What do ‘good’ geometry lessons look like? A comparative analysis of prospective primary school mathematics teachers’ images

Research has shown that teachers’ perceptions and beliefs about good teaching are closely related to their teaching style and, consequently, to effective classroom learning and student achievement. Although much research has been conducted on good mathematics teaching, its sub-discipline, geometry, is often neglected. Therefore, this longitudinal study focuses on geometry and uses participant-produced drawings to examine the images prospective primary school mathematics teachers have of good geometry lessons in terms of modes of instruction (teacher-directed, student-directed, balanced), both before and after attending a two-semester course, ‘Geometry and Teaching Geometry’. The study participants were trainee primary school teachers in their second year of a mathematics teacher education program at one German university department. Trends that emerged from the study sample (<i>N</i> = 101) showed that most of the prospective primary school mathematics teachers’ perceptions of what makes a good geometry lesson were aligned with teacher-directed mode of instruction, with the two-semester geometry course prompting a move towards a student-directed mode of instruction. Thus, the findings indicate that carefully designed university teacher training courses may stimulate changes in the belief systems of prospective primary school mathematics teachers, contributing to a more modern understanding of geometry teaching and learning.