN
flr-49	264	9	used	use	VERB
flr-49	264	10	the	the	DET
flr-49	264	11	bars	bar	NOUN
flr-49	264	12	in	in	ADP
flr-49	264	13	a	a	DET
flr-49	264	14	concrete	concrete	ADJ
flr-49	264	15	fashion	fashion	NOUN
flr-49	264	16	,	,	PUNCT
flr-49	264	17	but	but	CCONJ
flr-49	264	18	their	their	PRON
flr-49	264	19	usage	usage	NOUN
flr-49	264	20	is	be	AUX
flr-49	264	21	tempered	temper	VERB
flr-49	264	22	by	by	ADP
flr-49	264	23	affordances	affordance	NOUN
flr-49	264	24	in	in	ADP
flr-49	264	25	the	the	DET
flr-49	264	26	question	question	NOUN
flr-49	264	27	set	set	NOUN
flr-49	264	28	.	.	PUNCT
flr-49	265	1	recall	recall	VERB
flr-49	265	2	that	that	SCONJ
flr-49	265	3	we	we	PRON
flr-49	265	4	defined	define	VERB
flr-49	265	5	concrete	concrete	ADJ
flr-49	265	6	usage	usage	NOUN
flr-49	265	7	as	as	ADP
flr-49	265	8	drawing	draw	VERB
flr-49	265	9	longer	long	ADJ
flr-49	265	10	bars	bar	NOUN
flr-49	265	11	to	to	PART
flr-49	265	12	denote	denote	VERB
flr-49	265	13	larger	large	ADJ
flr-49	265	14	operands	operand	NOUN
flr-49	265	15	,	,	PUNCT
flr-49	265	16	with	with	ADP
flr-49	265	17	abstract	abstract	ADJ
flr-49	265	18	usage	usage	NOUN
flr-49	265	19	being	be	AUX
flr-49	265	20	indicated	indicate	VERB
flr-49	265	21	by	by	ADP
flr-49	265	22	the	the	DET
flr-49	265	23	lack	lack	NOUN
flr-49	265	24	of	of	ADP
flr-49	265	25	a	a	DET
flr-49	265	26	consistent	consistent	ADJ
flr-49	265	27	relation	relation	NOUN
flr-49	265	28	between	between	ADP
flr-49	265	29	the	the	DET
flr-49	265	30	length	length	NOUN
flr-49	265	31	of	of	ADP
flr-49	265	32	the	the	DET
flr-49	265	33	bars	bar	NOUN
flr-49	265	34	and	and	CCONJ
flr-49	265	35	magnitude	magnitude	NOUN
flr-49	265	36	of	of	ADP
flr-49	265	37	the	the	DET
flr-49	265	38	operands	operand	NOUN
flr-49	265	39	.	.	PUNCT
flr-49	266	1	children	child	NOUN
flr-49	266	2	are	be	AUX
flr-49	266	3	less	less	ADV
flr-49	266	4	likely	likely	ADJ
flr-49	266	5	to	to	PART
flr-49	266	6	engage	engage	VERB
flr-49	266	7	in	in	ADP
flr-49	266	8	a	a	DET
flr-49	266	9	concrete	concrete	ADJ
flr-49	266	10	fashion	fashion	NOUN
flr-49	266	11	when	when	SCONJ
flr-49	266	12	changes	change	NOUN
flr-49	266	13	in	in	ADP
flr-49	266	14	the	the	DET
flr-49	266	15	magnitude	magnitude	NOUN
flr-49	266	16	of	of	ADP
flr-49	266	17	operands	operand	NOUN
flr-49	266	18	across	across	ADP
flr-49	266	19	questions	question	NOUN
flr-49	266	20	are	be	AUX
flr-49	266	21	more	more	ADJ
flr-49	266	22	salient	salient	NOUN
flr-49	266	23	.	.	PUNCT
flr-49	267	1	findings	finding	NOUN
flr-49	267	2	from	from	ADP
flr-49	267	3	the	the	DET
flr-49	267	4	validation	validation	NOUN
flr-49	267	5	task	task	NOUN
flr-49	267	6	point	point	NOUN
flr-49	267	7	to	to	ADP
flr-49	267	8	a	a	DET
flr-49	267	9	different	different	ADJ
flr-49	267	10	conclusion	conclusion	NOUN
flr-49	267	11	.	.	PUNCT
flr-49	268	1	more	more	ADJ
flr-49	268	2	than	than	ADP
flr-49	268	3	half	half	NOUN
flr-49	268	4	of	of	ADP
flr-49	268	5	the	the	DET
flr-49	268	6	children	child	NOUN
flr-49	268	7	scored	score	VERB
flr-49	268	8	full	full	ADJ
flr-49	268	9	marks	mark	NOUN
flr-49	268	10	and	and	CCONJ
flr-49	268	11	demonstrated	demonstrate	VERB
flr-49	268	12	awareness	awareness	NOUN
flr-49	268	13	that	that	SCONJ
flr-49	268	14	the	the	DET
flr-49	268	15	absolute	absolute	ADJ
flr-49	268	16	size	size	NOUN
flr-49	268	17	of	of	ADP
flr-49	268	18	the	the	DET
flr-49	268	19	bars	bar	NOUN
flr-49	268	20	were	be	AUX
flr-49	268	21	not	not	PART
flr-49	268	22	essential	essential	ADJ
flr-49	268	23	to	to	ADP
flr-49	268	24	the	the	DET
flr-49	268	25	accuracy	accuracy	NOUN
flr-49	268	26	of	of	ADP
flr-49	268	27	the	the	DET
flr-49	268	28	model	model	NOUN
flr-49	268	29	representations	representation	NOUN
flr-49	268	30	.	.	PUNCT
flr-49	269	1	in	in	ADP
flr-49	269	2	contrast	contrast	NOUN
flr-49	269	3	to	to	ADP
flr-49	269	4	findings	finding	NOUN
flr-49	269	5	from	from	ADP
flr-49	269	6	the	the	DET
flr-49	269	7	production	production	NOUN
flr-49	269	8	task	task	NOUN
flr-49	269	9	,	,	PUNCT
flr-49	269	10	this	this	DET
flr-49	269	11	finding	finding	NOUN
flr-49	269	12	shows	show	VERB
flr-49	269	13	that	that	SCONJ
flr-49	269	14	the	the	DET
flr-49	269	15	majority	majority	NOUN
flr-49	269	16	of	of	ADP
flr-49	269	17	children	child	NOUN
flr-49	269	18	have	have	VERB
flr-49	269	19	quite	quite	ADV
flr-49	269	20	sophisticated	sophisticated	ADJ
flr-49	269	21	understanding	understanding	NOUN
flr-49	269	22	of	of	ADP
flr-49	269	23	how	how	SCONJ
flr-49	269	24	the	the	DET
flr-49	269	25	graphical	graphical	ADJ
flr-49	269	26	representations	representation	NOUN
flr-49	269	27	should	should	AUX
flr-49	269	28	be	be	AUX
flr-49	269	29	interpreted	interpret	VERB
flr-49	269	30	.	.	PUNCT
flr-49	270	1	indeed	indeed	ADV
flr-49	270	2	,	,	PUNCT
flr-49	270	3	for	for	ADP
flr-49	270	4	the	the	DET
flr-49	270	5	younger	young	ADJ
flr-49	270	6	children	child	NOUN
flr-49	270	7	,	,	PUNCT
flr-49	270	8	there	there	PRON
flr-49	270	9	was	be	VERB
flr-49	270	10	a	a	DET
flr-49	270	11	significant	significant	ADJ
flr-49	270	12	correlation	correlation	NOUN
flr-49	270	13	between	between	ADP
flr-49	270	14	performances	performance	NOUN
flr-49	270	15	on	on	ADP
flr-49	270	16	the	the	DET
flr-49	270	17	production	production	NOUN
flr-49	270	18	and	and	CCONJ
flr-49	270	19	validation	validation	NOUN
flr-49	270	20	tasks	task	NOUN
flr-49	270	21	.	.	PUNCT
flr-49	271	1	those	those	PRON
flr-49	271	2	who	who	PRON
flr-49	271	3	showed	show	VERB
flr-49	271	4	better	well	ADJ
flr-49	271	5	understanding	understanding	NOUN
flr-49	271	6	on	on	ADP
flr-49	271	7	the	the	DET
flr-49	271	8	validation	validation	NOUN
flr-49	271	9	task	task	NOUN
flr-49	271	10	were	be	AUX
flr-49	271	11	more	more	ADV
flr-49	271	12	likely	likely	ADJ
flr-49	271	13	to	to	PART
flr-49	271	14	produce	produce	VERB
flr-49	271	15	models	model	NOUN
flr-49	271	16	that	that	PRON
flr-49	271	17	conformed	conform	VERB
flr-49	271	18	to	to	ADP
flr-49	271	19	our	our	PRON
flr-49	271	20	definition	definition	NOUN
flr-49	271	21	of	of	ADP
flr-49	271	22	abstract	abstract	ADJ
flr-49	271	23	depiction	depiction	NOUN
flr-49	271	24	.	.	PUNCT
flr-49	272	1	our	our	PRON
flr-49	272	2	data	datum	NOUN
flr-49	272	3	provide	provide	VERB
flr-49	272	4	no	no	DET
flr-49	272	5	definitive	definitive	ADJ
flr-49	272	6	information	information	NOUN
flr-49	272	7	on	on	ADP
flr-49	272	8	why	why	SCONJ
flr-49	272	9	the	the	DET
flr-49	272	10	children	child	NOUN
flr-49	272	11	’s	’s	PART
flr-49	272	12	performance	performance	NOUN
flr-49	272	13	on	on	ADP
flr-49	272	14	the	the	DET
flr-49	272	15	production	production	NOUN
flr-49	272	16	task	task	NOUN
flr-49	272	17	was	be	AUX
flr-49	272	18	less	less	ADV
flr-49	272	19	sophisticated	sophisticated	ADJ
flr-49	272	20	than	than	ADP
flr-49	272	21	their	their	PRON
flr-49	272	22	performance	performance	NOUN
flr-49	272	23	on	on	ADP
flr-49	272	24	the	the	DET
flr-49	272	25	validation	validation	NOUN
flr-49	272	26	task	task	NOUN
flr-49	272	27	.	.	PUNCT
flr-49	273	1	the	the	DET
flr-49	273	2	findings	finding	NOUN
flr-49	273	3	point	point	VERB
flr-49	273	4	to	to	ADP
flr-49	273	5	another	another	DET
flr-49	273	6	case	case	NOUN
flr-49	273	7	of	of	ADP
flr-49	273	8	children	child	NOUN
flr-49	273	9	knowing	know	VERB
flr-49	273	10	and	and	CCONJ
flr-49	273	11	understanding	understand	VERB
flr-49	273	12	more	more	ADJ
flr-49	273	13	than	than	ADP
flr-49	273	14	what	what	PRON
flr-49	273	15	they	they	PRON
flr-49	273	16	can	can	AUX
flr-49	273	17	do	do	AUX
flr-49	273	18	.	.	PUNCT
flr-49	274	1	this	this	PRON
flr-49	274	2	is	be	AUX
flr-49	274	3	a	a	DET
flr-49	274	4	common	common	ADJ
flr-49	274	5	phenomenon	phenomenon	NOUN
flr-49	274	6	in	in	ADP
flr-49	274	7	the	the	DET
flr-49	274	8	development	development	NOUN
flr-49	274	9	of	of	ADP
flr-49	274	10	complex	complex	ADJ
flr-49	274	11	skills	skill	NOUN
flr-49	274	12	.	.	PUNCT
flr-49	275	1	in	in	ADP
flr-49	275	2	the	the	DET
flr-49	275	3	development	development	NOUN
flr-49	275	4	of	of	ADP
flr-49	275	5	memory	memory	NOUN
flr-49	275	6	strategies	strategy	NOUN
flr-49	275	7	,	,	PUNCT
flr-49	275	8	for	for	ADP
flr-49	275	9	example	example	NOUN
flr-49	275	10	,	,	PUNCT
flr-49	275	11	children	child	NOUN
flr-49	275	12	tend	tend	VERB
flr-49	275	13	not	not	PART
flr-49	275	14	to	to	PART
flr-49	275	15	deploy	deploy	VERB
flr-49	275	16	skills	skill	NOUN
flr-49	275	17	or	or	CCONJ
flr-49	275	18	strategies	strategy	NOUN
flr-49	275	19	spontaneously	spontaneously	ADV
flr-49	275	20	,	,	PUNCT
flr-49	275	21	but	but	CCONJ
flr-49	275	22	are	be	AUX
flr-49	275	23	able	able	ADJ
flr-49	275	24	to	to	PART
flr-49	275	25	do	do	VERB
flr-49	275	26	so	so	ADV
flr-49	275	27	successfully	successfully	ADV
flr-49	275	28	when	when	SCONJ
flr-49	275	29	either	either	CCONJ
flr-49	275	30	instructed	instruct	VERB
flr-49	275	31	or	or	CCONJ
flr-49	275	32	are	be	AUX
flr-49	275	33	given	give	VERB
flr-49	275	34	explicit	explicit	ADJ
flr-49	275	35	prompts	prompt	NOUN
flr-49	275	36	(	(	PUNCT
flr-49	275	37	flavell	flavell	PROPN
flr-49	275	38	,	,	PUNCT
flr-49	275	39	1970	1970	NUM
flr-49	275	40	;	;	PUNCT
flr-49	275	41	harnishfeger	harnishfeger	NOUN
flr-49	275	42	&	&	CCONJ
flr-49	275	43	bjorklund	bjorklund	PROPN
flr-49	275	44	,	,	PUNCT
flr-49	275	45	1990	1990	NUM
flr-49	275	46	)	)	PUNCT
flr-49	275	47	.	.	PUNCT
flr-49	276	1	here	here	ADV
flr-49	276	2	,	,	PUNCT
flr-49	276	3	both	both	CCONJ
flr-49	276	4	the	the	DET
flr-49	276	5	younger	young	ADJ
flr-49	276	6	and	and	CCONJ
flr-49	276	7	older	old	ADJ
flr-49	276	8	children	child	NOUN
flr-49	276	9	seem	seem	VERB
flr-49	276	10	to	to	PART
flr-49	276	11	be	be	AUX
flr-49	276	12	producing	produce	VERB
flr-49	276	13	graphical	graphical	ADJ
flr-49	276	14	depictions	depiction	NOUN
flr-49	276	15	in	in	ADP
flr-49	276	16	a	a	DET
flr-49	276	17	concrete	concrete	ADJ
flr-49	276	18	manner	manner	NOUN
flr-49	276	19	despite	despite	SCONJ
flr-49	276	20	having	have	VERB
flr-49	276	21	fairly	fairly	ADV
flr-49	276	22	sophisticated	sophisticated	ADJ
flr-49	276	23	understanding	understanding	NOUN
flr-49	276	24	.	.	PUNCT
flr-49	277	1	however	however	ADV
flr-49	277	2	,	,	PUNCT
flr-49	277	3	once	once	SCONJ
flr-49	277	4	the	the	DET
flr-49	277	5	manipulation	manipulation	NOUN
flr-49	277	6	of	of	ADP
flr-49	277	7	problem	problem	NOUN
flr-49	277	8	size	size	NOUN
flr-49	277	9	becomes	become	VERB
flr-49	277	10	apparent	apparent	ADJ
flr-49	277	11	,	,	PUNCT
flr-49	277	12	they	they	PRON
flr-49	277	13	are	be	AUX
flr-49	277	14	able	able	ADJ
flr-49	277	15	to	to	PART
flr-49	277	16	deploy	deploy	VERB
flr-49	277	17	their	their	PRON
flr-49	277	18	knowledge	knowledge	NOUN
flr-49	277	19	accordingly	accordingly	ADV
flr-49	277	20	.	.	PUNCT
flr-49	278	1	an	an	DET
flr-49	278	2	alternative	alternative	ADJ
flr-49	278	3	version	version	NOUN
flr-49	278	4	of	of	ADP
flr-49	278	5	this	this	DET
flr-49	278	6	explanation	explanation	NOUN
flr-49	278	7	,	,	PUNCT
flr-49	278	8	which	which	PRON
flr-49	278	9	focuses	focus	VERB
flr-49	278	10	on	on	ADP
flr-49	278	11	the	the	DET
flr-49	278	12	affordances	affordance	NOUN
flr-49	278	13	of	of	ADP
flr-49	278	14	the	the	DET
flr-49	278	15	production	production	NOUN
flr-49	278	16	task	task	NOUN
flr-49	278	17	,	,	PUNCT
flr-49	278	18	is	be	AUX
flr-49	278	19	that	that	SCONJ
flr-49	278	20	the	the	DET
flr-49	278	21	students	student	NOUN
flr-49	278	22	approached	approach	VERB
flr-49	278	23	the	the	DET
flr-49	278	24	task	task	NOUN
flr-49	278	25	with	with	ADP
flr-49	278	26	what	what	PRON
flr-49	278	27	is	be	AUX
flr-49	278	28	most	most	ADV
flr-49	278	29	familiar	familiar	ADJ
flr-49	278	30	.	.	PUNCT
flr-49	279	1	in	in	ADP
flr-49	279	2	the	the	DET
flr-49	279	3	production	production	NOUN
flr-49	279	4	task	task	NOUN
flr-49	279	5	,	,	PUNCT
flr-49	279	6	the	the	DET
flr-49	279	7	children	child	NOUN
flr-49	279	8	were	be	AUX
flr-49	279	9	not	not	PART
flr-49	279	10	given	give	VERB
flr-49	279	11	specific	specific	ADJ
flr-49	279	12	instructions	instruction	NOUN
flr-49	279	13	or	or	CCONJ
flr-49	279	14	directives	directive	NOUN
flr-49	279	15	on	on	ADP
flr-49	279	16	how	how	SCONJ
flr-49	279	17	the	the	DET
flr-49	279	18	bar	bar	NOUN
flr-49	279	19	diagrams	diagram	NOUN
flr-49	279	20	should	should	AUX
flr-49	279	21	be	be	AUX
flr-49	279	22	drawn	draw	VERB
flr-49	279	23	.	.	PUNCT
flr-49	280	1	although	although	SCONJ
flr-49	280	2	all	all	DET
flr-49	280	3	the	the	DET
flr-49	280	4	children	child	NOUN
flr-49	280	5	have	have	AUX
flr-49	280	6	had	have	VERB
flr-49	280	7	extensive	extensive	ADJ
flr-49	280	8	practice	practice	NOUN
flr-49	280	9	with	with	ADP
flr-49	280	10	the	the	DET
flr-49	280	11	use	use	NOUN
flr-49	280	12	of	of	ADP
flr-49	280	13	such	such	ADJ
flr-49	280	14	graphical	graphical	ADJ
flr-49	280	15	representations	representation	NOUN
flr-49	280	16	,	,	PUNCT
flr-49	280	17	it	it	PRON
flr-49	280	18	is	be	AUX
flr-49	280	19	possible	possible	ADJ
flr-49	280	20	that	that	SCONJ
flr-49	280	21	they	they	PRON
flr-49	280	22	drew	draw	VERB
flr-49	280	23	the	the	DET
flr-49	280	24	bars	bar	NOUN
flr-49	280	25	in	in	ADP
flr-49	280	26	a	a	DET
flr-49	280	27	more	more	ADV
flr-49	280	28	concrete	concrete	ADJ
flr-49	280	29	manner	manner	NOUN
flr-49	280	30	because	because	SCONJ
flr-49	280	31	this	this	PRON
flr-49	280	32	was	be	AUX
flr-49	280	33	what	what	PRON
flr-49	280	34	they	they	PRON
flr-49	280	35	did	do	VERB
flr-49	280	36	,	,	PUNCT
flr-49	280	37	and	and	CCONJ
flr-49	280	38	had	have	VERB
flr-49	280	39	to	to	PART
flr-49	280	40	do	do	VERB
flr-49	280	41	,	,	PUNCT
flr-49	280	42	with	with	ADP
flr-49	280	43	arithmetic	arithmetic	ADJ
flr-49	280	44	problems	problem	NOUN
flr-49	280	45	.	.	PUNCT
flr-49	281	1	findings	finding	NOUN
flr-49	281	2	from	from	ADP
flr-49	281	3	the	the	DET
flr-49	281	4	validation	validation	NOUN
flr-49	281	5	task	task	NOUN
flr-49	281	6	suggest	suggest	VERB
flr-49	281	7	that	that	SCONJ
flr-49	281	8	many	many	ADJ
flr-49	281	9	children	child	NOUN
flr-49	281	10	have	have	VERB
flr-49	281	11	some	some	DET
flr-49	281	12	appreciation	appreciation	NOUN
flr-49	281	13	of	of	ADP
flr-49	281	14	the	the	DET
flr-49	281	15	fact	fact	NOUN
flr-49	281	16	that	that	SCONJ
flr-49	281	17	the	the	DET
flr-49	281	18	absolute	absolute	ADJ
flr-49	281	19	length	length	NOUN
flr-49	281	20	of	of	ADP
flr-49	281	21	the	the	DET
flr-49	281	22	bars	bar	NOUN
flr-49	281	23	across	across	ADP
flr-49	281	24	questions	question	NOUN
flr-49	281	25	is	be	AUX
flr-49	281	26	unimportant	unimportant	ADJ
flr-49	281	27	.	.	PUNCT
flr-49	282	1	although	although	SCONJ
flr-49	282	2	this	this	PRON
flr-49	282	3	is	be	AUX
flr-49	282	4	just	just	ADV
flr-49	282	5	one	one	NUM
flr-49	282	6	aspect	aspect	NOUN
flr-49	282	7	in	in	ADP
flr-49	282	8	understanding	understand	VERB
flr-49	282	9	the	the	DET
flr-49	282	10	role	role	NOUN
flr-49	282	11	of	of	ADP
flr-49	282	12	variables	variable	NOUN
flr-49	282	13	in	in	ADP
flr-49	282	14	algebraic	algebraic	ADJ
flr-49	282	15	equations	equation	NOUN
flr-49	282	16	,	,	PUNCT
flr-49	282	17	from	from	ADP
flr-49	282	18	a	a	DET
flr-49	282	19	pedagogical	pedagogical	ADJ
flr-49	282	20	viewpoint	viewpoint	NOUN
flr-49	282	21	,	,	PUNCT
flr-49	282	22	it	it	PRON
flr-49	282	23	is	be	AUX
flr-49	282	24	comforting	comforting	ADJ
flr-49	282	25	to	to	PART
flr-49	282	26	know	know	VERB
flr-49	282	27	that	that	SCONJ
flr-49	282	28	the	the	DET
flr-49	282	29	use	use	NOUN
flr-49	282	30	of	of	ADP
flr-49	282	31	the	the	DET
flr-49	282	32	model	model	NOUN
flr-49	282	33	method	method	NOUN
flr-49	282	34	is	be	AUX
flr-49	282	35	not	not	PART
flr-49	282	36	overtly	overtly	ADV
flr-49	282	37	associated	associate	VERB
flr-49	282	38	with	with	ADP
flr-49	282	39	erroneous	erroneous	ADJ
flr-49	282	40	thinking	thinking	NOUN
flr-49	282	41	regarding	regard	VERB
flr-49	282	42	the	the	DET
flr-49	282	43	nature	nature	NOUN
flr-49	282	44	of	of	ADP
flr-49	282	45	what	what	PRON
flr-49	282	46	is	be	AUX
flr-49	282	47	being	be	AUX
flr-49	282	48	represented	represent	VERB
flr-49	282	49	.	.	PUNCT
flr-49	283	1	what	what	PRON
flr-49	283	2	is	be	AUX
flr-49	283	3	somewhat	somewhat	ADV
flr-49	283	4	worrisome	worrisome	ADJ
flr-49	283	5	is	be	AUX
flr-49	283	6	that	that	SCONJ
flr-49	283	7	the	the	DET
flr-49	283	8	secondary	secondary	ADJ
flr-49	283	9	school	school	NOUN
flr-49	283	10	children	child	NOUN
flr-49	283	11	’s	’s	PART
flr-49	283	12	performance	performance	NOUN
flr-49	283	13	on	on	ADP
flr-49	283	14	the	the	DET
flr-49	283	15	production	production	NOUN
flr-49	283	16	task	task	NOUN
flr-49	283	17	was	be	AUX
flr-49	283	18	no	no	ADV
flr-49	283	19	different	different	ADJ
flr-49	283	20	from	from	ADP
flr-49	283	21	the	the	DET
flr-49	283	22	primary	primary	ADJ
flr-49	283	23	school	school	NOUN
flr-49	283	24	children	child	NOUN
flr-49	283	25	’s	’s	PART
flr-49	283	26	.	.	PUNCT
flr-49	284	1	if	if	SCONJ
flr-49	284	2	the	the	DET
flr-49	284	3	younger	young	ADJ
flr-49	284	4	children	child	NOUN
flr-49	284	5	’s	’s	PART
flr-49	284	6	performance	performance	NOUN
flr-49	284	7	resulted	result	VERB
flr-49	284	8	from	from	ADP
flr-49	284	9	a	a	DET
flr-49	284	10	production	production	NOUN
flr-49	284	11	deficiency	deficiency	NOUN
flr-49	284	12	,	,	PUNCT
flr-49	284	13	the	the	DET
flr-49	284	14	older	old	ADJ
flr-49	284	15	children	child	NOUN
flr-49	284	16	,	,	PUNCT
flr-49	284	17	with	with	ADP
flr-49	284	18	more	more	ADJ
flr-49	284	19	experience	experience	NOUN
flr-49	284	20	with	with	ADP
flr-49	284	21	such	such	ADJ
flr-49	284	22	questions	question	NOUN
flr-49	284	23	,	,	PUNCT
flr-49	284	24	should	should	AUX
flr-49	284	25	have	have	AUX
flr-49	284	26	been	be	AUX
flr-49	284	27	able	able	ADJ
flr-49	284	28	to	to	PART
flr-49	284	29	use	use	VERB
flr-49	284	30	the	the	DET
flr-49	284	31	heuristic	heuristic	NOUN
flr-49	284	32	in	in	ADP
flr-49	284	33	a	a	DET
flr-49	284	34	more	more	ADV
flr-49	284	35	abstract	abstract	ADJ
flr-49	284	36	fashion	fashion	NOUN
flr-49	284	37	.	.	PUNCT
flr-49	285	1	although	although	SCONJ
flr-49	285	2	speculative	speculative	ADJ
flr-49	285	3	,	,	PUNCT
flr-49	285	4	one	one	NUM
flr-49	285	5	explanation	explanation	NOUN
flr-49	285	6	for	for	ADP
flr-49	285	7	why	why	SCONJ
flr-49	285	8	this	this	PRON
flr-49	285	9	was	be	AUX
flr-49	285	10	not	not	PART
flr-49	285	11	observed	observe	VERB
flr-49	285	12	is	be	AUX
flr-49	285	13	related	relate	VERB
flr-49	285	14	to	to	ADP
flr-49	285	15	the	the	DET
flr-49	285	16	way	way	NOUN
flr-49	285	17	in	in	ADP
flr-49	285	18	which	which	PRON
flr-49	285	19	algebra	algebra	NOUN
flr-49	285	20	is	be	AUX
flr-49	285	21	taught	teach	VERB
flr-49	285	22	.	.	PUNCT
flr-49	286	1	in	in	ADP
flr-49	286	2	secondary	secondary	ADJ
flr-49	286	3	schools	school	NOUN
flr-49	286	4	,	,	PUNCT
flr-49	286	5	students	student	NOUN
flr-49	286	6	are	be	AUX
flr-49	286	7	taught	teach	VERB
flr-49	286	8	symbolic	symbolic	ADJ
flr-49	286	9	algebra	algebra	NOUN
flr-49	286	10	and	and	CCONJ
flr-49	286	11	use	use	NOUN
flr-49	286	12	letter	letter	NOUN
flr-49	286	13	symbols	symbol	NOUN
flr-49	286	14	to	to	PART
flr-49	286	15	represent	represent	VERB
flr-49	286	16	unknown	unknown	ADJ
flr-49	286	17	values	value	NOUN
flr-49	286	18	.	.	PUNCT
flr-49	287	1	in	in	ADP
flr-49	287	2	some	some	DET
flr-49	287	3	schools	school	NOUN
flr-49	287	4	at	at	ADP
flr-49	287	5	least	least	ADJ
flr-49	287	6	,	,	PUNCT
flr-49	287	7	there	there	PRON
flr-49	287	8	is	be	VERB
flr-49	287	9	little	little	ADJ
flr-49	287	10	discussion	discussion	NOUN
flr-49	287	11	of	of	ADP
flr-49	287	12	differences	difference	NOUN
flr-49	287	13	and	and	CCONJ
flr-49	287	14	similarities	similarity	NOUN
flr-49	287	15	in	in	ADP
flr-49	287	16	using	use	VERB
flr-49	287	17	bar	bar	NOUN
flr-49	287	18	diagrams	diagram	NOUN
flr-49	287	19	versus	versus	ADP
flr-49	287	20	letter	letter	NOUN
flr-49	287	21	symbols	symbol	NOUN
flr-49	287	22	to	to	PART
flr-49	287	23	represent	represent	VERB
flr-49	287	24	known	known	ADJ
flr-49	287	25	and	and	CCONJ
flr-49	287	26	unknown	unknown	ADJ
flr-49	287	27	quantities	quantity	NOUN
flr-49	287	28	(	(	PUNCT
flr-49	287	29	ng	ng	PROPN
flr-49	287	30	,	,	PUNCT
flr-49	287	31	lee	lee	PROPN
flr-49	287	32	,	,	PUNCT
flr-49	287	33	ang	ang	PROPN
flr-49	287	34	,	,	PUNCT
flr-49	287	35	&	&	CCONJ
flr-49	287	36	khng	khng	PROPN
flr-49	287	37	,	,	PUNCT
flr-49	287	38	2006	2006	NUM
flr-49	287	39	)	)	PUNCT
flr-49	287	40	.	.	PUNCT
flr-49	288	1	it	it	PRON
flr-49	288	2	is	be	AUX
flr-49	288	3	perhaps	perhaps	ADV
flr-49	288	4	this	this	DET
flr-49	288	5	lack	lack	NOUN
flr-49	288	6	of	of	ADP
flr-49	288	7	explicit	explicit	ADJ
flr-49	288	8	linkage	linkage	NOUN
flr-49	288	9	that	that	PRON
flr-49	288	10	resulted	result	VERB
flr-49	288	11	in	in	ADP
flr-49	288	12	some	some	DET
flr-49	288	13	lingering	linger	VERB
flr-49	288	14	confusion	confusion	NOUN
flr-49	288	15	,	,	PUNCT
flr-49	288	16	which	which	PRON
flr-49	288	17	is	be	AUX
flr-49	288	18	reflected	reflect	VERB
flr-49	288	19	in	in	ADP
flr-49	288	20	the	the	DET
flr-49	288	21	children	child	NOUN
flr-49	288	22	’s	’s	PART
flr-49	288	23	performance	performance	NOUN
flr-49	288	24	on	on	ADP
flr-49	288	25	the	the	DET
flr-49	288	26	production	production	NOUN
flr-49	288	27	task	task	NOUN
flr-49	288	28	.	.	PUNCT
flr-49	289	1	nonetheless	nonetheless	ADV
flr-49	289	2	,	,	PUNCT
flr-49	289	3	given	give	VERB
flr-49	289	4	their	their	PRON
flr-49	289	5	performance	performance	NOUN
flr-49	289	6	on	on	ADP
flr-49	289	7	both	both	CCONJ
flr-49	289	8	the	the	DET
flr-49	289	9	validation	validation	NOUN
flr-49	289	10	task	task	NOUN
flr-49	289	11	and	and	CCONJ
flr-49	289	12	the	the	DET
flr-49	289	13	küchemann	küchemann	PROPN
flr-49	289	14	test	test	NOUN
flr-49	289	15	,	,	PUNCT
flr-49	289	16	their	their	PRON
flr-49	289	17	performance	performance	NOUN
flr-49	289	18	on	on	ADP
flr-49	289	19	the	the	DET
flr-49	289	20	production	production	NOUN
flr-49	289	21	task	task	NOUN
flr-49	289	22	should	should	AUX
flr-49	289	23	not	not	PART
flr-49	289	24	be	be	AUX
flr-49	289	25	viewed	view	VERB
flr-49	289	26	as	as	ADP
flr-49	289	27	a	a	DET
flr-49	289	28	major	major	ADJ
flr-49	289	29	deficit	deficit	NOUN
flr-49	289	30	.	.	PUNCT
flr-49	290	1	one	one	NUM
flr-49	290	2	pedagogical	pedagogical	ADJ
flr-49	290	3	approach	approach	NOUN
flr-49	290	4	that	that	PRON
flr-49	290	5	may	may	AUX
flr-49	290	6	further	far	ADV
flr-49	290	7	benefit	benefit	VERB
flr-49	290	8	student	student	NOUN
flr-49	290	9	is	be	AUX
flr-49	290	10	to	to	PART
flr-49	290	11	emphasize	emphasize	VERB
flr-49	290	12	the	the	DET
flr-49	290	13	different	different	ADJ
flr-49	290	14	situations	situation	NOUN
flr-49	290	15	under	under	ADP
flr-49	290	16	which	which	PRON
flr-49	290	17	the	the	DET
flr-49	290	18	two	two	NUM
flr-49	290	19	approaches	approach	NOUN
flr-49	290	20	are	be	AUX
flr-49	290	21	best	well	ADV
flr-49	290	22	suited	suit	VERB
flr-49	290	23	.	.	PUNCT
flr-49	291	1	although	although	SCONJ
flr-49	291	2	not	not	PART
flr-49	291	3	specifically	specifically	ADV
flr-49	291	4	focused	focus	VERB
flr-49	291	5	on	on	ADP
flr-49	291	6	the	the	DET
flr-49	291	7	model	model	NOUN
flr-49	291	8	method	method	NOUN
flr-49	291	9	,	,	PUNCT
flr-49	291	10	previous	previous	ADJ
flr-49	291	11	research	research	NOUN
flr-49	291	12	have	have	AUX
flr-49	291	13	shown	show	VERB
flr-49	291	14	that	that	SCONJ
flr-49	291	15	students	student	NOUN
flr-49	291	16	are	be	AUX
flr-49	291	17	more	more	ADV
flr-49	291	18	successful	successful	ADJ
flr-49	291	19	when	when	SCONJ
flr-49	291	20	they	they	PRON
flr-49	291	21	use	use	VERB
flr-49	291	22	more	more	ADJ
flr-49	291	23	concrete	concrete	ADJ
flr-49	291	24	or	or	CCONJ
flr-49	291	25	grounded	ground	VERB
flr-49	291	26	representations	representation	NOUN
flr-49	291	27	to	to	PART
flr-49	291	28	solve	solve	VERB
flr-49	291	29	simple	simple	ADJ
flr-49	291	30	algebra	algebra	NOUN
flr-49	291	31	questions	question	NOUN
flr-49	291	32	,	,	PUNCT
flr-49	291	33	but	but	CCONJ
flr-49	291	34	are	be	AUX
flr-49	291	35	more	more	ADV
flr-49	291	36	successful	successful	ADJ
flr-49	291	37	with	with	ADP
flr-49	291	38	more	more	ADJ
flr-49	291	39	abstract	abstract	ADJ
flr-49	291	40	,	,	PUNCT
flr-49	291	41	symbolic	symbolic	ADJ
flr-49	291	42	representations	representation	NOUN
flr-49	291	43	with	with	ADP
flr-49	291	44	more	more	ADJ
flr-49	291	45	complex	complex	ADJ
flr-49	291	46	problems	problem	NOUN
flr-49	291	47	(	(	PUNCT
flr-49	291	48	koedinger	koedinger	NOUN
flr-49	291	49	,	,	PUNCT
flr-49	291	50	alibali	alibali	ADJ
flr-49	291	51	,	,	PUNCT
flr-49	291	52	&	&	CCONJ
flr-49	291	53	nathan	nathan	PROPN
flr-49	291	54	,	,	PUNCT
flr-49	291	55	2008	2008	NUM
flr-49	291	56	;	;	PUNCT
flr-49	291	57	koedinger	koedinger	PROPN
flr-49	291	58	&	&	CCONJ
flr-49	291	59	nathan	nathan	PROPN
flr-49	291	60	,	,	PUNCT
flr-49	291	61	2004	2004	NUM
flr-49	291	62	)	)	PUNCT
flr-49	291	63	.	.	PUNCT
flr-49	292	1	findings	finding	NOUN
flr-49	292	2	from	from	ADP
flr-49	292	3	the	the	DET
flr-49	292	4	küchemann	küchemann	PROPN
flr-49	292	5	algebra	algebra	PROPN
flr-49	292	6	test	test	NOUN
flr-49	292	7	showed	show	VERB
flr-49	292	8	that	that	SCONJ
flr-49	292	9	the	the	DET
flr-49	292	10	majority	majority	NOUN
flr-49	292	11	of	of	ADP
flr-49	292	12	our	our	PRON
flr-49	292	13	secondary	secondary	ADJ
flr-49	292	14	2	2	NUM
flr-49	292	15	students	student	NOUN
flr-49	292	16	demonstrated	demonstrate	VERB
flr-49	292	17	a	a	DET
flr-49	292	18	level	level	NOUN
flr-49	292	19	of	of	ADP
flr-49	292	20	understanding	understanding	NOUN
flr-49	292	21	that	that	PRON
flr-49	292	22	is	be	AUX
flr-49	292	23	deemed	deem	VERB
flr-49	292	24	sufficient	sufficient	ADJ
flr-49	292	25	to	to	PART
flr-49	292	26	enable	enable	VERB
flr-49	292	27	them	they	PRON
flr-49	292	28	to	to	PART
flr-49	292	29	engage	engage	VERB
flr-49	292	30	in	in	ADP
flr-49	292	31	further	further	ADJ
flr-49	292	32	studies	study	NOUN
flr-49	292	33	in	in	ADP
flr-49	292	34	algebra	algebra	NOUN
flr-49	292	35	.	.	PUNCT
flr-49	293	1	one	one	NUM
flr-49	293	2	challenging	challenging	ADJ
flr-49	293	3	aspect	aspect	NOUN
flr-49	293	4	of	of	ADP
flr-49	293	5	the	the	DET
flr-49	293	6	findings	finding	NOUN
flr-49	293	7	is	be	AUX
flr-49	293	8	that	that	PRON
flr-49	293	9	performance	performance	NOUN
flr-49	293	10	on	on	ADP
flr-49	293	11	the	the	DET
flr-49	293	12	küchemann	küchemann	PROPN
flr-49	293	13	test	test	NOUN
flr-49	293	14	was	be	AUX
flr-49	293	15	not	not	PART
flr-49	293	16	related	relate	VERB
flr-49	293	17	to	to	ADP
flr-49	293	18	performances	performance	NOUN
flr-49	293	19	in	in	ADP
flr-49	293	20	either	either	CCONJ
flr-49	293	21	the	the	DET
flr-49	293	22	production	production	NOUN
flr-49	293	23	or	or	CCONJ
flr-49	293	24	validation	validation	NOUN
flr-49	293	25	tasks	task	NOUN
flr-49	293	26	.	.	PUNCT
flr-49	294	1	the	the	DET
flr-49	294	2	küchemann	küchemann	PROPN
flr-49	294	3	test	test	NOUN
flr-49	294	4	focuses	focus	VERB
flr-49	294	5	on	on	ADP
flr-49	294	6	how	how	SCONJ
flr-49	294	7	children	child	NOUN
flr-49	294	8	interpret	interpret	VERB
flr-49	294	9	letter	letter	NOUN
flr-49	294	10	symbols	symbol	NOUN
flr-49	294	11	in	in	ADP
flr-49	294	12	algebra	algebra	PROPN
flr-49	294	13	.	.	PUNCT
flr-49	295	1	in	in	ADP
flr-49	295	2	contrast	contrast	NOUN
flr-49	295	3	,	,	PUNCT
flr-49	295	4	our	our	PRON
flr-49	295	5	measures	measure	NOUN
flr-49	295	6	are	be	AUX
flr-49	295	7	focused	focus	VERB
flr-49	295	8	on	on	ADP
flr-49	295	9	children	child	NOUN
flr-49	295	10	’s	’s	PART
flr-49	295	11	usage	usage	NOUN
flr-49	295	12	and	and	CCONJ
flr-49	295	13	understanding	understanding	NOUN
flr-49	295	14	of	of	ADP
flr-49	295	15	the	the	DET
flr-49	295	16	bar	bar	NOUN
flr-49	295	17	diagrams	diagram	NOUN
flr-49	295	18	used	use	VERB
flr-49	295	19	to	to	PART
flr-49	295	20	represent	represent	VERB
flr-49	295	21	algebraic	algebraic	ADJ
flr-49	295	22	questions	question	NOUN
flr-49	295	23	.	.	PUNCT
flr-49	296	1	although	although	SCONJ
flr-49	296	2	an	an	DET
flr-49	296	3	understanding	understanding	NOUN
flr-49	296	4	of	of	ADP
flr-49	296	5	the	the	DET
flr-49	296	6	k.	k.	PROPN
flr-49	296	7	lee	lee	PROPN
flr-49	296	8	et	et	PROPN
flr-49	296	9	al	al	PROPN
flr-49	296	10	.	.	PROPN
flr-49	296	11	91	91	NUM
flr-49	297	1	|	|	ADV
flr-49	297	2	f	f	NOUN
flr-49	297	3	l	l	NOUN
flr-49	297	4	r	r	NOUN
flr-49	297	5	use	use	NOUN
flr-49	297	6	of	of	ADP
flr-49	297	7	letter	letter	NOUN
flr-49	297	8	symbols	symbol	NOUN
flr-49	297	9	to	to	PART
flr-49	297	10	represent	represent	VERB
flr-49	297	11	unknowns	unknown	NOUN
flr-49	297	12	should	should	AUX
flr-49	297	13	help	help	VERB
flr-49	297	14	children	child	NOUN
flr-49	297	15	’s	’s	PART
flr-49	297	16	performances	performance	NOUN
flr-49	297	17	in	in	ADP
flr-49	297	18	our	our	PRON
flr-49	297	19	tasks	task	NOUN
flr-49	297	20	,	,	PUNCT
flr-49	297	21	one	one	NUM
flr-49	297	22	interpretation	interpretation	NOUN
flr-49	297	23	of	of	ADP
flr-49	297	24	the	the	DET
flr-49	297	25	findings	finding	NOUN
flr-49	297	26	is	be	AUX
flr-49	297	27	that	that	SCONJ
flr-49	297	28	there	there	PRON
flr-49	297	29	is	be	VERB
flr-49	297	30	a	a	DET
flr-49	297	31	lack	lack	NOUN
flr-49	297	32	of	of	ADP
flr-49	297	33	transfer	transfer	NOUN
flr-49	297	34	between	between	ADP
flr-49	297	35	understanding	understand	VERB
flr-49	297	36	the	the	DET
flr-49	297	37	notion	notion	NOUN
flr-49	297	38	of	of	ADP
flr-49	297	39	variables	variable	NOUN
flr-49	297	40	when	when	SCONJ
flr-49	297	41	represented	represent	VERB
flr-49	297	42	as	as	ADP
flr-49	297	43	letter	letter	NOUN
flr-49	297	44	symbols	symbol	NOUN
flr-49	297	45	versus	versus	ADP
flr-49	297	46	when	when	SCONJ
flr-49	297	47	represented	represent	VERB
flr-49	297	48	in	in	ADP
flr-49	297	49	the	the	DET
flr-49	297	50	form	form	NOUN
flr-49	297	51	of	of	ADP
flr-49	297	52	bars	bar	NOUN
flr-49	297	53	.	.	PUNCT
flr-49	298	1	an	an	DET
flr-49	298	2	alternative	alternative	ADJ
flr-49	298	3	interpretation	interpretation	NOUN
flr-49	298	4	is	be	AUX
flr-49	298	5	that	that	SCONJ
flr-49	298	6	the	the	DET
flr-49	298	7	two	two	NUM
flr-49	298	8	types	type	NOUN
flr-49	298	9	of	of	ADP
flr-49	298	10	tasks	task	NOUN
flr-49	298	11	map	map	VERB
flr-49	298	12	onto	onto	ADP
flr-49	298	13	aspects	aspect	NOUN
flr-49	298	14	of	of	ADP
flr-49	298	15	algebraic	algebraic	ADJ
flr-49	298	16	understanding	understanding	NOUN
flr-49	298	17	that	that	PRON
flr-49	298	18	are	be	AUX
flr-49	298	19	more	more	ADV
flr-49	298	20	disparate	disparate	ADJ
flr-49	298	21	than	than	SCONJ
flr-49	298	22	we	we	PRON
flr-49	298	23	anticipated	anticipate	VERB
flr-49	298	24	.	.	PUNCT
flr-49	299	1	further	further	ADJ
flr-49	299	2	research	research	NOUN
flr-49	299	3	on	on	ADP
flr-49	299	4	linkages	linkage	NOUN
flr-49	299	5	between	between	ADP
flr-49	299	6	these	these	DET
flr-49	299	7	aspects	aspect	NOUN
flr-49	299	8	of	of	ADP
flr-49	299	9	algebra	algebra	NOUN
flr-49	299	10	may	may	AUX
flr-49	299	11	help	help	VERB
flr-49	299	12	bridge	bridge	VERB
flr-49	299	13	the	the	DET
flr-49	299	14	gap	gap	NOUN
flr-49	299	15	between	between	ADP
flr-49	299	16	what	what	PRON
flr-49	299	17	is	be	AUX
flr-49	299	18	taught	teach	VERB
flr-49	299	19	in	in	ADP
flr-49	299	20	the	the	DET
flr-49	299	21	primary	primary	ADJ
flr-49	299	22	and	and	CCONJ
flr-49	299	23	secondary	secondary	ADJ
flr-49	299	24	curricula	curricula	NOUN
flr-49	299	25	.	.	PUNCT
flr-49	300	1	5	5	X
flr-49	300	2	.	.	X
flr-49	300	3	conclusion	conclusion	NOUN
flr-49	300	4	the	the	DET
flr-49	300	5	main	main	ADJ
flr-49	300	6	aim	aim	NOUN
flr-49	300	7	of	of	ADP
flr-49	300	8	this	this	DET
flr-49	300	9	study	study	NOUN
flr-49	300	10	was	be	AUX
flr-49	300	11	to	to	PART
flr-49	300	12	understand	understand	VERB
flr-49	300	13	how	how	SCONJ
flr-49	300	14	primary	primary	ADJ
flr-49	300	15	and	and	CCONJ
flr-49	300	16	secondary	secondary	ADJ
flr-49	300	17	school	school	NOUN
flr-49	300	18	students	student	NOUN
flr-49	300	19	use	use	VERB
flr-49	300	20	and	and	CCONJ
flr-49	300	21	understand	understand	VERB
flr-49	300	22	the	the	DET
flr-49	300	23	bar	bar	NOUN
flr-49	300	24	diagrams	diagram	NOUN
flr-49	300	25	used	use	VERB
flr-49	300	26	for	for	ADP
flr-49	300	27	solving	solve	VERB
flr-49	300	28	algebraic	algebraic	ADJ
flr-49	300	29	questions	question	NOUN
flr-49	300	30	.	.	PUNCT
flr-49	301	1	findings	finding	NOUN
flr-49	301	2	from	from	ADP
flr-49	301	3	the	the	DET
flr-49	301	4	production	production	NOUN
flr-49	301	5	task	task	NOUN
flr-49	301	6	showed	show	VERB
flr-49	301	7	that	that	SCONJ
flr-49	301	8	children	child	NOUN
flr-49	301	9	generally	generally	ADV
flr-49	301	10	drew	draw	VERB
flr-49	301	11	longer	long	ADJ
flr-49	301	12	bars	bar	NOUN
flr-49	301	13	for	for	ADP
flr-49	301	14	bigger	big	ADJ
flr-49	301	15	operands	operand	NOUN
flr-49	301	16	.	.	PUNCT
flr-49	302	1	although	although	SCONJ
flr-49	302	2	this	this	DET
flr-49	302	3	finding	finding	NOUN
flr-49	302	4	shows	show	VERB
flr-49	302	5	that	that	SCONJ
flr-49	302	6	the	the	DET
flr-49	302	7	children	child	NOUN
flr-49	302	8	are	be	AUX
flr-49	302	9	using	use	VERB
flr-49	302	10	the	the	DET
flr-49	302	11	graphical	graphical	ADJ
flr-49	302	12	representations	representation	NOUN
flr-49	302	13	in	in	ADP
flr-49	302	14	a	a	DET
flr-49	302	15	more	more	ADV
flr-49	302	16	concrete	concrete	ADJ
flr-49	302	17	fashion	fashion	NOUN
flr-49	302	18	,	,	PUNCT
flr-49	302	19	findings	finding	NOUN
flr-49	302	20	from	from	ADP
flr-49	302	21	the	the	DET
flr-49	302	22	validation	validation	NOUN
flr-49	302	23	task	task	NOUN
flr-49	302	24	suggest	suggest	VERB
flr-49	302	25	that	that	SCONJ
flr-49	302	26	their	their	PRON
flr-49	302	27	understanding	understanding	NOUN
flr-49	302	28	is	be	AUX
flr-49	302	29	more	more	ADV
flr-49	302	30	sophisticated	sophisticated	ADJ
flr-49	302	31	.	.	PUNCT
flr-49	303	1	in	in	ADP
flr-49	303	2	the	the	DET
flr-49	303	3	validation	validation	NOUN
flr-49	303	4	task	task	NOUN
flr-49	303	5	,	,	PUNCT
flr-49	303	6	both	both	CCONJ
flr-49	303	7	the	the	DET
flr-49	303	8	younger	young	ADJ
flr-49	303	9	and	and	CCONJ
flr-49	303	10	the	the	DET
flr-49	303	11	older	old	ADJ
flr-49	303	12	children	child	NOUN
flr-49	303	13	demonstrated	demonstrate	VERB
flr-49	303	14	understanding	understanding	NOUN
flr-49	303	15	that	that	SCONJ
flr-49	303	16	the	the	DET
flr-49	303	17	bars	bar	NOUN
flr-49	303	18	can	can	AUX
flr-49	303	19	be	be	AUX
flr-49	303	20	used	use	VERB
flr-49	303	21	in	in	ADP
flr-49	303	22	an	an	DET
flr-49	303	23	abstract	abstract	ADJ
flr-49	303	24	manner	manner	NOUN
flr-49	303	25	and	and	CCONJ
flr-49	303	26	the	the	DET
flr-49	303	27	length	length	NOUN
flr-49	303	28	of	of	ADP
flr-49	303	29	the	the	DET
flr-49	303	30	bars	bar	NOUN
flr-49	303	31	need	need	AUX
flr-49	303	32	not	not	PART
flr-49	303	33	be	be	AUX
flr-49	303	34	tied	tie	VERB
flr-49	303	35	to	to	ADP
flr-49	303	36	the	the	DET
flr-49	303	37	size	size	NOUN
flr-49	303	38	of	of	ADP
flr-49	303	39	the	the	DET
flr-49	303	40	operands	operand	NOUN
flr-49	303	41	.	.	PUNCT
flr-49	304	1	the	the	DET
flr-49	304	2	mismatch	mismatch	NOUN
flr-49	304	3	between	between	ADP
flr-49	304	4	findings	finding	NOUN
flr-49	304	5	from	from	ADP
flr-49	304	6	the	the	DET
flr-49	304	7	production	production	NOUN
flr-49	304	8	and	and	CCONJ
flr-49	304	9	validation	validation	NOUN
flr-49	304	10	tasks	task	NOUN
flr-49	304	11	is	be	AUX
flr-49	304	12	interpreted	interpret	VERB
flr-49	304	13	as	as	ADP
flr-49	304	14	evidence	evidence	NOUN
flr-49	304	15	of	of	ADP
flr-49	304	16	a	a	DET
flr-49	304	17	production	production	NOUN
flr-49	304	18	deficit	deficit	NOUN
flr-49	304	19	.	.	PUNCT
flr-49	305	1	although	although	SCONJ
flr-49	305	2	it	it	PRON
flr-49	305	3	was	be	AUX
flr-49	305	4	surprising	surprising	ADJ
flr-49	305	5	that	that	SCONJ
flr-49	305	6	our	our	PRON
flr-49	305	7	primary	primary	ADJ
flr-49	305	8	and	and	CCONJ
flr-49	305	9	secondary	secondary	ADJ
flr-49	305	10	school	school	NOUN
flr-49	305	11	students	student	NOUN
flr-49	305	12	performed	perform	VERB
flr-49	305	13	in	in	ADP
flr-49	305	14	a	a	DET
flr-49	305	15	similar	similar	ADJ
flr-49	305	16	fashion	fashion	NOUN
flr-49	305	17	in	in	ADP
flr-49	305	18	the	the	DET
flr-49	305	19	production	production	NOUN
flr-49	305	20	task	task	NOUN
flr-49	305	21	,	,	PUNCT
flr-49	305	22	when	when	SCONJ
flr-49	305	23	the	the	DET
flr-49	305	24	totality	totality	NOUN
flr-49	305	25	of	of	ADP
flr-49	305	26	findings	finding	NOUN
flr-49	305	27	are	be	AUX
flr-49	305	28	considered	consider	VERB
flr-49	305	29	,	,	PUNCT
flr-49	305	30	we	we	PRON
flr-49	305	31	do	do	AUX
flr-49	305	32	not	not	PART
flr-49	305	33	think	think	VERB
flr-49	305	34	the	the	DET
flr-49	305	35	evidence	evidence	NOUN
flr-49	305	36	points	point	VERB
flr-49	305	37	to	to	ADP
flr-49	305	38	a	a	DET
flr-49	305	39	major	major	ADJ
flr-49	305	40	deficit	deficit	NOUN
flr-49	305	41	.	.	PUNCT
flr-49	306	1	despite	despite	SCONJ
flr-49	306	2	the	the	DET
flr-49	306	3	production	production	NOUN
flr-49	306	4	finding	finding	NOUN
flr-49	306	5	,	,	PUNCT
flr-49	306	6	for	for	ADP
flr-49	306	7	the	the	DET
flr-49	306	8	secondary	secondary	ADJ
flr-49	306	9	students	student	NOUN
flr-49	306	10	,	,	PUNCT
flr-49	306	11	performances	performance	NOUN
flr-49	306	12	on	on	ADP
flr-49	306	13	the	the	DET
flr-49	306	14	production	production	NOUN
flr-49	306	15	and	and	CCONJ
flr-49	306	16	validation	validation	NOUN
flr-49	306	17	tasks	task	NOUN
flr-49	306	18	were	be	AUX
flr-49	306	19	not	not	PART
flr-49	306	20	correlated	correlate	VERB
flr-49	306	21	.	.	PUNCT
flr-49	307	1	furthermore	furthermore	ADV
flr-49	307	2	,	,	PUNCT
flr-49	307	3	the	the	DET
flr-49	307	4	great	great	ADJ
flr-49	307	5	majority	majority	NOUN
flr-49	307	6	of	of	ADP
flr-49	307	7	secondary	secondary	ADJ
flr-49	307	8	school	school	NOUN
flr-49	307	9	students	student	NOUN
flr-49	307	10	showed	show	VERB
flr-49	307	11	quite	quite	ADV
flr-49	307	12	sophisticated	sophisticated	ADJ
flr-49	307	13	understanding	understanding	NOUN
flr-49	307	14	on	on	ADP
flr-49	307	15	both	both	CCONJ
flr-49	307	16	the	the	DET
flr-49	307	17	validation	validation	NOUN
flr-49	307	18	task	task	NOUN
flr-49	307	19	and	and	CCONJ
flr-49	307	20	the	the	DET
flr-49	307	21	küchemann	küchemann	PROPN
flr-49	307	22	test	test	NOUN
flr-49	307	23	.	.	PUNCT
flr-49	308	1	on	on	ADP
flr-49	308	2	the	the	DET
flr-49	308	3	other	other	ADJ
flr-49	308	4	hand	hand	NOUN
flr-49	308	5	,	,	PUNCT
flr-49	308	6	for	for	ADP
flr-49	308	7	the	the	DET
flr-49	308	8	primary	primary	ADJ
flr-49	308	9	students	student	NOUN
flr-49	308	10	,	,	PUNCT
flr-49	308	11	the	the	DET
flr-49	308	12	negative	negative	ADJ
flr-49	308	13	correlation	correlation	NOUN
flr-49	308	14	between	between	ADP
flr-49	308	15	the	the	DET
flr-49	308	16	production	production	NOUN
flr-49	308	17	and	and	CCONJ
flr-49	308	18	validation	validation	NOUN
flr-49	308	19	tasks	task	NOUN
flr-49	308	20	suggests	suggest	VERB
flr-49	308	21	that	that	SCONJ
flr-49	308	22	examining	examine	VERB
flr-49	308	23	the	the	DET
flr-49	308	24	way	way	NOUN
flr-49	308	25	these	these	DET
flr-49	308	26	students	student	NOUN
flr-49	308	27	depict	depict	VERB
flr-49	308	28	problems	problem	NOUN
flr-49	308	29	with	with	ADP
flr-49	308	30	different	different	ADJ
flr-49	308	31	operands	operand	NOUN
flr-49	308	32	does	do	AUX
flr-49	308	33	provide	provide	VERB
flr-49	308	34	some	some	DET
flr-49	308	35	indication	indication	NOUN
flr-49	308	36	of	of	ADP
flr-49	308	37	their	their	PRON
flr-49	308	38	understanding	understanding	NOUN
flr-49	308	39	.	.	PUNCT
flr-49	309	1	primary	primary	ADJ
flr-49	309	2	school	school	NOUN
flr-49	309	3	teachers	teacher	NOUN
flr-49	309	4	may	may	AUX
flr-49	309	5	wish	wish	VERB
flr-49	309	6	to	to	PART
flr-49	309	7	use	use	VERB
flr-49	309	8	similar	similar	ADJ
flr-49	309	9	sets	set	NOUN
flr-49	309	10	of	of	ADP
flr-49	309	11	questions	question	NOUN
flr-49	309	12	,	,	PUNCT
flr-49	309	13	presented	present	VERB
flr-49	309	14	in	in	ADP
flr-49	309	15	a	a	DET
flr-49	309	16	randomised	randomised	ADJ
flr-49	309	17	order	order	NOUN
flr-49	309	18	,	,	PUNCT
flr-49	309	19	to	to	PART
flr-49	309	20	gain	gain	VERB
flr-49	309	21	additional	additional	ADJ
flr-49	309	22	insight	insight	NOUN
flr-49	309	23	on	on	ADP
flr-49	309	24	students	student	NOUN
flr-49	309	25	’	'	PUNCT
flr-49	309	26	facility	facility	NOUN
flr-49	309	27	with	with	ADP
flr-49	309	28	algebraic	algebraic	ADJ
flr-49	309	29	concepts	concept	NOUN
flr-49	309	30	.	.	PUNCT
flr-49	310	1	it	it	PRON
flr-49	310	2	should	should	AUX
flr-49	310	3	be	be	AUX
flr-49	310	4	noted	note	VERB
flr-49	310	5	that	that	SCONJ
flr-49	310	6	what	what	PRON
flr-49	310	7	is	be	AUX
flr-49	310	8	important	important	ADJ
flr-49	310	9	is	be	AUX
flr-49	310	10	not	not	PART
flr-49	310	11	the	the	DET
flr-49	310	12	length	length	NOUN
flr-49	310	13	of	of	ADP
flr-49	310	14	the	the	DET
flr-49	310	15	bars	bar	NOUN
flr-49	310	16	produced	produce	VERB
flr-49	310	17	for	for	ADP
flr-49	310	18	each	each	DET
flr-49	310	19	individual	individual	ADJ
flr-49	310	20	question	question	NOUN
flr-49	310	21	,	,	PUNCT
flr-49	310	22	but	but	CCONJ
flr-49	310	23	the	the	DET
flr-49	310	24	pattern	pattern	NOUN
flr-49	310	25	of	of	ADP
flr-49	310	26	responses	response	NOUN
flr-49	310	27	to	to	ADP
flr-49	310	28	changes	change	NOUN
flr-49	310	29	in	in	ADP
flr-49	310	30	the	the	DET
flr-49	310	31	magnitude	magnitude	NOUN
flr-49	310	32	of	of	ADP
flr-49	310	33	operands	operand	NOUN
flr-49	310	34	that	that	PRON
flr-49	310	35	provide	provide	VERB
flr-49	310	36	insight	insight	NOUN
flr-49	310	37	to	to	ADP
flr-49	310	38	children	child	NOUN
flr-49	310	39	’s	’s	PART
flr-49	310	40	understanding	understanding	NOUN
flr-49	310	41	.	.	PUNCT
flr-49	311	1	discussing	discuss	VERB
flr-49	311	2	how	how	SCONJ
flr-49	311	3	bars	bar	NOUN
flr-49	311	4	of	of	ADP
flr-49	311	5	the	the	DET
flr-49	311	6	same	same	ADJ
flr-49	311	7	length	length	NOUN
flr-49	311	8	can	can	AUX
flr-49	311	9	be	be	AUX
flr-49	311	10	used	use	VERB
flr-49	311	11	to	to	PART
flr-49	311	12	represent	represent	VERB
flr-49	311	13	operands	operand	NOUN
flr-49	311	14	of	of	ADP
flr-49	311	15	different	different	ADJ
flr-49	311	16	magnitudes	magnitude	NOUN
flr-49	311	17	may	may	AUX
flr-49	311	18	also	also	ADV
flr-49	311	19	help	help	VERB
flr-49	311	20	teachers	teacher	NOUN
flr-49	311	21	make	make	VERB
flr-49	311	22	explicit	explicit	ADJ
flr-49	311	23	the	the	DET
flr-49	311	24	conceptual	conceptual	ADJ
flr-49	311	25	connections	connection	NOUN
flr-49	311	26	between	between	ADP
flr-49	311	27	the	the	DET
flr-49	311	28	bars	bar	NOUN
flr-49	311	29	and	and	CCONJ
flr-49	311	30	letter	letter	NOUN
flr-49	311	31	symbols	symbol	NOUN
flr-49	311	32	used	use	VERB
flr-49	311	33	in	in	ADP
flr-49	311	34	algebra	algebra	NOUN
flr-49	311	35	.	.	PUNCT
flr-49	312	1	although	although	SCONJ
flr-49	312	2	we	we	PRON
flr-49	312	3	were	be	AUX
flr-49	312	4	motivated	motivate	VERB
flr-49	312	5	by	by	ADP
flr-49	312	6	concerns	concern	NOUN
flr-49	312	7	regarding	regard	VERB
flr-49	312	8	the	the	DET
flr-49	312	9	role	role	NOUN
flr-49	312	10	of	of	ADP
flr-49	312	11	the	the	DET
flr-49	312	12	model	model	NOUN
flr-49	312	13	method	method	NOUN
flr-49	312	14	in	in	ADP
flr-49	312	15	the	the	DET
flr-49	312	16	curriculum	curriculum	NOUN
flr-49	312	17	,	,	PUNCT
flr-49	312	18	this	this	DET
flr-49	312	19	study	study	NOUN
flr-49	312	20	is	be	AUX
flr-49	312	21	not	not	PART
flr-49	312	22	an	an	DET
flr-49	312	23	evaluation	evaluation	NOUN
flr-49	312	24	of	of	ADP
flr-49	312	25	the	the	DET
flr-49	312	26	curriculum	curriculum	NOUN
flr-49	312	27	,	,	PUNCT
flr-49	312	28	nor	nor	CCONJ
flr-49	312	29	did	do	AUX
flr-49	312	30	we	we	PRON
flr-49	312	31	evaluate	evaluate	VERB
flr-49	312	32	whether	whether	SCONJ
flr-49	312	33	learning	learn	VERB
flr-49	312	34	the	the	DET
flr-49	312	35	model	model	NOUN
flr-49	312	36	method	method	NOUN
flr-49	312	37	aids	aid	NOUN
flr-49	312	38	in	in	ADP
flr-49	312	39	the	the	DET
flr-49	312	40	acquisition	acquisition	NOUN
flr-49	312	41	of	of	ADP
flr-49	312	42	letter	letter	NOUN
flr-49	312	43	symbolic	symbolic	ADJ
flr-49	312	44	algebra	algebra	PROPN
flr-49	312	45	.	.	PUNCT
flr-49	313	1	instead	instead	ADV
flr-49	313	2	,	,	PUNCT
flr-49	313	3	the	the	DET
flr-49	313	4	findings	finding	NOUN
flr-49	313	5	provide	provide	VERB
flr-49	313	6	some	some	DET
flr-49	313	7	answers	answer	NOUN
flr-49	313	8	to	to	ADP
flr-49	313	9	how	how	SCONJ
flr-49	313	10	children	child	NOUN
flr-49	313	11	use	use	VERB
flr-49	313	12	and	and	CCONJ
flr-49	313	13	understand	understand	VERB
flr-49	313	14	the	the	DET
flr-49	313	15	model	model	NOUN
flr-49	313	16	method	method	NOUN
flr-49	313	17	,	,	PUNCT
flr-49	313	18	which	which	PRON
flr-49	313	19	may	may	AUX
flr-49	313	20	assist	assist	VERB
flr-49	313	21	policy	policy	NOUN
flr-49	313	22	makers	maker	NOUN
flr-49	313	23	and	and	CCONJ
flr-49	313	24	curriculum	curriculum	NOUN
flr-49	313	25	designers	designer	NOUN
flr-49	313	26	when	when	SCONJ
flr-49	313	27	they	they	PRON
flr-49	313	28	evaluate	evaluate	VERB
flr-49	313	29	its	its	PRON
flr-49	313	30	role	role	NOUN
flr-49	313	31	in	in	ADP
flr-49	313	32	the	the	DET
flr-49	313	33	curriculum	curriculum	NOUN
flr-49	313	34	.	.	PUNCT
flr-49	314	1	to	to	ADP
flr-49	314	2	that	that	DET
flr-49	314	3	end	end	NOUN
flr-49	314	4	,	,	PUNCT
flr-49	314	5	we	we	PRON
flr-49	314	6	were	be	AUX
flr-49	314	7	encouraged	encourage	VERB
flr-49	314	8	by	by	ADP
flr-49	314	9	the	the	DET
flr-49	314	10	sophistication	sophistication	NOUN
flr-49	314	11	of	of	ADP
flr-49	314	12	the	the	DET
flr-49	314	13	children	child	NOUN
flr-49	314	14	’s	’s	PART
flr-49	314	15	responses	response	NOUN
flr-49	314	16	in	in	ADP
flr-49	314	17	the	the	DET
flr-49	314	18	validation	validation	NOUN
flr-49	314	19	task	task	NOUN
flr-49	314	20	and	and	CCONJ
flr-49	314	21	view	view	VERB
flr-49	314	22	these	these	DET
flr-49	314	23	findings	finding	NOUN
flr-49	314	24	as	as	ADP
flr-49	314	25	being	be	AUX
flr-49	314	26	supportive	supportive	ADJ
flr-49	314	27	of	of	ADP
flr-49	314	28	the	the	DET
flr-49	314	29	way	way	NOUN
flr-49	314	30	in	in	ADP
flr-49	314	31	which	which	PRON
flr-49	314	32	algebraic	algebraic	ADJ
flr-49	314	33	problem	problem	NOUN
flr-49	314	34	solving	solving	NOUN
flr-49	314	35	is	be	AUX
flr-49	314	36	taught	teach	VERB
flr-49	314	37	.	.	PUNCT
flr-49	315	1	keypoints	keypoint	NOUN
flr-49	315	2	unlike	unlike	ADP
flr-49	315	3	many	many	ADJ
flr-49	315	4	other	other	ADJ
flr-49	315	5	countries	country	NOUN
flr-49	315	6	,	,	PUNCT
flr-49	315	7	algebraic	algebraic	ADJ
flr-49	315	8	word	word	NOUN
flr-49	315	9	problems	problem	NOUN
flr-49	315	10	are	be	AUX
flr-49	315	11	introduced	introduce	VERB
flr-49	315	12	in	in	ADP
flr-49	315	13	the	the	DET
flr-49	315	14	primary	primary	ADJ
flr-49	315	15	school	school	NOUN
flr-49	315	16	years	year	NOUN
flr-49	315	17	in	in	ADP
flr-49	315	18	the	the	DET
flr-49	315	19	singapore	singapore	PROPN
flr-49	315	20	mathematics	mathematics	PROPN
flr-49	315	21	curriculum	curriculum	PROPN
flr-49	315	22	.	.	PUNCT
flr-49	316	1	this	this	DET
flr-49	316	2	study	study	NOUN
flr-49	316	3	examined	examine	VERB
flr-49	316	4	how	how	SCONJ
flr-49	316	5	children	child	NOUN
flr-49	316	6	understand	understand	VERB
flr-49	316	7	and	and	CCONJ
flr-49	316	8	use	use	VERB
flr-49	316	9	bar	bar	NOUN
flr-49	316	10	diagrams	diagram	NOUN
flr-49	316	11	that	that	PRON
flr-49	316	12	are	be	AUX
flr-49	316	13	used	use	VERB
flr-49	316	14	to	to	PART
flr-49	316	15	give	give	VERB
flr-49	316	16	them	they	PRON
flr-49	316	17	earlier	early	ADJ
flr-49	316	18	access	access	NOUN
flr-49	316	19	to	to	ADP
flr-49	316	20	such	such	ADJ
flr-49	316	21	problems	problem	NOUN
flr-49	316	22	.	.	PUNCT
flr-49	317	1	both	both	DET
flr-49	317	2	grade	grade	NOUN
flr-49	317	3	5	5	NUM
flr-49	317	4	and	and	CCONJ
flr-49	317	5	8	8	NUM
flr-49	317	6	students	student	NOUN
flr-49	317	7	showed	show	VERB
flr-49	317	8	an	an	DET
flr-49	317	9	abstract	abstract	ADJ
flr-49	317	10	understanding	understanding	NOUN
flr-49	317	11	of	of	ADP
flr-49	317	12	the	the	DET
flr-49	317	13	bar	bar	NOUN
flr-49	317	14	diagrams	diagram	NOUN
flr-49	317	15	.	.	PUNCT
flr-49	318	1	however	however	ADV
flr-49	318	2	,	,	PUNCT
flr-49	318	3	they	they	PRON
flr-49	318	4	tended	tend	VERB
flr-49	318	5	to	to	PART
flr-49	318	6	use	use	VERB
flr-49	318	7	the	the	DET
flr-49	318	8	diagrams	diagram	NOUN
flr-49	318	9	in	in	ADP
flr-49	318	10	a	a	DET
flr-49	318	11	more	more	ADV
flr-49	318	12	concrete	concrete	ADJ
flr-49	318	13	fashion	fashion	NOUN
flr-49	318	14	.	.	PUNCT
flr-49	319	1	discrepancy	discrepancy	NOUN
flr-49	319	2	between	between	ADP
flr-49	319	3	what	what	PRON
flr-49	319	4	the	the	DET
flr-49	319	5	students	student	NOUN
flr-49	319	6	produced	produce	VERB
flr-49	319	7	versus	versus	ADP
flr-49	319	8	what	what	PRON
flr-49	319	9	they	they	PRON
flr-49	319	10	understood	understand	VERB
flr-49	319	11	is	be	AUX
flr-49	319	12	indicative	indicative	ADJ
flr-49	319	13	of	of	ADP
flr-49	319	14	a	a	DET
flr-49	319	15	production	production	NOUN
flr-49	319	16	deficit	deficit	NOUN
flr-49	319	17	.	.	PUNCT
flr-49	320	1	k.	k.	PROPN
flr-49	320	2	lee	lee	PROPN
flr-49	320	3	et	et	PROPN
flr-49	320	4	al	al	PROPN
flr-49	320	5	.	.	PROPN
flr-49	321	1	92	92	NUM
flr-49	322	1	|	|	NOUN
flr-49	322	2	f	f	NOUN
flr-49	322	3	l	l	NOUN
flr-49	322	4	r	r	NOUN
flr-49	322	5	discussing	discuss	VERB
flr-49	322	6	how	how	SCONJ
flr-49	322	7	bars	bar	NOUN
flr-49	322	8	of	of	ADP
flr-49	322	9	the	the	DET
flr-49	322	10	same	same	ADJ
flr-49	322	11	length	length	NOUN
flr-49	322	12	can	can	AUX
flr-49	322	13	be	be	AUX
flr-49	322	14	used	use	VERB
flr-49	322	15	to	to	PART
flr-49	322	16	represent	represent	VERB
flr-49	322	17	operands	operand	NOUN
flr-49	322	18	of	of	ADP
flr-49	322	19	different	different	ADJ
flr-49	322	20	magnitudes	magnitude	NOUN
flr-49	322	21	in	in	ADP
flr-49	322	22	algebraic	algebraic	ADJ
flr-49	322	23	questions	question	NOUN
flr-49	322	24	may	may	AUX
flr-49	322	25	help	help	VERB
flr-49	322	26	teachers	teacher	NOUN
flr-49	322	27	make	make	VERB
flr-49	322	28	explicit	explicit	ADJ
flr-49	322	29	the	the	DET
flr-49	322	30	conceptual	conceptual	ADJ
flr-49	322	31	connections	connection	NOUN
flr-49	322	32	between	between	ADP
flr-49	322	33	the	the	DET
flr-49	322	34	bar	bar	NOUN
flr-49	322	35	diagrams	diagram	NOUN
flr-49	322	36	and	and	CCONJ
flr-49	322	37	letter	letter	NOUN
flr-49	322	38	symbols	symbol	NOUN
flr-49	322	39	.	.	PUNCT
flr-49	323	1	acknowledgements	acknowledgement	NOUN
flr-49	323	2	the	the	DET
flr-49	323	3	work	work	NOUN
flr-49	323	4	was	be	AUX
flr-49	323	5	supported	support	VERB
flr-49	323	6	by	by	ADP
flr-49	323	7	grants	grant	NOUN
flr-49	323	8	from	from	ADP
flr-49	323	9	the	the	DET
flr-49	323	10	centre	centre	NOUN
flr-49	323	11	for	for	ADP
flr-49	323	12	research	research	NOUN
flr-49	323	13	in	in	ADP
flr-49	323	14	pedagogy	pedagogy	NOUN
flr-49	323	15	and	and	CCONJ
flr-49	323	16	practice	practice	NOUN
flr-49	323	17	(	(	PUNCT
flr-49	323	18	#	#	SYM
flr-49	323	19	crp	crp	PROPN
flr-49	323	20	9/05	9/05	NUM
flr-49	323	21	kl	kl	PROPN
flr-49	323	22	)	)	PUNCT
flr-49	323	23	.	.	PUNCT
flr-49	324	1	views	view	NOUN
flr-49	324	2	expressed	express	VERB
flr-49	324	3	in	in	ADP
flr-49	324	4	this	this	DET
flr-49	324	5	article	article	NOUN
flr-49	324	6	do	do	AUX
flr-49	324	7	not	not	PART
flr-49	324	8	necessarily	necessarily	ADV
flr-49	324	9	reflect	reflect	VERB
flr-49	324	10	those	those	PRON
flr-49	324	11	of	of	ADP
flr-49	324	12	the	the	DET
flr-49	324	13	national	national	PROPN
flr-49	324	14	institute	institute	PROPN
flr-49	324	15	of	of	ADP
flr-49	324	16	education	education	PROPN
flr-49	324	17	,	,	PUNCT
flr-49	324	18	singapore	singapore	PROPN
flr-49	324	19	.	.	PUNCT
flr-49	325	1	we	we	PRON
flr-49	325	2	thank	thank	VERB
flr-49	325	3	the	the	DET
flr-49	325	4	students	student	NOUN
flr-49	325	5	who	who	PRON
flr-49	325	6	participated	participate	VERB
flr-49	325	7	in	in	ADP
flr-49	325	8	this	this	DET
flr-49	325	9	study	study	NOUN
flr-49	325	10	and	and	CCONJ
flr-49	325	11	the	the	DET
flr-49	325	12	school	school	NOUN
flr-49	325	13	administrators	administrator	NOUN
flr-49	325	14	who	who	PRON
flr-49	325	15	provided	provide	VERB
flr-49	325	16	access	access	NOUN
flr-49	325	17	and	and	CCONJ
flr-49	325	18	assistance	assistance	NOUN
flr-49	325	19	.	.	PUNCT
flr-49	326	1	appendix	appendix	VERB
flr-49	326	2	a	a	PRON
flr-49	326	3	here	here	ADV
flr-49	326	4	are	be	AUX
flr-49	326	5	some	some	DET
flr-49	326	6	word	word	NOUN
flr-49	326	7	problems	problem	NOUN
flr-49	326	8	.	.	PUNCT
flr-49	327	1	student	student	NOUN
flr-49	327	2	a	a	PRON
flr-49	327	3	and	and	CCONJ
flr-49	327	4	student	student	NOUN
flr-49	327	5	b	b	PROPN
flr-49	327	6	drew	draw	VERB
flr-49	327	7	the	the	DET
flr-49	327	8	models	model	NOUN
flr-49	327	9	for	for	ADP
flr-49	327	10	these	these	DET
flr-49	327	11	problems	problem	NOUN
flr-49	327	12	.	.	PUNCT
flr-49	328	1	you	you	PRON
flr-49	328	2	have	have	VERB
flr-49	328	3	to	to	PART
flr-49	328	4	pick	pick	VERB
flr-49	328	5	if	if	SCONJ
flr-49	328	6	student	student	NOUN
flr-49	328	7	a	a	PRON
flr-49	328	8	is	be	AUX
flr-49	328	9	correct	correct	ADJ
flr-49	328	10	,	,	PUNCT
flr-49	328	11	or	or	CCONJ
flr-49	328	12	student	student	NOUN
flr-49	328	13	b	b	PROPN
flr-49	328	14	is	be	AUX
flr-49	328	15	correct	correct	ADJ
flr-49	328	16	,	,	PUNCT
flr-49	328	17	or	or	CCONJ
flr-49	328	18	if	if	SCONJ
flr-49	328	19	both	both	PRON
flr-49	328	20	are	be	AUX
flr-49	328	21	correct	correct	ADJ
flr-49	328	22	.	.	PUNCT
flr-49	329	1	you	you	PRON
flr-49	329	2	can	can	AUX
flr-49	329	3	do	do	VERB
flr-49	329	4	this	this	PRON
flr-49	329	5	by	by	ADP
flr-49	329	6	checking	check	VERB
flr-49	329	7	the	the	DET
flr-49	329	8	box	box	NOUN
flr-49	329	9	next	next	ADV
flr-49	329	10	to	to	ADP
flr-49	329	11	the	the	DET
flr-49	329	12	options	option	NOUN
flr-49	329	13	.	.	PUNCT
flr-49	330	1	mary	mary	PROPN
flr-49	330	2	has	have	VERB
flr-49	330	3	some	some	DET
flr-49	330	4	marbles	marble	NOUN
flr-49	330	5	.	.	PUNCT
flr-49	331	1	john	john	PROPN
flr-49	331	2	has	have	VERB
flr-49	331	3	30	30	NUM
flr-49	331	4	marbles	marble	NOUN
flr-49	331	5	more	more	ADJ
flr-49	331	6	than	than	ADP
flr-49	331	7	mary	mary	PROPN
flr-49	331	8	.	.	PUNCT
flr-49	332	1	they	they	PRON
flr-49	332	2	have	have	VERB
flr-49	332	3	150	150	NUM
flr-49	332	4	marbles	marble	NOUN
flr-49	332	5	altogether	altogether	ADV
flr-49	332	6	.	.	PUNCT
flr-49	333	1	how	how	SCONJ
flr-49	333	2	many	many	ADJ
flr-49	333	3	marbles	marble	NOUN
flr-49	333	4	has	have	AUX
flr-49	333	5	mary	mary	PROPN
flr-49	333	6	?	?	PROPN
flr-49	333	7	student	student	PROPN
flr-49	333	8	a	a	DET
flr-49	333	9	drew	draw	VERB
flr-49	333	10	the	the	DET
flr-49	333	11	following	following	ADJ
flr-49	333	12	model	model	NOUN
flr-49	333	13	.	.	PUNCT
flr-49	334	1	student	student	PROPN
flr-49	334	2	b	b	PROPN
flr-49	334	3	drew	draw	VERB
flr-49	334	4	the	the	DET
flr-49	334	5	following	following	ADJ
flr-49	334	6	model	model	NOUN
flr-49	334	7	.	.	PUNCT
flr-49	335	1	who	who	PRON
flr-49	335	2	is	be	AUX
flr-49	335	3	correct	correct	ADJ
flr-49	335	4	?	?	PUNCT
flr-49	336	1			PRON
flr-49	336	2	student	student	VERB
flr-49	336	3	a	a	DET
flr-49	336	4			PROPN
flr-49	336	5	student	student	NOUN
flr-49	336	6	b	b	PROPN
flr-49	336	7			PROPN
flr-49	336	8	both	both	DET
flr-49	336	9	students	student	VERB
flr-49	336	10	a	a	PRON
flr-49	336	11	and	and	CCONJ
flr-49	336	12	b	b	NOUN
flr-49	336	13	check	check	VERB
flr-49	336	14	the	the	DET
flr-49	336	15	box	box	NOUN
flr-49	336	16	next	next	ADV
flr-49	336	17	to	to	ADP
flr-49	336	18	the	the	DET
flr-49	336	19	reason	reason	NOUN
flr-49	336	20	that	that	PRON
flr-49	336	21	best	good	ADJ
flr-49	336	22	explains	explain	VERB
flr-49	336	23	your	your	PRON
flr-49	336	24	choice	choice	NOUN
flr-49	336	25	.	.	PUNCT
flr-49	337	1			PRON
flr-49	337	2	student	student	VERB
flr-49	337	3	a	a	PRON
flr-49	337	4	is	be	AUX
flr-49	337	5	correct	correct	ADJ
flr-49	337	6	because	because	SCONJ
flr-49	337	7	the	the	DET
flr-49	337	8	numbers	number	NOUN
flr-49	337	9	are	be	AUX
flr-49	337	10	small	small	ADJ
flr-49	337	11	.	.	PUNCT
flr-49	338	1	therefore	therefore	ADV
flr-49	338	2	,	,	PUNCT
flr-49	338	3	the	the	DET
flr-49	338	4	rectangles	rectangle	NOUN
flr-49	338	5	are	be	AUX
flr-49	338	6	short	short	ADJ
flr-49	338	7	.	.	PUNCT
flr-49	339	1			PROPN
flr-49	339	2	student	student	NOUN
flr-49	339	3	b	b	PROPN
flr-49	339	4	is	be	AUX
flr-49	339	5	correct	correct	ADJ
flr-49	339	6	because	because	SCONJ
flr-49	339	7	the	the	DET
flr-49	339	8	numbers	number	NOUN
flr-49	339	9	are	be	AUX
flr-49	339	10	big	big	ADJ
flr-49	339	11	.	.	PUNCT
flr-49	340	1	therefore	therefore	ADV
flr-49	340	2	,	,	PUNCT
flr-49	340	3	the	the	DET
flr-49	340	4	rectangles	rectangle	NOUN
flr-49	340	5	are	be	AUX
flr-49	340	6	long	long	ADJ
flr-49	340	7	.	.	PUNCT
flr-49	341	1			PRON
flr-49	341	2	both	both	DET
flr-49	341	3	students	student	NOUN
flr-49	341	4	a	a	PRON
flr-49	341	5	and	and	CCONJ
flr-49	341	6	b	b	NOUN
flr-49	341	7	are	be	AUX
flr-49	341	8	correct	correct	ADJ
flr-49	341	9	because	because	SCONJ
flr-49	341	10	the	the	DET
flr-49	341	11	size	size	NOUN
flr-49	341	12	of	of	ADP
flr-49	341	13	the	the	DET
flr-49	341	14	rectangle	rectangle	NOUN
flr-49	341	15	does	do	AUX
flr-49	341	16	not	not	PART
flr-49	341	17	matter	matter	VERB
flr-49	341	18	.	.	PUNCT
flr-49	342	1			PRON
flr-49	342	2	both	both	DET
flr-49	342	3	students	student	NOUN
flr-49	342	4	a	a	PRON
flr-49	342	5	and	and	CCONJ
flr-49	342	6	b	b	NOUN
flr-49	342	7	are	be	AUX
flr-49	342	8	wrong	wrong	ADJ
flr-49	342	9	because	because	SCONJ
flr-49	342	10	the	the	DET
flr-49	342	11	models	model	NOUN
flr-49	342	12	are	be	AUX
flr-49	342	13	wrongly	wrongly	ADV
flr-49	342	14	drawn	draw	VERB
flr-49	342	15	.	.	PUNCT
flr-49	343	1	note	note	NOUN
flr-49	343	2	.	.	PUNCT
flr-49	344	1	one	one	NUM
flr-49	344	2	mark	mark	NOUN
flr-49	344	3	was	be	AUX
flr-49	344	4	awarded	award	VERB
flr-49	344	5	if	if	SCONJ
flr-49	344	6	the	the	DET
flr-49	344	7	student	student	NOUN
flr-49	344	8	chose	choose	VERB
flr-49	344	9	“	"	PUNCT
flr-49	344	10	both	both	DET
flr-49	344	11	students	student	NOUN
flr-49	344	12	a	a	PRON
flr-49	344	13	and	and	CCONJ
flr-49	344	14	b	b	NOUN
flr-49	344	15	”	"	PUNCT
flr-49	344	16	and	and	CCONJ
flr-49	344	17	no	no	DET
flr-49	344	18	marks	mark	NOUN
flr-49	344	19	were	be	AUX
flr-49	344	20	given	give	VERB
flr-49	344	21	for	for	ADP
flr-49	344	22	choosing	choose	VERB
flr-49	344	23	either	either	CCONJ
flr-49	344	24	“	"	PUNCT
flr-49	344	25	student	student	NOUN
flr-49	344	26	a	a	NOUN
flr-49	344	27	”	"	PUNCT
flr-49	344	28	or	or	CCONJ
flr-49	344	29	“	"	PUNCT
flr-49	344	30	student	student	NOUN
flr-49	344	31	b	b	NOUN
flr-49	344	32	”	"	PUNCT
flr-49	344	33	.	.	PUNCT
flr-49	345	1	one	one	NUM
flr-49	345	2	mark	mark	NOUN
flr-49	345	3	was	be	AUX
flr-49	345	4	awarded	award	VERB
flr-49	345	5	for	for	ADP
flr-49	345	6	choosing	choose	VERB
flr-49	345	7	the	the	DET
flr-49	345	8	answer	answer	NOUN
flr-49	345	9	“	"	PUNCT
flr-49	345	10	both	both	DET
flr-49	345	11	students	student	NOUN
flr-49	345	12	a	a	PRON
flr-49	345	13	and	and	CCONJ
flr-49	345	14	b	b	NOUN
flr-49	345	15	are	be	AUX
flr-49	345	16	correct	correct	ADJ
flr-49	345	17	because	because	SCONJ
flr-49	345	18	the	the	DET
flr-49	345	19	size	size	NOUN
flr-49	345	20	of	of	ADP
flr-49	345	21	the	the	DET
flr-49	345	22	rectangle	rectangle	NOUN
flr-49	345	23	does	do	AUX
flr-49	345	24	not	not	PART
flr-49	345	25	matter	matter	VERB
flr-49	345	26	”	"	PUNCT
flr-49	345	27	and	and	CCONJ
flr-49	345	28	no	no	DET
flr-49	345	29	marks	mark	NOUN
flr-49	345	30	were	be	AUX
flr-49	345	31	given	give	VERB
flr-49	345	32	for	for	ADP
flr-49	345	33	any	any	DET
flr-49	345	34	other	other	ADJ
flr-49	345	35	responses	response	NOUN
flr-49	345	36	.	.	PUNCT
flr-49	346	1	k.	k.	PROPN
flr-49	346	2	lee	lee	PROPN
flr-49	346	3	et	et	PROPN
flr-49	346	4	al	al	PROPN
flr-49	346	5	.	.	PROPN
flr-49	347	1	93	93	NUM
flr-49	348	1	|	|	NOUN
flr-49	348	2	f	f	NOUN
flr-49	348	3	l	l	NOUN
flr-49	348	4	r	r	NOUN
flr-49	348	5	student	student	NOUN
flr-49	348	6	a	a	NOUN
flr-49	348	7	and	and	CCONJ
flr-49	348	8	student	student	NOUN
flr-49	348	9	b	b	PROPN
flr-49	348	10	drew	draw	VERB
flr-49	348	11	models	model	NOUN
flr-49	348	12	for	for	ADP
flr-49	348	13	the	the	DET
flr-49	348	14	2	2	NUM
flr-49	348	15	questions	question	NOUN
flr-49	348	16	below	below	ADV
flr-49	348	17	.	.	PUNCT
flr-49	349	1	q.1	q.1	PROPN
flr-49	350	1	mary	mary	PROPN
flr-49	350	2	has	have	VERB
flr-49	350	3	some	some	DET
flr-49	350	4	marbles	marble	NOUN
flr-49	350	5	.	.	PUNCT
flr-49	351	1	john	john	PROPN
flr-49	351	2	has	have	VERB
flr-49	351	3	30	30	NUM
flr-49	351	4	marbles	marble	NOUN
flr-49	351	5	more	more	ADJ
flr-49	351	6	than	than	ADP
flr-49	351	7	mary	mary	PROPN
flr-49	351	8	.	.	PUNCT
flr-49	352	1	they	they	PRON
flr-49	352	2	have	have	VERB
flr-49	352	3	150	150	NUM
flr-49	352	4	marbles	marble	NOUN
flr-49	352	5	altogether	altogether	ADV
flr-49	352	6	.	.	PUNCT
flr-49	353	1	how	how	SCONJ
flr-49	353	2	many	many	ADJ
flr-49	353	3	marbles	marble	NOUN
flr-49	353	4	has	have	VERB
flr-49	353	5	mary	mary	PROPN
flr-49	353	6	?	?	PUNCT
flr-49	354	1	q.2	q.2	PROPN
flr-49	354	2	mary	mary	PROPN
flr-49	354	3	has	have	VERB
flr-49	354	4	some	some	DET
flr-49	354	5	marbles	marble	NOUN
flr-49	354	6	.	.	PUNCT
flr-49	355	1	john	john	PROPN
flr-49	355	2	has	have	VERB
flr-49	355	3	300	300	NUM
flr-49	355	4	marbles	marble	NOUN
flr-49	355	5	more	more	ADJ
flr-49	355	6	than	than	ADP
flr-49	355	7	mary	mary	PROPN
flr-49	355	8	.	.	PUNCT
flr-49	356	1	they	they	PRON
flr-49	356	2	have	have	VERB
flr-49	356	3	1500	1500	NUM
flr-49	356	4	marbles	marble	NOUN
flr-49	356	5	altogether	altogether	ADV
flr-49	356	6	.	.	PUNCT
flr-49	357	1	how	how	SCONJ
flr-49	357	2	many	many	ADJ
flr-49	357	3	marbles	marble	NOUN
flr-49	357	4	has	have	VERB
flr-49	357	5	mary	mary	PROPN
flr-49	357	6	?	?	PROPN
flr-49	357	7	student	student	PROPN
flr-49	357	8	a	a	DET
flr-49	357	9	drew	drew	NOUN
flr-49	357	10	:	:	PUNCT
flr-49	357	11	student	student	NOUN
flr-49	357	12	b	b	PROPN
flr-49	357	13	drew	draw	VERB
flr-49	357	14	:	:	PUNCT
flr-49	357	15	note	note	NOUN
flr-49	357	16	.	.	PUNCT
flr-49	358	1	one	one	NUM
flr-49	358	2	mark	mark	NOUN
flr-49	358	3	was	be	AUX
flr-49	358	4	awarded	award	VERB
flr-49	358	5	for	for	ADP
flr-49	358	6	choosing	choose	VERB
flr-49	358	7	“	"	PUNCT
flr-49	358	8	yes	yes	INTJ
flr-49	358	9	”	"	PUNCT
flr-49	358	10	for	for	ADP
flr-49	358	11	both	both	DET
flr-49	358	12	students	student	NOUN
flr-49	358	13	and	and	CCONJ
flr-49	358	14	no	no	DET
flr-49	358	15	marks	mark	NOUN
flr-49	358	16	were	be	AUX
flr-49	358	17	given	give	VERB
flr-49	358	18	for	for	ADP
flr-49	358	19	any	any	DET
flr-49	358	20	other	other	ADJ
flr-49	358	21	responses	response	NOUN
flr-49	358	22	.	.	PUNCT
flr-49	359	1	references	reference	NOUN
flr-49	359	2	akgün	akgün	NOUN
flr-49	359	3	,	,	PUNCT
flr-49	359	4	l.	l.	PROPN
flr-49	359	5	,	,	PUNCT
flr-49	359	6	&	&	CCONJ
flr-49	359	7	özdemir	özdemir	PROPN
flr-49	359	8	,	,	PUNCT
flr-49	359	9	m.	m.	NOUN
flr-49	359	10	e.	e.	PROPN
flr-49	359	11	(	(	PUNCT
flr-49	359	12	2006	2006	NUM
flr-49	359	13	)	)	PUNCT
flr-49	359	14	.	.	PUNCT
flr-49	360	1	students	student	NOUN
flr-49	360	2	'	'	PART
flr-49	360	3	understanding	understanding	NOUN
flr-49	360	4	of	of	ADP
flr-49	360	5	the	the	DET
flr-49	360	6	variable	variable	NOUN
flr-49	360	7	as	as	ADP
flr-49	360	8	general	general	ADJ
flr-49	360	9	number	number	NOUN
flr-49	360	10	and	and	CCONJ
flr-49	360	11	unknown	unknown	ADJ
flr-49	360	12	:	:	PUNCT
flr-49	360	13	a	a	DET
flr-49	360	14	case	case	NOUN
flr-49	360	15	study	study	NOUN
flr-49	360	16	.	.	PUNCT
flr-49	361	1	the	the	DET
flr-49	361	2	teaching	teaching	NOUN
flr-49	361	3	of	of	ADP
flr-49	361	4	mathematics	mathematic	NOUN
flr-49	361	5	,	,	PUNCT
flr-49	361	6	9(1	9(1	NUM
flr-49	361	7	)	)	PUNCT
flr-49	361	8	,	,	PUNCT
flr-49	361	9	45	45	NUM
flr-49	361	10	-	-	SYM
flr-49	361	11	51	51	NUM
flr-49	361	12	.	.	PUNCT
flr-49	361	13	is	be	AUX
flr-49	361	14	student	student	NOUN
flr-49	361	15	a	a	DET
flr-49	361	16	correct	correct	ADJ
flr-49	361	17	?	?	PUNCT
flr-49	362	1	yes	yes	INTJ
flr-49	362	2	no	no	INTJ
flr-49	362	3	is	be	AUX
flr-49	362	4	student	student	NOUN
flr-49	362	5	b	b	NOUN
flr-49	362	6	correct	correct	ADJ
flr-49	362	7	?	?	PUNCT
flr-49	363	1	yes	yes	INTJ
flr-49	364	1	no	no	INTJ
flr-49	365	1	k.	k.	PROPN
flr-49	365	2	lee	lee	PROPN
flr-49	365	3	et	et	PROPN
flr-49	365	4	al	al	PROPN
flr-49	365	5	.	.	PROPN
flr-49	365	6	94	94	NUM
flr-49	366	1	|	|	ADV
flr-49	366	2	f	f	NOUN
flr-49	366	3	l	l	NOUN
flr-49	366	4	r	r	NOUN
flr-49	366	5	booth	booth	NOUN
flr-49	366	6	,	,	PUNCT
flr-49	366	7	j.	j.	PROPN
flr-49	366	8	l.	l.	PROPN
flr-49	366	9	,	,	PUNCT
flr-49	366	10	&	&	CCONJ
flr-49	366	11	koedinger	koedinger	PROPN
flr-49	366	12	,	,	PUNCT
flr-49	366	13	k.	k.	PROPN
flr-49	366	14	r.	r.	PROPN
flr-49	366	15	(	(	PUNCT
flr-49	366	16	2010	2010	NUM
flr-49	366	17	)	)	PUNCT
flr-49	366	18	.	.	PUNCT
flr-49	367	1	facilitating	facilitate	VERB
flr-49	367	2	low	low	ADV
flr-49	367	3	-	-	PUNCT
flr-49	367	4	achieving	achieve	VERB
flr-49	367	5	students	student	NOUN
flr-49	367	6	’	'	PUNCT
flr-49	367	7	diagram	diagram	NOUN
flr-49	367	8	use	use	NOUN
flr-49	367	9	in	in	ADP
flr-49	367	10	algebraic	algebraic	ADJ
flr-49	367	11	story	story	NOUN
flr-49	367	12	problems	problem	NOUN
flr-49	367	13	.	.	PUNCT
flr-49	368	1	in	in	ADP
flr-49	368	2	s.	s.	PROPN
flr-49	368	3	ohlsson	ohlsson	PROPN
flr-49	368	4	&	&	CCONJ
flr-49	368	5	r.	r.	PROPN
flr-49	368	6	catrambone	catrambone	PROPN
flr-49	368	7	(	(	PUNCT
flr-49	368	8	eds	ed	NOUN
flr-49	368	9	.	.	PUNCT
flr-49	368	10	)	)	PUNCT
flr-49	368	11	,	,	PUNCT
flr-49	368	12	proceedings	proceeding	NOUN
flr-49	368	13	of	of	ADP
flr-49	368	14	the	the	DET
flr-49	368	15	32nd	32nd	ADJ
flr-49	368	16	annual	annual	ADJ
flr-49	368	17	meeting	meeting	NOUN
flr-49	368	18	of	of	ADP
flr-49	368	19	the	the	DET
flr-49	368	20	cognitive	cognitive	ADJ
flr-49	368	21	science	science	NOUN
flr-49	368	22	society	society	NOUN
flr-49	368	23	(	(	PUNCT
flr-49	368	24	pp	pp	ADJ
flr-49	368	25	.	.	PUNCT
flr-49	368	26	1649	1649	NUM
flr-49	368	27	-	-	SYM
flr-49	368	28	1654	1654	NUM
flr-49	368	29	)	)	PUNCT
flr-49	368	30	.	.	PUNCT
flr-49	369	1	austin	austin	PROPN
flr-49	369	2	,	,	PUNCT
flr-49	369	3	tx	tx	PROPN
flr-49	369	4	:	:	PUNCT
flr-49	369	5	cognitive	cognitive	ADJ
flr-49	369	6	science	science	NOUN
flr-49	369	7	society	society	NOUN
flr-49	369	8	.	.	PUNCT
flr-49	370	1	brown	brown	PROPN
flr-49	370	2	,	,	PUNCT
flr-49	370	3	m.	m.	NOUN
flr-49	370	4	,	,	PUNCT
flr-49	370	5	hart	hart	PROPN
flr-49	370	6	,	,	PUNCT
flr-49	370	7	k.	k.	PROPN
flr-49	370	8	,	,	PUNCT
flr-49	370	9	&	&	CCONJ
flr-49	370	10	kuchemann	kuchemann	PROPN
flr-49	370	11	,	,	PUNCT
flr-49	370	12	d.	d.	PROPN
flr-49	370	13	(	(	PUNCT
flr-49	370	14	1985	1985	NUM
flr-49	370	15	)	)	PUNCT
flr-49	370	16	.	.	PUNCT
flr-49	371	1	chelsea	chelsea	PROPN
flr-49	371	2	diagnostic	diagnostic	ADJ
flr-49	371	3	mathematics	mathematic	NOUN
flr-49	371	4	tests	test	NOUN
flr-49	371	5	and	and	CCONJ
flr-49	371	6	teacher	teacher	NOUN
flr-49	371	7	's	's	PART
flr-49	371	8	guide	guide	NOUN
flr-49	371	9	.	.	PUNCT
flr-49	372	1	windsor	windsor	NOUN
flr-49	372	2	:	:	PUNCT
flr-49	372	3	nfer	nfer	PROPN
flr-49	372	4	-	-	PUNCT
flr-49	372	5	nelson	nelson	PROPN
flr-49	372	6	publishing	publishing	PROPN
flr-49	372	7	company	company	PROPN
flr-49	372	8	ltd	ltd	PROPN
flr-49	372	9	.	.	PROPN
flr-49	372	10	capraro	capraro	PROPN
flr-49	372	11	,	,	PUNCT
flr-49	372	12	m.	m.	NOUN
flr-49	372	13	m.	m.	NOUN
flr-49	372	14	,	,	PUNCT
flr-49	372	15	&	&	CCONJ
flr-49	372	16	joffrion	joffrion	PROPN
flr-49	372	17	,	,	PUNCT
flr-49	372	18	h.	h.	PROPN
flr-49	372	19	(	(	PUNCT
flr-49	372	20	2006	2006	NUM
flr-49	372	21	)	)	PUNCT
flr-49	372	22	.	.	PUNCT
flr-49	373	1	algebraic	algebraic	ADJ
flr-49	373	2	equations	equation	NOUN
flr-49	373	3	:	:	PUNCT
flr-49	373	4	can	can	AUX
flr-49	373	5	middle	middle	ADJ
flr-49	373	6	-	-	PUNCT
flr-49	373	7	school	school	NOUN
flr-49	373	8	students	student	NOUN
flr-49	373	9	meaningfully	meaningfully	ADV
flr-49	373	10	translate	translate	VERB
flr-49	373	11	from	from	ADP
flr-49	373	12	words	word	NOUN
flr-49	373	13	to	to	ADP
flr-49	373	14	mathematical	mathematical	ADJ
flr-49	373	15	symbols	symbol	NOUN
flr-49	373	16	?	?	PUNCT
flr-49	374	1	reading	read	VERB
flr-49	374	2	psychology	psychology	NOUN
flr-49	374	3	,	,	PUNCT
flr-49	374	4	27(2	27(2	PROPN
flr-49	374	5	-	-	SYM
flr-49	374	6	3	3	NUM
flr-49	374	7	)	)	PUNCT
flr-49	374	8	,	,	PUNCT
flr-49	374	9	147	147	NUM
flr-49	374	10	-	-	SYM
flr-49	374	11	164	164	NUM
flr-49	374	12	.	.	PUNCT
flr-49	375	1	doi	doi	NOUN
flr-49	375	2	:	:	PUNCT
flr-49	375	3	10.1080/02702710600642467	10.1080/02702710600642467	NUM
flr-49	375	4	carpenter	carpenter	NOUN
flr-49	375	5	,	,	PUNCT
flr-49	375	6	t.	t.	PROPN
flr-49	375	7	p.	p.	PROPN
flr-49	375	8	,	,	PUNCT
flr-49	375	9	&	&	CCONJ
flr-49	375	10	levi	levi	PROPN
flr-49	375	11	,	,	PUNCT
flr-49	375	12	l.	l.	PROPN
flr-49	375	13	(	(	PUNCT
flr-49	375	14	2000	2000	NUM
flr-49	375	15	)	)	PUNCT
flr-49	375	16	.	.	PUNCT
flr-49	376	1	developing	develop	VERB
flr-49	376	2	conceptions	conception	NOUN
flr-49	376	3	of	of	ADP
flr-49	376	4	algebraic	algebraic	ADJ
flr-49	376	5	reasoning	reasoning	NOUN
flr-49	376	6	in	in	ADP
flr-49	376	7	the	the	DET
flr-49	376	8	primary	primary	ADJ
flr-49	376	9	grades	grade	NOUN
flr-49	376	10	.	.	PUNCT
flr-49	377	1	(	(	PUNCT
flr-49	377	2	res	re	NOUN
flr-49	377	3	.	.	PUNCT
flr-49	377	4	rep	rep	PROPN
flr-49	377	5	.	.	PROPN
flr-49	377	6	00	00	NUM
flr-49	377	7	-	-	SYM
flr-49	377	8	2	2	NUM
flr-49	377	9	)	)	PUNCT
flr-49	377	10	.	.	PUNCT
flr-49	378	1	madison	madison	PROPN
flr-49	378	2	,	,	PUNCT
flr-49	378	3	wi	wi	PROPN
flr-49	378	4	:	:	PUNCT
flr-49	378	5	national	national	ADJ
flr-49	378	6	center	center	NOUN
flr-49	378	7	for	for	ADP
flr-49	378	8	improving	improve	VERB
flr-49	378	9	student	student	NOUN
flr-49	378	10	learning	learning	NOUN
flr-49	378	11	and	and	CCONJ
flr-49	378	12	achievement	achievement	NOUN
flr-49	378	13	in	in	ADP
flr-49	378	14	mathematics	mathematic	NOUN
flr-49	378	15	and	and	CCONJ
flr-49	378	16	science	science	NOUN
flr-49	378	17	.	.	PUNCT
flr-49	379	1	retrieved	retrieve	VERB
flr-49	379	2	from	from	ADP
flr-49	379	3	http://ncisla.wceruw.org/publications/reports/rr-002.pdf	http://ncisla.wceruw.org/publications/reports/rr-002.pdf	PROPN
flr-49	379	4	carraher	carraher	NOUN
flr-49	379	5	,	,	PUNCT
flr-49	379	6	d.	d.	PROPN
flr-49	379	7	w.	w.	PROPN
flr-49	379	8	,	,	PUNCT
flr-49	379	9	schliemann	schliemann	PROPN
flr-49	379	10	,	,	PUNCT
flr-49	379	11	a.	a.	NOUN
flr-49	379	12	,	,	PUNCT
flr-49	379	13	brizuela	brizuela	PROPN
flr-49	379	14	,	,	PUNCT
flr-49	379	15	b.	b.	PROPN
flr-49	379	16	m.	m.	PROPN
flr-49	379	17	,	,	PUNCT
flr-49	379	18	&	&	CCONJ
flr-49	379	19	earnest	earnest	PROPN
flr-49	379	20	,	,	PUNCT
flr-49	379	21	d.	d.	PROPN
flr-49	379	22	(	(	PUNCT
flr-49	379	23	2006	2006	NUM
flr-49	379	24	)	)	PUNCT
flr-49	379	25	.	.	PUNCT
flr-49	380	1	arithmetic	arithmetic	PROPN
flr-49	380	2	and	and	CCONJ
flr-49	380	3	algebra	algebra	NOUN
flr-49	380	4	in	in	ADP
flr-49	380	5	early	early	ADJ
flr-49	380	6	mathematics	mathematic	NOUN
flr-49	380	7	education	education	NOUN
flr-49	380	8	.	.	PUNCT
flr-49	381	1	journal	journal	PROPN
flr-49	381	2	for	for	ADP
flr-49	381	3	research	research	NOUN
flr-49	381	4	in	in	ADP
flr-49	381	5	mathematics	mathematics	PROPN
flr-49	381	6	education	education	NOUN
flr-49	381	7	,	,	PUNCT
flr-49	381	8	37(2	37(2	PROPN
flr-49	381	9	)	)	PUNCT
flr-49	381	10	,	,	PUNCT
flr-49	381	11	87	87	NUM
flr-49	381	12	-	-	SYM
flr-49	381	13	115	115	NUM
flr-49	381	14	.	.	PUNCT
flr-49	382	1	dede	dede	NOUN
flr-49	382	2	,	,	PUNCT
flr-49	382	3	y.	y.	PROPN
flr-49	382	4	(	(	PUNCT
flr-49	382	5	2004	2004	NUM
flr-49	382	6	)	)	PUNCT
flr-49	382	7	.	.	PUNCT
flr-49	383	1	the	the	DET
flr-49	383	2	concept	concept	NOUN
flr-49	383	3	of	of	ADP
flr-49	383	4	variable	variable	NOUN
flr-49	383	5	and	and	CCONJ
flr-49	383	6	identification	identification	NOUN
flr-49	383	7	its	its	PRON
flr-49	383	8	learning	learning	NOUN
flr-49	383	9	difficulties	difficulty	NOUN
flr-49	383	10	.	.	PUNCT
flr-49	384	1	educational	educational	ADJ
flr-49	384	2	sciences	science	NOUN
flr-49	384	3	:	:	PUNCT
flr-49	384	4	theory	theory	NOUN
flr-49	384	5	&	&	CCONJ
flr-49	384	6	practice	practice	PROPN
flr-49	384	7	,	,	PUNCT
flr-49	384	8	4(1	4(1	NOUN
flr-49	384	9	)	)	PUNCT
flr-49	384	10	,	,	PUNCT
flr-49	384	11	50	50	NUM
flr-49	384	12	.	.	PUNCT
flr-49	384	13	duru	duru	PROPN
flr-49	384	14	,	,	PUNCT
flr-49	384	15	a.	a.	NOUN
flr-49	384	16	(	(	PUNCT
flr-49	384	17	2011	2011	NUM
flr-49	384	18	)	)	PUNCT
flr-49	384	19	.	.	PUNCT
flr-49	385	1	middle	middle	ADJ
flr-49	385	2	school	school	NOUN
flr-49	385	3	students	student	NOUN
flr-49	385	4	’	'	PUNCT
flr-49	385	5	reading	reading	NOUN
flr-49	385	6	comprehension	comprehension	NOUN
flr-49	385	7	of	of	ADP
flr-49	385	8	mathematical	mathematical	ADJ
flr-49	385	9	texts	text	NOUN
flr-49	385	10	and	and	CCONJ
flr-49	385	11	algebraic	algebraic	ADJ
flr-49	385	12	equations	equation	NOUN
flr-49	385	13	.	.	PUNCT
flr-49	386	1	international	international	ADJ
flr-49	386	2	journal	journal	PROPN
flr-49	386	3	of	of	ADP
flr-49	386	4	mathematical	mathematical	ADJ
flr-49	386	5	education	education	NOUN
flr-49	386	6	in	in	ADP
flr-49	386	7	science	science	NOUN
flr-49	386	8	and	and	CCONJ
flr-49	386	9	technology	technology	NOUN
flr-49	386	10	,	,	PUNCT
flr-49	386	11	42(4	42(4	PROPN
flr-49	386	12	)	)	PUNCT
flr-49	386	13	,	,	PUNCT
flr-49	386	14	447468	447468	NUM
flr-49	386	15	.	.	PUNCT
flr-49	387	1	doi	doi	NOUN
flr-49	387	2	:	:	PUNCT
flr-49	387	3	10.1080/0020739x.2010.550938	10.1080/0020739x.2010.550938	PROPN
flr-49	387	4	flavell	flavell	PROPN
flr-49	387	5	,	,	PUNCT
flr-49	387	6	j.	j.	PROPN
flr-49	387	7	h.	h.	PROPN
flr-49	387	8	(	(	PUNCT
flr-49	387	9	1970	1970	NUM
flr-49	387	10	)	)	PUNCT
flr-49	387	11	.	.	PUNCT
flr-49	388	1	developmental	developmental	ADJ
flr-49	388	2	studies	study	NOUN
flr-49	388	3	of	of	ADP
flr-49	388	4	mediated	mediate	VERB
flr-49	388	5	memory	memory	NOUN
flr-49	388	6	.	.	PUNCT
flr-49	389	1	in	in	ADP
flr-49	389	2	h.	h.	PROPN
flr-49	389	3	w.	w.	PROPN
flr-49	389	4	reese	reese	PROPN
flr-49	389	5	&	&	CCONJ
flr-49	389	6	l.	l.	PROPN
flr-49	389	7	p.	p.	PROPN
flr-49	389	8	lipsitt	lipsitt	PROPN
flr-49	389	9	(	(	PUNCT
flr-49	389	10	eds	ed	NOUN
flr-49	389	11	.	.	PUNCT
flr-49	389	12	)	)	PUNCT
flr-49	389	13	,	,	PUNCT
flr-49	389	14	advances	advance	NOUN
flr-49	389	15	in	in	ADP
flr-49	389	16	child	child	NOUN
flr-49	389	17	development	development	NOUN
flr-49	389	18	and	and	CCONJ
flr-49	389	19	child	child	NOUN
flr-49	389	20	behavior	behavior	NOUN
flr-49	389	21	(	(	PUNCT
flr-49	389	22	vol	vol	NOUN
flr-49	389	23	.	.	NOUN
flr-49	389	24	5	5	NUM
flr-49	389	25	)	)	PUNCT
flr-49	389	26	.	.	PUNCT
flr-49	390	1	new	new	PROPN
flr-49	390	2	york	york	PROPN
flr-49	390	3	:	:	PUNCT
flr-49	390	4	academic	academic	ADJ
flr-49	390	5	press	press	NOUN
flr-49	390	6	.	.	PUNCT
flr-49	391	1	fuchs	fuchs	PROPN
flr-49	391	2	,	,	PUNCT
flr-49	391	3	l.	l.	PROPN
flr-49	391	4	s.	s.	PROPN
flr-49	391	5	,	,	PUNCT
flr-49	391	6	compton	compton	PROPN
flr-49	391	7	,	,	PUNCT
flr-49	391	8	d.	d.	PROPN
flr-49	391	9	l.	l.	PROPN
flr-49	391	10	,	,	PUNCT
flr-49	391	11	fuchs	fuchs	PROPN
flr-49	391	12	,	,	PUNCT
flr-49	391	13	d.	d.	PROPN
flr-49	391	14	,	,	PUNCT
flr-49	391	15	powell	powell	PROPN
flr-49	391	16	,	,	PUNCT
flr-49	391	17	s.	s.	PROPN
flr-49	391	18	r.	r.	PROPN
flr-49	391	19	,	,	PUNCT
flr-49	391	20	schumacher	schumacher	PROPN
flr-49	391	21	,	,	PUNCT
flr-49	391	22	r.	r.	PROPN
flr-49	391	23	f.	f.	PROPN
flr-49	391	24	,	,	PUNCT
flr-49	391	25	hamlett	hamlett	PROPN
flr-49	391	26	,	,	PUNCT
flr-49	391	27	c.	c.	PROPN
flr-49	391	28	l.	l.	PROPN
flr-49	391	29	,	,	PUNCT
flr-49	391	30	et	et	PROPN
flr-49	391	31	al	al	PROPN
flr-49	391	32	.	.	PUNCT
flr-49	391	33	(	(	PUNCT
flr-49	391	34	2012	2012	NUM
flr-49	391	35	)	)	PUNCT
flr-49	391	36	.	.	PUNCT
flr-49	392	1	contributions	contribution	NOUN
flr-49	392	2	of	of	ADP
flr-49	392	3	domain	domain	NOUN
flr-49	392	4	-	-	PUNCT
flr-49	392	5	general	general	ADJ
flr-49	392	6	cognitive	cognitive	ADJ
flr-49	392	7	resources	resource	NOUN
flr-49	392	8	and	and	CCONJ
flr-49	392	9	different	different	ADJ
flr-49	392	10	forms	form	NOUN
flr-49	392	11	of	of	ADP
flr-49	392	12	arithmetic	arithmetic	ADJ
flr-49	392	13	development	development	NOUN
flr-49	392	14	to	to	ADP
flr-49	392	15	pre	pre	ADJ
flr-49	392	16	-	-	ADJ
flr-49	392	17	algebraic	algebraic	ADJ
flr-49	392	18	knowledge	knowledge	NOUN
flr-49	392	19	.	.	PUNCT
flr-49	393	1	developmental	developmental	ADJ
flr-49	393	2	psychology	psychology	NOUN
flr-49	393	3	,	,	PUNCT
flr-49	393	4	48(5	48(5	NUM
flr-49	393	5	)	)	PUNCT
flr-49	393	6	,	,	PUNCT
flr-49	393	7	1315	1315	NUM
flr-49	393	8	-	-	SYM
flr-49	393	9	1326	1326	NUM
flr-49	393	10	.	.	PUNCT
flr-49	394	1	doi	doi	NOUN
flr-49	394	2	:	:	PUNCT
flr-49	394	3	10.1037	10.1037	NUM
flr-49	394	4	/	/	SYM
flr-49	394	5	a0027475	a0027475	ADJ
flr-49	394	6	harnishfeger	harnishfeger	NOUN
flr-49	394	7	,	,	PUNCT
flr-49	394	8	k.	k.	PROPN
flr-49	394	9	k.	k.	PROPN
flr-49	394	10	,	,	PUNCT
flr-49	394	11	&	&	CCONJ
flr-49	394	12	bjorklund	bjorklund	PROPN
flr-49	394	13	,	,	PUNCT
flr-49	394	14	d.	d.	PROPN
flr-49	394	15	f.	f.	PROPN
flr-49	394	16	(	(	PUNCT
flr-49	394	17	1990	1990	NUM
flr-49	394	18	)	)	PUNCT
flr-49	394	19	.	.	PUNCT
flr-49	395	1	children	child	NOUN
flr-49	395	2	’s	’s	PART
flr-49	395	3	strategies	strategy	NOUN
flr-49	395	4	:	:	PUNCT
flr-49	395	5	a	a	DET
flr-49	395	6	brief	brief	ADJ
flr-49	395	7	history	history	NOUN
flr-49	395	8	.	.	PUNCT
flr-49	396	1	in	in	ADP
flr-49	396	2	d.	d.	PROPN
flr-49	396	3	f.	f.	PROPN
flr-49	396	4	bjorklund	bjorklund	PROPN
flr-49	396	5	(	(	PUNCT
flr-49	396	6	eds	ed	NOUN
flr-49	396	7	.	.	PUNCT
flr-49	396	8	)	)	PUNCT
flr-49	396	9	,	,	PUNCT
flr-49	396	10	children	child	NOUN
flr-49	396	11	’s	’s	PART
flr-49	396	12	strategies	strategy	NOUN
flr-49	396	13	:	:	PUNCT
flr-49	396	14	contemporary	contemporary	ADJ
flr-49	396	15	views	view	NOUN
flr-49	396	16	of	of	ADP
flr-49	396	17	cognitive	cognitive	ADJ
flr-49	396	18	development	development	NOUN
flr-49	396	19	.	.	PUNCT
flr-49	397	1	hillsdale	hillsdale	PROPN
flr-49	397	2	,	,	PUNCT
flr-49	397	3	nj	nj	PROPN
flr-49	397	4	:	:	PUNCT
flr-49	397	5	lawrence	lawrence	PROPN
flr-49	397	6	erlbaum	erlbaum	PROPN
flr-49	397	7	associates	associates	PROPN
flr-49	397	8	.	.	PUNCT
flr-49	398	1	hefferman	hefferman	NOUN
flr-49	398	2	,	,	PUNCT
flr-49	398	3	n.	n.	NOUN
flr-49	398	4	,	,	PUNCT
flr-49	398	5	&	&	CCONJ
flr-49	398	6	koedinger	koedinger	PROPN
flr-49	398	7	,	,	PUNCT
flr-49	398	8	k.	k.	PROPN
flr-49	398	9	r.	r.	PROPN
flr-49	398	10	(	(	PUNCT
flr-49	398	11	1997	1997	NUM
flr-49	398	12	)	)	PUNCT
flr-49	398	13	.	.	PUNCT
flr-49	399	1	the	the	DET
flr-49	399	2	composition	composition	NOUN
flr-49	399	3	effect	effect	NOUN
flr-49	399	4	in	in	ADP
flr-49	399	5	symbolizing	symbolize	VERB
flr-49	399	6	:	:	PUNCT
flr-49	399	7	the	the	DET
flr-49	399	8	role	role	NOUN
flr-49	399	9	of	of	ADP
flr-49	399	10	symbol	symbol	NOUN
flr-49	399	11	production	production	NOUN
flr-49	399	12	versus	versus	ADP
flr-49	399	13	text	text	NOUN
flr-49	399	14	comprehension	comprehension	NOUN
flr-49	399	15	.	.	PUNCT
flr-49	400	1	in	in	ADP
flr-49	400	2	m.	m.	NOUN
flr-49	400	3	g.	g.	PROPN
flr-49	400	4	shafto	shafto	PROPN
flr-49	400	5	&	&	CCONJ
flr-49	400	6	p.	p.	PROPN
flr-49	400	7	langley	langley	PROPN
flr-49	400	8	(	(	PUNCT
flr-49	400	9	eds	ed	NOUN
flr-49	400	10	.	.	PUNCT
flr-49	400	11	)	)	PUNCT
flr-49	400	12	,	,	PUNCT
flr-49	400	13	proceedings	proceeding	NOUN
flr-49	400	14	of	of	ADP
flr-49	400	15	the	the	DET
flr-49	400	16	nineteenth	nineteenth	ADJ
flr-49	400	17	annual	annual	ADJ
flr-49	400	18	conference	conference	NOUN
flr-49	400	19	of	of	ADP
flr-49	400	20	the	the	DET
flr-49	400	21	cognitive	cognitive	ADJ
flr-49	400	22	science	science	NOUN
flr-49	400	23	society	society	NOUN
flr-49	400	24	(	(	PUNCT
flr-49	400	25	pp	pp	ADJ
flr-49	400	26	.	.	PUNCT
flr-49	401	1	307	307	NUM
flr-49	401	2	-	-	SYM
flr-49	401	3	312	312	NUM
flr-49	401	4	)	)	PUNCT
flr-49	401	5	.	.	PUNCT
flr-49	402	1	mahwah	mahwah	PROPN
flr-49	402	2	,	,	PUNCT
flr-49	402	3	nj	nj	PROPN
flr-49	402	4	:	:	PUNCT
flr-49	402	5	lawrence	lawrence	PROPN
flr-49	402	6	erlbaum	erlbaum	PROPN
flr-49	402	7	associates	associates	PROPN
flr-49	402	8	.	.	PUNCT
flr-49	403	1	hu	hu	PROPN
flr-49	403	2	,	,	PUNCT
flr-49	403	3	w.	w.	PROPN
flr-49	403	4	(	(	PUNCT
flr-49	403	5	2010	2010	NUM
flr-49	403	6	)	)	PUNCT
flr-49	403	7	.	.	PUNCT
flr-49	404	1	making	make	VERB
flr-49	404	2	math	math	NOUN
flr-49	404	3	lessons	lesson	NOUN
flr-49	404	4	as	as	ADV
flr-49	404	5	easy	easy	ADJ
flr-49	404	6	as	as	ADP
flr-49	404	7	1	1	NUM
flr-49	404	8	,	,	PUNCT
flr-49	404	9	pause	pause	NOUN
flr-49	404	10	,	,	PUNCT
flr-49	404	11	2	2	NUM
flr-49	404	12	,	,	PUNCT
flr-49	404	13	pause	pause	NOUN
flr-49	404	14	...	...	PUNCT
flr-49	404	15	the	the	DET
flr-49	404	16	new	new	PROPN
flr-49	404	17	york	york	PROPN
flr-49	404	18	times	times	PROPN
flr-49	404	19	.	.	PUNCT
flr-49	405	1	retrieved	retrieve	VERB
flr-49	405	2	from	from	ADP
flr-49	405	3	http://www.nytimes.com/2010/10/01/education/01math.html?_r=0	http://www.nytimes.com/2010/10/01/education/01math.html?_r=0	PROPN
flr-49	405	4	hunter	hunter	NOUN
flr-49	405	5	,	,	PUNCT
flr-49	405	6	j.	j.	PROPN
flr-49	405	7	(	(	PUNCT
flr-49	405	8	2007	2007	NUM
flr-49	405	9	)	)	PUNCT
flr-49	405	10	.	.	PUNCT
flr-49	406	1	relational	relational	ADJ
flr-49	406	2	or	or	CCONJ
flr-49	406	3	calculational	calculational	ADJ
flr-49	406	4	thinking	thinking	NOUN
flr-49	406	5	:	:	PUNCT
flr-49	406	6	students	student	NOUN
flr-49	406	7	solving	solve	VERB
flr-49	406	8	open	open	ADJ
flr-49	406	9	number	number	NOUN
flr-49	406	10	equivalence	equivalence	NOUN
flr-49	406	11	problems	problem	NOUN
flr-49	406	12	.	.	PUNCT
flr-49	407	1	in	in	ADP
flr-49	407	2	j.	j.	PROPN
flr-49	407	3	watson	watson	PROPN
flr-49	407	4	&	&	CCONJ
flr-49	407	5	k.	k.	PROPN
flr-49	407	6	beswick	beswick	PROPN
flr-49	407	7	(	(	PUNCT
flr-49	407	8	eds	eds	PROPN
flr-49	407	9	.	.	PUNCT
flr-49	407	10	)	)	PUNCT
flr-49	407	11	,	,	PUNCT
flr-49	407	12	proceedings	proceeding	NOUN
flr-49	407	13	of	of	ADP
flr-49	407	14	the	the	DET
flr-49	407	15	30th	30th	ADJ
flr-49	407	16	annual	annual	ADJ
flr-49	407	17	conference	conference	NOUN
flr-49	407	18	of	of	ADP
flr-49	407	19	the	the	DET
flr-49	407	20	mathematics	mathematics	PROPN
flr-49	407	21	education	education	PROPN
flr-49	407	22	research	research	NOUN
flr-49	407	23	group	group	NOUN
flr-49	407	24	of	of	ADP
flr-49	407	25	australasia	australasia	PROPN
flr-49	407	26	(	(	PUNCT
flr-49	407	27	vol	vol	NOUN
flr-49	407	28	.	.	PROPN
flr-49	407	29	2	2	NUM
flr-49	407	30	,	,	PUNCT
flr-49	407	31	pp	pp	ADJ
flr-49	407	32	.	.	PUNCT
flr-49	408	1	421	421	NUM
flr-49	408	2	-	-	SYM
flr-49	408	3	429	429	NUM
flr-49	408	4	)	)	PUNCT
flr-49	408	5	.	.	PUNCT
flr-49	409	1	adelaide	adelaide	PROPN
flr-49	409	2	:	:	PUNCT
flr-49	410	1	merga	merga	PROPN
flr-49	410	2	.	.	PUNCT
flr-49	411	1	khng	khng	PROPN
flr-49	411	2	,	,	PUNCT
flr-49	411	3	k.	k.	PROPN
flr-49	411	4	h.	h.	PROPN
flr-49	411	5	,	,	PUNCT
flr-49	411	6	&	&	CCONJ
flr-49	411	7	lee	lee	PROPN
flr-49	411	8	,	,	PUNCT
flr-49	411	9	k.	k.	PROPN
flr-49	411	10	(	(	PUNCT
flr-49	411	11	2009	2009	NUM
flr-49	411	12	)	)	PUNCT
flr-49	411	13	.	.	PUNCT
flr-49	412	1	inhibiting	inhibit	VERB
flr-49	412	2	interference	interference	NOUN
flr-49	412	3	from	from	ADP
flr-49	412	4	prior	prior	ADJ
flr-49	412	5	knowledge	knowledge	NOUN
flr-49	412	6	:	:	PUNCT
flr-49	412	7	arithmetic	arithmetic	ADJ
flr-49	412	8	intrusions	intrusion	NOUN
flr-49	412	9	in	in	ADP
flr-49	412	10	algebra	algebra	NOUN
flr-49	412	11	word	word	NOUN
flr-49	412	12	problem	problem	NOUN
flr-49	412	13	solving	solve	VERB
flr-49	412	14	.	.	PUNCT
flr-49	413	1	learning	learning	NOUN
flr-49	413	2	and	and	CCONJ
flr-49	413	3	individual	individual	ADJ
flr-49	413	4	differences	difference	NOUN
flr-49	413	5	,	,	PUNCT
flr-49	413	6	19(2	19(2	NUM
flr-49	413	7	)	)	PUNCT
flr-49	413	8	,	,	PUNCT
flr-49	413	9	262	262	NUM
flr-49	413	10	-	-	SYM
flr-49	413	11	268	268	NUM
flr-49	413	12	.	.	PUNCT
flr-49	414	1	doi	doi	NOUN
flr-49	414	2	:	:	PUNCT
flr-49	414	3	10.1016	10.1016	NUM
flr-49	414	4	/	/	SYM
flr-49	414	5	j.lindif.2009.01.004	j.lindif.2009.01.004	PROPN
flr-49	414	6	kieran	kieran	PROPN
flr-49	414	7	,	,	PUNCT
flr-49	414	8	c.	c.	PROPN
flr-49	414	9	(	(	PUNCT
flr-49	414	10	1981	1981	NUM
flr-49	414	11	)	)	PUNCT
flr-49	414	12	.	.	PUNCT
flr-49	415	1	concepts	concept	NOUN
flr-49	415	2	associated	associate	VERB
flr-49	415	3	with	with	ADP
flr-49	415	4	the	the	DET
flr-49	415	5	equality	equality	NOUN
flr-49	415	6	symbol	symbol	NOUN
flr-49	415	7	.	.	PUNCT
flr-49	416	1	educational	educational	ADJ
flr-49	416	2	studies	study	NOUN
flr-49	416	3	in	in	ADP
flr-49	416	4	mathematics	mathematic	NOUN
flr-49	416	5	,	,	PUNCT
flr-49	416	6	12(3	12(3	NUM
flr-49	416	7	)	)	PUNCT
flr-49	416	8	,	,	PUNCT
flr-49	416	9	317	317	NUM
flr-49	416	10	-	-	SYM
flr-49	416	11	326	326	NUM
flr-49	416	12	.	.	PUNCT
flr-49	417	1	doi	doi	NOUN
flr-49	417	2	:	:	PUNCT
flr-49	417	3	10.1007	10.1007	NUM
flr-49	417	4	/	/	SYM
flr-49	417	5	bf00311062	bf00311062	PROPN
flr-49	417	6	knuth	knuth	NOUN
flr-49	417	7	,	,	PUNCT
flr-49	417	8	e.	e.	PROPN
flr-49	417	9	j.	j.	PROPN
flr-49	417	10	,	,	PUNCT
flr-49	417	11	stephens	stephens	PROPN
flr-49	417	12	,	,	PUNCT
flr-49	417	13	a.	a.	PROPN
flr-49	417	14	c.	c.	PROPN
flr-49	417	15	,	,	PUNCT
flr-49	417	16	mcneil	mcneil	PROPN
flr-49	417	17	,	,	PUNCT
flr-49	417	18	n.	n.	PROPN
flr-49	417	19	m.	m.	NOUN
flr-49	417	20	,	,	PUNCT
flr-49	417	21	&	&	CCONJ
flr-49	417	22	alibali	alibali	VERB
flr-49	417	23	,	,	PUNCT
flr-49	417	24	m.	m.	PROPN
flr-49	417	25	w.	w.	PROPN
flr-49	417	26	(	(	PUNCT
flr-49	417	27	2006	2006	NUM
flr-49	417	28	)	)	PUNCT
flr-49	417	29	.	.	PUNCT
flr-49	418	1	does	do	AUX
flr-49	418	2	understanding	understand	VERB
flr-49	418	3	the	the	DET
flr-49	418	4	equal	equal	ADJ
flr-49	418	5	sign	sign	NOUN
flr-49	418	6	matter	matter	NOUN
flr-49	418	7	?	?	PUNCT
flr-49	419	1	evidence	evidence	NOUN
flr-49	419	2	from	from	ADP
flr-49	419	3	solving	solve	VERB
flr-49	419	4	equations	equation	NOUN
flr-49	419	5	.	.	PUNCT
flr-49	420	1	journal	journal	PROPN
flr-49	420	2	for	for	ADP
flr-49	420	3	research	research	NOUN
flr-49	420	4	in	in	ADP
flr-49	420	5	mathematics	mathematic	NOUN
flr-49	420	6	education	education	NOUN
flr-49	420	7	,	,	PUNCT
flr-49	420	8	37(4	37(4	PROPN
flr-49	420	9	)	)	PUNCT
flr-49	420	10	,	,	PUNCT
flr-49	420	11	297	297	NUM
flr-49	420	12	-	-	SYM
flr-49	420	13	312	312	NUM
flr-49	420	14	.	.	PUNCT
flr-49	420	15	koedinger	koedinger	PROPN
flr-49	420	16	,	,	PUNCT
flr-49	420	17	k.	k.	PROPN
flr-49	420	18	r.	r.	PROPN
flr-49	420	19	,	,	PUNCT
flr-49	420	20	alibali	alibali	VERB
flr-49	420	21	,	,	PUNCT
flr-49	420	22	m.	m.	PROPN
flr-49	420	23	w.	w.	PROPN
flr-49	420	24	,	,	PUNCT
flr-49	420	25	&	&	CCONJ
flr-49	420	26	nathan	nathan	PROPN
flr-49	420	27	,	,	PUNCT
flr-49	420	28	m.	m.	PROPN
flr-49	420	29	j.	j.	PROPN
flr-49	420	30	(	(	PUNCT
flr-49	420	31	2008	2008	NUM
flr-49	420	32	)	)	PUNCT
flr-49	420	33	.	.	PUNCT
flr-49	421	1	trade	trade	NOUN
flr-49	421	2	-	-	PUNCT
flr-49	421	3	offs	off	NOUN
flr-49	421	4	between	between	ADP
flr-49	421	5	grounded	grounded	ADJ
flr-49	421	6	and	and	CCONJ
flr-49	421	7	abstract	abstract	ADJ
flr-49	421	8	representations	representation	NOUN
flr-49	421	9	:	:	PUNCT
flr-49	421	10	evidence	evidence	NOUN
flr-49	421	11	from	from	ADP
flr-49	421	12	algebra	algebra	NOUN
flr-49	421	13	problem	problem	NOUN
flr-49	421	14	solving	solving	NOUN
flr-49	421	15	.	.	PUNCT
flr-49	422	1	cognitive	cognitive	ADJ
flr-49	422	2	science	science	NOUN
flr-49	422	3	:	:	PUNCT
flr-49	422	4	a	a	DET
flr-49	422	5	multidisciplinary	multidisciplinary	ADJ
flr-49	422	6	journal	journal	NOUN
flr-49	422	7	,	,	PUNCT
flr-49	422	8	32(2	32(2	NUM
flr-49	422	9	)	)	PUNCT
flr-49	422	10	,	,	PUNCT
flr-49	422	11	366	366	NUM
flr-49	422	12	-	-	SYM
flr-49	422	13	397	397	NUM
flr-49	422	14	.	.	PUNCT
flr-49	423	1	doi	doi	NOUN
flr-49	423	2	:	:	PUNCT
flr-49	423	3	10.1080/03640210701863933	10.1080/03640210701863933	NUM
flr-49	423	4	koedinger	koedinger	NOUN
flr-49	423	5	,	,	PUNCT
flr-49	423	6	k.	k.	PROPN
flr-49	423	7	r.	r.	PROPN
flr-49	423	8	,	,	PUNCT
flr-49	423	9	&	&	CCONJ
flr-49	423	10	nathan	nathan	PROPN
flr-49	423	11	,	,	PUNCT
flr-49	423	12	m.	m.	PROPN
flr-49	423	13	j.	j.	PROPN
flr-49	423	14	(	(	PUNCT
flr-49	423	15	2004	2004	NUM
flr-49	423	16	)	)	PUNCT
flr-49	423	17	.	.	PUNCT
flr-49	424	1	the	the	DET
flr-49	424	2	real	real	ADJ
flr-49	424	3	story	story	NOUN
flr-49	424	4	behind	behind	ADP
flr-49	424	5	story	story	NOUN
flr-49	424	6	problems	problem	NOUN
flr-49	424	7	:	:	PUNCT
flr-49	424	8	effects	effect	NOUN
flr-49	424	9	of	of	ADP
flr-49	424	10	representations	representation	NOUN
flr-49	424	11	on	on	ADP
flr-49	424	12	quantitative	quantitative	ADJ
flr-49	424	13	reasoning	reasoning	NOUN
flr-49	424	14	.	.	PUNCT
flr-49	425	1	journal	journal	NOUN
flr-49	425	2	of	of	ADP
flr-49	425	3	the	the	DET
flr-49	425	4	learning	learn	VERB
flr-49	425	5	sciences	science	NOUN
flr-49	425	6	,	,	PUNCT
flr-49	425	7	13(2	13(2	PROPN
flr-49	425	8	)	)	PUNCT
flr-49	425	9	,	,	PUNCT
flr-49	425	10	129	129	NUM
flr-49	425	11	-	-	SYM
flr-49	425	12	164	164	NUM
flr-49	425	13	.	.	PUNCT
flr-49	426	1	koedinger	koedinger	PROPN
flr-49	426	2	,	,	PUNCT
flr-49	426	3	k.	k.	PROPN
flr-49	426	4	r.	r.	PROPN
flr-49	426	5	,	,	PUNCT
flr-49	426	6	&	&	CCONJ
flr-49	426	7	terao	terao	PROPN
flr-49	426	8	,	,	PUNCT
flr-49	426	9	a.	a.	NOUN
flr-49	426	10	(	(	PUNCT
flr-49	426	11	2002	2002	NUM
flr-49	426	12	)	)	PUNCT
flr-49	426	13	.	.	PUNCT
flr-49	427	1	a	a	DET
flr-49	427	2	cognitive	cognitive	ADJ
flr-49	427	3	task	task	NOUN
flr-49	427	4	analysis	analysis	NOUN
flr-49	427	5	of	of	ADP
flr-49	427	6	using	use	VERB
flr-49	427	7	pictures	picture	NOUN
flr-49	427	8	to	to	PART
flr-49	427	9	support	support	VERB
flr-49	427	10	pre	pre	ADJ
flr-49	427	11	-	-	ADJ
flr-49	427	12	algebraic	algebraic	ADJ
flr-49	427	13	reasoning	reasoning	NOUN
flr-49	427	14	.	.	PUNCT
flr-49	428	1	in	in	ADP
flr-49	428	2	c.d	c.d	PROPN
flr-49	428	3	.	.	PROPN
flr-49	428	4	schunn	schunn	PROPN
flr-49	428	5	&	&	CCONJ
flr-49	428	6	w.	w.	PROPN
flr-49	428	7	gray	gray	PROPN
flr-49	428	8	(	(	PUNCT
flr-49	428	9	eds	ed	NOUN
flr-49	428	10	.	.	PUNCT
flr-49	428	11	)	)	PUNCT
flr-49	428	12	,	,	PUNCT
flr-49	428	13	proceedings	proceeding	NOUN
flr-49	428	14	of	of	ADP
flr-49	428	15	the	the	DET
flr-49	428	16	twenty	twenty	NUM
flr-49	428	17	-	-	PUNCT
flr-49	428	18	fourth	fourth	ADJ
flr-49	428	19	annual	annual	ADJ
flr-49	428	20	conference	conference	NOUN
flr-49	428	21	of	of	ADP
flr-49	428	22	the	the	DET
flr-49	428	23	cognitive	cognitive	ADJ
flr-49	428	24	science	science	NOUN
flr-49	428	25	society	society	NOUN
flr-49	428	26	(	(	PUNCT
flr-49	428	27	pp	pp	ADJ
flr-49	428	28	.	.	PUNCT
flr-49	429	1	542	542	NUM
flr-49	429	2	-	-	NUM
flr-49	429	3	547	547	NUM
flr-49	429	4	)	)	PUNCT
flr-49	429	5	.	.	PUNCT
flr-49	430	1	mahwah	mahwah	PROPN
flr-49	430	2	,	,	PUNCT
flr-49	430	3	nj	nj	PROPN
flr-49	430	4	:	:	PUNCT
flr-49	430	5	lawrence	lawrence	PROPN
flr-49	430	6	erlbaum	erlbaum	PROPN
flr-49	430	7	associates	associates	PROPN
flr-49	430	8	.	.	PUNCT
flr-49	431	1	k.	k.	PROPN
flr-49	431	2	lee	lee	PROPN
flr-49	431	3	et	et	PROPN
flr-49	431	4	al	al	PROPN
flr-49	431	5	.	.	PROPN
flr-49	431	6	95	95	NUM
flr-49	432	1	|	|	NOUN
flr-49	432	2	f	f	NOUN
flr-49	432	3	l	l	NOUN
flr-49	432	4	r	r	NOUN
flr-49	432	5	küchemann	küchemann	PROPN
flr-49	432	6	,	,	PUNCT
flr-49	432	7	d.	d.	PROPN
flr-49	432	8	(	(	PUNCT
flr-49	432	9	1978	1978	NUM
flr-49	432	10	)	)	PUNCT
flr-49	432	11	.	.	PUNCT
flr-49	433	1	children	child	NOUN
flr-49	433	2	's	's	PART
flr-49	433	3	understanding	understanding	NOUN
flr-49	433	4	of	of	ADP
flr-49	433	5	numerical	numerical	ADJ
flr-49	433	6	variables	variable	NOUN
flr-49	433	7	.	.	PUNCT
flr-49	434	1	mathematics	mathematic	NOUN
flr-49	434	2	in	in	ADP
flr-49	434	3	school	school	NOUN
flr-49	434	4	,	,	PUNCT
flr-49	434	5	7(4	7(4	NUM
flr-49	434	6	)	)	PUNCT
flr-49	434	7	,	,	PUNCT
flr-49	434	8	2326	2326	NUM
flr-49	434	9	.	.	PUNCT
flr-49	435	1	kwokwc	kwokwc	NOUN
flr-49	435	2	.	.	PUNCT
flr-49	436	1	(	(	PUNCT
flr-49	436	2	2011	2011	NUM
flr-49	436	3	)	)	PUNCT
flr-49	436	4	.	.	PUNCT
flr-49	437	1	not	not	PART
flr-49	437	2	able	able	ADJ
flr-49	437	3	to	to	PART
flr-49	437	4	use	use	VERB
flr-49	437	5	algebra	algebra	NOUN
flr-49	437	6	in	in	ADP
flr-49	437	7	primary	primary	ADJ
flr-49	437	8	level	level	NOUN
flr-49	437	9	.	.	PUNCT
flr-49	438	1	retrieved	retrieve	VERB
flr-49	438	2	from	from	ADP
flr-49	438	3	http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=27&t=18728	http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=27&t=18728	PROPN
flr-49	438	4	lee	lee	PROPN
flr-49	438	5	,	,	PUNCT
flr-49	438	6	k.	k.	PROPN
flr-49	438	7	,	,	PUNCT
flr-49	438	8	lim	lim	PROPN
flr-49	438	9	,	,	PUNCT
flr-49	438	10	z.	z.	PROPN
flr-49	438	11	y.	y.	PROPN
flr-49	438	12	,	,	PUNCT
flr-49	438	13	yeong	yeong	PROPN
flr-49	438	14	,	,	PUNCT
flr-49	438	15	s.	s.	PROPN
flr-49	438	16	h.	h.	PROPN
flr-49	438	17	,	,	PUNCT
flr-49	438	18	ng	ng	PROPN
flr-49	438	19	,	,	PUNCT
flr-49	438	20	s.	s.	PROPN
flr-49	438	21	f.	f.	PROPN
flr-49	438	22	,	,	PUNCT
flr-49	438	23	venkatraman	venkatraman	NOUN
flr-49	438	24	,	,	PUNCT
flr-49	438	25	v.	v.	ADV
flr-49	438	26	,	,	PUNCT
flr-49	438	27	&	&	CCONJ
flr-49	438	28	chee	chee	NOUN
flr-49	438	29	,	,	PUNCT
flr-49	438	30	m.	m.	NOUN
flr-49	438	31	w.	w.	PROPN
flr-49	438	32	(	(	PUNCT
flr-49	438	33	2007	2007	NUM
flr-49	438	34	)	)	PUNCT
flr-49	438	35	.	.	PUNCT
flr-49	439	1	strategic	strategic	ADJ
flr-49	439	2	differences	difference	NOUN
flr-49	439	3	in	in	ADP
flr-49	439	4	algebraic	algebraic	ADJ
flr-49	439	5	problem	problem	NOUN
flr-49	439	6	solving	solve	VERB
flr-49	439	7	:	:	PUNCT
flr-49	439	8	neuroanatomical	neuroanatomical	ADJ
flr-49	439	9	correlates	correlate	NOUN
flr-49	439	10	.	.	PUNCT
flr-49	440	1	brain	brain	NOUN
flr-49	440	2	research	research	NOUN
flr-49	440	3	,	,	PUNCT
flr-49	440	4	1155	1155	NUM
flr-49	440	5	(	(	PUNCT
flr-49	440	6	june	june	PROPN
flr-49	440	7	)	)	PUNCT
flr-49	440	8	,	,	PUNCT
flr-49	440	9	163	163	NUM
flr-49	440	10	-	-	SYM
flr-49	440	11	171	171	NUM
flr-49	440	12	.	.	PUNCT
flr-49	441	1	doi	doi	NOUN
flr-49	441	2	:	:	PUNCT
flr-49	441	3	10.1016	10.1016	NUM
flr-49	441	4	/	/	SYM
flr-49	441	5	j.brainres.2007.04.040	j.brainres.2007.04.040	PROPN
flr-49	441	6	lee	lee	PROPN
flr-49	441	7	,	,	PUNCT
flr-49	441	8	k.	k.	PROPN
flr-49	441	9	,	,	PUNCT
flr-49	441	10	ng	ng	PROPN
flr-49	441	11	,	,	PUNCT
flr-49	441	12	s.	s.	PROPN
flr-49	441	13	f.	f.	PROPN
flr-49	441	14	,	,	PUNCT
flr-49	441	15	bull	bull	PROPN
flr-49	441	16	,	,	PUNCT
flr-49	441	17	r.	r.	PROPN
flr-49	441	18	,	,	PUNCT
flr-49	441	19	pe	pe	PROPN
flr-49	441	20	,	,	PUNCT
flr-49	441	21	m.	m.	NOUN
flr-49	441	22	l.	l.	PROPN
flr-49	441	23	,	,	PUNCT
flr-49	441	24	&	&	CCONJ
flr-49	441	25	ho	ho	PROPN
flr-49	441	26	,	,	PUNCT
flr-49	441	27	r.	r.	PROPN
flr-49	441	28	h.	h.	PROPN
flr-49	441	29	m.	m.	PROPN
flr-49	441	30	(	(	PUNCT
flr-49	441	31	2011	2011	NUM
flr-49	441	32	)	)	PUNCT
flr-49	441	33	.	.	PUNCT
flr-49	442	1	are	be	AUX
flr-49	442	2	patterns	pattern	NOUN
flr-49	442	3	important	important	ADJ
flr-49	442	4	?	?	PUNCT
flr-49	443	1	an	an	DET
flr-49	443	2	investigation	investigation	NOUN
flr-49	443	3	of	of	ADP
flr-49	443	4	the	the	DET
flr-49	443	5	relationships	relationship	NOUN
flr-49	443	6	between	between	ADP
flr-49	443	7	proficiencies	proficiency	NOUN
flr-49	443	8	in	in	ADP
flr-49	443	9	patterns	pattern	NOUN
flr-49	443	10	,	,	PUNCT
flr-49	443	11	computation	computation	NOUN
flr-49	443	12	,	,	PUNCT
flr-49	443	13	executive	executive	ADJ
flr-49	443	14	functioning	functioning	NOUN
flr-49	443	15	,	,	PUNCT
flr-49	443	16	and	and	CCONJ
flr-49	443	17	algebraic	algebraic	ADJ
flr-49	443	18	word	word	NOUN
flr-49	443	19	problems	problem	NOUN
flr-49	443	20	.	.	PUNCT
flr-49	444	1	journal	journal	NOUN
flr-49	444	2	of	of	ADP
flr-49	444	3	educational	educational	ADJ
flr-49	444	4	psychology	psychology	NOUN
flr-49	444	5	,	,	PUNCT
flr-49	444	6	103(2	103(2	NUM
flr-49	444	7	)	)	PUNCT
flr-49	444	8	,	,	PUNCT
flr-49	444	9	269	269	NUM
flr-49	444	10	-	-	SYM
flr-49	444	11	281	281	NUM
flr-49	444	12	.	.	PUNCT
flr-49	445	1	doi	doi	NOUN
flr-49	445	2	:	:	PUNCT
flr-49	445	3	10.1037	10.1037	NUM
flr-49	445	4	/	/	SYM
flr-49	445	5	a0023068	a0023068	PROPN
flr-49	445	6	lee	lee	PROPN
flr-49	445	7	,	,	PUNCT
flr-49	445	8	k.	k.	PROPN
flr-49	445	9	,	,	PUNCT
flr-49	445	10	yeong	yeong	PROPN
flr-49	445	11	,	,	PUNCT
flr-49	445	12	s.	s.	PROPN
flr-49	445	13	h.	h.	PROPN
flr-49	445	14	m.	m.	PROPN
flr-49	445	15	,	,	PUNCT
flr-49	445	16	ng	ng	PROPN
flr-49	445	17	,	,	PUNCT
flr-49	445	18	s.	s.	PROPN
flr-49	445	19	f.	f.	PROPN
flr-49	445	20	,	,	PUNCT
flr-49	445	21	venkatraman	venkatraman	NOUN
flr-49	445	22	,	,	PUNCT
flr-49	445	23	v.	v.	PROPN
flr-49	445	24	,	,	PUNCT
flr-49	445	25	graham	graham	PROPN
flr-49	445	26	,	,	PUNCT
flr-49	445	27	s.	s.	PROPN
flr-49	445	28	,	,	PUNCT
flr-49	445	29	&	&	CCONJ
flr-49	445	30	chee	chee	NOUN
flr-49	445	31	,	,	PUNCT
flr-49	445	32	m.	m.	NOUN
flr-49	445	33	w.	w.	PROPN
flr-49	445	34	l.	l.	PROPN
flr-49	445	35	(	(	PUNCT
flr-49	445	36	2010	2010	NUM
flr-49	445	37	)	)	PUNCT
flr-49	445	38	.	.	PUNCT
flr-49	446	1	computing	compute	VERB
flr-49	446	2	solutions	solution	NOUN
flr-49	446	3	to	to	ADP
flr-49	446	4	algebraic	algebraic	ADJ
flr-49	446	5	problems	problem	NOUN
flr-49	446	6	using	use	VERB
flr-49	446	7	a	a	DET
flr-49	446	8	symbolic	symbolic	NOUN
flr-49	446	9	versus	versus	ADP
flr-49	446	10	a	a	DET
flr-49	446	11	schematic	schematic	ADJ
flr-49	446	12	strategy	strategy	NOUN
flr-49	446	13	.	.	PUNCT
flr-49	447	1	zdm	zdm	NOUN
flr-49	447	2	,	,	PUNCT
flr-49	447	3	42(6	42(6	NOUN
flr-49	447	4	)	)	PUNCT
flr-49	447	5	,	,	PUNCT
flr-49	447	6	591	591	NUM
flr-49	447	7	-	-	SYM
flr-49	447	8	605	605	NUM
flr-49	447	9	.	.	PUNCT
flr-49	448	1	doi	doi	NOUN
flr-49	448	2	:	:	PUNCT
flr-49	448	3	10.1007	10.1007	NUM
flr-49	448	4	/	/	SYM
flr-49	448	5	s11858	s11858	NOUN
flr-49	448	6	-	-	PUNCT
flr-49	448	7	010	010	NUM
flr-49	448	8	-	-	PUNCT
flr-49	448	9	0265	0265	NUM
flr-49	448	10	-	-	SYM
flr-49	448	11	6	6	NUM
flr-49	448	12	lim	lim	PROPN
flr-49	448	13	,	,	PUNCT
flr-49	448	14	b.	b.	PROPN
flr-49	448	15	t.	t.	PROPN
flr-49	448	16	(	(	PUNCT
flr-49	448	17	2007	2007	NUM
flr-49	448	18	)	)	PUNCT
flr-49	448	19	.	.	PUNCT
flr-49	449	1	can	can	AUX
flr-49	449	2	algebra	algebra	NOUN
flr-49	449	3	be	be	AUX
flr-49	449	4	used	use	VERB
flr-49	449	5	to	to	PART
flr-49	449	6	solve	solve	VERB
flr-49	449	7	psle	psle	NOUN
flr-49	449	8	maths	math	NOUN
flr-49	449	9	problems	problem	NOUN
flr-49	449	10	,	,	PUNCT
flr-49	449	11	the	the	DET
flr-49	449	12	strait	strait	PROPN
flr-49	449	13	times	time	NOUN
flr-49	449	14	.	.	PUNCT
flr-49	450	1	retrieved	retrieve	VERB
flr-49	450	2	from	from	ADP
flr-49	450	3	http://www.moe.gov.sg/media/forum/2007/forum_letters/20070217.pdf	http://www.moe.gov.sg/media/forum/2007/forum_letters/20070217.pdf	PROPN
flr-49	450	4	macgregor	macgregor	PROPN
flr-49	450	5	,	,	PUNCT
flr-49	450	6	m.	m.	NOUN
flr-49	450	7	,	,	PUNCT
flr-49	450	8	&	&	CCONJ
flr-49	450	9	stacey	stacey	PROPN
flr-49	450	10	,	,	PUNCT
flr-49	450	11	k.	k.	PROPN
flr-49	450	12	(	(	PUNCT
flr-49	450	13	1997	1997	NUM
flr-49	450	14	)	)	PUNCT
flr-49	450	15	.	.	PUNCT
flr-49	451	1	students	student	NOUN
flr-49	451	2	'	'	PART
flr-49	451	3	understanding	understanding	NOUN
flr-49	451	4	of	of	ADP
flr-49	451	5	algebraic	algebraic	ADJ
flr-49	451	6	notation	notation	NOUN
flr-49	451	7	:	:	PUNCT
flr-49	451	8	11	11	NUM
flr-49	451	9	-	-	SYM
flr-49	451	10	15	15	NUM
flr-49	451	11	.	.	PUNCT
flr-49	452	1	educational	educational	ADJ
flr-49	452	2	studies	study	NOUN
flr-49	452	3	in	in	ADP
flr-49	452	4	mathematics	mathematic	NOUN
flr-49	452	5	,	,	PUNCT
flr-49	452	6	33(1	33(1	NUM
flr-49	452	7	)	)	PUNCT
flr-49	452	8	,	,	PUNCT
flr-49	452	9	1	1	NUM
flr-49	452	10	-	-	SYM
flr-49	452	11	19	19	NUM
flr-49	452	12	.	.	PUNCT
flr-49	452	13	doi	doi	NOUN
flr-49	452	14	:	:	PUNCT
flr-49	452	15	10.1023	10.1023	NUM
flr-49	452	16	/	/	SYM
flr-49	452	17	a:1002970913563	a:1002970913563	PROPN
flr-49	452	18	mayer	mayer	PROPN
flr-49	452	19	,	,	PUNCT
flr-49	452	20	r.	r.	PROPN
flr-49	452	21	e.	e.	PROPN
flr-49	452	22	(	(	PUNCT
flr-49	452	23	1989	1989	NUM
flr-49	452	24	)	)	PUNCT
flr-49	452	25	.	.	PUNCT
flr-49	453	1	systematic	systematic	ADJ
flr-49	453	2	thinking	thinking	NOUN
flr-49	453	3	fostered	foster	VERB
flr-49	453	4	by	by	ADP
flr-49	453	5	illustrations	illustration	NOUN
flr-49	453	6	in	in	ADP
flr-49	453	7	scientific	scientific	ADJ
flr-49	453	8	text	text	NOUN
flr-49	453	9	.	.	PUNCT
flr-49	454	1	journal	journal	PROPN
flr-49	454	2	of	of	ADP
flr-49	454	3	educational	educational	ADJ
flr-49	454	4	psychology	psychology	NOUN
flr-49	454	5	,	,	PUNCT
flr-49	454	6	81(2	81(2	NUM
flr-49	454	7	)	)	PUNCT
flr-49	454	8	,	,	PUNCT
flr-49	454	9	240	240	NUM
flr-49	454	10	.	.	PUNCT
flr-49	455	1	mayer	mayer	PROPN
flr-49	455	2	,	,	PUNCT
flr-49	455	3	r.	r.	PROPN
flr-49	455	4	e.	e.	PROPN
flr-49	455	5	(	(	PUNCT
flr-49	455	6	2002	2002	NUM
flr-49	455	7	)	)	PUNCT
flr-49	455	8	.	.	PUNCT
flr-49	456	1	multimedia	multimedia	PROPN
flr-49	456	2	learning	learning	NOUN
flr-49	456	3	.	.	PUNCT
flr-49	457	1	psychology	psychology	NOUN
flr-49	457	2	of	of	ADP
flr-49	457	3	learning	learning	NOUN
flr-49	457	4	and	and	CCONJ
flr-49	457	5	motivation	motivation	NOUN
flr-49	457	6	,	,	PUNCT
flr-49	457	7	41	41	NUM
flr-49	457	8	,	,	PUNCT
flr-49	457	9	85	85	NUM
flr-49	457	10	-	-	SYM
flr-49	457	11	139	139	NUM
flr-49	457	12	.	.	PUNCT
flr-49	458	1	meter	meter	NOUN
flr-49	458	2	,	,	PUNCT
flr-49	458	3	p.	p.	NOUN
flr-49	458	4	,	,	PUNCT
flr-49	458	5	&	&	CCONJ
flr-49	458	6	garner	garner	PROPN
flr-49	458	7	,	,	PUNCT
flr-49	458	8	j.	j.	PROPN
flr-49	458	9	(	(	PUNCT
flr-49	458	10	2005	2005	NUM
flr-49	458	11	)	)	PUNCT
flr-49	458	12	.	.	PUNCT
flr-49	459	1	the	the	DET
flr-49	459	2	promise	promise	NOUN
flr-49	459	3	and	and	CCONJ
flr-49	459	4	practice	practice	NOUN
flr-49	459	5	of	of	ADP
flr-49	459	6	learner	learner	NOUN
flr-49	459	7	-	-	PUNCT
flr-49	459	8	generated	generate	VERB
flr-49	459	9	drawing	drawing	NOUN
flr-49	459	10	:	:	PUNCT
flr-49	459	11	literature	literature	NOUN
flr-49	459	12	review	review	NOUN
flr-49	459	13	and	and	CCONJ
flr-49	459	14	synthesis	synthesis	NOUN
flr-49	459	15	.	.	PUNCT
flr-49	460	1	educational	educational	ADJ
flr-49	460	2	psychology	psychology	NOUN
flr-49	460	3	review	review	PROPN
flr-49	460	4	,	,	PUNCT
flr-49	460	5	17(4	17(4	NUM
flr-49	460	6	)	)	PUNCT
flr-49	460	7	,	,	PUNCT
flr-49	460	8	285	285	NUM
flr-49	460	9	-	-	SYM
flr-49	460	10	325	325	NUM
flr-49	460	11	.	.	PUNCT
flr-49	461	1	doi	doi	NOUN
flr-49	461	2	:	:	PUNCT
flr-49	461	3	10.1007	10.1007	NUM
flr-49	461	4	/	/	SYM
flr-49	461	5	s10648	s10648	NOUN
flr-49	461	6	-	-	PUNCT
flr-49	461	7	005	005	NUM
flr-49	461	8	-	-	PUNCT
flr-49	461	9	8136	8136	NUM
flr-49	461	10	-	-	SYM
flr-49	461	11	3	3	NUM
flr-49	461	12	mullis	mullis	NOUN
flr-49	461	13	,	,	PUNCT
flr-49	461	14	i.	i.	PROPN
flr-49	461	15	v.	v.	PROPN
flr-49	461	16	s.	s.	PROPN
flr-49	461	17	,	,	PUNCT
flr-49	461	18	martin	martin	PROPN
flr-49	461	19	,	,	PUNCT
flr-49	461	20	m.	m.	NOUN
flr-49	461	21	o.	o.	PROPN
flr-49	461	22	,	,	PUNCT
flr-49	461	23	gonzalez	gonzalez	PROPN
flr-49	461	24	,	,	PUNCT
flr-49	461	25	e.	e.	PROPN
flr-49	461	26	j.	j.	PROPN
flr-49	461	27	,	,	PUNCT
flr-49	461	28	&	&	CCONJ
flr-49	461	29	chrostowski	chrostowski	PROPN
flr-49	461	30	,	,	PUNCT
flr-49	461	31	s.	s.	PROPN
flr-49	461	32	j.	j.	PROPN
flr-49	461	33	(	(	PUNCT
flr-49	461	34	2004	2004	NUM
flr-49	461	35	)	)	PUNCT
flr-49	461	36	.	.	PUNCT
flr-49	462	1	timss	timss	PROPN
flr-49	462	2	2003	2003	NUM
flr-49	462	3	international	international	ADJ
flr-49	462	4	mathematics	mathematic	NOUN
flr-49	462	5	report	report	NOUN
flr-49	462	6	:	:	PUNCT
flr-49	462	7	findings	finding	NOUN
flr-49	462	8	from	from	ADP
flr-49	462	9	iea	iea	NOUN
flr-49	462	10	's	's	PART
flr-49	462	11	trends	trend	NOUN
flr-49	462	12	in	in	ADP
flr-49	462	13	international	international	ADJ
flr-49	462	14	mathematics	mathematic	NOUN
flr-49	462	15	and	and	CCONJ
flr-49	462	16	science	science	NOUN
flr-49	462	17	study	study	NOUN
flr-49	462	18	at	at	ADP
flr-49	462	19	the	the	DET
flr-49	462	20	fourth	fourth	ADJ
flr-49	462	21	and	and	CCONJ
flr-49	462	22	eighth	eighth	ADJ
flr-49	462	23	grades	grade	NOUN
flr-49	462	24	.	.	PUNCT
flr-49	463	1	chestnut	chestnut	PROPN
flr-49	463	2	hill	hill	PROPN
flr-49	463	3	,	,	PUNCT
flr-49	463	4	ma	ma	PROPN
flr-49	463	5	:	:	PUNCT
flr-49	463	6	boston	boston	PROPN
flr-49	463	7	college	college	PROPN
flr-49	463	8	.	.	PUNCT
flr-49	464	1	nathan	nathan	PROPN
flr-49	464	2	,	,	PUNCT
flr-49	464	3	m.	m.	PROPN
flr-49	464	4	j.	j.	PROPN
flr-49	464	5	,	,	PUNCT
flr-49	464	6	&	&	CCONJ
flr-49	464	7	koedinger	koedinger	PROPN
flr-49	464	8	,	,	PUNCT
flr-49	464	9	k.	k.	PROPN
flr-49	464	10	r.	r.	PROPN
flr-49	464	11	(	(	PUNCT
flr-49	464	12	2000	2000	NUM
flr-49	464	13	)	)	PUNCT
flr-49	464	14	.	.	PUNCT
flr-49	465	1	teachers	teacher	NOUN
flr-49	465	2	'	'	PART
flr-49	465	3	and	and	CCONJ
flr-49	465	4	researchers	researcher	NOUN
flr-49	465	5	'	'	PART
flr-49	465	6	beliefs	belief	NOUN
flr-49	465	7	about	about	ADP
flr-49	465	8	the	the	DET
flr-49	465	9	development	development	NOUN
flr-49	465	10	of	of	ADP
flr-49	465	11	algebraic	algebraic	ADJ
flr-49	465	12	reasoning	reasoning	NOUN
flr-49	465	13	.	.	PUNCT
flr-49	466	1	journal	journal	PROPN
flr-49	466	2	for	for	ADP
flr-49	466	3	research	research	NOUN
flr-49	466	4	in	in	ADP
flr-49	466	5	mathematics	mathematics	PROPN
flr-49	466	6	education	education	NOUN
flr-49	466	7	,	,	PUNCT
flr-49	466	8	31(2	31(2	NUM
flr-49	466	9	)	)	PUNCT
flr-49	466	10	,	,	PUNCT
flr-49	466	11	168	168	NUM
flr-49	466	12	-	-	SYM
flr-49	466	13	190	190	NUM
flr-49	466	14	.	.	PUNCT
flr-49	467	1	doi	doi	NOUN
flr-49	467	2	:	:	PUNCT
flr-49	467	3	10.2307/749750	10.2307/749750	NUM
flr-49	467	4	national	national	PROPN
flr-49	467	5	council	council	PROPN
flr-49	467	6	for	for	ADP
flr-49	467	7	teachers	teacher	NOUN
flr-49	467	8	of	of	ADP
flr-49	467	9	mathematics	mathematic	NOUN
flr-49	467	10	.	.	PUNCT
flr-49	468	1	(	(	PUNCT
flr-49	468	2	2000	2000	NUM
flr-49	468	3	)	)	PUNCT
flr-49	468	4	.	.	PUNCT
flr-49	469	1	principles	principle	NOUN
flr-49	469	2	and	and	CCONJ
flr-49	469	3	standards	standard	NOUN
flr-49	469	4	for	for	ADP
flr-49	469	5	school	school	NOUN
flr-49	469	6	mathematics	mathematic	NOUN
flr-49	469	7	.	.	PUNCT
flr-49	470	1	reston	reston	PROPN
flr-49	470	2	,	,	PUNCT
flr-49	470	3	va	va	PROPN
flr-49	470	4	:	:	PUNCT
flr-49	470	5	national	national	ADJ
flr-49	470	6	council	council	PROPN
flr-49	470	7	for	for	ADP
flr-49	470	8	teachers	teacher	NOUN
flr-49	470	9	of	of	ADP
flr-49	470	10	mathematics	mathematic	NOUN
flr-49	470	11	.	.	PUNCT
flr-49	471	1	national	national	PROPN
flr-49	471	2	mathematics	mathematics	PROPN
flr-49	471	3	advisory	advisory	ADJ
flr-49	471	4	panel	panel	NOUN
flr-49	471	5	.	.	PUNCT
flr-49	472	1	(	(	PUNCT
flr-49	472	2	2008	2008	NUM
flr-49	472	3	)	)	PUNCT
flr-49	472	4	.	.	PUNCT
flr-49	473	1	foundations	foundation	NOUN
flr-49	473	2	for	for	ADP
flr-49	473	3	success	success	NOUN
flr-49	473	4	:	:	PUNCT
flr-49	473	5	the	the	DET
flr-49	473	6	final	final	ADJ
flr-49	473	7	report	report	NOUN
flr-49	473	8	of	of	ADP
flr-49	473	9	the	the	DET
flr-49	473	10	national	national	PROPN
flr-49	473	11	mathematics	mathematics	PROPN
flr-49	473	12	advisory	advisory	ADJ
flr-49	473	13	panel	panel	NOUN
flr-49	473	14	.	.	PUNCT
flr-49	474	1	washington	washington	PROPN
flr-49	474	2	,	,	PUNCT
flr-49	474	3	dc	dc	PROPN
flr-49	474	4	:	:	PUNCT
flr-49	474	5	u.s	u.s	PROPN
flr-49	474	6	.	.	PROPN
flr-49	474	7	department	department	PROPN
flr-49	474	8	of	of	ADP
flr-49	474	9	education	education	NOUN
flr-49	474	10	.	.	PUNCT
flr-49	475	1	ng	ng	PROPN
flr-49	475	2	,	,	PUNCT
flr-49	475	3	s.	s.	PROPN
flr-49	475	4	f.	f.	PROPN
flr-49	475	5	(	(	PUNCT
flr-49	475	6	2003	2003	NUM
flr-49	475	7	)	)	PUNCT
flr-49	475	8	.	.	PUNCT
flr-49	476	1	how	how	SCONJ
flr-49	476	2	secondary	secondary	ADJ
flr-49	476	3	two	two	NUM
flr-49	476	4	express	express	ADJ
flr-49	476	5	stream	stream	NOUN
flr-49	476	6	students	student	NOUN
flr-49	476	7	used	use	VERB
flr-49	476	8	algebra	algebra	NOUN
flr-49	476	9	and	and	CCONJ
flr-49	476	10	the	the	DET
flr-49	476	11	model	model	NOUN
flr-49	476	12	method	method	NOUN
flr-49	476	13	to	to	PART
flr-49	476	14	solve	solve	VERB
flr-49	476	15	problems	problem	NOUN
flr-49	476	16	.	.	PUNCT
flr-49	477	1	the	the	DET
flr-49	477	2	mathematics	mathematics	NOUN
flr-49	477	3	educator	educator	NOUN
flr-49	477	4	,	,	PUNCT
flr-49	477	5	7(1	7(1	NUM
flr-49	477	6	)	)	PUNCT
flr-49	477	7	,	,	PUNCT
flr-49	477	8	1	1	NUM
flr-49	477	9	-	-	SYM
flr-49	477	10	17	17	NUM
flr-49	477	11	.	.	PUNCT
flr-49	477	12	ng	ng	PROPN
flr-49	477	13	,	,	PUNCT
flr-49	477	14	s.	s.	PROPN
flr-49	477	15	f.	f.	PROPN
flr-49	477	16	,	,	PUNCT
flr-49	477	17	&	&	CCONJ
flr-49	477	18	lee	lee	PROPN
flr-49	477	19	,	,	PUNCT
flr-49	477	20	k.	k.	PROPN
flr-49	477	21	(	(	PUNCT
flr-49	477	22	2005	2005	NUM
flr-49	477	23	)	)	PUNCT
flr-49	477	24	.	.	PUNCT
flr-49	478	1	how	how	SCONJ
flr-49	478	2	primary	primary	ADJ
flr-49	478	3	five	five	NUM
flr-49	478	4	pupils	pupil	NOUN
flr-49	478	5	use	use	VERB
flr-49	478	6	the	the	DET
flr-49	478	7	model	model	NOUN
flr-49	478	8	method	method	NOUN
flr-49	478	9	to	to	PART
flr-49	478	10	solve	solve	VERB
flr-49	478	11	word	word	NOUN
flr-49	478	12	problems	problem	NOUN
flr-49	478	13	.	.	PUNCT
flr-49	479	1	the	the	DET
flr-49	479	2	mathematics	mathematics	NOUN
flr-49	479	3	educator	educator	NOUN
flr-49	479	4	,	,	PUNCT
flr-49	479	5	9(1	9(1	NUM
flr-49	479	6	)	)	PUNCT
flr-49	479	7	,	,	PUNCT
flr-49	479	8	60	60	NUM
flr-49	479	9	-	-	SYM
flr-49	479	10	84	84	NUM
flr-49	479	11	.	.	PUNCT
flr-49	480	1	ng	ng	PROPN
flr-49	480	2	,	,	PUNCT
flr-49	480	3	s.	s.	PROPN
flr-49	480	4	f.	f.	PROPN
flr-49	480	5	,	,	PUNCT
flr-49	480	6	&	&	CCONJ
flr-49	480	7	lee	lee	PROPN
flr-49	480	8	,	,	PUNCT
flr-49	480	9	k.	k.	PROPN
flr-49	480	10	(	(	PUNCT
flr-49	480	11	2008	2008	NUM
flr-49	480	12	)	)	PUNCT
flr-49	480	13	.	.	PUNCT
flr-49	481	1	as	as	ADV
flr-49	481	2	long	long	ADV
flr-49	481	3	as	as	SCONJ
flr-49	481	4	the	the	DET
flr-49	481	5	drawing	drawing	NOUN
flr-49	481	6	is	be	AUX
flr-49	481	7	logical	logical	ADJ
flr-49	481	8	,	,	PUNCT
flr-49	481	9	size	size	NOUN
flr-49	481	10	does	do	AUX
flr-49	481	11	not	not	PART
flr-49	481	12	matter	matter	VERB
flr-49	481	13	.	.	PUNCT
flr-49	482	1	the	the	DET
flr-49	482	2	korean	korean	ADJ
flr-49	482	3	journal	journal	NOUN
flr-49	482	4	of	of	ADP
flr-49	482	5	thinking	thinking	NOUN
flr-49	482	6	&	&	CCONJ
flr-49	482	7	problem	problem	NOUN
flr-49	482	8	solving	solving	NOUN
flr-49	482	9	,	,	PUNCT
flr-49	482	10	18(1	18(1	NUM
flr-49	482	11	)	)	PUNCT
flr-49	482	12	,	,	PUNCT
flr-49	482	13	67	67	NUM
flr-49	482	14	-	-	SYM
flr-49	482	15	82	82	NUM
flr-49	482	16	.	.	PUNCT
flr-49	482	17	ng	ng	PROPN
flr-49	482	18	,	,	PUNCT
flr-49	482	19	s.	s.	PROPN
flr-49	482	20	f.	f.	PROPN
flr-49	482	21	,	,	PUNCT
flr-49	482	22	&	&	CCONJ
flr-49	482	23	lee	lee	PROPN
flr-49	482	24	,	,	PUNCT
flr-49	482	25	k.	k.	PROPN
flr-49	482	26	(	(	PUNCT
flr-49	482	27	2009	2009	NUM
flr-49	482	28	)	)	PUNCT
flr-49	482	29	.	.	PUNCT
flr-49	483	1	model	model	NOUN
flr-49	483	2	method	method	PROPN
flr-49	483	3	:	:	PUNCT
flr-49	483	4	singapore	singapore	PROPN
flr-49	483	5	children	children	PROPN
flr-49	483	6	's	's	PART
flr-49	483	7	tool	tool	NOUN
flr-49	483	8	for	for	ADP
flr-49	483	9	representing	represent	VERB
flr-49	483	10	and	and	CCONJ
flr-49	483	11	solving	solve	VERB
flr-49	483	12	algebra	algebra	NOUN
flr-49	483	13	word	word	NOUN
flr-49	483	14	problems	problem	NOUN
flr-49	483	15	.	.	PUNCT
flr-49	484	1	journal	journal	PROPN
flr-49	484	2	for	for	ADP
flr-49	484	3	research	research	NOUN
flr-49	484	4	in	in	ADP
flr-49	484	5	mathematics	mathematics	PROPN
flr-49	484	6	education	education	NOUN
flr-49	484	7	,	,	PUNCT
flr-49	484	8	40(3	40(3	NUM
flr-49	484	9	)	)	PUNCT
flr-49	484	10	,	,	PUNCT
flr-49	484	11	282	282	NUM
flr-49	484	12	-	-	SYM
flr-49	484	13	313	313	NUM
flr-49	484	14	.	.	PUNCT
flr-49	485	1	ng	ng	PROPN
flr-49	485	2	,	,	PUNCT
flr-49	485	3	s.	s.	PROPN
flr-49	485	4	f.	f.	PROPN
flr-49	485	5	,	,	PUNCT
flr-49	485	6	lee	lee	PROPN
flr-49	485	7	,	,	PUNCT
flr-49	485	8	k.	k.	PROPN
flr-49	485	9	,	,	PUNCT
flr-49	485	10	ang	ang	PROPN
flr-49	485	11	,	,	PUNCT
flr-49	485	12	s.	s.	PROPN
flr-49	485	13	y.	y.	PROPN
flr-49	485	14	,	,	PUNCT
flr-49	485	15	&	&	CCONJ
flr-49	485	16	khng	khng	PROPN
flr-49	485	17	,	,	PUNCT
flr-49	485	18	f.	f.	PROPN
flr-49	485	19	(	(	PUNCT
flr-49	485	20	2006	2006	NUM
flr-49	485	21	)	)	PUNCT
flr-49	485	22	.	.	PUNCT
flr-49	486	1	model	model	NOUN
flr-49	486	2	method	method	PROPN
flr-49	486	3	:	:	PUNCT
flr-49	486	4	obstacle	obstacle	NOUN
flr-49	486	5	or	or	CCONJ
flr-49	486	6	bridge	bridge	NOUN
flr-49	486	7	to	to	ADP
flr-49	486	8	learning	learn	VERB
flr-49	486	9	symbolic	symbolic	ADJ
flr-49	486	10	algebra	algebra	NOUN
flr-49	486	11	.	.	PUNCT
flr-49	487	1	in	in	ADP
flr-49	487	2	w.	w.	PROPN
flr-49	487	3	bokhorst	bokhorst	PROPN
flr-49	487	4	-	-	PUNCT
flr-49	487	5	heng	heng	PROPN
flr-49	487	6	,	,	PUNCT
flr-49	487	7	m.	m.	NOUN
flr-49	487	8	osborne	osborne	PROPN
flr-49	487	9	&	&	CCONJ
flr-49	487	10	k.	k.	PROPN
flr-49	487	11	lee	lee	PROPN
flr-49	487	12	(	(	PUNCT
flr-49	487	13	eds	eds	PROPN
flr-49	487	14	.	.	PUNCT
flr-49	487	15	)	)	PUNCT
flr-49	487	16	,	,	PUNCT
flr-49	487	17	redesigning	redesign	VERB
flr-49	487	18	pedagogies	pedagogy	NOUN
flr-49	487	19	(	(	PUNCT
flr-49	487	20	pp	pp	ADJ
flr-49	487	21	.	.	PUNCT
flr-49	488	1	227	227	NUM
flr-49	488	2	-	-	NUM
flr-49	488	3	242	242	NUM
flr-49	488	4	)	)	PUNCT
flr-49	488	5	.	.	PUNCT
flr-49	489	1	ny	ny	PROPN
flr-49	489	2	:	:	PUNCT
flr-49	489	3	sense	sense	NOUN
flr-49	489	4	.	.	PUNCT
flr-49	490	1	oecd	oecd	PROPN
flr-49	490	2	(	(	PUNCT
flr-49	490	3	2010	2010	NUM
flr-49	490	4	)	)	PUNCT
flr-49	490	5	.	.	PUNCT
flr-49	491	1	pisa	pisa	PROPN
flr-49	491	2	2009	2009	NUM
flr-49	491	3	results	result	NOUN
flr-49	491	4	:	:	PUNCT
flr-49	491	5	executive	executive	ADJ
flr-49	491	6	summary	summary	NOUN
flr-49	491	7	.	.	PUNCT
flr-49	492	1	retrieved	retrieve	VERB
flr-49	492	2	from	from	ADP
flr-49	492	3	http://www.oecd.org/pisa/pisaproducts/46619703.pdf	http://www.oecd.org/pisa/pisaproducts/46619703.pdf	PROPN
flr-49	492	4	philipp	philipp	PROPN
flr-49	492	5	,	,	PUNCT
flr-49	492	6	r.	r.	PROPN
flr-49	492	7	(	(	PUNCT
flr-49	492	8	1992	1992	NUM
flr-49	492	9	)	)	PUNCT
flr-49	492	10	.	.	PUNCT
flr-49	493	1	the	the	DET
flr-49	493	2	many	many	ADJ
flr-49	493	3	uses	use	NOUN
flr-49	493	4	of	of	ADP
flr-49	493	5	algebraic	algebraic	ADJ
flr-49	493	6	variables	variable	NOUN
flr-49	493	7	.	.	PUNCT
flr-49	494	1	mathematics	mathematic	NOUN
flr-49	494	2	teacher	teacher	NOUN
flr-49	494	3	,	,	PUNCT
flr-49	494	4	85	85	NUM
flr-49	494	5	,	,	PUNCT
flr-49	494	6	557	557	NUM
flr-49	494	7	-	-	SYM
flr-49	494	8	561	561	NUM
flr-49	494	9	.	.	PUNCT
flr-49	495	1	stacey	stacey	PROPN
flr-49	495	2	,	,	PUNCT
flr-49	495	3	k.	k.	PROPN
flr-49	495	4	,	,	PUNCT
flr-49	495	5	&	&	CCONJ
flr-49	495	6	macgregor	macgregor	PROPN
flr-49	495	7	,	,	PUNCT
flr-49	495	8	m.	m.	NOUN
flr-49	495	9	(	(	PUNCT
flr-49	495	10	1999	1999	NUM
flr-49	495	11	)	)	PUNCT
flr-49	495	12	.	.	PUNCT
flr-49	496	1	learning	learn	VERB
flr-49	496	2	the	the	DET
flr-49	496	3	algebraic	algebraic	ADJ
flr-49	496	4	method	method	NOUN
flr-49	496	5	of	of	ADP
flr-49	496	6	solving	solve	VERB
flr-49	496	7	problems	problem	NOUN
flr-49	496	8	.	.	PUNCT
flr-49	497	1	the	the	DET
flr-49	497	2	journal	journal	NOUN
flr-49	497	3	of	of	ADP
flr-49	497	4	mathematical	mathematical	ADJ
flr-49	497	5	behavior	behavior	NOUN
flr-49	497	6	,	,	PUNCT
flr-49	497	7	18(2	18(2	NUM
flr-49	497	8	)	)	PUNCT
flr-49	497	9	,	,	PUNCT
flr-49	497	10	149	149	NUM
flr-49	497	11	-	-	SYM
flr-49	497	12	167	167	NUM
flr-49	497	13	.	.	PUNCT
flr-49	498	1	steinberg	steinberg	PROPN
flr-49	498	2	,	,	PUNCT
flr-49	498	3	r.	r.	PROPN
flr-49	498	4	m.	m.	PROPN
flr-49	498	5	,	,	PUNCT
flr-49	498	6	sleeman	sleeman	PROPN
flr-49	498	7	,	,	PUNCT
flr-49	498	8	d.	d.	PROPN
flr-49	498	9	h.	h.	PROPN
flr-49	498	10	,	,	PUNCT
flr-49	498	11	&	&	CCONJ
flr-49	498	12	ktorza	ktorza	PROPN
flr-49	498	13	,	,	PUNCT
flr-49	498	14	d.	d.	PROPN
flr-49	498	15	(	(	PUNCT
flr-49	498	16	1991	1991	NUM
flr-49	498	17	)	)	PUNCT
flr-49	498	18	.	.	PUNCT
flr-49	499	1	algebra	algebra	PROPN
flr-49	499	2	students	student	NOUN
flr-49	499	3	'	'	PART
flr-49	499	4	knowledge	knowledge	NOUN
flr-49	499	5	of	of	ADP
flr-49	499	6	equivalence	equivalence	NOUN
flr-49	499	7	of	of	ADP
flr-49	499	8	equations	equation	NOUN
flr-49	499	9	.	.	PUNCT
flr-49	500	1	journal	journal	PROPN
flr-49	500	2	for	for	ADP
flr-49	500	3	research	research	NOUN
flr-49	500	4	in	in	ADP
flr-49	500	5	mathematics	mathematics	PROPN
flr-49	500	6	education	education	NOUN
flr-49	500	7	,	,	PUNCT
flr-49	500	8	22(2	22(2	NUM
flr-49	500	9	)	)	PUNCT
flr-49	500	10	,	,	PUNCT
flr-49	500	11	112	112	NUM
flr-49	500	12	-	-	SYM
flr-49	500	13	121	121	NUM
flr-49	500	14	.	.	PUNCT
flr-49	501	1	swafford	swafford	PROPN
flr-49	501	2	,	,	PUNCT
flr-49	501	3	j.	j.	PROPN
flr-49	501	4	o.	o.	PROPN
flr-49	501	5	,	,	PUNCT
flr-49	501	6	&	&	CCONJ
flr-49	501	7	langrall	langrall	PROPN
flr-49	501	8	,	,	PUNCT
flr-49	501	9	c.	c.	PROPN
flr-49	501	10	w.	w.	PROPN
flr-49	501	11	(	(	PUNCT
flr-49	501	12	2000	2000	NUM
flr-49	501	13	)	)	PUNCT
flr-49	501	14	.	.	PUNCT
flr-49	502	1	grade	grade	NOUN
flr-49	502	2	6	6	NUM
flr-49	502	3	students	student	NOUN
flr-49	502	4	'	'	PART
flr-49	502	5	preinstructional	preinstructional	ADJ
flr-49	502	6	use	use	NOUN
flr-49	502	7	of	of	ADP
flr-49	502	8	equations	equation	NOUN
flr-49	502	9	to	to	PART
flr-49	502	10	describe	describe	VERB
flr-49	502	11	and	and	CCONJ
flr-49	502	12	represent	represent	VERB
flr-49	502	13	problem	problem	NOUN
flr-49	502	14	situations	situation	NOUN
flr-49	502	15	.	.	PUNCT
flr-49	503	1	journal	journal	PROPN
flr-49	503	2	for	for	ADP
flr-49	503	3	research	research	NOUN
flr-49	503	4	in	in	ADP
flr-49	503	5	mathematics	mathematics	PROPN
flr-49	503	6	education	education	NOUN
flr-49	503	7	,	,	PUNCT
flr-49	503	8	31(1	31(1	NUM
flr-49	503	9	)	)	PUNCT
flr-49	503	10	,	,	PUNCT
flr-49	503	11	89	89	NUM
flr-49	503	12	-	-	SYM
flr-49	503	13	112	112	NUM
flr-49	503	14	.	.	PUNCT
flr-49	504	1	k.	k.	PROPN
flr-49	504	2	lee	lee	PROPN
flr-49	504	3	et	et	PROPN
flr-49	504	4	al	al	PROPN
flr-49	504	5	.	.	PROPN
flr-49	504	6	96	96	NUM
flr-49	505	1	|	|	NOUN
flr-49	505	2	f	f	NOUN
flr-49	505	3	l	l	NOUN
flr-49	505	4	r	r	NOUN
flr-49	505	5	tolar	tolar	PROPN
flr-49	505	6	,	,	PUNCT
flr-49	505	7	t.	t.	PROPN
flr-49	505	8	d.	d.	PROPN
flr-49	505	9	,	,	PUNCT
flr-49	505	10	lederberg	lederberg	PROPN
flr-49	505	11	,	,	PUNCT
flr-49	505	12	a.	a.	PROPN
flr-49	505	13	r.	r.	PROPN
flr-49	505	14	,	,	PUNCT
flr-49	505	15	&	&	CCONJ
flr-49	505	16	fletcher	fletcher	PROPN
flr-49	505	17	,	,	PUNCT
flr-49	505	18	j.	j.	PROPN
flr-49	505	19	m.	m.	PROPN
flr-49	505	20	(	(	PUNCT
flr-49	505	21	2009	2009	NUM
flr-49	505	22	)	)	PUNCT
flr-49	505	23	.	.	PUNCT
flr-49	506	1	a	a	DET
flr-49	506	2	structural	structural	ADJ
flr-49	506	3	model	model	NOUN
flr-49	506	4	of	of	ADP
flr-49	506	5	algebra	algebra	PROPN
flr-49	506	6	achievement	achievement	NOUN
flr-49	506	7	:	:	PUNCT
flr-49	506	8	computational	computational	ADJ
flr-49	506	9	fluency	fluency	NOUN
flr-49	506	10	and	and	CCONJ
flr-49	506	11	spatial	spatial	ADJ
flr-49	506	12	visualisation	visualisation	NOUN
flr-49	506	13	as	as	ADP
flr-49	506	14	mediators	mediator	NOUN
flr-49	506	15	of	of	ADP
flr-49	506	16	the	the	DET
flr-49	506	17	effect	effect	NOUN
flr-49	506	18	of	of	ADP
flr-49	506	19	working	work	VERB
flr-49	506	20	memory	memory	NOUN
flr-49	506	21	on	on	ADP
flr-49	506	22	algebra	algebra	PROPN
flr-49	506	23	achievement	achievement	NOUN
flr-49	506	24	.	.	PUNCT
flr-49	507	1	educational	educational	ADJ
flr-49	507	2	psychology	psychology	NOUN
flr-49	507	3	:	:	PUNCT
flr-49	507	4	an	an	DET
flr-49	507	5	international	international	ADJ
flr-49	507	6	journal	journal	NOUN
flr-49	507	7	of	of	ADP
flr-49	507	8	experimental	experimental	ADJ
flr-49	507	9	educational	educational	ADJ
flr-49	507	10	psychology	psychology	NOUN
flr-49	507	11	,	,	PUNCT
flr-49	507	12	29(2	29(2	NUM
flr-49	507	13	)	)	PUNCT
flr-49	507	14	,	,	PUNCT
flr-49	507	15	239	239	NUM
flr-49	507	16	-	-	SYM
flr-49	507	17	266	266	NUM
flr-49	507	18	.	.	PUNCT
flr-49	508	1	usiskin	usiskin	PROPN
flr-49	508	2	,	,	PUNCT
flr-49	508	3	z.	z.	PROPN
flr-49	508	4	(	(	PUNCT
flr-49	508	5	1988	1988	NUM
flr-49	508	6	)	)	PUNCT
flr-49	508	7	.	.	PUNCT
flr-49	509	1	conceptions	conception	NOUN
flr-49	509	2	of	of	ADP
flr-49	509	3	school	school	NOUN
flr-49	509	4	algebra	algebra	NOUN
flr-49	509	5	and	and	CCONJ
flr-49	509	6	uses	use	NOUN
flr-49	509	7	of	of	ADP
flr-49	509	8	variables	variable	NOUN
flr-49	509	9	.	.	PUNCT
flr-49	510	1	in	in	ADP
flr-49	510	2	a.	a.	PROPN
flr-49	510	3	f.	f.	PROPN
flr-49	510	4	coxford	coxford	PROPN
flr-49	510	5	&	&	CCONJ
flr-49	510	6	a.	a.	PROPN
flr-49	510	7	p.	p.	PROPN
flr-49	510	8	schulte	schulte	PROPN
flr-49	510	9	(	(	PUNCT
flr-49	510	10	eds	eds	PROPN
flr-49	510	11	.	.	PUNCT
flr-49	510	12	)	)	PUNCT
flr-49	510	13	,	,	PUNCT
flr-49	510	14	the	the	DET
flr-49	510	15	ideas	idea	NOUN
flr-49	510	16	of	of	ADP
flr-49	510	17	algebra	algebra	NOUN
flr-49	510	18	(	(	PUNCT
flr-49	510	19	pp	pp	ADJ
flr-49	510	20	.	.	PUNCT
flr-49	510	21	8	8	NUM
flr-49	510	22	-	-	SYM
flr-49	510	23	19	19	NUM
flr-49	510	24	)	)	PUNCT
flr-49	510	25	.	.	PUNCT
flr-49	511	1	reston	reston	PROPN
flr-49	511	2	,	,	PUNCT
flr-49	511	3	va	va	PROPN
flr-49	511	4	:	:	PUNCT
flr-49	511	5	national	national	ADJ
flr-49	511	6	council	council	PROPN
flr-49	511	7	of	of	ADP
flr-49	511	8	teachers	teacher	NOUN
flr-49	511	9	of	of	ADP
flr-49	511	10	mathematics	mathematics	PROPN
flr-49	511	11	.	.	PUNCT
flr-49	512	1	warren	warren	PROPN
flr-49	512	2	,	,	PUNCT
flr-49	512	3	e.	e.	PROPN
flr-49	512	4	,	,	PUNCT
flr-49	512	5	&	&	CCONJ
flr-49	512	6	cooper	cooper	PROPN
flr-49	512	7	,	,	PUNCT
flr-49	512	8	t.	t.	PROPN
flr-49	512	9	(	(	PUNCT
flr-49	512	10	2005	2005	NUM
flr-49	512	11	)	)	PUNCT
flr-49	512	12	.	.	PUNCT
flr-49	513	1	introducing	introduce	VERB
flr-49	513	2	functional	functional	ADJ
flr-49	513	3	thinking	thinking	NOUN
flr-49	513	4	in	in	ADP
flr-49	513	5	year	year	NOUN
flr-49	513	6	2	2	NUM
flr-49	513	7	:	:	PUNCT
flr-49	513	8	a	a	DET
flr-49	513	9	case	case	NOUN
flr-49	513	10	study	study	NOUN
flr-49	513	11	of	of	ADP
flr-49	513	12	early	early	ADJ
flr-49	513	13	algebra	algebra	NOUN
flr-49	513	14	teaching	teaching	NOUN
flr-49	513	15	.	.	PUNCT
flr-49	514	1	contemporary	contemporary	ADJ
flr-49	514	2	issues	issue	NOUN
flr-49	514	3	in	in	ADP
flr-49	514	4	early	early	ADJ
flr-49	514	5	childhood	childhood	NOUN
flr-49	514	6	,	,	PUNCT
flr-49	514	7	6(2	6(2	NUM
flr-49	514	8	)	)	PUNCT
flr-49	514	9	,	,	PUNCT
flr-49	514	10	150	150	NUM
flr-49	514	11	-	-	SYM
flr-49	514	12	162	162	NUM
flr-49	514	13	.	.	PUNCT
flr-49	515	1	warren	warren	PROPN
flr-49	515	2	,	,	PUNCT
flr-49	515	3	e.	e.	PROPN
flr-49	515	4	,	,	PUNCT
flr-49	515	5	&	&	CCONJ
flr-49	515	6	cooper	cooper	PROPN
flr-49	515	7	,	,	PUNCT
flr-49	515	8	t.	t.	PROPN
flr-49	515	9	j.	j.	PROPN
flr-49	515	10	(	(	PUNCT
flr-49	515	11	2009	2009	NUM
flr-49	515	12	)	)	PUNCT
flr-49	515	13	.	.	PUNCT
flr-49	516	1	developing	develop	VERB
flr-49	516	2	mathematics	mathematic	NOUN
flr-49	516	3	understanding	understanding	NOUN
flr-49	516	4	and	and	CCONJ
flr-49	516	5	abstraction	abstraction	NOUN
flr-49	516	6	:	:	PUNCT
flr-49	516	7	the	the	DET
flr-49	516	8	case	case	NOUN
flr-49	516	9	of	of	ADP
flr-49	516	10	equivalence	equivalence	NOUN
flr-49	516	11	in	in	ADP
flr-49	516	12	the	the	DET
flr-49	516	13	elementary	elementary	ADJ
flr-49	516	14	years	year	NOUN
flr-49	516	15	.	.	PUNCT
flr-49	517	1	mathematics	mathematic	NOUN
flr-49	517	2	education	education	PROPN
flr-49	517	3	research	research	NOUN
flr-49	517	4	journal	journal	NOUN
flr-49	517	5	,	,	PUNCT
flr-49	517	6	21(2	21(2	NUM
flr-49	517	7	)	)	PUNCT
flr-49	517	8	,	,	PUNCT
flr-49	517	9	76	76	NUM
flr-49	517	10	-	-	SYM
flr-49	517	11	95	95	NUM
flr-49	517	12	.	.	PUNCT
flr-49	518	1	wei	wei	PROPN
flr-49	518	2	,	,	PUNCT
flr-49	518	3	w.	w.	PROPN
flr-49	518	4	,	,	PUNCT
flr-49	518	5	yuan	yuan	PROPN
flr-49	518	6	,	,	PUNCT
flr-49	518	7	h.	h.	PROPN
flr-49	518	8	b.	b.	PROPN
flr-49	518	9	,	,	PUNCT
flr-49	518	10	chen	chen	PROPN
flr-49	518	11	,	,	PUNCT
flr-49	518	12	c.	c.	PROPN
flr-49	518	13	s.	s.	PROPN
flr-49	518	14	,	,	PUNCT
flr-49	518	15	&	&	CCONJ
flr-49	518	16	zhou	zhou	PROPN
flr-49	518	17	,	,	PUNCT
flr-49	518	18	x.	x.	PROPN
flr-49	518	19	l.	l.	PROPN
flr-49	518	20	(	(	PUNCT
flr-49	518	21	2012	2012	NUM
flr-49	518	22	)	)	PUNCT
flr-49	518	23	.	.	PUNCT
flr-49	519	1	cognitive	cognitive	ADJ
flr-49	519	2	correlates	correlate	NOUN
flr-49	519	3	of	of	ADP
flr-49	519	4	performance	performance	NOUN
flr-49	519	5	in	in	ADP
flr-49	519	6	advanced	advanced	ADJ
flr-49	519	7	mathematics	mathematic	NOUN
flr-49	519	8	.	.	PUNCT
flr-49	520	1	british	british	ADJ
flr-49	520	2	journal	journal	PROPN
flr-49	520	3	of	of	ADP
flr-49	520	4	educational	educational	ADJ
flr-49	520	5	psychology	psychology	NOUN
flr-49	520	6	,	,	PUNCT
flr-49	520	7	82(1	82(1	NOUN
flr-49	520	8	)	)	PUNCT
flr-49	520	9	,	,	PUNCT
flr-49	520	10	157	157	NUM
flr-49	520	11	-	-	SYM
flr-49	520	12	181	181	NUM
flr-49	520	13	.	.	PUNCT
flr-49	521	1	doi	doi	NOUN
flr-49	521	2	:	:	PUNCT
flr-49	521	3	10.1111	10.1111	NUM
flr-49	521	4	/	/	SYM
flr-49	521	5	j.20448279.2011.02049.x	j.20448279.2011.02049.x	NOUN