The Effects of Blended Instruction and Visual Representations on Area Problems Involving Quadratic Expressions for Secondary Students with Mathematics Difficulties

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The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions. The instructional package included a blend of research-based instructional practices for secondary students with LD (i.e., concrete-representation-abstract instruction, graphic organizers, and components of explicit instruction) and the process standards recommended by the National Council of Teachers of Mathematics process standards (i.e., problem solving, reasoning and proof, communication, connections, and representations). A concurrent embedded mixed methods design was utilized with the quantitative data representing the main strand, while qualitative data provided supplemental data (Creswell & Clark, 2011). Specifically, the quantitative data were collected from a multiple-probe design across two groups replicated over five students. The participants were five high school students identified as a learning disability or difficulty in mathematics. The qualitative analysis of transcriptions from instructional sessions, field notes, and work samples was completed on one participant, who represented a critical case (Creswell, 2007). Results of the study indicated that all five participants improved their algebraic accuracy on tasks involving quadratic expressions embedded within an area context. Further, providing multiple representations allowed participants to make connections to algebraic content and enhanced their metacognition. Additionally all participants maintained their performance up to six weeks following intervention. Three participants also transferred the performance to novel and more complex tasks. The study suggests that students with MD may be successful with higher-level algebra content when provided blended instruction and visual representations.