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Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity
rotation, translation, magnification, and folding) as well as perspective changes that occur as one moves to new locations. Spatial thinking is involved in navigating in the environment to reach goal locations and to find one’s way back to one’s starting point. Use of spatial symbolic systems, including language, maps, graphs, and diagrams, and spatial tools, such as measuring devices, extend and refine the ability to think spatially.
As is the case for the development of number knowledge, recent research has shown strong starting points for spatial thinking. In contrast to Piaget’s view, which is in opposition to the gradual unfolding of spatial skills over the course of development, recent evidence shows that infants are able to code spatial information about objects, shapes, distances, locations, and spatial relations. This early emergence of spatial skills is consistent with an evolutionary perspective that emphasizes the adaptive importance of navigation for all mobile species (e.g., Newcombe and Huttenlocher, 2000, 2006; Wang and Spelke, 2002). That said, humans are unique in that their spatial skills are extended through symbolic systems, such as spatial language, measurement units, maps, graphs, and diagrams. Thus, it is not surprising that the trajectory of children’s spatial development depends heavily on their spatially relevant experiences, including those involving spatial language and spatial activities, such as block building, puzzle play, and experience with certain video games.
Starting Points in Infancy
Even young infants are able to segment their complex visual environments into objects that have stable shapes, using such principles as cohesion, boundedness, and rigidity (e.g., see Spelke, 1990). Infants also perceive the similarities between three-dimensional objects and photographs of these objects (DeLoache, Strauss, and Maynard, 1979). In habituation studies, infants show sensitivity to shape similarities across exemplars (e.g., Bomba and Siqueland, 1983). In addition, they are able to recognize invariant aspects of a shape shown from different angles of view (e.g., Slater and Morison, 1985).
Infants are also capable of forming categories of spatial relations—a claim that is widely supported; however, different views exist regarding the developmental sequence for children’s understanding of space categories (Quinn, 1994, 2004; van Hiele, 1986). As stated by Bruner, Goodnow, and Austin (1956), categorization entails treating instances that are discriminable as the same. Using this criterion, Quinn showed that 3-month-old infants are sensitive to the categories above versus below (e.g., Quinn, 1994) and left versus right (e.g., Quinn, 2004). Both of these categories involve the relationship of an object and a single referent object (e.g., a horizontal or vertical bar). However, infants are not able to code the rela-