Rent 9780130270931 | Error Patterns in Computation : Using Error Patterns to Improve Instruction

Summary Table of Contents

This book is the only one of its kind that instructs teachers to identify typical error patterns, to receive feedback on their diagnosis, and to gain insight regarding why a child may have adopted an incorrect procedure. Revised to link content to the new NCTM Standards, this new edition emphasizes the meaning of operations and using the appropriate method of computation. As in previous editions, it retains its focus on placing paper-and pencil instructional activities within the context of problem solving. Chapter topics cover diagnosing misco... MORE

PART ONE DIAGNOSIS AND INSTRUCTION

(96)

Computing with Paper and Pencil in an Age of Calculators and Computers

(8)

Instruction in Mathematics Today

... MORE

(1)

Instruction in Computation Today

(3)

Algorithms

(1)

Conceptual Learning and Procedural Learning

(1)

Error Patterns in Computation

(1)

Paper-and-Pencil Procedures Today

(2)

Diagnosing Misconceptions and Error Patterns in Computation

(34)

Learning Misconceptions and Error Patterns

(5)

Overgeneralizing

(2)

Overspecializing

(1)

Encouraging Self-Assessment

(4)

Involving Peers in Assessment

(1)

Interviewing: Observing, Recording, and Reflecting

(11)

Getting at a Student's Thinking

(2)

Observing Student Behavior

(1)

Recording Student Behavior

(2)

Watching language: Ours and Theirs

(1)

Probing for Key Understandings

(2)

Designing Questions and Tasks

(1)

Using Graphic Organizers for Diagnosis

(4)

Using Tests and Computers for Diagnosis

(2)

Guiding Diagnosis in Computation

(4)

Providing Needed Instruction in Computation

(52)

Developing Number Sense

(1)

Understanding Concepts and Principles

(3)

Numeration

(2)

Equals

(1)

Other Concepts and Principles

(1)

Understanding Operations

(2)

Attaining Computational Fluency

(2)

Teaching Mental Computation

(1)

Teaching Students to Estimate

(2)

Teaching Students to Use Calculators

(2)

Teaching Paper-and-Pencil Procedures

(7)

Instruction in Grades 1 - 2

(1)

The Role of Manipulatives

(1)

Developmental Instruction

(4)

Corrective Instruction

(1)

Acquiring Specialized Vocabulary

(2)

Using Models and Concrete Materials

(2)

Understanding and Recalling Basic Number Combinations

(5)

Talking and Writing Mathematics

(4)

Using Graphic Organizers for Instruction

(5)

Using Alternative Algorithms

(2)

Addition of Whole Numbers: Hutching's Low-Stress Method

(1)

Subtraction of Whole Numbers: The Equal Additions (or European-Latino) Method

(1)

Subtraction of Rational Numbers: The Equal Additions Method

(1)

Using Peer Tutoring

(1)

Helping Individuals through Cooperative Groups

(1)

Using Portfolios to Monitor Progress during Instruction

(2)

Guiding Instruction

(3)

Focus on the Student

(1)

Teach Concepts and Skills

(1)

Provide Instruction

(1)

Use Concrete Materials

(1)

Provide Practice

(1)

Reflecting on Instructional in Computation

(5)

PART TWO HELPING STUDENTS WHO HAVE LEARNED ERROR PATTERNS

(159)

Whole Numbers: Addition and Subtraction

(25)

Identifying Patterns

100

(6)

Error Pattern N-C-1

100

(1)

Error Pattern A-W-1

100

(1)

Error Pattern A-W-2

101

(1)

Error Pattern A-W-3

101

(1)

Error Pattern A-W-4

102

(1)

Error Pattern S-W-1

103

(1)

Error Pattern S-W-2

104

(1)

Error Pattern S-W-3

104

(1)

Error Pattern S-W-4

105

(1)

Describing Instruction

106

(7)

Error Pattern N-C-1

106

(1)

Error Pattern A-W-1

106

(1)

Error Pattern A-W-2

107

(1)

Error Pattern A-W-3

108

(1)

Error Pattern A-W-4

109

(1)

Error Pattern S-W-1

110

(1)

Error Pattern S-W-2

111

(1)

Error Pattern S-W-3

112

(1)

Error Pattern S-W-4

112

(1)

Considering Alternatives

113

(10)

Error Pattern N-C-1

113

(1)

Error Pattern A-W-1

114

(1)

Error Pattern A-W-2

115

(1)

Error Pattern A-W-3

116

(1)

Error Pattern A-W-4

117

(1)

Error Pattern S-W-1

118

(1)

Error Pattern S-W-2

119

(1)

Error Pattern S-W-3

120

(2)

Error Pattern S-W-4

122

(1)

Conclusion

123

(1)

Whole Numbers: Multiplication and Division

124

(21)

Identifying Patterns

124

(6)

Error Pattern M-W-1

124

(1)

Error Pattern M-W-2

125

(1)

Error Pattern M-W-3

126

(1)

Error Pattern D-W-1

127

(1)

Error Pattern D-W-2

128

(1)

Error Pattern D-W-3

129

(1)

Describing Instruction

130

(4)

Error Pattern M-W-1

130

(1)

Error Pattern M-W-2

131

(1)

Error Pattern M-W-3

131

(1)

Error Pattern D-W-1

132

(1)

Error Pattern D-W-2

133

(1)

Error Pattern D-W-3

134

(1)

Considering Alternatives

134

(10)

Error Pattern M-W-1

134

(3)

Error Pattern M-W-2

137

(1)

Error Pattern M-W-3

138

(2)

Error Pattern D-W-1

140

(1)

Error Pattern D-W-2

141

(1)

Error Pattern D-W-3

142

(2)

Conclusion

144

(1)

Fractions: Concepts and Equivalence

145

(15)

Identifying Patterns

145

(4)

Error Pattern F-C-1

145

(1)

Error Pattern F-C-2

146

(1)

Error Pattern F-E-1

147

(1)

Error Pattern F-E-2

148

(1)

Describing Instruction

149

(3)

Error Pattern F-C-1

149

(1)

Error Pattern F-C-2

150

(1)

Error Pattern F-E-1

151

(1)

Error Pattern F-E-2

152

(1)

Considering Alternatives

152

(6)

Error Pattern F-C-1

152

(1)

Error Pattern F-C-2

153

(2)

Error Pattern F-E-1

155

(2)

Error Pattern F-E-2

157

(1)

Conclusion

158

(2)

Fractions and Decimals: Addition and Subtraction

160

(24)

Identifying Patterns

161

(7)

Error Pattern A-F-1

161

(1)

Error Pattern A-F-2

162

(1)

Error Pattern A-F-3

163

(1)

Error Pattern S-F-1

164

(1)

Error Pattern S-F-2

165

(1)

Error Pattern S-F-3

166

(1)

Error Pattern A-D-1

167

(1)

Error Pattern S-D-1

167

(1)

Describing Instruction

168

(6)

Error Pattern A-F-1

168

(1)

Error Pattern A-F-2

169

(1)

Error Pattern S-F-3

169

(1)

Error Pattern S-F-1

170

(1)

Error Pattern S-F-2

171

(1)

Error Pattern S-F-3

171

(1)

Error Pattern A-D-1

172

(1)

Error Pattern S-D-1

173

(1)

Considering Alternatives

174

(9)

Error Pattern A-F-1

174

(1)

Error Pattern A-F-2

175

(1)

Error Pattern A-F-3

176

(1)

Error Pattern S-F-1

177

(1)

Error Pattern S-F-2

178

(1)

Error Pattern S-F-3

179

(1)

Error Pattern A-D-1

180

(2)

Error Pattern S-D-1

182

(1)

Conclusion

183

(1)

Fractions and Decimals: Multiplication and Division

184

(18)

Identifying Patterns

185

(5)

Error Pattern M-F-1

185

(1)

Error Pattern M-F-2

186

(1)

Error Pattern D-F-1

186

(1)

Error Pattern D-F-2

187

(1)

Error Pattern M-D-1

188

(1)

Error Pattern D-D-1

189

(1)

Describing Instruction

190

(4)

Error Pattern M-F-1

190

(1)

Error Pattern M-F-2

191

(1)

Error Pattern D-F-1

192

(1)

Error Pattern D-F-2

192

(1)

Error Pattern M-D-1

193

(1)

Error Pattern D-D-1

193

(1)

Considering Alternatives

194

(7)

Error Pattern M-F-1

194

(1)

Error Pattern M-F-2

195

(1)

Error Pattern D-F-1

196

(1)

Error Pattern D-F-2

197

(1)

Error Pattern M-D-1

198

(1)

Error Pattern D-D-1

199

(2)

Conclusion

201

(1)

Percent Problems

202

(10)

Identifying Patterns

202

(3)

Error Pattern P-P-1

202

(2)

Error Pattern P-P-2

204

(1)

Describing Instruction

205

(2)

Error Pattern P-P-1

205

(1)

Error Pattern P-P-2

206

(1)

Considering Alternatives

207

(4)

Error Pattern P-P-1

207

(2)

Error Pattern P-P-2

209

(2)

Conclusion

211

(1)

Geometry and Measurement

212

(26)

Identifying Patterns

213

(9)

Error Pattern G-M-1

213

(1)

Error Pattern G-M-2

214

(1)

Error Pattern G-M-3

214

(2)

Error Pattern G-M-4

216

(1)

Error Pattern G-M-5

217

(2)

Error Pattern G-M-6

219

(2)

Error Pattern G-M-7

221

(1)

Describing Instruction

222

(6)

Error Pattern G-M-1

222

(1)

Error Pattern G-M-2

223

(1)

Error Pattern G-M-3

224

(1)

Error Pattern G-M-4

225

(1)

Error Pattern G-M-5

226

(1)

Error Pattern G-M-6

226

(2)

Error Pattern G-M-7

228

(1)

Considering Alternatives

228

(9)

Error Pattern G-M-1

228

(2)

Error Pattern G-M-2

230

(1)

Error Pattern G-M-3

231

(1)

Error Pattern G-M-4

232

(1)

Error Pattern G-M-5

233

(1)

Error Pattern G-M-6

234

(2)

Error Pattern G-M-7

236

(1)

Conclusion

237

(1)

Integers

238

(9)

Identifying Patterns

238

(2)

Error Pattern A-I-1

238

(1)

Error Pattern A-I-2

239

(1)

Error Pattern S-I-1

240

(1)

Describing Instruction

240

(2)

Error Pattern A-I-1

240

(1)

Error Pattern A-I-2

241

(1)

Error Pattern S-I-1

241

(1)

Considering Alternatives

242

(4)

Error Pattern A-I-1

242

(1)

Error Pattern A-I-2

243

(2)

Error Pattern S-I-1

245

(1)

Conclusion

246

(1)

Algebra

247

(9)

Identifying Patterns

247

(3)

Error Pattern ALG-1

247

(1)

Error Pattern ALG-2

248

(1)

Error Pattern ALG-3

249

(1)

Error Pattern ALG-4

249

(1)

Describing Instruction

250

(2)

Error Pattern ALG-1

250

(1)

Error Pattern ALG-2

250

(1)

Error Pattern ALG-3

251

(1)

Error Pattern ALG-4

251

(1)

Considering Alternatives

252

(3)

Error Pattern ALG-1

252

(1)

Error Pattern ALG-2

252

(1)

Error Pattern ALG-3

253

(1)

Error Pattern ALG-4

254

(1)

Conclusion

255

(1)

Glossary

256

(5)

Selected Resources

261

(1)

Assessment and Diagnosis

261

(5)

Instruction

266

(8)

Appendices

Appendix A Selected Student Papers and Key

274

(9)

Appendix B Research on Errors in Computation

283

(6)

Appendix C Gamelike Activities with Base Blocks

289

(8)

Appendix D Sample Activities for Cooperative Groups

297

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Error Patterns in Computation : Using Error Patterns to Improve Instruction

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