How a Measuring Perspective Influences Pre-service Teachers Reasoning about Fractions with Discrete and Continuous Models

Abstract

How teachers interpret and express fractions critically influences their teaching and their students’ fraction knowledge. Internationally, the mathematics education community has been studying ways to enhance pre-service elementary teachers’ rational number knowledge, particularly fractions. To address the challenge of augmenting pre-service teachers’ fraction knowledge warrants theoretical and empirical revisions to standardized practices for teaching fractions. This study investigates how reexamining fractions from a distinctive measuring perspective influences pre-service teachers’ reasoning about fractions. For four 75-minute sessions, 46 pre-service teachers enrolled in a teacher preparation program at a university in the United States revisited fractions from a measuring perspective. They engaged in tasks that focused on comparing continuous quantities and identifying relative magnitudes. The data for this study comprise their pre- and post-tests that assessed how they identify and represent fractions with discrete and continuous models. For each model, we analyzed participants’ reasoning by attending to their written strategies. Findings revealed three main strategies: partition, construction, and symbolic manipulation. In general, participants expressed more strategies on the post-test for all fraction models. Partitioning was the most frequent strategy on the pre- and post-tests. However, the frequencies of strategies changed after the intervention. For example, with all models, there was an increase in partitioning strategy and a decrease in symbolic manipulation strategy. The results highlight affordances of a measuring perspective to support participants to shift from procedural strategies such as symbolic manipulation to more conceptual strategies to identify and represent fractions.