Geogebra-Assisted Teaching Experiment on Students' Conceptual Change in Multivariable Calculus

This study explores students’ conceptual change in understanding gradients and tangent planes through a GeoGebra-assisted teaching experiment in a multivariable calculus course. The study involved eight second year undergraduate mathematics students enrolled at the Mathematics Department of a university in West Java, Indonesia. Data were collected through diagnostic tests, classroom observations, students’ written work, and reflective notes, and semi sructured interviews, then analyzed qualitatively using coding, triangulation, and retrospective analysis.The findings revealed that, at the outset, students were able to perform symbolic differentiation of partial derivatives but struggled to interpret the gradient vector conceptually or relate it to the tangent plane. Through guided use of GeoGebra, students gradually reconceptualized the gradient as representing both the direction and rate of steepest ascent, demonstrating a shift from procedural to structural understanding. This study contributes to the theory of conceptual change by illustrating how dynamic visualization and guided reinvention can facilitate the transformation of students’ procedural knowledge into coherent conceptual models. Practically, the findings provide insights for designing technology-assisted instruction to address persistent misconceptions in multivariable calculus learning.