Content uploaded by Douglas H. Clements

Author content

All content in this area was uploaded by Douglas H. Clements on Aug 09, 2018

Content may be subject to copyright.

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

375

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 specic 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;

377

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).

379

NCTM Research Committee

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

381

NCTM Research Committee

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

383

NCTM Research Committee

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 McDufe, 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 McDufe, 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), 385–401. 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’

reections 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

Glaneld, 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 specic 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 “verbication” 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. Glaneld (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), 481–496 .

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/keyndings/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 McDufe, 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 McDufe, 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 McDufe, 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., Glaneld, 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 /