Engendering Algebraic Readiness through Pictorial Representations

Prior to leaving middle school, students are expected to be able to solve linear equations with one unknown using multiple modes of representation, including pictorial models. Although solving these linear equations is important, many students do not have the conceptual understanding to solve these types of linear equations successfully. In this article, the authors report on an investigation of the ways that middle school students use pictorial representations to set up and solve word problems involving linear equations with one unknown. A multiple case study design was used to analyze 16 students' responses to two word problems involving linear equation tasks. Findings revealed that students were able to invoke the equivalence-relation meaning of the equal sign, apply properties of mathematical operations, use definitions of operations, and use strategic decomposition to set up and solve word problems involving linear equations with one unknown. The findings further suggest that the use of pictorial representations offered students multiple points of entry for setting up and solving word problems successfully.