chapter  3
14 Analysis of Young Children's Spatial Constructions
Pages 13

Although much of mathematics involves analytical reasoning, it is clear from a careful reading of the literature that spatial reasoning also plays an important role in mathematical thought (Bishop, 1980; Guay & McDaniel, 1977; Hadamard, 1954; Lean & Clements, 1981; Lin, 1979; Smith, 1964; Turner, 1982). Fischbein (1987), for example, spoke of the dialectical relationship between images and concepts in mathematical reasoning. Mathematical problem solving is often a matter of reasoning analytically, constructing an image, using the image to support additional conceptual reasoning, which in tum may suggest an elaborated image. Kosslyn (1983) called it the "race between words and pictures" (p. 162). This process of building from images to analysis and analysis to images may continue through many cycles. In studying young children's mathematical worlds, an understanding of their use of imagery becomes important. Mathematics is the activity of creating relationships, many of which are based in visual imagery.