Effect of Graphica3d on students’ visualization and sketching of 3D graphs in multivariable calculus

Developing skills in visualizing, interpreting, and sketching three-dimensional (3D) graphs is essential for learning multiple integrals, a key topic in multivariable calculus. However, many students struggle with these skills, creating barriers to understanding and solving related problems. While dynamic mathematics software like GeoGebra can support visualization, existing teaching materials often lack structured integration of technology to strengthen 3D graph learning. To address this gap, an interactive module, Graphica3D, was developed. The module combines explanatory notes on 3D graphs with embedded GeoGebra applets that enable interactive visualization. This study evaluated the effectiveness of the Graphica3D module using a pre–post test design. Participants were 44 engineering students enrolled in Further Calculus for Engineers at UiTM Cawangan Pulau Pinang. Data were analyzed using a non-parametric test, namely ANOVA-type statistics and results showed significant improvements in students’ ability to visualize and sketch 3D graphs. Moreover, no interaction between test performance (pre vs. post) and gender was observed, suggesting that the module benefits students equitably. These findings demonstrate that Graphica3D is a valuable supplementary tool for enhancing spatial visualization in multivariable calculus and for supporting inclusive teaching practices in higher education mathematics.