Rent 9780131198869 | Error Patterns in Computation: Using Error Patterns to Improve Instruction

Summary Table of Contents

Reflecting many of the concerns of NCTM's Principles and Standards for School Mathematics, the ninth edition of Error Patterns in Computation is the only book available that assists teachers with identifying typical error patterns, receiving feedback on their diagnosis, and gaining insight regarding why a child may have adopted an incorrect procedure. Two major causes of error patterns - over-generalizing and over-specializing - are discussed. Simple and well organized, this book explains common errors students make in computation in every math... MORE

PART ONE DIAGNOSIS AND INSTRUCTION

(98)

Number and Operations: Computation

(9)

Instruction in Mathematics

... MORE

(1)

Computational Fluency

(3)

Algorithms

(1)

Conceptual Learning and Procedural Learning

(2)

Error Patterns in Computation

(1)

Paper-and-Pencil Procedures Today

(3)

Diagnosing Misconceptions and Error Patterns in Computation

(33)

Learning Misconceptions and Error Patterns

(6)

Overgeneralizing

(2)

Overspecializing

(1)

Encouraging Self-Assessment

(2)

Interviewing

(12)

Getting at a Student's Thinking

(2)

Observing Student Behavior

(1)

Recording Student Behavior

(1)

Watching Language: Ours and Theirs

(2)

Probing for Key Understandings

(1)

Designing Questions and Tasks

(2)

Using Graphic Organizers for Diagnosis

(2)

Using Tests

(4)

Guiding Diagnosis in Computation

(1)

Reflecting on Diagnosis of Misconceptions and Error Patterns

(3)

Providing Data-Driven Instruction in Computation

(54)

Developing Number Sense

(1)

Helping Students Understand Big Ideas

(4)

Numeration

(2)

Equals and Equivalent

(1)

Other Concepts and Principles

(1)

Using Models and Concrete Materials

(2)

Helping Students Understand Operations

(2)

Attaining Computational Fluency

(1)

Teaching Mental Computation

(1)

Teaching Students to Estimate

(2)

Teaching Students to Use Calculators

(2)

Teaching Paper-and-Pencil Procedures

(8)

Instruction in Grades 1--2

(2)

The Role of Manipulatives

(1)

Developmental Instruction

(4)

Corrective Instruction

(1)

Students with Learning Disabilities

(2)

Developing Mathematical Vocabulary

(2)

Talking and Writing Mathematics

(3)

Using Graphic Organizers for Instruction

(5)

Understanding and Recalling Basic Number Combinations

(5)

Using Alternative Algorithms

(2)

Addition of Whole Numbers: Hutchings'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)

Involving Peers

(3)

Using Portfolios to Monitor Progress During Instruction

(1)

Working with Parents

(1)

Guiding Instruction

(3)

Focus on the Student

(1)

Involve Parents

(1)

Teach Concepts and Skills

(1)

Provide Instruction

(1)

Use Concrete Materials

(1)

Provide Practice

(1)

Reflecting on Instruction in Computation

(5)

PART TWO HELPING STUDENTS WHO HAVE LEARNED ERROR PATTERNS

(128)

Whole Numbers: Addition and Subtraction

101

(19)

Identifying Patterns

101

(7)

Planning Instruction

108

(11)

Conclusion

119

(1)

Whole Numbers: Multiplication and Division

120

(17)

Identifying Patterns

120

(6)

Planning Instruction

126

(10)

Conclusion

136

(1)

Fractions and Decimals: Concepts and Equivalence

137

(14)

Identifying Patterns

137

(5)

Planning Instruction

142

(7)

Conclusion

149

(2)

Fractions and Decimals: Addition and Subtraction

151

(20)

Identifying Patterns

151

(8)

Planning Instruction

159

(10)

Conclusion

169

(2)

Fractions and Decimals: Multiplication and Division

171

(15)

Identifying Patterns

172

(5)

Planning Instruction

177

(8)

Conclusion

185

(1)

Percent and Proportion

186

(8)

Identifying Patterns

186

(3)

Planning Instruction

189

(4)

Conclusion

193

(1)

Geometry and Measurement

194

(19)

Identifying Patterns

194

(10)

Planning Instruction

204

(8)

Conclusion

212

(1)

Integers

213

(7)

Identifying Patterns

213

(2)

Planning Instruction

215

(4)

Conclusion

219

(1)

Algebra

220

(7)

Identifying Patterns

220

(3)

Planning Instruction

223

(3)

Conclusion

226

(1)

Glossary

227

(5)

Selected Resources

232

(40)

Assessment and Diagnosis

232

(4)

Instruction

236

(8)

Appendices

Appendix A Selected Student Papers and Key

244

(9)

Appendix B Research on Errors in Computation

253

(6)

Appendix C Game-Like Activities with Base Blocks

259

(7)

Appendix D Sample Activities for Cooperative Groups

266

(6)

Appendix E A Diagnostic Interview

272

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Error Patterns in Computation: Using Error Patterns to Improve Instruction

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