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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

TABLE 6-2 Space and Shapes in Three Dimensions

 Steps/Ages (Levels of Thinking) Goals A. Perceive, Say, Describe/Discuss, and Construct Objects in 3-D Space B. Perceive, Say, Describe/Discuss, and Construct Spatial Relations in 3-D Space C. Perceive, Say, Describe/Discuss, and Construct Compositions and Decompositions in 3-D Space Step 1 (Ages 2 and 3) Thinking visually/holistically See and describe pictures of objects of all sorts (3-D to 2-D).* Understand and use relational language, including “in,” “out,” “on,” “off,” and “under,” along with such vertical directionality terms as “up” and “down. Represent real-world objects with blocks that have a similar shape. Combine unit blocks by stacking. Thinking about parts Discriminate between 2-D and 3-D shapes intuitively, marked by accurate matching or naming. Step 2 (Age 4) Thinking visually/holistically Describe the difference between 2-D and 3-D shapes, and names common 3-D shapes informally and with mathematical names (“ball”/sphere; “box” or rectangular prism, “rectangular block,” or “triangular block”; “can”/cylinder). Match 3-D shapes. Uses relational words of proximity, such as “beside,” “next to” and “between,” “above,” “below,” “over,” and “under.” Thinking about parts Identify faces of 3-D objects as 2-D shapes and name those shapes. Use relational language involving frames of reference such as “in front of,” “in back of,” “behind,” “before.” Identify (matches) the faces of 3-D shapes to (congruent) 2-D shapes, and match faces of congruent 2-D shapes, naming the 2-D shapes. Represent 2-D and 3-D relationships with objects. Combine building blocks, using multiple spatial relations.
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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)