Learning and teaching visualization tasks in secondary mathematics classrooms

In the new British Columbia’s Mathematics curriculum, students are expected to “visualize to explore mathematical concepts.” Although research shows that spatial skills can improve with targeted intervention, oftentimes these skills are considered to be difficult to transmit and to assess. In this study, students in Mathematics 8 and Mathematics 9/10 classes engaged in visualization tasks inspired by Caleb Gattegno’s practice. They imagined a scenario described by the teacher, drew a sketch of the scenario, and discussed their solution with peers. Through drawing, the students developed strategies including showing hidden edges of three-dimensional shapes, and stepwise rotation of shapes and learning how to draw loci. Through discourse, they stated conjectures and arguments, applying their own mathematical agency. Students developed awareness of definitions, conventions and properties of shapes and the ability to consider multiple constraints of task and to generalize. Additionally, they developed awareness of their own and their peers’ thinking.