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| Preface | |
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| Foundations | |
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| Mathematics in Today's Schools: The Context for Learning Challenges | |
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| Mathematical Dispositions | |
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| Student Dispositions | |
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| Encouraging Students with Learning Problems | |
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| Mathematics Reform | |
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| National Mathematics Standards | |
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| Scope of the Mathematics Curriculum | |
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| Process Standards | |
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| Content Standards | |
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| High-Stakes Testing and Implications for Students with Learning Problems | |
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| Today's Mathematics Classrooms: A Case for Collaboration | |
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| Chapter Summary | |
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| Resources | |
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| Foundations of Mathematics Learning | |
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| Precursors of Mathematics Learning | |
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| Brain Development | |
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| Concepts and Skills Developed during Early Childhood | |
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| Development of Cognitive Structures Related to Mathematics | |
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| Importance of Informal Mathematics Knowledge | |
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| Signs of Learning Problems in Young Children | |
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| Developmentally Appropriate Mathematics for Young Children | |
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| Theories about Learning Applied to Mathematics | |
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| Behaviorist Theories | |
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| Cognitive Theories | |
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| Socio-Cultural Theories | |
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| Interrelated Theories | |
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| Constructivism | |
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| What Is Constructivism? | |
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| How Is Constructivism Related to Mathematics Learning? | |
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| Is Constructivism Relevant for Students with Learning Problems? | |
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| A Balanced View | |
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| Theories about Mathematics Disabilities and Student Characteristics | |
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| Specific Mathematics Disabilities | |
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| Characteristics of Students' Mathematics Learning Problems | |
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| Chapter Summary | |
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| Resources | |
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| Assessment and Instruction | |
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| Mathematics Assessment of Students with Learning Problems | |
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| Purposes of Assessment | |
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| Assessment for Students with Disabilities | |
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| Response to Intervention | |
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| Purposes of Broader Assessments | |
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| Assessment Standards | |
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| Standardized Tools for Individualized Mathematics Assessment | |
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| Alternative Mathematics Assessment of Students with Learning Problems | |
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| Curriculum-Based Assessment | |
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| Performance Tasks | |
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| Portfolios | |
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| Assessment Strategies | |
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| Classroom Assessment Systems | |
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| Assessing Higher-Order Processes | |
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| Collaboration for Assessment | |
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| Chapter Summary | |
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| Resources | |
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| Effective Mathematics Instruction for Students with Learning Problems | |
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| Principles of Mathematics Instruction | |
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| Planning and Delivering Instruction | |
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| Planning with Principles in Mind | |
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| Lesson-Specific Planning | |
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| Types of Mathematics Lessons | |
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| Developing a Student-Centered Mathematics Curriculum | |
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| Unit Planning in Mathematics | |
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| Advanced Mathematics Study in High School | |
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| Teacher Collaboration for Instruction | |
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| Chapter Summary | |
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| Resources | |
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| Problem-Solving Instruction for Students with Learning Problems | |
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| The Importance of Problem-Solving Skills | |
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| Characteristics of Problem Solvers | |
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| Research on Students with Disabilities | |
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| Problem-Solving Sequences | |
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| Teaching Problem-Solving Strategies | |
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| Strategies for "Understand the Problem" | |
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| Strategies for "Develop a Plan" | |
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| Strategies for "Carry Out the Plan" | |
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| Strategies for "Look Back" | |
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| Curriculum Concerns | |
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| Problem-Solving Curricula | |
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| Problem Solving across the Curriculum | |
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| Problem-Solving Instructional Guidelines | |
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| Chapter Summary | |
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| Resources | |
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| Resources and Extensions | |
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| Materials and Resources to Support Mathematics Instruction | |
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| Universal Design | |
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| Curricula for Special-Needs Students | |
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| Strategic Math Series | |
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| Direct Instruction Mathematics | |
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| Adaptations for Special Populations | |
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| TouchMath | |
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| General Education Materials: Concerns and Adaptations | |
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| Mathematics Textbooks: Criteria and Review | |
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| General Education Materials: Research Base | |
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| Adapting Mathematics Textbooks | |
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| Selecting, Creating, and Using Manipulatives | |
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| Creating Materials | |
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| Commercial Manipulatives | |
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| Technology Support | |
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| Calculators | |
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| Software | |
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| Interactive Web | |
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| Computer Environments | |
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| Other Resources | |
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| Newspapers and Print Media | |
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| Organizations and Projects | |
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| Chapter Summary | |
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| Resources | |
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| Integrating Mathematics with Content Areas and Life Skills | |
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| Integrating Mathematics with Other Content Areas | |
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| The Math-Science Connection | |
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| Mathematics as a Tool for Social Studies | |
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| Writing in Mathematics | |
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| Literature and Mathematics | |
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| The Art of Mathematics | |
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| Other Considerations for Content Area Integration | |
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| Career Education and Life-Skills Mathematics | |
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| Career Education | |
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| Life-Skills Mathematics | |
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| Applied Math | |
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| Transition Planning | |
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| Chapter Summary | |
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| Resources | |
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| Introduction to the Content Strands | |
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| Number Sense and Place Value | |
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| Number Sense | |
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| Importance of Number Sense for Mathematical Achievement | |
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| Promoting Number Sense Development | |
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| Mental Mathematics | |
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| Estimation | |
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| Number Meaning | |
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| The Language of Mathematics | |
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| Place Value | |
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| Before Place Value | |
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| The Value of Place Value | |
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| Teaching Place Value Concepts | |
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| Data Analysis | |
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| Resources | |
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| Whole-Number Relationships | |
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| Understanding Single-Digit Operations | |
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| Counting, Addition, and Subtraction Concepts | |
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| Concept of Equivalence | |
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| Multiplication and Division Concepts | |
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| Multi-Digit Computation | |
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| Multi-Digit Addition and Subtraction | |
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| Multi-Digit Multiplication and Division | |
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| Alternative Algorithms | |
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| Multicultural Connection | |
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| Resources | |
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| Spatial Sense | |
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| Importance of Spatial Sense | |
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| Development and Assessment of Spatial Abilities | |
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| Development of Spatial Abilities | |
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| Assessment of Spatial Abilities | |
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| Research with Students with Disabilities | |
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| Developing Spatial Abilities across the Mathematics Curriculum | |
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| Promoting Spatial Development: K-2 | |
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| Promoting Spatial Development: 3-5 | |
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| Promoting Spatial Development: Middle Grades | |
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| Promoting Spatial Development: High School | |
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| Integration of Number and Spatial Sense | |
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| Multicultural Connection | |
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| Resources | |
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| Rational Numbers | |
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| Rational Numbers | |
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| Part-Whole Comparison | |
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| Quotient | |
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| Ratio | |
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| Operator | |
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| Measure | |
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| Related Concepts | |
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| Equivalence | |
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| Proportion | |
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| Probability | |
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| Common Problems and Recommendations for Instruction | |
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| Common Problems | |
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| Instructional Strategies for Fraction Concepts | |
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| Strategies for Teaching Decimal Concepts and Calculations | |
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| Strategies for Teaching Related Concepts | |
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| Multicultural Connection | |
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| Resources | |
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| Functions | |
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| Development of the Concept of Function | |
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| Functions across the Mathematics Curriculum | |
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| Instructional Methods for Challenging Concepts | |
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| Algebraic Notation | |
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| Simplifying Algebraic Expressions and Solving Equations | |
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| Coordinate Plane Graphing | |
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| Linear Functions | |
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| Extensions of Functions | |
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| Multicultural Connection | |
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| Resources | |
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| Resources | |
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| References | |
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| Index | |