Enhancing 3D graph visualisation in multivariable calculus using graphica3D

Saad, Siti Mariam and Abu Mansor, Siti Nurleena and Azudin, Ahmad Rashidi and Omar, Mahanim (2025) Enhancing 3D graph visualisation in multivariable calculus using graphica3D. International Journal on E-Learning and Higher Education (IJELHE), 20 (2): 5. pp. 74-88. ISSN eISSN: 3030-6663

Abstract

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.

Metadata

Item Type: Article
Creators:
Creators
Email / ID Num.
Saad, Siti Mariam
smariam.saad@uitm.edu.my
Abu Mansor, Siti Nurleena
sitin140@uitm.edu.my
Azudin, Ahmad Rashidi
ahmadrashidi@uitm.edu.my
Omar, Mahanim
mahanim@uitm.edu.my
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > Multivariate analysis. Cluster analysis. Longitudinal method
Divisions: Universiti Teknologi MARA, Shah Alam > Institute Of Continuing Education & Professional Studies (iCEPS)
Journal or Publication Title: International Journal on E-Learning and Higher Education (IJELHE)
UiTM Journal Collections: UiTM Journals > International Journal of e-Learning and Higher Education (IJELHE)
ISSN: eISSN: 3030-6663
Volume: 20
Number: 2
Page Range: pp. 74-88
Keywords: 3-dimensional graphs, GeoGebra, Interactive learning, Multiple integrals, Multivariable calculus
Date: June 2025
URI: https://ir.uitm.edu.my/id/eprint/118699
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