How and What to Teach Students With Disabilities in Mathematics: Controversies and Complexities Raised by the NCTM/CEC Position Statement

Recently, the Council for Exceptional Children (CEC) and the National Council of Teachers of Mathematics (NCTM) released a joint position statement, Teaching Mathematics to Students with Disabilities (NCTM, 2024). To its credit, the position statement (PS) confronted head-on a challenge faced by special education students and their teachers: What are the best ways to implement the Individuals with Disabilities Education Act (IDEA) mandates that schools provide students with disabilities access to the same grade-level curriculum standards and content as their peers (IDEA, 2004/2023)?

The PS reasonably assumes that students with disabilities in mathematics receive instruction in a grade-level (Tier 1) mathematics classroom. This was documented in the 2023 report from the National Center on Educational Statistics (NCES), which found that three fourths of these students receive over 80% of their instruction in general education classrooms (Irwin et al., 2023). This figure has consistently increased over the past dozen years. In this sense, the document is timely. IDEA (2004/2023) clarified that access to the general curriculum is to be interpreted as access to grade-level curriculum and material that covers grade-level standards. Recent Office of Special Education Program (OSEP) guidance (OSEP, 2023) stresses the obligation of states to monitor and ensure that IEPs are standards-based and align with state academic content standards for a child's grade level.

In our recent experience working with schools, we have noted how district and school leadership have consistently stressed that instruction for students with disabilities covers grade-level standards, and invariably this entails placement in grade-level mathematics classes. To that end, we have observed two different approaches in wide use (Jayanthi et al., 2024). The first entails students receiving mathematics instruction in a grade-level classroom with supplemental support by a special educator in addition to core classroom instruction. The second consists of co-teaching of the class by a mathematics teacher and a special educator.

The research on co-teaching (e.g., Stroglios et al., 2023) generally finds that many teachers and students like co-teaching. Teachers report students seem to learn more, feel better about using grade-level textbooks, and like being in a regular class. Students have also reported that they often receive better grades in general mathematics classes than in special education classes (Friend et al., 2010). However, teachers invariably complain of a lack of planning time and chronic ambiguity in roles, and in some cases, feel that they often serve as a classroom teaching assistant and helper rather than as a teacher, a finding recently replicated in a 2022 survey of a national sample of special and general educators (Sparks, 2022).

Van Garderen et al. (2012) noted that few studies reported student outcomes, reporting inconsistent patterns of impacts on student learning, with outcomes ranging from positive to negative to null effects. However, an analysis of six prior syntheses by Solis and colleagues (2012) concluded that the research suggests that students with and without disabilities benefit from certain specific instructional practices when they are infused into core instruction. These practices include study guides, hands-on activities, and instructional activities that create active student involvement in lessons.

Unfortunately, the NCTM/CEC PS avoids this type of specificity. Instead, it provides a romantic notion of the realities of co-teaching and does not offer concrete solutions for how to address the problems, such as how to schedule daily collaborative sessions between special education and mathematics teachers. The PS also fails to acknowledge the paucity of rigorous research on co-teaching (e.g., Strogilos et al., 2023) and the extremely limited evidence of its effectiveness.

Teachers also must grapple with another key problem: How to teach challenging grade-level content such as fraction division to students who lack a fundamental understanding of what division is and lack any type of proficiency with basic whole-number division and multiplication. A document that provides guidance on how to implement co-teaching to support students as they attempt to learn grade-level material would be extremely useful.

To its credit, the PS does provide suggestions for those involved in co-teaching and delivering or overseeing Tier 2 and Tier 3 interventions. Specifically, it argues for the use of peer-mediated instruction (e.g., Baker et al., 2004; Fuchs et al., 1995) so students can practice both solving problems and explaining their mathematical reasoning with a peer in a nonthreatening fashion. It sensibly suggests that “interventions use the exact language, representations, and problem-solving strategies across Tier 1 and intervention” (PS, p. 3). It also recommends active sharing of expertise between special educators and mathematics teachers when planning joint lessons for whole-class instruction or developing lesson plans for daily interventions that quickly “fill in” gaps in students’ foundational knowledge relevant to each day's lesson.

There is no question that special educators and mathematics teachers can truly benefit from collaboration. Mathematics education can inform special education practice in many innovative ways: providing prompts that stimulate student explanations (Dougherty et al., 2015); using engaging hands-on activities that build conceptual understanding (Blanton et al., 2015); using precise accurate mathematical language and ensuring teachers do not teach rules that expire (Karp et al., 2015); and using the concrete-semi-concrete-abstract (CSA) method, also known as concrete-representation-abstract (e.g., Ebner et al., 2024), to help students visualize and understand concepts such as equivalence, the nature of a linear function, and linkage between decimals and conventional fraction notation.

However, one wonders how useful a one-day “fill-in” lesson on the meaning of division or fraction equivalence will be for students with disabilities in mathematics. Without systematic instruction at a pace that is appropriate, will students truly understand this material enough to follow the grade-level lesson? The PS fails to acknowledge the existence of learning trajectories in mathematics and how access to grade-level content often requires proficiency in material covered, but not mastered, in earlier grades. Can students understand grade-level material with only a brief “fill-in” lesson on concepts that underlie grade-level material? The answer, I believe, is sometimes yes, but often no.

The PS calls for stakeholders to “identify and systematically blend into practice empirically supported instructional strategies [emphasis added] that integrate the expertise of general education and special education [teachers]” (p. 4). Yet, it fails to practice what it preaches. As noted by the Aletheia Society (2024), the specific actions recommended in the PS are not grounded in empirical evidence. Rather, they are aspirations. They rely heavily on rhetorical flourish and are short on detail. As such, the PS fails to consider the large body of high-quality research conducted over the past 20 years, which has documented effective practices for teaching students with difficulties in mathematics receiving mathematics interventions.

How the Research on Evidence-Based Practices Could Be Utilized

A good deal of high-quality research over the past 20 years has addressed interventions in mathematics for students in Grades K-8, often concentrating on difficult-to-teach but essential topics such as fractions, proportions, and arithmetic word problems. The findings have been synthesized in a variety of meta-analyses using either the CEC Quality Indicators (e.g., Rojo et al., 2023) or the more rigorous Institute of Education Sciences (IES) What Works Clearinghouse Standards (e.g., Krowka et al., 2024). Furthermore, this research is consistent with an earlier meta-analysis of the research conducted on students with identified learning disabilities (Gersten et al., 2009).

This body of knowledge was summarized in a recent IES practice guide (Fuchs et al., 2021), which utilized meta-analytic techniques to synthesize the evidence base from 44 rigorous studies on elementary school mathematics interventions using randomized control trials and quasi-experimental designs. This body of research is rich, incorporating ideas and insights from both the fields of mathematics education and special education into the design of many of the interventions. An expert panel interpreted the evidence into six recommendations for improving the quality of intervention, which are summarized in Figure 1.

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Figure 1.

Evidence-based practices for mathematics intervention. (1) Provide systematic instruction during intervention to develop student understanding of mathematical ideas. (2) Teach clear and concise mathematical language and support students’ use of the language to help students effectively communicate their understanding of mathematical concepts. (3) Use a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures. (4) Use the number line to facilitate the learning of mathematical concepts and procedures, build an understanding of grade-level material, and prepare students for advanced mathematics. (5) Provide deliberate instruction on word problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas to real (or imagined) contexts. (6) Regularly include timed activities as one way to build fluency. Note. Adapted from Fuchs et al. (2021).

It is hard to understand why the PS ignored this body of research. The authors only mentioned one of the six findings from the practice guide: use of concrete and semi-concrete representations. They failed to even mention the other five, despite their replication in numerous rigorous randomized controlled trials.

Although the PS does not do so, one might also argue that the evidence for the recommendations is from intervention studies rather than from studies conducted in whole-class settings, which is the focus of this PS. There are two serious limitations in applying the evidence base from the intervention literature to serve as a basis for effective differentiated Tier 1 instruction that meets the needs of students with disabilities. First, the intervention studies in the research base invariably deal with small groups of 3–8 students and provide no concrete guidance on how to orchestrate for a whole class of 18–30. Second, and most problematic, instruction in virtually all the interventions synthesized in Fuchs et al. (2021) moves at a deliberate pace, whereas teachers must move at a brisk pace in Tier 1 to teach all the material contained in contemporary state standards. We believe that moving through the material systematically at a pace that ensures that students really understand and master the material is a key reason these interventions are successful. Conceptualizing how these fit into Tier 1 is an engineering challenge, one that we as a field need to address.