For courses in undergraduate Elementary and Middle School Mathematics Education With an emphasis on inquiry and process, Teaching Mathematics in Elementary and Middle School embraces active mathematics instruction and the development of mathematical thinking through problem solving.  The text challenges future teachers to prepare their K-8 students for a world that requires a higher level of mathematical literacy and enables them to compete in a global society. Teachers will develop their own mathematical abilities allowing them to help students discover a rich combination of thinking processes and problem-solving strategies, raising the learning expectations for all.

Table of Contents:
CHAPTER 1    Teaching Mathematics in the 21st Century Being a Teacher in the 21st Century     Beyond Shop-and-Yard Mathematics     In Step with the New Mathematical Literacy Changing Views About Who should Learn Mathematics     Tradition and Myths     Equity Reforms Changing Views About What Should Be Learned     Tying the Curriculum to Mental Age and Social Utility     Responding to a Bigger World Building Consensus and Setting Standards     National Standards for Mathematics Education     State and Local Standards Meeting the Challenges of the 21st Century     Meeting the Challenges as a Nation     Meeting the Challenges in the Classroom     Questions for Discussion, Thought, and Further Research   CHAPTER 2    Empowering Children to Learn Mathematics Teaching Important Mathematics to All Students     Legislation for Equity and Excellence     Important Mathematics     Understanding How Students Learn Mathematics     Changing Perspectives of Learning     Matching Teaching to Learning: Modesl for Diversity     Mastery Learning     Inquiry-based Learning     Universal Design for Learning Mathematics     Questions for Thought, Discussion, and Further Research          CHAPTER 3    Preparing Students to Think Mathematically Learning to Think and Reason Mathematically     The Importance of Mathematical Thinking     The Processes of Mathematical Thinking Understanding Interactions That Affect Mathematical Thinking and Learning     The Cognitive Domain     The Affective Domain     Interactions Applying Mathematical Thinking in Problem Solving     Polya's Four Steps to Problem Solving     Problem-Solving Approach to Learning     Multiple Solutions/New Beginning Developing a Mathematical World View Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, Research CHAPTER 4    Enhancing Mathematics Learning Through Instruction and Assessment Flexible Mathematics Instruction     Multiple Means of Engagement     Multiple Means of Representation     Multiple Means of Expression     Multiple Means of Assessment Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research CHAPTER 5    Understanding Numbers Understanding the Mathematics of Young Children Learning the Language of Numbers Developing Verbal and Nonverbal Mathematical Skills     Concrete Mathematics and Nonverbal Skills     Spoken and Written Mathematics and Verbal Skills Discovering Number in Patterns and Relationships     What is more, less, or the same?     Why is something more, less, the same? Counting and Number Sense Understanding Number Systems     What is a number system?     Why do we need number systems?     Number Systems and Time     Number Systems and Measurement     Number Systems and Money     The Decimal Number System Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussions, and Research CHAPTER 6    Working with Whole Numbers: Addition and Subtraction The Changing Faces of Whole Numbers: Cardinal, Ordinal, Measurement     Cardinal Numbers     Ordinal Numbers     Measurement Single-Digit Addition and Subtraction     Children's Strategies for Adding     Children's Strategies for Subtracting     Fingermath     Mental Addition and Subtraction Multi-digit Addition and Subtraction     Building Concepts for Working with Multi-digit Numbers     Adding and Subtracting Multi-digit Numbers     Understanding Standard Algorithms     Understanding Alternative Algorithms Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research Chapter 7    Working with Whole Numbers: Multiplying and Dividing Discovering Multiplication and Division in Early Grades Understanding Multiplication     What is a multiplication algorithm?     What kinds of multiplication algorithms do students invent?     How might teachers introduce other multiplication algorithms? Understanding Division     What kinds of division algorithms do students invent?     How do students handle division problems with remainders?     How can teachers help students understand other division algorithms? Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion and Research  CHAPTER 8    Geometric Thinking Across the Grades  Geometry as the Mathematicas of Living Space and the Living World     The Four Faces of Geometry Geometric Thinking from Level to Level Early Experiences with Shapes and Space Later Experiences with Shapes and Space     Symmetry     Transformations     Symmetry, Transformations, and NCTM Standards Explorations in Two and Three Dimensions: Plane and Solid Geometry     The Early Grades     The Middle Grades     The Upper Grades Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research CHAPTER 9    Understanding and Using Measurement Concepts Measurement Sense     Early Stages in Understanding Measurement     The Three Knowledge Bases of Measurement     The Mental Tools of Measurement Measurement Systems     Teaching the Metric System     Measuring Time and Temperature Measurement and Geometry     Plane Geometry     Solid Geometry Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research Chapter 10    Algabraic Thinking Across the Grades Changing "Algebra for Some" to "Algebra for All" Understanding Algebraic Thinking     Identifying Patterns in Algebraic Thinking     Fostering Algebraic Thinking     Problem Solving and Algebraic Thinking Understanding the Big Ideas of Algebra     Equality/Balance     Variable     Functions     Representation     Proportion Building Bridges from Arithmetic to Algebra     Hands-on Algebra     Real-life and Imaginative Contexts     Connections Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research CHAPTER 11    Working with Data Worlds of Data The Processes of Working with Data     Collecting and Organizing Data     Analyzing Data     Displaying and Interpreting Data     Understanding and Using Data Probability     Talking about Probability     Calculating Probability The Process Plus Probability: The M&Ms Project Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research CHAPTER 12    Exploring Part-Whole Relationships: Fractions Students, Teachers, and Fractions--Complex Topic, Complex Relationship A Hands-on Pedagogy for Teaching Fractions: Connecting Constructed Knowledge and Instructed Knowledge     Real-life Contexts     Hands-on Explorations     Multiple Representations     Language Connections Big Ideas of Fractions     Properties of Fractions     Operations with Fractions Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research CHAPTER 13    Exploring Part-Whole Relationships: Decimals, Percents, Ratio, and Proportion Understanding Decimals and Percents Connecting Fractons, Decimals, and Percents Exploring Decimals and Percents as Mathematical Concepts     Decimals     Percents Converting Percents, Decimals, and Fractions Performing Operations with Decimals and Percents     Addition and Subtraction     Multiplication and Division Understanding Decimals and Percents in Practical Applications Understanding Ratio and Proportion     Ratio     Proportion     Strategies for Developing Proportional Reasoning Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research CHAPTER 14    Building Bridges Making the Transition     Reviewing the Research     Identifying the Gaps Building Affective and Conceptual Bridges     Affective Bridges     Cognitive Bridges Diversity in Learning and Thinking Mathematically     Questions for Further Thought, Discussion, and Research APPENDIX A:     Make Your Own Manipulatives and Blackline Masters Make Your Own Manipulatives     Fraction Strips     Fraction Squares     Fraction Circles     Pattern Shapes     Tangrams     Geoboard     Base-10 Blocks     Counters     Decimal Squares     Multiplication Arrays     Polygon Cut-outs Blackline Masters     Modified Cartesian Coordinate Grid     Geoboard Dot Paper     One-Centimeter Grid Paper     Triangular Grid Paper     Classroom Observation Form     Learning/Teaching Plan Form APPENDIX B:    Resources, Mathematics in Literature For Elementary and Middle School NCTM Standard: Number and Operations     Number Sense     Counting     Addition     Subtraction     Multiplication     Decimals/Percentages     Division/Fractions     Ratio and/or Proportion     Place Value     Time     Money     Classification     Order NCTM Standard: Algebra NCTM Standard: Geometry     Geometric Progression     Tangrams     Geometric Shapes     Area     Perimeter     Dimensionality NCTM Standard: Measurement NCTM Standard: Data Analysis and Probability Other Topics     Multicultural     Cartesian Coordinate System     Code-Breaking (Problem Solving Involving Codes)     Classic Literature     Geography and Reading Maps     Spanish Language     Prime Numbers     Multiples/Factors References/Readings