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Error Patterns in Computation

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ISBN-10: 0023042125

ISBN-13: 9780023042126

Edition: 6th 1994

Authors: Robert B. Ashlock

List price: $20.00
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Description:

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.
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Book details

List price: $20.00
Edition: 6th
Copyright year: 1994
Publisher: Prentice Hall PTR
Binding: Paperback
Pages: 256
Weight: 0.110
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…    

Diagnosis and Instruction
Number and Operations: Computation
Instruction in Mathematics
Computational Fluency
Algorithms
Conceptual Learning and Procedural Learning
Error Patterns in Computation
Paper-and-Pencil Procedures Today
Diagnosing Misconceptions and Error Patterns in Computation
Learning Misconceptions and Error Patterns
Overgeneralizing
Overspecializing
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
Guiding Diagnosis in Computation
Reflecting on Diagnosis of Misconceptions and Error Patterns
Providing Data-Driven Instruction in Computation
Developing Number Sense
Helping Students Understand Big Ideas
Numeration
Equals and Equivalent
Other Concepts and Principles
Using Models and Concrete Materials
Helping Students Understand Operations
Attaining Computational Fluency
Teaching Mental Computation
Teaching Students to Estimate
Teaching Students to Use Calculators
Teaching Paper-and-Pencil Procedures
Instruction in Grades 1-2
The Role of Manipulatives
Developmental Instruction
Corrective Instruction
Students with Learning Disabilities
Developing Mathematical Vocabulary
Talking and Writing Mathematics
Using Graphic Organizers for Instruction
Understanding and Recalling Basic Number Combinations
Using Alternative Algorithms
Addition of Whole Numbers: Hutchings's Low-Stress Method
Subtraction of Whole Numbers: The Equal Additions (or European-Latino) Method
Subtraction of Rational Numbers: The Equal Additions Method
Involving Peers
Using Portfolios to Monitor Progress During Instruction
Working with Parents
Guiding Instruction
Focus on the Student
Involve Parents
Teach Concepts and Skills
Provide Instruction
Use Concrete Materials
Provide Practice
Reflecting on Instruction in Computation
Helping Students Who Have Learned Error Patterns
Whole Numbers: Addition and Subtraction
Identifying Patterns
Planning Instruction
Conclusion
Whole Numbers: Multiplication and Division
Identifying Patterns
Planning Instruction
Conclusion
Fractions and Decimals: Concepts and Equivalence
Identifying Patterns
Planning Instruction
Conclusion
Fractions and Decimals: Addition and Substraction
Identifying Patterns
Planning Instruction
Conclusion
Fractions and Decimals: Multiplication and Division
Identifying Patterns
Planning Instruction
Conclusion
Percent and Proportion
Identifying Patterns
Planning Instruction
Conclusion
Geometry and Measurement
Identifying Patterns
Planning Instruction
Conclusion
Integers
Identifying Patterns
Planning Instruction
Conclusion
Algebra
Identifying Patterns
Planning Instruction
Conclusion
Glossary
Selected Resources
Assessment and Diagnosis
Instruction
Appendices
Selected Student Papers and Key