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Abstract: Mathematics education highlights the importance of helping students understand mathematical content and the ability to think critically about mathematics. Mathematical practice standards outline expectations for engaging students in meaningful mathematics activities to encourage a deep understanding of mathematical concepts and content. For some students, however, engagement in mathematical practices may not come naturally, and therefore will need to be explicitly taught. Students with autism spectrum disorder have communication and executive functioning deficits that are likely to decrease their engagement in mathematical practices. A multiple probe across behaviors single-case design was used to investigate the effectiveness of a modified schema-based instructional (MSBI) strategy on the use of mathematical practices of a middle school student with autism spectrum disorder (ASD). The student was taught to solve equal group, proportional, and percent of change word problems using MSBI. Results provide evidence of a functional relation between MSBI and mathematical practices with three demonstrations of an effect. Results from social validity questionnaires also support the importance of the skills taught, along with an observed behavioral change for the student during mathematics instruction in his classroom setting. Implications for teaching and future research are discussed.
Mathematics education is no longer thought to be a one-dimensional task requiring memorization of facts and figures. Students today are asked to use critical thinking to prepare them for unique situations they will face outside school walls. Mathematics education reform emphasizes the importance of both what students should know about mathematics as well as how students engage in mathematical tasks (Kilpatrick et al., 2001). The Common Core State Standards for Mathematics include not only content standards, but also standards for mathematical practice. The practice standards (i.e., mathematical practices) are based on process standards published by the National Council for Teachers of Mathematics (NCTM, 2000) along with the strands of mathematical proficiency reported in the National Research Council's report "Adding It Up" ([NRC], Kilpatrick et al., 2001). Together, the content and practice standards in the Common Core State Standards emphasize the importance of helping students understand mathematics and communicate their mathematical understanding. Difficulty in communication is one of the diagnostic criteria for individuals with autism spectrum disorder (ASD). Therefore, teachers need ways to help students with ASD communicate their mathematical thinking in a way...