Abstract
Keywords
Thirty years following the “Math Wars,” one might question whether our country is anywhere closer to resolving the deep, underlying disagreements that divide researchers in education. Vestiges of the old debates about “reform-oriented” and “traditional” mathematics still show up in disagreements between mathematics educators in special education and general education (Schwartz, 2023). Just recently, we have seen the National Council on Teachers of Mathematics (NCTM) release position statements making claims about the appropriate order of mathematics teaching, noting that “conceptual understanding must precede and coincide with instruction on procedure” (NCTM, 2023, Declaration 1). At the same time, a group of special educators have advocated for a new
In this paper, we suggest that these longstanding disagreements are the pernicious effects of what sociologists have referred to as “epistemic bunkers” (Furman, 2023) or “epistemic echo chambers” that divide the general and special education researchers who focus on mathematics teaching and learning (C. T. Nguyen, 2020). Put simply, the fields of mathematics education and special education have, over time, come to filter out sources of evidence or new knowledge from the other community. Efforts to promote agreement around key features of “high-quality” mathematics instruction, such as the National Mathematics Advisory Panel (2008) report, resulted in widespread dissensus and critique from mathematics educators (e.g., Boaler, 2008; Lobato, 2008). These critiques focused on many of the same issues that persist today, including methodological and epistemological questions around how we “know” teaching is effective. Fostering discussion about such questions is challenging because special educators and mathematics educators continue to attend different conferences, publish in distinct journals, and rarely have opportunities to engage in dialogue (Hunt & Tzur, 2017; Sheppard & Wieman, 2020; Van Garderen et al., 2020). The consequences of each group’s failure to learn from the other have landed squarely at the feet of students, both those with identified mathematics disabilities, and those who may benefit from a wider repertoire of instructional strategies than those articulated by either community.
We focus in this paper on how scholars of mathematics education—both from general and special education—discuss “good mathematics teaching” alongside the roles of teachers and students in mathematics classrooms. We draw on interview data from 22 scholars who are prominent in each community and who were purposively sampled to provide some insight into how these discourse communities think about teaching and learning. Our hope was to better understand some potential sources of the divisions between these communities, as well as some points of convergence and avenues for bridge building that may have been obscured in recent debates. Our central aim is to see what middle ground we can identify between the two communities. We see this as a starting place, a conceptual argument supported with empirical data, about the ways the different research communities think and talk about mathematics instruction.
Finding a middle ground is imperative, as data from National Assessment for Educational Progress (NAEP) suggest that 64% of fourth grade students do not meet mathematics proficiency levels, and nearly 25% do not meet NAEP’s basic achievement level (National Center for Education Statistics, 2023). This suggests an urgent need to consider instructional solutions for supporting
It seems uncontroversial to suggest that general educators be prepared to support students with disabilities (SWDs). However, at least in the case of mathematics teaching, evidence suggests we are far from this goal. Preservice general educators rarely receive adequate training in their preparation programs (Blanton et al., 2017), and surveys of practicing general educators consistently point to their feeling underprepared to support this population of students (Sparks, 2023). Given that the vast majority of SWDs spend much of their school day in general education, and given longstanding concerns about academic outcomes among SWDs, it is worth asking why we have not done a better job preparing general educators to support SWDs. We suggest that a key barrier to better preparing general educators is the longstanding gap between special and general education researchers, which is especially pronounced in mathematics education. 1
These cross-field divisions are not simply academic handwringing. Well-established teaching strategies known to support SWDs are untouched in general teacher education coursework (Jones et al., 2023). At the same time, prospective special educators lack exposure to many key instructional principles and practices from mathematics education (Boyd & Bargerhuff, 2009; Scherer & Bertram, 2024; Tan et al., 2022). Differences across the two fields leave educators facing pressing, but daunting, questions: What role should systematic, explicit instruction play in general education? What role should ambitious mathematics instruction that positions students as sense makers play in supporting SWDs? These are hard questions with no ready answers, but we argue that both fields need to take seriously helping teachers wrestle with them.
The goal of this article is to understand some sources of these divisions. We report results from interviews with 22 mathematics education researchers from general and special education, focusing on their views about the goals of mathematics education, teacher and student roles in achieving those goals, and challenges involved in addressing the needs of SWDs in general education. We wanted to better understand the perspectives of the two fields, identify points of convergence, and surface challenges that exist in designing instruction that is responsive to SWDs.
Background and Motivation
Supporting Students With Mathematics-Related Disabilities
How should we think about the population of students who struggle with mathematics? Existing research indicates that there is a wide variation in the kinds of mathematics difficulties experienced by students with mathematics-related disabilities. Some struggle with computational difficulties, such as fact retrieval and fluency, while others struggle with making sense of word problems (Cirino et al., 2015; Lin et al., 2021; Peng et al., 2018). Students can also often exhibit challenges related to attention and working memory (Barnes et al., 2020). To address these challenges, scholars have recommended instructional strategies that help to reduce “cognitive load” (L. Fuchs et al., 2020; Richland et al., 2017; Sweller, 2011; van Lieshout & Zenidou-Dervou, 2020). These include providing modeling metacognitive strategies for making sense of mathematical concepts and supporting fluency with frequent practice and teacher feedback (L. S. Fuchs et al., 2021; Woodward et al., 2012). This focus on teacher-directed scaffolding contrasts general educators’ oft-recommended inquiry-based approaches, which start with an introduction of a task, followed by students working collaboratively, before concluding with a whole class discussion to support students in making mathematical connections (Jackson et al., 2013; Van de Walle et al. 2018).
At the same time, SWDs represent only one subgroup of the student population who have challenges related to mathematics achievement. Indeed, recent NAEP results suggest a far broader pool of students may experience difficulties in mathematics than the ~8% formally identified as having a mathematics-related learning disability (National Center for Education Statistics, 2023). Thus, while we focus here on SWDs, our findings likely have implications for a broader student population. The complexity of the assets and challenges students bring to learning mathematics demands a concerted effort to marshal all available evidence from both special education and general education to better support all students.
Lack of Preparation to Support SWDs
Few general educators receive more than a single course on how to support SWDs, and rarely do these courses focus on instructional methods, instead characterizing a wide range of disabilities with little specific attention to how to differentiate or scaffold accordingly (Florian, 2012). Largely untouched are well-established instructional methods from special education research (L. S. Fuchs et al., 2021). There are also few opportunities for prospective general educators to work directly with SWDs during pre-service preparation (Brownell et al., 2020; NCLD, 2019; Pugach et al., 2020).
We recently conducted a study that examined over 200 mathematics methods syllabi, and found that these courses rarely dedicated readings, assignments, or learning objectives to SWDs (Jones et al., 2023). When references did occur, SWDs were often grouped with other students, such as English learners, needing “differentiation,” broadly construed (Jones et al., 2023). These calls for more preparation focused on supporting SWDs are not new. For decades, researchers have highlighted the limited opportunities mathematics teachers have to learn about specific instructional strategies and accommodations known to support SWDs in preservice programs (Kozleski et al., 2000; Maccini & Gagnon, 2006).
Epistemic Echo Chambers and Bunkers
These limited learning opportunities in teacher preparation likely stem, in part, from the fact that the academic communities of general and special education have distinct perspectives of both teaching and learning. That is, the field of general education has a well-defined view of what “good mathematics teaching” looks like and is working towards, which is distinct from definitions of “good mathematics teaching” in special education (Hunt & Tzur, 2017; Sheppard & Wieman, 2020). Moreover, the two communities rarely have opportunities to discuss the affordances and constraints of different approaches. This divide is not always intentional, and researchers
In theorizing this issue, we draw on recent work in sociology underscoring the ways in which “epistemic bunkers” (Furman, 2023) and “epistemic echo chambers” (C. T. Nguyen, 2020) can impede productive disagreement and the development of new ideas. By filtering out sources of evidence or new knowledge that do not correspond with existing beliefs or views, these bunkers or echo chambers serve to reinforce—perhaps reify—the status quo in discourse communities—in our case, the fields of special and general mathematics education. Inside an epistemic bunker, members of the community have priority status. Their “testimony,” or research evidence, has more credence than “outside” views. Messages that diverge from established views about teaching and learning are kept at bay by preferential engagement in knowledge building with others from the same community. Indeed, it is extremely rare to find general and special educators collaborating on research around mathematics teaching and learning (Sheppard & Wieman, 2020).
These bunkers are then bolstered by the distinct empirical traditions of general and special mathematics education. Special education often relies on quantitative evidence from experimental tests of academic interventions (Cook et al., 2014; Gersten et al., 2005; Tan et al., 2022; Toste et al., 2023). General mathematics education research often features qualitative, descriptive methods (Kilpatrick et al., 2001; Munter et al., 2015). These methodological and substantive distinctions can provide a ready reason why the “evidence” of the other community should be discounted. As a result, members of each community have limited opportunities—perhaps by design—to hear the perspectives of the other. Put plainly, a general educator already committed to inquiry-oriented mathematics instruction that is responsive to students’ thinking might not choose to read a journal or attend a conference highlighting the benefits of systematic, explicit instruction, assuming this form of instruction is antithetical to what they believe (and that their community’s evidence suggests) is best for students. The opposite is just as likely true for a special educator regarding evidence from general education. “Bunkering down” in this way can provide a sense of epistemic safety (Furman, 2023) and comfort (Bardon, 2019).
There are obvious downsides to this bunkerization. Our knowledge of “effective teaching” will inevitably be limited when it is not refined by divergent—sometimes contradictory—viewpoints. Moreover, by limiting challenging dialogue across epistemic divides, bunkers also fortify divisions between communities, creating increasingly polarized differences in viewpoints. Inside an epistemic bunker, it is all too easy to “other” those outside, creating “straw men,” or overly generalized and caricatured versions of the other community’s approaches to conducting research and knowledge building.
We recognize that researchers’ empirical traditions and epistemological viewpoints are deeply held and reflect values about teaching and learning (Nasir & de Royston, 2013; Larnell et al., 2016). However, 25 years ago, Sfard (1998) cautioned researchers about the “dangers of choosing one metaphor for learning” during a time when scholars were debating the relative merits of the “content acquisition” and “participation” metaphors (p. 4). She argued that each metaphor has relative advantages which the other cannot afford, and only when we wrestle with both “incessantly screen[ing] for possible weakness,” can we develop new, more expansive theories that support the interests of all teachers and learners. Our goal in engaging researchers with diverse theories of teaching and learning is to open intellectual spaces and corresponding tools that promote such expansion. Each of these communities of practice have distinct expertise that can inform our preparation of novice teachers and the supports we afford to practicing teachers. We are unlikely to prepare teachers who understand the nuances of different instructional approaches for different students if we—as teacher educators and researchers of teaching—do not also see value in myriad instructional methods and recognize the validity of research findings outside of our specific discourse communities.
The existing cross-field divide has created an enormous social justice issue for SWDs, who are among the most marginalized children in K-12 school settings (Pugach et al., 2020; Woulfin & Jones, 2024). To improve their academic success, it will be necessary to confront these differences head on, identify points of convergence, and cultivate new models of supporting teachers that incorporate the perspectives of both general and special education. We see these analyses as a starting place for such efforts.
Research Approach
Sample
Our overall research project aimed to develop instructional materials for mathematics teacher educators that highlight evidence-based practices known to support students with mathematics difficulties and disabilities (L. S. Fuchs et al., 2021). Before building those materials, we wanted to better understand why so little of this content had been previously integrated into general education mathematics methods courses (Jones et al., 2023). Thus, our team aimed to talk to researchers in both general and special mathematics education who we hoped would provide a broad lens on these issues.
Our sampling approach followed a snowball method (Naderifar et al., 2017). We began by consulting our grant’s advisory board—national leaders in special education and mathematics education—for nominations. Our research team also compiled an initial list of prominent researchers in both fields and asked those researchers to suggest additional interviewees, ensuring a diverse range of perspectives.
Across these efforts, we sought mathematics educators who had focused on students with disabilities in their research, as well as special educators whose scholarship had an explicit emphasis on mathematics. Given our focus on building materials for preservice teacher preparation, we included mathematics and special educators whose scholarship centers on teacher education. Because of the methodological and epistemological tensions noted above, we also intentionally interviewed scholars who utilize a range of methodological approaches with varied epistemological stances. Several participants described themselves as “critical scholars” and several others as “experimentalists.” Casting a wide net in sampling was crucial in being able to draw inferences about the variation within and across these discourse communities.
We began this process by emailing participants. In this communication, we acknowledged their expertise in mathematics education, explained that our larger research project involved developing a suite of curricular materials for mathematics methods courses that will give pre-service teachers opportunities to learn and enact instructional practices known to support students with disabilities, and described the purpose of the interviews. The purpose of these interviews was to better inform our work by helping us understand the pedagogical and epistemological beliefs of mathematics educators working in special and/or general education. We also hoped to use these interviews to surface tensions and points of intersection between special and general mathematics education fields. In turn, this information helped us set the foundation for generating detailed specifications of teaching practices for our project that were responsive to the empirical evidence and epistemological stances in special and general mathematics education.
Everyone we invited accepted, which included 11 university-based researchers 2 whose primary academic appointment was in special education and research focused squarely on students with mathematics difficulties or disabilities, and 11 university-based researchers whose primary appointment was in general education and research focused on mathematics teaching and learning without a focus on disability or difficulty. These classifications into admittedly broad and variegated discourse communities were confirmed with participants through member checking. Five identified as men, the remaining 17 as women. Nine identified as scholars of color, from a range of ethnic and racial backgrounds. We included researchers at a range of career stages, from assistant professors to professors emerita.
When we asked participants to characterize their professional identities, however, few identified only as a “general education mathematics educator” or a “special education mathematics researcher.” Many noted attendant identities ranging from “an individual with a disability who is deeply concerned with the intersection of disability and mathematics education” to “educational psychologist” to “applied assessment expert” to “someone who investigates instructional practices that encourage the thriving of marginalized and minoritized students.” We do not provide additional details about these individuals, or reference their individual identities in the quotes below, because of our commitment to preserving their anonymity.
Importantly, we acknowledge that this is a particular subset of 22 scholars, and that there are hundreds of researchers working in this space. A different sample may well have surfaced additional or distinct conceptions of mathematics teaching and learning. That said, we feel confident that the patterns we note here, particularly the between group differences, would hold with different samples of participants. These findings correspond with the existing literature on the epistemological and methodological differences between the mathematics education and special education research communities, as well as the distinct knowledge bases of those in the two communities (Maccini & Gagnon, 2006; Munter et al., 2015; Tan et al., 2022). Moreover, we shared the themes detailed here with the expert advisory board of the grant supporting our work, and they confirmed that our findings reflected their experiences working for many years in mathematics education and special education. Several of our board members served on the National Mathematics Advisory Panel, whose 2008 report sparked so much debate in the field. They noted how many of the issues we surface here were tacit in the discussions around that report nearly 2 decades ago. We view this as valuable corroboration of what we present below. At a high level, we see these interviews as a starting place for unearthing some key differences and points of convergence between fields, in the service of building models of teacher education and professional development that are responsive to both.
Interviews
In designing our interview protocol, we drew on Munter’s (2014) notion of instructional vision, which draws on Goodwin’s (1994) idea of professional vision, to surface general and special educators’ goals for mathematics education and conceptualizations of teacher and student roles in instructional activities. Drawing on Munter’s (2014) instructional vision framework also allowed us to understand mathematics educators’ conceptualization of the “ideal” classroom practice around which they might orient preservice or inservice learning opportunities for teachers (see also Hammerness, 2001).
Four members of our research team, including all three authors of this paper, conducted all interviews. The semi-structured interview protocol was piloted and refined over multiple iterations to ensure consistent implementation across interviewers. Because we were interested in understanding the participants' views of the goals for mathematics teaching and learning in K-12 education, we began by asking participants to describe, from their perspective, what the goals of mathematics instruction are. First, we probed participants for their perspectives on the knowledge and practices that should be foregrounded during mathematics instruction, as well as what counted as “success” for students’ development in mathematics classrooms. Next, we asked them whether the goals they described were consistent for all students, or whether they would look different for different populations. We then asked each participant to describe the role of the teacher in the learning process, followed by questions related to whether the role of the teacher shifts when supporting students with difficulties in mathematics. Also, we asked whether and to what extent there was a role for “explicit instruction” in teaching, and we asked participants to describe what this type of instruction might look like. Then, we asked them to describe the role of the student in the mathematics learning process and whether the role looks the same or different for students with disabilities. We then asked them to comment on some key ideas in mathematics teaching, including the role of conceptual and procedural understanding of mathematical ideas, the role of productive struggle, the role of discourse in the mathematics classroom, and the role of independent and guided practice. Finally, we asked participants to describe what instruction would look like in a general education classroom that effectively includes students with disabilities in mathematics. Interviews lasted for about 1 hour and were conducted and recorded over Zoom. Fifteen of the 22 interviews were conducted by pairs of interviewers.
All interviews were transcribed and structurally coded by research question: one focusing on goals, one on teachers, and one on students (Saldaña, 2014). Each author read all the excerpts for each of the structural codes, and we iteratively developed memos synthesizing themes within and across special and general education. At all stages, we placed a priority on searching for confirming and disconfirming evidence, noting differences within and between groups (Dyson & Genishi, 2005).
Positionality Statement
All authors identify as White researchers. Two identify as female and one as male. We all conduct research on teacher learning, were former K–12 teachers, and have worked as university-based teacher educators. In some ways, we represent three different communities: a general teacher educator who works across content areas; a special educator who also works across content areas; and a general mathematics teacher educator. We have intentionally been engaged in collective work to bring our communities into closer contact in the service of better preparing general educators to work with SWDs. The goal of more productive dialogue between our fields informed our desire to better understand what might divide them, and also to identify points of intersection.
Goals of Mathematics Instruction
Our interview data suggest that neither special educators nor general educators are monolithic groups. There was considerable heterogeneity within each group about the goals and respective roles of teachers and students in mathematics instruction. That said, there were also clear themes within each group and notable distinctions between groups. To indicate the prevalence of certain ideas identified by individuals within a group, we used categories: nearly all, most (a majority), many (around half), or some (less than half). In accordance with reflexive thematic analysis (Braun & Clark, 2022), we intentionally did not use numerical values as our goal was not to make definitive empirical claims about the magnitude in which general or special educators espouse certain views, or make a claim that we exhaustively coded every instance of each emerged theme in the data corpus. Instead, our goal in this analysis was to detect patterns within and across groups and to discern whether and to what extent there was a consensus within each group and common ground across groups. Thus, in reporting our findings, we aimed to give readers a sense of when there was and was not agreement within and across the groups.
Convergence in Goals
Special and general educators alike described the centrality and primacy of conceptual understanding as students’ learned mathematics. Prior “straw man” arguments of the respective communities—that special educators are entirely procedurally oriented (Woodward, 2004; Woodward & Montague, 2002) and general educators are solely devoted to concepts at the expense of fluency (Codding et al., 2023)—did not hold up. Educators in both communities emphasized “deeper” knowledge of mathematical concepts which should develop alongside knowledge of procedures and computational fluency. Some special educators explicitly noted the importance of “teaching facts,” but nearly all foregrounded the importance of conceptual understanding and application. Among general educators, a small number did not mention procedural fluency, but the vast majority explicitly noted it. Critical thinking and application of mathematical ideas were also mentioned as crucial across nearly all interviews. Almost all 22 participants highlighted the importance of fostering students’ productive dispositions toward mathematics and identity development.
Divergence in Goals
Despite these many points of convergence, there were also notable differences. Most special educators detailed more “school-based” goals for mathematics, which included proficiency of standards, readiness for more advanced mathematics in high school and college, and workforce readiness. General educators tended to focus on considerably broader goals, which extended beyond school walls. Many noted that students should understand how to use mathematics as a tool for problematizing, critiquing, and ultimately changing the world. Special educators framed their goals based on the world as it is, pushing for change, but without necessarily challenging the status quo structure of K–12 schools. General educators, by contrast, more often proposed radical change to that status quo, underscoring ideas about the world as it should be and proposing goals to reimagine why we learn mathematics. For many, the focus was on leveraging mathematics classrooms to disrupt existing systemic injustices.
Many special educators emphasized the need for “data” to “know” whether goals have been met, alongside a focus on efficiency and strategic allocation of instructional time to ensure students were “ready” for increasingly complex mathematical work in school. This is likely because many SWDs are performing below grade level in mathematics, creating a sense of urgency to make up ground. The notion of “time as valuable real estate” was brought up repeatedly by many participants. This efficiency logic was evident across special educator interviews, reflective of an urgency to ensure students do not fall behind their peers and develop negative self-concepts.
Several participants oriented their responses around school-based goals, such as “progressing and performing on state assessments” to support “readiness for more advanced mathematics courses” and “course taking patterns in high school.” Undergirding many responses was the notion of preparing students for “the workforce.” But not all special educators framed mathematics this way. One special educator described “mathematics as a tool to figuratively understand the world around us . . . a basic human need,” and another emphasized the need for students “to build a sense of the place of mathematics in the world.”
Some special educators seemed to anticipate the critique of their view that school-based mathematics should prepare students for the science, technology, engineering, and mathematics (STEM) workforce. One noted, “the whole idea of getting people to ‘love math’. . . is one of the great fantasies of people inside of [the] NCTM and who are, you know, math-o-philes.” They went on to explain that “mathematical knowledge in the 21st century . . . is workforce driven, rather than philosophical. . . . The big picture is, can you get them through community college algebra? To better prepare for a living wage, workforce outcome?” They and several other special educators underscored the instrumental goals of mathematics, which they perceived general educators as wrongly discounting, to the detriment of students.
Many general educators suggested more expansive goals, such as the cultivation of “joy . . . around the mathematics we encounter every day in our world,” “mathematical authorship,” and the appreciation of mathematics as a “beautiful, visual, creative subject; not a set of numbers or methods.” Most general educators named specific examples of political issues that necessitated mathematical reasoning and logic, from gerrymandering to policing to climate change, underscoring the importance of mathematics as a human and democratic pursuit, rather than a purely academic one.
Nearly all general educator participants highlighted relationships among mathematics, power, and social efficiency logic. One mathematics educator summarized the tension succinctly: “Math carries such gatekeeper status. It greatly shapes who has access to even go to college. . . .How we look at who’s smart, and who isn’t, is often dictated by how they’re positioned in their math classroom.” Many general educators detailed a resistance to the logic of mathematics as a tool for workforce development, indicating that the goals of mathematics should not “be limited to supporting the STEM pipeline.” Another rebuffed these “really limited achievement goals . . . intended toward moving people into . . . their slotted social position.” In contrast, they identified their goals as helping students to develop “quantitative reasoning to create their own worlds.” Another noted that their priority was to “use mathematics to transform our democracy and create openings for challenging inequality.”
The Roles of Teacher and Students
Convergence in Teacher and Student Roles
There was consensus around teachers knowing students as mathematical learners, so they could better tailor instruction and respond to individual needs. One special educator described how teachers “need to know where [a student is] in terms of understanding mathematics . . . [in order] to design appropriate learning opportunities.” Similarly, a general educator stated that teachers need “to listen, to start from a place of building on students’ assets.” All 22 participants described the importance of teachers understanding that students have prior experience and knowledge and assessing students’ mathematical ideas to design activities that “build on students’ prior knowledge” and support students’ learning mathematical ideas.
Nearly all participants also converged on the idea that teachers should provide some “explicit instruction” or “scaffolding” as necessary for some students. Most agreed that explicit instruction was when the teacher made their mathematical thinking accessible, which they juxtaposed with “direct instruction,” where the teacher directly modeled how to solve a problem. One special educator described the difference thus: “Explicit instruction [is] making mathematical thinking more explicit. . . . I’m not telling you how to solve it. I’m telling you how I approach things.” One general educator explained, “sometimes I am modeling my thinking, but then stepping back and [asking] what’s the intellectual work that I’m leaving for the student?” Educators across communities highlighted the importance of preserving students’ intellectual autonomy, while making disciplinary processes and reasoning visible.
Special educators and general educators also agreed that students should take an active role in learning, and not be passive recipients of teachers’ instruction. A special educator noted, “If the student doesn’t see themself as a productive member of the math learning community, their role is . . . as a passive recipient of mathematics.” Many underscored the negative consequences of passive roles, expressing worry that negative mathematics experiences would lead to learned helplessness, especially for SWDs who have repeatedly been told that they “cannot do math.” As one special educator shared, it can be common to see students approach mathematics from the perspective of, “If I wait long enough, you’re going to tell me how to do it, and I don’t have to think this through.” Indeed, many general educators cautioned against instructional approaches in which teachers “solve problems for children.” Educators across communities foregrounded the importance of students being actively engaged in instruction.
Divergence in Teacher and Student Roles
There were notable differences, however, in how researchers characterized explicitness, when it should occur, and the degree to which and ways in which a teacher should scaffold student learning. Among general educators, there was a fear that teachers could over-scaffold learning opportunities. Nearly all emphasized that students need to engage with “rich tasks” that “focus on developing conceptual understanding,” and to have “hands-on experiences” to “make sense of the mathematics” for themselves before the teacher uses explicit instruction. Nearly all general educators expressed concern that if teachers scaffolded before students had opportunities to “engage in discourse communities” and “make sense of problems independently first,” they risked robbing students of agency. Because of the historic marginalization of students of color in mathematics, general educators also expressed suspicion about teachers taking a primary role, which they worried could unintentionally reinforce beliefs about who is seen as capable of doing mathematics. One special educator also cautioned that while “teachers should model for students,” it should not be “right away,” nor the “primary form of instruction.”
When referencing how teachers could support SWDs, general educators’ responses often lacked specificity; most did not demonstrate familiarity with mathematics-related disabilities. For example, when naming specific disabilities, one general educator only mentioned physical differences, blindness, and deafness. Several others noted that “a lot of text” could be a barrier to learning. Two explicitly mentioned that they lacked knowledge of how to support SWDs. Additionally, when describing how teachers could be responsive to the needs of SWDs, general educators were far more likely to identify the need for changes to the environment (e.g., “providing access and opportunity for all students,” or “recognizing and leveraging different forms of participation”) than the need for specific instructional practices to scaffold understanding of mathematical concepts.
In contrast, most special educators specifically referenced the value of using explicit instruction to break down and demonstrate complex mathematical reasoning before students start working on problems. As one special educator noted, “these teaching principles have . . . been validated through numerous studies, [including] clearly explaining targeted content. With struggling learners, when you’re introducing complex content, you’re overtly demonstrating things first.” Many special educators also noted the importance of multiple opportunities for student practice, with specific feedback, with teachers playing an active and consistent role in scaffolding, and, crucially, using “evidence-based strategies” to help manage students’ cognitive load.
Special educators suggested SWDs struggle to engage fully with more inductive approaches to learning, such as the independent development of solution methods or classroom discussion. Instead, they argued that it was imperative that teachers help students “accurately and precisely verbalize their mathematical understanding” and “demonstrate their understanding with concrete objects like manipulatives.” Notably absent from the special educators’ interviews were mentions of issues of race and power in their discussion of teacher and student roles.
Even though our interviews suggested considerable overlap in pedagogical perspectives, we heard several references to the other community that mischaracterized their beliefs. General educators sometimes described special educators as entirely wanting to tell students how to solve problems. For example, one general educator noted, “I don’t think [students] need more time in lecture mode, or more time in I do, we do, you do mode.” Another general educator expressed a fear that special education methods could incline teachers to just “pour the information into students’ heads,” particularly for students whom they perceive as “struggling.” Much recent special education research has underscored the importance of conceptually oriented teaching practices—such as schema-based instruction and a focus on cognitive, rather than procedural, strategies—to support SWDs (L. S. Fuchs et al., 2021; Jitendra et al., 2019; Powell & Fuchs, 2018). However, general educators still largely characterized special education methods as rote and focused on procedural rather than conceptual understanding. Many mathematics educators described special education methods and perspectives as deficit-oriented, overly focused on “chang[ing] young people” rather than “trying to change [the] school to better fit young people.” One detailed, “my view of special ed is we’ve done a terrible job of designing school so that the variety of young people with all of their strengths, and all of the things they’re still working on, can participate together.” None of the special educators we interviewed focused on changing young people, and they all described the importance of evidence-based instructional methods to support mathematical engagement for SWDs.
In contrast, special educators described general educators as often leaving students to flounder as they struggled to construct mathematical understandings on their own. As one special educator noted, “we have students that struggle, and they develop learned helplessness. We need to intervene in an earlier sense than general educators often promote,” which many special educators indicated included repeated practice. One special educator described how important it is “for students to do a lot of math” suggesting: There is the potential to develop insights into the ideas by doing, solving a lot, a lot of problems. And that has sometimes gotten neglected in the move towards discourse rich math instruction and a focus on discussing multiple solution methods to a single problem.
Another suggested that mathematics educators “ignor[e] oodles of research from the neuroscience and the cognitive folks,” noting that students with “processing issues or limits with working memory” need to focus on “fluency and automaticity with math facts” to “open up the cognitive capacity to do problem solving, reasoning and explaining,” which they saw as disregarded in position statements by NCTM. Yet another noted, I’m frustrated because I would never say deductive reasoning is always good or inductive discovery is bad. . . . That never comes out of my mouth. However, there are a lot of people at NCTM that say fluency is always bad, practice is always bad, procedures are always bad.
Only a few of the general educators we interviewed characterized a focus on fluency as negative, and none suggested that students should not learn procedures, although many suggested they should be learned inductively through students working together to solve a range of problems.
Implications
The failure of special education and general education to share knowledge across research communities has been an obstacle to promoting equitable and just outcomes for SWDs, as well as students more broadly who continue to struggle with learning mathematics. The status quo of mathematics instruction is simply not working for too many students, and we need to reconcile what we have learned in both fields and find more common ground, so we can, in turn, support mathematics teaching that better supports students in engaging with complex mathematical ideas.
By engaging scholars in both fields in a focused conversation around a shared problem—how mathematics instruction could better support all students—we hoped to better understand barriers and ultimately improve the connection between our fields. Our longer-term aim is to bring educators together to develop instructional materials for teacher preparation and ongoing professional development that reflect the epistemological beliefs of both fields and articulate conceptions of teaching and learning that connect these two communities. We need frameworks, materials, and supports that recognize the value and utility of multiple instructional models. Simply put, both teachers and teacher educators alike need a broader and more robust repertoire of instructional strategies at their disposal. This would include a deep understanding of the affordances and constraints of different approaches for different students at different times.
A key takeaway from these interviews is that there are numerous points of intersection, providing clear opportunities for bridge building. Researchers across communities foregrounded the importance of conceptual understanding and the need to make disciplinary practices and mathematical ideas explicit and visible to students, in service of scaffolding students’ sensemaking (Cohen, 2018; Kilpatrick et al., 2001; Lampert et al., 2013; Weick, 2001). They also detailed a shared belief in student-centered instruction that is responsive to individual students. Both groups recognized the potential for students, especially SWDs, to be passive in mathematics classrooms and made clear that teachers must take responsibility for promoting more active engagement. Both voiced real concerns that mathematics classrooms can convey messages about who is “smart and capable,” which could lead to long-term harm (Horn, 2007; Louie, 2017).
At the same time, the interviews also surfaced numerous differences around the goals of mathematics and whether, when, and in what ways teachers should be explicit. These tensions around explicit instruction are not specific to our study. A recent position statement from the NCTM and the Council for Exceptional Children (CEC; 2024) focused on the importance of teaching mathematics in ways that would better support students with disabilities, emphasizing the need to engage SWDS with grade-level content with “appropriate supports.” The position statement did not, however, mention systematic, explicit instruction as an evidence-based approach to providing that support. Prominent special education researchers have issues detailed responses focused on this omission (Gersten, 2025; Powell et al., 2025).
There were additional, conceptually important points of divergence. General educators far more often underscored the intersectional identities of SWDs, whereas issues of race and power were almost never mentioned by special educators. This is noteworthy given the clear evidence that schools sort students into special education differentially by race. Specifically, scholars have demonstrated patterns of overrepresentation of Black and Latinx students receiving special education services, particularly in schools that are predominantly White (Artiles & Bal, 2008; Cooc & Kiru, 2018; Elder et al., 2021; Fish, 2019; Sullivan, 2011). There is also some evidence to suggest that the risks of identification into special education are higher for students of color who experience behavioral challenges (Fish, 2017). Further, research indicates the underrepresentation of students of color in gifted education (Grissom & Redding, 2015; Pearman & McGee, 2022).
General educators articulated broader and more expansive goals that challenge an array of deeply entrenched narratives about why we learn mathematics and who gets access to mathematics (Bullock, 2013). Special educators, by contrast, largely oriented themselves around school- and workforce-based goals, and focused on supporting individual students in meeting academic standards, driven largely by the legal requirement placed on schools to ensure that special education produces “appropriate progress” for a given student’s needs (Yell & Bateman, 2017) . These two sets of goals are not necessarily mutually exclusive or incompatible with each other. For example, one could well argue that access to higher-level mathematics in high school and postsecondary education would afford individuals power that could be leveraged to disrupt injustices and change the world. That said, the foregrounding of one set of goals over another does have implications for the design of instructional experiences in the short term and the prioritizing of specific learning goals and assessment formats.
In addition to distinctions in the foregrounding of some goals at the expense of others, special educators also more often argued for active teacher roles in scaffolding student understanding, providing numerous opportunities to practice with teacher support (L. S. Fuchs et al., 2021). They noted SWDs may need approaches that diverge from constructivist learning methods and discourse-oriented instruction. They also emphasized that many general educators are not knowledgeable about how to scaffold in research-aligned ways. Indeed, many interviews with general educators suggested a lack of awareness of the value of a range of methods known to support SWDs.
One could look at this lack of consensus as an inevitable reality: these are two fields that will simply never come to agreement because of deep methodological, epistemological, and normative differences. However, we call back to Sfard’s (1998) argument for the benefits of multiple metaphors. Each group’s metaphor for learning and purpose for learning attended to some issues and some students, and ignored others. Often what was not said revealed as much important insight into a community’s worldview as what was said. Specifically, general educators’ conceptions of effective teaching did not incorporate the vast body of research from special education, including research that suggests the importance of managing cognitive load for SWDs and incorporating instructional methods that foster students’ development of the kinds of deep conceptual understanding that both groups prize. Special educators, in contrast, seldom discussed issues of race and power, despite the undeniable role these factors play in mathematics instruction (Martin et al., 2017). If we start from the perspective of how best to support future educators to make their instruction more inclusive of and accessible to SWDs, it is clear each community offers unique expertise and theoretical perspectives. The challenge is how to motivate the communities to see value in each other’s perspectives.
More cross-community conversation could help ensure that special educators have a deep understanding of the intersectional identities of SWDs, and the equity issues that are endemic in special education in America, and that general educators recognize the value of methods that can help SWDs to have access to learning and feel a sense of agency. We recognize that different goal orientations are not easy to navigate and reflect deeply held beliefs—not just about mathematics, but also about schools and schooling. There are no easy answers here, but we see value in both groups recognizing the importance of more proximal, school-based goals underscored by the special educators, alongside the more distal, less-context bound goals described by general educators. Both matter for students, and we need to prepare and support teachers who are oriented towards both.
How might these fields pursue cross-disciplinary interactions? Here, we return to the sociological literature and strategies identified in breaking down “epistemic bunkers” (Furman, 2023). In particular, we highlight the importance of “managed discussion spaces” and “insider-outsider emissaries” who are neutral and can speak within and across communities (Furman, 2023, p. 204). Academic conferences and journals can serve as managed discussion spaces, but only if members of the two groups attend the same meetings and read shared journals, which might necessitate organizational incentives to encourage engagement in research venues that are less typically attended by members of either discourse community. For example, the Teacher Education division of the Council for Exceptional Children might host a meeting during its annual conference focused on bridging divides in mathematics teacher education, with travel stipends to support general educator attendance and facilitators in place to support meaningful dialogue. That said, the special education research community’s negative responses (Gersten, 2025; Powell et al., 2025) to the NCTM-CEC joint position statement make clear that such efforts need to intentionally incorporate diverse viewpoints and work through central tensions, rather than focusing only on easier points of intersection (NCTM and Council for Exceptional Children, 2024). Specifically, to move forward in finding common ground, the two communities will need to directly work through questions of explicitness and the role of systematic instruction in supporting SWDs.
Beyond simply talking more to one another, conducting these interviews revealed areas of instruction where further research might be beneficial. We highlight two examples. First, some special education researchers nominated strategies teachers could employ to ensure that inquiry-focused instruction could be more inclusive of students with disabilities. This might include, for example, providing explicit instruction on discourse moves that would allow students to meaningfully engage in and make meaning from a class discussion. Such an instructional approach would reflect the priorities of both communities: students would still be leading the instruction but would benefit from the expertise of an educator to model making meaning through discussion. A second example is metacognitive modeling in the context of word problem solving, which is the current focus of our work in an ongoing grant funded by the National Science Foundation. Here again, the teacher would play the role of modeling for students what it looks and sounds like to think about one’s thinking. For many students with disabilities, having a teacher model the kinds of moves more experienced problem-solvers make when they approach word problems would address the concern that they may come into classrooms with less problem-solving experience. Importantly, this kind of metacognitive modeling would be distinct from procedural modeling, where a teacher would show students how they solve a problem. In each of these examples, we need further research about how to successfully implement these practices in general education classrooms that prioritize student sensemaking, not in the kinds of intervention contexts where special education research is often situated.
Teacher preparation programs are also a critical—and currently underutilized—site for bridging and de-bunkering, effectively equipping new teachers with knowledge and skills to support SWDs. Mathematics methods courses co-taught by general and special educators could launch teachers who are knowledgeable about research in both fields and the affordances and constraints of different pedagogical approaches. However, power dynamics are key considerations in co-teaching in higher education in the same way they are in K-12 classrooms (Friend & Barron, 2016; Morelock et al., 2017). If, for example, a newly minted assistant professor of special education is paired with a more senior professor of mathematics education, it could be challenging to engage in truly collaborative co-planning and co-teaching.
General and special educators simply need more time and space to learn from each other. As teacher educators, we argue that this must start in our preparation programs, modeled by program faculty. Doing this work will take time and incentives for collaboration across fields in terms of research, teaching, and material development, but we see such investments as imperative if we are to better prepare educators to support the needs of all students in their mathematics classrooms.
Mathematics teacher educators have a responsibility to equip novices with knowledge of a wide range of instructional methods for teaching mathematics, including practices known to support SWDs and other learners who struggle to engage with mathematical ideas solely through inquiry methods. Explicit instruction is not synonymous with direct instruction and can foreground the importance of deep understanding of conceptually important mathematical ideas (Cohen, 2018). So, too, would special educators benefit from more recognition of the many ways in which race and power are brought to bear in mathematics classrooms. In other words, we need all new teachers to engage with a wide range of instructional methods and to understand the complexity of the contexts and histories in which those methods are situated.
In conclusion, we leave this paper with optimism about the places where special educators and general educators converge. Ultimately, each community prioritizes the role of teachers in facilitating the development of students’ conceptual understanding. To a person, the researchers we interviewed stressed the pressing importance of an increased focus on SWDs in mathematics classrooms. We echo their urgency. Teachers need clear and consistent guidance from education research communities. As researchers, we can ill afford to continue bunkering in epistemic spaces that are safe but that ultimately leave us positioned to give incomplete—or worse, contradictory—recommendations for practice.
Footnotes
Declaration of Conflicting Interests
Funding
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