Enhancing 3D Graph Visualisation in Multivariable Calculus Using Graphica3D

One of the biggest challenges in learning multivariable calculus, particularly multiple integrals, is developing the skills to visualise, interpret and illustrate 2-dimensional (2D) and 3-dimensional (3D) graphs. These skills are crucial, as students must accurately identify integration regions and determine the limits of integration. However, many existing teaching materials for multivariable calculus often lack technological integration to support 3D graph visualisation, making it difficult for students to develop these essential skills. To address this gap, Graphica3D, an interactive educational module, has been created. The module integrates GeoGebra, an open-source mathematical software, to provide an interactive learning environment for exploring 2D and 3D graphs. In addition to explanatory notes on 3D graphs, Graphica3D features a GeoGebra applet that allows students to visualise various 3D graphs and their projections onto coordinate planes. The effectiveness of Graphica3D was evaluated through a survey of 37 engineering students enrolled in Further Calculus for Engineers at UiTM Cawangan Pulau Pinang. Before using the module, 40.5% of students admitted to struggling with 3D graph visualisation and sketching. After its implementation, all students agreed that the module enhanced their ability to visualise, interpret and sketch 3D graphs. The module’s ease of use and interactive design make it a valuable supplement to traditional teaching methods, fostering a more visual and intuitive understanding of complex mathematical concepts.