Dynamical visualization for mathematics education. I'm interested in how dynamical visualization can contribute to learning mathematics. What benefits/affordances does it have that static visualization has not? Additionaly, I'm interested in the role of embodied simulation in dynamical visualization. Can we increase the learning outcome of animated videos by applying ideas and principles from embodied and grounded cognition? My research in this area developed from the Mathematics D Online project in which we develop (animated) instructional videos for mathematics at secondary level.

Below an animation form a research project on metaphor-based algebra animation with Winand Renkema.

Below a video on time dilation, for a next project on algebra animation, with Rick Oosterwijk.

Abstraction, compression and problem solving. A key feature of mathematics is that it is abstract. It is also a main reason why humans (students) find it difficult. What epistemic and cognitive structures underlie abstraction? How do humans think in abstracto? How do we teach students to think more abstractly? A way abstraction is produced is reorganizing mathematical knowledge by compression: details are filed to long-term memory and attention is shifted to abstract properties of the object. The challenge of solving a problem can generally be recognized as the challenge of decompressing in two related ways: (1) seeing how to apply an abstract/compressed concept or technique in the contgext of a concrete problem (2) recollecting and adapting the details of a concept or technique to the problem situation. I propose Heuristic Trees as a digital didactical help-seeking tool to facilitate students to maneuver between compressed and decompressed knowledge. Clicking the previous link takes you to a digital learning and designer environment for heuristic trees developed by Theo van den Bogaart. Below a talk on heuristic trees: 

Heuristic trees are now used in courses in a Bachelor algebra course at the UU, and at a master Number theory course at the HU University of applied sciences.

Embodiment. There is increasing evidence that it makes sense to consider cognition as an act not exclusively performed by the brain, but that it extends to the sensori-motorical systems of the whole body: so-called embodied cognition. Can students develop mathematical cognition through tasks that activate these sensori-motor systems? Can a student express an understanding of mathematics, before they can communicate this through language? Does embodied cognition provide a window to the way we unconsciously mathematize and reason mathematically? These are the questions I find interesting in this context. I researched them in the context of the Augmented Reality Sandbox developed by my colleague Nico Rutten.

Calculus education

In 2021-2022, I co-edited a special issue on on tools to support meaning-making in calculus and pre-calculus education. You can find it here.