The Effects of the Concrete-Representational-Abstract-Integration Sequence to Teach Students with Disabilities Binomial Multiplication and Quadratic Transformations into Factored Form

Abstract

Algebra is the foundational mathematics course that students take as they begin their high school career and is often difficult for the average learner. In order for students with disabilities and those with mathematics difficulties to meet the high expectations of future mathematical courses, providing quality instruction by implementing evidenced based practices within the inclusive setting is essential to improving the academic achievement of students in courses such as algebra. The concrete-representational-abstract (CRA) sequence is an evidenced based practice that is proven effective in increasing students’ mathematical skills. The development of a modified version of the CRA sequence, the concrete-representation-abstract-integration sequence (CRA-I), was shown to be effective in teaching advanced mathematics skills to three students with disabilities (Strickland, 2012). However, the research in teaching secondary students with disabilities advanced mathematical skills is lacking. Therefore, this study investigated if receiving supplemental algebra instruction using the CRA-I sequence, a graphic organizer, the BOX Method, and mnemonic instruction would affect students’ performance in multiplying binomial expressions to form quadratic expressions and transforming quadratic expressions into factored form. Similar to previous CRA research, this intervention taught students two mnemonics, FACTOR and HUMP BACK FACTOR, to develop procedural fluency in the transformation of quadratic expressions into factored form. There was no current research that implemented the use of CRA-I and mnemonic strategy instruction for advanced algebra skills, although CRA and mnemonic instruction is shown effective for improving basic algebra skills.