id	sid	tid	token	lemma	pos
educationr-2789	1	1	review	review	NOUN
educationr-2789	1	2	of	of	ADP
educationr-2789	1	3	how	how	SCONJ
educationr-2789	1	4	students	student	NOUN
educationr-2789	1	5	think	think	VERB
educationr-2789	1	6	when	when	SCONJ
educationr-2789	1	7	doing	do	VERB
educationr-2789	1	8	algebra	algebra	PROPN
educationr-2789	1	9	kassel	kassel	PROPN
educationr-2789	1	10	,	,	PUNCT
educationr-2789	1	11	a.	a.	NOUN
educationr-2789	1	12	(	(	PUNCT
educationr-2789	1	13	2020	2020	NUM
educationr-2789	1	14	,	,	PUNCT
educationr-2789	1	15	april	april	PROPN
educationr-2789	1	16	1	1	NUM
educationr-2789	1	17	)	)	PUNCT
educationr-2789	1	18	.	.	PUNCT
educationr-2789	2	1	review	review	NOUN
educationr-2789	2	2	of	of	ADP
educationr-2789	2	3	how	how	SCONJ
educationr-2789	2	4	students	student	NOUN
educationr-2789	2	5	think	think	VERB
educationr-2789	2	6	when	when	SCONJ
educationr-2789	2	7	doing	do	VERB
educationr-2789	2	8	algebra	algebra	NOUN
educationr-2789	2	9	by	by	ADP
educationr-2789	2	10	s.	s.	PROPN
educationr-2789	2	11	rhine	rhine	PROPN
educationr-2789	2	12	,	,	PUNCT
educationr-2789	2	13	r.	r.	PROPN
educationr-2789	2	14	harrington	harrington	PROPN
educationr-2789	2	15	,	,	PUNCT
educationr-2789	2	16	&	&	CCONJ
educationr-2789	2	17	c.	c.	PROPN
educationr-2789	2	18	starr	starr	PROPN
educationr-2789	2	19	.	.	PUNCT
educationr-2789	3	1	education	education	PROPN
educationr-2789	3	2	review	review	PROPN
educationr-2789	3	3	,	,	PUNCT
educationr-2789	3	4	27	27	NUM
educationr-2789	3	5	.	.	PUNCT
educationr-2789	4	1	http://dx.doi.org/10.14507/er.v27.2789	http://dx.doi.org/10.14507/er.v27.2789	ADJ
educationr-2789	4	2	april	april	PROPN
educationr-2789	4	3	1	1	NUM
educationr-2789	4	4	,	,	PUNCT
educationr-2789	4	5	2020	2020	NUM
educationr-2789	4	6	issn	issn	VERB
educationr-2789	4	7	1094	1094	NUM
educationr-2789	4	8	-	-	SYM
educationr-2789	4	9	5296	5296	NUM
educationr-2789	4	10	rhine	rhine	NOUN
educationr-2789	4	11	,	,	PUNCT
educationr-2789	4	12	s.	s.	PROPN
educationr-2789	4	13	,	,	PUNCT
educationr-2789	4	14	harrington	harrington	PROPN
educationr-2789	4	15	,	,	PUNCT
educationr-2789	4	16	r.	r.	PROPN
educationr-2789	4	17	,	,	PUNCT
educationr-2789	4	18	&	&	CCONJ
educationr-2789	4	19	starr	starr	PROPN
educationr-2789	4	20	,	,	PUNCT
educationr-2789	4	21	c.	c.	PROPN
educationr-2789	4	22	(	(	PUNCT
educationr-2789	4	23	2019	2019	NUM
educationr-2789	4	24	)	)	PUNCT
educationr-2789	4	25	.	.	PUNCT
educationr-2789	5	1	how	how	SCONJ
educationr-2789	5	2	students	student	NOUN
educationr-2789	5	3	think	think	VERB
educationr-2789	5	4	when	when	SCONJ
educationr-2789	5	5	doing	do	VERB
educationr-2789	5	6	algebra	algebra	NOUN
educationr-2789	5	7	.	.	PUNCT
educationr-2789	6	1	information	information	NOUN
educationr-2789	6	2	age	age	NOUN
educationr-2789	6	3	publishing	publishing	NOUN
educationr-2789	6	4	.	.	PUNCT
educationr-2789	7	1	pp	pp	ADJ
educationr-2789	7	2	.	.	PUNCT
educationr-2789	8	1	344	344	NUM
educationr-2789	8	2	isbn	isbn	NOUN
educationr-2789	8	3	:	:	PUNCT
educationr-2789	8	4	978	978	NUM
educationr-2789	8	5	-	-	SYM
educationr-2789	8	6	1	1	NUM
educationr-2789	8	7	-	-	PUNCT
educationr-2789	8	8	64113	64113	NUM
educationr-2789	8	9	-	-	PUNCT
educationr-2789	8	10	411	411	NUM
educationr-2789	8	11	-	-	SYM
educationr-2789	8	12	8	8	NUM
educationr-2789	8	13	reviewed	review	VERB
educationr-2789	8	14	by	by	ADP
educationr-2789	8	15	amy	amy	PROPN
educationr-2789	8	16	kassel	kassel	PROPN
educationr-2789	8	17	university	university	PROPN
educationr-2789	8	18	of	of	ADP
educationr-2789	8	19	wyoming	wyoming	PROPN
educationr-2789	8	20	united	united	PROPN
educationr-2789	8	21	states	states	PROPN
educationr-2789	8	22	the	the	DET
educationr-2789	8	23	national	national	PROPN
educationr-2789	8	24	council	council	PROPN
educationr-2789	8	25	for	for	ADP
educationr-2789	8	26	teachers	teacher	NOUN
educationr-2789	8	27	of	of	ADP
educationr-2789	8	28	mathematics	mathematic	NOUN
educationr-2789	8	29	set	set	VERB
educationr-2789	8	30	the	the	DET
educationr-2789	8	31	stage	stage	NOUN
educationr-2789	8	32	for	for	ADP
educationr-2789	8	33	equitable	equitable	ADJ
educationr-2789	8	34	mathematics	mathematic	NOUN
educationr-2789	8	35	learning	learn	VERB
educationr-2789	8	36	for	for	ADP
educationr-2789	8	37	all	all	DET
educationr-2789	8	38	students	student	NOUN
educationr-2789	8	39	in	in	ADP
educationr-2789	8	40	principles	principle	NOUN
educationr-2789	8	41	to	to	ADP
educationr-2789	8	42	actions	action	NOUN
educationr-2789	8	43	:	:	PUNCT
educationr-2789	8	44	ensuring	ensure	VERB
educationr-2789	8	45	mathematical	mathematical	ADJ
educationr-2789	8	46	success	success	NOUN
educationr-2789	8	47	for	for	ADP
educationr-2789	8	48	all	all	PRON
educationr-2789	8	49	(	(	PUNCT
educationr-2789	8	50	2014	2014	NUM
educationr-2789	8	51	)	)	PUNCT
educationr-2789	8	52	.	.	PUNCT
educationr-2789	9	1	teachers	teacher	NOUN
educationr-2789	9	2	are	be	AUX
educationr-2789	9	3	challenged	challenge	VERB
educationr-2789	9	4	to	to	PART
educationr-2789	9	5	provide	provide	VERB
educationr-2789	9	6	learning	learning	NOUN
educationr-2789	9	7	experiences	experience	NOUN
educationr-2789	9	8	so	so	SCONJ
educationr-2789	9	9	that	that	SCONJ
educationr-2789	9	10	every	every	DET
educationr-2789	9	11	student	student	NOUN
educationr-2789	9	12	has	have	VERB
educationr-2789	9	13	the	the	DET
educationr-2789	9	14	support	support	NOUN
educationr-2789	9	15	necessary	necessary	ADJ
educationr-2789	9	16	to	to	PART
educationr-2789	9	17	perform	perform	VERB
educationr-2789	9	18	high	high	ADJ
educationr-2789	9	19	-	-	PUNCT
educationr-2789	9	20	quality	quality	NOUN
educationr-2789	9	21	mathematics	mathematic	NOUN
educationr-2789	9	22	work	work	NOUN
educationr-2789	9	23	.	.	PUNCT
educationr-2789	10	1	understanding	understand	VERB
educationr-2789	10	2	how	how	SCONJ
educationr-2789	10	3	students	student	NOUN
educationr-2789	10	4	think	think	VERB
educationr-2789	10	5	about	about	ADP
educationr-2789	10	6	algebraic	algebraic	ADJ
educationr-2789	10	7	concepts	concept	NOUN
educationr-2789	10	8	can	can	AUX
educationr-2789	10	9	arm	arm	VERB
educationr-2789	10	10	teachers	teacher	NOUN
educationr-2789	10	11	with	with	ADP
educationr-2789	10	12	the	the	DET
educationr-2789	10	13	necessary	necessary	ADJ
educationr-2789	10	14	knowledge	knowledge	NOUN
educationr-2789	10	15	to	to	PART
educationr-2789	10	16	make	make	VERB
educationr-2789	10	17	this	this	DET
educationr-2789	10	18	type	type	NOUN
educationr-2789	10	19	of	of	ADP
educationr-2789	10	20	learning	learn	VERB
educationr-2789	10	21	a	a	DET
educationr-2789	10	22	reality	reality	NOUN
educationr-2789	10	23	for	for	ADP
educationr-2789	10	24	all	all	DET
educationr-2789	10	25	students	student	NOUN
educationr-2789	10	26	.	.	PUNCT
educationr-2789	11	1	in	in	ADP
educationr-2789	11	2	an	an	DET
educationr-2789	11	3	effort	effort	NOUN
educationr-2789	11	4	to	to	PART
educationr-2789	11	5	provide	provide	VERB
educationr-2789	11	6	teachers	teacher	NOUN
educationr-2789	11	7	with	with	ADP
educationr-2789	11	8	information	information	NOUN
educationr-2789	11	9	necessary	necessary	ADJ
educationr-2789	11	10	to	to	PART
educationr-2789	11	11	support	support	VERB
educationr-2789	11	12	algebraic	algebraic	ADJ
educationr-2789	11	13	thinking	thinking	NOUN
educationr-2789	11	14	,	,	PUNCT
educationr-2789	11	15	rhine	rhine	PROPN
educationr-2789	11	16	,	,	PUNCT
educationr-2789	11	17	harrington	harrington	PROPN
educationr-2789	11	18	,	,	PUNCT
educationr-2789	11	19	and	and	CCONJ
educationr-2789	11	20	starr	starr	PROPN
educationr-2789	11	21	have	have	AUX
educationr-2789	11	22	synthesized	synthesize	VERB
educationr-2789	11	23	35	35	NUM
educationr-2789	11	24	years	year	NOUN
educationr-2789	11	25	of	of	ADP
educationr-2789	11	26	research	research	NOUN
educationr-2789	11	27	on	on	ADP
educationr-2789	11	28	algebraic	algebraic	ADJ
educationr-2789	11	29	thinking	thinking	NOUN
educationr-2789	11	30	to	to	PART
educationr-2789	11	31	produce	produce	VERB
educationr-2789	11	32	how	how	SCONJ
educationr-2789	11	33	students	student	NOUN
educationr-2789	11	34	think	think	VERB
educationr-2789	11	35	when	when	SCONJ
educationr-2789	11	36	doing	do	VERB
educationr-2789	11	37	algebra	algebra	NOUN
educationr-2789	11	38	.	.	PUNCT
educationr-2789	12	1	these	these	DET
educationr-2789	12	2	authors	author	NOUN
educationr-2789	12	3	have	have	VERB
educationr-2789	12	4	a	a	DET
educationr-2789	12	5	variety	variety	NOUN
educationr-2789	12	6	of	of	ADP
educationr-2789	12	7	classroom	classroom	NOUN
educationr-2789	12	8	experiences	experience	NOUN
educationr-2789	12	9	,	,	PUNCT
educationr-2789	12	10	from	from	ADP
educationr-2789	12	11	teaching	teach	VERB
educationr-2789	12	12	high	high	ADJ
educationr-2789	12	13	school	school	NOUN
educationr-2789	12	14	and	and	CCONJ
educationr-2789	12	15	college	college	NOUN
educationr-2789	12	16	mathematics	mathematic	NOUN
educationr-2789	12	17	to	to	ADP
educationr-2789	12	18	teaching	teach	VERB
educationr-2789	12	19	pre	pre	ADJ
educationr-2789	12	20	-	-	ADJ
educationr-2789	12	21	service	service	ADJ
educationr-2789	12	22	mathematics	mathematic	NOUN
educationr-2789	12	23	teachers	teacher	NOUN
educationr-2789	12	24	to	to	ADP
educationr-2789	12	25	providing	provide	VERB
educationr-2789	12	26	professional	professional	ADJ
educationr-2789	12	27	development	development	NOUN
educationr-2789	12	28	to	to	ADP
educationr-2789	12	29	mathematics	mathematics	PROPN
educationr-2789	12	30	teachers	teacher	NOUN
educationr-2789	12	31	.	.	PUNCT
educationr-2789	13	1	they	they	PRON
educationr-2789	13	2	have	have	AUX
educationr-2789	13	3	also	also	ADV
educationr-2789	13	4	studied	study	VERB
educationr-2789	13	5	and	and	CCONJ
educationr-2789	13	6	researched	research	VERB
educationr-2789	13	7	mathematics	mathematic	NOUN
educationr-2789	13	8	education	education	NOUN
educationr-2789	13	9	.	.	PUNCT
educationr-2789	14	1	their	their	PRON
educationr-2789	14	2	experience	experience	NOUN
educationr-2789	14	3	with	with	ADP
educationr-2789	14	4	teachers	teacher	NOUN
educationr-2789	14	5	and	and	CCONJ
educationr-2789	14	6	teaching	teaching	NOUN
educationr-2789	14	7	has	have	AUX
educationr-2789	14	8	helped	help	VERB
educationr-2789	14	9	shaped	shape	VERB
educationr-2789	14	10	this	this	DET
educationr-2789	14	11	book	book	NOUN
educationr-2789	14	12	into	into	ADP
educationr-2789	14	13	a	a	DET
educationr-2789	14	14	usable	usable	ADJ
educationr-2789	14	15	text	text	NOUN
educationr-2789	14	16	for	for	ADP
educationr-2789	14	17	in	in	ADP
educationr-2789	14	18	-	-	PUNCT
educationr-2789	14	19	service	service	NOUN
educationr-2789	14	20	teachers	teacher	NOUN
educationr-2789	14	21	.	.	PUNCT
educationr-2789	15	1	education	education	NOUN
educationr-2789	15	2	review	review	NOUN
educationr-2789	15	3	2	2	NUM
educationr-2789	15	4	in	in	ADP
educationr-2789	15	5	this	this	DET
educationr-2789	15	6	practitioner	practitioner	NOUN
educationr-2789	15	7	-	-	PUNCT
educationr-2789	15	8	focused	focus	VERB
educationr-2789	15	9	guide	guide	NOUN
educationr-2789	15	10	to	to	ADP
educationr-2789	15	11	algebraic	algebraic	ADJ
educationr-2789	15	12	thinking	thinking	NOUN
educationr-2789	15	13	,	,	PUNCT
educationr-2789	15	14	teachers	teacher	NOUN
educationr-2789	15	15	,	,	PUNCT
educationr-2789	15	16	instructional	instructional	ADJ
educationr-2789	15	17	coaches	coach	NOUN
educationr-2789	15	18	,	,	PUNCT
educationr-2789	15	19	and	and	CCONJ
educationr-2789	15	20	professional	professional	ADJ
educationr-2789	15	21	development	development	NOUN
educationr-2789	15	22	providers	provider	NOUN
educationr-2789	15	23	will	will	AUX
educationr-2789	15	24	learn	learn	VERB
educationr-2789	15	25	why	why	SCONJ
educationr-2789	15	26	students	student	NOUN
educationr-2789	15	27	’	'	PUNCT
educationr-2789	15	28	algebraic	algebraic	ADJ
educationr-2789	15	29	thinking	thinking	NOUN
educationr-2789	15	30	makes	make	VERB
educationr-2789	15	31	sense	sense	NOUN
educationr-2789	15	32	to	to	ADP
educationr-2789	15	33	them	they	PRON
educationr-2789	15	34	and	and	CCONJ
educationr-2789	15	35	how	how	SCONJ
educationr-2789	15	36	to	to	PART
educationr-2789	15	37	improve	improve	VERB
educationr-2789	15	38	instructional	instructional	ADJ
educationr-2789	15	39	practices	practice	NOUN
educationr-2789	15	40	to	to	PART
educationr-2789	15	41	minimize	minimize	VERB
educationr-2789	15	42	student	student	NOUN
educationr-2789	15	43	misconceptions	misconception	NOUN
educationr-2789	15	44	.	.	PUNCT
educationr-2789	16	1	the	the	DET
educationr-2789	16	2	book	book	NOUN
educationr-2789	16	3	is	be	AUX
educationr-2789	16	4	a	a	DET
educationr-2789	16	5	research	research	NOUN
educationr-2789	16	6	-	-	PUNCT
educationr-2789	16	7	based	base	VERB
educationr-2789	16	8	,	,	PUNCT
educationr-2789	16	9	comprehensive	comprehensive	ADJ
educationr-2789	16	10	examination	examination	NOUN
educationr-2789	16	11	of	of	ADP
educationr-2789	16	12	algebraic	algebraic	ADJ
educationr-2789	16	13	thinking	thinking	NOUN
educationr-2789	16	14	and	and	CCONJ
educationr-2789	16	15	teaching	teaching	NOUN
educationr-2789	16	16	practices	practice	NOUN
educationr-2789	16	17	that	that	PRON
educationr-2789	16	18	will	will	AUX
educationr-2789	16	19	provide	provide	VERB
educationr-2789	16	20	all	all	DET
educationr-2789	16	21	stakeholders	stakeholder	NOUN
educationr-2789	16	22	with	with	ADP
educationr-2789	16	23	the	the	DET
educationr-2789	16	24	necessary	necessary	ADJ
educationr-2789	16	25	information	information	NOUN
educationr-2789	16	26	to	to	PART
educationr-2789	16	27	support	support	VERB
educationr-2789	16	28	students	student	NOUN
educationr-2789	16	29	in	in	ADP
educationr-2789	16	30	engaging	engage	VERB
educationr-2789	16	31	in	in	ADP
educationr-2789	16	32	meaningful	meaningful	ADJ
educationr-2789	16	33	algebraic	algebraic	ADJ
educationr-2789	16	34	work	work	NOUN
educationr-2789	16	35	.	.	PUNCT
educationr-2789	17	1	i	i	PRON
educationr-2789	17	2	believe	believe	VERB
educationr-2789	17	3	teachers	teacher	NOUN
educationr-2789	17	4	who	who	PRON
educationr-2789	17	5	engage	engage	VERB
educationr-2789	17	6	with	with	ADP
educationr-2789	17	7	this	this	DET
educationr-2789	17	8	text	text	NOUN
educationr-2789	17	9	will	will	AUX
educationr-2789	17	10	deepen	deepen	VERB
educationr-2789	17	11	their	their	PRON
educationr-2789	17	12	understanding	understanding	NOUN
educationr-2789	17	13	of	of	ADP
educationr-2789	17	14	algebraic	algebraic	ADJ
educationr-2789	17	15	thinking	thinking	NOUN
educationr-2789	17	16	and	and	CCONJ
educationr-2789	17	17	,	,	PUNCT
educationr-2789	17	18	hence	hence	ADV
educationr-2789	17	19	,	,	PUNCT
educationr-2789	17	20	improve	improve	VERB
educationr-2789	17	21	their	their	PRON
educationr-2789	17	22	practice	practice	NOUN
educationr-2789	17	23	so	so	SCONJ
educationr-2789	17	24	that	that	SCONJ
educationr-2789	17	25	all	all	DET
educationr-2789	17	26	students	student	NOUN
educationr-2789	17	27	have	have	VERB
educationr-2789	17	28	rich	rich	ADJ
educationr-2789	17	29	mathematical	mathematical	ADJ
educationr-2789	17	30	learning	learning	NOUN
educationr-2789	17	31	experiences	experience	NOUN
educationr-2789	17	32	.	.	PUNCT
educationr-2789	18	1	although	although	SCONJ
educationr-2789	18	2	this	this	DET
educationr-2789	18	3	text	text	NOUN
educationr-2789	18	4	was	be	AUX
educationr-2789	18	5	written	write	VERB
educationr-2789	18	6	to	to	PART
educationr-2789	18	7	support	support	VERB
educationr-2789	18	8	inexperienced	inexperienced	ADJ
educationr-2789	18	9	teachers	teacher	NOUN
educationr-2789	18	10	,	,	PUNCT
educationr-2789	18	11	experienced	experienced	ADJ
educationr-2789	18	12	teachers	teacher	NOUN
educationr-2789	18	13	and	and	CCONJ
educationr-2789	18	14	other	other	ADJ
educationr-2789	18	15	professionals	professional	NOUN
educationr-2789	18	16	will	will	AUX
educationr-2789	18	17	also	also	ADV
educationr-2789	18	18	find	find	VERB
educationr-2789	18	19	it	it	PRON
educationr-2789	18	20	a	a	DET
educationr-2789	18	21	useful	useful	ADJ
educationr-2789	18	22	tool	tool	NOUN
educationr-2789	18	23	in	in	ADP
educationr-2789	18	24	their	their	PRON
educationr-2789	18	25	continued	continue	VERB
educationr-2789	18	26	development	development	NOUN
educationr-2789	18	27	.	.	PUNCT
educationr-2789	19	1	the	the	DET
educationr-2789	19	2	authors	author	NOUN
educationr-2789	19	3	argue	argue	VERB
educationr-2789	19	4	that	that	SCONJ
educationr-2789	19	5	teachers	teacher	NOUN
educationr-2789	19	6	must	must	AUX
educationr-2789	19	7	understand	understand	VERB
educationr-2789	19	8	the	the	DET
educationr-2789	19	9	multiple	multiple	ADJ
educationr-2789	19	10	ways	way	NOUN
educationr-2789	19	11	students	student	NOUN
educationr-2789	19	12	think	think	VERB
educationr-2789	19	13	about	about	ADP
educationr-2789	19	14	and	and	CCONJ
educationr-2789	19	15	struggle	struggle	VERB
educationr-2789	19	16	with	with	ADP
educationr-2789	19	17	mathematics	mathematic	NOUN
educationr-2789	19	18	in	in	ADP
educationr-2789	19	19	order	order	NOUN
educationr-2789	19	20	to	to	PART
educationr-2789	19	21	make	make	VERB
educationr-2789	19	22	sound	sound	ADJ
educationr-2789	19	23	pedagogical	pedagogical	ADJ
educationr-2789	19	24	decisions	decision	NOUN
educationr-2789	19	25	to	to	PART
educationr-2789	19	26	help	help	VERB
educationr-2789	19	27	students	student	NOUN
educationr-2789	19	28	develop	develop	VERB
educationr-2789	19	29	conceptual	conceptual	ADJ
educationr-2789	19	30	understanding	understanding	NOUN
educationr-2789	19	31	of	of	ADP
educationr-2789	19	32	mathematics	mathematic	NOUN
educationr-2789	19	33	.	.	PUNCT
educationr-2789	20	1	they	they	PRON
educationr-2789	20	2	suggest	suggest	VERB
educationr-2789	20	3	that	that	SCONJ
educationr-2789	20	4	novice	novice	NOUN
educationr-2789	20	5	teachers	teacher	NOUN
educationr-2789	20	6	“	"	PUNCT
educationr-2789	20	7	lack	lack	VERB
educationr-2789	20	8	the	the	DET
educationr-2789	20	9	experience	experience	NOUN
educationr-2789	20	10	to	to	PART
educationr-2789	20	11	anticipate	anticipate	VERB
educationr-2789	20	12	important	important	ADJ
educationr-2789	20	13	moments	moment	NOUN
educationr-2789	20	14	in	in	ADP
educationr-2789	20	15	their	their	PRON
educationr-2789	20	16	students	student	NOUN
educationr-2789	20	17	’	'	PUNCT
educationr-2789	20	18	learning	learning	NOUN
educationr-2789	20	19	”	"	PUNCT
educationr-2789	20	20	(	(	PUNCT
educationr-2789	20	21	p.	p.	NOUN
educationr-2789	20	22	3	3	NUM
educationr-2789	20	23	)	)	PUNCT
educationr-2789	20	24	.	.	PUNCT
educationr-2789	21	1	hence	hence	ADV
educationr-2789	21	2	,	,	PUNCT
educationr-2789	21	3	this	this	DET
educationr-2789	21	4	text	text	NOUN
educationr-2789	21	5	was	be	AUX
educationr-2789	21	6	written	write	VERB
educationr-2789	21	7	to	to	PART
educationr-2789	21	8	support	support	VERB
educationr-2789	21	9	inexperienced	inexperienced	ADJ
educationr-2789	21	10	teachers	teacher	NOUN
educationr-2789	21	11	’	'	PUNCT
educationr-2789	21	12	learning	learning	NOUN
educationr-2789	21	13	of	of	ADP
educationr-2789	21	14	students	student	NOUN
educationr-2789	21	15	’	'	PUNCT
educationr-2789	21	16	common	common	ADJ
educationr-2789	21	17	errors	error	NOUN
educationr-2789	21	18	,	,	PUNCT
educationr-2789	21	19	misconceptions	misconception	NOUN
educationr-2789	21	20	,	,	PUNCT
educationr-2789	21	21	and	and	CCONJ
educationr-2789	21	22	struggles	struggle	NOUN
educationr-2789	21	23	while	while	SCONJ
educationr-2789	21	24	doing	do	VERB
educationr-2789	21	25	algebra	algebra	NOUN
educationr-2789	21	26	.	.	PUNCT
educationr-2789	22	1	experienced	experience	VERB
educationr-2789	22	2	teachers	teacher	NOUN
educationr-2789	22	3	will	will	AUX
educationr-2789	22	4	also	also	ADV
educationr-2789	22	5	find	find	VERB
educationr-2789	22	6	the	the	DET
educationr-2789	22	7	pedagogical	pedagogical	ADJ
educationr-2789	22	8	content	content	NOUN
educationr-2789	22	9	knowledge	knowledge	NOUN
educationr-2789	22	10	discussed	discuss	VERB
educationr-2789	22	11	rich	rich	ADJ
educationr-2789	22	12	and	and	CCONJ
educationr-2789	22	13	thoughtprovoking	thoughtprovoking	ADJ
educationr-2789	22	14	.	.	PUNCT
educationr-2789	23	1	instructional	instructional	ADJ
educationr-2789	23	2	coaches	coach	NOUN
educationr-2789	23	3	and	and	CCONJ
educationr-2789	23	4	professional	professional	ADJ
educationr-2789	23	5	development	development	NOUN
educationr-2789	23	6	providers	provider	NOUN
educationr-2789	23	7	will	will	AUX
educationr-2789	23	8	appreciate	appreciate	VERB
educationr-2789	23	9	talking	talking	NOUN
educationr-2789	23	10	points	point	NOUN
educationr-2789	23	11	that	that	PRON
educationr-2789	23	12	can	can	AUX
educationr-2789	23	13	be	be	AUX
educationr-2789	23	14	used	use	VERB
educationr-2789	23	15	to	to	PART
educationr-2789	23	16	expand	expand	VERB
educationr-2789	23	17	teachers	teacher	NOUN
educationr-2789	23	18	’	'	PUNCT
educationr-2789	23	19	repertoire	repertoire	NOUN
educationr-2789	23	20	of	of	ADP
educationr-2789	23	21	instructional	instructional	ADJ
educationr-2789	23	22	strategies	strategy	NOUN
educationr-2789	23	23	.	.	PUNCT
educationr-2789	24	1	improving	improve	VERB
educationr-2789	24	2	teachers	teacher	NOUN
educationr-2789	24	3	’	'	PUNCT
educationr-2789	24	4	pedagogical	pedagogical	ADJ
educationr-2789	24	5	content	content	NOUN
educationr-2789	24	6	knowledge	knowledge	NOUN
educationr-2789	24	7	will	will	AUX
educationr-2789	24	8	facilitate	facilitate	VERB
educationr-2789	24	9	the	the	DET
educationr-2789	24	10	decision	decision	NOUN
educationr-2789	24	11	-	-	PUNCT
educationr-2789	24	12	making	make	VERB
educationr-2789	24	13	processes	process	NOUN
educationr-2789	24	14	teachers	teacher	NOUN
educationr-2789	24	15	use	use	VERB
educationr-2789	24	16	daily	daily	ADV
educationr-2789	24	17	in	in	ADP
educationr-2789	24	18	their	their	PRON
educationr-2789	24	19	work	work	NOUN
educationr-2789	24	20	with	with	ADP
educationr-2789	24	21	students	student	NOUN
educationr-2789	24	22	.	.	PUNCT
educationr-2789	25	1	the	the	DET
educationr-2789	25	2	decisions	decision	NOUN
educationr-2789	25	3	teachers	teacher	NOUN
educationr-2789	25	4	make	make	VERB
educationr-2789	25	5	when	when	SCONJ
educationr-2789	25	6	responding	respond	VERB
educationr-2789	25	7	to	to	ADP
educationr-2789	25	8	student	student	NOUN
educationr-2789	25	9	thinking	thinking	NOUN
educationr-2789	25	10	impact	impact	NOUN
educationr-2789	25	11	how	how	SCONJ
educationr-2789	25	12	students	student	NOUN
educationr-2789	25	13	learn	learn	VERB
educationr-2789	25	14	mathematics	mathematic	NOUN
educationr-2789	25	15	.	.	PUNCT
educationr-2789	26	1	these	these	DET
educationr-2789	26	2	“	"	PUNCT
educationr-2789	26	3	mathematically	mathematically	ADV
educationr-2789	26	4	significant	significant	ADJ
educationr-2789	26	5	opportunities	opportunity	NOUN
educationr-2789	26	6	to	to	PART
educationr-2789	26	7	build	build	VERB
educationr-2789	26	8	on	on	ADP
educationr-2789	26	9	students	student	NOUN
educationr-2789	26	10	’	'	PUNCT
educationr-2789	26	11	thinking	thinking	NOUN
educationr-2789	26	12	”	"	PUNCT
educationr-2789	26	13	(	(	PUNCT
educationr-2789	26	14	mosts	most	NOUN
educationr-2789	26	15	)	)	PUNCT
educationr-2789	26	16	(	(	PUNCT
educationr-2789	26	17	leatham	leatham	PROPN
educationr-2789	26	18	,	,	PUNCT
educationr-2789	26	19	peterson	peterson	PROPN
educationr-2789	26	20	,	,	PUNCT
educationr-2789	26	21	stockero	stockero	NOUN
educationr-2789	26	22	,	,	PUNCT
educationr-2789	26	23	&	&	CCONJ
educationr-2789	26	24	vanzoest	vanzo	ADJ
educationr-2789	26	25	,	,	PUNCT
educationr-2789	26	26	2015	2015	NUM
educationr-2789	26	27	)	)	PUNCT
educationr-2789	26	28	are	be	AUX
educationr-2789	26	29	the	the	DET
educationr-2789	26	30	connections	connection	NOUN
educationr-2789	26	31	between	between	ADP
educationr-2789	26	32	mathematics	mathematic	NOUN
educationr-2789	26	33	,	,	PUNCT
educationr-2789	26	34	pedagogy	pedagogy	NOUN
educationr-2789	26	35	,	,	PUNCT
educationr-2789	26	36	and	and	CCONJ
educationr-2789	26	37	student	student	NOUN
educationr-2789	26	38	thinking	thinking	NOUN
educationr-2789	26	39	.	.	PUNCT
educationr-2789	27	1	these	these	DET
educationr-2789	27	2	instructional	instructional	ADJ
educationr-2789	27	3	decisions	decision	NOUN
educationr-2789	27	4	can	can	AUX
educationr-2789	27	5	impact	impact	VERB
educationr-2789	27	6	the	the	DET
educationr-2789	27	7	mosts	most	NOUN
educationr-2789	27	8	within	within	ADP
educationr-2789	27	9	classroom	classroom	NOUN
educationr-2789	27	10	structure	structure	NOUN
educationr-2789	27	11	.	.	PUNCT
educationr-2789	28	1	the	the	DET
educationr-2789	28	2	introduction	introduction	NOUN
educationr-2789	28	3	is	be	AUX
educationr-2789	28	4	a	a	DET
educationr-2789	28	5	compelling	compelling	ADJ
educationr-2789	28	6	read	read	NOUN
educationr-2789	28	7	,	,	PUNCT
educationr-2789	28	8	as	as	SCONJ
educationr-2789	28	9	it	it	PRON
educationr-2789	28	10	provides	provide	VERB
educationr-2789	28	11	a	a	DET
educationr-2789	28	12	great	great	ADJ
educationr-2789	28	13	deal	deal	NOUN
educationr-2789	28	14	of	of	ADP
educationr-2789	28	15	context	context	NOUN
educationr-2789	28	16	for	for	ADP
educationr-2789	28	17	this	this	DET
educationr-2789	28	18	topic	topic	NOUN
educationr-2789	28	19	.	.	PUNCT
educationr-2789	29	1	the	the	DET
educationr-2789	29	2	authors	author	NOUN
educationr-2789	29	3	base	base	VERB
educationr-2789	29	4	their	their	PRON
educationr-2789	29	5	work	work	NOUN
educationr-2789	29	6	on	on	ADP
educationr-2789	29	7	research	research	NOUN
educationr-2789	29	8	about	about	ADP
educationr-2789	29	9	why	why	SCONJ
educationr-2789	29	10	algebraic	algebraic	ADJ
educationr-2789	29	11	thinking	thinking	NOUN
educationr-2789	29	12	is	be	AUX
educationr-2789	29	13	vital	vital	ADJ
educationr-2789	29	14	for	for	SCONJ
educationr-2789	29	15	all	all	DET
educationr-2789	29	16	students	student	NOUN
educationr-2789	29	17	to	to	PART
educationr-2789	29	18	learn	learn	VERB
educationr-2789	29	19	and	and	CCONJ
educationr-2789	29	20	why	why	SCONJ
educationr-2789	29	21	algebra	algebra	NOUN
educationr-2789	29	22	is	be	AUX
educationr-2789	29	23	difficult	difficult	ADJ
educationr-2789	29	24	for	for	SCONJ
educationr-2789	29	25	students	student	NOUN
educationr-2789	29	26	to	to	PART
educationr-2789	29	27	understand	understand	VERB
educationr-2789	29	28	.	.	PUNCT
educationr-2789	30	1	the	the	DET
educationr-2789	30	2	introduction	introduction	NOUN
educationr-2789	30	3	details	detail	NOUN
educationr-2789	30	4	research	research	NOUN
educationr-2789	30	5	in	in	ADP
educationr-2789	30	6	piagetian	piagetian	PROPN
educationr-2789	30	7	theory	theory	NOUN
educationr-2789	30	8	,	,	PUNCT
educationr-2789	30	9	dweck	dweck	PROPN
educationr-2789	30	10	’s	’s	PART
educationr-2789	30	11	fixed	fix	VERB
educationr-2789	30	12	and	and	CCONJ
educationr-2789	30	13	growth	growth	NOUN
educationr-2789	30	14	mindset	mindset	NOUN
educationr-2789	30	15	theory	theory	NOUN
educationr-2789	30	16	,	,	PUNCT
educationr-2789	30	17	and	and	CCONJ
educationr-2789	30	18	the	the	DET
educationr-2789	30	19	algebraic	algebraic	ADJ
educationr-2789	30	20	habits	habit	NOUN
educationr-2789	30	21	of	of	ADP
educationr-2789	30	22	mind	mind	NOUN
educationr-2789	30	23	and	and	CCONJ
educationr-2789	30	24	how	how	SCONJ
educationr-2789	30	25	these	these	DET
educationr-2789	30	26	theories	theory	NOUN
educationr-2789	30	27	apply	apply	VERB
educationr-2789	30	28	to	to	ADP
educationr-2789	30	29	algebraic	algebraic	ADJ
educationr-2789	30	30	thinking	thinking	NOUN
educationr-2789	30	31	.	.	PUNCT
educationr-2789	31	1	in	in	ADP
educationr-2789	31	2	particular	particular	ADJ
educationr-2789	31	3	,	,	PUNCT
educationr-2789	31	4	they	they	PRON
educationr-2789	31	5	highlight	highlight	VERB
educationr-2789	31	6	connections	connection	NOUN
educationr-2789	31	7	between	between	ADP
educationr-2789	31	8	the	the	DET
educationr-2789	31	9	research	research	NOUN
educationr-2789	31	10	and	and	CCONJ
educationr-2789	31	11	how	how	SCONJ
educationr-2789	31	12	students	student	NOUN
educationr-2789	31	13	develop	develop	VERB
educationr-2789	31	14	algebraic	algebraic	ADJ
educationr-2789	31	15	reasoning	reasoning	NOUN
educationr-2789	31	16	,	,	PUNCT
educationr-2789	31	17	how	how	SCONJ
educationr-2789	31	18	students	student	NOUN
educationr-2789	31	19	develop	develop	VERB
educationr-2789	31	20	misconceptions	misconception	NOUN
educationr-2789	31	21	,	,	PUNCT
educationr-2789	31	22	and	and	CCONJ
educationr-2789	31	23	how	how	SCONJ
educationr-2789	31	24	students	student	NOUN
educationr-2789	31	25	think	think	VERB
educationr-2789	31	26	about	about	ADP
educationr-2789	31	27	specific	specific	ADJ
educationr-2789	31	28	concepts	concept	NOUN
educationr-2789	31	29	in	in	ADP
educationr-2789	31	30	algebra	algebra	NOUN
educationr-2789	31	31	.	.	PUNCT
educationr-2789	32	1	the	the	DET
educationr-2789	32	2	organization	organization	NOUN
educationr-2789	32	3	of	of	ADP
educationr-2789	32	4	the	the	DET
educationr-2789	32	5	book	book	NOUN
educationr-2789	32	6	is	be	AUX
educationr-2789	32	7	structured	structure	VERB
educationr-2789	32	8	to	to	PART
educationr-2789	32	9	provide	provide	VERB
educationr-2789	32	10	an	an	DET
educationr-2789	32	11	easy	easy	ADJ
educationr-2789	32	12	reference	reference	NOUN
educationr-2789	32	13	for	for	ADP
educationr-2789	32	14	teachers	teacher	NOUN
educationr-2789	32	15	and	and	CCONJ
educationr-2789	32	16	other	other	ADJ
educationr-2789	32	17	professionals	professional	NOUN
educationr-2789	32	18	as	as	SCONJ
educationr-2789	32	19	they	they	PRON
educationr-2789	32	20	plan	plan	VERB
educationr-2789	32	21	for	for	ADP
educationr-2789	32	22	their	their	PRON
educationr-2789	32	23	algebra	algebra	NOUN
educationr-2789	32	24	course	course	NOUN
educationr-2789	32	25	.	.	PUNCT
educationr-2789	33	1	the	the	DET
educationr-2789	33	2	authors	author	NOUN
educationr-2789	33	3	designed	design	VERB
educationr-2789	33	4	this	this	DET
educationr-2789	33	5	book	book	NOUN
educationr-2789	33	6	with	with	ADP
educationr-2789	33	7	the	the	DET
educationr-2789	33	8	goal	goal	NOUN
educationr-2789	33	9	of	of	ADP
educationr-2789	33	10	enhancing	enhance	VERB
educationr-2789	33	11	teachers	teacher	NOUN
educationr-2789	33	12	’	'	PUNCT
educationr-2789	33	13	pedagogical	pedagogical	ADJ
educationr-2789	33	14	content	content	NOUN
educationr-2789	33	15	knowledge	knowledge	NOUN
educationr-2789	33	16	so	so	SCONJ
educationr-2789	33	17	that	that	SCONJ
educationr-2789	33	18	instructional	instructional	ADJ
educationr-2789	33	19	decisions	decision	NOUN
educationr-2789	33	20	can	can	AUX
educationr-2789	33	21	be	be	AUX
educationr-2789	33	22	made	make	VERB
educationr-2789	33	23	to	to	PART
educationr-2789	33	24	improve	improve	VERB
educationr-2789	33	25	mosts	most	NOUN
educationr-2789	33	26	.	.	PUNCT
educationr-2789	34	1	each	each	DET
educationr-2789	34	2	chapter	chapter	NOUN
educationr-2789	34	3	is	be	AUX
educationr-2789	34	4	devoted	devote	VERB
educationr-2789	34	5	to	to	ADP
educationr-2789	34	6	an	an	DET
educationr-2789	34	7	algebraic	algebraic	ADJ
educationr-2789	34	8	category	category	NOUN
educationr-2789	34	9	:	:	PUNCT
educationr-2789	34	10	variables	variable	NOUN
educationr-2789	34	11	and	and	CCONJ
educationr-2789	34	12	expressions	expression	NOUN
educationr-2789	34	13	,	,	PUNCT
educationr-2789	34	14	algebraic	algebraic	ADJ
educationr-2789	34	15	relations	relation	NOUN
educationr-2789	34	16	,	,	PUNCT
educationr-2789	34	17	analysis	analysis	NOUN
educationr-2789	34	18	of	of	ADP
educationr-2789	34	19	change	change	NOUN
educationr-2789	34	20	,	,	PUNCT
educationr-2789	34	21	patterns	pattern	NOUN
educationr-2789	34	22	and	and	CCONJ
educationr-2789	34	23	functions	function	NOUN
educationr-2789	34	24	,	,	PUNCT
educationr-2789	34	25	and	and	CCONJ
educationr-2789	34	26	modeling	modeling	NOUN
educationr-2789	34	27	and	and	CCONJ
educationr-2789	34	28	word	word	NOUN
educationr-2789	34	29	problems	problem	NOUN
educationr-2789	34	30	.	.	PUNCT
educationr-2789	35	1	within	within	ADP
educationr-2789	35	2	each	each	DET
educationr-2789	35	3	chapter	chapter	NOUN
educationr-2789	35	4	,	,	PUNCT
educationr-2789	35	5	the	the	DET
educationr-2789	35	6	authors	author	NOUN
educationr-2789	35	7	begin	begin	VERB
educationr-2789	35	8	by	by	ADP
educationr-2789	35	9	offering	offer	VERB
educationr-2789	35	10	teachers	teacher	NOUN
educationr-2789	35	11	a	a	DET
educationr-2789	35	12	researchbased	researchbase	VERB
educationr-2789	35	13	description	description	NOUN
educationr-2789	35	14	of	of	ADP
educationr-2789	35	15	the	the	DET
educationr-2789	35	16	algebraic	algebraic	ADJ
educationr-2789	35	17	concept	concept	NOUN
educationr-2789	35	18	that	that	SCONJ
educationr-2789	35	19	challenges	challenge	VERB
educationr-2789	35	20	and	and	CCONJ
educationr-2789	35	21	deepens	deepen	VERB
educationr-2789	35	22	pedagogical	pedagogical	ADJ
educationr-2789	35	23	content	content	NOUN
educationr-2789	35	24	knowledge	knowledge	NOUN
educationr-2789	35	25	.	.	PUNCT
educationr-2789	36	1	they	they	PRON
educationr-2789	36	2	offer	offer	VERB
educationr-2789	36	3	reasons	reason	NOUN
educationr-2789	36	4	why	why	SCONJ
educationr-2789	36	5	students	student	NOUN
educationr-2789	36	6	struggle	struggle	VERB
educationr-2789	36	7	with	with	ADP
educationr-2789	36	8	each	each	DET
educationr-2789	36	9	algebraic	algebraic	ADJ
educationr-2789	36	10	concept	concept	NOUN
educationr-2789	36	11	,	,	PUNCT
educationr-2789	36	12	ranging	range	VERB
educationr-2789	36	13	from	from	ADP
educationr-2789	36	14	the	the	DET
educationr-2789	36	15	nature	nature	NOUN
educationr-2789	36	16	of	of	ADP
educationr-2789	36	17	the	the	DET
educationr-2789	36	18	algebra	algebra	NOUN
educationr-2789	36	19	to	to	ADP
educationr-2789	36	20	common	common	ADJ
educationr-2789	36	21	teaching	teaching	NOUN
educationr-2789	36	22	practices	practice	NOUN
educationr-2789	36	23	that	that	PRON
educationr-2789	36	24	often	often	ADV
educationr-2789	36	25	contribute	contribute	VERB
educationr-2789	36	26	to	to	ADP
educationr-2789	36	27	students	student	NOUN
educationr-2789	36	28	’	’	PART
educationr-2789	36	29	misunderstandings	misunderstanding	NOUN
educationr-2789	36	30	.	.	PUNCT
educationr-2789	37	1	the	the	DET
educationr-2789	37	2	chapters	chapter	NOUN
educationr-2789	37	3	are	be	AUX
educationr-2789	37	4	then	then	ADV
educationr-2789	37	5	divided	divide	VERB
educationr-2789	37	6	into	into	ADP
educationr-2789	37	7	subsections	subsection	NOUN
educationr-2789	37	8	and	and	CCONJ
educationr-2789	37	9	referenced	reference	VERB
educationr-2789	37	10	to	to	ADP
educationr-2789	37	11	specific	specific	ADJ
educationr-2789	37	12	common	common	ADJ
educationr-2789	37	13	core	core	NOUN
educationr-2789	37	14	state	state	NOUN
educationr-2789	37	15	standards	standard	NOUN
educationr-2789	37	16	.	.	PUNCT
educationr-2789	38	1	each	each	DET
educationr-2789	38	2	subsection	subsection	NOUN
educationr-2789	38	3	has	have	VERB
educationr-2789	38	4	a	a	DET
educationr-2789	38	5	consistant	consistant	ADJ
educationr-2789	38	6	framework	framework	NOUN
educationr-2789	38	7	so	so	SCONJ
educationr-2789	38	8	that	that	SCONJ
educationr-2789	38	9	teachers	teacher	NOUN
educationr-2789	38	10	can	can	AUX
educationr-2789	38	11	easily	easily	ADV
educationr-2789	38	12	locate	locate	VERB
educationr-2789	38	13	information	information	NOUN
educationr-2789	38	14	.	.	PUNCT
educationr-2789	39	1	first	first	ADV
educationr-2789	39	2	,	,	PUNCT
educationr-2789	39	3	they	they	PRON
educationr-2789	39	4	identify	identify	VERB
educationr-2789	39	5	the	the	DET
educationr-2789	39	6	thinking	thinking	NOUN
educationr-2789	39	7	centered	center	VERB
educationr-2789	39	8	around	around	ADP
educationr-2789	39	9	the	the	DET
educationr-2789	39	10	algebraic	algebraic	ADJ
educationr-2789	39	11	concept	concept	NOUN
educationr-2789	39	12	and	and	CCONJ
educationr-2789	39	13	what	what	PRON
educationr-2789	39	14	the	the	DET
educationr-2789	39	15	review	review	NOUN
educationr-2789	39	16	of	of	ADP
educationr-2789	39	17	how	how	SCONJ
educationr-2789	39	18	students	student	NOUN
educationr-2789	39	19	think	think	VERB
educationr-2789	39	20	when	when	SCONJ
educationr-2789	39	21	doing	do	VERB
educationr-2789	39	22	algebra	algebra	NOUN
educationr-2789	39	23	3	3	NUM
educationr-2789	39	24	algebraic	algebraic	ADJ
educationr-2789	39	25	misconceptions	misconception	NOUN
educationr-2789	39	26	look	look	VERB
educationr-2789	39	27	like	like	ADP
educationr-2789	39	28	symbolically	symbolically	ADV
educationr-2789	39	29	.	.	PUNCT
educationr-2789	40	1	second	second	ADV
educationr-2789	40	2	,	,	PUNCT
educationr-2789	40	3	they	they	PRON
educationr-2789	40	4	specify	specify	VERB
educationr-2789	40	5	how	how	SCONJ
educationr-2789	40	6	students	student	NOUN
educationr-2789	40	7	think	think	VERB
educationr-2789	40	8	about	about	ADP
educationr-2789	40	9	the	the	DET
educationr-2789	40	10	algebraic	algebraic	ADJ
educationr-2789	40	11	concept	concept	NOUN
educationr-2789	40	12	and	and	CCONJ
educationr-2789	40	13	the	the	DET
educationr-2789	40	14	misconceptions	misconception	NOUN
educationr-2789	40	15	.	.	PUNCT
educationr-2789	41	1	third	third	ADJ
educationr-2789	41	2	,	,	PUNCT
educationr-2789	41	3	they	they	PRON
educationr-2789	41	4	discuss	discuss	VERB
educationr-2789	41	5	the	the	DET
educationr-2789	41	6	mathematics	mathematic	NOUN
educationr-2789	41	7	in	in	ADP
educationr-2789	41	8	relation	relation	NOUN
educationr-2789	41	9	to	to	ADP
educationr-2789	41	10	why	why	SCONJ
educationr-2789	41	11	the	the	DET
educationr-2789	41	12	misconceptions	misconception	NOUN
educationr-2789	41	13	may	may	AUX
educationr-2789	41	14	occur	occur	VERB
educationr-2789	41	15	.	.	PUNCT
educationr-2789	42	1	finally	finally	ADV
educationr-2789	42	2	,	,	PUNCT
educationr-2789	42	3	they	they	PRON
educationr-2789	42	4	offer	offer	VERB
educationr-2789	42	5	specific	specific	ADJ
educationr-2789	42	6	instructional	instructional	ADJ
educationr-2789	42	7	moves	move	NOUN
educationr-2789	42	8	that	that	PRON
educationr-2789	42	9	could	could	AUX
educationr-2789	42	10	help	help	VERB
educationr-2789	42	11	students	student	NOUN
educationr-2789	42	12	develop	develop	VERB
educationr-2789	42	13	a	a	DET
educationr-2789	42	14	deeper	deep	ADJ
educationr-2789	42	15	understanding	understanding	NOUN
educationr-2789	42	16	of	of	ADP
educationr-2789	42	17	the	the	DET
educationr-2789	42	18	mathematical	mathematical	ADJ
educationr-2789	42	19	idea	idea	NOUN
educationr-2789	42	20	.	.	PUNCT
educationr-2789	43	1	in	in	ADP
educationr-2789	43	2	the	the	DET
educationr-2789	43	3	discussions	discussion	NOUN
educationr-2789	43	4	,	,	PUNCT
educationr-2789	43	5	the	the	DET
educationr-2789	43	6	authors	author	NOUN
educationr-2789	43	7	clearly	clearly	ADV
educationr-2789	43	8	demonstrate	demonstrate	VERB
educationr-2789	43	9	algebraic	algebraic	ADJ
educationr-2789	43	10	thinking	thinking	NOUN
educationr-2789	43	11	and	and	CCONJ
educationr-2789	43	12	the	the	DET
educationr-2789	43	13	related	relate	VERB
educationr-2789	43	14	misconceptions	misconception	NOUN
educationr-2789	43	15	.	.	PUNCT
educationr-2789	44	1	it	it	PRON
educationr-2789	44	2	is	be	AUX
educationr-2789	44	3	noteworthy	noteworthy	ADJ
educationr-2789	44	4	that	that	SCONJ
educationr-2789	44	5	they	they	PRON
educationr-2789	44	6	examine	examine	VERB
educationr-2789	44	7	algebraic	algebraic	ADJ
educationr-2789	44	8	thinking	thinking	NOUN
educationr-2789	44	9	centered	center	VERB
educationr-2789	44	10	around	around	ADP
educationr-2789	44	11	paper	paper	NOUN
educationr-2789	44	12	-	-	PUNCT
educationr-2789	44	13	and	and	CCONJ
educationr-2789	44	14	-	-	PUNCT
educationr-2789	44	15	pencil	pencil	NOUN
educationr-2789	44	16	tasks	task	NOUN
educationr-2789	44	17	as	as	ADV
educationr-2789	44	18	well	well	ADV
educationr-2789	44	19	as	as	ADP
educationr-2789	44	20	the	the	DET
educationr-2789	44	21	role	role	NOUN
educationr-2789	44	22	technology	technology	NOUN
educationr-2789	44	23	plays	play	VERB
educationr-2789	44	24	in	in	ADP
educationr-2789	44	25	both	both	PRON
educationr-2789	44	26	helping	help	VERB
educationr-2789	44	27	and	and	CCONJ
educationr-2789	44	28	hindering	hinder	VERB
educationr-2789	44	29	algebraic	algebraic	ADJ
educationr-2789	44	30	thinking	thinking	NOUN
educationr-2789	44	31	.	.	PUNCT
educationr-2789	45	1	in	in	ADP
educationr-2789	45	2	addition	addition	NOUN
educationr-2789	45	3	to	to	ADP
educationr-2789	45	4	this	this	DET
educationr-2789	45	5	framework	framework	NOUN
educationr-2789	45	6	,	,	PUNCT
educationr-2789	45	7	the	the	DET
educationr-2789	45	8	authors	author	NOUN
educationr-2789	45	9	provide	provide	VERB
educationr-2789	45	10	a	a	DET
educationr-2789	45	11	comprehensive	comprehensive	ADJ
educationr-2789	45	12	list	list	NOUN
educationr-2789	45	13	of	of	ADP
educationr-2789	45	14	the	the	DET
educationr-2789	45	15	research	research	NOUN
educationr-2789	45	16	at	at	ADP
educationr-2789	45	17	the	the	DET
educationr-2789	45	18	end	end	NOUN
educationr-2789	45	19	of	of	ADP
educationr-2789	45	20	each	each	DET
educationr-2789	45	21	chapter	chapter	NOUN
educationr-2789	45	22	so	so	SCONJ
educationr-2789	45	23	that	that	SCONJ
educationr-2789	45	24	teachers	teacher	NOUN
educationr-2789	45	25	can	can	AUX
educationr-2789	45	26	reference	reference	VERB
educationr-2789	45	27	an	an	DET
educationr-2789	45	28	original	original	ADJ
educationr-2789	45	29	source	source	NOUN
educationr-2789	45	30	for	for	ADP
educationr-2789	45	31	further	further	ADJ
educationr-2789	45	32	reading	reading	NOUN
educationr-2789	45	33	.	.	PUNCT
educationr-2789	46	1	the	the	DET
educationr-2789	46	2	design	design	NOUN
educationr-2789	46	3	of	of	ADP
educationr-2789	46	4	the	the	DET
educationr-2789	46	5	text	text	NOUN
educationr-2789	46	6	allows	allow	VERB
educationr-2789	46	7	teachers	teacher	NOUN
educationr-2789	46	8	to	to	PART
educationr-2789	46	9	read	read	VERB
educationr-2789	46	10	cover	cover	NOUN
educationr-2789	46	11	-	-	PUNCT
educationr-2789	46	12	to	to	AUX
educationr-2789	46	13	-	-	PUNCT
educationr-2789	46	14	cover	cover	VERB
educationr-2789	46	15	for	for	ADP
educationr-2789	46	16	a	a	DET
educationr-2789	46	17	comprehensive	comprehensive	ADJ
educationr-2789	46	18	overview	overview	NOUN
educationr-2789	46	19	,	,	PUNCT
educationr-2789	46	20	read	read	VERB
educationr-2789	46	21	a	a	DET
educationr-2789	46	22	chapter	chapter	NOUN
educationr-2789	46	23	for	for	ADP
educationr-2789	46	24	a	a	DET
educationr-2789	46	25	deeper	deep	ADJ
educationr-2789	46	26	understanding	understanding	NOUN
educationr-2789	46	27	of	of	ADP
educationr-2789	46	28	a	a	DET
educationr-2789	46	29	broader	broad	ADJ
educationr-2789	46	30	topic	topic	NOUN
educationr-2789	46	31	,	,	PUNCT
educationr-2789	46	32	or	or	CCONJ
educationr-2789	46	33	home	home	NOUN
educationr-2789	46	34	in	in	ADV
educationr-2789	46	35	on	on	ADP
educationr-2789	46	36	a	a	DET
educationr-2789	46	37	specific	specific	ADJ
educationr-2789	46	38	subsection	subsection	NOUN
educationr-2789	46	39	for	for	ADP
educationr-2789	46	40	an	an	DET
educationr-2789	46	41	in	in	ADP
educationr-2789	46	42	-	-	PUNCT
educationr-2789	46	43	depth	depth	NOUN
educationr-2789	46	44	examination	examination	NOUN
educationr-2789	46	45	.	.	PUNCT
educationr-2789	47	1	at	at	ADP
educationr-2789	47	2	the	the	DET
educationr-2789	47	3	core	core	NOUN
educationr-2789	47	4	of	of	ADP
educationr-2789	47	5	book	book	NOUN
educationr-2789	47	6	are	be	AUX
educationr-2789	47	7	the	the	DET
educationr-2789	47	8	specific	specific	ADJ
educationr-2789	47	9	,	,	PUNCT
educationr-2789	47	10	practical	practical	ADJ
educationr-2789	47	11	examples	example	NOUN
educationr-2789	47	12	to	to	PART
educationr-2789	47	13	improve	improve	VERB
educationr-2789	47	14	instructional	instructional	ADJ
educationr-2789	47	15	practices	practice	NOUN
educationr-2789	47	16	.	.	PUNCT
educationr-2789	48	1	in	in	ADP
educationr-2789	48	2	each	each	DET
educationr-2789	48	3	subsection	subsection	NOUN
educationr-2789	48	4	,	,	PUNCT
educationr-2789	48	5	the	the	DET
educationr-2789	48	6	authors	author	NOUN
educationr-2789	48	7	examine	examine	VERB
educationr-2789	48	8	student	student	NOUN
educationr-2789	48	9	thinking	thinking	NOUN
educationr-2789	48	10	,	,	PUNCT
educationr-2789	48	11	offer	offer	VERB
educationr-2789	48	12	specific	specific	ADJ
educationr-2789	48	13	suggestions	suggestion	NOUN
educationr-2789	48	14	for	for	ADP
educationr-2789	48	15	teacher	teacher	NOUN
educationr-2789	48	16	planning	planning	NOUN
educationr-2789	48	17	,	,	PUNCT
educationr-2789	48	18	and	and	CCONJ
educationr-2789	48	19	suggest	suggest	VERB
educationr-2789	48	20	overarching	overarching	ADJ
educationr-2789	48	21	instructional	instructional	ADJ
educationr-2789	48	22	strategies	strategy	NOUN
educationr-2789	48	23	.	.	PUNCT
educationr-2789	49	1	for	for	ADP
educationr-2789	49	2	example	example	NOUN
educationr-2789	49	3	,	,	PUNCT
educationr-2789	49	4	they	they	PRON
educationr-2789	49	5	offer	offer	VERB
educationr-2789	49	6	concrete	concrete	ADJ
educationr-2789	49	7	examples	example	NOUN
educationr-2789	49	8	of	of	ADP
educationr-2789	49	9	student	student	NOUN
educationr-2789	49	10	thinking	thinking	NOUN
educationr-2789	49	11	from	from	ADP
educationr-2789	49	12	interviews	interview	NOUN
educationr-2789	49	13	,	,	PUNCT
educationr-2789	49	14	examination	examination	NOUN
educationr-2789	49	15	questions	question	NOUN
educationr-2789	49	16	,	,	PUNCT
educationr-2789	49	17	and	and	CCONJ
educationr-2789	49	18	problem	problem	NOUN
educationr-2789	49	19	-	-	PUNCT
educationr-2789	49	20	solving	solve	VERB
educationr-2789	49	21	situations	situation	NOUN
educationr-2789	49	22	.	.	PUNCT
educationr-2789	50	1	comparing	compare	VERB
educationr-2789	50	2	and	and	CCONJ
educationr-2789	50	3	contrasting	contrast	VERB
educationr-2789	50	4	the	the	DET
educationr-2789	50	5	reader	reader	NOUN
educationr-2789	50	6	’s	’s	PART
educationr-2789	50	7	students	student	NOUN
educationr-2789	50	8	’	'	PUNCT
educationr-2789	50	9	thinking	think	VERB
educationr-2789	50	10	to	to	ADP
educationr-2789	50	11	the	the	DET
educationr-2789	50	12	thinking	thinking	NOUN
educationr-2789	50	13	summarized	summarize	VERB
educationr-2789	50	14	in	in	ADP
educationr-2789	50	15	each	each	DET
educationr-2789	50	16	section	section	NOUN
educationr-2789	50	17	can	can	AUX
educationr-2789	50	18	offer	offer	VERB
educationr-2789	50	19	insights	insight	NOUN
educationr-2789	50	20	into	into	ADP
educationr-2789	50	21	instructional	instructional	ADJ
educationr-2789	50	22	moves	move	NOUN
educationr-2789	50	23	and	and	CCONJ
educationr-2789	50	24	questions	question	NOUN
educationr-2789	50	25	that	that	PRON
educationr-2789	50	26	can	can	AUX
educationr-2789	50	27	be	be	AUX
educationr-2789	50	28	used	use	VERB
educationr-2789	50	29	to	to	PART
educationr-2789	50	30	rectify	rectify	VERB
educationr-2789	50	31	misconceptions	misconception	NOUN
educationr-2789	50	32	or	or	CCONJ
educationr-2789	50	33	further	further	ADJ
educationr-2789	50	34	student	student	NOUN
educationr-2789	50	35	thinking	thinking	NOUN
educationr-2789	50	36	.	.	PUNCT
educationr-2789	51	1	at	at	ADP
educationr-2789	51	2	times	time	NOUN
educationr-2789	51	3	,	,	PUNCT
educationr-2789	51	4	the	the	DET
educationr-2789	51	5	text	text	NOUN
educationr-2789	51	6	lapses	lapse	NOUN
educationr-2789	51	7	into	into	ADP
educationr-2789	51	8	dense	dense	ADJ
educationr-2789	51	9	language	language	NOUN
educationr-2789	51	10	and	and	CCONJ
educationr-2789	51	11	definitions	definition	NOUN
educationr-2789	51	12	rather	rather	ADV
educationr-2789	51	13	than	than	ADP
educationr-2789	51	14	practitioners	practitioner	NOUN
educationr-2789	51	15	’	'	PUNCT
educationr-2789	51	16	language	language	NOUN
educationr-2789	51	17	.	.	PUNCT
educationr-2789	52	1	because	because	SCONJ
educationr-2789	52	2	of	of	ADP
educationr-2789	52	3	the	the	DET
educationr-2789	52	4	research	research	NOUN
educationr-2789	52	5	-	-	PUNCT
educationr-2789	52	6	based	base	VERB
educationr-2789	52	7	discussions	discussion	NOUN
educationr-2789	52	8	of	of	ADP
educationr-2789	52	9	algebraic	algebraic	ADJ
educationr-2789	52	10	thinking	thinking	NOUN
educationr-2789	52	11	,	,	PUNCT
educationr-2789	52	12	a	a	DET
educationr-2789	52	13	new	new	ADJ
educationr-2789	52	14	teacher	teacher	NOUN
educationr-2789	52	15	may	may	AUX
educationr-2789	52	16	find	find	VERB
educationr-2789	52	17	many	many	ADJ
educationr-2789	52	18	explanations	explanation	NOUN
educationr-2789	52	19	to	to	PART
educationr-2789	52	20	be	be	AUX
educationr-2789	52	21	overwhelming	overwhelming	ADJ
educationr-2789	52	22	and	and	CCONJ
educationr-2789	52	23	difficult	difficult	ADJ
educationr-2789	52	24	to	to	PART
educationr-2789	52	25	understand	understand	VERB
educationr-2789	52	26	.	.	PUNCT
educationr-2789	53	1	however	however	ADV
educationr-2789	53	2	,	,	PUNCT
educationr-2789	53	3	novice	novice	NOUN
educationr-2789	53	4	teachers	teacher	NOUN
educationr-2789	53	5	can	can	AUX
educationr-2789	53	6	use	use	VERB
educationr-2789	53	7	this	this	DET
educationr-2789	53	8	information	information	NOUN
educationr-2789	53	9	as	as	ADP
educationr-2789	53	10	an	an	DET
educationr-2789	53	11	overview	overview	NOUN
educationr-2789	53	12	as	as	SCONJ
educationr-2789	53	13	they	they	PRON
educationr-2789	53	14	begin	begin	VERB
educationr-2789	53	15	to	to	PART
educationr-2789	53	16	prepare	prepare	VERB
educationr-2789	53	17	for	for	ADP
educationr-2789	53	18	each	each	DET
educationr-2789	53	19	new	new	ADJ
educationr-2789	53	20	unit	unit	NOUN
educationr-2789	53	21	in	in	ADP
educationr-2789	53	22	algebra	algebra	PROPN
educationr-2789	53	23	.	.	PUNCT
educationr-2789	54	1	as	as	SCONJ
educationr-2789	54	2	they	they	PRON
educationr-2789	54	3	begin	begin	VERB
educationr-2789	54	4	to	to	PART
educationr-2789	54	5	accumulate	accumulate	VERB
educationr-2789	54	6	more	more	ADJ
educationr-2789	54	7	examples	example	NOUN
educationr-2789	54	8	of	of	ADP
educationr-2789	54	9	student	student	NOUN
educationr-2789	54	10	thinking	thinking	NOUN
educationr-2789	54	11	,	,	PUNCT
educationr-2789	54	12	they	they	PRON
educationr-2789	54	13	can	can	AUX
educationr-2789	54	14	go	go	VERB
educationr-2789	54	15	back	back	ADV
educationr-2789	54	16	and	and	CCONJ
educationr-2789	54	17	reread	reread	VERB
educationr-2789	54	18	the	the	DET
educationr-2789	54	19	text	text	NOUN
educationr-2789	54	20	to	to	PART
educationr-2789	54	21	find	find	VERB
educationr-2789	54	22	suggestions	suggestion	NOUN
educationr-2789	54	23	for	for	ADP
educationr-2789	54	24	correcting	correct	VERB
educationr-2789	54	25	student	student	NOUN
educationr-2789	54	26	misconceptions	misconception	NOUN
educationr-2789	54	27	.	.	PUNCT
educationr-2789	55	1	new	new	ADJ
educationr-2789	55	2	teachers	teacher	NOUN
educationr-2789	55	3	can	can	AUX
educationr-2789	55	4	also	also	ADV
educationr-2789	55	5	use	use	VERB
educationr-2789	55	6	the	the	DET
educationr-2789	55	7	information	information	NOUN
educationr-2789	55	8	to	to	PART
educationr-2789	55	9	gain	gain	VERB
educationr-2789	55	10	insight	insight	NOUN
educationr-2789	55	11	into	into	ADP
educationr-2789	55	12	their	their	PRON
educationr-2789	55	13	students	student	NOUN
educationr-2789	55	14	’	'	PUNCT
educationr-2789	55	15	thinking	think	VERB
educationr-2789	55	16	as	as	SCONJ
educationr-2789	55	17	they	they	PRON
educationr-2789	55	18	begin	begin	VERB
educationr-2789	55	19	their	their	PRON
educationr-2789	55	20	career	career	NOUN
educationr-2789	55	21	.	.	PUNCT
educationr-2789	56	1	all	all	DET
educationr-2789	56	2	teachers	teacher	NOUN
educationr-2789	56	3	have	have	AUX
educationr-2789	56	4	wondered	wonder	VERB
educationr-2789	56	5	“	"	PUNCT
educationr-2789	56	6	what	what	PRON
educationr-2789	56	7	in	in	ADP
educationr-2789	56	8	the	the	DET
educationr-2789	56	9	world	world	NOUN
educationr-2789	56	10	where	where	SCONJ
educationr-2789	56	11	they	they	PRON
educationr-2789	56	12	thinking	think	VERB
educationr-2789	56	13	?	?	PUNCT
educationr-2789	56	14	”	"	PUNCT
educationr-2789	56	15	as	as	SCONJ
educationr-2789	56	16	they	they	PRON
educationr-2789	56	17	examined	examine	VERB
educationr-2789	56	18	students	student	NOUN
educationr-2789	56	19	’	’	PART
educationr-2789	56	20	work	work	NOUN
educationr-2789	56	21	,	,	PUNCT
educationr-2789	56	22	read	read	VERB
educationr-2789	56	23	students	student	NOUN
educationr-2789	56	24	’	’	PART
educationr-2789	56	25	explanations	explanation	NOUN
educationr-2789	56	26	,	,	PUNCT
educationr-2789	56	27	or	or	CCONJ
educationr-2789	56	28	listened	listen	VERB
educationr-2789	56	29	to	to	ADP
educationr-2789	56	30	students	student	NOUN
educationr-2789	56	31	’	'	PUNCT
educationr-2789	56	32	justifications	justification	NOUN
educationr-2789	56	33	.	.	PUNCT
educationr-2789	57	1	how	how	SCONJ
educationr-2789	57	2	students	student	NOUN
educationr-2789	57	3	think	think	VERB
educationr-2789	57	4	when	when	SCONJ
educationr-2789	57	5	doing	do	VERB
educationr-2789	57	6	algebra	algebra	NOUN
educationr-2789	57	7	offers	offer	VERB
educationr-2789	57	8	useful	useful	ADJ
educationr-2789	57	9	insights	insight	NOUN
educationr-2789	57	10	as	as	ADP
educationr-2789	57	11	to	to	ADP
educationr-2789	57	12	why	why	SCONJ
educationr-2789	57	13	students	student	NOUN
educationr-2789	57	14	believe	believe	VERB
educationr-2789	57	15	their	their	PRON
educationr-2789	57	16	thinking	thinking	NOUN
educationr-2789	57	17	makes	make	VERB
educationr-2789	57	18	sense	sense	NOUN
educationr-2789	57	19	and	and	CCONJ
educationr-2789	57	20	how	how	SCONJ
educationr-2789	57	21	teachers	teacher	NOUN
educationr-2789	57	22	can	can	AUX
educationr-2789	57	23	mitigate	mitigate	VERB
educationr-2789	57	24	algebraic	algebraic	ADJ
educationr-2789	57	25	thinking	thinking	NOUN
educationr-2789	57	26	misconceptions	misconception	NOUN
educationr-2789	57	27	in	in	ADP
educationr-2789	57	28	their	their	PRON
educationr-2789	57	29	teaching	teaching	NOUN
educationr-2789	57	30	.	.	PUNCT
educationr-2789	58	1	i	i	PRON
educationr-2789	58	2	recommend	recommend	VERB
educationr-2789	58	3	a	a	DET
educationr-2789	58	4	three	three	NUM
educationr-2789	58	5	-	-	PUNCT
educationr-2789	58	6	pronged	pronged	ADJ
educationr-2789	58	7	reading	reading	NOUN
educationr-2789	58	8	approach	approach	NOUN
educationr-2789	58	9	to	to	ADP
educationr-2789	58	10	this	this	DET
educationr-2789	58	11	book	book	NOUN
educationr-2789	58	12	for	for	ADP
educationr-2789	58	13	teachers	teacher	NOUN
educationr-2789	58	14	,	,	PUNCT
educationr-2789	58	15	instructional	instructional	ADJ
educationr-2789	58	16	coaches	coach	NOUN
educationr-2789	58	17	,	,	PUNCT
educationr-2789	58	18	and	and	CCONJ
educationr-2789	58	19	professional	professional	ADJ
educationr-2789	58	20	development	development	NOUN
educationr-2789	58	21	providers	provider	NOUN
educationr-2789	58	22	.	.	PUNCT
educationr-2789	59	1	in	in	ADP
educationr-2789	59	2	the	the	DET
educationr-2789	59	3	first	first	ADJ
educationr-2789	59	4	reading	reading	NOUN
educationr-2789	59	5	,	,	PUNCT
educationr-2789	59	6	look	look	VERB
educationr-2789	59	7	for	for	ADP
educationr-2789	59	8	ways	way	NOUN
educationr-2789	59	9	to	to	PART
educationr-2789	59	10	recognize	recognize	VERB
educationr-2789	59	11	and	and	CCONJ
educationr-2789	59	12	correct	correct	ADJ
educationr-2789	59	13	student	student	NOUN
educationr-2789	59	14	misconceptions	misconception	NOUN
educationr-2789	59	15	in	in	ADP
educationr-2789	59	16	your	your	PRON
educationr-2789	59	17	teaching	teaching	NOUN
educationr-2789	59	18	moves	move	NOUN
educationr-2789	59	19	.	.	PUNCT
educationr-2789	60	1	in	in	ADP
educationr-2789	60	2	the	the	DET
educationr-2789	60	3	second	second	ADJ
educationr-2789	60	4	reading	reading	NOUN
educationr-2789	60	5	,	,	PUNCT
educationr-2789	60	6	align	align	VERB
educationr-2789	60	7	your	your	PRON
educationr-2789	60	8	instructional	instructional	ADJ
educationr-2789	60	9	strategies	strategy	NOUN
educationr-2789	60	10	and	and	CCONJ
educationr-2789	60	11	lesson	lesson	NOUN
educationr-2789	60	12	plans	plan	NOUN
educationr-2789	60	13	to	to	PART
educationr-2789	60	14	reflect	reflect	VERB
educationr-2789	60	15	the	the	DET
educationr-2789	60	16	recommendations	recommendation	NOUN
educationr-2789	60	17	.	.	PUNCT
educationr-2789	61	1	in	in	ADP
educationr-2789	61	2	the	the	DET
educationr-2789	61	3	third	third	ADJ
educationr-2789	61	4	reading	reading	NOUN
educationr-2789	61	5	,	,	PUNCT
educationr-2789	61	6	be	be	AUX
educationr-2789	61	7	aware	aware	ADJ
educationr-2789	61	8	of	of	ADP
educationr-2789	61	9	how	how	SCONJ
educationr-2789	61	10	the	the	DET
educationr-2789	61	11	research	research	NOUN
educationr-2789	61	12	can	can	AUX
educationr-2789	61	13	inform	inform	VERB
educationr-2789	61	14	your	your	PRON
educationr-2789	61	15	practice	practice	NOUN
educationr-2789	61	16	.	.	PUNCT
educationr-2789	62	1	it	it	PRON
educationr-2789	62	2	can	can	AUX
educationr-2789	62	3	be	be	AUX
educationr-2789	62	4	used	use	VERB
educationr-2789	62	5	to	to	PART
educationr-2789	62	6	home	home	VERB
educationr-2789	62	7	in	in	ADP
educationr-2789	62	8	on	on	ADP
educationr-2789	62	9	specific	specific	ADJ
educationr-2789	62	10	trouble	trouble	NOUN
educationr-2789	62	11	spots	spot	NOUN
educationr-2789	62	12	in	in	ADP
educationr-2789	62	13	a	a	DET
educationr-2789	62	14	groups	group	NOUN
educationr-2789	62	15	’	'	PUNCT
educationr-2789	62	16	algebraic	algebraic	ADJ
educationr-2789	62	17	thinking	thinking	NOUN
educationr-2789	62	18	,	,	PUNCT
educationr-2789	62	19	provide	provide	VERB
educationr-2789	62	20	a	a	DET
educationr-2789	62	21	holistic	holistic	ADJ
educationr-2789	62	22	overview	overview	NOUN
educationr-2789	62	23	of	of	ADP
educationr-2789	62	24	the	the	DET
educationr-2789	62	25	teaching	teaching	NOUN
educationr-2789	62	26	and	and	CCONJ
educationr-2789	62	27	thinking	thinking	NOUN
educationr-2789	62	28	of	of	ADP
educationr-2789	62	29	algebra	algebra	NOUN
educationr-2789	62	30	,	,	PUNCT
educationr-2789	62	31	and	and	CCONJ
educationr-2789	62	32	be	be	AUX
educationr-2789	62	33	a	a	DET
educationr-2789	62	34	jumping	jumping	NOUN
educationr-2789	62	35	off	off	ADP
educationr-2789	62	36	point	point	NOUN
educationr-2789	62	37	to	to	PART
educationr-2789	62	38	start	start	VERB
educationr-2789	62	39	conversations	conversation	NOUN
educationr-2789	62	40	about	about	ADP
educationr-2789	62	41	how	how	SCONJ
educationr-2789	62	42	to	to	PART
educationr-2789	62	43	implement	implement	VERB
educationr-2789	62	44	change	change	NOUN
educationr-2789	62	45	in	in	ADP
educationr-2789	62	46	the	the	DET
educationr-2789	62	47	teaching	teaching	NOUN
educationr-2789	62	48	and	and	CCONJ
educationr-2789	62	49	learning	learning	NOUN
educationr-2789	62	50	of	of	ADP
educationr-2789	62	51	algebra	algebra	PROPN
educationr-2789	62	52	.	.	PUNCT
educationr-2789	63	1	i	i	PRON
educationr-2789	63	2	believe	believe	VERB
educationr-2789	63	3	all	all	DET
educationr-2789	63	4	teachers	teacher	NOUN
educationr-2789	63	5	can	can	AUX
educationr-2789	63	6	find	find	VERB
educationr-2789	63	7	gems	gem	NOUN
educationr-2789	63	8	of	of	ADP
educationr-2789	63	9	information	information	NOUN
educationr-2789	63	10	in	in	ADP
educationr-2789	63	11	this	this	DET
educationr-2789	63	12	book	book	NOUN
educationr-2789	63	13	that	that	PRON
educationr-2789	63	14	will	will	AUX
educationr-2789	63	15	improve	improve	VERB
educationr-2789	63	16	instructional	instructional	ADJ
educationr-2789	63	17	practices	practice	NOUN
educationr-2789	63	18	so	so	SCONJ
educationr-2789	63	19	that	that	SCONJ
educationr-2789	63	20	all	all	DET
educationr-2789	63	21	students	student	NOUN
educationr-2789	63	22	develop	develop	VERB
educationr-2789	63	23	strong	strong	ADJ
educationr-2789	63	24	algebraic	algebraic	ADJ
educationr-2789	63	25	thinking	thinking	NOUN
educationr-2789	63	26	,	,	PUNCT
educationr-2789	63	27	make	make	VERB
educationr-2789	63	28	connections	connection	NOUN
educationr-2789	63	29	between	between	ADP
educationr-2789	63	30	representations	representation	NOUN
educationr-2789	63	31	,	,	PUNCT
educationr-2789	63	32	and	and	CCONJ
educationr-2789	63	33	have	have	VERB
educationr-2789	63	34	a	a	DET
educationr-2789	63	35	deep	deep	ADJ
educationr-2789	63	36	conceptual	conceptual	ADJ
educationr-2789	63	37	understanding	understanding	NOUN
educationr-2789	63	38	of	of	ADP
educationr-2789	63	39	algebra	algebra	NOUN
educationr-2789	63	40	.	.	PUNCT
educationr-2789	64	1	education	education	NOUN
educationr-2789	64	2	review	review	VERB
educationr-2789	64	3	4	4	NUM
educationr-2789	64	4	references	reference	NOUN
educationr-2789	64	5	leatham	leatham	PROPN
educationr-2789	64	6	,	,	PUNCT
educationr-2789	64	7	k.	k.	PROPN
educationr-2789	64	8	r.	r.	PROPN
educationr-2789	64	9	,	,	PUNCT
educationr-2789	64	10	peterson	peterson	PROPN
educationr-2789	64	11	,	,	PUNCT
educationr-2789	64	12	b.	b.	PROPN
educationr-2789	64	13	e.	e.	PROPN
educationr-2789	64	14	,	,	PUNCT
educationr-2789	64	15	stockero	stockero	NOUN
educationr-2789	64	16	,	,	PUNCT
educationr-2789	64	17	s.	s.	PROPN
educationr-2789	64	18	,	,	PUNCT
educationr-2789	64	19	&	&	CCONJ
educationr-2789	64	20	vanzoest	vanzo	ADJ
educationr-2789	64	21	,	,	PUNCT
educationr-2789	64	22	l.	l.	PROPN
educationr-2789	64	23	r.	r.	PROPN
educationr-2789	64	24	(	(	PUNCT
educationr-2789	64	25	2015	2015	NUM
educationr-2789	64	26	)	)	PUNCT
educationr-2789	64	27	.	.	PUNCT
educationr-2789	65	1	conceptualizing	conceptualize	VERB
educationr-2789	65	2	mathematical	mathematical	ADJ
educationr-2789	65	3	significant	significant	ADJ
educationr-2789	65	4	pedagogical	pedagogical	ADJ
educationr-2789	65	5	opportunities	opportunity	NOUN
educationr-2789	65	6	to	to	PART
educationr-2789	65	7	build	build	VERB
educationr-2789	65	8	on	on	ADP
educationr-2789	65	9	student	student	NOUN
educationr-2789	65	10	thinking	thinking	NOUN
educationr-2789	65	11	.	.	PUNCT
educationr-2789	66	1	journal	journal	PROPN
educationr-2789	66	2	for	for	ADP
educationr-2789	66	3	research	research	NOUN
educationr-2789	66	4	in	in	ADP
educationr-2789	66	5	mathematics	mathematics	PROPN
educationr-2789	66	6	education	education	NOUN
educationr-2789	66	7	,	,	PUNCT
educationr-2789	66	8	88	88	NUM
educationr-2789	66	9	-	-	SYM
educationr-2789	66	10	124	124	NUM
educationr-2789	66	11	.	.	PUNCT
educationr-2789	67	1	national	national	PROPN
educationr-2789	67	2	council	council	PROPN
educationr-2789	67	3	of	of	ADP
educationr-2789	67	4	teachers	teacher	NOUN
educationr-2789	67	5	of	of	ADP
educationr-2789	67	6	mathematics	mathematic	NOUN
educationr-2789	67	7	.	.	PUNCT
educationr-2789	68	1	(	(	PUNCT
educationr-2789	68	2	2014	2014	NUM
educationr-2789	68	3	)	)	PUNCT
educationr-2789	68	4	.	.	PUNCT
educationr-2789	69	1	principles	principle	NOUN
educationr-2789	69	2	to	to	ADP
educationr-2789	69	3	actions	action	NOUN
educationr-2789	69	4	:	:	PUNCT
educationr-2789	69	5	ensuring	ensure	VERB
educationr-2789	69	6	mathematical	mathematical	ADJ
educationr-2789	69	7	success	success	NOUN
educationr-2789	69	8	for	for	ADP
educationr-2789	69	9	all	all	PRON
educationr-2789	69	10	.	.	PUNCT
educationr-2789	70	1	author	author	NOUN
educationr-2789	70	2	.	.	PUNCT
educationr-2789	71	1	about	about	ADP
educationr-2789	71	2	the	the	DET
educationr-2789	71	3	reviewer	reviewer	NOUN
educationr-2789	71	4	amy	amy	PROPN
educationr-2789	71	5	kassel	kassel	PROPN
educationr-2789	71	6	is	be	AUX
educationr-2789	71	7	currently	currently	ADV
educationr-2789	71	8	the	the	DET
educationr-2789	71	9	secondary	secondary	ADJ
educationr-2789	71	10	mathematics	mathematic	NOUN
educationr-2789	71	11	curriculum	curriculum	NOUN
educationr-2789	71	12	coordinator	coordinator	NOUN
educationr-2789	71	13	and	and	CCONJ
educationr-2789	71	14	mathematics	mathematics	PROPN
educationr-2789	71	15	instructional	instructional	ADJ
educationr-2789	71	16	coach	coach	NOUN
educationr-2789	71	17	for	for	ADP
educationr-2789	71	18	laramie	laramie	PROPN
educationr-2789	71	19	county	county	PROPN
educationr-2789	71	20	school	school	NOUN
educationr-2789	71	21	district	district	NOUN
educationr-2789	71	22	#	#	SYM
educationr-2789	71	23	1	1	NUM
educationr-2789	71	24	in	in	ADP
educationr-2789	71	25	cheyenne	cheyenne	PROPN
educationr-2789	71	26	,	,	PUNCT
educationr-2789	71	27	wyoming	wyoming	PROPN
educationr-2789	71	28	.	.	PUNCT
educationr-2789	72	1	she	she	PRON
educationr-2789	72	2	is	be	AUX
educationr-2789	72	3	a	a	DET
educationr-2789	72	4	national	national	ADJ
educationr-2789	72	5	board	board	NOUN
educationr-2789	72	6	certified	certify	VERB
educationr-2789	72	7	teacher	teacher	NOUN
educationr-2789	72	8	and	and	CCONJ
educationr-2789	72	9	taught	teach	VERB
educationr-2789	72	10	high	high	ADJ
educationr-2789	72	11	school	school	NOUN
educationr-2789	72	12	mathematics	mathematic	NOUN
educationr-2789	72	13	for	for	ADP
educationr-2789	72	14	26	26	NUM
educationr-2789	72	15	years	year	NOUN
educationr-2789	72	16	.	.	PUNCT
educationr-2789	73	1	she	she	PRON
educationr-2789	73	2	has	have	AUX
educationr-2789	73	3	completed	complete	VERB
educationr-2789	73	4	the	the	DET
educationr-2789	73	5	math	math	NOUN
educationr-2789	73	6	teacher	teacher	NOUN
educationr-2789	73	7	leadership	leadership	NOUN
educationr-2789	73	8	program	program	NOUN
educationr-2789	73	9	at	at	ADP
educationr-2789	73	10	the	the	DET
educationr-2789	73	11	university	university	PROPN
educationr-2789	73	12	of	of	ADP
educationr-2789	73	13	northern	northern	PROPN
educationr-2789	73	14	colorado	colorado	PROPN
educationr-2789	73	15	,	,	PUNCT
educationr-2789	73	16	earned	earn	VERB
educationr-2789	73	17	the	the	DET
educationr-2789	73	18	arch	arch	ADJ
educationr-2789	73	19	coal	coal	NOUN
educationr-2789	73	20	teacher	teacher	NOUN
educationr-2789	73	21	achievement	achievement	NOUN
educationr-2789	73	22	award	award	PROPN
educationr-2789	73	23	,	,	PUNCT
educationr-2789	73	24	and	and	CCONJ
educationr-2789	73	25	is	be	AUX
educationr-2789	73	26	the	the	DET
educationr-2789	73	27	recipient	recipient	NOUN
educationr-2789	73	28	of	of	ADP
educationr-2789	73	29	the	the	DET
educationr-2789	73	30	2017	2017	NUM
educationr-2789	73	31	presidential	presidential	ADJ
educationr-2789	73	32	award	award	NOUN
educationr-2789	73	33	for	for	ADP
educationr-2789	73	34	excellence	excellence	NOUN
educationr-2789	73	35	in	in	ADP
educationr-2789	73	36	mathematics	mathematics	PROPN
educationr-2789	73	37	and	and	CCONJ
educationr-2789	73	38	science	science	NOUN
educationr-2789	73	39	teaching	teaching	NOUN
educationr-2789	73	40	.	.	PUNCT
educationr-2789	74	1	she	she	PRON
educationr-2789	74	2	earned	earn	VERB
educationr-2789	74	3	her	she	PRON
educationr-2789	74	4	b.s.ed	b.s.ed	NOUN
educationr-2789	74	5	.	.	PROPN
educationr-2789	74	6	in	in	ADP
educationr-2789	74	7	mathematics	mathematics	PROPN
educationr-2789	74	8	from	from	ADP
educationr-2789	74	9	southeast	southeast	PROPN
educationr-2789	74	10	missouri	missouri	PROPN
educationr-2789	74	11	state	state	PROPN
educationr-2789	74	12	university	university	PROPN
educationr-2789	74	13	,	,	PUNCT
educationr-2789	74	14	m.s	m.s	PROPN
educationr-2789	74	15	.	.	PROPN
educationr-2789	75	1	in	in	ADP
educationr-2789	75	2	mathematics	mathematic	NOUN
educationr-2789	75	3	from	from	ADP
educationr-2789	75	4	western	western	ADJ
educationr-2789	75	5	illinois	illinois	PROPN
educationr-2789	75	6	state	state	PROPN
educationr-2789	75	7	university	university	PROPN
educationr-2789	75	8	,	,	PUNCT
educationr-2789	75	9	and	and	CCONJ
educationr-2789	75	10	is	be	AUX
educationr-2789	75	11	currently	currently	ADV
educationr-2789	75	12	a	a	DET
educationr-2789	75	13	ph.d	ph.d	PROPN
educationr-2789	75	14	.	.	PUNCT
educationr-2789	75	15	student	student	NOUN
educationr-2789	75	16	in	in	ADP
educationr-2789	75	17	mathematics	mathematics	PROPN
educationr-2789	75	18	education	education	NOUN
educationr-2789	75	19	at	at	ADP
educationr-2789	75	20	the	the	DET
educationr-2789	75	21	university	university	PROPN
educationr-2789	75	22	of	of	ADP
educationr-2789	75	23	wyoming	wyoming	PROPN
educationr-2789	75	24	.	.	PUNCT
educationr-2789	76	1	she	she	PRON
educationr-2789	76	2	can	can	AUX
educationr-2789	76	3	be	be	AUX
educationr-2789	76	4	contacted	contact	VERB
educationr-2789	76	5	at	at	ADP
educationr-2789	76	6	amy.kassel@laramie1.org	amy.kassel@laramie1.org	PROPN
educationr-2789	76	7	education	education	NOUN
educationr-2789	76	8	review	review	NOUN
educationr-2789	76	9	/	/	SYM
educationr-2789	76	10	reseñas	reseñas	PROPN
educationr-2789	76	11	educativas	educativas	PROPN
educationr-2789	76	12	/	/	SYM
educationr-2789	76	13	resenhas	resenhas	PROPN
educationr-2789	76	14	educativas	educativas	NOUN
educationr-2789	76	15	is	be	AUX
educationr-2789	76	16	supported	support	VERB
educationr-2789	76	17	by	by	ADP
educationr-2789	76	18	the	the	DET
educationr-2789	76	19	scholarly	scholarly	ADJ
educationr-2789	76	20	communications	communication	NOUN
educationr-2789	76	21	group	group	NOUN
educationr-2789	76	22	at	at	ADP
educationr-2789	76	23	the	the	DET
educationr-2789	76	24	mary	mary	PROPN
educationr-2789	76	25	lou	lou	PROPN
educationr-2789	76	26	fulton	fulton	PROPN
educationr-2789	76	27	teachers	teachers	PROPN
educationr-2789	76	28	college	college	PROPN
educationr-2789	76	29	,	,	PUNCT
educationr-2789	76	30	arizona	arizona	PROPN
educationr-2789	76	31	state	state	PROPN
educationr-2789	76	32	university	university	PROPN
educationr-2789	76	33	.	.	PUNCT
educationr-2789	77	1	copyright	copyright	NOUN
educationr-2789	77	2	is	be	AUX
educationr-2789	77	3	retained	retain	VERB
educationr-2789	77	4	by	by	ADP
educationr-2789	77	5	the	the	DET
educationr-2789	77	6	first	first	ADJ
educationr-2789	77	7	or	or	CCONJ
educationr-2789	77	8	sole	sole	ADJ
educationr-2789	77	9	author	author	NOUN
educationr-2789	77	10	,	,	PUNCT
educationr-2789	77	11	who	who	PRON
educationr-2789	77	12	grants	grant	VERB
educationr-2789	77	13	right	right	ADV
educationr-2789	77	14	of	of	ADP
educationr-2789	77	15	first	first	ADJ
educationr-2789	77	16	publication	publication	NOUN
educationr-2789	77	17	to	to	ADP
educationr-2789	77	18	the	the	DET
educationr-2789	77	19	education	education	NOUN
educationr-2789	77	20	review	review	NOUN
educationr-2789	77	21	.	.	PUNCT
educationr-2789	78	1	readers	reader	NOUN
educationr-2789	78	2	are	be	AUX
educationr-2789	78	3	free	free	ADJ
educationr-2789	78	4	to	to	PART
educationr-2789	78	5	copy	copy	VERB
educationr-2789	78	6	,	,	PUNCT
educationr-2789	78	7	display	display	NOUN
educationr-2789	78	8	,	,	PUNCT
educationr-2789	78	9	and	and	CCONJ
educationr-2789	78	10	distribute	distribute	VERB
educationr-2789	78	11	this	this	DET
educationr-2789	78	12	article	article	NOUN
educationr-2789	78	13	,	,	PUNCT
educationr-2789	78	14	as	as	ADV
educationr-2789	78	15	long	long	ADV
educationr-2789	78	16	as	as	SCONJ
educationr-2789	78	17	the	the	DET
educationr-2789	78	18	work	work	NOUN
educationr-2789	78	19	is	be	AUX
educationr-2789	78	20	attributed	attribute	VERB
educationr-2789	78	21	to	to	ADP
educationr-2789	78	22	the	the	DET
educationr-2789	78	23	author(s	author(s	NOUN
educationr-2789	78	24	)	)	PUNCT
educationr-2789	78	25	and	and	CCONJ
educationr-2789	78	26	education	education	NOUN
educationr-2789	78	27	review	review	NOUN
educationr-2789	78	28	,	,	PUNCT
educationr-2789	78	29	it	it	PRON
educationr-2789	78	30	is	be	AUX
educationr-2789	78	31	distributed	distribute	VERB
educationr-2789	78	32	for	for	ADP
educationr-2789	78	33	non	non	ADJ
educationr-2789	78	34	-	-	ADJ
educationr-2789	78	35	commercial	commercial	ADJ
educationr-2789	78	36	purposes	purpose	NOUN
educationr-2789	78	37	only	only	ADV
educationr-2789	78	38	,	,	PUNCT
educationr-2789	78	39	and	and	CCONJ
educationr-2789	78	40	no	no	DET
educationr-2789	78	41	alteration	alteration	NOUN
educationr-2789	78	42	or	or	CCONJ
educationr-2789	78	43	transformation	transformation	NOUN
educationr-2789	78	44	is	be	AUX
educationr-2789	78	45	made	make	VERB
educationr-2789	78	46	in	in	ADP
educationr-2789	78	47	the	the	DET
educationr-2789	78	48	work	work	NOUN
educationr-2789	78	49	.	.	PUNCT
educationr-2789	79	1	more	more	ADJ
educationr-2789	79	2	details	detail	NOUN
educationr-2789	79	3	of	of	ADP
educationr-2789	79	4	this	this	DET
educationr-2789	79	5	creative	creative	ADJ
educationr-2789	79	6	commons	common	NOUN
educationr-2789	79	7	license	license	NOUN
educationr-2789	79	8	are	be	AUX
educationr-2789	79	9	available	available	ADJ
educationr-2789	79	10	at	at	ADP
educationr-2789	79	11	http://creativecommons.org/licenses/by-nc-sa/3.0/.	http://creativecommons.org/licenses/by-nc-sa/3.0/.	NOUN
educationr-2789	79	12	all	all	DET
educationr-2789	79	13	other	other	ADJ
educationr-2789	79	14	uses	use	NOUN
educationr-2789	79	15	must	must	AUX
educationr-2789	79	16	be	be	AUX
educationr-2789	79	17	approved	approve	VERB
educationr-2789	79	18	by	by	ADP
educationr-2789	79	19	the	the	DET
educationr-2789	79	20	author(s	author(s	NOUN
educationr-2789	79	21	)	)	PUNCT
educationr-2789	79	22	or	or	CCONJ
educationr-2789	79	23	education	education	NOUN
educationr-2789	79	24	review	review	NOUN
educationr-2789	79	25	.	.	PUNCT
educationr-2789	80	1	education	education	NOUN
educationr-2789	80	2	review	review	NOUN
educationr-2789	80	3	is	be	AUX
educationr-2789	80	4	published	publish	VERB
educationr-2789	80	5	by	by	ADP
educationr-2789	80	6	the	the	DET
educationr-2789	80	7	scholarly	scholarly	ADJ
educationr-2789	80	8	communications	communication	NOUN
educationr-2789	80	9	group	group	NOUN
educationr-2789	80	10	of	of	ADP
educationr-2789	80	11	the	the	DET
educationr-2789	80	12	mary	mary	PROPN
educationr-2789	80	13	lou	lou	PROPN
educationr-2789	80	14	fulton	fulton	PROPN
educationr-2789	80	15	teachers	teachers	PROPN
educationr-2789	80	16	college	college	PROPN
educationr-2789	80	17	,	,	PUNCT
educationr-2789	80	18	arizona	arizona	PROPN
educationr-2789	80	19	state	state	PROPN
educationr-2789	80	20	university	university	PROPN
educationr-2789	80	21	.	.	PUNCT
educationr-2789	81	1	disclaimer	disclaimer	ADJ
educationr-2789	81	2	:	:	PUNCT
educationr-2789	81	3	the	the	DET
educationr-2789	81	4	views	view	NOUN
educationr-2789	81	5	or	or	CCONJ
educationr-2789	81	6	opinions	opinion	NOUN
educationr-2789	81	7	presented	present	VERB
educationr-2789	81	8	in	in	ADP
educationr-2789	81	9	book	book	NOUN
educationr-2789	81	10	reviews	review	NOUN
educationr-2789	81	11	are	be	AUX
educationr-2789	81	12	solely	solely	ADV
educationr-2789	81	13	those	those	PRON
educationr-2789	81	14	of	of	ADP
educationr-2789	81	15	the	the	DET
educationr-2789	81	16	author(s	author(s	NOUN
educationr-2789	81	17	)	)	PUNCT
educationr-2789	81	18	and	and	CCONJ
educationr-2789	81	19	do	do	AUX
educationr-2789	81	20	not	not	PART
educationr-2789	81	21	necessarily	necessarily	ADV
educationr-2789	81	22	represent	represent	VERB
educationr-2789	81	23	those	those	PRON
educationr-2789	81	24	of	of	ADP
educationr-2789	81	25	education	education	NOUN
educationr-2789	81	26	review	review	NOUN
educationr-2789	81	27	.	.	PUNCT
educationr-2789	82	1	connect	connect	VERB
educationr-2789	82	2	with	with	ADP
educationr-2789	82	3	education	education	NOUN
educationr-2789	82	4	review	review	NOUN
educationr-2789	82	5	on	on	ADP
educationr-2789	82	6	facebook	facebook	PROPN
educationr-2789	82	7	(	(	PUNCT
educationr-2789	82	8	https://www.facebook.com/pages/educationreview/178358222192644	https://www.facebook.com/pages/educationreview/178358222192644	NOUN
educationr-2789	82	9	)	)	PUNCT
educationr-2789	82	10	and	and	CCONJ
educationr-2789	82	11	on	on	ADP
educationr-2789	82	12	twitter	twitter	NOUN
educationr-2789	82	13	@educreview	@educreview	PROPN
educationr-2789	82	14	mailto:amy.kassel@laramie1.org	mailto:amy.kassel@laramie1.org	PROPN
educationr-2789	82	15	https://www.facebook.com/pages/education-review/178358222192644	https://www.facebook.com/pages/education-review/178358222192644	X
educationr-2789	82	16	https://www.facebook.com/pages/education-review/178358222192644	https://www.facebook.com/pages/education-review/178358222192644	PUNCT
educationr-2789	82	17	review	review	NOUN
educationr-2789	82	18	of	of	ADP
educationr-2789	82	19	how	how	SCONJ
educationr-2789	82	20	students	student	NOUN
educationr-2789	82	21	think	think	VERB
educationr-2789	82	22	when	when	SCONJ
educationr-2789	82	23	doing	do	VERB
educationr-2789	82	24	algebra	algebra	NOUN
educationr-2789	82	25	5	5	NUM