This text is the product of a seven year effort to develop an elementary mathematics methods text that fully implements the NCTM standards for mathematics teaching and learning. These standards do not recommend a band-aid approach to reform, that is, supplementing existing practices with some new techniques to better accomplish the same old goals. Instead the standards propose radical surgery, profound changes in what and how mathematics is taught and assessed. That is the purpose of this text, to show how to make mathematics instruction consistent with all three of the central NCTM tenets:
1. Making mathematics relevant to the everyday lives of students.
2. Making mathematics a problem-based or reasoning-based activity.
3. Making mathematics a meaningful (understandable) learning activity.
Investigative Approach--The author imbeds these three tenets in what he labels the investigative approach to mathematics instruction. It involves a unique format in which students interact with the text material through a series of reader inquiries that explore key ideas about mathematics, children's mathematical learning, and mathematical teaching. These inquiries constitute the core of the book.
Personalized Teaching Guide--To encourage personalized learning, the pages of this book have been perforated and 3-hole punched so that its contents can be reorganized and/or mixed with materials from other sources to form a Personalized Teaching Guide. In short, this book should be viewed as a starting point in the long road to professional development in mathematics instruction.
Contents: Preface. Prologue: Understanding This Teaching Guide and the Role of Affect in the Teaching-Learning Process. Fostering Mathematical Power: The Need for Purposeful, Inquiry-Based, and Meaningful Instruction. Processes of Mathematical Inquiry: Problem Solving, Reasoning, and Communicating. Fostering and Evaluating Meaningful Learning: Making Connections and Assessing Understanding. Basic Mathematical Tools: Numbers and Numerals. Introducing Arithmetic: Understanding the Whole-Number Operations and Mastering the Basic Number Combinations. Understanding Base-Ten, Place-Value Skills: Reading, Writing, and Arithmetic With Multidigit Numbers. Thinking With Whole Numbers: Number Sense, Estimation, and Mental Computation. Exploring Numbers Further: Number Theory and Integers & Operations on Integers. Working With "Parts of a Whole" and Other Meanings of Rational Numbers and Common Fractions. Understanding Operations on Common Fractions. Place-Value Representations of Fractional Parts: Decimal Fractions, Decimals, and Operations on Decimals. Comparing Quantities Fairly: Ratios, Proportions, and Percent. Making Sense of Information and Using It to Make Everyday Decisions: Statistics and Probability. The Mathematics of Our Environment: Geometry and Spatial Sense. Sizing up Things: Measurement and Measurement Formulas. The Transition From Arithmetic to Algebra: Prealgebra and Functions. Reflections on Teaching: Organizing Instruction to Enhance Mathematical Power, Professional Development, and Epilogue. Appendices: Footnotes. Bibliography. Publishers and Distributors of Educational Materials. Subject Index. Index of Reader Inquiries. Index of Children's Literature (by Title and by Subject). Technology Index (Web sites; Software, Videos, & Laserdisks; Calculator Applications by Subject; Computer Applications by Subject). Questions for Promoting Mathematical Power.