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Chapter 4: Exploring geometry

Chapter 4: Exploring geometry

pp. 82-120

Authors

, University of New England, Australia, , University of Tasmania, , University of Tasmania
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Summary

LEARNING OUTCOMES

By the end of this chapter, you will:

  • • understand the breadth of concepts included in the geometry section of curriculum documents generally, particularly the Australian Curriculum: Mathematics and the New Zealand Mathematics Curriculum

  • • be familiar with a theoretical framework used as a lens through which to view students’ geometrical thinking, known as the van Hiele theory

  • • have a pedagogical framework that is useful for designing sequential student tasks to assist students to grow in their understandings of geometrical concepts

  • • understand the important role of language and maintaining ‘student ownership’ of the geometrical ideas

  • • be familiar with the use of technological tools to enhance our teaching of geometrical concepts for the e-generation.

  • KEY TERMS

  • Bisect: Divide into two equal parts

  • Congruent figures: Figures that are exactly the same size and shape

  • Dissect: Divide into two parts

  • Edge: The interval where two faces of a solid meet

  • Face: A flat surface of a polyhedron

  • Isometric projection: A corner view of an object

  • Spatial awareness: the ability to be aware of oneself in space. It involves the organised knowledge of objects in relation to oneself in that given space and an understanding of the relationship of these objects when there is a change of position.

  • Three-dimensional (3D) objects: Having three dimensions, requiring three coordinates to specify a point

  • Transformation: Shifting or modifying a shape, including reflecting, enlarging, translating and rotating

  • Two-dimensional (2D) figures: Having two dimensions, a flat surface with no depth, requiring two coordinates to specify a point

  • Vertices: Plural of vertex; a point on a 3D shape where three or more straight edges meet to make a corner

  • Visualisation: A mental image that is similar to a visual perception

  • Educationally, we are in an exciting time in terms of geometrical investigations in the classroom. While the manipulation of concrete materials to enable student construction of 2D figures and 3D objects has been readily available for many years, there are a growing number of mathematics classrooms that have access to dynamic geometry software and interactive sites that enable real-time creation and exploration of geometric figures and their properties.

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