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## Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity (2009) Center for Education (CFE)

### Citation Manager

. "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

“Daddy/Mommy/Baby” and “big/little/tiny” helped children as young as 3 years to represent and apply higher order seriation abilities, even in the face of distracting visual factors, an improvement equivalent to a 2-year gain.

At the visual/holistic level (see Table 6-3), children begin by informally recognizing length as extent of 1-D space. For example, they may remark of a road made with building blocks, “This is long.” They can then compare two objects directly and recognize and describe their equality (e.g., “You are just as tall as I am!”) or inequality (e.g., “My pencil is longer than yours”) in length.

###### Compositions and Decompositions

At the visual/holistic level, children compose lengths intuitively. For example, they may lay building blocks along a path to “make a long road.”

##### Step 2 (Age 4)
###### Objects and Spatial Relations

At the thinking about parts level, preschool children learn to compare the length of two objects by representing them with a third object and using transitive reasoning (i.e., indirect comparison) (Boulton-Lewis et al., 1996). Again, language, such as the differences between counting-based terms (e.g., a toy, two trucks) and mass terms (e.g., some sand), can help children form relationships between counting and continuous measurement (Huntley-Fenner, 2001).

Preschoolers also begin actual measurement by laying physical units end to end and counting them to measure a length. However, they may not recognize the need for equal-length units and initially may make errors, such as leaving gaps between units. One way to engage in discussions of such concepts is to apply the resulting measures to comparison situations. These concepts and skills develop in parallel with competencies in seriating lengths, which emerge last and mark the first level of thinking about relating parts and wholes.

Preschoolers also begin to be able to cover a rectangular space with physical tiles and represent their tilings with simple drawings, although they may leave gaps in each and may not align all the squares.

###### Compositions and Decompositions

At the thinking about parts level, preschoolers understand that lengths can be concatenated in this way. This understanding, initially implicit, is revealed as children operate on objects.

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 Front Matter (R1-R12) Summary (1-4) Part I: Introduction and Research on Learning (5-6) 1: Introduction (7-20) 2 Foundational Mathematics Content (21-58) 3 Cognitive Foundations for Early Mathematics Learning (59-94) 4 Developmental Variation, Sociocultural Influences, and Difficulties in Mathematics (95-120) Part II: Teaching-Learning Paths (121-126) 5 The Teaching-Learning Paths for Number, Relations, and Operations (127-174) 6 The Teaching-Learning Paths for Geometry, Spatial Thinking, and Measurement (175-222) Part III: Contexts for Teaching and Learning (223-224) 7 Standards, Curriculum, Instruction, and Assessment (225-288) 8 The Early Childhood Workforce and Its Professional Development (289-328) Part IV: Future Directions for Policy, Practice, and Research (329-330) 9 Conclusions and Recommendations (331-350) Appendix A: Glossary (351-358) Appendix B: Concepts of Measurement (359-362) Appendix C: Biographical Sketches of Committee Members and Staff (363-370) Index (371-386)