PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Student Thinking of Function Composition and its Impact on their Ability to Set up the Difference Quotients of the Derivative
Page: 2-565
While the limit in the definitions of the derivative is troubling to many students, a difficulty that preceded this confusion was observed: students were not able to correctly set up the difference quotients as required in the definitions. The purpose of this study is to investigate the cognitive processes involved in setting up the difference quotients and the associated errors. This explanatory case study seeks to explain why these particular errors occur from the perspective of student thinking of function composition. At the end of the study, a framework that aggregates criteria used (by past studies and this study) to assign student membership into a function conception category will be produced in an attempt to move towards a systematic classification of students’ cognitive processes. Implications from this study can inform teaching practices by exposing students to expected errors. As observed from the data, this can lead to rich discussions on the concept of function itself.