3D printed mathematics visualisations by STEAM teachers

Visualising abstract concepts such as for example geometrical objects in mathematics can be a valuable support for learners. Visualisation, however, is a process involving several steps that influence each other. Duval (1998) uses steps connecting reasoning by an explanation or proof to a construction step involving tools creating a visualisation to a production of a visual representation leading to new insights about a geometrical object. Vágová (2020) argues that visualising geometrical objects needs the ability to create, manipulate, and transform mental images by an internal and an external representation which both require information about the spatial arrangement. 3D modelled and then visualised geometrical objects can support the development and train visualisation skills.
Steps of visualisation processes require visuospatial competencies and are also important for other subjects in Science, Technology, Engineering, Arts and Mathematics (STEAM) education (Ng 2017). Being able to understand representations and their spatial rotations, transitions between 2D and 3D and being able to manipulate representations are valuable for STEAM related subjects (Kok 2020). Martin-Dorta et al. (2008) says that spatial abilities can be improved using real and computer-aided models. 3D printing can therefore be an interesting activity as it also combines the mentioned steps in a mathematical modelling way. This approach was used in a beginners course for pre-service mathematics teachers and some of them chose to create mathematical proofs as visualisation. We will look at 3D printed objects, which concepts they visualise and what teachers' ideas behind visualisations were.