All students, including students with disabilities, are expected to learn mathematics at high levels. As algebra is considered to be the gatekeeper to higher level mathematics and beyond, it is essential for teachers to use effective practices, including the use of manipulatives, to support student learning. This alternative dissertation is comprised of three studies that explored teaching algebra to secondary students with high-incidence disabilities. The first was an evidence-based systematic review of literature investigating instructional practices to teach algebra to secondary students with high-incidence disabilities. Twenty studies published from 1999-2019 were reviewed and analyzed, of which 14 met the standards of high quality set by the Council for Exceptional Children (CEC), and five practices earned the label of potentially evidence-based (i.e., concrete-representational-abstract framework, manipulatives, enhanced anchor instruction, schema based instruction, and peer-assisted learning strategies). The second study used an alternating treatment design to compare the effectiveness of concrete algebra tiles to virtual algebra tiles to support middle school students with disabilities as they solved linear equations. Students were successful solving linear equations regardless of the type of manipulative they used, but preferred using the virtual tool. The final study used a multiple probe across behaviors, replicated across participant design to examine the effectiveness of the VA framework to support secondary students with high-incidence disabilities in their acquisition of algebra skills. A functional relationship existed between the VA framework and student performance on algebra probes, and students scored better on maintenance probes compared to baseline data. While there remains a need for more high-quality research examining effective practices in supporting secondary students with high-incidence disabilities in the area of algebra, the studies in this alternative dissertation suggest manipulatives, both as a stand-alone tool and as part of a process is an effective, and efficient intervention.
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