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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 | |