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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.

 Page 188

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Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity

sents a unique role or function in the picture (e.g., one shape for one leg). Children can fill simple frame-based shapes puzzles using trial and error, but they may have limited ability to use turns or flips to do so; they cannot use motions to see shapes from different perspectives. Thus, children view shapes only as wholes and see few geometric relationships between shapes or between parts of shapes (i.e., a property of the shape).

Composition with 3-D shapes usually begins with stacking blocks. Children then learn to stack congruent blocks and make horizontal “lines.” Next they build a vertical and horizontal structure, such as a floor or a simple wall. Later, some 3-year-olds begin to extend their buildings in multiple directions, possibly creating arches, enclosures, corners, and crosses, but often using unsystematic trial and error and simple addition of pieces.

##### Step 2 (Age 4)
###### 2-D and 3-D Objects

Beginning at the visual/holistic level, preschoolers learn to recognize a wide variety of shapes, including shapes that are different sizes and are presented at different orientations. They also begin to recognize that geometric figures can belong to the same shape class, but have different measures and proportions. Similarly, preschoolers learn to describe the differences between 2-D and 3-D shapes informally. They also learn to name common 3-D shapes informally and with mathematical names (ball/sphere, box/rectangular prism, rectangular block, triangular block, can/cylinder). They name and describe these shapes, first using their own descriptions and increasingly adopting mathematical language. For example, “diamond” gives way to “rhombus” and “corners” become “angles” (or vertices). Eventually, they adopt the terminology of the thinking about parts level, such as identifying shapes as triangles because they have three sides. Faces of 3-D shapes are identified as specific 2-D shapes.

Such descriptions build geometric concepts, as well as reasoning skills and language. They encourage children to view shapes analytically. Children begin to describe some shapes in terms of their properties, such as saying that squares have four sides of equal length, and thus make initial forays into thinking at the relating parts and wholes step. They informally describe the properties of blocks in functional contexts, such as that some blocks roll and others do not.

###### Spatial Relations

Also beginning at the visual/holistic level, preschool children learn to extend their vocabulary of spatial relations with such terms as “beside,”

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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)