Erik Jacobson

Using Coordination Classes to Analyze Preservice Middle-Grades Teachers’ Difficulties in Determining Direct Proportion Relationships

Numerous studies, primarily conducted with school children, have reported the misapplication of direct proportion reasoning strategies to situations in which two quantities do not covary in a fixed ratio relationship. In the present study, preservice middle-grades mathematics teachers (N = 28) evidenced similar difficulties in a content and methods course. In particular, they correctly explained relationships between quantities that were not direct proportions but still tried to solve problems involving those quantities using direct proportions. To understand how this could occur, we used the coordination class construct (diSessa and Sherin, International Journal of Science Education 20(10):1155–1191, 1998) to analyze knowledge resources that the preservice teachers used before, during, and after a unit on proportions. Where past research has often characterized the misapplication of direct proportion reasoning strategies as the result of intuitive or impulsive responses to familiar missing-value problem presentations, our analysis suggests that recognizing directly proportional relationships is more complex than carefully interpreting problem statements.