Abstract
We discuss results of a second research cycle on student understanding of the differential calculus of functions of two variables, focusing on the role that slope plays in a meaningful understanding of plane, tangent plane, total differential, and directional derivative. Results compare the performance of students in a section that used research-based activities and a corresponding pedagogical strategy, to that of students in a regular section.
We show how students using the research-based activities were able to construct slope as an object they could build upon in order to understand other important notions of the differential calculus, while students in the regular section showed the same understandings of slope in the differential calculus as reported in previous studies.