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Teaching algebra-based concepts to students with learning disabilities: The effects of preteaching using a gradual instructional sequence
by Sarah Jean Watt
An Abstract of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Teaching and Learning Special Education) in the Graduate College of The University of Iowa May 2013
Thesis Supervisor: Associate Professor William J. Therrien
Research to identify validated instructional approaches to teach math to students with LD and those at-risk for failure in both core and supplemental instructional settings is necessary to assist teachers in closing the achievement gaps that exist across the country. The concrete-to-representational-to-abstract instructional sequence (CRA) has been identified through the literature as a promising approach to teaching students with and without math difficulties (Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Cass, Cates, Smith, & Jackson (e.g. CSA), 2003; Flores, 2010). The CRA sequence transitions students from the use of concrete manipulatives to abstract symbols through the use of explicit instruction to increase computational and conceptual understanding.
The main purpose of this study was to assess the effects of preteaching essential pre-algebra skills on the overall algebra achievement scores for students with disabilities and those at-risk for failure in math. Specifically the study examined the following research questions: (1) What are the effects of preteaching math units using the CRA instructional sequence on the algebra achievement of students with LD and those at risk for math failure? (2) What are the effects of preteaching math units using the CRA instructional sequence on the transfer of algebra-based skills of students with LD and those at risk for math failure to the general education setting? (3) What are the effects of preteaching math units using the CRA instructional sequence on the maintenance of algebra-based skills for students with LD and those at risk for math failure?
Summary of Study Design and Findings
Thirty-two students enrolled in one of four 6th grade classrooms across two elementary schools participated in this study. Sixth grade students who currently receive tier 2 or tier 3 supplemental and intensive instruction in math; and those identified as having a math learning disability will be participants. A treatment and control, pre/post experimental design was used to examine the effect of the intervention on students' math achievement. The intervention was replicated across two math units related to teaching algebra-based concepts: Solving Equations and Fractions. The treatment condition consisted of a combination of preteaching and the use of the CRA instructional sequence. Prior to each unit, Solving Equations and Fractions, researchers pretaught students 3 essential prerequisite skills necessary for success in the upcoming unit, at the concrete, representational, and abstract levels of learning. Each preteaching session lasted for ten days, 30 minutes each day. Immediate, delayed, and follow-up measures were used to support the examination of the research questions and hypotheses.
Overall findings indicate that the combination of preteaching using the CRA gradual sequence is effective at improving the overall algebra performance for students with disabilities.