The first three pages of the seven-page NCTM/CEC position statement describe three declarations (see Table 1). We agree that all three declarations are essential for success in mathematics, with the first two supported by federal legislation and recent case law (see Table 1 for examples). Those same two declarations describe the importance of instruction on grade-level content; however, the statement provides no guidance on how to help students with grade-level content when they likely have had difficulty with content from previous grade levels. Although this declaration challenges the common but harmful assumption that students with mathematics disability or difficulties should be limited to learning content and skills commensurate with their current level of performance, it overlooks the cumulative nature of mathematics. That is, foundational mathematics content is important for later success with more complex mathematics content (Claessens & Engel, 2013; Davis-Kean et al., 2022; Geary et al., 2013; Jordan et al., 2017; Morgan et al., 2009). As a result, teachers are unable to focus solely on grade-level content if students have unfinished learning from earlier grades. A previous statement from 11 organizations that address disability and difficulties noted the essential focus on grade-level content and also included language on the need for supplemental instruction to meet individual student needs (Council for Learning Disabilities, 2019). Such language would greatly improve the NCTM/CEC position statement. Furthermore, while the final declaration about educators being supportive of students’ abilities is an important highlight, "the recommendations in the position statement that follow fail to provide teachers with actionable steps to increase students’ mathematical knowledge.

Before moving on to the actionable recommendations, we want to make one additional point. In the first declaration regarding the supports needed for success with grade-level content, the position statement suggests that co-teaching and collaboration serve as effective vehicles for addressing this need. Co-teaching, a service delivery model that may provide increased access to research-validated practices, remains an area in which the research on its effects on student achievement is still in its infancy, particularly in mathematics. In a recent review, co-teaching experts and researchers made the following observations about the instructional practice:

Some meta-analyses have reported positive effects of co-teaching for students with disabilities, yet more research needs to be conducted to understand the characteristics that moderate co-teaching (King-Sears et al., 2021) and to identify the specific characteristics of high-quality co-taught mathematics instruction. In addition, authors of meta-analyses about co-teaching have reported methodological or study quality concerns related to co-teaching studies (Losinski et al., 2019). Regardless, it is worth noting that co-teaching is only as effective as the extent to which research-validated instructional practices are integrated into the co-teaching model—a nuance that the position statement does not address.

In the next section, we review the cited research included within the position statement. As mentioned earlier in this paper, reliance on research-validated practices for instruction is described as essential in both general education legislation (i.e., ESSA) and special education legislation (i.e., IDEA) in the United States as well as in the teacher preparation standards from the CEC. Therefore, we would expect a position statement to be firmly grounded in research.

Table 2 provides an overview of the 34 citations included in the position statement. Approximately half of the citations were documents from organizations or book citations. Given that books are seldom peer reviewed and authors often do not explain the research conducted for the book, we consider book citations to be less reliable than research from peer-reviewed journal articles. Of the 13 publications from peer-reviewed articles in the position statement, only six were specific to mathematics. Notably, while the position statement aimed to address mathematics instruction for students with disabilities, less than half (n = 6) of the peer-reviewed articles included any mention of students with disabilities. Only four studies addressed mathematics and disability (Cooper & Farkas, 2023; Heyd-Metzuyanim, 2013; Root, Saunders, et al., 2021; Scheuermann et al., 2009) and only one of these studies (Scheuermann et al., 2009) shared original research evaluating academic student outcomes.

While several of these citations may be appropriate in the NCTM/CEC position statement, what was absent from the position statement was a reliance on the large corpus of high-quality research studies in the area of mathematics disability and difficulties. A large corpus of hundreds of experimental studies examining the effects of mathematics interventions for students with mathematics disability and difficulties has been conducted over the last several decades, published in journals after rounds of peer review. For instance, G. Nelson and McMaster (2019) named 34 studies focused on early-numeracy intervention, with student samples including students with mathematics disability or difficulties; Lein et al. (2020) reviewed 31 studies with word-problem interventions for students with mathematics difficulties; Ennis and Losinski (2019) identified 10 studies about fraction interventions for students with a disability; and Bone et al. (2021) reviewed 18 studies focused on algebra and students with a learning disability. Browder et al. (2008) identified 68 experimental studies about mathematics instruction for students with significant disabilities, and Bowman et al. (2019) updated this effort by adding 24 additional studies. As another example, Hughes and Yakubova (2019) reviewed 11 studies about mathematics instruction using technology for students with autism. Notably, many of the studies in these systematic reviews of students with mathematics disability or difficulties have to do with instruction in domains of mathematics that are critical for higher level mathematical thinking and performance for all students (National Mathematics Advisory Panel Report, 2008).

Across mathematics content areas, Chodura et al. (2015) reviewed 35 studies on interventions for students with mathematics difficulties; Jitendra et al. (2018) named 19 studies focused on mathematics interventions at the secondary level; and Rojo et al. (2024) identified 223 studies across the elementary and secondary levels in which researchers implemented a mathematics intervention with students with mathematics disability or difficulties. In fact, the literature on instructional practices for students with mathematics disability or difficulties is well documented going back decades. For example, over 20 years ago, Baker et al. (2002) identified 15 studies on mathematics interventions to improve the outcomes for students with mathematics difficulties. The omission of such research from the position statement is a significant shortcoming, especially given that CEC advocates for and produces documentation about high-quality research (B. G. Cook et al., 2015) and the use of research-validated practices through their high-leverage practices (Aceves & Kennedy, 2024).

In the next section, we delve into the research supporting the actionable recommendations for mathematics instruction for students with mathematics disability and difficulties that were included in the position statement.

After the three pages of declarations, the position statement provided two pages of “actionable recommendations” (p. 3) for educational partners. We recommend that future author teams explore the research base underlying the recommendations for teacher educators and state education departments, school and district-level leadership, funding agencies, researchers, and professional organizations. In this section, we explore the research base for the eight actionable recommendations for general and special education teachers of mathematics, because teachers are essential to providing mathematics instruction to students with mathematics disability or difficulties. Please note, the bolded header presents the exact language from the position statement.

1. Incorporate Universal Design for Learning framework in unit and lesson planning. Universal Design for Learning (UDL) offers a framework for designing learning environments that are maximally accessible to all students. UDL highlights three aspects of the learning environment in which flexibility can be incorporated: (a) multiple representations of the content, (b) multiple means of action and expression of students’ knowledge, and (c) multiple means of engaging with the content and peers (CAST, 2024; Smith et al., 2019). Although UDL provides a comprehensive approach to accessibility, research on its efficacy in improving learning outcomes remains limited (Boysen, 2024). In a systematic review of 32 studies investigating the implementation of UDL on student learning, Zhang et al. (2024) noted considerable variability in how the framework was conceptualized and operationalized. Furthermore, some experts, such as Anastasiou et al. (2024), suggested that UDL principles may conflict with cognitive load theory, particularly the use of multiple representations, which could be overwhelming to some students. While some evidence points to the potential of UDL for supporting student learning, this evidence is weak for mathematics specifically. In a meta-analysis of experimental studies, King-Sears et al. (2023) observed a moderate, positive effect for UDL-based instruction on STEM-related content, yet this only included one mathematics intervention study (which had insignificant effects). The aggregated findings across content areas suggested that the effect of UDL-based instruction for students with a disability was greater than for those without. These results indicate that UDL may have promise but further investigation is warranted.

Similar to co-teaching, UDL could serve as a framework that facilitates access to research-validated practices for students. However, due to inconsistent implementation of the UDL guidelines and challenges in measuring UDL outcomes (Edyburn, 2021), it is impossible to draw conclusions about the efficacy of UDL in improving accessibility, and consequently, learning outcomes. As such, UDL might not be the ideal first actionable recommendation for teachers in the position statement. Although the UDL framework holds theoretical promise and is content, age, and setting neutral, it may be more productive to recommend future research to use UDL to guide the selection and implementation of research-validated instructional practices for students with mathematics disability or difficulties.

2. Use appropriate and accurate multiple representations, such as simultaneously presenting Concrete-Semiconcrete-Abstract (CSA). The practice of teaching mathematics concepts and procedures through use of hands-on manipulatives (i.e., concrete), static drawings (i.e., semi-concrete), and abstract symbols has a research base in mathematics education and special education dating back nearly 60 years (Bruner, 1966). This approach, sometimes referred to as CRA (concrete-representational-abstract) or scaffolded representations (which is different from UDL’s multiple means of representation), enables students to see and interact with mathematics using a variety of tools and models to deepen understanding of concepts and procedures.

Recent systematic reviews have identified several types of representations as efficacious for improving student mathematics outcomes. For example, Carbonneau et al. (2013) identified instruction with concrete manipulatives to have an advantage compared to instruction with only abstract symbols in general education. Similarly, Peltier, Morin, et al. (2020) determined concrete manipulatives were important for improving mathematics outcomes for students with mathematics disability or difficulties. Park et al. (2022) identified virtual manipulatives as a contributing factor to improved mathematics outcomes for students with a learning disability. Bouck et al. (2018) and Ebner et al. (2025) determined the CSA approach as a significant tool for the learning of mathematics, and numerous systematic reviews have identified multiple representations more broadly as integral to efficacious mathematics interventions for students with mathematics disability or difficulties across preschool, elementary, and secondary settings (S. C. Cook et al., 2020; Hwang et al., 2019; Jitendra et al., 2018; Liu et al., 2021; Mononen et al., 2014; Morin & Agrawal, 2022; Myers et al., 2021; G. Nelson, Crawford, et al., 2022; Powell, Doabler, et al., 2020; Powell, Mason, et al., 2021; Spooner et al., 2019; Zhang & Xin, 2012).

Given the strong and consistent research base supporting multiple representations, their adoption should be featured in a list of actionable recommendations for teachers. It would be helpful to provide greater details on CSA as well as its variations with virtual representations (e.g., virtual-representational-abstract stages), whether through sequential (e.g., Bouck et al., 2019; Flores et al., 2014; Satsangi & Sigmon, 2024) or integrated approaches (e.g., Bouck et al., 2024; Hinton & Flores, 2024; Root, Cox, et al., 2021; Satsangi, Hammer, & Evmenova, 2018; Satsangi, Hammer, & Hogan, 2018). These detailed recommendations are necessary so that teachers can have a deeper understanding of the nuances of using representations and discern how to use multiple representations to focus on mathematical reasoning while applying operational knowledge (Morano, Flores, et al., 2020). Furthermore, greater detail about the use of CSA would build insight into more efficient ways to create active learning experiences through multiple representations to teach mathematics content to students who may have a wide range of skills and needs and to understand which representations are most appropriate for teaching specific mathematics content to different groups of students at various stages of learning.

3. Plan proactively using a preventative model for instruction. There are several parts of this recommendation’s sentence that could be important for teaching mathematics, but without clarity in the position statement, the expectations for teachers remain ambiguous. First, the phrase “plan proactively” warrants attention. So much of supporting students with a mathematics disability or difficulties involves proactive planning, including writing IEP goals, planning effective instructional approaches to teach specific content in order to reach those goals, and planning assessments to measure progress. Interestingly, assessment (and the collection of student data) was not mentioned in the NCTM/CEC position statement. The use of student assessment data to analyze instructional practices and make necessary adjustments to improve student outcomes is one of the six high-leverage pillar practices described by CEC (Aceves & Kennedy, 2024) and the use of assessment to support learning and provide useful information to teachers and students is one of NCTM’s six principles for school mathematics (NCTM, n.d.). Furthermore, more than 90% of states use a multi-tiered system of supports (MTSS) framework driven by direct collection and analysis of student performance data (I-MTSS Research Network, 2024). It is a major oversight not to have any mention of assessment in a position statement focused on students with mathematics disability or difficulties.

Relatedly, within this recommendation, the use of a “preventative model,” could be perceived as a reference to MTSS, a common approach with research to support its use in supporting all learners in mathematics (Choi et al., 2020). The choice of the term “preventative” is noteworthy, given there was no distinction between teaching mathematics for students with mathematics disability and those with mathematics difficulties (i.e., at risk for disability). Often, MTSS or response-to-intervention (RtI) is used by schools to support students with mathematics difficulties to prevent the identification of a disability. However, a single teacher cannot implement MTSS on their own. MTSS has to involve an entire district, with leadership and teachers working together (Freeman et al., 2015). Also, any conversations about MTSS should include all students, even those with significant cognitive disabilities (Thurlow et al., 2020). Beyond academics, and of particular importance to students with a disability, any mention of MTSS should also involve a focus on behavior (Adamson et al., 2019; Grigorenko et al., 2020; Nitz et al., 2023).

In both planning and prevention, the use of data-based decision making (DBDM; Schildkamp, 2019), sometimes referred to as data-based individualization or DBI (Powell et al., 2024), is essential. Within a DBDM framework, teachers use data to drive decisions about instruction and whether the instruction is meeting individual student needs (Schumacher et al., 2017). DBDM is essential in the teaching of students with mathematics disability or difficulties as the framework promotes responsiveness to individual student needs. In a recent meta-analysis, Jung et al. (2018) determined that DBDM was a viable framework for supporting students who have intensive academic needs. Whether through MTSS, DBDM, or a combination of both, successful implementation requires a financial investment by districts so that teachers have access to (a) planning time and professional development, (b) a thoughtfully structured school day to ensure dedicated intervention time is built into the daily schedule beyond core mathematics instruction, and (c) qualified mathematics interventionists to provide targeted and intensive intervention to students. We emphasize these components of successful MTSS or DBDM implementation because they should be taken into consideration when any preventative model is mentioned within such a position statement. These are not easy or inexpensive things to do, and often teachers do not have control over many levers that could lead to successful implementation (Mason et al., 2019).

4. Position students with disabilities as valuable owners and contributors to the mathematics being learned. Although we agree that students should be regarded as valuable owners and contributors to mathematics, it is difficult to pinpoint direct empirical evidence for this claim. One way to frame this recommendation is to draw on the literature addressing the development of self-regulation or self-determination skills for students with mathematics disability or difficulties, which is particularly important for secondary transition (Chiang & Howe, 2024) and has been incorporated in mathematics interventions for secondary students with an intellectual disability (e.g., Gilley et al., 2021; Gilley et al., 2023). In a recent systematic review, Elhusseini et al. (2022) determined self-regulation interventions could lead to improved academic outcomes for students with and without a disability. A position statement could provide detailed guidance on self-regulation and offer teachers practical strategies to support its development.

Within this actionable recommendation, it might be important to focus on student mathematics anxiety and self-efficacy. Students with mathematics disability or difficulties often demonstrate higher mathematics anxiety (Devine et al., 2018; Namkung et al., 2024). Although mathematics anxiety generally has a moderately negative impact on mathematics performance (Barroso et al., 2021; Namkung et al., 2019), difficulties in foundational mathematics skills have a much stronger impact on mathematics outcomes for students with mathematics difficulties, above and beyond the effects of mathematics anxiety (Codding et al., 2023). Similarly, within this actionable recommendation, the literature on student mindset towards mathematics may be important. Burnette et al. (2023) reported that mindset interventions were significantly related to multiple academic outcomes (not only mathematics outcomes), though the effects were very small. Macnamara and Burgoyne (2023) identified no impact of mindset interventions on academic outcomes. This is similar to a study by L. S. Fuchs, Wang, et al. (2021) in which they noted no significant advantage for students who participated in mindset activities embedded within a mathematics intervention. Clarity around this actionable recommendation could help teachers spend instructional time on factors that more substantially enhance mathematics understanding of students with disability or difficulties.

5. Provide paired time for students to share and rehearse their thinking and ideas in multi-modal ways before moving to a whole group discussion. There are many ideas to unpack in this single sentence. First, the term “paired time” could imply that students must work exclusively in pairs, yet it is unclear whether small groups, such as those with three or four would suffice. Research is inconclusive that students taught in smaller group formats (e.g., two students) have an advantage over students taught in larger small group formats (e.g., five or more students; see Doabler et al., 2019 and Clarke et al., 2022 for a comparison). A meta-analysis of 223 mathematics intervention studies from Grades K through 12 identified no significant differences in mathematics outcomes when comparing individual interventions to small groups or whole group interventions to small groups (Rojo et al., 2024). Second, “share” and “rehearse” are different practices. Sharing involves communicating mathematical ideas, whether through speech, gestures, writing, or other means. Rehearsing involves practice until proficiency is achieved, which research has demonstrated as important for the learning of mathematics (Burns et al., 2019). Although self-explanations from students may be related to sharing and rehearsing, impactful self-explanations require scaffolded support from teachers (Rittle-Johnson et al., 2017) and may not yield additional improvements in mathematics outcomes beyond those achieved through mathematics practice alone (L. S. Fuchs, Schumacher, et al., 2016). Third, the term “multi-modal” needs clarification as to whether this refers to multiple representations described in the second actionable recommendation. Fourth, “before moving to a whole group discussion” implies a fixed sequence to instruction, a topic that remains one of the largest debates in the teaching of mathematics.

Rather than trying to unpack this actionable recommendation’s unclear message, it may be more helpful to review the research related to cognitive load, which could help teachers design instruction that accounts for a student’s working memory capacity and processing of new information (Kirschner, 2002). Cognitive load theory (Sweller, 1988) is based on the framework that working memory has a limited capacity for temporarily storing and manipulating information. When this capacity is overloaded, learning becomes less effective, leading to decreased performance. As described by Kennedy and Romig (2024), working memory can be overloaded when students are tasked with technical language by increasing the demands of language comprehension, presented too many concepts at once, provided with irrelevant information, asked to digest a large amount of text at one time, or given abstract ideas without visual representations.

Reducing cognitive load via effective instruction is especially important for students with mathematics disability or difficulties, who often have limited working memory compared to other students (Barnes et al., 2020; Lanfranchi et al., 2012; Swanson et al., 2021; Willcutt et al., 2013). Therefore, teachers need to design instruction that mitigate these demands on students’ limited working memory. With this in mind, teachers can help students take new knowledge and organize it in meaningful ways into pre-existing schemas within long-term memory (Sweller & Chandler, 1991). Effective instruction also needs to move from easier content to more difficult content in manageable chunks, with various levels of scaffolding provided to students (van Merrië nboer & Sluijsmans, 2009), which includes attention to the cognitive-linguistic load of mathematics (Alt et al., 2014; Arizmendi et al., 2021). Researchers have also linked successful word-problem interventions for students with mathematics disability or difficulties to the recognition of common schemas within word problems (Alghamdi et al., 2020; Cox & Root, 2020; L. S. Fuchs, Seethaler, et al., 2021; Peltier, Sinclair, et al., 2020; Powell, Berry, et al., 2021; Root & Browder, 2019). While it is unclear whether this actionable recommendation is focused on cognitive load, we suggest two improvements. First, the statement should clarify the meaning of each of the components of this recommendation. Second, it should include explicit information about cognitive load and strategies for designing instruction to support cognitive load for students with mathematics disability or difficulties.

6. Provide a variety of interactive learning experiences. This recommendation is notably underspecified. We would expect all mathematics instruction to be “interactive.” Explicit instruction, which will be described later in this paper, is highly interactive and engaging with a continuous feedback loop provided to students via frequent opportunities to respond (Doabler et al., 2015; Hughes et al., 2017). Verbalizations and purposeful discourse also have research support, which could be another avenue for interactive learning experiences (Liu & Xin, 2017; Rosenzweig et al., 2011). Although the use of multiple representations, such as CSA, can provide an interactive learning experience, the recommendation should clarify what constitutes a “variety” of learning experiences. While this sixth recommendation alludes to ways that students with mathematics disability or difficulties can engage in the learning of mathematics, which is essential for the learning of mathematics (Doabler et al., 2015), clarification is necessary to understand how this might be implemented in a school setting.

7. Use flexible grouping structures to cultivate a community of learning. Although flexible grouping is identified as one of the high-leverage practices for students with disabilities (McLeskey et al., 2017), there is a lack of clarity about the meaning or implementation of this recommendation for mathematics. For targeted mathematics support on specific mathematics content, research suggests homogeneous groupings may lead to efficient gains (Steenbergen-Hu et al., 2016), particularly in mathematics within an MTSS framework (Choi et al., 2020). “Grouping structures” could encompass peer tutoring or peer-assisted learning strategies, which has a strong evidence base to support its use in mathematics (Allsopp, 1997; Bowman-Perrott et al., 2013; Codding, Chan-Iannetta, et al., 2011; Dobbins et al., 2014; L. S. Fuchs et al., 2002; Hawkins et al., 2009) and with students with a disability (Ledford & Wolery, 2013; Sperry et al., 2010; Zhang & Wheeler, 2011). As with the prior actionable recommendations, we propose that this recommendation should offer more detailed guidance to make this truly actionable.

8. Build meaningful connections between concepts and procedures. It has long been argued that conceptual understanding and procedural fluency must coexist for students to truly grasp mathematics (Ball et al., 2005). The “Math Wars,” in which tension arose about the role of conceptual understanding and procedural fluency, were largely settled in the early 2000s with the recognition that these elements are intertwined with students’ ability to reason quantitatively, apply strategies, and think mathematically (Baroody et al., 2007; Rittle-Johnson, 2017; Star, 2005). Together, they form the foundation of mathematical proficiency and problem solving (National Academies of Sciences, Engineering, and Medicine [NASEM], 2001). There is no dispute that students must build meaningful connections between concepts and procedures.

Conceptual understanding involves knowing the fundamental ideas that underlie working with numbers, such as concepts, operations, and relations (Crooks & Alibali, 2014). It is not about knowing isolated and disconnected facts but having an integrated understanding of important mathematical ideas (NASEM, 2001). Procedural fluency is defined as knowing procedures; when and how to use them appropriately; and performing them flexibly, accurately, and efficiently (NASEM, 2001; Rittle-Johnson et al., 2001). It is not just about performing operations quickly but about solving problems efficiently, identifying and correcting errors, applying algorithms in contextualized settings, and generalizing understanding to novel situations (Star, 2005). Given the interplay between conceptual and procedural knowledge and the necessity to balance conceptual and procedural instruction (Heatly et al., 2015), it would be constructive for a position statement to provide research-validated guidance about the dual development of conceptual and procedural knowledge as well as clarify that one (i.e., conceptual knowledge) does not have to develop before another (i.e., procedural knowledge; Rittle-Johnson et al., 2015). In many ways, the use of multiple representations (CSA) could help students see connections between concepts and procedures (Agrawal & Morin, 2016). Further, explicit instruction could be used to help students develop deep mathematical knowledge about concepts and procedures in a way that other instructional approaches (e.g., inquiry) may leave too much up to chance and the individual student.

In reviewing the research underlying the eight actionable recommendations, we determined that many of these recommendations were underspecified or lacked a substantive research base, particularly for students with mathematics disability or difficulties. We also noted that several commonly recommended practices for the mathematics instruction of students with mathematics disability or difficulties were absent from the position statement. In the next section, we propose research-validated practices that should have been included in the NCTM/CEC position statement.