An analysis of how visualisation capabilities in dynamic geometric software develop meaning-making of mathematical concepts in selected Grade 11 learners

Abstract

Visualisation plays a central role in developing mathematical ideas because it can be used to make these ideas explicit and visible, and thus has the potential to advance understanding. This study centred around the GeoGebra Literacy Initiative Project (GLIP), a teacher development initiative in Mthatha that aimed to grow and develop appropriate Information and Communication Technology (ICT) skills in teachers, to harness the teaching and learning potential of GeoGebra. GeoGebra is a dynamic geometric software package that is very interactive and makes use of powerful features to create images which can be moved around the computer screen for mathematical exploration. This research project was located within GLIP and analysed how GeoGebra applets develop conceptual and procedural understanding in selected Grade 11 learners. One aspect of GLIP was for teachers to use GeoGebra applets that they had developed themselves and implemented in their classrooms in pre-determined cycles that were aligned to the curriculum. My study specifically focused on how the selected learners made use of these applets and explored how learning had taken place in terms of developing mathematical meaning-making. This interpretive research study was designed as a case study. The case was a cohort of selected Grade 11 learners who had been taught by GLIP teachers, and my unit of analysis was the learners' interaction with the applets. A screen capturing software package was used to capture learners' interactions with the GeoGebra. My data consisted mainly of recorded observations and interviews. An analytical framework derived from the works of Kilpatrick, Swafford, and Findell (2001) and Carter et al. (2009) guided and informed the data analysis of the learners' activities with the GeoGebra. The theoretical orientation of this study was constructivist learning. An in-depth analysis and detailed descriptions of the participants' interactions enabled me to gain a comprehensive understanding of their meaning-making processes in a technological classroom context. An analysis across the participants identified distinguishable patterns or differences in the development of the learners' mathematical proficiency and making sense of mathematical ideas. The research argued that technology enabled visualisation was a powerful tool to not only enrich mathematically activities, but to also enrich conceptual and procedural understanding. The findings recognised that exploration of, or manipulation on mathematical objects in GeoGebra was a key activity in the participants' meaning-making process. It also enabled learners to offer self-proclaimed theories