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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

from visual representations that show the ten inside teen numbers in order to understand what quantities these words represent (see the discussion in the kindergarten level).

There are two patterns in the English number words from 20 to 100 that children need to understand if each word is to have its value as some number of tens and some number of ones, as in Chinese words (52 is said as five ten two). One is the irregular pattern in the decade words that name the tens multiples: twenty (twin-tens), thirty (three-tens), forty, fifty (five tens), sixty, seventy, eighty, ninety. As with the teens, the relationships of the decade words to the numbers below ten become really clear only for the last four words because only then are the six, seven, eight, nine said. The irregularities in twenty through fifty interfere with seeing the meaning of these words as two tens, three tens, four tens, five tens, etc., and thus with learning these in order by using the list below ten, as Chinese-speaking children can do (see Chapter 4). Also, as with the teen words, the ten is not said explicitly but is said as a different suffix, –ty. Therefore, as discussed later for Grade 1, children need to work explicitly with groups of tens and ones to understand these meanings for the number words from 20 to 100.

The second pattern is the pattern of a decade word followed by the decade word with the numbers one through nine: twenty, twenty-one, twenty-two, twenty-three,, twenty-nine. Children can begin to learn this second pattern quite early. Because the transition to ten and the teens words is not clear in English, children often initially do not stop at twenty-nine but continue to count twenty-nine, twenty-ten, twenty-eleven, twenty-twelve, twenty-thirteen (Fuson, 1988). This error can be a mixture of not yet understanding that the pattern ends at nine and difficulty stopping the usual counting at nine in order to shift to another decade.

Children in the United States tend to learn the pattern of the decade word followed by a number (1-9) before learning the order of the decade words (e.g., Fuson, 1988; Fuson, Richards, and Briars, 1982; Miller and Stigler, 1987; Siegler and Robinson, 1982). Although some 2- and 3-year-olds begin learning and practicing the patterns for the teens and decade words, the teen pattern can be mastered by almost all 4-year-olds with support and practice, as can the early decades (two cycles of the pattern from twenty through thirty-nine). Many 4-year-olds learn more than this, but mastering the correct order of the decades and using this with the n-ty through n-ty-nine pattern is for many children a kindergarten achievement (e.g., Fuson, 1988; Fuson, Richards, and Briars, 1982; Miller et al., 1995). Structured learning experiences can decrease the time it takes to learn this pattern of decades to 100, but without such experiences this learning effort can continue even to age 6. Counting by tens to 100 to learn this decade sequence is a goal for kindergarten and is discussed in that section.

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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)