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Math Instruction for Students with Learning Problems / Edition 1

Math Instruction for Students with Learning Problems / Edition 1

by Susan P. Gurganus
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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 book 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 first page, as are other student learning issues such as language, specific mathematics disabilities, prior experiences, and cognitive and metacognitive factors. Written in a clear and engaging style this book is also organized to make it easy for practicing teachers to locate material, ensuring the text will continue to serve as a valuable reference in the classroom as well.

“The author has a good overall view of what is needed to teach the target students. The format of the book flows well and gives needed support to each section as needed. … The rationale for this book is very much in line with the current thinking as I see it for a book dealing with this type and scope of material.” –J. Patrick Brennan, Ed.D., Armstrong Atlantic State University


  • References national mathematics content and process standards (NCTM) – standards often ignored by special education texts.
  • Pre-K to 12 scope that enhances student ability to diagnose gaps in learning and provides appropriate content connections, a benefit that addresses NCLB’s “highly qualified” requirement.
  • Attention to both pedagogical issues and approaches and specific content area instruction, enabling students to develop a comprehensive pedagogical repertoire and strong content understanding.
  • Realistic teacher vignettes incorporated in each chapter that connect to chapter concepts and offer additional opportunities for discussion.
  • “Try This” boxes that actively engage students with the material during reading and instructors can draw on these additional exercises during class activities

Product Details

ISBN-13: 9780205460892
Publisher: Pearson
Publication date: 11/27/2006
Edition description: 1ST
Pages: 368
Product dimensions: 7.40(w) x 9.00(h) x 0.90(d)

About the Author

Susan Perry Gurganus is Professor Emeritus of Special Education at the College of Charleston, USA.

Table of Contents

Preface     xiii
Mathematics in Today's Schools: The Context for Learning Challenges     1
Mathematical Dispositions     3
Student Dispositions     6
Encouraging Students with Learning Problems     8
Mathematics Reform     9
National Mathematics Standards     10
Scope of the Mathematics Curriculum     15
Process Standards     15
Content Standards     17
High-Stakes Testing and Implications for Students with Learning Problems     23
Today's Mathematics Classrooms: A Case for Collaboration     24
Chapter Summary     26
Resources     27
Foundations of Mathematics Learning     28
Precursors of Mathematics Learning     29
Brain Development     30
Concepts and Skills Developed during Early Childhood     31
Development of Cognitive Structures Related to Mathematics     33
Importance of Informal Mathematics Knowledge     34
Signs of Learning Problems in Young Children     36
Developmentally Appropriate Mathematics for Young Children     36
Theories about Learning Applied to Mathematics     41
Behaviorist Theories     42
Cognitive Theories     43
Socio-Cultural Theories     44
Interrelated Theories     45
Constructivism     48
What Is Constructivism?     49
How Is Constructivism Related to Mathematics Learning?     51
Is Constructivism Relevant for Students with Learning Problems?     51
A Balanced View     52
Theories about Mathematics Disabilities and Student Characteristics     53
Specific Mathematics Disabilities     53
Characteristics of Students' Mathematics Learning Problems     54
Chapter Summary     57
Resources     58
Assessment and Instruction
Mathematics Assessment of Students with Learning Problems     59
Purposes of Assessment     60
Assessment for Students with Disabilities     60
Response to Intervention     61
Purposes of Broader Assessments     62
Assessment Standards     64
Standardized Tools for Individualized Mathematics Assessment     66
Alternative Mathematics Assessment of Students with Learning Problems     71
Curriculum-Based Assessment     73
Performance Tasks     77
Portfolios     79
Assessment Strategies      81
Classroom Assessment Systems     86
Assessing Higher-Order Processes     88
Collaboration for Assessment     92
Chapter Summary     93
Resources     93
Effective Mathematics Instruction for Students with Learning Problems     94
Principles of Mathematics Instruction     96
Planning and Delivering Instruction     112
Planning with Principles in Mind     112
Lesson-Specific Planning     118
Types of Mathematics Lessons     122
Developing a Student-Centered Mathematics Curriculum     126
Unit Planning in Mathematics     127
Advanced Mathematics Study in High School     132
Teacher Collaboration for Instruction     134
Chapter Summary     137
Resources     138
Problem-Solving Instruction for Students with Learning Problems     139
The Importance of Problem-Solving Skills     140
Characteristics of Problem Solvers     144
Research on Students with Disabilities     145
Problem-Solving Sequences     146
Teaching Problem-Solving Strategies     150
Strategies for "Understand the Problem"     150
Strategies for "Develop a Plan"     153
Strategies for "Carry Out the Plan"     161
Strategies for "Look Back"     162
Curriculum Concerns     162
Problem-Solving Curricula     164
Problem Solving across the Curriculum     166
Problem-Solving Instructional Guidelines     168
Chapter Summary     169
Resources     169
Resources and Extensions
Materials and Resources to Support Mathematics Instruction     171
Universal Design     172
Curricula for Special-Needs Students     174
Strategic Math Series     175
Direct Instruction Mathematics     176
Adaptations for Special Populations     178
TouchMath     178
General Education Materials: Concerns and Adaptations     180
Mathematics Textbooks: Criteria and Review     180
General Education Materials: Research Base     182
Adapting Mathematics Textbooks     184
Selecting, Creating, and Using Manipulatives     188
Creating Materials     189
Commercial Manipulatives     193
Technology Support     198
Calculators     198
Software     200
Interactive Web      202
Computer Environments     202
Other Resources     204
Newspapers and Print Media     204
Organizations and Projects     204
Chapter Summary     206
Resources     207
Integrating Mathematics with Content Areas and Life Skills     208
Integrating Mathematics with Other Content Areas     209
The Math-Science Connection     211
Mathematics as a Tool for Social Studies     213
Writing in Mathematics     215
Literature and Mathematics     219
The Art of Mathematics     221
Other Considerations for Content Area Integration     225
Career Education and Life-Skills Mathematics     225
Career Education     226
Life-Skills Mathematics     229
Applied Math     237
Transition Planning     238
Chapter Summary     242
Resources     243
Introduction to the Content Strands     245
Number Sense and Place Value     246
Number Sense     247
Importance of Number Sense for Mathematical Achievement     248
Promoting Number Sense Development     249
Mental Mathematics      249
Estimation     253
Number Meaning     254
The Language of Mathematics     256
Place Value     257
Before Place Value     257
The Value of Place Value     258
Teaching Place Value Concepts     259
Data Analysis     262
Resources     264
Whole-Number Relationships     266
Understanding Single-Digit Operations     267
Counting, Addition, and Subtraction Concepts     268
Concept of Equivalence     273
Multiplication and Division Concepts     275
Multi-Digit Computation     278
Multi-Digit Addition and Subtraction     279
Multi-Digit Multiplication and Division     281
Alternative Algorithms     283
Multicultural Connection     288
Resources     288
Spatial Sense     289
Importance of Spatial Sense     291
Development and Assessment of Spatial Abilities     292
Development of Spatial Abilities     294
Assessment of Spatial Abilities     296
Research with Students with Disabilities     297
Developing Spatial Abilities across the Mathematics Curriculum      299
Promoting Spatial Development: K-2     300
Promoting Spatial Development: 3-5     303
Promoting Spatial Development: Middle Grades     304
Promoting Spatial Development: High School     305
Integration of Number and Spatial Sense     407
Multicultural Connection     308
Resources     309
Rational Numbers     310
Rational Numbers     311
Part-Whole Comparison     312
Quotient     312
Ratio     312
Operator     313
Measure     313
Related Concepts     314
Equivalence     314
Proportion     316
Probability     316
Common Problems and Recommendations for Instruction     317
Common Problems     317
Instructional Strategies for Fraction Concepts     318
Strategies for Teaching Decimal Concepts and Calculations     323
Strategies for Teaching Related Concepts     324
Multicultural Connection     327
Resources     328
Functions     329
Development of the Concept of Function     331
Functions across the Mathematics Curriculum      333
Instructional Methods for Challenging Concepts     334
Algebraic Notation     335
Simplifying Algebraic Expressions and Solving Equations     338
Coordinate Plane Graphing     341
Linear Functions     343
Extensions of Functions     345
Multicultural Connection     346
Resources     347
Resources     348
References     359
Index     380

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