Error Patterns in Computation Using Error Patterns to Help Each Student Learn

ISBN-10: 0135009103
ISBN-13: 9780135009109
Edition: 10th 2010
List price: $54.00 Buy it from $18.56
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Book details

List price: $54.00
Edition: 10th
Copyright year: 2010
Publisher: Allyn & Bacon, Incorporated
Publication date: 1/13/2009
Binding: Paperback
Pages: 288
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 0.924
Language: English

Robert Ashlockbegan his career in 1957 as a fourth and fifth grade teacher with a bachelorrsquo;s degree in elementary education. He later received a masterrsquo;s degree in elementary school administration from Butler University and a doctorate in elementary education from Indiana University. He became a graduate assistant and teaching associate at Indiana University in 1964 and went on to teach at several institutions including the University of Maryland, Reformed Theological Seminary, Belhaven College, and finally, Covenant College in Lookout Mountain, Georgia.nbsp; Ashlock came to Covenant in 1988 to fill the need for a specialist in elementary education who could also teach on the graduate level.nbsp; He directed the Master of Education Program, taught both undergraduate and graduate education courses, and coordinated the process necessary for the teacher education program to be approved by the Georgia Professional Standards Commission. nbsp; He is one of only two professors ever to receive the title Professor Emeritus at Covenant.nbsp; He is known throughout the education community for his book,Error Patterns in Computation: Using Error Patterns to Improve Instruction, which is currently in its tenth edition. Although retired, Ashlock continues to teach a few classes.

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

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