PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Mental constructions involved in differentiating a function to a function power
Page: 1412
Functions of the form ! ! = (! ! )!(!), including constant functions, power functions, and exponential functions, are fundamental examples of functions that differential calculus students should be able to differentiate. Yet students often struggle to distinguish between these forms. Drawing on APOS (Action-Process-Object-Schema) theory as well as Piaget and Garcia’s triad of schema development, this paper offers a genetic decomposition of the schemas students build for determining the derivative of a function to a function power. In particular, we analyze how students determine which differentiation rules to use with different function structures of a function to a function power and how students construct a conception of logarithmic differentiation. An initial genetic decomposition informed by existing literature was refined using the results of a series of three clinical interviews with each of two calculus students. Findings include the necessity of a strong background in functions, logarithms, and other differentiation rules.