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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
 Steps/Ages (Level of Thinking) Goals A. Perceive, Say, Describe/Discuss, and Construct Objects in 2-D Space B. Perceive, Say, Describe/Discuss, and Construct Spatial Relations in 2-D Space C. Perceive, Say, Describe/Discuss, and Construct Compositions and Decompositions in 2-D Space Thinking about parts Shape by number of sides and corners (including new shapes). Create and record original compositions made using squares, right triangles, and rectangles on grid paper. Extend to equilateral grids and pattern blocks (those with multiples of 60° and 120° angles). Begin to use relational language of “right” and “left.” Draw a complete covering of a rectangle area. Count squares in rectangular arrays correctly and (increasingly) systematically. Relating parts and wholes Measure of sides (simple units), gross comparison of angle sizes. Compare area using superimposition. For rectangular regions, draw and count by rows (initially may only count some rows as rows). Identify and create symmetric figures using motions (e.g., paper folding; also mirrors as reflections). Composition on grids and in puzzles with systematicity and anticipation, using a variety of shape sets (e.g., pattern blocks; rectangular grids with squares, right triangles, and rectangles; tangrams). NOTE: Most of the time should be spent on 2-D, about 85 percent (there are many beneficial overlapping activities).

equality of angles another relation). Owing usually to a lack of good experiences, many students do not reach this level until late in their schooling. However, with appropriate learning experiences, even preschoolers can begin to develop this level of thinking. In Table 6-1 this is called the “relating parts and wholes” level.

###### Development of Shape Concepts

What ideas do preschool children form about common shapes? Decades ago, Fuson and Murray (1978) reported that, by 3 years of age, over

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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)