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Diagnosis and Instruction | |
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Number and Operations: Computation | |
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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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Error Patterns in Computation | |
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Paper-and-Pencil Procedures Today | |
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Diagnosing Misconceptions and Error Patterns in Computation | |
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Learning Misconceptions and Error Patterns | |
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Overgeneralizing | |
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Overspecializing | |
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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 | |
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Guiding Diagnosis in Computation | |
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Reflecting on Diagnosis of Misconceptions and Error Patterns | |
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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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Numeration | |
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Equals and Equivalent | |
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Other Concepts and Principles | |
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Using Models and Concrete Materials | |
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Helping Students Understand Operations | |
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Attaining Computational Fluency | |
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Teaching Mental Computation | |
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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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The Role of Manipulatives | |
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Developmental Instruction | |
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Corrective Instruction | |
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Students with Learning Disabilities | |
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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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Understanding and Recalling Basic Number Combinations | |
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Using Alternative Algorithms | |
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Addition of Whole Numbers: Hutchings's Low-Stress Method | |
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Subtraction of Whole Numbers: The Equal Additions (or European-Latino) Method | |
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Subtraction of Rational Numbers: The Equal Additions Method | |
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Involving Peers | |
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Using Portfolios to Monitor Progress During Instruction | |
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Working with Parents | |
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Guiding Instruction | |
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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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Reflecting on Instruction in Computation | |
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Helping Students Who Have Learned Error Patterns | |
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Whole Numbers: Addition and Subtraction | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Whole Numbers: Multiplication and Division | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Fractions and Decimals: Concepts and Equivalence | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Fractions and Decimals: Addition and Substraction | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Fractions and Decimals: Multiplication and Division | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Percent and Proportion | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Geometry and Measurement | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Integers | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Algebra | |
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Identifying Patterns | |
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Planning Instruction | |
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Conclusion | |
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Glossary | |
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Selected Resources | |
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Assessment and Diagnosis | |
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Instruction | |
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Appendices | |
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Selected Student Papers and Key | |