Pre-service elementary education teachers’ solutions for word problems: Using strip diagram vs. algebraic approach

Creating, connecting, and translating multiple representation are “important cognitive processes that lead students to develop robust mathematical understandings” (Huntley, Marcus, Kahan, & Miller, 2007, p. 117). These cognitive processes are also considered to be crucial elements of preservice teachers’ (PSTs’) pedagogical content knowledge (Dreher, Kuntze, & Lerman, 2016). In order to investigate PSTs’ cognitive processes regarding multiple representations, we collected data from 73 PSTs, who enrolled in a mathematics content course for elementary education majors in Spring 2019. We analyzed PSTs’ solutions to an assessment task following seven weeks of instruction related to the use of strip diagrams, double number lines, and algebraic equations to solve problems involving ratio and proportional relationships and word problems (Beckmann, 2014). The PSTs were asked to determine the total number of cookies Bonnie baked when given information about the cookie types (e.g., 1/3 of the cookies were chocolate chip, 1/6 were peanut butter, 1/6 were oatmeal raisin, and 24 were cinnamon) in two ways: using a strip diagram and writing and solving an algebraic equation. We used an error analysis technique (Radatz, 1979) to sort and interpret the responses based on fluency with strip diagram and algebraic solutions. The PSTs who exhibited complete reasoning were able to use both representations and the PSTs who exhibited incomplete reasoning were unable to use at least one of the representations. The preliminary analysis of solutions revealed the following themes in the PSTs’ strategies (Table 1).