PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
Discursive Approach to Students’ Thinking About the Derivative
Page: 1-360
This study explores features of university calculus students' discourses on the derivative using a communicational approach to cognition. The data was collected from a survey and interviews in three calculus classes at a public Midwestern university. During the interview, 12 students explained their solution processes on the survey problems. The analysis of interviews focuses on students' descriptions about the derivative and the relationships between a function, the derivative function, and the derivative at a point. The results show that their descriptions were closely related to how they think about the derivative as a number and as a function. A common description of the derivative as a tangent line, which is a point-specific object but also a function defined on an interval, was identified. This description was closely related to their use of the word, "derivative" for both "the derivative function" and "the derivative at a point."