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Preface | |
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Misconceptions and Error Patterns | |
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Computaion, Misconceptions, and Error Patterns | |
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Instruction in Mathematics | |
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Computational Fluency | |
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Algorithms | |
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Conceptual Learning and Procedural Learning | |
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Paper-and-Pencil Procedures Today | |
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Learning Misconceptions and Error Patterns | |
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Overgeneralizing | |
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Overspecializing | |
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Error Patterns in Computation | |
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Further Reflection | |
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References | |
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Error Patterns: Addition and Subtraction with Whole Numbers | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Further Reflection | |
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Additional Practice | |
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References | |
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Error Patterns: Multiplication and Division with Whole Numbers | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Further Reflection | |
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Additional Practice | |
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Misconceptions and Error Patterns: Concepts and Equivalence with Fractions and Decimals | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Further Reflection | |
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Refrence | |
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Error Patterns: Addition and Subtraction with Fractions and Decimals | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Further Reflection | |
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Additional Practice | |
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Refrences | |
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Error Patterns: Multiplication and Division with Fractions and Measurement | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Further Reflection | |
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Additional Practice | |
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Introduction to Misconceptions and Error Patterns: Geometry and Measurement | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Further Reflection | |
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Introduction to Misconceptions and Error Patterns: Percent, Proportion, Integers, and Algebra | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Further Reflection | |
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Additional Practice | |
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Diagnosis and Instruction | |
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Diagnosing Misconceptions and Error Patterns in Computation and in Other Mathematical Topics | |
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Assessing for Varied Purposes | |
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Using Formative Assessment: Diagnosing | |
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Using Open-Ended Assessment | |
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Encouraging Self-Assessment | |
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Interviewing | |
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Getting at a Student's Thinking | |
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Observing Student Behavior | |
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Recording Student Behavior | |
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Watching Language: Ours and Theirs | |
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Probing for Key Understandings | |
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Designing Questions and Tasks | |
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Using Graphic Organizers for Diagnosis | |
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Using Tests for Diagnosis | |
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Using Problem Writing for Diagnosis | |
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Assessing Dispositions | |
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Guiding Diagnosis in Computation | |
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Conclusion | |
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Further Reflection | |
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Refrences | |
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Providing Data-Driven Instruction in Computation | |
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Developing Number Sense | |
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Helping Students Understand Big Ideas | |
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Many Names for a Number | |
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Numeration | |
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Equals and Equivalent | |
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Operations | |
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Other Concepts and Principles | |
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Making Connections | |
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Understanding and Recalling Basic Number Facts | |
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Attaining Computational Fluency | |
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Teaching Mental Computaion | |
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Teaching Students to Estimate | |
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Teaching Students to Use Calculators | |
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Teaching Paper-and-Pencil Procedures | |
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Instruction in Grades 1-2 | |
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Developmental Instruction | |
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Corrective Instruction | |
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Students with Special Needs | |
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Conclusion | |
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Further Reflection | |
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References | |
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Enriching Instruction in Computation and Other Mathematical Topics | |
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Teaching So Students Can Use What They Learn | |
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Using Representations | |
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The Role of Representations in Learning | |
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Using Representations When Teaching | |
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Developing Mathematical Vocabulary | |
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Talking and Writing Mathematics | |
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Using Graphic Organizers for Instruction | |
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Using Classroom Discourse | |
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Using Portfolios to Monitor and Encourage Progress | |
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Conclusion | |
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Focus on the student | |
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Involve Parents | |
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Teach Concepts and Skills | |
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Provide Instruction | |
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Use Concrete Materials | |
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Provide Practice | |
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Further Reflection | |
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References | |
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Glossary | |
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Key For Additional Practice | |
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Selected Resources | |
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Assessment and Diagnosis | |
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Instruction | |
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Appendixes | |
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Using Alternative Algorithms | |
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Addition of Whole Numbers: Hutchings's Low-Stress Method | |
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Subraction of Whole Numbers: The Equal Additions (or European-Latino) Method | |
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Subraction of Rational Numbers: The Equal Additions Method | |
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Involving Peers | |
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Working with Parents | |
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Game-Like Activities with Base Blocks or the Equivalent | |
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Activities for Cooperative Groups | |
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Introducing Total-and-Parts Meanings for Operations | |
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A Diagnostic Interview | |
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A Thematic Unit Can Make Connections Clear | |