An exploration of the use of virtual manipulatives in enhancing understanding of circle geometry : a case of level 4 national vocational students

Abstract

This study explored the impact of virtual manipulatives (VMs), specifically GeoGebra, on enhancing National Certificate Vocational (NC(V)) Level 4 students’ understanding of circle geometry. It investigated how technology-integrated instruction can address learning challenges in Euclidean Geometry. The research was guided by three key objectives: (i) to identify the challenges students face in understanding circle geometry (ii) to examine the nature of VM-based activities that promote comprehension, and (iii) to determine how virtual tools help minimise learning barriers. The study was framed within the Pirie-Kieren theory of the growth of mathematical understanding, which views learning as a dynamic and recursive process. A spiral action research methodology was employed, progressing through three instructional phases: conventional teaching, practical hands-on activities and VM-based learning using GeoGebra. Thirty Level 4 students from Molapo Campus, located in the South West Gauteng TVET College, participated in the study. Qualitative data was collected through semi-structured interviews, questionnaires, as well as pre- and post-tests structured in line with the Pirie-Kieren theory of the growth of mathematical understanding. The final results showed that the baseline assessment revealed significant gaps in students’ foundational understanding of circle geometry. In particular, many students struggled to recognise and apply key properties of circles, especially when these properties needed to be used in combination with triangles and straight lines. Although the introduction of practical instruction improved student engagement—most notably during lessons involving cyclic theorems—its impact was limited by time constraints and students’ difficulties in accurately using measurement instruments. Furthermore, several students reported that they had minimal exposure to mathematics outside the classroom, which restricted opportunities for revision, practice, and consolidation of newly learned concepts. The introduction of GeoGebra significantly improved conceptual clarity, visualisation and interactive learning. Students demonstrated enhanced confidence, better problem-solving skills and a deeper grasp of geometric relationships. VM-based learning allowed learners to explore, test theories and connect geometric ideas more effectively than through traditional methods. This study highlights the transformative potential of digital tools in mathematics education, especially in bridging conceptual gaps in challenging topics like circle geometry. It advocates for the integration of VMs into NC(V) instructional strategies to promote deeper understanding, active engagement and improved academic performance in mathematics.