Our product design philosophy
Tools that deepen student engagement
As tool designers we aim to support mathematics teachers by developing geometry learning aids that can engage middle school students more deeply. If students can remain connected with the concrete geometric experiences of their primary school years while engaging with the more abstract concepts required in secondary school, then they will achieve a much deeper understanding of the geometric relationships they are being challenged to understand*. A tool such as the Mathomat geometry template can do this by presenting students with basic geometric shapes, such as circles, ellipses, quadrilaterals and other polygons in physical form. Students are able to retain a physical connection to these shapes while being challenged to understand the abstract relationships that define them mathematically.
For Raymond Duval’s work on changing the mode of student thinking in geometry see:
Duval, R. (2005). Les conditions cognitives de l’apprentissage de la géométrie : développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements. [Cognitive conditions of geometric learning: developing visualisation. distinguishing various kinds of reasoning and coordination of their operation]. Annales of Didactics and Cognitive Sciences/ Annales de Didactique et Sciences Cognitives, 10, 5-53.
For an understanding of an approach to geometry teaching which uses physical drawing instruments to keep middle school leaners in touch with concrete experience from primary school while they engage with abstract secondary school concepts, see the following article by Marie Jean Perrin-Glorian and colleagues:
Perrin-Glorian, M.-J., & Godin, M. (2018). Plane geometry: For a coherent approach from the beginning of school to the end of college. HAL, 01660837v2, 1-41
Paul White and Mike Mitchelmore also advocate an approach to teaching basic concepts in geometry which keeps students connected to real world experience as they engage with abstract ideas. Such as the following:
White, P., & Mitchelmore, M. (2010). Teaching for abstraction: A model. Mathematical Thinking and Learning, 12(3), 205-226.