| |
| |
| Chapter 1 | |
| |
| |
| Learning Mathematics | |
| |
| |
| Societal Needs | |
| |
| |
| Calls for Change | |
| |
| |
| National and International Achievement | |
| |
| |
| The Identification of Standards | |
| |
| |
| Principles and Standards for School Mathematics | |
| |
| |
| Implementing the Process Standards | |
| |
| |
| Describing A Contemporary Mathematics Program | |
| |
| |
| Levels of Abstraction | |
| |
| |
| Theoretical Foundations for a Contemporary Mathematics Program | |
| |
| |
| Theory into Practice | |
| |
| |
| Closure | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Chapter 2 | |
| |
| |
| Teaching Mathematics | |
| |
| |
| The NCTM Principles and Standards for School Mathematics | |
| |
| |
| The NCTM Professional Teaching Standards: Mathematics Teaching Today | |
| |
| |
| An Example of a Teaching Standard | |
| |
| |
| Lesson Planning Processes and Purposes | |
| |
| |
| Issues in Designing Mathematics Lessons | |
| |
| |
| Mathematics Objectives | |
| |
| |
| The Role of Motivation and Follow-Up | |
| |
| |
| The Assessment of Learning and Teaching | |
| |
| |
| Adjusting Instruction to Meet Individual Needs | |
| |
| |
| Classroom Instructional Aids | |
| |
| |
| Closure | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Chapter 3 | |
| |
| |
| Assessing Mathematics | |
| |
| |
| NCTM Assessment Standards for School Mathematics | |
| |
| |
| An Example of an Assessment Standard | |
| |
| |
| A Classroom Assessment Vignette | |
| |
| |
| Purposes for Assessment | |
| |
| |
| Assessment Strategies | |
| |
| |
| Closure | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Chapter 4 | |
| |
| |
| Technology in K-8 Mathematics | |
| |
| |
| A Brief History of Technology's Influence on Education | |
| |
| |
| Calculators and Exploration of Mathematical Concepts | |
| |
| |
| Calculator Features and Functions | |
| |
| |
| Examples of Effective Calculator Use | |
| |
| |
| Tools for Measuring Motion | |
| |
| |
| Computers and Mathematics Instruction | |
| |
| |
| Instructional Software in the Mathematics Classroom | |
| |
| |
| Application Software in the Mathematics Classroom | |
| |
| |
| Virtual Manipulatives | |
| |
| |
| Design Issues and Advantages of Virtual Manipulatives | |
| |
| |
| Classification Attributes for Virtual Manipulatives | |
| |
| |
| Capsule Descriptions of the National Library of Virtual Manipulatives | |
| |
| |
| Multimedia in the Mathematics Classroom | |
| |
| |
| The Internet in the Mathematics Classroom | |
| |
| |
| Programming Computers and Calculators | |
| |
| |
| Closure | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Chapter 5 | |
| |
| |
| Problem Solving and Mathematical Language | |
| |
| |
| The Nature of Problem Solving | |
| |
| |
| Problem-Solving Strategies | |
| |
| |
| Approaching Word Problems Effectively | |
| |
| |
| Logic and Reasoning | |
| |
| |
| The Language of Logic | |
| |
| |
| The Language of Mathematics | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 6 | |
| |
| |
| Number Sense, Numeration, and Place Value | |
| |
| |
| A Foundation for Mathematics Development | |
| |
| |
| Patterns and Other Relationships in the Primary Curriculum | |
| |
| |
| Number Sense | |
| |
| |
| Number Relations | |
| |
| |
| Extending Numberness Concepts | |
| |
| |
| Place-Value Numeration | |
| |
| |
| Decimal Numeration | |
| |
| |
| Ancient Numeration Systems | |
| |
| |
| Number Bases Other Than Ten | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 7 | |
| |
| |
| Addition and Subtraction of Whole Numbers | |
| |
| |
| Creating a Sound Base for Addition and Subtraction | |
| |
| |
| Meaning and Models for Addition | |
| |
| |
| Developing Basic Addition Facts | |
| |
| |
| Memorizing Basic Addition Facts Using Structures | |
| |
| |
| Extending Basic Addition Facts Using Place Value | |
| |
| |
| Regrouping in the Addition Process | |
| |
| |
| Meaning and Models for Subtraction | |
| |
| |
| Developing Basic Subtraction Facts | |
| |
| |
| Memorizing Basic Subtraction Facts Using Structures | |
| |
| |
| Extending Basic Subtraction Facts Using Place Value | |
| |
| |
| Regrouping in the Subtraction Process | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 8 | |
| |
| |
| Multiplication and Division of Whole Numbers | |
| |
| |
| Meaning and Models for Multiplication | |
| |
| |
| Developing and Memorizing Basic Multiplication Facts | |
| |
| |
| Expanding Basic Multiplication Facts Through Place Value | |
| |
| |
| Regrouping in Multiplication | |
| |
| |
| Meaning and Models for Division | |
| |
| |
| Developing and Memorizing Basic Division Facts | |
| |
| |
| Remainders in Division | |
| |
| |
| Expanding Basic Division Facts Through Place Value | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 9 | |
| |
| |
| Number Theory and Number Systems | |
| |
| |
| The Language of Number Theory | |
| |
| |
| The Sieve of Eratosthenes | |
| |
| |
| Factor Trees | |
| |
| |
| Prime Factorization | |
| |
| |
| Divisibility ''Rules'' | |
| |
| |
| Least Common Multiples and Greatest Common Factors | |
| |
| |
| Number Systems | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 10 | |
| |
| |
| Algebraic Reasoning: Generalizing Patterns and Relationships | |
| |
| |
| The Content of Algebra | |
| |
| |
| Algebra in Problem Solving | |
| |
| |
| Promoting Algebraic Thinking in the Lower Elementary Grades | |
| |
| |
| Enhancing Algebraic Thinking in the Upper Elementary and Middle Grades | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 11 | |
| |
| |
| Rational Numbers Expressed as Fractions: Concepts | |
| |
| |
| A Fraction of the History of Fractional Numbers | |
| |
| |
| Rational Numbers-A Definition and Description | |
| |
| |
| The Regions Model for Fractional Numbers | |
| |
| |
| The Groups of Objects Model for Fractional Numbers | |
| |
| |
| The Number Line Model for Fractional Numbers | |
| |
| |
| Knowledge and Understandings Prior to Operations on Rational Numbers Expressed as Fractions | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 12 | |
| |
| |
| Rational Numbers Expressed as Fractions: Operations | |
| |
| |
| Addition of Fractional Numbers | |
| |
| |
| Subtraction of Fractional Numbers | |
| |
| |
| Multiplication of Fractional Numbers | |
| |
| |
| Division of Fractional Numbers | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 13 | |
| |
| |
| Rational Numbers Expressed as Decimals | |
| |
| |
| Models That Give Decimals Meaning | |
| |
| |
| Place Value-A Foundation for Decimals | |
| |
| |
| Exponential Notation | |
| |
| |
| Addition with Decimal Numbers | |
| |
| |
| Subtraction with Decimal Numbers | |
| |
| |
| Multiplication with Decimal Numbers | |
| |
| |
| Division with Decimal Numbers | |
| |
| |
| Relating Decimals and Fractions | |
| |
| |
| Scientific Notation | |
| |
| |
| Ratio, Proportion, and Percent | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 14 | |
| |
| |
| Data Analysis: Graphs, Statistics, and Probability | |
| |
| |
| A Child's View of Statistics | |
| |
| |
| Measures of Central Tendency in Data | |
| |
| |
| Organizing and Interpreting Data | |
| |
| |
| Taking a ''Chance'' | |
| |
| |
| Experimental Probability | |
| |
| |
| Theoretical Probability | |
| |
| |
| Permutations and Combinations | |
| |
| |
| Models for Exploring Probability | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 15 | |
| |
| |
| Measurement | |
| |
| |
| The Historical Development of Measurement Systems | |
| |
| |
| Contemporary Measurement Systems | |
| |
| |
| The Process of Measurement | |
| |
| |
| Computing with Denominate Numbers | |
| |
| |
| Money and Time as Measures | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 16 | |
| |
| |
| Geometry: Basic Concepts and Structures | |
| |
| |
| Early Experiences in Geometry | |
| |
| |
| The ''Building Blocks'' of Geometry | |
| |
| |
| Extending the Basics-Curves, Regions, and Rays | |
| |
| |
| Angles and Angle Measure | |
| |
| |
| Exploring Geometric Constructions | |
| |
| |
| Symmetry and Transformational Geometry | |
| |
| |
| Other Devices for Exploring Geometric Concepts | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |
| |
| |
| Chapter 17 | |
| |
| |
| Geometry: Polygons and Polyhedra | |
| |
| |
| Defining Polygons | |
| |
| |
| A Closer Look at Triangles | |
| |
| |
| A Closer Look at Quadrilaterals | |
| |
| |
| A Closer Look at Circles | |
| |
| |
| Area, Perimeter, and Circumference Measurement | |
| |
| |
| Defining Polyhedra | |
| |
| |
| Closure | |
| |
| |
| Practice Exercises for Teachers | |
| |
| |
| Teaching Competencies and Self-Assessment Tasks | |
| |
| |
| Sample Instructional and Assessment Activities | |