PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Preliminary genetic decomposition for implicit differentiation and its connections to multivariable calculus
Page: 947
Derivatives are an important concept in undergraduate mathematics and across the STEM fields. There have been many studies on student understanding of derivatives, from graphing derivatives to applying them in different scientific areas. However, there is little research on how students construct an understanding of multivariable calculus from their understanding of single variable calculus. This poster uses APOS theory to hypothesize the mental reflections and constructions students need to make in order to solve and interpret an implicit differentiation problem and examine the connections to multivariable calculus. Implicit differentiation is often the first time students are introduced to the notion of a function defined by two dependent variables, a concept vital in multivariable calculus. Investigating how students initially reconcile this new idea of two variable functions can provide knowledge of how students think about multivariable calculus.