- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics.
Contents
PREFACE Chapter 0 Prologue: Understanding This Teaching Guide and the Role of Affect in the Teaching-Learning Process 0-1 to 0-24 Chapter 1 Fostering Mathematical Power: The Need for Purposeful, Inquiry-Based, and Meaningful Instruction 1-1 to 1-38 Chapter 2 Processes of Mathematical Inquiry: Problem Solving, Reasoning, and Communicating 2-1 to 2-40 Chapter 3 Fostering and Evaluating Meaningful Learning: Making Connections and Assessing Understanding 3-1 to 3-40 Chapter 4 Basic Mathematical Tools: Numbers and Numerals 4-1 to 4-Chapter 5 Introducing Arithmetic: Understanding the Whole-Number Operations and Mastering the Basic Number Combinations Chapter 6 Understanding Base-Ten, Place-Value Skills: Reading, Writing, and Arithmetic with Multidigit Numbers 6-1 to 6-32 Chapter 7 Thinking with Whole Numbers: Number Sense, Estimation, and Mental Computation 7-1 to 7-34 Chapter 8 Exploring Numbers Further: Number Theory and Integers & Operations on Integers 8-1 to 8-34 Chapter 9 Working with Parts of a Whole and Other Meanings of Rational Numbers and Common Fractions 9-1 to 9-28 Chapter 10 Understanding Operations on Common Fractions 10-1 to 10-24 Chapter 11 Place-Value Representations of Fractional Parts: Decimal Fractions, Decimals, and Operations on Decimals 11-1 to 11-32 Chapter 12 Comparing Quantities Fairly: Ratios, Proportions, and Percent Chapter 13 Making Sense of Information and Using It to Make Everyday Decisions: Statistics and Probability 13-1 to 13-32 Chapter 14 The Mathematics of Our Environment: Geometry and Spatial Sense...14-1 to 14-28 Chapter 15 Sizing Up Things: Measurement and Measurement Formulas 15-1 to 15-30 Chapter 16 The Transition from Arithmetic to Algebra: Prealgebra and Functions 16-1 to 16-32 Prealgebra and Algebra Chapter 17 Reflections on Teaching: Organizing Instruction to Enhance Mathematical Power, Professional Development, and Epilogue
