Evidence‐Based Practices: Applications of Concrete Representational Abstract Framework across Math Concepts for Students with Mathematics Disabilities

Abstract

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.

Virtual Algebra Tiles: A pedagogical tool to teach and learn algebra through geometry

“…These findings support the outcomes of previous studies (Agrawal & Morin, ; Saraswati et al, ; Richardson & Bachman, ). These studies have shown that the use of these mathematical manipulatives helps to increase student learning because they encourage relational thinking and promote algebraic reasoning.…”

“…The efficacy of the algebra tiles as a pedagogical tool to teach and learn algebra concepts has been widely proven (Agrawal & Morin, ). However, nowadays, students feel more comfortable when they are taught by using new technologies having into account that they were born in a digital era (Venkatesh, Croteau, & Rabah, ).…”

A metacognitive intervention for teaching fractions to students with or at-risk for learning disabilities in mathematics

“…In the third stage of SRSD, students continue to observe the teacher and peers as they progress to the emulation level of the development of self-regulation by imitating the teacher's behaviors as he or she models each step of the FACT + R 2 C 2 strategy to solve problems using multiple representations, such as the concrete-representational-abstract (CRA) sequence. Using multiple representations has received considerable empirical support, particularly in the domain of fractions, and CRA has been shown to be particularly effective with students with or at risk for MLD (Agrawal and Morin 2016;Carbonneau et al 2013;Rau and Matthews 2017). With repeated observation and emulation of the teacher's behaviors of the FACT + R 2 C 2 components and CRA instruction, students begin to own the strategy by developing closer and closer approximations of those behaviors (Schunk and Zimmerman, 2007).…”

Mining Instruction From Student Mistakes: Conducting an Error Analysis for Mathematical Problem Solving

“…McLaughlin & Skinner, 1996) The student (a) looks at a math fact, (b) covers the problem and the answer (stimulus), (c) writes the problem and the answer, (d) uncovers the stimulus, and (e) self-evaluates the written response by comparing it with the stimulus. If incorrect, the student repeats the procedures until it is correct Choosing the Incorrect Operation Schema Instruction (Jitendra et al, 2009;Powell & Fuchs, 2018) Teach students additive (combine, change, compare) or multiplicative (equal groups, comparison, proportions, or ratio) schemas explicitly and systematically, practicing each type before generalizing to new problem structures Computation Concrete-Representational-Abstract Framework (Agrawal & Morin, 2016) DRAW (Miller & Mercer, 1993) When teaching concepts, first have students practice with manipulatives. Then, teach students how this relates to representations, or drawings, of problems and support them to draw problems by hand.…”

“…For this student, Ms. Schmid could focus strictly on computation intervention. She could align instruction with the concreterepresentational-abstract framework (CRA; Agrawal & Morin, 2016) to teach the student how to use the standard algorithm for addition and subtraction-requiring regrouping (see Table 2). The teacher might reteach addition and subtraction with regrouping using base 10 blocks before the student creates his own pictorial representation and finally, abstract notation.…”