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## Adding It Up: Helping Children Learn Mathematics (2001) Center for Education (CFE)

### Citation Manager

. "5 The Mathematical Knowledge Children Bring to School." Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.

 Page 166

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Adding + It Up: Helping Children Learn Mathematics

Names for numbers above 10 diverge in interesting ways among these different languages, as the second part of Box 5–1 demonstrates. The Chinese number-naming system maps directly onto the Hindu-Arabic number system used to write numerals. For example, a word-for-word translation of shi qi (17) into English produces ten-seven. English has unpredictable names for 11 and 12 that bear only a historical relation to one and two.21 Whether the boundary between 10 and 11 is marked in some way can be very significant because this boundary can offer the first clue that number names are organized according to a base-10 system. The English names for numbers in the teens beyond 12 do have an internal structure, but it is obscured by phonetic modifications of many of the elements used in the first 10 numbers (e.g., ten becomes -teen, three becomes thir-, and five becomes fif-). Furthermore, the order of word formation reverses the place value, unlike the Hindu-Arabic and Chinese systems (and the English system above 20), naming the smaller value before the larger value. Spanish follows the same basic pattern for English to begin the teens, although there may be a clearer parallel between uno, dos, tres and once, doce, trece than between one, two, three and eleven, twelve, thirteen. The biggest difference between Spanish and English is that after 15 the number names in Spanish abruptly take on a different structure. Thus the name for 16 in Spanish, diez y seis (literally ten and six), follows the same basic structure as Arabic numerals and Chinese number names (starting with the tens value and then naming the ones value), rather than the structures of the number names in English from 13 to 19 and the names in Spanish from 11 to 15 (starting with the ones value and then naming the tens value).

Above 20, all these number-naming systems converge on the Chinese structure of naming the larger value before the smaller one. Despite this convergence, the systems continue to differ in the clarity of the connection between the decade names and the corresponding unit values. Chinese numbers are consistent in forming decade names by combining a unit value and the base (ten). Decade names in English and Spanish generally can be derived from the name for the corresponding unit value, with varying degrees of phonetic modification (e.g., five becomes fif- in English, cinco becomes cincuenta in Spanish) and with some notable exceptions, primarily the special name for 20 used in Spanish.

Psychological consequences of number names. Although all the number-naming systems being reviewed are essentially base-10 systems, they differ in the consistency and transparency with which that structure is reflected in the number names. Several studies comparing English-

 Page 166
 Front Matter (R1-R20) Executive Summary (1-14) 1 Looking at Mathematics and Learning (15-30) 2 The State of School Mathematics in the United States (31-70) 3 Number: What Is There to Know? (71-114) 4 The Strands of Mathematical Proficiency (115-156) 5 The Mathematical Knowledge Children Bring to School (157-180) 6 Developing Proficiency with Whole Numbers (181-230) 7 Developing Proficiency with Other Numbers (231-254) 8 Developing Mathematical Proficiency Beyond Number (255-312) 9 Teaching for Mathematical Proficiency (313-368) 10 Developing Proficiency in Teaching Mathematics (369-406) 11 Conclusions and Recommendations (407-432) Biographical Sketches (433-440) Index (441-454)