Digital Mazes and Spatial Reasoning: Using Colour and Movement to Explore the 4th Dimension

de Freitas, Elizabeth (2017) Digital Mazes and Spatial Reasoning: Using Colour and Movement to Explore the 4th Dimension. In: Innovation and technology enhancement in mathematics education. Mathematics Education in the Digital Era . Springer Verlag, pp. 237-257. ISBN 978-3-319-61488-5

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Abstract

This chapter focuses on innovative developments of four-dimensional digital mazes, examining how these mazes tap into the ideas of mathematician and fiction writer Charles Hinton (1853-1907) who wrote extensively on perception of a 4th geometric dimension. Hinton treats mathematical objects as physical and material movements, and draws on non-Euclidean geometry to argue for a virtual dimension to matter. I discuss recent attempts to build digital mazes that develop spatial sense in four dimensions, and show how these are directly linked to Hinton’s ideas. I focus on how colour and movement in digital environments are used to develop a distinctive kind of spatial sense. This chapter sheds light on innovative uses of digital software for developing student spatial sense. My aim is to explicate the new materialism of Charles Hinton, contribute to discussions about the nature of spatial sense and spatial reasoning, and to point to possible directions for future research on inventive approaches to geometry.