Tackling 3D problems in virtual classrooms: an exploratory study of synchronous online mathematics instruction with GeoGebra

Abstract

Introduction – Synchronous online instruction creates learning opportunities for students outside of school. However, teaching mathematics fully online poses challenges, particularly in tackling 3D problems. This study explores approaches to enhancing this instructional environment using variation theory and GeoGebra applets. Methods – Nineteen Grade 11 students participated in a synchronous online enrichment programme. We used visual learning analytics (VLA) to examine teaching practices and interactions during class. We further analysed students' test and survey results to assess their mastery of learning materials and engagement. Results – The VLA results indicated that the GeoGebra applets and Kahoot! quizzes enabled teacher discussions on a series of varied examples to facilitate students' learning and participation in class activities. The pre-test–post-test results indicated significantly higher scores in the students' mathematics achievement with a large effect, which was sustained over a two-week period, as evidenced by their delayed post-test performance. Furthermore, they reported significantly higher levels of cognitive engagement. These quantitative results aligned with interview findings in which the students described a willingness to invest additional time in engaging with the GeoGebra applets for after-class mathematical exploration. Discussion – Based on our findings, we propose three overarching design principles for synchronous online mathematics instruction, covering resource development, lesson implementation, and post-class reinforcement of student learning. This study's findings will support preparation for potential disruptions to normal schooling and facilitate a seamless transition to online instruction when necessary.