Knowing_and_Teaching_Elementary_Mathemat (1)

Recommendations

Info

To Jianfeng, Sushu, and John,and to Cathy Kessel,with deepest love and appreciation
ContentsAuthor’s Preface to the Anniversary EditionSeries Editor’s Introduction to the Anniversary EditionA Note about the Anniversary EditionForewordAcknowledgmentsIntroductionixxiiixvxvixxxxiii1. Subtraction With Regrouping: Approaches To Teaching A Topic 1The U.S. Teachers’ Approach: Borrowing Versus Regrouping 2The Chinese Teachers’ Approach: “Decomposing a Higher Value Unit” 6Discussion 18Summary 222. Multidigit Number Multiplication: Dealing With Students’ Mistakes 24The U.S. Teachers’ Approach: Lining Up Versus Separating Into 25Three ProblemsThe Chinese Teachers’ Approach: Elaborating the Concept of33Place ValueDiscussion 44Summary 463. Generating Representations: Division By Fractions 47The U.S. Teachers’ Performance on Calculation 47The Chinese Teachers’ Performance on Calculation 49The U.S. Teachers’ Representations of Division by Fractions 55The Chinese Teachers’ Approach to the Meaning of Division61by FractionsDiscussion 69Summary 714. Exploring New Knowledge: The Relationship Between Perimeter 72And AreaHow the U.S. Teachers Explored the New Idea 73How the Chinese Teachers Explored the New Idea 77Discussion 89Summary 91
Page 2 and 3: Knowing and TeachingElementary Math
Page 4 and 5: Knowing and TeachingElementary Math
Page 8 and 9: viii Contents5. Teachers’ Subject
Page 10 and 11: xAuthor’s Preface to the Annivers
Page 12 and 13: xiiAuthor’s Preface to the Annive
Page 14 and 15: xivSeries Editor’s Introduction t
Page 16 and 17: ForewordLee S.ShulmanThe Carnegie F
Page 18 and 19: xviii Forewordbe tests that assess
Page 20 and 21: AcknowledgmentsAbout 30 years ago,
Page 22 and 23: xxii AcknowledgmentsI would like to
Page 24 and 25: xxiv Introductionthe measurement mo
Page 26 and 27: xxvi Introductionschool or college
Page 28 and 29: xxviii IntroductionChapters 1 throu
Page 30 and 31: Chapter 1Subtraction With Regroupin
Page 32 and 33: Subtraction with Regrouping: Approa
Page 54 and 55: Multidigit Number Multiplication: D
Page 56 and 57:
Multidigit Number Multiplication: D
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Chapter 3Generating Representations
Page 78 and 79:
For some reason it is in the back o
Page 80 and 81:
Generating Representations: Divisio
Page 82 and 83:
We also encourage students to solve
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
of math.” She said she used to ha
Page 92 and 93:
Page 94 and 95:
been changed. Now what is known is
Page 96 and 97:
Page 98 and 99:
While the U.S. teachers tended to u
Page 100 and 101:
Page 102 and 103:
Exploring New Knowledge: The Relati
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Teachers’ Subject Matter Knowledg
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
105These four properties are interr
Page 136 and 137:
Chapter 6Profound Understanding Of
Page 138 and 139:
Profound Understanding of Fundament
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Chapter 7ConclusionAs I said at the
Page 154 and 155:
Conclusion 125as necessarily preced
Page 156 and 157:
Conclusion 127Time is an issue here
Page 158 and 159:
Conclusion 129evidence, students wo
Page 160 and 161:
AppendixFIG. A.1. The U.S. teachers
Page 162 and 163:
ReferencesArmstrong, B., & Bezuk, N
Page 164 and 165:
References 135Kaput, J., & Nemirovs
Page 166 and 167:
References 137Stein, M., Baxter, J.
Page 168 and 169:
Fang and Paine’s “Bridging pola
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Liping Ma’s “Knowing and Teachi
Page 190 and 191:
Author Index161Ferrucci, B., 150, 1
Page 192 and 193:
Author Index163Simon, M., xxviii, x
Page 194 and 195:
Subject Index165commutative law, 39
Page 196 and 197:
Subject Index167knowledge,see also
Page 198:
Subject Index169teacher preparation
show all

Knowing_and_Teaching_Elementary_Mathemat (1)

Create successful ePaper yourself

Delete template?

Save as template?