Cognitive readiness for solving equations

Abstract

In this chapter we examine cognitive readiness for solving equations in the domain of pre-algebra. We describe the knowledge required to solve a multistep equation, and present a novel technique for developing assessment items and a novel assessment item format, designed to measure both the prerequisites of cognitive readiness for solving equations and the skills themselves. Assessment items were drawn from the solution path of a complex multistep equation. The items used a next step format, which asked students to write only the first step of their solution. Using a sample of 42 middle school students, data were gathered on item performance and how performance on the next step item compared to performance on the more traditional solve for x format. Unsurprisingly, students performed higher the simpler the equation was but large drops in performance occurred at steps that were essential to isolating a variable (i.e., applying the equality properties of addition and multiplication). Students performed higher on the traditional items compared to next step items and there was some evidence that performance on the next step item predicted performance on the traditional items. Assessment and instructional implications of this work include diagnosing precisely where in the solution path students have difficulty, which is tantamount to identifying students' cognitive readiness for solving equations.