and Hynd, 1990; Spiers, 1987). Other evidence shows specific spatially related learning disabilities in arithmetic, possibly more so for boys than girls (Share, Moffitt, and Silva, 1988). Primary school children’s thinking about units and units of units was found to be consistent in both spatial and numerical problems (Clements et al., 1997a). In this and other ways, specific spatial abilities appear to be related to other mathematical competencies (Brown and Wheatley, 1989; Clements and Battista, 1992; Fennema and Carpenter, 1981; Wheatley, Brown, and Solano, 1994). Geometric measurement connects the spatial and numeric realms explicitly.

SUMMARY

This chapter describes geometry and spatial thinking and measurement, which comprise the second essential domain for young children’s mathematical development. The research in this domain is less developed than for number, but it does provide guidance for educators regarding what young children can and should do to develop competence in these areas. The teaching-learning path for geometry and spatial relations demonstrates how young children move through levels of thinking as they learn about 2-D and 3-D objects. The use of manipulatives, pictures, and computers play an important role in facilitating children’s progress along this path. Early childhood teachers should help children extend their thinking by building on simple conventional models (e.g., child represents classroom with cut out pictures) and challenge them by asking them to use geometric correspondences (e.g., direction—which way?, identification—which object?) to solve problems.

Measurement, the second major area covered in this chapter, connects and enriches the two crucial domains of geometry and number. The teaching-learning path for measurement describes children’s developing competence in linear measurement and initial steps toward understanding areas and volume. The teaching-learning path outlined for length emphasizes the need to provide experiences that allow children to compare the size of objects and to connect number to length. Children also need opportunities to solve real measurement problems which can help build their understanding of units, length-unit iteration, correct alignment and the zero-point concept. Children’s early competency in measurement is facilitated by play with structured materials, such as unit blocks, pattern blocks, and tiles and strengthened through opportunities to reflect on and discuss their experiences.

It is important to note that the potential of young children’s learning in geometry and measurement if a conscientious, sequenced development of spatial thinking and geometry were provided to them throughout their earliest years is not yet known. Research on the learning of shapes and



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