The Effectiveness of GeoGebra for Developing Mathematical Knowledge in Transformations of Functions and Graphs
DOI:
https://doi.org/10.57125/FED.2025.12.19Keywords:
GeoGebra, Mathematics, Knowledge, Transformations in functions and graphs, STEMAbstract
This study aimed at assessing the effectiveness of GeoGebra while exploring how dynamic visualisation supports connections between symbolic rules and graphical behaviour, and examining students’ engagement with GeoGebra applets during active learning within the SciMathUS bridging programme at Stellenbosch University in South Africa. A sequential explanatory mixed-methods design, a two-phase research approach where quantitative data were first collected through a pre-experimental design, after which the results were used to inform and conduct a second phase of qualitative data collection through a case study design guided by Yin’s (2009) conditions for case selection to explain, interpret, or elaborate on the initial numerical findings. The sample for the study consisted of 48 students drawn from a cohort of 99, constituting a convenience sample. The intervention included active-learning tactics and GeoGebra-based activities across several computer-lab sessions. The data collected were analysed using paired t-tests and content-marking analysis. The quantitative findings from the analysis revealed statistically significant improvements (p < 0.05) with large-to-huge effect sizes (Cohen’s d = 0.95–2.33), thereby confirming the rejection of the null hypotheses. The qualitative findings indicated that GeoGebra strengthened structural understanding by linking algebraic and graphical representations, enabling students to generalise transformation properties across various functions, including trigonometric ones. Students demonstrated more concise solution steps and greater confidence in visualising and articulating transformations. Demonstrated statistically significant improvements (p < 0.05) with substantial effect sizes, corroborating the rejection of null hypotheses. The study emphasises the importance of integrating dynamic technology into mathematics instruction to foster a deeper conceptual understanding and promote active learning. It recommends the broader adoption of GeoGebra as an instructional tool to address persistent challenges in learning function transformations. These findings affirm the educational benefits of dynamic mathematics environments and advocate for more participatory, technology-enhanced STEM education.
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