Definition and Teaching Situation
Geometry (Ancient Greek: γεωμετρία; geo “earth,” metron “measurement”) is a mathematical area concerned with the space around us, with the shapes in the space, their properties, and different “patterns” and “thinking patterns” for which they serve as trigger and basis. As Freudenthal (1973) states it: “Geometry can only be meaningful if it exploits the relation of geometry to the experienced space… Geometry is one of the best opportunities that exist to learn how to mathematise reality” (p. 407).
From its very beginning, more than two and a half thousand years ago, geometry was developed along a few main aspects:
- (a)
Interacting with shapes in a space. This aspect arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes and concerning shapes’ attributes and the relationships among them (the practical-intuitive aspect).
- (b)
Shapes, their attributes, and their changes in space as...
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Hershkowitz, R. (2020). Shape and Space: Geometry Teaching and Learning. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_138
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