Backward Transfer From Quadratic Functions Instruction Onto Different Levels of Development of Conceptions of Linear Function

This study examined backward transfer , which we define as how students’ ways of reasoning about previously encountered concepts are modified when learning about new concepts. We examined the backward transfer produced when students learned about quadratic functions. We were specifically interested in how backward transfer may vary for students whose incoming conceptions about linear functions were at different levels of development. Our study comprised a two-week quadratic functions instructional unit emphasizing covariational reasoning bracketed by pre- and postassessments and interviews. Our analysis focused on four students with incoming linear functions conceptions at different levels of development. Findings revealed that students experienced different kinds of backward transfer. This study generated new insights into backward transfer in the context of mathematics education.