Deepening Learners' Conceptualization of Functions Using Autograph Technology: An APOS Theory Perspective

The use of dynamic mathematical software as pedagogical tools in mathematics education is widely believed to enrich learning experiences and offer enhanced opportunities for learners to reconceptualize mathematical content. However, there is a dearth of empirically supported literature on how these technological tools facilitate learners’ construction of mathematical knowledge. This study employed the Action–Process–Object–Schema (APOS) theoretical lens to explore the utilization of Autograph technology in deepening learners’ conceptualization of hyperbolic functions at a marginalized rural high school in South Africa. The study adopted a descriptive qualitative case study methodology, where data were collected through diagnostic testing and task-based clinical interviews. Qualitative and textual analysis of data revealed compelling evidence that the representational affordance of Autograph facilitates capacity for logical and reflective thinking, which ultimately promotes adaptive reasoning. The participant learners were able to encapsulate the hyperbolic function concept as an object in totality that could be transformed or manipulated, as demonstrated by their flexibility in switching between the algebraic and graphical representations of the function. The study cogently recommends that Autograph, and other relevant mathematical software, should be made available to mathematics teachers, particularly in marginalized schools in South Africa, and targeted efforts be made to develop the teachers’ technical and pedagogical competency. Further research is recommended to explore the use of Autograph technology in the teaching of other problematic topics, such as geometry, measurement, statistics and probability.