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Abstract: This study used modified schema-based instruction (MSBI) to teach mathematical word problem solving to three students with ASD in fifth and sixth grade. Following explicit strategy instruction, the participants learned to use an 8-step task analysis and a graphic organizer to solve and discriminate between math word problems requiring algebraic reasoning. A multiple probe across participants design was used to establish a functional relation between MSBI and word problem solving with a non-parametric measure (Tau-U) confirming visual analysis of a large effect (.87). Results indicated students increased the number of steps ofthe task analysis solved independently correct, total problems solved, and discrimination ofproblem type. Implications for practice and future research are discussed.
State standards like the Common Core State Standards Mathematics (CCSSM) help educators set targets for mathematical learning experiences. One domain of mathematics emphasized throughout grade levels in the CCSSM is algebra (Common Core State Standards Initiative, 2015). Algebraic reasoning serves as a bridge for the "cognitive gap" students often experience between arithmetic and algebra (Herscovics & Linchevski, 1994; Witzel, 2016). The foundations of algebraic reasoning are laid in early elementary grades as children learn to form generalizations about numbers, notice patterns, and reason about equivalence (Van de Walle, Karp, & Bay-Williams, 2016). For example, identifying whether two groups of objects have an equal quantity of items is an essential prerequisite skill to understanding properties and solving equations. This skill is necessary when deciding whether a given quantity is "enough" or "not enough" for a given task and what further steps might need to be taken. Reasoning is a defining feature of mathematics and is essential for conceptual understanding (NCTM, 2000).
There is a relationship between algebraic reasoning and word problem solving. Powell and Fuchs (2014) found second grade students who struggled with word problem solving performed lower on algebraic reasoning tasks than students who had difficulty with calculation alone. Problem solving experiences in school settings are typically structured in the format of story problems. In the context of word problem solving, stories present situations requiring a mathematical solution (Stein, Kinder, Silbert, & Carnine, 2006). Learning to solve word problems is the basis for learning to solve real-world problems (Van de Walle et al., 2016). Consideration of the "school effects" of mathematics...