. "6 The Teaching-Learning Paths for Geometry, Spatial Thinking, and Measurement." Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Washington, DC: The National Academies Press, 2009.
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Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity
Spatial Visualization and Imagery
Spatial images are internally experienced, holistic representations of objects that are to a degree isomorphic to their referents (Kosslyn, 1983). Spatial visualization is understanding and performing imagined movements of 2-D and 3-D objects. To do this, you need to be able to create a mental image and manipulate it, showing the close relationship between these two cognitive abilities.
An image is not a “picture in the head.” It is more abstract, more malleable, and less crisp than a picture. It is often segmented into parts. Some images can cause difficulties, especially if they are too inflexible, vague, or filled with irrelevant details. People’s first images are static. They can be mentally recreated, and even examined, but not transformed. For example, one might attempt to think of a group of people around a table. In contrast, dynamic images can be transformed. For example, you might mentally “move” the image of one shape (such as a book) to another place (such as a bookcase, to see if it will fit). In mathematics, you might mentally move (slide) and rotate an image of one shape to compare that shape to another one. Piaget argued that most children cannot perform full dynamic motions of images until the primary grades (Piaget and Inhelder, 1967, 1971). However, preschool children show initial transformational abilities (Clements et al., 1997a; Del Grande, 1986; Ehrlich et al., 2005; Levine et al., 1999). With guidance, 4-year-olds and some younger children can generate strategies for verifying congruence for some tasks, moving from more primitive strategies, such as edge matching (Beilin, 1984; Beilin, Klein, and Whitehurst, 1982) to the use of geometric transformations and superposition. Interventions can improve the spatial skills of young children, especially when embedded in a story context (Casey, 2005). Computers are especially helpful, as the screen tools make motions more accessible to reflection and thus bring them to an explicit level of awareness for children (Clements and Sarama, 2003; Sarama et al., 1996).
Similarly, other types of imagery can be developed. Manipulative work with shapes, such as tangrams (a puzzle consisting of seven flat shapes, called tans, which are put together in different ways to form distinct geometric shapes), pattern blocks, and other shape sets, provides a valuable foundation (Bishop, 1980). After such explorations, it is useful to engage children in puzzles in which they see only the outline of several pieces and have them find ways to fill in that outline with their own set of tangrams. Similarly, children can begin to develop a foundation for spatial structuring by forming arrays with square tiles and cubes (this is discussed in more detail in the section on measurement).
Also challenging to spatial visualization and imagery are “snapshot” activities (Clements, 1999b; Yackel and Wheatley, 1990). Children briefly