Interactive Mathematical Maps (SKILL.de - De-fragmentation)

Felix Klein (1924/2016) described the “double discontinuity”, which concerns problems of future teachers when transitioning from school to university and back to school. Winsløw and Grønbæk (2013) showed that this problem is still relevant today. Klein (1924/2016) stated that the lack of connections between mathematical contents at school and university results in teachers falling back on traditional teaching culture after graduating from university. 

In order to counteract the problem of the double discontinuity and its consequences, we design and evaluate an innovative teaching format based on the theory of praxeology (c.f. Bosch & Gascon, 2014). Using the notion of praxeology (θ), the problem under consideration is Klein’s “double discontinuity” (T) and the technique to counteract this problem is the presented innovative teaching format (τ). Specifically, the teaching format consists of a course (τ1), which should illustrate the interdependencies of mathematics taught at school and mathematics taught at university. In order to facilitate this, an interactive “mathematical map” (τ2) (Brandl, 2009) as a digital learning tool is developed and used. In the interactive three-dimensional mathematical map, nodes in space display mathematical contents. Edges symbolize historical developments, which emphasize mathematics as an emerging science. Felix Klein, as a famous advocate of this type of learning, described it as „intuitive and genetic, i.e., the entire structure is gradually erected on the basis of familiar, concrete things“ (1924/2016, p. 9). The “mathematical map” is intended to offer the student an optimal solution for establishing successful learning processes by integrating the historical origin of mathematical concepts as well as interdependencies between them. It combines these two characteristics in one three-dimensional representation, a kind of graph or tree.