Future Teachers’ Use of Multiplication and Fractions When Expressing Proportional Relationships

The purpose of this study was to investigate how six future middle grades mathematics teachers used explicit, quantitative definitions for multiplication and for fractions when reasoning about proportional relationships. The future teachers were recruited from a preparation program in the United States based on their performance on a fractions survey. The data collection consisted of 1-hour semi-structured interviews with each future teacher. An explanatory case study was used to make comparisons across the future teachers. Results revealed that explicit use of the quantitative definition of multiplication is a helpful organizing tool for future teachers to generate and explain equations for proportional relationships.