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

### Citation Manager

. "5 The Teaching-Learning Paths for Number, Relations, and Operations." Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Washington, DC: The National Academies Press, 2009.

 Page 142

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Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity
###### Cardinality

Children at this level continue to extend to larger numbers their conceptual subitizing of small groups to make a larger number, for example, I see one thumb and four fingers make my five fingers (this is part of the relation and operation core and is discussed more there). The 5-groups are particularly important and useful. These 5-groups provide a good way to understand the numbers 6, 7, 8, 9, 10 as 5 + 1, 5 + 2, 5 + 3, 5 + 4, 5 + 5 (see Figure 5-1). The convenient relationship to fingers (5 on one hand) provides a kinesthetic component as well as a visual aspect to this knowledge. Without focused experience with 5-groups, children’s notions of the numbers 6 through 10 tend to be hazy beyond a general sense that the numbers are getting larger. Knowing the 5-groups is helpful at the next level, as children add and subtract numbers 6 through 10; the patterns are problem-solving tools that can be drawn or used mentally. Children in East Asia learn and use these 5-group patterns throughout their early numerical learning (Duncan, Lee, and Fuson, 2000). Children can continue to experience and begin remembering other addends that make totals (e.g., 3 and 3 make 6, 8 is 4 and 4).

###### Number Word List

As noted, beyond the first ten words, which are arbitrary in most languages (e.g., see the extensive review in Menninger, 1958/1969), most languages begin to have patterns that make them easier to learn. English, however, has irregularities that are challenging for children. A major difficulty in understanding the meaning of the teens words is that English words do not explicitly say the ten that is in the teen number (teen does not mean ten even to many adults), so English-speaking children can benefit

FIGURE 5-1 Five groups to understand the numbers 6, 7, 8, 9, and 10.

 Page 142
 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)