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“This book would be a great tool for helping [today’s future elementary teachers] acquire a ‘gut level’ understanding of mathematics concepts.”
- Hester Lewellen, Baldwin-Wallace College, OH
“The writing in this text is very clear and would easily be understood by the intended audience. The real-world examples put the various math concepts into a context that is easily understood. The vignettes at the beginning of each chapter are interesting and they get the reader to begin thinking about the math concepts that will follow. Each of the chapters seem to build on one another and the author often refers back to activities and concepts from previous chapters which is meaningful to the reader because it lets the reader know that the information they are learning builds their conceptual understanding of other mathematical concepts. “
- Melany L. Rish, University of South Carolina, Aiken
Organized around five key concepts or “powerful ideas” in mathematics, this book presents elementary mathematics content in a concise and nonthreatening manner for teachers.
Designed to sharpen teachers’ mathematics pedagogical content knowledge, the friendly writing style and vignettes relate math concepts to “real life” situations so that they may better present the content to their students. The five “powerful ideas” (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the book thoroughly integrates discussion of the five NCTM process strands.
Most chapters include "Preview," "Chapter Review," "Self-Check," "Selected References, "Online Activities" and "Activities and Exercises"
Chapter 1: The changing landscape of elementary mathematics teaching and learning
A distinction between conceptual knowledge and procedural knowledge
Communication in a mathematics classroom
Patterns and Change
Chapter 2: The Powerful ideas: Composition, Decomposition, Relationships, Representation, and Context 39
Chapter 3: Powerful ideas related to the number system
What is counting? (How Many?)
What are numbers?
How do we represent numbers?
What is a number system?
How have number systems developed differently in the past (and what’s so special about today’s number system?)
The idea of base
Basic Digits and Place Value
Chapter 4: Powerful ideas related to arithmetic
Addition and Subtraction
Chapter 5: Powerful ideas related to geometry
What is geometry?
Why learn geometry?
Why do people have difficulty with geometry?
Spatial visualization and properties of shapes
Translations, Rotations, Reflections (or Slides, Turns, and Flips)
Similarity and Congruence
Reasoning about types of shapes
Chapter 6: Powerful ideas related to parts and wholes
Reprise: One Whole or Many Parts?
Decomposition and Partitioning
What is the whole? (and Why does it matter?)
Various meanings of fractions
Equivalent Fractions and Simplest Form
Adding and subtracting with fractions
Multiplying with fractions
Dividing with fractions
Caution about a possible point of confusion
Chapter 7: Powerful ideas related to the decimal numbers
Relationship between decimal numbers and fractions
Relationship between decimal numbers and place value concepts
Special uses of decimal numbers: money and percent
Arithmetic: Special concerns with decimal numbers
Chapter 8: Powerful ideas related to measurement
The concept of measurement
Why does measurement matter?
Linear measurement as compared with area measurement
Measurement of volume
Measurement of weight
Measurement of time
Units as standards
The power of the metric system
Uncertainty and degrees of precision
Choosing the best measurement unit
The use of formulas (or not?)
Chapter 9: Powerful ideas related to data analysis
Some general thoughts about statistics
Posing statistical questions
Organizing and displaying data
Measures of center
The concept of distribution
Chapter 10: Powerful ideas related to probability
What is probability?
Finding the Number of Outcomes
Some Problem Situations
What about “Odds?”
Some Common Misconceptions
Chapter 11: Powerful ideas related to ratio and proportion
What about Non-linear Relationships
Chapter 12: Powerful ideas related to reasoning
The Yin and Yang of Using Inductive Reasoning and Deductive Reasoning
Evaluation of mathematical thought.
Chapter 13: Powerful ideas related to algebra
Basics of Algebra
Graphing Functions on the Coordinate System
Appendix A: Explanations of Complex Formulas
The Combinations Formula
Cross-multiplication for Solving Proportions
The Lattice Method of Multiplication
Appendix B: Answers to Self-Check and Activities