PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Student Understandings of Division, Rate, and Derivative
Page: 2-358
We have conducted a preliminary investigation of university Calculus students’ conceptions of division and rate of change because these ideas are used to define the derivative. We conducted exploratory interviews focused on building models of student understandings of division and rate. Retrospective analysis revealed the students interviewed had a variety of meanings for these concepts. Difficulty thinking about division as multiplicative comparisons of relative size was observed in multiple students. Additionally a student who explained rate as an amount added in equivalent x-intervals struggled to determine if a quantity was changing at a constant rate over unequally spaced x intervals. We hypothesize that difficulty conceptualizing division as quotient, and quotient as a measure of relative size2 of two quantities, obstructs students’ understandings of average and instantaneous rate of change. This research will further our goal of understanding student difficulties with derivatives.