Rent 9780023042126 | Error Patterns in Computation | Robert B. Ashlock @knetbooks.com

Summary Table of Contents

As your students learn about mathematical operations and methods of computation, they may adopt erroneous procedures and misconceptions, despite your best efforts. This engaging book was written to model how you, the teacher, can make thoughtful analyses of your student's work, and in doing so, discover patterns in the errors they make. The text considers reasons why students may have learned erroneous procedures and presents strategies for helping those students. You will come away from the reading with a clear vision of how you can use student error patterns to gain more specific knowledge of their strengths on which to base your future instruction. Book jacket.

Diagnosis and Instruction	p. 1
Number and Operations: Computation	p. 3
Instruction in Mathematics	p. 3
Computational Fluency	p. 4
Algorithms	p. 7
Conceptual Learning and Procedural Learning	p. 7
Error Patterns in Computation	p. 9
Paper-and-Pencil Procedures Today	p. 9
Diagnosing Misconceptions and Error Patterns in Computation	... MOREp. 12
Learning Misconceptions and Error Patterns	p. 15
Overgeneralizing	p. 18
Overspecializing	p. 20
Encouraging Self-Assessment	p. 21
Interviewing	p. 23
Getting at a Student's Thinking	p. 26
Observing Student Behavior	p. 28
Recording Student Behavior	p. 29
Watching Language: Ours and Theirs	p. 30
Probing for Key Understandings	p. 32
Designing Questions and Tasks	p. 33
Using Graphic Organizers for Diagnosis	p. 35
Using Tests	p. 37
Guiding Diagnosis in Computation	p. 41
Reflecting on Diagnosis of Misconceptions and Error Patterns	p. 42
Providing Data-Driven Instruction in Computation	p. 45
Developing Number Sense	p. 46
Helping Students Understand Big Ideas	p. 47
Numeration	p. 48
Equals and Equivalent	p. 50
Other Concepts and Principles	p. 51
Using Models and Concrete Materials	p. 51
Helping Students Understand Operations	p. 53
Attaining Computational Fluency	p. 55
Teaching Mental Computation	p. 56
Teaching Students to Estimate	p. 57
Teaching Students to Use Calculators	p. 59
Teaching Paper-and-Pencil Procedures	p. 61
Instruction in Grades 1-2	p. 61
The Role of Manipulatives	p. 63
Developmental Instruction	p. 63
Corrective Instruction	p. 67
Students with Learning Disabilities	p. 67
Developing Mathematical Vocabulary	p. 69
Talking and Writing Mathematics	p. 71
Using Graphic Organizers for Instruction	p. 74
Understanding and Recalling Basic Number Combinations	p. 79
Using Alternative Algorithms	p. 84
Addition of Whole Numbers: Hutchings's Low-Stress Method	p. 85
Subtraction of Whole Numbers: The Equal Additions (or European-Latino) Method	p. 85
Subtraction of Rational Numbers: The Equal Additions Method	p. 86
Involving Peers	p. 86
Using Portfolios to Monitor Progress During Instruction	p. 89
Working with Parents	p. 90
Guiding Instruction	p. 91
Focus on the Student	p. 91
Involve Parents	p. 92
Teach Concepts and Skills	p. 92
Provide Instruction	p. 92
Use Concrete Materials	p. 93
Provide Practice	p. 94
Reflecting on Instruction in Computation	p. 94
Helping Students Who Have Learned Error Patterns	p. 99
Whole Numbers: Addition and Subtraction	p. 101
Identifying Patterns	p. 101
Planning Instruction	p. 108
Conclusion	p. 119
Whole Numbers: Multiplication and Division	p. 120
Identifying Patterns	p. 120
Planning Instruction	p. 126
Conclusion	p. 136
Fractions and Decimals: Concepts and Equivalence	p. 137
Identifying Patterns	p. 137
Planning Instruction	p. 142
Conclusion	p. 149
Fractions and Decimals: Addition and Substraction	p. 151
Identifying Patterns	p. 151
Planning Instruction	p. 159
Conclusion	p. 169
Fractions and Decimals: Multiplication and Division	p. 171
Identifying Patterns	p. 172
Planning Instruction	p. 177
Conclusion	p. 185
Percent and Proportion	p. 186
Identifying Patterns	p. 186
Planning Instruction	p. 189
Conclusion	p. 193
Geometry and Measurement	p. 194
Identifying Patterns	p. 194
Planning Instruction	p. 204
Conclusion	p. 212
Integers	p. 213
Identifying Patterns	p. 213
Planning Instruction	p. 215
Conclusion	p. 219
Algebra	p. 220
Identifying Patterns	p. 220
Planning Instruction	p. 223
Conclusion	p. 226
Glossary	p. 227
Selected Resources	p. 232
Assessment and Diagnosis	p. 232
Instruction	p. 236
Appendices
Selected Student Papers and Key	p. 244
Table of Contents provided by Ingram. All Rights Reserved.

RENT TEXTBOOKS

Error Patterns in Computation

Why Rent from Knetbooks?

Top 5 reasons to order all your textbooks from Knetbooks:

Related Products