PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Reasoning covariationally about constant rate of change: The case of Samantha
Page: 563
We present the results of a teaching experiment designed to foster a pre-service secondary teacher’s construction of a scheme for constant rate of change through engendering reflecting and reflected abstractions. Although the research participant developed a productive conception of rate of change as an interiorized ratio, images of chunky continuous covariation imposed an obstacle to her ability to reason efficiently across a variety of contexts. The participant’s rate of change scheme was grounded in reflected abstraction, which enabled her to become consciously aware of its essential aspects and to appreciate its applicability across a variety of contexts.