How scaffolding rate of change problems promotes positive mathematical transferability

This thesis reports on action research conducted by the author while teaching rate of change problems to first-semester Calculus students at a public university in the United States, with the purpose to ensure transfer of learning, and increase students’ conceptual understanding of rate of change and their performance on solving rate of change problems. The action research cycles (planning, action/implementation, evaluation) involved scaffolding to promote positive mathematical transferability through conceptual understanding. The result is a Lesson Guide consisting of a learning task designed using scaffolding and abiding by principles developed and supported by the research literature on the theory of transfer, an assessment task, and a self-evaluation tool for students. Future action research cycles may be informed by the Lesson Guide developed in this study. Calculus I instructors can use the Lesson Guide in the teaching of rate of change problems. This study contributes to the progressive perspective of the transfer of learning in mathematics education and adds to the growing number of theses conducted with action research methodology