PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Calculus students’ understanding of interpreting slope and derivative and using them appropriately to make predictions
Page: 263
Studies have shown that students have difficulty with the concepts of slope and derivative, especially in the case of real-life contexts. Following up from a previous study, written surveys were used to collect data from 69 differential calculus students, and 7 clinical interviews were conducted. On the surveys, students answered questions about linear and nonlinear relationships and interpretations of slope and derivative. They also critiqued the reasoning and accuracy of a hypothetical person’s predictions. In interviews, students explained their thought processes and reasoning while answering questions similar to the written survey but in a different context. Results indicate that students struggle with knowing what the derivative represents and how to use it appropriately to make predictions. These struggles might stem in part from students’ incorrect interpretations of slope as a ratio of totals, as opposed to a ratio of changes over a particular interval.