PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Slope and Derivative: Calculus Students’ Understanding of Rates of Change
Page: 299
Studies have shown that students have difficulties with the concepts of slope and derivative, especially in the case of real-life contexts. I used a written survey to collect data from 74 differential calculus students. Students answered questions about linear and nonlinear relationships and interpretations of slope and derivative. My analysis focused on students’ understanding of slope as a constant rate of change and derivative as an instantaneous rate of change, and what these meant in the context of the problems. Preliminary results indicate that students have more success with slope questions than derivative questions (McNemar’s test, p<0.05), and that while students correctly use the slope of a linear relationship to make predictions, they do not demonstrate an understanding of the derivative as an instantaneous rate of change and an estimate of the marginal change.