Geofold - Where geometry unfolds
A toolkit that helps high school students develop spatial skills through tangible play and structured exploration
A.E.C. Heilig (TU Delft - Industrial Design Engineering)
P.J. Stappers – Graduation committee member (TU Delft - Codesigning Social Change)
A.J.M. van Leeuwen – Mentor (TU Delft - Perceptual Intelligence)
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Abstract
Mathematics education in secondary schools is often experienced as abstract and disconnected from reality, leading to declining motivation among students. To address this, both the Dutch Ministry of Education and the SLO are working to integrate spatial skills more explicitly into the curriculum. Simultaneously, there is growing interest in inquiry- and design-based learning, which aligns well with the spatial, tangible changes that are coming.
This research investigates the question: How can 12 to 15 year old havo/vwo students develop their spatial skills during math classes through a tangible object? Sub-questions explore the definition of spatial skills and the structure of a typical math lesson.
The process was divided into a research cycle and a design cycle. The research cycle involved literature review, interviews, and observations, and used context mapping to identify similarities and differences between student needs and school systems. The design cycle followed a research through design approach, with iterative prototyping and user testing.
The literature review revealed that spatial skills are not just about mental rotation or perspective-taking, but depend on the object, its surroundings, and how we engage with it; mentally, physically, or through movement in the environment. The context mapping analysis shows that schools prioritize structure, efficiency, and test preparation, while students expressed a desire for interactive and collaborative experiences. This led to a design space that balances both needs: structured lessons that still allow for active exploration.
The resulting concept is a magnetic cube toolkit designed to enhance spatial reasoning through geometry tasks that align with the curriculum. Instead of adding extra work, the tool replaces optional exercises with open-ended, spatial challenges. Students select an assignment card and build with modular cubes, progressing from 2D to 3D thinking and from closed to open questions.
User testing showed that the haptic experience of the magnetic cube increased engagement. However, improvements were needed in the clarity and length of task descriptions, since the connection between the questions and the cube was not always clear. The physical size and production cost of the prototype were also mentioned as limitations, making large scale classroom implementation unrealistic in its current form.
As a recommendation, a more affordable, compact version was developed, even if this means losing the tactile quality of the magnets. Future steps include refining the design for production and conducting full-classroom trials to test feasibility and educational impact.