Abstract
Functions are essential in Mathematics Education to conceptualise interrelated topics like calculus and trigonometry. However, mathematics pre-service teachers (MPTs) find teaching functions challenging if they do not have adequate pedagogical content knowledge (PCK) to address learners’ misconceptions and errors related to the topic. Using GeoGebra in a socially interactive environment allows MPTs to explore innovative pedagogical approaches in their learning-to-teach functions. GeoGebra could make mathematics more enjoyable and promote multiple representations of functions, which may encourage a deeper understanding of the topic. Hence, this study aimed to investigate the experiences of using GeoGebra in the learning-to-teach functions by MPTs.
Theoretically, this study was underpinned by social constructivism and adapted the technology in social interaction and self-exploration for visualisation and understanding (T2S4VU) conceptual framework. The dimensions in this conceptual framework involve technology and a focus on social interaction and self-exploration to enhance visualisation and understanding.
Interpretivism was adopted as the research paradigm in this study. Thirty-five third-year Bachelor of Education (BEd) students at a South African university specialising in Senior Phase and Further Education and Training (FET) mathematics teaching were purposively selected. A phenomenological research strategy allowed the researcher to interpret how those MPTs experienced the use of GeoGebra in their learning-to-teach functions. This exploratory qualitative study was conducted in three phases: Phase 1 (before MPTs use GeoGebra in their learning-to-teach functions), Phase 2 (MPTs’ use of GeoGebra during their learning-to-teach functions), and Phase 3 (after MPTs use GeoGebra in their learning-to-teach functions). Qualitative data were accumulated using semi-structured one-on-one interviews (Phases 1 and 3) and lesson plans and observations (Phase 2). The data gathered from these phases were deductively analysed through thematic analysis according to the themes/constructs in the T2S4VU conceptual framework: the use of technology, social interaction, self-exploration, and visualisation and understanding. The findings indicate that MPTs experienced the use of GeoGebra as an educational technology that can make the topic of functions less abstract and allow them to
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conceptualise multiple representations (i.e., algebraic and graphical) of functions interactively. Using GeoGebra in a socially interactive environment allows MPTs to learn how to integrate GeoGebra, which they experienced as a supportive learning environment. Exploring functions is considered crucial and beneficial if support and guidance are provided, especially to MPTs unfamiliar with the software. Finally, using GeoGebra to self-explore (e.g., learning through discovery) the transformation of functions in a socially interactive environment could develop a robust understanding of the function concept. Ultimately, MPTs hold positive and constructivist views about using GeoGebra in their learning-to-teach functions. The findings, therefore, contribute to the limited research studies that focus specifically on MPTs’ use of GeoGebra in their learning-to-teach functions within a South African context. Additionally, the study contributes methodologically by adopting the T2S4VU conceptual framework as an analytical lens to collect and analyse data in preparing MPTs to use GeoGebra in mathematics teaching. GeoGebra also has practical value because it is time-efficient. Socially interacting with peers while using GeoGebra created a supportive learning environment for MPTs, and a deeper understanding of functions can be achieved when MPTs explore functions using GeoGebra.
Key words: GeoGebra; functions; mathematics pre-service teachers; learning; technology