Pre-service teachers' perceptions of the use of representations and suggestions for students' incorrect use

In this study, we investigated how elementary pre-service teachers (PSTs) perceive using representations in teaching mathematics and what fractional representations (e.g., manipulatives or models) they suggest to guide students' incorrect use of representations in learning fractions. A written questionnaire was administrated to 151 PSTs at a large Southwestern university in the US. An inductive content analysis approach including both qualitative and quantitative analyses was used to analyze the data. Findings suggested that fraction-related topics were the PSTs' main choices for using representations, and they valued understanding concepts and making connections between representations and concepts. Also, the findings showed the PSTs' tendency to use models procedurally and their predominant dependency on a few types of models (e.g., wedged circular models) in guiding students who use representations incorrectly. Implications for designing mathematics methods courses that support effective use of representations are discussed.