The Role of Covariational Reasoning in Pre-Service Teachers’ Meanings for Quadratic and Exponential Relationships

Researchers have indicated that students have difficulties recognizing quadratic and exponential change and do not maintain productive meanings for these relationships. Other researchers have documented that students are capable of developing productive meanings for mathematical ideas via covariational reasoning. This dissertation reports the results of an investigation into ways in which preservice teachers can leverage covariational reasoning to develop meanings for quadratic and exponential relationships. I collected data by engaging two preservice teachers in semi-structured clinical interviews and a semester long teaching experiment. My analyses reveal that whereas in the pre-interviews, the participants did not have meanings that supported differentiating between quadratic and exponential relationships, engaging in activities that offered opportunities to reason covariationally during the teaching experiment supported in developing productive meanings for quadratic and exponential relationships. By the end of the teaching experiment, the preservice teachers had developed ways to differentiate between these two relationships