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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.

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Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity
 BOX 5-8 Step 3 in the Number Core Age 5 or Kindergarten Integrate All Core Components, See a Ten and Some Ones in Teen Numbers, Relate Ten Ones to One Ten, and Extend the Core Components to Larger Numbers Children at particular ages/grades may exceed the specified numbers and be able to work correctly with larger numbers. The numbers for each age/grade are the foundational and achievable content for children at this age/grade. The major types of new learning for each age/grade are given in italics. Each level assumes that children have had sufficient learning experiences at the lower level to learn that content; many children can still learn the content at a level without having fully mastered the content at the lower level if they have sufficient time to learn and practice. Cardinality: Extends conceptual subitizing to a new visual group, a group of tens: can see a ten in each teen number (18 = 10 + 8). Number word list: Extends to learn all of the decades in order as a new number word list counting by tens; uses this decade order with the decade pattern to count to 100 by ones: says the tens list 10, 20, 30, …, 90, 100; says 1 to 100 by ones. 1-to-1 counting correspondences: Continues to extend accurate correspondences to larger sets; accuracy will still vary with effort: counts 25 things in a row with effort. Written number symbols: Coordinates knowledge of symbols 1 to 9 to write teen numbers: reads and writes 1 to 19; reads 1 to 100 arranged in groups of ten when counting 1 to 100. Integrates all of the above for teen numbers so that ten ones = 1 ten, relating the unitary cardinality relationship ten ones + eight ones make eighteen ones to the written symbols 18 as 10 with an 8 on top of the 0 ones in ten.

dren to understand each cardinal teen number as consisting of two groups: 1 group of ten things and a group of the ones (the extra over ten). So, for example, 11 is 1 group of ten and 1 one (11 = 10 + 1), 14 is 1 group of ten and 4 ones (14 = 10 + 4), and 18 is 1 group of ten and 8 ones (18 = 10 + 8). The second crucial understanding that builds on the above is that ten ones equal one ten. That is, the written teen number symbols such as 18 mean 1 group of ten (1 ten rather than ten ones) and 8 ones. Being able to see ten ones as one ten is a crucial step on the learning path.

It can be helpful for English-speaking children to have experiences seeing 18 things separated into ten and eight and relating these quantities to both the number words “eighteen is ten and eight” and to the written number symbols (18). It may also be helpful to use the written symbol version of this as 18 = 10 + 8. Repeated experiences with all of these relation-

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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)