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Math Instruction for Students with Learning Problems

ISBN: 9780205460892 | 0205460895
Edition: 1st
Format: Paperback
Publisher: Pearson
Pub. Date: 11/13/2006

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SummaryTable of Contents
A field-tested and research-based approach to mathematics instruction for students with learning problems designed to build the confidence and competence of pre-service and in-service teachers (Pre-K-12). Field-testing over a three-year period showed the approaches in this text resulted in significantly improved teacher candidate attitudes about mathematics, increased mathematics content understanding, and professional-level skills in mathematics assessment and instruction. Teacher and student attitudes about mathematics are addressed from the ... MORE
Prefacexiii
FOUNDATIONS
Mathematics in Today's Schools: The Context for Learning Challenges
1(27)
... MORE
Mathematical Dispositions
3(6)
Student Dispositions
6(2)
Encouraging Students with Learning Problems
8(1)
Mathematics Reform
9(1)
National Mathematics Standards
10(5)
Scope of the Mathematics Curriculum
15(8)
Process Standards
15(2)
Content Standards
17(6)
High-Stakes Testing and Implications for Students with Learning Problems
23(1)
Today's Mathematics Classrooms: A Case for Collaboration
24(2)
Chapter Summary
26(1)
Resources
27(1)
Foundations of Mathematics Learning
28(31)
Precursors of Mathematics Learning
29(7)
Brain Development
30(1)
Concepts and Skills Developed during Early Childhood
31(2)
Development of Cognitive Structures Related to Mathematics
33(1)
Importance of Informal Mathematics Knowledge
34(2)
Signs of Learning Problems in Young Children
36(1)
Developmentally Appropriate Mathematics for Young Children
36(5)
Theories about Learning Applied to Mathematics
41(7)
Behaviorist Theories
42(1)
Cognitive Theories
43(1)
Socio-Cultural Theories
44(1)
Interrelated Theories
45(3)
Constructivism
48(5)
What Is Constructivism?
49(2)
How Is Constructivism Related to Mathematics Learning?
51(1)
Is Constructivism Relevant for Students with Learning Problems?
51(1)
A Balanced View
52(1)
Theories about Mathematics Disabilities and Student Characteristics
53(4)
Specific Mathematics Disabilities
53(1)
Characteristics of Students' Mathematics Learning Problems
54(3)
Chapter Summary
57(1)
Resources
58(1)
ASSESSMENT AND INSTRUCTION
Mathematics Assessment of Students with Learning Problems
59(35)
Purposes of Assessment
60(4)
Assessment for Students with Disabilities
60(1)
Response to Intervention
61(1)
Purposes of Broader Assessments
62(2)
Assessment Standards
64(2)
Standardized Tools for Individualized Mathematics Assessment
66(5)
Alternative Mathematics Assessment of Students with Learning Problems
71(17)
Curriculum-Based Assessment
73(4)
Performance Tasks
77(2)
Portfolios
79(2)
Assessment Strategies
81(5)
Classroom Assessment Systems
86(2)
Assessing Higher-Order Processes
88(4)
Collaboration for Assessment
92(1)
Chapter Summary
93(1)
Resources
93(1)
Effective Mathematics Instruction for Students with Learning Problems
94(45)
Principles of Mathematics Instruction
96(16)
Planning and Delivering Instruction
112(14)
Planning with Principles in Mind
112(6)
Lesson-Specific Planning
118(4)
Types of Mathematics Lessons
122(4)
Developing a Student-Centered Mathematics Curriculum
126(8)
Unit Planning in Mathematics
127(5)
Advanced Mathematics Study in High School
132(2)
Teacher Collaboration for Instruction
134(3)
Chapter Summary
137(1)
Resources
138(1)
Problem-Solving Instruction for Students with Learning Problems
139(32)
The Importance of Problem-Solving Skills
140(4)
Characteristics of Problem Solvers
144(2)
Research on Students with Disabilities
145(1)
Problem-Solving Sequences
146(4)
Teaching Problem-Solving Strategies
150(12)
Strategies for ``Understand the Problem''
150(3)
Strategies for ``Develop a Plan''
153(8)
Strategies for ``Carry Out the Plan''
161(1)
Strategies for ``Look Back''
162(1)
Curriculum Concerns
162(7)
Problem-Solving Curricula
164(2)
Problem Solving across the Curriculum
166(2)
Problem-Solving Instructional Guidelines
168(1)
Chapter Summary
169(1)
Resources
169(2)
RESOURCES AND EXTENSIONS
Materials and Resources to Support Mathematics Instruction
171(37)
Universal Design
172(2)
Curricula for Special-Needs Students
174(6)
Strategic Math Series
175(1)
Direct Instruction Mathematics
176(2)
Adaptations for Special Populations
178(1)
TouchMath
178(2)
General Education Materials: Concerns and Adaptations
180(8)
Mathematics Textbooks: Criteria and Review
180(2)
General Education Materials: Research Base
182(2)
Adapting Mathematics Textbooks
184(4)
Selecting, Creating, and Using Manipulatives
188(10)
Creating Materials
189(4)
Commercial Manipulatives
193(5)
Technology Support
198(6)
Calculators
198(2)
Software
200(2)
Interactive Web
202(1)
Computer Environments
202(2)
Other Resources
204(2)
Newspapers and Print Media
204(1)
Organizations and Projects
204(2)
Chapter Summary
206(1)
Resources
207(1)
Integrating Mathematics with Content Areas and Life Skills
208(37)
Integrating Mathematics with Other Content Areas
209(16)
The Math-Science Connection
211(2)
Mathematics as a Tool for Social Studies
213(2)
Writing in Mathematics
215(4)
Literature and Mathematics
219(2)
The Art of Mathematics
221(4)
Other Considerations for Content Area Integration
225(1)
Career Education and Life-Skills Mathematics
225(17)
Career Education
226(3)
Life-Skills Mathematics
229(8)
Applied Math
237(1)
Transition Planning
238(4)
Chapter Summary
242(1)
Resources
243(2)
INTRODUCTION TO THE CONTENT STRANDS
245(1)
Number Sense and Place Value
246(20)
Number Sense
247(1)
Importance of Number Sense for Mathematical Achievement
248(1)
Promoting Number Sense Development
249(8)
Mental Mathematics
249(4)
Estimation
253(1)
Number Meaning
254(2)
The Language of Mathematics
256(1)
Place Value
257(2)
Before Place Value
257(1)
The Value of Place Value
258(1)
Teaching Place Value Concepts
259(3)
Data Analysis
262(2)
Resources
264(2)
Whole-Number Relationships
266(23)
Understanding Single-Digit Operations
267(11)
Counting, Addition, and Subtraction Concepts
268(5)
Concept of Equivalence
273(2)
Multiplication and Division Concepts
275(3)
Multi-Digit Computation
278(10)
Multi-Digit Addition and Subtraction
279(2)
Multi-Digit Multiplication and Division
281(2)
Alternative Algorithms
283(5)
Multicultural Connection
288(1)
Resources
288(1)
Spatial Sense
289(21)
Importance of Spatial Sense
291(1)
Development and Assessment of Spatial Abilities
292(7)
Development of Spatial Abilities
294(2)
Assessment of Spatial Abilities
296(1)
Research with Students with Disabilities
297(2)
Developing Spatial Abilities across the Mathematics Curriculum
299(8)
Promoting Spatial Development: K--2
300(3)
Promoting Spatial Development: 3--5
303(1)
Promoting Spatial Development: Middle Grades
304(1)
Promoting Spatial Development: High School
305(2)
Integration of Number and Spatial Sense
307(1)
Multicultural Connection
308(1)
Resources
309(1)
Rational Numbers
310(19)
Rational Numbers
311(3)
Part--Whole Comparison
312(1)
Quotient
312(1)
Ratio
312(1)
Operator
313(1)
Measure
313(1)
Related Concepts
314(3)
Equivalence
314(2)
Proportion
316(1)
Probability
316(1)
Common Problems and Recommendations for Instruction
317(10)
Common Problems
317(1)
Instructional Strategies for Fraction Concepts
318(5)
Strategies for Teaching Decimal Concepts and Calculations
323(1)
Strategies for Teaching Related Concepts
324(3)
Multicultural Connection
327(1)
Resources
328(1)
Functions
329(19)
Development of the Concept of Function
331(2)
Functions across the Mathematics Curriculum
333(1)
Instructional Methods for Challenging Concepts
334(11)
Algebraic Notation
335(3)
Simplifying Algebraic Expressions and Solving Equations
338(3)
Coordinate Plane Graphing
341(2)
Linear Functions
343(2)
Extensions of Functions
345(1)
Multicultural Connection
346(1)
Resources
347(1)
Appendix: Resources348(11)
References359(21)
Index380


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