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.
Tools that change the way students’ see geometry
Traditional geometry education asks students to think initially as botanists (handling whole shapes such as manipulatives) and then like surveyors (learning rules that are founded in geometric measurement). Our Mathomat template and its student manuals ask students instead to think like builders, by using our tools to construct designs. Over time we encourage students to think like inventors, where they create new designs based on abstract mathematical ideas. This product design philosophy builds on the ideas of the French educator Raymond Duval*. Our vision of successful geometry learning involves a central role for tools.
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.