Chapter 10: Understanding Elementary Students’ Mathematical Thinking Using Visual Methodologies

Visual representations are a way for children to make sense of and develop their own inherent meaning of a mathematics concept. Mathematical story problems that encourage children to share their thinking visually have the power to uncover mathematical ideas in ways that words might not. As part of an elementary mathematics methods course requirement, prospective teachers each implemented a story problem with a focus student, analyzed their student’s work, and completed a reflection based on their analysis. In this chapter, we examine two elementary students’ multimodal responses to a story problem. We explore the following research question: “How do second-grade students visually represent their thinking when solving story problems and what does that communicate about their mathematical understanding?” We use a multimodal approach to analyze visual data. Data reveal notable differences in the way these two students use visuals to translate their thinking mathematically, particularly as it relates to the synergy between students’ use of symbolic, pictorial, and graphic representations. These findings offer valuable insight into students’ conceptual and procedural knowledge, adding depth to our understanding of student thinking. They also illustrate the power of using visual methodologies to expand prospective teachers’ attention to and interpretation of students’ thinking. We conclude by discussing implications for research and pedagogy.