Discrete or continuous change: Can a dynamic representation facilitate development of reasoning in mathematics?

Presented by Dr Sue Forsythe, The University of Leicester

In order to investigate how students develop the concept of inclusivity between classes of 2D shapes I used a Design Based Research method to develop and refine a task, based on a dynamic figure, which students dragged to generate different triangles and quadrilaterals. Pairs of 13 year old students and one whole teaching group worked with the dynamic figure whilst their dialogue and on-screen activity were recorded. A number of themes emerged from the data, in particular the importance of symmetry in how the students generated the shapes. This was evident when students dragged to maintain the symmetry (DMS) of the figure, a strategy with the potential to mediate the concept of a ‘dragging family’ of shapes. As such DMS is a ‘dragging utilisation scheme’ in the Vygotskyan sense. However, in order to move towards this understanding it is necessary that students perceive dragging activity on the figure as an action resulting in a continuously changing figure which morphs through an infinite number of shapes. I describe how I used an animation of the figure under DMS as the catalyst to move the students’ thinking towards the ‘dragging family’. My findings suggest that enabling students to view change through continuous rather than discrete representations helped to develop inclusive thinking.

Refreshments will be available