Teaching mathematics
Teaching mathematics

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3 Developing problem-solving skills in geometry

So far this week, you have read about children’s geometrical thinking as it develops through the early to the middle school years. This has been linked to the description of the properties of shapes. You have looked at definitions of shapes and how these can be written in an inclusive way to include some shapes as special cases of others. You have considered triangles and how these can generate special quadrilaterals by reflecting a triangle in one of its sides or rotating the triangle using a half-turn around the midpoint of one of its sides.

In this section you will think about developing learners’ problem-solving skills in geometry. Many problems in geometry are entirely abstract from the point of view that there may be no practical real-world application. However, geometry can be approached in a practical way and this makes it accessible and engaging for learners. Geometry does also have real-world applications in nature, in design and architecture for example.

Three problems will be posed that you will be asked to have a go at answering. After each one you will consider how to best pose these problems for learners, including the resources needed and how to manage these in the classroom context.

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