Harnessing GeoGebra as a modelling tool to mitigate undergraduate engineering mathematics students’ misconceptions and errors associated with complex numbers

Abstract

This article reports on the effectiveness of GeoGebra as a modelling tool to mitigate undergraduate engineering mathematics students’ misconceptions and errors associated with complex numbers. GeoGebra is a transformative open-source mathematical software that allows students to visualise and manipulate mathematical objects on different types of digital devices. Despite the centrality of complex numbers in studying vital mathematical concepts such as vectors, eigenvalues, and eigenvectors, studies revealed a prevalence of misconceptions and errors associated with complex numbers. Some students confuse the complex number’s representations; others view the representations as autonomous and unrelated. The study adopted a methodological pragmatism research design. It involved volunteering first-year first-semester engineering mathematics students from purposefully selected specialisation groups that included mechanical, industrial, and electrical engineering, at a South African university. The empirical intervention was underpinned by the Realistic Mathematics Education (RME) framework; the data for students’ misconceptions and errors were collected from their pre-test and post-test scripts and analysed qualitatively using Donaldson and Orton’s errors categories as a lens and quantised or quantitised using a chi-square test. The total frequencies of misconceptions and errors yielded a chi-square statistic of 7.9584 and a p-value of 0.004787, which was statistically significant at p < 0.05.

Contribution: The study’s key findings strongly suggest that GeoGebra-facilitated intervention effectively mitigates undergraduate engineering mathematics students’ total misconceptions and errors associated with complex numbers more than the traditional intervention. This indicates teachers can harness GeoGebra, reducing students’ misconceptions and errors associated with complex numbers and improving the quality of teaching and learning complex numbers and tertiary engineering mathematics education.