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.
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.
In dit project ontwikkelen we een blended leertraject voor wiskundeonderwijs op secundair niveau; in het bijzonder voor het keuzevak wiskunde D.
Projectpartners zijn de Foundation Mathematics D Online en het Teaching and Learning Lab van de Universiteit Utrecht.
The main goal of this project is to improve functional thinking in a transnational perspective drawing on the partners’ specific and complementary expertise. Therefore, one of the project’s objectives is to develop digital-embodied, situated learning environments for inquiry that can be implemented in mathematics classroom from primary to upper secondary school in order to support students’ functional thinking. These learning environments will innovatively combine promising elements such as learning with digital tools, real-world situations, and embodiment activities through inquiry that all have empirically proven their benefit in teaching about functions but have never been merged in a coherent way. Moreover, they will be worked out – alongside with extensive teacher guides – in in the sense of a comprehensive learning trajectory, i. e., they will enhance functional thinking in a coherent and continuous way bridging between different school grades, and hence, overcoming teaching different function classes and aspects in an isolated, non-interrelated way.
Project " TIME - Teachers' Inquiry in Mathematics Education", approved within Erasmus+ programme – Strategic Partnerships for school education, started with its activities in December 2019.
The main objective of the project Teachers’ inquiry on mathematics education (TIME) is to explore how a community of math teachers working together in one school can improve their practice through joint exploration, planning and interaction between themselves and with university professors. The project includes 14 partners from 4 countries.
Het MERIA-project heeft tot doel de kwaliteit en relevantie van wiskundeonderwijs op middelbare scholen te verbeteren met behulp van op onderzoek gebaseerd onderwijs en de professionele ontwikkeling van leraren in heel Europa te ondersteunen. Projectpartners zijn scholen en academische instellingen in Kroatië, Denemarken, Slovenië en Nederland.