PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Future Middle Grades Teachers’ Coordination of Knowledge Within the Multiplicative Conceptual Field
Page: 852
We report theoretical and empirical results generated through studying several cycles of a number and operations content course offered to future middle grades mathematics teachers. A main feature of the course is using an explicit, quantitative definition for multiplication to connect a range of topics in the multiplicative conceptual field (Vergnaud, 1983, 1988). Course topics include multiplication and division with both whole numbers and fractions, proportional relationships, and linear functions. The theoretical results include a mathematical analysis of multiplication as coordinated measurement and a (still emerging) psychological framework that emphasizes coordinating diverse cognitive resources. Empirical data come from clinical interviews conducted with 6 future teachers enrolled in the content course in Fall 2016. One empirical result is the importance of connecting partitioning quantities, dividing measurements by whole numbers, and multiplying measurements by unit fractions when expressing relationships between quantities through multiplication expressions and equations.