The incorporation of GeoGebra as a visualisation tool to teach calculus in teacher education institutions: the Zambian case - Kangwa, Lemmy (Rhodes University, Faculty of Education, Department of Education)
This qualitative case study investigated teacher educators' (lecturers) use of the dynamic mathematics software, GeoGebra, to teach calculus in three teacher education institutions (TEIs) in Zambia. Visualisation, a key characteristic of GeoGebra, is increasingly gaining recognition of playing a critical role in mathematics teaching and learning, especially in problem solving tasks. It is considered a powerful didactical tool for students to construct mental and physical representations that can enhance conceptual understanding of mathematics. GeoGebra is a visualisation tool that can be used for problem-oriented teaching and foster mathematical experiments and discoveries. GeoGebra's inherent visualisation characteristics align well with the teaching of calculus, the mathematical domain of this study. The study (whose research methodology was underpinned by the interpretive paradigm) was undertaken with a broader goal of designing and implementing GeoGebra applets and instructional materials on various calculus topics. The study is located within the "Teaching and Learning Mathematics with GeoGebra (TLMG) project" "“ a project that involves mathematics teachers and lecturers in Zambia. The case in this study is the six mathematics lecturers who co-designed and used GeoGebra applets to teach derivatives and integrals to pre-service mathematics teachers in TEIs. The unit of analysis therefore is the six lecturers' use of GeoGebra as a visualisation tool to teach calculus to enhance conceptual understanding, their perceptions and experiences of using GeoGebra and the enabling and constraining factors of using GeoGebra to teach and learn mathematics. The data for the study were video recordings of observations and interviews of lecturers. The data was analysed thematically and was guided and informed by an analytical framework adopted from the theory of constructivism "“ the umbrella theoretical framework of this study "“ and the models of Technological Pedagogical Content Knowledge (TPACK), and the Technology Acceptance Model (TAM). A detailed analysis of the lecturers' interactions with the applets enabled me to gain insights into the participants' experiences and perceptions of GeoGebra applets in the teaching and learning process. The findings of the study revealed that the visualisation characteristics of GeoGebra generally enhanced the conceptual understanding of calculus. It also revealed that adequate training, coupled with sufficient knowledge of the subject matter in calculus, were necessary for lecturers to use GeoGebra effectively, and that the lack of resources and expertise were major hindrances in the use of GeoGebra to teach mathematics in TEIs. It also revealed that there is a need to equip GeoGebra with other features that would make it more versatile, and suggested a teaching approach that would complement the use of conventional methods and GeoGebra to provide a link between abstract and concrete concepts of calculus.
Keywords: GeoGebra; Calculus-- Study and teaching (Secondary) Zambia; Visual learning