RUME 28
2026
Alexandria, Virginia
A Comparative Case Study of Student Reasoning About Planes and Vertical Change in Multivariable Differential Calculus
Page: 109
This is part of a larger APOS-grounded study where we investigate students’ reasoning about and between multiple components of multivariable differential calculus. We report on the different reasoning of the strongest interview participants from two sections taught by the same instructor. One section used the locally linear approach; the other was taught traditionally. The locally linear approach leverages the geometric understanding of the point-slopes equation of a plane to help students develop key ideas for the differential calculus of two-variable functions. We used semi-structured interviews to investigate students’ understanding of multiple components of differential calculus and the relations established between those components. In this report, our analysis focuses on the relations that two high-performing students established between the components of plane and vertical change. Findings suggest that the locally linear approach may help students obtain a deeper understanding of vertical change on a plane than traditional instruction.