Adding It Up: Helping Children Learn Mathematics

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Table of Contents
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

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Box 5–1 Number Names in Chinese, English, and Spanish

a. One to ten

Arabic numeral	1	2	3	4	5
Chinese (spoken)	yi	er	san	si	wu
English	one	two	three	four	five
Spanish	uno	dos	tres	cuatro	cinco

b. Eleven to twenty

Arabic numeral	11	12	13	14	15
Chinese (spoken)	shi yi	shi er	shi san	shi si	shi wu
English	eleven	twelve	thirteen	fourteen	fifteen
Spanish	once	doce	trece	catorce	quince

c. Twenty to ninety-nine

Language	Rule
Chinese (spoken)	Decade name (unit name+shi)+unit name
English	Decade name [(twen, thir, for, fif, six, seven, eight, nine) +-ty]+unit name
Spanish	Decade name (veinte, treinta, cuarenta, cincuenta, sesenta, setenta, ochenta, noventa)+and (y)+unit name

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