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Asset-Based Approaches to Equitable Mathematics Education Research and Practice

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Abstract

In July 2017, the National Council of Teachers of Mathematics (NCTM) released a new mission statement that shifts the organization's primary focus to supporting and advocating for the highest quality mathematics teaching and learning for all students. A key strategy for achieving this goal is to advance “a culture of equity where each and every person has access to high quality teaching and is empowered as a learner and doer of mathematics” (NCTM, 2017, “Strategic Framework,” para. 2). Increasing equity and ensuring the highest quality mathematics teaching and learning for all students requires systemic change (National Council of Supervisors of Mathematics [NCSM] & TODOS: Mathematics for ALL, 2016). As educators are called to enact NCTM's new mission, we acknowledge that such change is complex. We also acknowledge that our own experiences conducting equity work that is grounded in an asset-based approach are at different stages of development, ranging from beginning levels to lived experiences as diverse mathematics learners and mathematics education researchers. We see this change in mission as a call to both act politically (Aguirre et al., 2017) and to change story lines (i.e., “broad, culturally shared narrative[s]”; Herbel-Eisenmann et al., 2016, p. 104) that dominate the public perception of mathematics learning and teaching. We acknowledge that systemic barriers are part of a larger educational issue, but for the purposes of this commentary, we focus on mathematics.
Research Committee
Asset-Based Approaches to Equitable Mathematics
Education Research and Practice
Sylvia Celedón-Pattichis
University of New Mexico
Lisa Lunney Borden
St. Francis Xavier University
Stephen J. Pape
John Hopkins University
Douglas H. Clements
University of Denver
Susan A. Peters
University of Louisville
Joshua R. Males
Lincoln Public Schools
Olive Chapman
University of Calgary
Jacqueline Leonard
University of Wyoming
In July 2017, the National Council of Teachers of Mathematics (NCTM) released
a new mission statement that shifts the organization’s primary focus to supporting
and advocating for the highest quality mathematics teaching and learning for all
students. A key strategy for achieving this goal is to advance “a culture of equity
where each and every person has access to high quality teaching and is empowered
as a learner and doer of mathematics” (NCTM, 2017, “Strategic Framework,” para.
2). Increasing equity and ensuring the highest quality mathematics teaching and
learning for all students requires systemic change (National Council of Supervisors
of Mathematics [NCSM] & TODOS: Mathematics for ALL, 2016). As educators
are called to enact NCTM’s new mission, we acknowledge that such change is
complex. We also acknowledge that our own experiences conducting equity work
that is grounded in an asset-based approach are at different stages of development,
ranging from beginning levels to lived experiences as diverse mathematics
learners and mathematics education researchers. We see this change in mission as
a call to both act politically (Aguirre et al., 2017) and to change story lines (i.e.,
“broad, culturally shared narrative[s]”; Herbel-Eisenmann et al., 2016, p. 104) that
dominate the public perception of mathematics learning and teaching. We
acknowledge that systemic barriers are part of a larger educational issue, but for
the purposes of this commentary, we focus on mathematics.
We first briefly focus on several systemic barriers that have impeded the equi-
table development of students’ mathematics knowledge, including school and
Journal for Research in Mathematics Education
2018, Vol. 49, No. 4, 373–389
We would like to thank Julia M. Aguirre and Beth Herbel-Eisenmann for
their feedback on this manuscript and on the projects that support teachers’ and
teacher educators’ engagement in asset-based and equity work. We also want to
thank the JRME Editorial Panel for its suggestions on improving this manuscript.
Copyright © 2018 by the National Council of Teachers of Mathematics, Inc., www.nctm.org. All rights reserved. This
material may not be copied or distributed electronically or in other formats without written permission from NCTM.
374 Asset-Based Approaches to Equitable Mathematics Education
school-system structures that foster the social reproduction of inequity (Boaler &
Staples, 2008; Ladson-Billings, 2017; NCSM & TODOS: Mathematics for ALL,
2016; Oakes, 2005). School funding formulae that instantiate inequities or
“between-school tracking” (Organisation for Economic Co-operation and
Development [OECD], 2016) alter children’s opportunities to learn mathematics.
The OECD (2014) report provides continued evidence that differential opportunity
to learn starts early (Carpenter, Fennema, Franke, Levi, & Empson, 2014;
Clements & Sarama, 2014; Turner, Celedón-Pattichis, & Marshall, 2008; Turner,
Celedón-Pattichis, Marshall, & Tennison, 2009; Turner & Celedón-Pattichis, 2011)
and is largely a function of socioeconomic status. Practices such as tracking as
well as differences in teacher preparedness across communities with varied socio-
economic statuses differentially impact student exposure to mathematics content
(OECD, 2016). Teachers’ and students’ beliefs about mathematics and learners of
mathematics also serve as barriers to equity in mathematics learning (Horn, 2007;
Sztajn, 2003). To develop an equitable context for all students to learn mathe-
matics, we need to change beliefs about students, about particular groups of
students, about how students learn, and about grouping students (Berlin & Berry,
2018).
The current system of tracking in the United States that has arisen from these
beliefs situates students from historically marginalized communities in lower
track classroom instruction that typically does not challenge all students equally.
Furthermore, this system fosters inequitable beliefs about both the nature of math-
ematics and how students view themselves as mathematics learners (Boaler, 2002,
2011; Boaler & Staples, 2008; Oakes, 2005). This instruction often leads to histo-
ries of learning that limit opportunities for low-resource communities and students
of color. If we are really going to make systemic change, we will need collabora-
tions among mathematics education researchers that include policymakers,
lawmakers, and practitioners as well as many others who serve as partners to
examine the system and work together toward change. Research has shown the
benefits of complex instruction and detracked classrooms (Boaler, 2002, 2011;
Boaler & Staples, 2008); however, others have argued that authentic equity work
requires a more critical approach (Gutiérrez, 2017; Rubel, 2017). We argue that
asset-based approaches to teaching in which students’ language and culture are
viewed as intellectual resources to engage with mathematics in the classroom
(Civil, 2007; Gonzalez, Moll, & Amanti, 2005) are needed to create change.
The purpose of this commentary is to extend the message of the 2017 report of
the NCTM Research Committee (Aguirre et al., 2017) by providing select exam-
ples of asset-based approaches to constructing instructional contexts in which all
students may gain mathematics knowledge. We call the mathematics education
research community toward an understanding of equitable practices based on
asset-based approaches to teaching and learning mathematics that are aligned with
this mission from Pre-K–Grade 16. We challenge the mathematics education
research community to consider a systems approach when thinking about the
complexities and nuances of inequitable practices that limit mathematical
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NCTM Research Committee
understanding for all children. Students and teachers must be considered within
the context of the school, the school system, parents, society, and government.
These systems are connected to and networked within policy systems that require
mathematics educators to engage with political conocimiento, which is knowledge
that involves the understanding of how systems operate to reproduce oppressive
discourses and willingness to subvert them, for which many may not be prepared
(G ut i é r rez, 2017 ).
Asset-Based Approaches to Mathematics Education Research and Practice
Asset-based approaches to mathematics education are a conscious way to move
away from deficit perspectives that view students, parents, and communities as
lacking in different aspects that enable them to be ready for schooling (Coleman,
Bruce, White, Boykin, & Tyler, 2016). An asset-based approach is grounded in
the belief that students’, families’, and communities’ ways of knowing, including
their language and culture, serve as intellectual resources and contribute greatly
to the teaching and learning of high-quality mathematics (Civil, 2017). This
approach draws from funds-of-knowledge work in which researchers and teachers
learn with and from students, parents, and communities (González et al., 2005).
There is valorization of knowledge (Civil, 2016); that is, different ways of doing
mathematics are acknowledged and honored. Thus, funds of knowledge positions
the home language and culture as assets that can serve as a foundation upon which
educators may construct mathematics lesson plans, for example, or con ceptualize
research.
The funds-of-knowledge work started as a collaborative research project
between anthropology and education in Tucson, Arizona. The research team
studied working-class Mexican1 communities’ household and classroom practices.
The central purpose of this work was to draw from local household and community
knowledge to innovate teaching practices (González et al., 2005). As part of this
work, teachers visited the students’ homes to learn about the literacy practices in
the home setting of primarily Latinx students (Moll, Amanti, Neff, & Gonzalez,
1992). This work has been extended to include funds of knowledge in mathe-
matics—in particular, engaging parents to participate in the mathematics educa-
tion of their children (Civil, 2016), integrating funds of knowledge to engage
students in Cognitively Guided Instruction (CGI) using their home language
(Celedón-Pattichis & Turner, 2012; Turner & Celedón-Pattichis, 2011), and
preparing preservice and in-service teachers to integrate funds of knowledge and
children’s mathematical thinking through programs such as the TEACH Math
project, which is explained below (Bartell et al., 2017).
1 Throughout the article, we have attempted to use the most appropriate ter minology to describe
people, peoples, and nat ions. We recognize that naming can be complex and seek throughout the
article to prioritize the way communities are naming themselves, recognizing that this too may
change wit h time. When referenci ng specic bodies of work, we made the decision to use the ter m
used by the authors of that work unless problematic.
376 Asset-Based Approaches to Equitable Mathematics Education
Asset-based projects often focus on working collaboratively with community
stakeholders to develop culturally based curriculum materials and culturally
responsive pedagogical practices (e.g., Dawson, 2013; Lunney Borden, 2013;
Nicol, Archibald, & Baker, 2013). The Math in a Cultural Context (MCC) supple-
mental curriculum resource is perhaps the best known example of such an asset-
based approach to curriculum development. These materials were designed by
researchers and Yup’ik elders and include “the embedded mathematical knowledge
contained in everyday solutions to a subsistence-oriented lifestyle, expert–appren-
tice modeling that elders use to teach novices, and spatial abilities and reasoning
that permeate everyday activities” (Kisker et al., 2012, p. 79). An examination of
the impact of using two MCC modules with second-grade students showed that
such use resulted in a significant positive effect on student performance for both
Alaskan Native students and non-Native Alaskans alike (Kisker et al., 2012).
An assets-based approach calls upon educators to provide high-quality math-
ematics that draws from strengths of students, families, and communities
(Celedón-Pattichis, White, & Civil, 2017) and emphasizes higher order concepts
and skills at each grade level as well as foundational knowledge and skills
(Clements & Sarama, 2008; Fryer & Levitt, 2004). Students should be afforded
opportunities to learn mathematics in their first or second language or languages
so that they have multiple opportunities to make meaning for mathematical
concepts and engage in problem solving (Celedón-Pattichis, Musanti, & Marshall,
2010; Celedón-Pattichis & Turner, 2012; Espada, 2012; Moschkovich, 2010; Turner
& Celedón-Pattichis, 2011).
Creating Opportunities to Learn High-Quality Mathematics
Beginning With Young Learners
Research focused on understanding children’s mathematical thinking can
inform educators about how to create learning opportunities for students. For
example, Clements and colleagues (Clements, Sarama, Spitler, Lange, & Wolfe,
2011; Clements, Sarama, Wolfe, & Spitler, 2013) provided a learning-trajectories-
based, conceptual, problem-solving curriculum for preschoolers. This curriculum
explicitly supported African American students’ participation in increasingly
sophisticated forms of mathematical communication and argumentation (e.g.,
asking “How do you know?”) and maintained a language-rich environment that
expected each child to invent solution strategies (cf. Carr, Steiner, Kyser, &
Biddlecomb, 2008; Fennema, Carpenter, Jacobs, Franke, & Levi, 1998). This
intervention supported preschoolers from low-resource communities to learn
substantially more mathematics than students who experienced the existing
mathematics curriculum. Also, African American students made greater gains
than students in other groups (Clements et al., 2011, 2013).
Using asset-based approaches to plan instruction focuses teachers’ attention
on students’ thinking and learning of mathematics and what children are capable
of doing and aids teachers in avoiding biases that impair teaching and learning
(Alexander, Entwisle, & Thompson, 1987; Martin, 2007; McLoyd, 1998;
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NCTM Research Committee
U.S. Department of Health and Human Services, Administration for Children
and Families, 2010). That is, including enthusiastic interaction with children that
focuses teachers on mathematics that they believe children can learn can change
their views of African American students’ mathematical capabilities (Jackson,
2011). A key point is that young children’s capacity to engage in challenging
mathematical thinking and problem solving is often underestimated (Carpenter
et al., 2014; Carpenter, Franke, Jacobs, Fennema, & Empson, 1998; Clements &
Sarama, 2014; Leonard, in press; Sarama & Clements, 2009; Turner & Celedón-
Pattichis, 2011; Turner et al., 2008). This is especially true for children in
historically marginalized communities for whom estimates are perniciously low.
A broad body of research has shown that CGI positively impacts students’
learning when teachers use it to inform their teaching (Carpenter, Fennema,
Peterson, & Carey, 1988; Carpenter, Fennema, Peterson, Chiang, & Loef, 1989;
Fennema et al., 1996; Franke, Carpenter, Levi, & Fennema, 2001). CGI prioritizes
a particular area of mathematics (i.e., number and operation) as well as a partic-
ular theoretical framing (i.e., cognitive). Asset-based approaches to teaching also
implement research that has shown, for example, that not all communities and
families focus on counting and operations in the specific way that CGI has
described. For instance, some researchers who study mathematics learning in
Aboriginal communities have shown that some of the students with whom they
work quantify (Meaney & Evans, 2013) in ways not captured by CGI and tend
more toward the use of spatial reasoning in quantifying (e.g., Hunting, 1987;
Lunney Borden & Munroe, 2016; Macpherson, 1987). Although the CGI approach
builds on children’s informal knowledge and invented processes, its descriptions
of those processes can inadvertently mask other mathematical strengths that
children might bring to the classroom.
Additional research using CGI as a framework has been conducted in culturally
and linguistically diverse settings in the United States, particularly with Latinx
students in bilingual and English as a Second Language classrooms (Celedón-
Pattichis & Turner, 2012; Secada, 1991; Turner et al., 2009; Turner & Celedón-
Pattichis, 2011). For example, when Latinx kindergartners learned mathematics
problem solving using the CGI framework, all children showed growth, and those
whose teachers spent more time on challenging problems, provided consistent
access to students’ native language, and used storytelling twice as much learned
the most (Turner & Celedón-Pattichis, 2011). Furthermore, CGI in combination
with culturally responsive instruction (CRI; see Closing the Mathematics
Achievement Gap [CMAG] project) improved the mathematics performance of
Native American students with learning disabilities (Hankes, Skoning, Fast, &
Mason-Williams, 2013). These studies provide examples of how culturally and
linguistically diverse students can engage in complex problem solving when
given the opportunity to do so and when teachers draw from language and culture
as intellectual resources (Celedón-Pattichis et al., 2010; Turner et al., 2008).
Globally, there has been a focus on transforming mathematics education for
Indigenous students by integrating Indigenous ways of knowing, being, and doing
378 Asset-Based Approaches to Equitable Mathematics Education
(Aikenhead, 2017; Meaney, Trinick, & Fairhill, 2013). Many of these projects
have focused on integrating cultural practices as a starting point for learning
mathematics (Beatty & Blair, 2015; Wagner & Lunney Borden, 2011). The Show
Me Your Math (SMYM) project in Canada stands as an example of shifting story
lines to center community knowledge as a place in which mathematics can
emerge (Wagner & Lunney Borden, 2012). In this program, the researchers
shifted their own positioning to remove themselves as the central characters in
the research and instead worked with community-based teachers to create a
program in which the students interact with community elders and knowledge
keepers to explore the ways of reasoning in their own community contexts that
align with school mathematics. Similar use of positioning theory in equity-based
research has been employed by Turner, Dominguez, Maldonado, and Empson
(2013) to examine the impact of positioning students as competent problem
solvers in mathematics classrooms. In SMYM, the work has been extended to
position students as researchers who learn from elders and share their learning
with their teachers and the wider community at an annual mathematics fair
(Lunney Borden, Wagner, & Johnson, 2018). Projects such as making paddles,
maple syrup, and drums have become commonplace in the Mi’kmaw schools that
participate in this program, and this, in turn, positions community knowledge
not only as an asset but as a place from which rich learning may emerge (Lunney
Borden & Wiseman, 2016).
Collectively, these research studies change the story line of who can do math-
ematics and whose mathematics is learned because culturally and linguistically
diverse students are positioned as doers of mathematics, and the programs take
an asset-based approach that honors and acknowledges the ways of knowing and
using mathematics in communities (Civil, 2007, 2016; González, Andrade, Civil,
& Moll, 2001). The studies documenting mathematical learning in Latinx,
African American, Indigenous, and multilingual settings provide powerful
examples of projects that affect professional practice. These asset-based
approaches do not ask “Is the child ready to learn?” but accept that every child
is ready (Institute of Medicine [IOM] and National Research Council [NRC],
2015) and eager (NRC, 2001) to learn—and have substantial potential and compe-
tencies on which to base future learning. Asset-based approaches similarly build
on funds of knowledge (González et al., 2001; Moll et al., 1992) in which linguistic
and cultural resources in the child and community are viewed as intellectual
resources to engage with mathematics in the classroom.
There are pedagogical strategies that promote equitable instruction, but equally
important are approaches to modify systems at the school, district, state, and
national levels that maintain inequitable structures. Equitable practices focused
on asset-based approaches must be implemented comprehensively so that all
students’ experiences are devoid of labeling, prejudice, and unequal access to
opportunities to learn (Bishop & Forgasz, 2007).
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Supporting Teachers to Engage in Teaching and Learning Mathematics
From an Asset-Based Approach
There have been a number of studies that take up the important work of
providing teacher preparation to support teachers to enact equitable, asset-based
approaches to mathematics education. Using Gutiérrez’s (2012) framework, Rubel
(2017) identified four common equitable teaching practices that are often used to
bring about greater equity in the classroom. She argued that practices such as
standards-based teaching and complex instruction address what Gutiérrez referred
to as the dominant axis, where the main focus is on supporting access and achieve-
ment of historically marginalized students. She also argued that strategies such as
culturally responsive pedagogy and teaching mathematics for social justice are
better aligned with Gutiérrez’s critical axis in that they address issues of identity
and power in the mathematics classroom. Many teachers in this study identified
as White and were teaching in hyper-segregated schools. Although the teachers
that she observed seemed adept at using the more dominant practices, they
struggled with the critical approaches to teaching mathematics. Rubel argues that
there is a need to address the more critical approaches in teacher development so
that teachers are better prepared to build the necessary knowledge of community
and engage with more complex notions of equity, identity, and power.
Wiseman, Glanfield, and Lunney Borden (2017), in a systematic review of
literature relating to Indigenous knowledge in mathematics and science education
in Canada, highlighted the significant need for teacher learning that counters the
deficit views of Indigenous peoples and communities that have been perpetuated
by colonial systems of education. In the 2017 Research Committee report (Aguirre
et al., 2017), mathematics education researchers were called to acquire the knowl-
edge necessar y to do equity work; this is also a need for mathematics teachers who
must unlearn the deficit views to be open to asset-based approaches. In this
section, we highlight two projects—Access, Agency, and Allies in Mathematical
Systems (A3IMS; Larnell et al., 2016; LópezLeiva, Herbel-Eisenmann, Yolcu, &
Jones, 2015) and Teachers Empowered to Advance Change in Mathematics
(TEACH MATH; Turner et al., 2012)—that are striving to advance work on equity
in mathematics education by supporting such teacher learning. We include these
two projects because they involve cross-site researchers in equity and mathematics
education who also draw from asset-based approaches and because they engage
K–Grade 9 teachers in critically ref lecting on equitable teaching practices to
improve students’ outcomes. (See the Center for the Mathematics Education of
Latinos/as [CEMELA] at http://cemela.math.arizona.edu for more examples that
draw from an asset-based approach to preparing teachers.)
The stated goal of A3IMS is to design professional development (PD) that
makes central an equitable system (Larnell et al., 2016; LópezLeiva et al., 2015).
An equitable system, according to this project, comprises intersecting levels of
mathematics education that “function synergistically to support the fair distribu-
tion of opportunities to learn (Hand, Penuel, & Gutiérrez, 2012)” (Scroggins,
Herbel-Eisenmann, Harper, & Bartell, 2017, p. 847). The PD involved a summer
380 Asset-Based Approaches to Equitable Mathematics Education
institute in which teachers considered access, agency, and ally work in relation to
four strands: mathematical discourse practices such as argumentation and justifi-
cation, algebraic thinking, culture and community, and positionality. Following
the institute, participating teachers engaged in action research related to ideas
from the strands that they wanted to systematically study to better support oppor-
tunities to learn. In particular, A3IMS is researching the nature of students’,
teachers’, and mathematics teacher educators’ opportunities to learn with respect
to access, agency, and allies. Such work is critical in developing teachers’ and
mathematics teacher educators’ political conocimiento for teaching mathematics
(Gutiérrez, 2017) and is the first step needed for teachers and mathematics teacher
educators to recognize and challenge their own privilege to empower all students
in the classroom. This ongoing National Science Foundation (NSF) funded
research and PD project is representative of the work needed to forward preservice
and in-service teacher learning opportunities in mathematics education that hold
promise for supporting equitable practice more broadly.
TEACH MATH was a 5-year multi-institution collaborative NSF-funded project
focused on transforming K–Grade 8 mathematics teacher preparation and early
career teaching so that new generations of teachers are equipped with equity-
based, culturally responsive mathematics pedagogies to increase the mathematics
learning and achievement of youth in the United States. The TEACH MATH
project researched and developed instructional modules for teacher education and
PD settings to support teachers to connect to children’s mathematical thinking
and cultural-, linguistic-, and community-based funds of knowledge, or what the
project called students’ multiple mathematical knowledge bases in instruction (see
Bartell et al., 2017; Drake et al., 2015; Turner et al., 2012). The pedagogical tools
and strategies embedded in these modules facilitate an asset-based orientation to
mathematics teaching that supports students’ mathematical learning and engage-
ment. The Case Study Module affords preservice teachers an opportunity to get
to know one student from a culturally or linguistically different background from
their own by interviewing the student and conducting problem-solving interviews.
The ultimate goal is to support preservice teachers in advancing that child’s math-
ematics learning. In an empirical study of 96 mathematics tasks developed from
these mathematics learning case studies, 97% of the tasks directly attended to
children’s mathematical thinking and knowledge of the child’s interests.
Furthermore, almost half (46%) of the mathematics tasks aimed to foster the child’s
mathematical reasoning and connect to specific knowledge about the child’s out-
of-school experiences to leverage mathematical learning (Turner et al., 2016).
The Classroom Practices Module supports teachers in observing and ref lecting
on their own practice (or that of others) related to learning, teaching, mathematical
tasks, and power and participation (see Roth McDuffie, Foote, Drake, et al., 2014,
for ways to use these lenses to analyze mathematics teaching using video cases).
The researchers found that preservice teachers’ use of these lenses to analyze
videos of instructional practice deepened their capacities to notice children’s
multiple mathematical knowledge bases and instructional moves and interactions
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that promote mathematics learning. In prior studies, teachers’ noticing was found
to be challenging to develop with in-service teachers (Roth McDuffie, Foote,
Bolson, et al., 2014). The Community Exploration Module engages teachers in
learning about the mathematical practices in students’ families and communities
and drawing from these to create standards-based mathematics lessons that are
meaningful and culturally relevant to the students (see Aguirre et al., 2013; Turner
et al., 2014). An empirical study that analyzed 70 Community Mathematics
Exploration projects representing the work of 113 preservice teachers found that
almost half of the projects (47%) attended to multiple mathematical knowledge
bases in ways that demonstrate that preservice teachers can be supported to design
and implement standards-based instruction from an asset-based approach, an
often-cited challenge for in-service teachers to incorporate into their practice
(Aguirre & Zavala, 2013). Given the theoretical, empirical, and practice-based
contributions of the TEACH MATH modules, more institutions continue to field-
test the modules in mathematics methods courses throughout the United States
and currently use them to support in-service teachers at different institutions
(www.teach math.info).
What is common across these two projects is the continued support that is
needed for teachers to develop asset-based pedagogical dispositions over time
through PD that addresses equity in mathematics education. Although the first
project is still in the early stages, teachers have the potential to make statistically
significant changes in student achievement (Marzano, 2003), and we believe that
the mathematics education research community needs to consider teacher dispo-
sitions as we work toward greater equity. We now turn to research strands that are
needed to advance the work on equity in mathematics education.
Research Needed in Equity in Mathematics Education
Having considered examples of projects that forge a path toward equitable
teaching and learning through asset-based approaches and teacher education
programs that foster equitable instructional practices, we now turn toward areas
of need within mathematics education research. The research community is called
to build our collective understanding of instructional practices, political acts, and
teacher education efforts that hold potential to suppor t more equitable instructional
practices that create powerful learning experiences for all students. Asset-based
approaches are equally applicable for both practice and research. In the 2017
Research Committee report, the mathematics education research community was
asked to consider the following four questions:
1. What is my researcher positionality?
2. What theoretical frameworks and literature will I draw from and why?
3. How will the research design be informed by the communities with whom
I work?
4. How do I engage the community or population in the findings I report in the
research? (Aguirre et al., 2017, pp. 133–134)
382 Asset-Based Approaches to Equitable Mathematics Education
These questions can guide researchers to use an asset-based lens in planning,
designing, and engaging in research alongside communities. We have described
examples above that demonstrate the contributions of asset-based approaches to
the field and identify the implications of such asset-based approaches to research.
Though not an exhaustive list, the literature reviewed shows that such research
must begin with:
1. believing that all students can engage with challenging mathematics,
2. engaging the community to build relationships in meaningful ways so that the
strengths of the community are seen as a starting point for research and
teaching,
3. drawing upon the linguistic and cultural strengths in the community (funds
of knowledge) to inform mathematics education research and practice, and
4. critically examining and challenging systemic inequities within existing
practices.
Below, we point toward f ive areas of research necessary to move discussion and
practice forward toward equitable mathematics education that has the potential to
support all learners to learn significant and powerful mathematics. These include
research that (a) explicitly reveals effective practices that have successfully
changed outcomes for mathematics learners, (b) supports our understanding of
asset-based approaches, (c) builds understanding of effective teacher education
and induction programs, (d) renews efforts to problematize what we mean by
mathematics and mathematics competence, and (e) takes up the political acts that
we were challenged to consider within the 2017 Research Committee report
(Aguirre et al., 2017).
First, the mathematics education community is encouraged to continue impor-
tant work related to reversing systems of inequity. The negative impacts of
tracking on historically marginalized students, for example, are well documented
(Oakes, 2005), but there are far fewer studies that support our understanding of
effective, equity-focused, detracked classrooms and schools (e.g., Burris, Wiley,
Welner, & Murphy, 2008). We also have little understanding of the work required
to truly transform a school context into one that supports the mathematics learning
of all students, including historically marginalized populations. We call for more
case studies that contextualize mathematics education research within systemic
barriers that continue to perpetuate and reinforce inequities in mathematics
teaching and learning. Rich descriptions of efforts to provide such equitable
instruction that take into consideration the systems in which these inequitable
practices exist will provide exemplars that may support future efforts to effectively
educate all students for future mathematical success.
Second, we call for more asset-based research that embraces and sustains cultur-
ally responsive and relational pedagogy (Aikenhead, 2017; Glanfield, Sterenberg,
& Donald, 2013; Leonard, Napp, & Adeleke, 2009) and expands our understanding
of cultural ways of knowing as well as the impact of such work. This research
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highlights the necessary step of educators building relationships with communities
and coming to understand ways of knowing and doing mathematics within these
communities (Wiseman et al., 2017). To do such work, we need to build genuine
collaborations as we conduct research to deeply understand communities and their
ways of knowing (Aguirre et al., 2017; Wiseman, Glanfield, & Lunney Borden,
2017). Moreover, we acknowledge the importance of teaching mathematics for
social justice as a means of honoring communities of color and addressing the
challenges that these communities face in obtaining educational parity and
accessing equitable mathematics instruction (Leonard, Brooks, Barnes-Johnson,
& Berry, 2010). Finally, we call for longitudinal studies of these equitable teaching
practices to begin to understand the sustained benefits of learning mathematics
for all students.
Third, we call on the mathematics education community to deeply examine
teacher education programs that foster real change through long-term immersion
within communities of traditionally marginalized (Seidl et al., 2015) and
Indigenous peoples (Lunney Borden & Wiseman, 2016). Teachers need to develop
a rich store of knowledge relative to the ways of being or ways of knowing in
mathematics as well as the cultural tools that students bring to the classroom that
facilitate their learning (Lunney Borden, 2011, 2013). Both teachers’ and students’
beliefs about mathematics as a discipline and the purpose of school mathematics
need to be reconsidered to create equitable contexts for all students to learn math-
ematics (Aguirre et al., 2017). Further, we know that much of the learning in
teacher education programs can be dissipated if it is not supported with rich and
supportive induction programs. We encourage the examination of powerful induc-
tion programs that rely on hybrid contexts for busy teachers to create multiple
opportunities to engage with colleagues during the early years of a teacher’s career
(Kobett, 2016).
Fourth, in addition to the political acts described in the 2017 Research
Committee report (Aguirre et al., 2017), we call on the mathematics education
community to change the narrative (Herbel-Eisenmann et al., 2016) around what
it means to be mathematically competent and the ways in which mathematics
classrooms foster conceptions of competence (Gresalfi, Martin, Hand, & Greeno,
2009). The mathematics education community not only needs rich descriptions of
pedagogy that challenges all students to learn mathematics but also examples that
challenge what it means to be mathematically competent or to engage in a math-
ematics community. We must take up the important work of changing story lines
about what it means to do mathematics (Aguirre et al., 2017; Herbel-Eisenmann
et al., 2016). Parents and other inf luences on mathematics teaching, such as the
news media, must be supported to understand the importance of thinking differ-
ently about mathematics (Herbel-Eisenmann et al., 2016).
Finally, we urge the mathematics education community to seriously consider
and to take up the call of the 2017 Research Committee report (Aguirre et al.,
2017) to “enhance mathematics education research with an equity lens” (p. 128),
“acquire the knowledge necessary to do genuine equity work” (p. 129), “challenge
384 Asset-Based Approaches to Equitable Mathematics Education
the false dichotomy between mathematics and equity” (p. 130), and “expand the
view of what counts as ‘mathematics’” (p. 132). It is through these political acts
as well as the call for the research outlined above that we will expand our under-
standing of and ability to foster the development of mathematics classroom
contexts that support the readiness of all students to engage in high-level mathe-
matics that opens future opportunities.
References
Aguirre, J., Herbel-Eisenmann, B., Celedón-Pattichis, S., Civil, M., Wilkerson, T., Stephan, M.,
. . . Clements, D. H. (2017). Equity within mathematics education research as a political act:
Moving from choice to intentional collective professional responsibility. Journal for Research in
Mathematics Education, 48(2), 124–147. doi:10.5951/jresematheduc.48.2.0124
Aguirre, J. M., Turner, E. E., Bartell, T. G., Kalinec-Craig, C., Foote, M. Q., Roth McDufe, A.,
& Drake, C. (2013). Making con nections in practice: How prospective elementary teachers
connect to children’s mathematics thin king and community funds of knowledge in mathematics
instruction. Journal of Teacher Education, 64( 2) , 178 –192 . do i:10.1177/002 2 487112 4 669 00
Aguirre, J. M., & Zavala, M. R. (2013). Making cult urally responsive mathematics teaching explicit:
A lesson analysis tool. Pedagogies: An International Journal, 8(2), 163–190. d oi:10.108 0/1554 4
80X. 2013.768518
Aikenhead, G. S. (2017). Enhancing school mathematics culturally: A path of reconciliat ion.
Canadian Journal of Science, Mathematics and Technolog y Education, 17 (2), 73 –14 0. doi :10.10
80/14926156.2017.1308043
Alexander, K. L., Entwisle, D. R., & Thompson, M. S. (1987). School perfor mance, status relations,
and the structure of sentiment: Bring ing the teacher back in. American Sociological Review,
52(5), 665–682. doi:10.2307/2095602
Bartell, T., Turner, E. E., Aguir re, J. M., Drake, C., Foote, M. Q., & Roth McDufe, A. (2017).
Connecting children’s mathematical th inking wit h family and communit y knowledge in
mathematics instruction. Teaching Children Mathematics, 23(6), 326 –328.
Beatty, R., & Blair, D. (2015). Indigenous pedagogy for early mathematics: Algonquin loomi ng in a
Grade 2 m ath classroom. The Interna tional Journal of Holistic Early Learning and De velopment,
1, 3–24.
Berlin, R., & Berry, R. Q. III. (2018). Confronting the lies I tell myself. In S. Crespo, S. Celedón-
Pattichis, & M. Civil (Eds.), Access and equit y: Promoting high-quality mathematics in Grades
3–5, pp. 9–20. Reston, VA: National Council of Teachers of Mathematics.
Bishop, A. J., & Forgasz, H. J. (2007). Issues in access and equit y in mathematics education. In F.
K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2,
pp. 1145–1167). Charlotte, NC: Information Age.
Boaler, J. (2002). Experiencing school mathe matics: Traditional and reform approaches to teaching
and their impact on student learning ( Rev. ed.). Mahwah, NJ: Erlbaum.
Boaler, J. (2011). Chang ing student s’ lives thr ough the de-t racking of urba n mathematics cla ssrooms.
Journal of Urban Mathematic s Education, 4(1), 7–14.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching
approach: T he case of Railside School. Teachers College Record, 110 (3), 608– 645.
Burr is, C. C., Wiley, E., Welner, K., & Mur phy, J. (2008). Accountability, rigor, and det racking:
Achievement effects of embracing a challenging cur riculum as a universal good for all st udents.
The Teachers College Record, 110 (3), 57 1– 607.
Carpenter, T. P., Fennema, E. H., Franke, M. L., Levi, L., & Empson, S. B. (2014). Children’s
mathematics: Cognitively guided instruction. Portsmouth, NH: Heineman n.
Carpenter, T. P., Fennema, E., Peterson, P. L., & Carey, D. A. (1988). Teachers’ pedagogical content
knowledge of students’ problem solving in elementa ry arithmetic. Jour nal for Research in
Mathematics Education, 19(5), 385401. doi :10.230 7/74 9173
385
NCTM Research Committee
Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge
of children’s mathematics think ing in classroom teaching: An experimental st udy. American
Educational Research Journal, 26(4), 4 99–531. do i:10. 3102/ 0 0 02 83120 260 0449 9
Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal
study of invention and underst anding in children’s multidigit addition and subtraction. Journal
for Research in Mathematics Education, 29(1), 3–20. doi:10.2307/749715
Carr, M., Steiner, H. H., Kyser, B., & Biddlecomb, B. (2008). A comparison of predictors of early
emerging gender differences in mathemat ics competency. Learning and Individual Differences,
18(1), 61–75. doi:10.1016/j.lind if.2007.04.005
Celedón-Pat tichis, S., Musanti, S. I., & Marshall, M. E. (2010). Bilingual elementary teachers’
reections on using st udents’ native la nguage and cultu re to teach mathematics. I n M. Q. Foote
(E d.), Mathematics teaching & learning in K–12: Equity and professional development (pp.
7–24). New York, NY: Palgrave Macmillan. doi:10.1057/9780230109889_2
Celedón-Pat tichis, S., & Turner, E. E. (2012). “Explícame tu respuesta”: Support ing the development
of mathemat ical discourse in emergent biling ual kindergarten students. Biling ual Research
Journal, 35 (2), 19 7–216. doi :10.1080 /152358 82.2012 .703635
Celedón-Pat tichis, S., White, D. Y., & Civil, M. (Eds.). (2017). Acce ss and equity: Promoting high-
qualit y mathematic s in pre-K–G rade 2. Reston, VA: National Coun cil of Te achers of Mathem atics.
Civil, M. (2007 ). Building on commu nity knowledge: A n avenue to equity i n mathematics ed ucation.
In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversit y and equity in the
classroom (pp. 105–117). New York, NY: Teachers College Press.
Civil, M. (2016). STEM learning research th rough a f unds of knowledge lens. Cultural Studies of
Science Education, 11(1), 41– 59. doi:10.10 07/s1142 2- 014-9 6 48-2
Civil, M. (2017). Preface. In S. Celedón-Pattichis, D. Y. White, & M. Civil (Eds.), Access and
equity: Promoting high quality mathematics in pre-K– Grade 2 (pp. v–viii). Reston, VA: National
Council of Teachers of Mathemat ics.
Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a research-based
preschool mathematics cur riculum. American Educational Research Journal, 45(2), 443– 494.
do i:10. 310 2 /0 0 0 2 831 207 312 908
Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The lear ning trajectories
approach (2nd ed.). New York, NY: Routledge.
Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics
learned by young children i n an intervent ion based on learning trajector ies: A large -scale cluster
randomized trial. Journal for Re search in Mathematics Education, 42(2), 127–166. doi:10.5951/
jresematheduc.42.2.0127
Clements, D. H., Sarama, J., Wolfe, C. B., & Spitler, M. E. (2013). Longitudinal evaluation of a
scale-up model for teaching mathematics with trajector ies and technologies: Persistence
of effects in the thi rd year. American Educational Research Journal, 50(4), 812–850.
do i:10. 310 2 /0 0 0 2 831 212 4 692 70
Coleman, S. T., Bruce, A. W., White, L. J., Boykin, A. W., & Tyler, K. (2016). Communal and
individual lear ning contexts as they relate to mathematics achievement under simulated
classroom c ondit ions. Jou rna l of Black Ps ycholog y, 43(6), 543–56 4. doi:10.1177/0095798416 665966
Dawson, A. J. S. (2013). Mathematics and culture in Micronesia: The str uctu re and f unction of a
capacity building project. Mathemat ics Education Re search Journal, 25(1), 43 –56. d oi :10.1007/
s13394-012-0057-0
Drake, C., Land, T. J., Bar tell, T. G., Aguirre, J. M., Foote, M. Q., Roth McDuf e, A., & Turner,
E. E. (2015). Three strategies for opening cur riculum spaces. Teaching Children Mathematics,
21(6), 346 –353.
Espada, J. P. (2012). T he native la nguage in teaching kindergarten mathematics. Journal of
International Education Research, 8(4), 359–366. doi:10.19030/jier.v8i4.7282
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A
longitud inal study of learning to use children’s thinking in mathematics instr uction. Journal for
Research in Mathematics Education, 27(4), 403–434. doi:10.2307/749875
386 Asset-Based Approaches to Equitable Mathematics Education
Fennema, E., Carpenter, T. P., Jacobs, V. R., Franke, M. L., & Levi, L. W. (1998). A longitudinal
study of gender differences in young children’s mathematical think ing. Educational Researcher,
27(5), 6 –11.
Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative
change: A follow-up study of professional development in mathematics. American Educational
Research Journal, 38(3), 653–689. doi:10.3102/00028312038003653
Fryer, R. G., Jr., & Levitt, S. D. (2004). Underst anding the Black–White test score gap in
the rst two years of school. The Review of Economics and Statistics, 86(2), 447–464.
doi :10.1162/ 0034 653 04323031049
Glaneld, F., Sterenberg, G., & Donald, D. (2013, April). Sustaining equity in mathematics
performance through cult urally relational practices. Paper presented at the an nual meeting of
the National Council of Teachers of Mathematics, Denver, CO.
González, N., Andrade, R., Civil, M., & Moll, L. (2001). Bridging funds of distributed knowledge:
Creating zones of practices i n mathematics. Journal of Education for Students Placed at Risk,
6(1–2), 115 –132. doi:10.1207/S15327671ESPR0601-2 _7
González, N., Moll, L. C., & Amanti, C. (2005). Funds of k nowledge: Theorizing practices in
households, communities, and classrooms. Mahwah, NJ: Erlbaum.
Gresal, M., Martin, T., Hand, V., & Greeno, J. (2009). Const ructing competence: An analysis of
student part icipation i n the act ivity systems of mathematics classrooms. Educational Studies in
Mathematics, 70(1), 49–70. do i:10.10 07/s1064 9- 008-9141-5
Gutiér rez, R. (2012). Context matters: How should we concept ualize equit y in mat hematics
education? In B. Herbel-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in
discourse for mathematic s education: Theories, practices, and policies ( pp. 17–33). Dordrecht,
the Netherlands: Springer.
Gutiér rez, R. (2017). Political conocimiento for teaching mathematics: W hy teachers need it a nd
how to develop it. In S. E. Kastberg, A. M. Tyminski, A. L. Lischka , & W. B. Sanchez (Eds.),
Building support for scholarly practices in mathematics methods (pp. 11–37). Charlotte, NC:
Information Age.
Hankes, J., Skoning, S., Fast, G., & Mason-Williams, L. (2013). Closing the math gap of Native
American students identi ed as lear ning disabled. Investigations in Mathematics Learning, 5(3),
44 –59. doi:10.10 80 /2 4727466.2013.11790326
Herbel-Eise nmann , B., Sinclair, N., Chval, K. B., Cleme nts, D. H., Civil, M., Pape, S. J., . . . Wil kerson,
T. L. (2016). Positioning mathemat ics education researchers to in uence stor ylines. Journal for
Research in Mathematics Education, 47(2), 102 –117. doi:10.5951/j re sem at heduc.47.2 .010 2
Horn, I. S. (2007). Fast kids, slow kids, lazy kids: Framing t he mismatch problem in
mathematics teachers’ conversations. Journal of the Learning Sciences, 16(1), 37–79.
doi:10.1080/10508400709336942
Hunting, R. P. (1987). Mathematics and Australian Aboriginal culture. For the Learning of
Mathematics, 7(2), 5 –10.
Instit ute of Medicine & National Resear ch Council. (2015). Tran sforming the workforce for child ren
birth through age 8: A unifying foundation. Washington, DC: National Academies Press.
Jackson, K . (2011, Apr il). Exploring relat ionships betwe en mathematic s teachers’ views of students’
mathematical capabilities, visions of instruction, and instructional practices. Paper presented at
the annual meeting of the American Educational Research Association, New Orleans, LA.
Kisker, E. E., Lipka, J., Adams, B. L., Rickard, A., Andrew-Ihrke, D., Yanez, E. E., & Millard, A.
(2012). The potential of a culturally based supplemental mathematics cu rriculum to improve
the mathematics performance of Alaska Native and other students. Journal for Research in
Mathematics Education, 43(1), 75–113. doi:10.5951/jresem atheduc.43.1.0075
Kobett, M. E. (2016). A university-led beginning teacher mathematics community (Doctoral
dissertation). Retrieved from http://jhir.library.jhu.edu/handle/1774.2/40334
Ladson-Billings, G. (2017). “Makes me wanna holler”: Refuting the “culture of poverty” discourse
in urba n schooling. The AN NALS of the American Academy of Political and Social S cience,
673(1), 80–90. doi:10.1177/0002716217718793
387
NCTM Research Committee
Larnell, G., López Leiva, C., Scroggins, A., Amidon, J., Foote, M., Hand, V., . . . Wager, A. (2016,
Nove mber). Challenging the reframing of equity in mathematical systems: Access, agency, and
allies. Paper presented at the an nual meeting of the North A merican Chapter of the International
Group for the Psychology of Mathematics Education, Tucson, AZ.
Leonard, J. (in press). Culturally specic pedagogy in the mathematics classroom: Strategies for
teachers and students (2nd ed.). New York, N Y: Routledge.
Leonar d, J., Brooks, W., Barnes-Joh nson, J., & Berr y, R. Q., III. (2010). The nuances and c omplexities
of teaching mathematics for cultural relevance and social justice. Journal of Teacher Education,
61(3), 261–270. doi:10.1177/0022487109359927
Leonard, J., Napp, C., & Adeleke, S. (2009). The complexities of culturally relevant pedagog y:
A case study of two secondary mathematics teachers and their ESOL students. High School
Journal, 93 (1), 3–22. doi:10.1353/ hsj.0.0038
LópezLeiva, C., Herbel-Eisenmann, B., Yolcu, A., & Jones, D. (2015, November). Equity in
mathematics education: Who is an ally? Paper presented at the annu al meeting of the Nor th
American Chapter of the International G roup for the Psychology of Mathematics Education, East
Lansing, MI.
Lunney Borden, L. (2011). The “verbication” of mathematics: Using the grammatical structures of
Mi’kmaq to suppor t student lear ning. For the Learning of Mathematics, 31(3), 8–13.
Lunney Borden, L. (2013). What’s the word for…? Is there a word for…? How understanding
Mi’kmaw language can help support Mi’kmaw learners in mathematics. Mathematics Education
Research Journal, 25(1), 5 –22. doi:10.10 07/s13394-012- 0 04 2-7
Lunney Borden, L., & Munroe, E. (2016). Speaking English isn’t thin king English: Exploring
young Aboriginal children’s mathematical experiences through Aboriginal perspectives. In A.
Anderson, J. Anderson, J. Hare, & M. McTavish (Eds.), Language, learning, and cult ure in early
childhood: Home, school, and community contexts (pp. 64–81). New York, NY: Routledge.
Lunney Borden, L., Wagner, D., & Johnson, N. (2018). Show me your math: Mi’kmaw community
members explore mathematics. In C. Nicol, S. Dawson, J. Archibald, & F. Glaneld (Eds.),
Living cult urally responsive mathematics curriculum and pedagog y: Making a difference
with/in indigenous communities. Rotterdam, the Netherlands: Sense.
Lunney Borden, L., & Wiseman, D. (2016). Considerations from places where indigenous and
Western ways of knowing, being, and doing circulate together: STEM as artifact of teaching and
learning. Canadian Journal of Science, Mathematics and Technology Education, 16(2), 140–152.
doi:10 .10 80 /14 92615 6.2 016.116629 2
Macpherson, J. (1987). Norman. For the Learning of Mathematics, 7(2), 24–26.
Martin, D. B. (2007). Beyond missionaries or cannibals: Who should teach mathematics to Af rican
American children? The High School Journal, 91(1), 6 –28. doi:10.1353/hsj.200 7.0023
Marzano, R. J. (2003). What work s in schools: Translating research into action. Alexandria, VA:
Association for Super vision and Cur riculum Development.
McLoyd, V. C. (1998). Socioeconomic disadvantage and ch ild development. American Psychologist,
53(2), 185–204. doi:10.1037/0003-066X.53.2.185
Meaney, T., & Evans, D. (2013). What is the responsibility of mathematics education to the
Indigenous students that it serves? Educational Studies in Mathematics, 82(3), 481496 .
doi :10.10 07/s10 649-012-9439-1
Meaney, T., Trinick, T., & Fairhall, U. (2013). One size does NOT t all: Achieving equity in Māori
mathematics classrooms. Journal for Research in Mathematics Education, 44(1), 235–263.
doi:10.5951/jresematheduc.4 4.1.0235
Moll, L. C., Ama nti, C., Neff, D., & Gon zalez, N. (1992). Funds of knowledge for teaching: Using
a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132–141.
doi:10.1080/00405849209543534
Moschkovich, J. N. (Ed.). (2010). Lang uage and mathematics education: Multiple perspectives and
directions for research. Charlotte, NC: Information Age.
National Cou ncil of Supervisors of Mathematics & TODOS: Mathematics for ALL. (2016).
Mathematics education through the lens of social justice: Acknowledgme nt, act ions, and
accountability. Retrieved from http://www.todos-math.org/assets/ docs2016/2016Enews/3.
pospaper16_wtodos_8pp.pdf
388 Asset-Based Approaches to Equitable Mathematics Education
National Cou ncil of Teachers of Mathematics. (2017). Positioning NCTM for a second century.
Retrieved from https://www.nctm.org/secondcentury/
National Research Cou ncil. (2001). Eager to learn: Educating our preschoolers. Washington, DC:
National Academy Press.
Nicol, C., Archibald, J.-A., & Baker, J. (2013). Designing a model of culturally responsive
mathematics education: Place, relationships and stor ywork. Mathe matics Education Research
Journal, 25(1), 73 –89. doi:10.100 7/s13394 - 012-0 062-3
Oakes, J. (2005). Keeping track: How schools structure inequalit y (2nd ed.). New Haven, CT: Yale
University Press.
Organisation for Economic Co -operation and Development. (2014). PISA 2012 results in focus:
What 15-year-olds k now and what they can do with what they know. Retrieved from https://ww w.
oecd.org/pisa/keyndings/pisa-2012-results-overview.pdf
Organisation for Economic Co -operation and Development. (2016). Equations and inequalities:
Making mathemat ics accessible to all. Paris, France: Author. doi:10.1787/9789264258495-en
Roth McDufe, A., Foote, M. Q., Bolson, C., Tur ner, E. E., Aguirre, J. M., Bartell, T. G., . . . Land, T.
(2014). Using video analysis to support prospect ive K–8 teachers’ noticing of st udents’ multiple
mathematical knowledge bases. Journal of Mathematics Teacher Education, 17(3), 245–270.
doi:10.1007/s10857- 013-9257- 0
Roth McDuf e, A., Foote, M.Q., Drake, C., Turner, E., Aguirre, J., Bartell, T. G., & Bolson , C.
(2014). Use of video analysis to suppor t prospective K–8 teachers’ noticing of equit able practices.
Mathematics Teacher Educator, 2(2), 108 –140. doi:10.5951/mathteaceduc.2.2.0108
Rubel, L. H. (2017). Equity-directed inst ructional practices: Beyond the dom inant perspective.
Journal of Urban Mathematic s Education, 10 (2), 66–105.
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning
trajectories for young children. New York, NY: Routledge.
Scroggins, A. D., Herbel-Eisenmann, B., Harper, F., & Bartell, T. (2017). Mathematics teacher
professional development toward equitable systems: Weaving together mathematics, discourse,
community, positionality, and action research. In A. Chronaki (Ed.), Mathematics education and
life at times of crisis: Proceedings of the ninth International Mathematics Education and Society
Conference (Vol. 2, pp. 846– 855). Volos, Greece: MES9.
Secada , W. G. (1991). Degree of bilingualism and arith metic problem solving in H ispan ic rst
graders. The Elementary School Jour nal, 92(2), 213 –231. doi:10.1086/461689
Seidl, B. L., Monobe, G., Conley, M. D., Burgos, L. P., Rivera, H. J., & Uchida, C. H. (2015).
Multicult ural apprenticeships in teacher education. Teacher Education, 26(3), 2 94 –309. d oi:10.1
080/10 476210.2 014.9 96747
Sztajn, P. (2003). Adapting refor m ideas in different mathematics classrooms: Beliefs
beyond mathematics. Journal of Mathematics Teacher Education, 6(1), 53–75.
doi :10.1023/A:10221715312 85
Turner, E., Ag uir re, J., Ba rtell, T., Drake, C., Foote, M., & Roth McDufe, A. (2014). Making
meaningful connections with mathematics and the communit y: Lessons from prospective
teachers. In T. G. Bartell & A. Flores (Eds.), TODOS research monograph 3: Embracing
resources of children, families, communities, and cultures in mathematics learning ( pp. 60–100).
San Bernardino, CA: TODOS: Mathematics for All.
Turner, E. E., & Celedón-Pattichis, S. (2011). Mathematical problem solving among Latina/o
kindergarteners: An analysis of opportunities to learn. Journal of Latinos and Education 10 (2),
146–169. doi:10.1080/15348431.2011.556524
Turner, E. E., Celedón-Pattichis, S., & Marshall, M. (2008). Cultu ral and linguistic resources to
promote problem solving and mathematical discourse among Hispanic kindergarten students. I n
R. Kitchen & E. Silver (Eds.), The inaug ural TODOS: Promoting high participation and success
in mathematics by Hispanic students: Examining opport unities and probing promising practices
(Vol. 1, pp. 19–42). Washington, DC: National Education Association and TODOS: Mathematics
for ALL.
389
NCTM Research Committee
Turner, E. E., Celedón-Pattichis, S., Marshall, M., & Tennison, A. (2009). “Fíjense amorcitos, les
voy a contar una historia”: The power of story to support solving and d iscussing mathematical
problems among Latino and Latina kindergarten students. In D. Wh ite & J. S. Spitzer (Eds.),
Mathematics for every st udent: Responding to diversity, Grades pre-K–5 (pp. 23–41). Reston,
VA: National Council of Teachers of Mat hematics.
Turner, E., Dominguez, H., Maldonado, L., & Empson, S. (2013). English learners’ participation in
mathematical discussion: Shifting positionings and dynamic identities. Journal for Research in
Mathematics Education, 44(1), 199–234. doi:10.5951/jresematheduc.44.1.0199
Turner, E. E., Drake, C., Roth McDuf e, A., Aguirre, J., Bartell, T. G., & Foote, M. Q. (2012).
Promoting equit y in mathematics teacher preparation: A framework for advancing teacher
learn ing of children’s multiple mathematics k nowledge bases. Journal of Mathematics Teacher
Education, 15(1), 67 82. do i:10.1007/s108 57- 011-9196-6
Turner, E. E., Foote, M. Q., Stoehr, K. J., Roth McDufe, A., Aguir re, J. M., Bartell, T. G., & D rake,
C. (2016). Learning to leverage children’s multiple mathematical knowledge bases in i nstruction.
Journal of Urban Mathematic s Education, 9(1) , 4 8 –7 8.
U.S. Department of Health and Human Ser vices, Admin istration for Children and Families. (2010).
Head Start impact study. Final report. Washington, DC: Author.
Wagner, D., & Lunney Borden, L. (2011). Qualities of respectful positioning and their con nections
to quality mathematics. In B. Atweh, M. Graven, W. Secada, & P. Valero (Eds.), Mapping equit y
and qualit y in mathematics education ( pp. 379–391). Dordrecht, the Netherlands: Springer.
Wagner, D., & Lunney Borden, L. (2012). Aiming for equity in ethnomathematics research. In B.
Herbel-Eise nmann , J. Choppin, D. Wagner, & D. Pimm ( Eds.), Equity in di scourse for mat hematics
educat ion: Theories, practices and policies (pp. 69–87). Dordrecht, the Netherlands: Springer.
Wiseman, D., Glaneld, F., & Lunney Borden, L. (2017). How we are coming to k now: Ways in which
Indigenou s and non-Indigenous ways of knowing, being, and doing might circulate together in
mathematics and science teaching and learning. Retrieved from http://showmeyourmath.ca/
coming toknow/re port /
... In this conceptual article, we use a sociopolitical perspective informed by critical theories (i.e., Critical Theory and Critical Race Theory) to consider the bounds of the use of Cognitively Guided Instruction (CGI: Carpenter et al., 1989Carpenter et al., , 1993Fennema et al., 1996) as a widely used researchbased mathematical instructional framework. CGI is one of the most influential frameworks currently in use in mathematics teacher education and professional development (Battista et al., 2009;Celedón-Pattichis et al., 2018). However, our field is continuing to grasp how educational research that embodies a "math for all" approach to equitable instruction (Martin, 2003) should in fact heed issues of the "social" and "political" to even make a dent toward dismantling continued inequitable mathematics teaching and learning. ...
... First, CGI presented an asset-based approach that recognized children's mathematical abilities and intuitions (Franke et al., 2001). This perspective has been extended to draw attention to children's funds of knowledge more broadly, enabling teachers to connect their mathematics instruction not only to children's mathematical thinking but also to their daily lives, experiences, and cultures (Carey et al., 1995;Celedón-Pattichis & Turner, 2012a;Celedón-Pattichis et al., 2018). CGI has also been linked to student agency, supporting students to make sense of strategies that make sense to them, and calls to attend to student positioning in classroom discussions (Carey et al., 1995;Turner et al., 2013). ...
Article
Elementary mathematics teacher education often draws on research-based frameworks that center children as mathematical thinkers, grounding teaching in children’s mathematical strategies and ideas and as a means to attend to equity in mathematics teaching and learning. In this conceptual article, a group of critical mathematics teacher educators of color reflect on the boundaries of Cognitively Guided Instruction (CGI) as a research-based mathematical instructional framework advancing equity through a sociopolitical perspective of mathematics instruction connected to race, power, and identity. We specifically discuss CGI along the dominant and critical approaches to equity outlined by Gutiérrez’s (2007, 2009) framework. We present strategies used to extend our work with CGI and call for the field to continue critical conversations of examining mathematical instructional frameworks as we center equity and criticality.
... Here, we note that the dominant-versus-critical analytic and their implied orthogonality have been seen as quite functional by researchers who identify with the critical axis (e.g., Celedón-Pattichis et al., 2018;Madkins & McKinney de Royston, 2019;Myers et al., 2015;Rubel, 2017). To the extent that leaders in the field have employed and reemployed the axis metaphor, their work arguably may serve to perpetuate the conception that the two axes are distinct, and this stands in tension with the widespread belief that casting equity-focused work as a separate limb is somehow inappropriate. ...
... A joint position statement by TODOS: Mathematics for All and the National Council of Supervisors of Mathematics (2016), describes justice in mathematics learning in K-12 and the importance of acknowledging, acting, and being accountable for next steps in seeking a just mathematics education for learners. Based on this position statement, and related research (e.g., Aguirre, Turner, et al., 2013, Gutstein & Peterson, 2013Celedón-Pattichis, et al., 2018), Table 1 offers examples of components in a just mathematics classroom, along with a brief description of each. As you review the list, reflect on Kara's pre-algebra experience and the extent to which these components were a part of her mathematics learning. ...
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This chapter is an introduction to justice in the post-secondary context of mathematics courses for prospective teachers. The chapter is a research-to-practice report (i.e., it describes an aspect of instruction and discusses how it is informed by, connects to, or is illustrative of findings from research). While the reader might be any type of mathematics teacher educator, the focus here is supporting those who teach mathematics content courses for elementary school teacher candidates. In addition to having an effect on discipline-specific knowledge, college mathematics classes contribute to the ways candidates communicate in/with/through mathematics in working with children. The chapter includes discussion of the keys of mathematical literacy: mathematics for and of justice and examples of what the ideas look like in practice. The examples include information from research and a reference case presented as the accumulation of experiences for Kara Thomas and Dr. Rhodes. The case is a means for exemplifying issues such as equity, agency, and identity in the mathematics classroom.
... As a result, equitable teaching and learning of mathematics of multilingual learners should involve focusing on students' identities as essential aspects of teaching mathematics rather than on schooling and equality (Gutiérrez, 2008;Moschkovich, 2013). This perspective refers to an asset-based approach (Celedón-Pattichis et al., 2018), which values the students and their identities, languages, and cultures as intellectual resources that can be leveraged to support their learning of mathematics (Civil, 2007;González et al., 2005) and computing. ...
The purpose of this qualitative research study is to portray the complex language practices of multilingual children when learning mathematics. To do so, I draw on data collected as part of a three-year research study that was designed to understand the relationship between young children's language use and mathematics learning, focusing on students’ work as well as interactions collected through research journal entries and audio recordings. I center the practice of thick description as a path to advance disruptive understanding of multimodal representations of children's language use while learning mathematics. I then consider the necessary movement from a preconceived understanding of language to enacting an understanding of language that is responsive to the experiences and diverse language practices of children. I argue that a disruptive understanding and enactment of language can foster meaningful mathematics learning by dismantling hierarchical power structures.
Article
In this article, we report on a mixed method study conducted through a previously validated bilingual instrument. The purpose was to understand elementary bilingual and dual language (BDL) teachers’ perspectives of science and engineering (S&E) teaching in Massachusetts and Puerto Rico with the goal of developing situated professional development in science and engineering (S&E). Our findings suggest that an asset-based, and content-language integrated approach is needed to develop BDL professional development models attuned to specific locations, program models, and grade levels. Implications for our findings transferred to academic practices for BDL teachers are included.
Article
Artan göç dalgalarıyla birlikte Türkiye’deki okulların kültürel ve etnik yapısı gün geçtikçe daha çeşitli hale gelmiş ve adil matematik öğrenme fırsatlarına odaklanma gerekliliği ortaya çıkmıştır. Bu çalışmanın amacı sınıf öğretmenlerinin ve ortaokul matematik öğretmenlerinin kültürel çeşitlilik gösteren öğrencilerin matematik öğrenme fırsatlarına yönelik bakış açılarını araştırmak ve matematiği erişilebilir kılmak için belirledikleri pedagojik stratejileri ortaya çıkarmaktır. Bu doğrultuda nitel bir anket formu hazırlanarak 83 öğretmene ulaşılmıştır. Yapılan analizlerin sonucunda, çalışmaya katılan öğretmenler kültürel çeşitlilik gösteren öğrencilerin matematik derslerine katılımının daha az ve matematik öğretirken en zorlanılan konunun ise dil farklılıkları ve sınıf içi iletişim problemi olduğunu ifade ederken farklı kültürlere sahip öğrencilerinden temel matematik bilgi ve becerileri öğrenmesini beklemektedirler. Kültürel olarak çeşitli olan sınıflarda matematiğe adil erişim için kullanılan pedagojik stratejiler arasında temel olarak görsel materyal ve resimlerin kullanma, seviyelerine göre farklılaştırma ve günlük yaşantılarından örnekler verme sayılabilir. Ancak katılımcıların dörtte biri matematik öğrenmek için Türkçe dilinin öğrenilmesi gerektiğini savunmuşlardır. Bulgular ışığında, kültürel ve dilsel olarak duyarlı matematik pedagojilerinin çok kültürlü sınıflarda görev yapan öğretmenler ile mesleki gelişim projeleriyle paylaşılması ve uygulamaya koyulması önerilebilir. Ayrıca matematik öğrenme fırsatlarını derinlemesine inceleyen nitel çalışmalara ihtiyaç vardır.
Article
Background/Context We lack a nuanced understanding of the potentials and needs of multilingual families, particularly those with forced displacement histories, in contributing to children’s mathematics learning. As educators seek to increase refugee students’ access to powerful mathematics learning, an understanding of how refugee families view and participate in their children’s mathematics learning can offer insights for how we might reach the goal of equitable educational access. Purpose/Focus of Study In the GÖÇ-MAT project, we focused on developing equitable mathematics teaching practices with teachers (K–3) in schools highly populated with refugee children. The research that we present here, drawing on notions of community cultural wealth capital, offers a multifaceted view of how families of young children with refugee status articulated understandings of their roles in children’s mathematics learning. Setting Our fieldwork took place in four different cities highly populated by people with refugee status in Turkey, the country located at the center of the worldwide trend of mass migration. Participants We examined data from families (N = 54, mainly from Syria) who participated in the family engagement component of the larger project, carried out through multilingual family mathematics workshops. Research Design We employed qualitative research methods and conducted two-year-long observations and video recordings in the context of multilingual family mathematics workshops. In the workshops, families, teachers, and researchers engaged in patterns and early algebra activities, as well as in family conversations facilitated through open-ended prompts, mathematics picture books, and educational journey maps. Over two years, we collected data comprising recorded dialogues with families, artifacts produced in the workshops, and video data of families’ mathematical interactions. Findings Our analysis yielded two key understandings: (1) Family engagement practices around mathematics set a context to realize the nuanced nature of refugee families’ cultural wealth and efforts for their children’s education; and (2) refugee families’ knowledge of mathematics itself as a discipline and their mathematical capital, which are typically not recognized in school contexts, can serve as resources for mathematics teaching. Conclusions/Recommendations The findings provide insight for teachers, researchers, and policy makers about how we might engage multilingual children and families with refugee status in powerful ways in mathematics education.
Chapter
Collaboration is essential to modern biological research, and the ability for scientists to be an effective member of a diverse team is critical for professional and personal growth. Modeling collaborative research in an undergraduate course provides an opportunity for students to learn how to navigate inclusive collaborations successfully. Undergraduate biology students have likely never engaged in collaborative research prior to starting their coursework, and it may be the first time students are working with individuals from different racial, ethnic, socioeconomic, and religious backgrounds. For students to become successful research collaborators, educators must provide a framework for students to recognize their own assets and appreciate the contributions of all stakeholders. Here we provide a narrative demonstrating challenges to student research collaboration, an analysis of these challenges, and specific recommendations for teaching effective collaboration.
Article
My goal with this conceptual paper is to describe how Black Language can be valued, utilized, and incorporated into mathematics pedagogy. This framing requires a critical orientation towards language because Black Language is often a site of marginalization. I begin this conversation by defining Black Language and identifying its roots. I then highlight the connection between language and identity and suggest that since mathematics education scholars have noted the important role of identity in mathematics learning, then Black Language is an important part of the discussion for many Black children. Black linguistic practices are conceptualized here as a part of a Black ontology and situated in a more general notion of Blackness. Finally, I provide details about how these linguistic practices manifest in the mathematics classroom in the form of mathematics discourse and provide some strategies for moving the field forward towards emancipation for Black mathematics learners.
Chapter
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Imagine if teachers were trained with as much skill and practice in dealing with the politics of teaching as they were with lesson planning, assessment, strategic instructional decisions, classroom management, connecting topics within mathematics, and relating to students. Instead of just carrying out local practices that are valued or have been in place for years, they might question whether those practices are in the best interest of students. They might be more inclined to engage in dialogue and influence others to consider new perspectives. Rather than stand by while new policies are being created that go against their sense of justice, they might advocate for their students or themselves and, perhaps, more talented teachers might stay in the profession longer. In this chapter, I argue a) mathematics teaching is political, b) mathematics teachers need political knowledge, c) teacher education programs can develop political knowledge with teachers through particular activities, and d) when mathematics teachers have opportunities to understand and deal with the politics of teaching, they are able to use that knowledge in their practice.
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In this article, the author synthesizes four equity-directed instructional practices: standards-based mathematics instruction, complex instruction, culturally relevant pedagogy (CRP), and teaching mathematics for social justice (TMfSJ). The author organizes these practices according to the dominant and critical axes in Gutiérrez’s (2007a) equity framework. Among 12 teachers from 11 schools in a large urban school district, the author presents case studies of 3 teachers who excelled with the aforementioned dominant equity-directed practices but struggled with the critical practices of connecting to students’ experiences called for in CRP and critical mathematics called for in TMfSJ. The analysis explicitly explores the role of whiteness in these struggles. The author presents implications and recommendations for mathematics teacher education on how to better support teachers for equitable teaching that includes these critical equity-directed practices.
Book
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Anthony Fernandes, Sandra Crespo, and Marta Civil, volume editors; Marta Civil, series editor, Access and Equity: Promoting High-Quality Mathematics Series NCTM's Access and Equity Principle states that “all students [should] have access to a high-quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential.” This book offers math educators strategies and resources for putting that principle into practice. Practice-based vignettes open each chapter, inviting readers to relate to and engage with the issues of access and equity discussed in these middle school mathematics classrooms. Questions at the end of chapters encourage readers to reflect on what they have read and then take action in adapting the suggested approaches to their own contexts. The book focuses on diversity as a resource and addresses three critical and intertwined factors: Teaching practices that build on students' strengths of students Rigorous content that draws on students' experiences Fostering relationships with diverse students Chapters (many written in collaboration between researchers and practitioners) show students engaging in powerful mathematical discussions; teachers adapting instruction to meet the needs of all students while maintaining high expectations; curriculum that draws on the resources that students bring to the classroom; teachers examining their own beliefs and expectations about teaching and learning; tools that encourage teachers to analyze and review their lessons with an equity lens; and more. Turn to this book for ideas, inspiration, and information about promoting empowerment, meaningful participation, and success for each and every student in the mathematics classroom.
Book
This book is part of a book series that was proposed by the Educational Materials Committee at the National Council of Teachers of Mathematics (NCTM) to address the Access and Equity Principle for school mathematics as described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014). The series aims to support teachers in using rigorous mathematical tasks, learning how to adapt mathematics curriculum materials so that they meet the Access and Equity Principle, exploring productive and unproductive beliefs in relation to access and equity, among others.
Article
A common explanation of why urban students fail to succeed in the classroom is that they are coming from a “culture of poverty.” This article argues that urban students, particularly those who are African American, face a series of structural and institutional barriers that impede their pathways to success. Lack of access to quality healthcare, affordable housing, and quality schools means that the nation’s most disadvantaged children remain disadvantaged. Yet classrooms with highly qualified teachers who believe in the efficacy of their practice and the ability of all students to learn can make a difference in these children’s lives.
Article
Mathematics teacher educators (MTEs) designed and studied a video analysis activity intended to support prospective teachers (PSTs) in learning to notice equitable instructional practices. PSTs from 4 sites (N = 73) engaged in the activity 4 to 5 times during the semester, using a set of 4 “lenses” to analyze teaching and learning as shown in videos. In an earlier analysis of this activity, the authors found that PSTs increased their depth and expanded their foci in noticing equitable instructional practices (Roth McDuffie et al., 2013). In this analysis, the authors shift the focus to their work as MTEs: They examine their decisions and moves in facilitating the video analysis activity with a focus on equity and discuss implications for other MTEs.
Article
The current study builds on previous communalism research by exploring the enduring facilitative effects of communal learning contexts on academic achievement for African American children over extended time and while calling on critical thinking skills. In addition, this study sought to explore the communalism construct in a more applied academic environment that approximated real classroom conditions. This study examined performance differences in fraction problem solving among 96 low-income African American students in Grades 3 to 6 participating in either a communal or individual learning context. Pretest to posttest gains showed that students randomly selected for the communal learning context significantly outperformed students who learned in the individualistic context. Additionally, communal learning students outperformed their individual counterparts during each weekly domain assessments. Several promising results obtained draws the communalism construct to a more applied culturally relevant pedagogical tool.
Article
Make these small adjustments to your syllabus and watch spaces open to connect to children's multiple mathematical knowledge bases.