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Chapter 1 | |

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Learning Mathematics | |

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Societal Needs | |

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Calls for Change | |

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National and International Achievement | |

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The Identification of Standards | |

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Principles and Standards for School Mathematics | |

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Implementing the Process Standards | |

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Describing A Contemporary Mathematics Program | |

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Levels of Abstraction | |

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Theoretical Foundations for a Contemporary Mathematics Program | |

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Theory into Practice | |

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Closure | |

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Teaching Competencies and Self-Assessment Tasks | |

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Chapter 2 | |

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Teaching Mathematics | |

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The NCTM Principles and Standards for School Mathematics | |

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The NCTM Professional Teaching Standards: Mathematics Teaching Today | |

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An Example of a Teaching Standard | |

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Lesson Planning Processes and Purposes | |

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Issues in Designing Mathematics Lessons | |

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Mathematics Objectives | |

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The Role of Motivation and Follow-Up | |

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The Assessment of Learning and Teaching | |

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Adjusting Instruction to Meet Individual Needs | |

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Classroom Instructional Aids | |

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Closure | |

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Teaching Competencies and Self-Assessment Tasks | |

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Chapter 3 | |

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Assessing Mathematics | |

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NCTM Assessment Standards for School Mathematics | |

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An Example of an Assessment Standard | |

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A Classroom Assessment Vignette | |

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Purposes for Assessment | |

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Assessment Strategies | |

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Closure | |

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Teaching Competencies and Self-Assessment Tasks | |

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Chapter 4 | |

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Technology in K-8 Mathematics | |

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A Brief History of Technology's Influence on Education | |

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Calculators and Exploration of Mathematical Concepts | |

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Calculator Features and Functions | |

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Examples of Effective Calculator Use | |

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Tools for Measuring Motion | |

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Computers and Mathematics Instruction | |

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Instructional Software in the Mathematics Classroom | |

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Application Software in the Mathematics Classroom | |

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Virtual Manipulatives | |

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Design Issues and Advantages of Virtual Manipulatives | |

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Classification Attributes for Virtual Manipulatives | |

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Capsule Descriptions of the National Library of Virtual Manipulatives | |

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Multimedia in the Mathematics Classroom | |

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The Internet in the Mathematics Classroom | |

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Programming Computers and Calculators | |

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Closure | |

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Teaching Competencies and Self-Assessment Tasks | |

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Chapter 5 | |

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Problem Solving and Mathematical Language | |

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The Nature of Problem Solving | |

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Problem-Solving Strategies | |

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Approaching Word Problems Effectively | |

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Logic and Reasoning | |

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The Language of Logic | |

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The Language of Mathematics | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 6 | |

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Number Sense, Numeration, and Place Value | |

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A Foundation for Mathematics Development | |

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Patterns and Other Relationships in the Primary Curriculum | |

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Number Sense | |

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Number Relations | |

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Extending Numberness Concepts | |

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Place-Value Numeration | |

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Decimal Numeration | |

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Ancient Numeration Systems | |

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Number Bases Other Than Ten | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 7 | |

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Addition and Subtraction of Whole Numbers | |

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Creating a Sound Base for Addition and Subtraction | |

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Meaning and Models for Addition | |

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Developing Basic Addition Facts | |

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Memorizing Basic Addition Facts Using Structures | |

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Extending Basic Addition Facts Using Place Value | |

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Regrouping in the Addition Process | |

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Meaning and Models for Subtraction | |

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Developing Basic Subtraction Facts | |

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Memorizing Basic Subtraction Facts Using Structures | |

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Extending Basic Subtraction Facts Using Place Value | |

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Regrouping in the Subtraction Process | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 8 | |

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Multiplication and Division of Whole Numbers | |

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Meaning and Models for Multiplication | |

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Developing and Memorizing Basic Multiplication Facts | |

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Expanding Basic Multiplication Facts Through Place Value | |

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Regrouping in Multiplication | |

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Meaning and Models for Division | |

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Developing and Memorizing Basic Division Facts | |

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Remainders in Division | |

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Expanding Basic Division Facts Through Place Value | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 9 | |

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Number Theory and Number Systems | |

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The Language of Number Theory | |

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The Sieve of Eratosthenes | |

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Factor Trees | |

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Prime Factorization | |

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Divisibility ''Rules'' | |

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Least Common Multiples and Greatest Common Factors | |

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Number Systems | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 10 | |

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Algebraic Reasoning: Generalizing Patterns and Relationships | |

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The Content of Algebra | |

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Algebra in Problem Solving | |

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Promoting Algebraic Thinking in the Lower Elementary Grades | |

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Enhancing Algebraic Thinking in the Upper Elementary and Middle Grades | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 11 | |

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Rational Numbers Expressed as Fractions: Concepts | |

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A Fraction of the History of Fractional Numbers | |

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Rational Numbers-A Definition and Description | |

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The Regions Model for Fractional Numbers | |

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The Groups of Objects Model for Fractional Numbers | |

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The Number Line Model for Fractional Numbers | |

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Knowledge and Understandings Prior to Operations on Rational Numbers Expressed as Fractions | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 12 | |

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Rational Numbers Expressed as Fractions: Operations | |

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Addition of Fractional Numbers | |

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Subtraction of Fractional Numbers | |

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Multiplication of Fractional Numbers | |

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Division of Fractional Numbers | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 13 | |

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Rational Numbers Expressed as Decimals | |

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Models That Give Decimals Meaning | |

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Place Value-A Foundation for Decimals | |

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Exponential Notation | |

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Addition with Decimal Numbers | |

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Subtraction with Decimal Numbers | |

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Multiplication with Decimal Numbers | |

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Division with Decimal Numbers | |

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Relating Decimals and Fractions | |

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Scientific Notation | |

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Ratio, Proportion, and Percent | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 14 | |

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Data Analysis: Graphs, Statistics, and Probability | |

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A Child's View of Statistics | |

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Measures of Central Tendency in Data | |

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Organizing and Interpreting Data | |

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Taking a ''Chance'' | |

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Experimental Probability | |

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Theoretical Probability | |

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Permutations and Combinations | |

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Models for Exploring Probability | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 15 | |

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Measurement | |

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The Historical Development of Measurement Systems | |

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Contemporary Measurement Systems | |

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The Process of Measurement | |

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Computing with Denominate Numbers | |

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Money and Time as Measures | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 16 | |

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Geometry: Basic Concepts and Structures | |

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Early Experiences in Geometry | |

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The ''Building Blocks'' of Geometry | |

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Extending the Basics-Curves, Regions, and Rays | |

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Angles and Angle Measure | |

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Exploring Geometric Constructions | |

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Symmetry and Transformational Geometry | |

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Other Devices for Exploring Geometric Concepts | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |

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Chapter 17 | |

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Geometry: Polygons and Polyhedra | |

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Defining Polygons | |

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A Closer Look at Triangles | |

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A Closer Look at Quadrilaterals | |

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A Closer Look at Circles | |

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Area, Perimeter, and Circumference Measurement | |

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Defining Polyhedra | |

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Closure | |

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Practice Exercises for Teachers | |

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Teaching Competencies and Self-Assessment Tasks | |

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Sample Instructional and Assessment Activities | |