By:
**Mark Ellis, Ph.D.**, * Professor of Secondary Education*, California State University, Fullerton

**Cathery Yeh, Ph.D.**, * Assistant Professor of Education*, Chapman University

*Authors Yeh and Ellis invite you to listen to Emilia Frias, pictured above, who teaches 5th and 6th graders classified with moderate and severe disabilities.*

**The Need to Disrupt Normalcy in Mathematics Education**

There is wide agreement that when mathematics curriculum and pedagogy value and build on students’ cultural identities and ways of knowing this not only strengthens mathematics understanding but also cultivates a sense of curiosity, wonder, and joy toward mathematics (see, for example, our book about *Reimagining the Mathematics Classroom*). And there has been for the past decade or more increasing attention given to the importance of understanding the root causes of inequities in mathematics education and how these can be redressed by attending to issues of access, identity, agency, and power. However, in the majority of these discussions, students with dis/abilities are left out. Dominant ideologies pervade school contexts and shape the ways in which normalcy, difference, and identities are constructed within systems of education. We intentionally use the term dis/ability to highlight our stance that “disability” is both a component of one’s identity and a social, political, and cultural phenomenon, often intersecting with other social positions such as race, gender, and economic class. Our work is an effort to disrupt what is taken as normal and normative in mathematics education including the pervasive use of labels and placements that indelibly and inequitably rank, sort, and deny students, especially those with dis/abilities, access to conceptually rich mathematics learning. How might approaches to mathematics education research and the teaching of mathematics change if decentered from the normative non-dis/abled gaze? In what follows we share some insights and pose many questions to which we acknowledge not having all the answers. Our intent is to stimulate others to contribute to this important body of work and increase the field’s understanding of what’s possible when we move beyond the constraints of socially constructed ideas of what is normal.

We build on the work of a growing number of equity-focused mathematics educators to identify and challenge borders of exclusion – physical and ideological – that continue to privilege some students at the expense of others (Louie 2017; Yeh & Rubel, 2020). You might think about your own experiences with school mathematics: which students were given access to meaningful, rigorous mathematical learning aimed at sense-making and problem solving and which students were not? It is rare that the responses we get to this question place students with dis/abilities in the first category. Engagement for the student with a dis/ability all too commonly consists of sitting alone working on rote computation while non-dis/abled peers have access to more cognitively demanding and communicatively engaging work. Furthermore, research about mathematics education for students with dis/abilities has traditionally focused on remediation and intervention to get the learner to conform to normalized expectations through rote learning; rarely do we find studies designed from the perspective of the student and what we can learn about their ways of perceiving, knowing, and communicating mathematical concepts and relationships (Tan & Kastberg, 2017; Yeh, Ellis, & Mahmood, 2020).

**An Alternative Framework**

We recognize that ableism is based on deeply entrenched and dominant ideologies and located within social and institutional structures as well as personal attitudes. Ableism is a normalizing process that, like racism (and often together with racism), works in ways that are unspoken and taken for granted. An ableist perspective is pervasive in education and reflected in societal perceptions: it is preferable for a child to read print rather than Braille, walk rather than use a wheelchair, read written text rather than listen to an audiobook, and be in classrooms with non-dis/abled students rather than with other students with dis/abilities. These preferences reflect dominant ideologies of ableism that position students with social identities different from the referent norm into the social and physical margins of education. Because ableism is so enmeshed in the fabric of our social order, appearing both normal and natural, confronting ableism requires unmasking and exposing normalizing processes as they operate in mathematics education. The framework that follows represents our attempt to challenge, disrupt, and reorient dominant ideologies around dis/ability and mathematics education that reify normalcy and perpetuate ableism. A more detailed description of the framework elements and its application to research can be found in Yeh, Ellis, & Mahmood (2020).

**Historical-Political Awareness**

There is a legacy in education of the intentional segregation of students by so-called “ability” as early as the elementary grades together with pedagogies that over-emphasize mimicry and repetition (Ellis, 2008; Ellis & Berry, 2005). The roots of this system of mathematics education are found in the racist, classist, and ableist beliefs about human potential that coalesced into the eugenics movement (Ellis, 2008; Valencia, 1997). From our 21st century vantage point, it is easy to identify how what passed as eugenics research was biased and even falsified. But in the early 1900s, these false claims seemed to (and were manipulated to) confirm the prejudices of those in positions of power and privilege and were taken as truths upon which to base policies and establish practices in many areas of everyday life including in education (Duster, 2003). Indeed, the practice of tracking and use of labels such as “gifted” and “special” emerged during this period as solutions to what was perceived to be a problem in education – how to structure schooling for the increasingly diverse children who populated the classrooms of early 20th century America (Baker, 2002; Ellis, 2005). It is essential that we acknowledge this legacy of racism, classism, and ableism in structures of education and recognize that the limiting labels and constrained expectations for students with dis/abilities in mathematics are social constructions. It is not accidental but intentional that one finds, even in the year 2020, an over-representation of Black, Latinx, and Native American students in special education and lower track mathematics pathways while the same groups are underrepresented in gifted and honors pathways. Think about this as an issue of access; which students are given access to learn rigorous content, access to engage in meaningful learning activities, and even access to be seen and valued in common educational spaces?

**Some questions to ask as you reflect on this element include:**

**• Whose identities are centered in current policies and practices of mathematics education?**

**• What approaches help you and others to interrogate and challenge deficit views about mathematics learning and student identities, including race, class, gender, language, and ability status?**

**• How can research and classroom practice take into account the historical and political context of presumed intelligence and mathematics ability and recognize that assessments and their results are also social constructions that may not be objective or equitable?**

**Mathematics as Cultural and Relational**

Mathematics education traditionally presents knowledge as a discrete external commodity and learning as the acquisition of specific knowledge and concepts along a fixed developmental progression guided by teacher facilitation. This linear transfer metaphor is widespread within Western education and gives the impression that mathematics concepts are discrete and the development of mathematical understanding is ordered and hierarchical (i.e., the notion that certain mathematics concepts must be taught and mastered before student engagement in cognitively rigorous tasks or broader mathematical relationships). Yet mathematical ideas are deeply cultural and collective, having emerged from centuries of human creative thought, activity, and interaction in every part of the world, a process that continues to this day (Bishop, 1988; Lakoff & Núñez, 2000; Saiber & Turner, 2009). When mathematics is divorced from its cultural and collective moorings and presented as standardized and normalized to allow for labeling, tracking, and segregation, both students and subject matter are dehumanized. Such simplistic constructions of mathematics and narrow perceptions of ability must be rejected in order to better capture and leverage students’ ways of thinking and reasoning with and about quantities and quantitative contexts as well as their ways of interacting and communicating as a foundation upon which to refine and extend their mathematical understandings.

**Some questions to ask as you reflect on this element include:**

**• How does my teaching allow students to recognize mathematics as coherent and connected?**

**• How do I give students access to varied pathways to examine and make sense of mathematical concepts and relationships?**

**• How can the questions posed by researchers better examine and help to illuminate the interconnected nature of mathematical ideas and the nonlinear pathways students might take to mathematical understanding?**

**Dis/ability as Cultural Identity**

Gloria Ladson-Billings (1995) published “Toward a Theory of Culturally Relevant Pedagogy” twenty-five years ago and inspired the education community to consider what it means to make teaching and learning relevant and responsive to students’ identities – their languages, literacies, and cultural practices across categories of difference. While culturally relevant pedagogy is now considered “good teaching practice,” it is still far from common practice in the mathematics education of students with dis/abilities. We argue for the recognition of dis/ability as a cultural identity shaped by individual differences and the ways those differences are (de)valued in social contexts. Siebers (2013) uses the term “complex embodiment” to describe how identity is situated, a combination of one’s individual corporeal reality together with how one is positioned within society. For example, Siebers asks us to consider the person in a wheelchair who is forced to enter from the back of a building next to the garbage dumpsters since that is where the only ramp exists: What is their experience having to pass through this space? And how does this socially constructed context serve to disable and devalue the individual relative to those who are non-dis/abled and enter from the front? Shifting to the context of mathematics education, for some students their only entrance to mathematics is through deficit frames that fail to value their abilities and ways of knowing; this figurative back door experience is disabling. The concept of embodied cognition highlights the importance of our having knowledge about dis/ability from the dis/abled perspective. School mathematics, as traditionally represented, explained, and assessed, privileges verbal and written communication; this limits the capacity to fully experience the beauty of mathematics and ignores the mathematics capabilities of students with different bodyminds (a term that recognizes the body and mind as constituent parts of one integrated whole; Price, 2009).

**Some questions to ask as you reflect on this element include:**

**• How is your mathematics instruction inquiry-based, culturally responsive, and inclusive of the identities, abilities, and experiences of the students you serve?**

**• How do students see themselves – their diverse ways of being, knowing, interacting – reflected in the mathematics curriculum and the assessments of what they know and can do?**

**• In studying mathematics education for students with dis/abilities, how do your queries and methods reflect a curiosity about and respect for the varied ways they might engage with mathematical ideas and express their mathematical thinking?**

**Putting the Framework into Action**

Challenging ableism in mathematics education requires unpacking dominant ideologies and our own identities that mediate our role as educators and researchers. We’ve found this work difficult because it requires confronting deeply entrenched cultural perspectives and taken-for-granted practices and embracing new ways of perceiving the world of mathematics and our students’ interactions with mathematics.

**Implications**

The insights we are sharing resulted from a three-year collaboration with special education teachers and learners with dis/abilities, grounded in mutual respect and a commitment to challenge ourselves to attend to personal biases as well as to learn to recognize the social, historical and institutional contexts that affect mathematics teaching and learning for students with dis/abilities.

**Researchers**–

o Largely absent from and sorely needed in mathematics education is research that explores how the sociocultural context of learning disables students, that attends to multiple marginalizing processes for students at intersections of multiple social identities (such as race, gender, and economic class), and that identifies and learns from the cultural strengths of students with dis/abilities (Tan & Kastberg, 2017; Yeh, et al. 2020).

o Thinking about research involving students with dis/abilities, there must be a shift away from (and repudiation of) perspectives and methodologies that equate dis/ability with deficit and that rely on narrowly constructed normative measures of achievement and engagement in mathematics.

o Recognizing and valuing dis/ability as a cultural identity requires researchers to center the learning of mathematics as a generative process of becoming involving students’ diverse bodyminds.**Teachers and Teacher Educators**–

o The borders of exclusion – both physical and ideological – that persist based upon students’ social locations reveal the built-in biases of our system of mathematics education. It is important to deepen one’s understanding of this history and to actively disrupt the practices that emerged from it.

o Thinking about mathematics education for students with dis/abilities, we must shift away from deficit-driven, dehumanizing practices that focus on individual remediation through rote acquisition of knowledge and instead design learning activities that allow students to experience mathematics as cultural, relational, and connected.

o Honoring dis/ability as a cultural identity means that educators must recognize and embrace students’ capabilities and modes of cognition and expression.

**Educator Example**

One of the educators we’ve worked with and learned from, Emilia Frias, teaches fifth and sixth grade students classified with moderate and severe dis/abilities. She works hard to engage her students in mathematical activities in ways that reflect the elements of the framework. Ms. Frias recognizes her students as mathematics doers and thinkers and with a particular embodiment of the world that may be both similar to and different from her own. She foregrounds students’ voices and ideas, always attending to and leveraging multiple and diverse ways of being, knowing, and doing mathematics, and in return expands the meaning of mathematics as an embodied and collective experience. By refusing to set normative constraints on her students, Emilia’s students flourish. Such a research collaboration that blurs distinctions between researcher and practitioner, between mathematics education and special education, and between expert and learner has allowed us to identify and work towards challenging traditional borders of exclusion – both physical and ideological – in mathematics education and to recognize mathematics classrooms as spaces for inspiration and optimum learning for researchers and practitioners.

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