More so than many of the other chapters, this chapter will focus on how children learn geometry in addition to describing their geometrical thinking. Simply stated, children learn geometric concepts through repeated manipulation and motor actions on objects (this includes drawing), and their internal reflection upon these actions and ideas (Piaget & Inhelder, 1967). To elaborate, children learn through their active manipulation of objects and things around them and their reflection upon these actions (Clements, 2003). Children need to build, tear down, manipulate, draw and reflect upon their physical activity! Children need to interact with shapes extensively in order to understand them. Pictures are useful in teaching geometry to children. However, manipulatives or children manipulating objects are always superior to just seeing pictures. For the most part, children cannot act on or manipulate pictures! Activities such as making shapes with their bodies or making shapes with toothpicks and marshmallows are invaluable in helping children develop rich understandings of geometry. Children’s work in computer environments, where they have to draw pictures, may also serve as an interactive tool similar to working with manipulatives!
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