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Towards Anti-Deficit Education in Undergraduate Mathematics Education: How Deficit Perspectives Work to Structure Inequality and What Can Be Done About It

Authors:

Abstract

A deficit perspective is a propensity to locate the source of academic problems in deficiencies within students, their families, their communities, or their membership in social categories (such as race and gender). While the deficit perspective is a common topic of discussion in K-12 mathematics education, it is a much rarer topic of discussion in undergraduate mathematics education. I argue that undergraduate mathematics instructors should take the deficit perspective seriously, because it structures educational experiences for students and instructors. In this survey article, I provide a brief review of the literature on deficit perspectives in mathematics education, and I offer practical suggestions for education from an anti-deficit perspective.
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Towards"anti-deficit"education"in"undergraduate"mathematics"education:"How"
deficit"perspectives"work"to"structure"inequality"and"what"can"be"done"about"it"
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Frederick"Peck"
University"of"Montana"
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frederick.peck@umontana.edu""
+1"406.243.4053"
@frederickpeck"
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Citation:""
Peck, F. A. (2020). Towards anti-deficit education in undergraduate mathematics
education: How deficit perspectives work to structure inequality and what can be
done about it. PRIMUS. Online first publication.
https://doi.org/10.1080/10511970.2020.1781721
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Abstract:"A"deficit"perspective"is"a"propensity"to"locate"the"source"of"academic"
problems"in"deficiencies"within"students,"their"families,"their"communities,"or"their"
membership"in"social"categories"(such"as"race"and"gender)."While"the"deficit"
perspective"is"a"common"topic"of"discussion"in"K-12"mathematics"education,"it"is"a"
much"rarer"topic"of"discussion"in"undergraduate"mathematics"education."I"argue"
that"undergraduate"mathematics"instructors"should"take"the"deficit"perspective"
seriously,"because"it"structures"educational"experiences"for"students"and"
instructors."In"this"survey"article,"I"provide"a"brief"review"of"the"literature"on"deficit"
perspectives"in"mathematics"education,"and"I"offer"practical"suggestions"for"
education"from"an"anti-deficit"perspective."
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Keywords:"Deficit"perspective,"anti-deficit,"assets,"asset-based"education"
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Towards"anti-deficit"education"in"undergraduate"mathematics"education:"How"
deficit"perspectives"work"to"structure"inequality"and"what"can"be"done"about"it"
1. INTRODUCTION!
For"the"past"four"decades"policy-makers"and"educators"in"mathematics"have"been"
preoccupied"with"so-called"“gaps”"between"student"groups."For"example,"on"many"
large-scale"standardized"tests"of"mathematics,"the"mean"scores"for"White"and"Asian"
students"are"higher"than"the"mean"scores"for"Black"students,"Latinx"students,"and"
students"from"other"systemically"oppressed"groups
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."This"has"been"branded"the"
“achievement"gap”"(Reardon"&"Robinson,"2007)."Within"undergraduate"
mathematics,"there"is"also"a"“participation"gap”"by"gender"and"by"race/ethnicity."
White"males"are"over"represented"in"college-level"mathematics,"while"other"groups"
are"underrepresented"(C."Rodriguez"et"al.,"2012;"Smith,"2011)."Similar"“gaps”"exist"
by"social"class,"with"upper-"and"middle-class"students"having"higher"mean"scores"on"
standardized"tests"and"enjoying"overrepresentation"in"college-level"mathematics
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.""
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"I"use"this"term"to"refer"to"people"who"have"systemically"been"denied"access"to"valued"cultural"
resources"based"on"socially-constructed"category"systems."I"use"the"term"“oppressed”"instead"of"the"
more"common"term"“underrepresented”"because"I"view"underrepresentation"as"an"outcome"of"
oppression."Using"the"term"oppression"foregrounds"the"cause,"not"the"effect,"and"makes"salient"the"
fact"that"underrepresentation"is"neither"natural"not"neutral."That"said,"I"realize"that"the"term"
“oppressed”"can"conjure"images"of"people"without"hope"or"agency."As"I"describe"later"in"this"paper,"
that"is"an"inaccurate"perception"of"people"in"oppressed"groups,"and"it"is"not"my"intention"to"
perpetuate"it."
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"Focusing"on"“gaps”"is"problematic"for"many"reasons"(R."Gutiérrez,"2008;"Martin,"2009)."Chief"among"
these"reasons"is"because"such"a"focus"promotes"a"deficit"perspective,"the"topic"of"this"review."Thus"I"
begin"the"review"with"a"discussion"of"“gaps”"not"to"reify"the"term,"but"rather"because"in"recent"
history"the"discourse"on"“gaps”"has"been"a"large"driver"of"deficit"perspectives."Due"to"this"history,"I"
use"quote"marks"to"mark"“gaps”"as"a"problematic"term.`"
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One"response"to"these"“gaps”"is"to"attribute"them"to"some"sort"of"deficiency"in"
oppressed"groups."This"tendency"has"come"to"be"known"as"a"deficit'perspective."
Deficit"perspectives"are"pervasive"in"STEM"(Science,"Technology,"Engineering"and"
Mathematics)"education"(Castro,"2014),"and"they"have"a"profound"effect"on"
students’"educational"experiences"and"opportunities"(Adiredja"&"Andrews-Larson,"
2017;"Adiredja"&"Louie,"2020).""
Discourse"about"deficit"perspectives"is"commonplace"in"the"K-12"educational"
literature"and"there"is"an"emerging"body"of"powerful"work"that"discusses"the"deficit"
perspective"in"undergraduate"STEM"education"(Adiredja,"2019b,"2019a,"2020;"
Adiredja"&"Andrews-Larson,"2017;"Adiredja,"Bélanger-Rioux,"&"Zandieh,"2020;"
Castro,"2012,"2014;"Hagman,"2019;"Leyva,"2016)."In"this"article,"I"aim"to"contribute"
to"this"literature"by"providing"a"practitioner-focused"survey"of"the"literature"related"
to"the"deficit"perspective,"and"practical"suggestions"for"anti-deficit"education."The"
paper"is"structured"as"follows."In"the"next"section"I"define"the"deficit"perspective,"
provide"a"brief"history,"and"give"examples"from"the"STEM"education"literature."I"
then"discuss"why"it’s"important"that"we"understand"deficit"perspectives,"showing"
how"they"work"to"structure"experiences"for"students"and"instructors."Finally,"I"
describe"alternative"models"for"education"from"an"anti-deficit"or"asset"perspective."
2. HISTORY!AND!EXAMPLES!OF!THE!DEFICIT!
PERSPECTIVE!
Box"1"provides"a"definition"of"the"deficit"perspective"in"educational"contexts.""
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Definition:
The deficit perspective is a propensity to locate the source of academic problems in
deficiencies within students, their families, their communities, or their membership in social
categories (such as race and gender)."
Box"1."Definition"of"the"deficit"perspective"
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While"contemporary"uses"of"the"deficit"perspective"are"often"associated"with"
attempts"to"explain"achievement"and"participation"gaps,"the"deficit"perspective"has"a"
much-longer"history,"stretching"back"to"the"beginning"of"the"so-called"
enlightenment"period"and"the"social"construction"of"race"(Valencia,"2010)."Whereas"
historically,"deficit"perspectives"were"levied"on"racial"groups,"contemporary"deficit"
perspectives"in"education"are"directed"at"many"levels"including"individual"students,"
families,"communities,"and"social"groups."Deficit"perspectives"come"from"a"variety"of"
sources,"including"instructors,"administrators,"and"policy"documents"(Shields,"
Bishop,"&"Mazawi,"2005)."Box"2"shows"four"examples"of"contemporary"deficit"
perspectives"in"STEM."In"Example"A,"a"university"administrator"exhibits"a"deficit"
perspective"toward"individual"students."In"Examples"B"and"C,"instructors"
demonstrate"deficit"perspectives"towards"students"(Example"B)"and"families"
(Example"C)."In"Example"D,"a"prominent"policy"document"takes"a"deficit"perspective"
towards"families"and"social"groups"by"suggesting"that"they"do"not"have"a"history"of"
engagement"in"mathematical"practices.""
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Example A (from administrator towards students):
Post-secondary Administrator: “…they [the students in our program] are not prepared.” (Castro,
2012, p. 3, p. 3)
Example B (from instructor towards students):
Instructor (describing their perception of why students did not enter school ready to learn): “One
of the problems with the kids we’re putting in [the 2-year algebra course] is they don’t have the
logic component.(Horn, 2007, p. 62, p. 62)
Example C (from instructor towards families):
Instructor: “Today a lot of these kids are from broken homes. They have parents who are
criminals.” (García & Guerra, 2004, p. 159, p. 159)
Example D (from policy document towards families and social groups):
Policy document: “In the United States, mathematics is primarily part of upper- and middle-class
male culture. Except for shopkeeper arithmetic of a bygone age taught in the elementary school,
few parts of mathematics are embedded in the family or cultural traditions of the many large
developing countriesthat make up the American mosaic.” (National Research Council, 1989, p.
20) (as cited in Martin (2009, p. 309). Italics added by Martin)"
Box"2."Four"examples"of"the"deficit"perspective.""
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A"preferable"perspective"is"to"attend"to"systemic"oppression."For"example,"
some"scholars"locate"oppression"in"the"ways"that"school"systems"have"historically"
and"contemporaneously"operated"to"deny"access"to"opportunities"based"on"a"
person’s"skin"color,"ethnic"background,"gender,"or"social"class."These"scholars"
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reframe"the"achievement"gap"as"an"“opportunity"gap”"(Carter"&"Welner,"2013)"or"
“education"debt”"(Ladson-Billings,"2006).""
One"might"question"the"utility"of"this"reframing."Is"it"just"an"issue"of"semantics,"and"if"
so,"what"difference"does"it"make?"I"address"this"question"in"the"next"section."
3. EFFECTS!OF!THE!DEFICIT!PERSPECTIVE!
The"deficit"perspective"is"more"than"just"a"semantic"turn"of"phrase."Rather,"the"
deficit"perspective"works"to"structure"students’"and"educators’"experiences"in"STEM"
education."In"particular,"the"deficit"perspective:"(a)"limits"access"to"educational"
opportunities;"(b)"results"in"lowered"expectations"for"students;"(c)"limits"the"role"
that"instructors"can"play"in"a"student’s"education;"and"(d)"works"with"“culture"free”"
beliefs"about"STEM"curricula"to"prevent"powerful"forms"of"cognition"from"entering"
the"classroom."Perhaps"most"perniciously,"deficit"perspectives"keep"all"of"the"above"
hidden,"thus"(e)"preventing"critical"introspection;"and"(f)"perpetuating"oppression"
and"privilege."Below,"I"elaborate"on"each"of"the"above."
The'deficit'perspective'limits'educational'opportunities'and'results'in'lowered'
expectations'for'students"(Adiredja,"2019a,"2020;"Adiredja"et"al.,"2020;"Adiredja"&"
Zandieh,"2020;"Ford"&"Grantham,"2003;"Ford,"Harris,"Tyson,"&"Trotman,"2001;"
García"&"Guerra,"2004;"Horn,"2007;"Martin,"2006,"2009;"Shields"et"al.,"2005;"
Valencia,"2010)."It"is"well-documented"that"members"of"traditionally"oppressed"
groups"are"over-represented"in"remedial"courses"(Adelman,"2000;"Sparks"&"Malkus,"
2013),"and"that"the"sorting"of"students"into"such"courses"is"not"independent"of"
privilege"(Darling-Hammond,"2010;"Oakes,"1990)."These"courses"are"often"focused"
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on"memorizing"facts"and"procedures"rather"than"engaging"students"in"cognitively"
demanding"mathematical"activity"(Larnell,"2016;"Oakes,"1990)."The"result"is"that"
students’"individual"experiences"with"STEM"are"racialized"(Larnell,"2016;"Martin,"
2006;"Valenzuela,"1999)"and"gendered"(Burton,"1995),"and"the"macro-level"result"is"
the"disproportionate"access"to"opportunity"discussed"above.""
The'deficit'perspective'limits'the'role'that'instructors'can'play'in'a'student’s'
education"(Horn,"2007)."Imagine"that"you’re"the"instructor"quoted"in"Example"B"or"C"
in"Box"2."You’ve"noticed"a"“mismatch”"between"the"curriculum"that"you’re"supposed"
to"teach"and"the"students"in"your"classroom."You’ve"located"the"source"of"that"
mismatch"in"the"students’"abilities"(Example"B)"or"the"student’s"families"(Example"
C)."As"a"instructor,"what"can"you"do?"You"can’t"control"the"students’"abilities!"You"
can’t"control"their"families!"The"deficit"perspective"has"effectively"limited"your"
options."The"only"way"to"remedy"the"mismatch"is"to"“fix”"these"students,"say"by"
assigning"them"to"remedial"courses"as"discussed"above."Now,"to"be"clear,"students"
arrive"in"our"classes"with"very"different"mathematical"histories."However,"this"
heterogeneity"does"not"have"to"be"understood"from"a"deficit"perspective."
Suggestions"for"alternatives"are"discussed"in"Section"4"(see"also,"Adiredja,"2019b,"
2020;"Adiredja"et"al.,"2020;"Adiredja"&"Zandieh,"2020).""
The'deficit'perspective'works'with'culture-free'beliefs'of'STEM'to'prevent'
powerful'forms'of'cognition'from'entering'the'classroom'(Adiredja"&"Louie,"2020;"
Bang,"Warren,"Rosebery,"&"Medin,"2012;"Frade,"Acioly-Régnier,"&"Jun,"2013).'There"
are"large"literatures"that"demonstrate"the"ways"that"both"cognition"(Cole,"2010;"
Hutchins,"1995a;"LCHC,"1983;"Radford,"2008)"and"mathematics"(Ascher,"2002;"
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Joseph,"2011;"Mukhopadhyay"&"Roth,"2012;"Peck,"2018;"Pinxten,"2016;"Pinxten,"Van"
Dooren,"&"Harvey,"1983)"are"not"culture-free,"but"rather"are"intertwined"with"
culture."However,"STEM"disciplines—especially"mathematics—are"often"seen"as"
universal"or"culture-free"(Bang"et"al.,"2012;"Ernest,"1998)."For"example,"just"before"
the"Example"D"in"Box"2,"the"quoted"policy"document"states:"“Among"the"many"
subjects"taught"in"school,"mathematics"is"probably"the"most"universal,"depending"
least"on"a"student's"background"and"culture”"(National"Research"Council,"1989,"p."
20)."Although"widespread,"these"beliefs"in"a"“culture-free”"mathematics"are"belied"
by"studies"of"mathematics"across"history"and"societies"(Peck,"2018),"which"reveal"
“various"types"of"mathematics,"irreducible"to"each"other”(Radford,"2008,"p."457)."
For"example,"Pinxten"and"colleagues"(Pinxten"et"al.,"1983)"describe"how"a"Navajo"
community"understood"space"very"differently"from"that"of"a"Western,"Euclidean"
perspective.""
Such"“culture-free”"beliefs"about"mathematics"can"be"damaging"for"students."
When"these"beliefs"about"mathematics"are"combined"with"deficit"perspectives"of"
students,"students’"out-of-school"ways"of"knowing"and"doing"mathematics"are"
ignored"or"trivialized"(as"exemplified"by"Example"D"in"Box"2)."This"prevents"
powerful"forms"of"cognition"(e.g.,"the"Navajo"community’s"ways"of"understanding"
space"in"Pinxten"et"al.,"1983)"from"entering"the"classroom,"and"puts"students"in"
untenable"epistemological"positions"that"work"against"engagement"in"meaningful"
learning”"(Bang"et"al.,"2012,"p."304;"see"also,"Bishop,"1990;"Frade"et"al.,"2013;"Shields"
et"al.,"2005).""
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Deficit'perspectives'work'to'keep'the'above'hidden,"preventing'critical'
introspection'on'the'part'of'educators'and'perpetuating'the'privilege'of'dominant'
groups"(Castro,"2012;"Frade"et"al.,"2013;"García"&"Guerra,"2004;"Horn,"2007;"Martin,"
2006,"2009;"Parsons,"2008;"Shields"et"al.,"2005)."Perhaps"the"most"pernicious"aspect"
of"deficit"perspectives"is"that,"by"locating"deficiencies"outside"of"the"school,"deficit"
perspectives"prevent"educators"from"seeing"their"role"in"the"systems"that"
perpetuate"oppression
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."Deficit"perspectives"thus"become"a"self-fulfilling"prophesy,"
both"the"beginning"and"the"ending"of"a"description-explanation-prediction-
prescription"cycle"(Valencia,"2010)"in"which:""
"
[F]irst"educators"describe"deficits,"deficiencies,"limitations,"and"shortcomings"
in"[students]"of"color"and"[students]"from"low-income"homes;"next,"educators"
explain"these"deficits"by"locating"them"in"such"factors"as"limited"intelligence"
or"dysfunctional"families;"then,"educators"predict"the"perpetuation"and"
accumulation"of"the"deficits;"and,"finally,"educators"prescribe"educational"
interventions"designed"to"remediate"the"deficits"(Skrla"&"Scheurich,"2001,"p."
236,"p."236)"
"
As"we’ve"seen,"the"result"of"these"prescriptions"are"racialized"and"gendered"
experiences"in"mathematics"(Larnell,"2016;"Leyva,"Quea,"Weber,"Battey,"&"López,"
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"This"phrasing"is"important,"lest"we"fall"into"the"trap"of"applying"deficit"perspectives"to"educators."It"
is"not"my"intention"to"locate"fault"inside"educators"–"myself"included!"Rather,"the"fault"lies"in"the"
deficit"perspective"itself,"which"works"on"and"through"educators"to"structure"inequitable"educational"
opportunities."
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2019)"and"inequitable"access"to"educational"opportunities."Thus"deficit"perspectives"
lead"educators"to"differentially"structure"educational"opportunity"while"
simultaneously"obscuring"the"educator’s"role."This"in"turn"perpetuates"a"system"of"
privilege"and"oppression."
"It"could"be"otherwise."In"the"next"section,"I"describe"the"possibilities"that"can"
accrue"to"students,"instructors,"schools,"and"society"when"deficit"models"are"
abandoned.""
4. ANTI-DEFICIT!EDUCATION!
Alternatives"to"deficit"perspectives"are"often"called"“anti-deficit”"or"“asset”"models"
(Adiredja,"2019b,"2019a;"Adiredja"et"al.,"2020;"Hagman,"2019)."In"this"paper,"I"use"
the"term"anti-deficit'to"draw"attention"to"the"active"work"that"it"takes"to"resists"
deficit"perspectives."Box"3"provides"a"definition"of"an"anti-deficit"perspective."
"
Definition:
Anti-deficit perspectives locate the source of academic problems within institutional
structures that work to limit access to educational opportunities. The focus is on the assets that
students bring to the classroom, rather than what they lack."
Box"3."Definition"of"the"anti-deficit,"asset-based"perspective"
"
Education"from"an"anti-deficit"perspective"repositions"student’s"histories,"
families,"communities,"and"cultures"as"sources"of"assets"rather"than"deficits'
(Adiredja,"2019a;"K."D."Gutiérrez,"Hunter,"&"Arzubiaga,"2009;"Moll,"Amanti,"Neff,"&"
Gonzalez,"1992;"Rosebery,"Ogonowski,"DiSchino,"&"Warren,"2010;"Turner,"Gutiérrez,"
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Simic-Muller,"&"Díez-Palomar,"2009)."What"this"means"is"that"students’"backgrounds"
are"brought"into,"rather"than"excluded"from,"the"classroom."The"resulting"
heterogeneity"is"leveraged"as"a"resource"for"all"students,"leading"to"opportunities"for"
understandings"that"include,"but"go"beyond,"those"prescribed"by"course"curricula.""
In"these"classrooms,"students"play"a"more"active"and"agential"role"in"their"
education."In"particular,"education"from"an"anti-deficit"perspective"positions"
students"as"epistemic"(knowledge-building)"agents"and"ontological"(world-building)"
agents."Epistemic"agency"involves"giving"students"the"authority"to"make"and"share"
meaning"in"the"classroom"(Bang"et"al.,"2012;"Burton,"1995;"Owens,"2015;"Valencia,"
2010)."Within"the"undergraduate"mathematics"community,"this"has"been"
popularized"through"Inquiry-Based'Mathematics'Education'(IBME)'(Ernst,"Hodge,"&"
Yoshinobu,"2017;"Laursen"&"Rasmussen,"2019)."IBME"(and"other"forms"of"active"
learning"(Freeman"et"al.,"2014)"may"be"particularly"powerful"for"members"of"
traditionally"oppressed"groups"(Laursen,"Hassi,"Kogan,"&"Weston,"2014;"Theobald"et"
al.,"2020),"and"can"be"a"powerful"tool"for"anti-deficit"teaching"(Tang"et"al.,"2017)"(but"
that"potential"is"not"automatically"realized,"Johnson,"Keller,"Andrews-Larson,"
Fortune,"&"Keene,"2020)."Ontological"agency"involves"positioning"students"as"actors"
who"can"use"mathematics"to"both"understand"the"world"from"a"critical"perspective"
and"author"new"roles"for"themselves"in"new,"more"socially"just"visions"the"world
4
"
(K."D."Gutiérrez"et"al.,"2009;"Gutstein,"2006;"Turner"et"al.,"2009)."Within"the"
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"It"should"be"clear"that"students"don’t"need"instructors’"“permission”"to"act"agentially"in"the"world."
Students"are,"and"always"have"been,"epistemic"and"onotological"actors."It’s"just"that"institutions"often"
work"to"suppress"these"forms"of"agency"in"the"classroom,"especially"for"students"in"oppressed"
groups."What"I’m"arguing"for"here"are"classroom"practices"that"foreground"and"support"student"
agency,"but"I"don’t"mean"to"suggest"that"students"cannot"act"agentially"in"the"absence"of"such"
practices."""
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mathematics"education"community,"this"has"been"taken"up"largely"though"
Mathematics'for'Social'Justice"(Gutstein"&"Peterson,"2006;"Karaali"&"Khadjavi,"2019;"
Wager"&"Stinson,"2012)"(see"also,"the"Special"Issue"of"PRIMUS"on"Mathematics"for"
Social"Justice,"Volume"29"Issue"3-4)".""
There"are"two"tensions"here."With"respect"to"epistemic"agency"there"is"a"
tension"between"giving"students"epistemic"agency"and"ensuring"that"students"learn"
institutionally-valued"disciplinary"knowledge."With"respect"to"ontological"agency,"
there"is"a"tension"between"allocating"limited"classroom"time"to"teaching"the"STEM"
curriculum"and"to"engaging"students"in"world-building,"social"justice"activity"
(Gutiérrez"(2009)"calls"this"“playing"the"game”"and"“changing"the"game”)."Different"
authors"negotiate"these"tensions"in"various"ways."It’s"beyond"the"scope"of"this"
review"to"discuss"these"in"depth,"but"suffice"it"to"say"that"the"tensions"are"essential"
to"teaching"from"an"anti-deficit"perspective"(R."Gutiérrez,"2006,"2007)."For"a"reviews"
of"the"tension"between"epistemic"agency"and"disciplinary"knowledge,"see"(Nasir,"
Hand,"&"Taylor,"2008)"and"(Radford,"2012)."For"discussions"of"the"tension"between"
teaching"STEM"and"engaging"students"in"world-building,"social"justice"activity"see"
(Gutstein,"2006)"and"(R."Gutiérrez,"2007).""
Regardless"of"how"these"tensions"are"negotiated,"it"should"be"clear"that"
education"from"an"anti-deficit"perspective"involves"changes"to"classroom"practices"
and"changes"to"how"mathematics"itself"is"conceptualized."Classrooms"become"active"
and"discursive"spaces"for"making"meaning,"and"disciplinary"knowledge"becomes"
terrain"to"be"analyzed"and"contested"(Frade"et"al.,"2013;"Owens,"2015;"Peck,"2018)."
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It"takes"work"to"make"these"changes."First,"instructors"must"(a)"examine"how"
institutional"practices"operate"in"ways"that"perpetuate"privilege"and"oppression,"
and"how"deficit"perceptions"obscure"these"practices"(García"&"Guerra,"2004);"(b)"
become"aware"of"their"own"agency"to"change"these"practices"(Shields"et"al.,"2005);"
(c)"understand"that"all"ways"of"knowing—including"those"that"are"institutionally"
valued—are"cultural"(Bryan"&"Atwater,"2002)"and"that"disciplinary"knowledge"is"
not"“settled”"but"rather"is"constantly"being"contested"by"practitioners"(Bang"et"al.,"
2012;"Ernest,"1994,"1998);"and"(d)"learn"to"teach"in"ways"that"are"“relevant"and"
responsive”"to"students’"social"realities,"their"cultural"practices,"and"their"identities"
(Martin,"2007,"p."18;"Ladson-Billings,"1991,"1999;"A."J."Rodriguez"&"Kitchen,"2005),"
including"ways"of"incorporating"heterogeneity"as"a"resource"(e.g.,"Adiredja"et"al.,"
2020).""
In"addition,"instructors"must"build"real,"human"relationships"with"students,"
including"understanding"students’"unique"histories."This"is"important"for"many"
reasons."First,"it"is"essential"if"instructors"are"going"to"leverage"diversity"without"
reducing"students"to"stereotypical"traits"based"on"their"membership"in"social"
categories"like"gender,"race,"and"ethnicity"(K."D."Gutiérrez"&"Rogoff,"2003)."Second,"it"
allows"instructors"to"structure"activities"that"are"not"only"relevant"to"students’"
histories,"but"also"to"their"futures"(Shields"et"al.,"2005)."Finally,"it"allows"for"more"
expansive"versions"of"learning,"one"which"rejects"individuation"as"the"goal"of"
education"and"instead"conceptualizes"education"as"a"social"project,"where"we"“come"
together"to"recognize"ourselves"as"historical"and"political"beings"and"where"we"
15"
critically"labour"together"to"make"the"common"world"a"better"place"for"all”"(Radford,"
2012,"p."116;"see"also"Noddings,"1992).""
Below,"I"will"share"some"examples"of"how"I"try"to"engage"in"this"work"in"my"
own"practice."Although"I"present"these"ideas"at"a"high"level"of"generality,"I"do"not"
mean"to"suggest"that"all"ideas"work"the"same"for"all"students."Indeed,"I"would"
suggest"the"opposite."Because"students"have"diverse"histories"with"mathematics,"it"
is"important"that"instructors"are"attentive"to"these"histories"in"all"classroom"
interactions."This"is"likely"of"particular"importance"for"students"from"systemically"
oppressed"groups,"who"must"be"understood"as"individuals"but"whose"membership"
in"oppressed"social"categories"often"influences"their"mathematical"experiences"
(Larnell,"2016;"Leyva"et"al.,"2019)."
4.1. Example!1:!Dismantling!rigid!course!sequences.!
In"university"math"departments,"courses"are"often"structured"in"a"rigid"
hierarchical"sequence,"in"which"access"to"one"course"is"dependent"on"passing"a"“pre-
requisite”"course."Incoming"students"are"placed"into"this"sequence"based"on"a"
placement"test."In"some"cases,"students"must"take"multiple"semesters"of"remedial"
(non-credit-bearing)"courses"just"to"access"their"first"credit-bearing"math"class"
(Bailey,"Jeong,"&"Cho,"2010)."When"students"are"placed"into"remedial"courses,"they"
are"more"likely"to"drop-out"before"earning"their"degree"(Ganga,"Mazzariello,"&"
Edgecombe,"2018).""
Placement"into"this"sequence"is"not"independent"of"privilege"(Larnell,"2016)."
Students"from"oppressed"groups"are"overrepresented"in"remedial,"non"credit-
16"
bearing"courses,"where"they"accumulate"debt"but"often"do"not"get"a"degree"(Bailey"
et"al.,"2010)."Meanwhile"students"from"privileged"backgrounds"are"more"likely"to"be"
placed"into"credit-bearing"courses,"and"go"on"to"graduate."In"this"way,"this"system"of"
rigid"course"sequencing"works"to"perpetuate"privilege"and"oppression."At"the"same"
time,"the"workings"of"the"system"are"obscured"behind"deficit"perspectives."Because"
placement"is"done"through"supposedly"neutral"means"(most"often,"a"standardized"
examwhich,"as"I"address"below,"artificially"constrain"the"kinds"of"knowledge"that"
students"can"demonstrate),"the"fault"for"placement"in"remedial"classes"can"be"
located"inside"of"students"(e.g.,"“students…"are"not"prepared,”"from"Example"A"in"
Box"2).""
However,"when"students"are"given"the"right"kinds"of"support,"many"students"
who"would"otherwise"be"assigned"to"remedial"courses"can"be"successful"in"credit-
bearing"courses—they"can"“jump"the"sequence.”"One"powerful"form"of"support"is"co-
requisite"courses."In"this"system,"the"rigid"system"of"pre-requisites"is"dismantled."
Students"are"placed"into"credit-bearing"courses"immediately"upon"enrollment."At"
the"same"time,"they"are"enrolled"in"supportive"co-requisite"courses"(Complete"
College"America,"2016).""
In"my"department"at"the"University"of"Montana,"we"have"undertaken"a"
corequisite"initiative'to"place"students"in"credit-bearing"courses"immediately,"while"
providing"supportive"corequisite"courses."So"far,"we"have"implemented"this"system"
for"College"Algebra"and"Precalculus,"and"we"are"piloting"corequisite"courses"for"
Calculus"I."This"work,"spearheaded"by"my"colleague"Laruen"Fern,"has"been"guided"by"
the"Math'Pathways'initiative"from"the"Charles"M."Dana"Center"at"the"University"of"
17"
Texas"(see"(Complete"College"America,"2016)"and"(“Charles"A."Dana"Center:"Co-
requisite"support"materials,”"n.d.)"for"resources)."Corequisite"courses"meet"once"or"
twice"per"week."They"do"not"have"additional"homework"and"are"graded"as"
credit/no-credit."The"courses"are"taught"by"the"same"instructor"as"the"credit-
bearing"course."The"content"of"the"corequisite"class"is"designed"to"be"responsive"to"
the"credit-bearing"course,"such"that"the"corequisite"courses"helps"students"more-
fully"participate"in"their"credit-bearing"class"that'week."This"is"called"just-in-time"
preparation."In"this"way,"the"corequisite"courses"are"tightly"coupled"with"their"
related"credit-bearing"courses."Our"results"have"been"encouraging,"with"a"
substantial"reduction"in"remedial"course"taking,"and"an"increase"in"student"success"
in"credit-bearing"courses."Departments"across"the"country"have"seen"similar"results"
(Complete"College"America,"2016).""
4.2. Example!2:!More!expansive!forms!of!summative!
assessment!
Educators"differentiate"between"formative'uses"of"assessment"and"summative'
uses."When"assessments"are"used"formatively,"they"are"used"to"guide"teaching"and"
learning."When"assessments"are"used"summatively,"they"are"used"to"evaluate"
learning."In"this"example,"I"will"focus"on"summative"assessment."In"undergraduate"
mathematics"classrooms,"summative"assessments"often"have"a"singular"form:"
pencil-and-paper"testing.""Traditional"pencil"and"paper"tests"are"often"treated"as"the"
de'facto"means"by"which"students"display"their"knowledge"for"evaluation"purposes."
18"
In"many"departments,"testing"is"so"ubiquitous"that"it"doesn’t"even"feel"like"a"
decision."
There"are"reasons"to"question"the"unquestioned"ubiquity"of"testing."In"many"
ways,"traditional"pencil-and-paper"tests"narrowly"constrain"the"sorts"of"knowledge"
that"can"be"assessed"and"the"means"by"which"it"can"be"displayed."Such"tests"are"
individualistic"even"though"problem"solving"is"often"collaborative,"and"proof"is"
inherently"social"(Lakatos,"1979;"MacKenzie,"1999)."Tests"restrict"access"to"
resources,"even"though"mathematical"cognition"often"incorporates"tools,"resources,"
and"other"features"of"the"material"and"cultural"environment"(Bass,"2011;"Hutchins,"
1995b;"Lave,"1988;"Taylor,"2009;"Wertsch,"1998)."Tests"are"time-constrained,"even"
though"mathematical"work"is"slow"and"thoughtful,"and"often"requires"periods"of"
downtime"(Hadamard,"1945;"Liljedahl,"2009)."Tests"require"responses"to"fixed"
problems,"even"though"mathematical"competence"is"multi-faceted"and"there"are"
many"ways"to"show"mastery"of"a"concept."Traditionally,"students"have"only"one"
chance"to"take"a"test,"even"though"mathematical"work"involves"making"and"learning"
from"mistakes"(Liljedahl,"2009)."Altogether,"tests"privilege"a"very"narrow"slice"of"
mathematical"competence"while"ignoring"vast"amounts."The"erasure"of"expertise"
may"be"more"profound"for"students"from"oppressed"communities,"who"often"have"
rich"histories"of"community-based"mathematical"practices"that"look"very"different"
from"pencil-and-paper"tests"(Darling,"2016;"Taylor,"2009)."
An"anti-deficit"approach"incorporates"more"expansive"forms"of"summative"
assessment."In"my"own"practice,"I"use"student-generated"portfolios"as"the"primary"
means"by"which"students"demonstrate"their"mastery"of"the"course"objectives."I"
19"
provide"students"with"a"set"of"objectives"and"a"developmental"progression"that"
describes"increasing"levels"of"mastery"for"each"objective."Throughout"the"unit,"
students"self-assess"their"mastery"of"the"objective"according"to"the"developmental"
progression."At"the"end"of"the"unit,"students"choose"the"work"that"best"demonstrates"
their"mastery"and"write"an"argument"for"why"this"work"demonstrates"mastery"of"
the"objective."They"can"choose"work"produced"individually"or"collectively,"in"or"
outside"of"class,"with"or"without"external"resources."For"students"who"prefer"a"
traditional"test,"I"provide"a"set"of"questions"that"can"function"as"a"take-home"test"
(students"still"must"write"an"argument"for"how"their"work"on"the"questions"shows"
their"mastery"of"the"objectives)."After"they"get"feedback,"students"can"revise"and"
resubmit"their"portfolios"an"unlimited"number"of"times."For"examples,"see"Appendix"
A.""
Portfolios"are"powerful"tools"for"assessment"from"an"anti-deficit"perspective,"
because"they"broaden"the"forms"of"knowledge"that"can"be"assessed"and"the"means"
by"which"it"can"be"displayed."Whereas"tests"are"individualistic"and"restrict"access"to"
resources,"portfolios"allow"students"to"submit"work"that"was"produced"
collaboratively"and"with"resources."Whereas"tests"are"time-constrained,"portfolios"
provide"an"opportunity"for"students"to"submit"slow,"thoughtful"work."Whereas"tests"
require"students"to"respond"to"fixed"problems,"portfolios"give"students"flexibility"in"
choosing"how"they"demonstrate"mastery"of"a"concept.""Whereas"tests"often"do"not"
allow"for"revision,"portfolios"provide"an"opportunity"for"students"to"learn"from"their"
mistakes"through"the"revision"process.""
20"
Portfolios"are"not"the"only"way"to"broaden"assessment"practices"for"anti-
deficit"teaching."One"alternative"to"traditional"one-time"testing"that"is"gaining"
currency"in"the"field"is"“mastery"grading,”"(See"upcoming"special"issue"of"PRIMUS)."
Mastery"Grading"uses"individual"pencil-and-paper"testing"for"summative"
assessment,"but"with"two"crucial"differences"from"traditional"testing:"(1)"students"
are"graded"based"on"their"demonstrated"mastery"of"an"objective"using"pre-
determined"criteria,"rather"than"the"percentage"of"points"earned,"and"(2)"students"
are"allowed"to"reassess"to"demonstrate"improved"mastery."From"an"anti-deficit"
perspective,"mastery"grading"is"powerful"because"it"allows"students"to"make"and"
learn"from"mistakes,"and"because"it"can"alleviate"the"time"pressure"of"traditional"
testing."However,"because"mastery"grading"generally"relies"on"traditional"paper-
and-pencil"tests,"it"can"still"constrain"the"kinds"of"knowledge"that"can"be"assessed"
and"the"means"by"which"students"can"express"it."For"examples"of"more"expansive"
forms"of"summative"assessment,"see:"(Brilleslyper"et"al.,"2012;"Gold,"Keith,"&"
Marion,"1999;"Hanusch,"2019;"Huntley"&"Flores,"2011;"Omar,"Karakok,"Savic,"
Turkey,"&"Tang,"2018;"Rash,"1997)."
"
4.3. Example!3:!Landscapes!of!investigation!
In"our"graduate"program"for"math"teachers,"we"have"some"math"content"
courses"that"are"taken"by"elementary,"middle,"and"high"school"teachers,"all"in"the"
same"course."Some"participants"have"an"undergraduate"math"degree,"including"
experience"with"abstract"mathematics"and"formal"proof."Others"may"have"deep"
21"
knowledge"of"elementary"mathematics,"but"little"experience"with"the"traditional"
undergraduate"mathematics"curriculum."Thus,"these"classes"have"a"great"
heterogeneity"in"terms"of"students’"background."
Anti-deficit"teaching"requires"giving"all"students"an"opportunity"to"develop"as"
mathematicians."With"this"level"of"heterogeneity"of"background,"it"would"not"be"
appropriate"to"assign"narrow"mathematical"exercises,"as"these"would"not"be"open"
enough"to"accommodate"the"heterogeneity"in"the"class."Instead,"I"assign"landscapes'
of'investigation"(see"Skovsmose"(2001)"for"a"detailed"description"and"Appendix"B"
for"an"example)."Students"are"given"a"scenario"or"mathematical"object."From"there,"
they:"""
1. Pose'questions"that,"for"them,"require"problem"solving"(that"is,"the"
students"do"not"know"the"answer,"nor"do"they"know"of"a"method"to"find"
the"answer;"Bolognese"and"Steward"(2017)"call"these"“level"3”"questions.)"
2. Explore'those'questions"by,"e.g.,"noticing,"imagining,"playing,"conjecturing,"
exploring,"creating,"visualizing,"generalizing,"verifying,"explaining,"and"
justifying""
3. Produce'a'writeup,'written"with"their"colleagues"in"mind."The"writeup"
should"be"understandable"to"everyone"in"the"class.'
4. Provide'a'peer'review,"in"which"class"members"give"their"colleagues"
feedback"on"the"following"questions:"Do"I"find"the"work,"including"the"
questions"that"are"being"explored,"to"be"clear"and"understandable?;"Why"
is"the"reasoning"sensible"from"the"author’s"perspective?;"Would"the"
mathematical"community"be"likely"to"accept"the"reasoning?;"and"What"
22"
connections"do"I"see"in"the"work,"and"what"further"questions"can"be"
explored,"based"on"the"work?"(Radford,"2012)"
5. Revise'the'investigation'based"on"peer"feedback."""
Landscapes"of"investigation"are"powerful"tools"in"anti-deficit"teaching"for"at"
least"three"reasons."First,"they"both"accommodate"heterogeneity"and"leverage"it"as"a"
resource."In"steps"1"and"2,"landscapes"of"investigation"accommodate"heterogeneity."
Because"students"can"pose"their"own"questions"(step"1),"they"are"each"working"on"
challenging"mathematics"in"step"2,"even"though"that"can"look"very"different"for"
different"students."In"steps"3"and"4,"landscapes"of"investigation"leverage"
heterogeneity"as"a"resource,"as"students"have"to"write"for,"and"get"feedback"from,"a"
diverse"audience."In"doing"so,"landscapes"of"investigation"position"students"as"
epistemic"agents"with"the"ability"to"make,"share,"and"contest"mathematics.""
Second,"landscapes"of"investigation"provide"students"with"multiple"ways"to"
show"mathematical"competence,"including:"asking"good"questions,"being"creative,"
visualizing"complex"ideas,"developing"and"using"representations"and"notations,""
writing"cogent"and"convincing"explanations,"reading"graciously"and"skeptically,"and"
making"connections"(c.f.,"Horn,"2012).""
Third,"landscapes"of"investigation"help"to"foster"more"expansive"forms"of""
learning,"including"developing"empathy,"courage,"and"humility."Producing"and"
reading"a"write-up"involves"perspective"taking,"which"fosters"empathy."When"
producing"a"write-up,"students"must"take"the"perspective"of"a"reader,"and"consider"
how"their"text"will"be"understood"by"people"with"different"backgrounds"from"their"
own."When"reading"a"write-up,"peer"reviewers"must"take"the"perspective"of"the"
23"
authors"(“why"is"the"reasoning"sensible"from"the"author’s"perspective?”),"and"of"the"
mathematical"community"(“would"the"mathematical"community"be"likely"to"accept"
the"reasoning?”)."Sharing"the"writeups"with"others"is"risky,"and"thus"doing"so"
develops"courage"and"humility"(Lampert,"1990;"Radford,"2012).""
4.4. Example!4:!Building!human!relationships!
Anti-deficit"teaching"requires"authentic"relationships"between"teachers"and"
students."In"the"beginning"of"the"semester,"I"use"three"techniques"to"get"to"know"my"
students"(there"are"many"other"techniques,"these"are"examples"that"have"worked"for"
me).""
1. I"ask"students"to"write"an"autobiography"during"the"first"week"(Braun,"2014;"
Pinter,"2014)."I"ask"them"to"address"their"history"and"relationship"with"
mathematics,"to"share"something"that"they"are"proud"of,"and"to"describe"their"
desired"future"trajectory.""
2. I"invite"students"to"have"a"low-stakes,"written"conversation"with"me"via"a"
“conversation"form.”"(based"on"work"by"Van"Der"Werf,"in"Horn,"2017,"pp."36–
37)."The"form"has"two"spaces"for"each"day"of"the"first"week."The"first"space"is"
for"the"student"to"write"something,"and"the"second"space"is"for"my"response."
On"the"first"day"of"class"I"give"students"a"sheet"of"paper"that"is"blank"on"one"
side"and"which"has"the"conversation"form"printed"on"the"other."I"ask"students"
to"fold"the"paper"into"a"name"tent,"with"the"form"on"the"interior."This"is"their"
name"tent"for"the"first"few"days"of"class."In"the"last"five"minutes"of"class,"I"ask"
24"
students"to"write"me"a"note"in"the"slot"for"“day"1.”"I"then"respond"to"each"
note,"and"we"continue"like"this"for"the"rest"of"the"week.""
3. It"is"difficult"for"me"to"learn"students’"names."I"openly"admit"this"to"students."
At"the"same"time,"I"strive"to"learn"every"name"within"two"class"sessions."To"
do"that,"I"take"a"class"photo"with"everyone"holding"their"name"tents"on"the"
first"day,"and"I"study"this"photo"for"the"rest"of"the"week."When"I"am"
responding"to"a"student"on"the"conversation"form,"I"find"them"in"the"class"
picture."When"I"read"their"autobiographies,"I"find"their"conversation"form"
and"their"picture."In"this"way"I"am"able"to"associate"names,"faces,"histories,"
and"futures.""
"
When"I"know"a"student’s"history"with"mathematics,"I"can"structure"the"class"
to"be"mindful"of"that"history."For"example,"many"undergraduate"pre-service"
elementary"teachers"report"negative"histories"with"school"mathematics."For"these"
students,"math"has"often"meant"“getting"correct"answers"following"rote"procedures"
under"time"pressure.”"Thus,"an"emergent"goal"of"my"class"with"them"is"to"foster"a"
more"positive"conception"of"mathematics"as"a"creative"and"sensible"human"activity.""
When"students"share"what"they"are"proud"of,"I"can"try"to"incorporate"some"of"
these"strengths"into"the"class."For"example,"one"year"I"had"many"students"describe"
their"artistic"accomplishments."We"therefore"did"a"project"in"which"we"explored"
patterns"in"geometric"artwork"and"created"our"own"pieces.""
When"I"know"a"student’s"future,"I"can"work"with"them"to"align"the"course"
assignments"and"assessments"to"that"future."For"example,"we"have"a"course"for"
25"
graduate"students"in"mathematics"called"Teaching"College"Math."Students"in"the"
course"have"a"variety"of"imagined"futures,"including"teaching"at"2-year"institutions,"
4-year"teaching-intensive"institutions,"and"research-intensive"institutions."A"student"
aiming"for"a"2-year"institution"may"be"interested"in"resources"for"teaching"calculus"
(e.g.,"Driskell"&"Malagon,"2013;"Oehrtman,"2008;"Speiser"&"Walter,"2008;"Thompson"
&"Silverman,"2008),"a"graduate"student"in"Algebra"may"be"interested"in"learning"
more"about"resources"for"Abstract"Algebra"(e.g.,"Cook,"2015;"Larsen,"2013;"Larsen"&"
Lockwood,"2013),"and"a"student"in"statistics"might"be"more"interested"in"resources"
for"undergraduate"statistics"(e.g.,"GAISE"College"Report"ASA"Revision"Committee,"
2016;"Garfield,"DelMas,"&"Zieffler,"2012;"Hathaway,"1994)."Thus,"in"addition"to"
learning"about"general"principles"for"evidence-based"teaching"(Schoenfeld,"2014),"I"
also"provide"resources"specific"to"a"variety"of"courses,"and"assignments"that"enable"
students"to"engage"with"the"resources"of"their"choosing."
Building"relationships"with"students"helps"me"align"courses"to"their"histories,"
their"strengths,"and"their"futures."It"also"helps"to"foster"belongingness—the"sense"
that"one"is"cared"for"by"members"of"the"community"(Horn,"2017)."While"the"
strategies"listed"above"help"to"foster"belongingness"in"the"beginning"of"the"year,"the"
most"important"strategy"is"to"simply"be"present,"listen"to"students,"and"affirm"their"
experiences."If"a"student"needs"to"tell"me"a"story"about"why"they"were"absent,"why"
they"need"an"extension,"or"why"they"feel"joyful"or"frustrated,"I"always"make"time"for"
it."I"have"taken"long"walks"around"campus"with"students,"as"they"tell"me"stories—of"
hardship,"of"friendship,"of"kinship."Whatever"is"the"reason"that"they"want"to"talk,"I"
make"sure"that"I"prioritize"it."Students"recognize"these"caring"interactions."More"
26"
than"once,"students"have"told"me"that"they"likely"would"have"dropped-out"had"I"not"
been"so"receptive"to"them."
Caring"for"students"can"be"difficult"in"the"rush"of"a"semester."It"can"be"
tempting"to"reduce"students"to"only"their"mathematical"behaviors—often,"as"
discussed"above,"only"the"very"narrow"set"of"those"behaviors"that"become"inscribed"
on"tests."As"Noddings"(1988)"explains,"“In"every"human"encounter,"there"arises"the"
possibility"of"a"caring"occasion."(…")"Teaching"is"filled"with"caring"occasions,"or,"
quite"often,"with"attempts"to"avoid"such"occasions”"(p."222)."Anti-deficit"teaching"
means"insisting"on"treating"every"occasion"as"a"caring"occasion,"and"on"treating"
every"student"as"a"full"human
5
.""
For"more"examples"of"anti-deficit"work"in"real"undergraduate"mathematics"
courses,"see:"(Adiredja,"2019b,"2020;"Adiredja"et"al.,"2020;"Adiredja"&"Zandieh,"
2020;"K."D."Gutiérrez"et"al.,"2009;"Moreno"&"Rutledge,"2017)."
5. CONCLUSION!
I"began"this"review"by"focusing"on"achievement."I"showed"how"deficit"perspectives"
work"to"structure"differential"patterns"of"achievement,"conscripting"students"and"
instructors"to"narrow"roles"that"perpetuate"inequality."I"then"presented"an"alternate"
vision"of"education"from"an"anti-deficit"perspective."This"perspective"honors"
"""""""""""""""""""""""""""""""""""""""""""""""""""""""
"
5
"It"should"go"without"saying"that,"even"though"I"have"discussed"the"pedagogical"benefits"of"getting"to"
know"students,"the"primary"purpose"is"not"transactional"but"rather"relational."Moreover,"it"is"
important"to"note"that"institutional"structures"can"produce"power"imbalances"between"instructors"
and"students,"and"these"can"interact"with"other"societally-produced"imbalances,"such"as"if"instructors"
and"students"are"of"different"genders."Instructors"should"be"mindful"of"these"imbalances,"without"
allowing"a"fear"of"imbalance"to"prevent"caring"interactions.""
27"
students"and"their"histories"and"leverages"diversity"to"create"new"opportunities"and"
more"expansive"forms"of"learning.""
I"hope"that"this"piece"serves"as"an"invitation"to"those"who"are"new"to"the"
work"of"anti-deficit"teaching,"and"as"encouragement"to"those"who"are"engaged"in"it."
Given"the"difficulty"of"the"work,"we"must"sustain"each"other."In"that"spirit,"I"would"
like"to"conclude"by"sharing"two"quotations"that"have"recently"nourished"my"
commitment"to"the"work."The"first"comes"from"the"philosopher"Simone"Weil;"I"was"
made"aware"of"the"quote"by"Francis"Su"(Su"&"Jackson,"2020)."The"second"comes"
from"the"educator"Maxine"Green;"I"was"made"aware"of"the"quote"by"Ilana"Horn"
(Horn,"2019)."
"
“Every"being"cries"out"silently"to"be"read"differently”"(Simone"Weil)"
"
In"this"powerful"statement,"Simone"Weil"reminds"us"that"people"are"often"
judged"in"ways"that"diminish"them."All"of"us,"and"all"of"our"students,"have"powerful"
histories"with"and"diverse"repertoires"for"mathematics."We"all"deserve"to"be"seen"
for"these"strengths,"but"too"often"we"reduce"our"students"to"their"deficits."Let"us"
hear"our"students’"silent"cries"to"be"read"differently."Let"us"read"our"students"from"
an"anti-deficit"perspective.""
This"is"hard"work,"because"all"too"often"the"structures"and"normative"
practices"of"our"institutions"seem"to"facilitate"deficit"perspectives"of"students."It"is"
difficult"to"change"institutional"structures,"difficult"to"work"against"normative"
practice."The"good"news"is"that"these"structures"and"practices"are"not"set"in"stone."
28"
As"I"write"this,"the"normative"practices"of"many"institutions"have"been"massively"
disrupted"by"a"global"pandemic."This"rupture"in"the"taken-for-granted"exposes"how"
institutions"are"produced"by"us,"and"can"be"changed"by"us."Rather"than"be"
constrained"by"“what"is,”"then,"let"us"imagine,"
""
“what"could"be?”"(Maxine"Green)"
"
What"could"be"if"we"read"students"differently?""
What"could"be"if"we"expanded"our"notions"of"mathematical"competence,"so"
that"we"could"see"it"in"all"of"our"students?""
What"could"be"if"we"reorganized"our"institutions"to"focus"on"students’"
strengths,"rather"than"their"deficits?""
What"could"be?""
I"hope"you"will"join"me"in"imagining"what"could"be,"and"in"working"towards"a"
more"just,"humane,"and"expansive"future.""
!"
29"
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" "
42"
7. APPENDIX!A:!EXAMPLE!PORTFOLIOS!
Course: Number and operations for K-8 teachers
Objective: I understand the structure of fractions from a units
perspective
Not there yet
Approaching mastery
Mastery
I mostly or solely conceptualize
fractions from a “pieces out of
pieces perspective:
I mostly conceptualize th e
numerator and denominator as
“numbers of pieces,”
I mostly conceptualize a
fraction as a specified number
of pieces out of a total number
of pieces (e.g., !
" as “three
pieces out of four pieces”)
I can coordinate two levels of units:
I can create u nit fraction s given
a whole
I can create a whole given a
unit fraction
I can show how fractions are
composed of unit fractions
(i.e., “expanded form”)
I can explain the limitations of
an “out of” perspective.
I can coordinate three levels of
units (All of “approaching,” plus):
I can show multiple ways to
create fractions, some of which
do not require partitioning the
entire whole (e.g., I can create
3/4 withou t partitioning a
whole into four pieces)
I can create any fraction from
any other fraction (e.g., given a
bar that represents 3/5, I c an
find the bar that represents
4/3).
Find examples: Find examples in your work that demonstrate that you understand the
structure of fractions from a units perspective, or create new pieces from the
supplemental questions
Make an argument: Explain how the piece(s) you chose demonstrates your mastery of
this objective:
43"
Course: Calculus I
Objective: I understand accumulator functions.
Not there yet
Approaching mastery
Mastery
I do not understand integrals with
variable endpoints, or how they
relate to antiderivatives
I can explain the meaning of
functions written in the form,
#$%&' ( )$*&+*
,
-
I can evaluate accumulator
functions:
o Graphically, using geometry
o Numerically, using a calculator
o Analytically, using the FTC
I can differentiate accu mulator
functions of the form,
#$%&' ( )$*&+*
,
-
All of “approaching,” plus:
I can find the antiderivative of
any function
I can differentiate accu mulator
functions of the form,
#$%&' ( )$*&+*
.$,&
-
Find examples: Find examples in your work that demonstrate that you understand
accumulator functions, or create new pieces from the supplemental questions
Make an argument: Explain how the piece(s) you chose demonstrates your mastery of
this objective:
"
" "
44"
8. APPENDIX!B:!EXAMPLE!LANDSCAPE!OF!
INVESTIGATION!
Note:"The"example"below"comes"from"a"course"on"algebra"for"teachers."In"the"
course,"we"defined"algebra"as"follows:"“Algebra"is"the"human"activity"of"
algebratizing:"structuring"the"world"(including"the"mathematical"world)"by"finding"
relationships,"generalizing,"abstracting,"and"justifying.”"
"
"
Invitation:!Staircase!numbers!a""
"
"
"
a"From"Josh"Zucker"at"the"Julia"Robinson"Math"Festival"
"
5
Staircase Numbers
suggested by Joshua Zucker, Julia Robinson Mathematics Festival
EXTENSION:
Which numbers can’t be expressed as the sum of two or more consecutive positive
integers?
Which numbers can’t be expressed as the sum of three or more consecutive positive
integers?
Find more Julia Robinson Mathematics Festival problem sets at jrmf.org/problems.php.
... When averaged with the remaining data, those stories were drowned out by deficit messages repeated in much of the literature on students' understandings of functions: "They don't get it", "They don't get it", "They don't get it". This was despite my explicit efforts to use asset-based, anti-deficit approaches (Peck, 2020) to conceptualize student learning. I knew I needed to change my approach if I wanted to allow students' stories to shine. ...
... 23). In this section, I reject the view that tables, graphs, and expressions mean nothing to students and instead take up an anti-deficit (Peck, 2020) perspective by attending to literature on students' coherence seeking across situations that might be seen by a disciplinary expert as involving function(s). I focus not on the ways students "struggle" to adopt disciplinary meta-narratives pertaining to function but rather on normalizing and explaining their varied interpretations of our curricular stories. ...
Thesis
Full-text available
A common educational assumption is that coherence is a pre-requisite for a “good” curriculum. Indeed, in mathematics education this perspective has persisted both nationally and internationally as a foundational principle for curriculum design, reform, and evaluation. While curricular coherence is often unquestioningly accepted as desirable for student learning, some researchers have urged caution, arguing that “curricular coherence” is loosely defined with no widespread agreement over its meaning. Yet, disciplinary, logico-rational forms of coherence (i.e., retrospective expert perspectives) tend to dominate curricular discourses in mathematics education, often in ways that position these disciplinary forms of coherence as objective evaluations of curricula. Other perspectives on what it means for curricula to be “coherent”—particularly those of students—are rarely centered, which has epistemological as well as ethical consequences for who/what is positioned as coherent (i.e., “ideal”) and who/what is positioned as incoherent (i.e., abnormal, aberrant, incomplete). This binary imposes a distribution of “sensible” mathematics learning, thereby perpetuating a harmful culture of exclusion in mathematics education. In this dissertation, I critically investigate curricular coherence in mathematics education by interrogating the notion of coherence itself and problematizing the dominance of a singular perspective on coherence. To do so, I conceptualize curriculum as a storied artform and view coherence as an individual’s holistic aesthetic judgement of curricular stories. These judgements are highly subjective and may vary from person to person as well as discipline to discipline, destabilizing the myth that curricular coherence is an objective evaluation with a singular definition. Rather, I contend that curricular coherence must be defined kaleidoscopically via a plurality of disciplinary and stakeholder perspectives. To this end, I investigate three interrelated questions: (1) Ontologically, what is coherence in its many forms? In other words, what does “coherence” refer to in both mathematics and science education, as well as in other disciplines? Additionally, according to these ontologies, who is positioned with the authority to make judgements or evaluations of (in)coherence? (2) What are the aesthetic, ethical, and onto-epistemological foundations behind the common (and often implicit) assumption that coherence (in its many forms) is desirable? What are the consequences of these philosophical assumptions for curriculum? For learning? For how learners as positioned? In other words, I question curricular coherence for what purpose? (3) Finally, what are the flexible possibilities (and tensions) for conceptualizing curriculum using an aesthetic curriculum-as-story metaphor to investigate various forms of curricular (in)coherence from multiple stakeholder perspectives? I inquire about these overarching questions through three interrelated studies—one theoretical and the other two empirical—situated within an arts-based research paradigm. These investigations serve as a type of disciplinary-cultural analysis and artistic critique from both my own and students’ perspectives with the overriding goal of interrogating and shifting the normative value of (curricular) coherence in mathematics education. More broadly, this dissertation spotlights the aesthetic dimension of learning mathematics as well as the danger of divisive and dehumanizing politics of aesthetics inherent to uncritical conceptualizations of so-called “desirable” modes of teaching and learning, such as the privileged logico-rational definition of curricular coherence that is the current status quo.
... Lastly, university administrators and engineering program administrators have tried to solve the engineering inequality problem by employing individualized, deficit designed methods and situating the problem on the students (Peck, 2020), hence, keeping the racist system untouched (McGee, 2020;McGee et al., 2021). To solve this problem, we recommend that universities and program coordinators develop interventions for women, AHN, and dominant groups, including the students and faculty. ...
... Engineering developing programs and engineering institutions should showcase participatory-based program designs to encourage AHN students' early engagement in professional engineering society and also encourage diversity, equity, and inclusion efforts in engineering programs (Peters et al., 2021); this will help women and AHN students to connect with possible mentors who share the same ethnic/racial, gender statuses with them (Campbell-Montalvo et al., In press;Campbell-Montalvo et al., 2020;Smith et al., 2021). Finally, university administrators and engineering program administrators have tried to solve the engineering inequality problem by employing individualized, deficit-designed methods and situating the problem on the students (Peck, 2020), hence keeping the racist system untouched (McGee, 2020;McGee et al., 2021). ...
Article
This article explores the unique experiences and challenges faced by women, African Americans, Hispanic/Latino, Native Americans/Alaskan Natives (AHN) AHN students pursuing an engineering degree program. Drawing from existing research and literature, the article examines issues such as underrepresentation, biases, and stereotypes that can impact the academic and professional experiences of these students. It also highlights strategies and resources that women and AHN students utilize to navigate these challenges and succeed in the field of engineering. The purpose of this phenomenological descriptive qualitative study is to explore AHN engineering students' experiences as they pursued their engineering programs, and to contribute to efforts to promote diversity and inclusion in the engineering profession.
... Then add first generation and identifying with an underrepresented group in engineering or computer science. Managing deficit thinking which holds students accountable for missing elements impacting academic preparation can control bias and break stereotypes [31]- [33]. New perspectives in viewing AUP student perceptions can lead to warm welcomes matching extended invitations. ...
... Despite the demonstrated role of student agency, we argue that it is the responsibility of institutional and discipline stakeholders, not students, to humanize STEM education. Indeed, an emphasis on changing institutions and systems rather than changing students is a central tenet of anti-deficit based approaches to inclusive and equitable education (e.g., García and Guerra, 2004;Peck, 2021). Therefore, in considering the applications of the ecological model for human development (Bronfenbrenner and Ceci, 1994;Bronfenbrenner and Morris, 2006) to the student level, we focus on the role of other stakeholders in amplifying the impact of student voices within the STEM education ecosystem and empowering students toward greater agency and self-actualization in STEM education. ...
Article
Full-text available
STEM higher education in the U.S. has long been an uninviting space for minoritized individuals, particularly women, persons of color, and international students and scholars. In recent years, the contemporary realities of a global pandemic, sociopolitical divides, and heightened racial tensions, along with elevated levels of mental illness and emotional distress among college students, have intensified the need for an undergraduate STEM education culture and climate that recognizes and values the humanity of our students. The purpose of this article is to advance a more humanized undergraduate STEM education and to provide a framework to guide efforts toward achieving that vision. We argue that humanizing approaches recognize and value the complexity of individuals and the cultural capital that they bring to their education, and that this is particularly important for empowering minoritized students who are subordinated in status in STEM higher education. A STEM education that centers students’ humanity gives rise to equity and promotes human well-being and flourishing alongside knowledge acquisition and skill development. We then offer a guiding framework for conceptualizing the broader ecosystem in which undergraduate STEM students are embedded, and use it to outline the individual and collective roles that different stakeholders in the ecosystem can play in humanizing STEM education.
... In recent years, there has been an increase in empirical research studies and critical scholarship that has critiqued the traditional notions and dominant narratives of STEM culture. In particular, scholars have challenged the notion of the deficit solely lying with the individual and have provided substantial evidence that many of these challenges are perpetuated by systematic and structural policies, practices, and ideologies interwoven into the fabric of the STEM enterprise [15][16][17][18][19]. Further, scholars have posited that to broaden STEM participation for marginalized groups, we must critically disrupt the dominant STEM culture and narrative rooted in white and male dominance [20][21][22]. ...
Article
Full-text available
Grounded in a conceptual framework incorporating intersectionality, motivation, self-determination, and self-efficacy, this empirical study investigated how individuals’ identities, mindsets, and resources in educational environments intentionally cultivated to support their decision-making, development, and connections in the science community, can significantly increase the recruitment, persistence, and success of low-income, academically talented science students from diverse backgrounds. Several factors—academic performance in coursework, self-image, self-agency, financial support, and social integration in the science culture—continue to significantly impact student retention and persistence in STEM disciplines. Many of these factors are negatively affected based on a students’ intersecting identities, which can be detrimental to their academic success if not addressed. We found that additional considerations to factor in concerning low-income students from diverse backgrounds that is pertinent to supporting their persistence and success in the postsecondary STEM educational context.
... In the second year of my doctoral program, students are tasked with designing, proposing, and carrying out their own research study. My theoretical framework featured a variant of social semiotic theory (Presmeg et al., 2016) that emphasized students' meta-representational competence (diSessa, 2004) in an attempt to catalog students' symbolic representation systems from an anti-deficit perspective (Peck, 2020). Although finding and networking these theories to create a framework for my study had been challenging, I felt good about my choices. ...
Conference Paper
Full-text available
In the mathematics education literature, there is plenty written on the roles that theoretical frameworks should play once they are already crafted; however, there is much less guidance on how scholars-especially emerging scholars-might construct a theoretical framework that serves these roles. When guidance is provided, it focuses on issues of epistemology and ontology. In this brief theoretical report, I emphasize the importance of the oft-ignored aesthetic dimension of theorizing. I first argue that aesthetics cannot be separated from our everyday behaviors and choices and therefore our research practice. I then share my experience about how reflecting on my personal aesthetics allowed me to craft a framework that enables me to bring my whole self-worldviews and all-into my research. By sharing my story, I hope to support other emerging scholars in bringing their ways of being, thinking, and feeling into their research.
... These narrow and misconstrued framings of Latine students have tangible consequences as they inform pedagogical practices, assessment designs, research, and how we define knowledge and success in STEM (Peck, 2021). Educators' deficit-based expectations and dispositions toward students of color have been documented quantitatively and qualitatively as negatively affecting students' academic performance and motivations to learn (Berlak, 2001;Bruton and Robles-Piña, 2009). ...
Article
Full-text available
Latine students continue to persist in science, technology, engineering and mathematics (STEM) fields despite the numerous obstacles in place that stifle their academic potential and contributions. Instead of fostering the strengths Latine students possess that help them succeed despite these obstacles, the field of STEM education has traditionally examined these students’ experiences and challenges through a deficit lens. Deficit perspectives posit that any existing disparities in educational outcomes in STEM for Latine students are a product of the students’ lack of interest in STEM fields, poor academic preparation and/or motivation, among other ‘faults.’ In this manner, this deficit approach absolves educators, educational institutions, administrators, and researchers from any responsibility in mediating the disparate outcomes and negates the roles that outdated pedagogical practices, structural racism, discrimination and disciplinary bias have in limiting Latine students’ success in STEM. These deficit-understandings of these inequities are pervasive in all aspects of STEM education, guiding curricular choices, pedagogical approaches, assessment designs, interventions and even how STEM fields define knowledge and success. To counter these harmful constructions, this article discusses how STEM educators can draw on Latino Critical Race Theory (LatCrit) and Community Cultural Wealth (CCW) epistemologies to foster learning ecologies that draw on Latine students’ cultural strengths rather than deficits. To this end, this article introduces LatCrit and CCW frameworks in the context of STEM education, and combines them to propose an asset-based LatCrit pedagogical approach to STEM curriculum design and teaching. It also contributes guiding questions and application examples STEM educators can reference to advance asset-based LatCrit pedagogical approaches that promote justice and equity within STEM classrooms and beyond. Contributing to this underdeveloped line of scholarship in the field of STEM, we apply these critical frames to help educators (re)imagine postsecondary STEM pedagogies and reforms around the wealth of skills, dispositions, and cultural practices that Latine students possess.
... The skill of noticing students' mathematical strengths is complex and challenging to learn, especially given that deficit thinking is deeply ingrained in mathematics education (Adiredja & Louie, 2020;Peck, 2021). To address this issue, the author developed a course for prospective secondary mathematics teachers to promote critical reflection on their and others' framing of students' mathematical thinking. ...
Article
Full-text available
Noticing the strengths in students’ mathematical thinking is a critical skill that teachers need to develop, but it can be challenging due to the prevalence of deficit-based thinking in mathematics education. To address this challenge, a teacher education course was designed to encourage prospective teachers to engage in critical reflection on their own and others’ framings of students’ thinking and shift their focus towards noticing students’ strengths. The study analyzed written responses from the prospective teachers, collected at the beginning and end of the course, to investigate their framing and noticing of students’ mathematical thinking. The analysis focused on the aspects of students’ thinking that the prospective teachers paid attention to, the stances they took when interpreting students’ thinking, and the instructional moves they proposed in response to their thinking. Furthermore, the study established a spectrum of deficit-based and strength-based framings on students’ mathematical thinking. This spectrum allowed for the identification of each participant’s written noticing responses within a range of possibilities, contributing to a more nuanced understanding of the changes in teachers’ framing and noticing of students’ thinking over time.
... When faculty embrace anti-deficit perspectives, they imagine what students enrolled in their classes might contribute and achieve-rightly viewing the students as capable collaborators (Valencia, 2010). Faculty attitudes are important to student success (Vetter et al., 2019), and carefully designed and contextually appropriate practices are essential to changing deficit-based dynamics (Peck, 2020). This understanding provides a basis for inviting students who have taken prescribed courses to participate in the kinds of activities that have been widely demonstrated to promote student success. ...
Article
Local volunteer opportunities hold the potential for university students to develop as leaders and engaged membersof the academic community, but students taking prescribed (sometimes termed developmental education) coursesmay be overlooked as candidates for these kinds of opportunities. Taking an anti-deficit stance, university faculty maypromote student success by recruiting students from prescribed courses to participate in carefully-designed volunteerprograms. In this qualitative case study, I explored the perceptions of growth in the areas of academic engagementand leadership and the motivation to participate in future community volunteer service in student volunteers who hadpreviously been enrolled in prescribed reading courses. Three such university student volunteers reflected on theirexperience as leaders in a short-term academic outreach program for high school students. In open-ended surveyand interview responses, the university volunteers described their development of specific skills as well as changesin self-perception. Their responses indicated that they perceived the volunteer experience as effectual in all theinvestigated areas. Notably, they reported that serving as role models for youth encouraged specific academic habits.The study includes descriptions of the academic outreach program with supporting theory for its design because thecontext of the volunteer service cannot be separated from the findings. This study is a unique contribution to studentsuccess literature—there is no previous model linking students from prescribed courses with community volunteeropportunities.
... One of these conditions is the application of learning from offline to online. These problems include academic stress (Cornilla & Maureen, 2021), rarely discuss (Peck, 2021), collaboration and problem solving skills (Chai & Subramaniam, 2021), teacher readiness in providing subject matter and utilizing learning media (Basar, 2021), and well-being (Anis, Calia, Demir, Doyran, & Hacifazlioglu, 2021). If this problem is not handled by a college counselor, it will lead to academic burnout and it is possible to cause psychological welfare for students in the future. ...
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