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Error Patterns in Computation,9780135731970

Error Patterns in Computation

by Ashlock, Robert B.
Edition:
7th
ISBN13:

9780135731970

ISBN10:
0135731976
Format:
Paperback
Pub. Date:
6/1/1997
Publisher(s):
Prentice Hall
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Summary

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.

Table of Contents

PART ONE DIAGNOSIS AND INSTRUCTION 1(90)
CHAPTER One Computing with Paper and Pencil in an Age of Calculators and Computers
3(6)
Paper-and-Pencil Computation Procedures Today
3(3)
Importance of Conceptual Understanding
6(1)
Error Patterns in Computation
7(2)
CHAPTER Two Diagnosing Error Patterns in Computation
9(35)
Learning Error Patterns
10(5)
Overgeneralizing and Overspecializing
15(2)
Encouraging Self-Assessment
17(3)
Using Graphic Organizers for Diagnosis
20(2)
Using Tests as a Part of Diagnosis
22(5)
Using Computers for Diagnosis
27(1)
Interviewing: Observing, Recording, and Reflecting
27(13)
Getting at a Student's Thinking
29(3)
Observing Student Behavior
32(1)
Recording Student Behavior
33(1)
Watching Language: Yours and Theirs
34(1)
Probing for Key Understandings
35(3)
Designing Questions and Tasks
38(2)
Guiding Diagnosis of Written Computation
40(4)
CHAPTER Three Providing Needed Instruction in Computation
44(49)
Understanding Concepts and Principles
46(4)
Numeration
47(1)
Equals
48(1)
Other Concepts and Principles
49(1)
Acquiring Specialized Vocabulary
50(1)
Using Models and Manipulatives
51(3)
Recalling the Basic Facts
54(4)
Stressing Estimation
58(2)
Teaching Students to Compute
60(6)
Talking and Writing Mathematics
66(3)
Using Graphic Organizers for Instruction
69(5)
Using Calculators and Computers
74(2)
Using Alternative Algorithms
76(2)
Subtraction of Whole Numbers: The Equal Additions Method
77(1)
Subtraction of Rational Numbers: The Equal Additions Method
77(1)
Using Cooperative Groups
78(2)
Monitoring Progress with Portfolios
80(2)
Guiding Instruction
82(9)
Focus on the Student
82(1)
Teach Concept and Skills
83(1)
Provide Instruction
83(1)
Use Concrete Materials
84(1)
Provide Practice
85(6)
PART TWO IDENTIFYING, ANALYZING, AND HELPING STUDENTS CORRECT SPECIFIC ERROR PATTERNS 91(175)
CHAPTER Four Whole Numbers: Addition and Subtraction
93(29)
CHAPTER Five Whole Numbers: Multiplication and Division
122(28)
CHAPTER Six Rational Numbers: Concepts and Equivalence
150(19)
CHAPTER Seven Rational Numbers: Addition and Subtraction
169(30)
CHAPTER Eight Rational Numbers: Multiplication and Division
199(20)
CHAPTER Nine Rational Numbers: Percent Problems
219(11)
CHAPTER Ten Geometry and Measurement
230(27)
CHAPTER Eleven Integers
257(9)
SELECTED REFERENCES 266(21)
References Focusing on Assessment and Diagnosis
266(11)
References Focusing on Instruction
277(10)
APPENDICES 287
Appendix A Additional Student Papers and Key to Error Patterns 287(25)
Appendix B Research on Errors in Computation 312(6)
Appendix C Sample Activities for Cooperative Groups 318


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