Learning Disabilities Research & Practice, 31(1), 34–44 C  2016 The Division for Learning Disabilities of the Council for Exceptional Children DOI: 10.1111/ldrp.12093 Evidence-Based Practices: Applications of Concrete Representational Abstract Framework across Math Concepts for Students with Mathematics Disabilities Jugnu Agrawal George Mason University Lisa L. Morin Old Dominion University Students with mathematics disabilities (MD) experience difficulties with both conceptual and procedural knowledge of different math concepts across grade levels. Research shows that concrete representational abstract framework of instruction helps to bridge this gap for students with MD. In this article, we provide an overview of this strategy embedded within the explicit instruction framework. We highlight effective practices for each component of the framework across different mathematical strands. Implications for practice are also discussed and a detailed case study is provided. Mathematics disability (MD) is a relatively nascent field of research (Watson & Gable, 2013). Estimates for the preva- lence of MD vary widely, from 3 to 9 percent of the entire school-age population (Fuchs et al., 2010; Swanson, 2012). Although researchers have agreed on many commonalities of the characteristics of MD, they have also found that MD is highly complex with many factors. These factors include age, grade level, math content, and tasks, along with read- ing disability comorbidity. Some researchers have warned that MD should not be considered a “homogenous disorder” (Chong & Siegel, 2008, p. 314) because students deemed to have MD may have very different cognitive and skill deficits. This particularly impacts students with MD in math word problem solving, a multifaceted task that requires simulta- neously decoding information presented linguistically and applying math concepts, creating representations, and carry- ing out procedural mathematical operations (Zheng, Flynn, & Swanson, 2013). While researchers differ in their use of the terms MD and learning disability (LD), for the purpose of this article, mathematics skills deficits will be referred to as MD. The recommendations of the National Council of Teachers of Mathematics (NCTM, 2000) specify that students should have an opportunity to develop understanding of mathemati- cal concepts and procedures by engaging in meaningful math instruction. Common Core’s Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) highlight process standards that give priority to math rea- soning and making connections. The findings of a review of math interventions for low-achieving students indicate that instruction for students with disabilities focuses on teaching computational skills and procedures rather than conceptual Requests for reprints should be sent to Lisa L. Morin, Old Dominion University. Electronic inquiries should be sent to lmorin@odu.edu knowledge (Bottge, 2001). Additionally, the achievement gap for math between typically developing students and students with disabilities continues to increase because students with disabilities progress at a much slower rate as compared to their typically developing peers (Bottge, 2001; Cawley & Miller, 1989). Conceptual knowledge is developing a deeper under- standing of the mathematical concepts by linking new phenomenon to previously existing phenomenon and under- standing the relationships and patterns among these different pieces of information (Miller & Hudson, 2007). For example, the student understands that multiplication and division have an inverse relationship. Therefore, he/she uses this knowl- edge to check the answer to a multiplication problem by dividing the product with one of the multipliers. Concep- tual knowledge also develops when students connect a newly learned math concept to a previously learned and stored concept. For example, the student understands place value of whole numbers but when he/she learns decimals, he/she connects the new math concept with the previously learned math concept of place value (Hattikudur, 2011; Kridler, 2012; Miller & Hudson, 2007; Mulcahy & Krezmien, 2009). Miller and Hudson (2007) define “procedural knowledge as the ability to solve a mathematical task” (p. 50). It is also defined as the ability to follow step-by-step proce- dures to solve a math problem (Bottge, 2001; Carnine, 1997; Goldman, Hasselbring, & The Cognition and Technology Group at Vanderbilt, 1997). Procedural knowledge can be used for solving problems ranging from simple addition and subtraction to complex word problems. The development of procedural knowledge has been researched extensively for students with MD (Hattikudur, 2011; Kridler, 2012; Miller & Hudson, 2007; Montague, 1992; Mulcahy & Krezmien, 2009). Both conceptual and procedural knowledge are essen- tial for improving math achievement of students with MD