Students' conception of partial derivatives of a function of several variables

Abstract

The study aimed to explore and assess students' conceptual understanding of partial derivatives in functions of several variables. A case study research design was employed, with four classes randomly selected for participation. Qualitative data were collected through interviews and open-ended questions developed by the researchers. The analysis was conducted using APOS theory, based on the proposed genetic decomposition. The findings reveal that the majority of students’ understanding falls under action conception, interpreting partial derivatives similarly to single-variable derivatives. Additionally, many students struggled to extend their knowledge from single-variable derivatives to partial derivatives and faced difficulties in converting between algebraic/symbolic and graphical representations. Based on these results, the researchers recommend that educators adopt instructional strategies that foster deeper conceptual understanding, rather than relying on traditional teaching methods.

Keywords: APOS Theory; conceptual understanding; function of several variables; partial derivatives