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Publisher:

John Wiley

Publication Date:

2008

Number of Pages:

1072

Format:

Hardcover

Edition:

8

Price:

109.95

ISBN:

978-0-470-10583-2

Category:

Textbook

[Reviewed by , on ]

Janet D. Wansick

03/27/2008

As the title suggests, this is a textbook to be used in instructing future elementary teachers. The book provides chapters consistent with what is taught in most elementary math concepts courses, covering sets, whole numbers, number theory, fractions, decimals, percents, ratio, proportion, integers, probability, statistics, measurement and geometry. This text could be used in a variety of elementary math education courses.

What is somewhat unique to this book is that the chapters are shorter and more centered on a specific topic, so that the book includes more chapters than many other text of its kind. As with other texts, the content is tied to the National Council of Mathematics’ *Principles and Standards for School Mathematics,* and *Curriculum Focal Points.* In fact, the standards are listed inside the front cover of the book as well as placed with specific content in the body of the book.

A feature of the book that should be helpful for teachers is the “reflections from research” that are scattered throughout the book. These provide the reader with statements from research that reinforce the variety of ways the authors are “teaching” the concepts. In addition, *Mathematical Morsels* are also presented on various pages in the text. These morsels tell cute stories related in some way to mathematics. Another unique feature of this text is that after each section two problem sets are presented. Answers to the first set are provided at the end of the book. This would allow instructors some flexibility in the work they assign to students using this text.

While I like many things about this text, I feel I must point out that although the authors show many ways to teach concepts, I would not truly consider many of them to be conceptual. The text does a good job of showing how to teach specific concepts, but still in many cases does not delve deep enough into the “whys.” For example, in the section on subtraction of integers, the authors show a couple of brief example problems using the chip model. However, these examples come with little explanation of why or how they used the chips as they did. Then the authors go directly into additive inverse, called adding the opposite, again without much explanation of why that works.

In my experience teaching math concepts classes to potential elementary teachers, they need much more explanation and they need to be presented with the “whys.” Students at this level tend to not understand math conceptually, and therefore are limited in what they can teach to their students when they get into the classroom. It is important that, instead of showing a lot of definitions, theorems and rules, we provide them with a greater understanding of the underlying mathematical concepts. While this text does provide some of that, I do not feel like it goes far enough in that direction to improve significantly on the majority of texts that are currently available.

Janet D. Wansick (jwansick@ecok.edu ) is an assistant professor of mathematics at East Central University in Ada, OK. She began her teaching career in the middle school classroom teaching 7^{th} and 8^{th} grade mathematics before moving to the high school and eventually to the college level. She works with numerous classroom teachers at all levels and conducts mathematics partnership workshops. Her research areas of interest include mathematics education, curriculum and pedagogy, and mathematical assessment.

Preface xi

1 Introduction to Problem Solving 1

1.1 The Problem Solving Process and Strategies 3

1.2 Three Additional Strategies 20

2 Sets, Whole Numbers, and Numeration 43

2.1 Sets as a Basis for Whole Numbers 45

2.2 Whole Numbers and Numeration 59

2.3 The Hindu–Arabic System 70

2.4 Relations and Functions 82

3 Whole Numbers: Operations and Properties 107

3.1 Addition and Subtraction 109

3.2 Multiplication and Division 123

3.3 Ordering and Exponents 140

4 Whole Number Computation—Mental, Electronic,

and Written 155

4.1 Mental Math, Estimation, and Calculators 157

4.2 Written Algorithms for Whole-Number Operations 171

4.3 Algorithms in Other Bases 192

5 Number Theory 203

5.1 Primes, Composites, and Tests for Divisibility 205

5.2 Counting Factors, Greatest Common Factor, and Least Common Multiple 219

6 Fractions 237

6.1 The Sets of Fractions 239

6.2 Fractions: Addition and Subtraction 255

6.3 Fractions: Multiplication and Division 266

7 Decimals, Ratio, Proportion, and Percent 285

7.1 Decimals 287

7.2 Operations with Decimals 297

7.3 Ratios and Proportion 310

7.4 Percent 320

8 Integers 341

8.1 Addition and Subtraction 343

8.2 Multiplication, Division, and Order

9 Rational Numbers, Real Numbers, and Algebra 379

9.1 The Rational Numbers 381

9.2 The Real Numbers 399

9.3 Functions and Their Graphs 417

10 Statistics 439

10.1 Organizing and Picturing Information 441

10.2 Misleading Graphs and Statistics 464

10.3 Analyzing Data 484

11 Probability 513

11.1 Probability and Simple Experiments 515

11.2 Probability and Complex Experiments 532

11.3 Additional Counting Techniques 549

11.4 Simulation, Expected Value, Odds, and Conditional Probability 560

12 Geometric Shapes 581

12.1 Recognizing Geometric Shapes 583

12.2 Analyzing Shapes 600

12.3 Properties of Geometric Shapes: Lines and Angles 615

12.4 Regular Polygons and Tessellations 628

12.5 Describing Three-Dimensional Shapes 640

13 Measurement 665

13.1 Measurement with Nonstandard and Standard Units 667

13.2 Length and Area 686

13.3 Surface Area 707

13.4 Volume 717

14 Geometry Using Triangle Congruence

and Similarity 739

14.1 Congruence of Triangles 741

14.2 Similarity of Triangles 752

14.3 Basic Euclidean Constructions 765

14.4 Additional Euclidean Constructions 777

14.5 Geometric Problem Solving Using Triangle Congruence and Similarity 790

15 Geometry Using Coordinates 807

15.1 Distance and Slope in the Coordinate Plane 809

15.2 Equations and Coordinates 822

15.3 Geometric Problem Solving Using Coordinates 834

16 Geometry Using Transformations 849

16.1 Transformations 851

16.2 Congruence and Similarity Using Transformations 875

16.3 Geometric Problem Solving Using Transformations 893

Epilogue: An Eclectic Approach to Geometry 909

Topic 1. Elementary Logic 912

Topic 2. Clock Arithmetic: A Mathematical System 923

Answers to Exercise/Problem Sets—Part A, Chapter Tests,

and Topics A1

Photograph Credits P1

Index I1

1 Introduction to Problem Solving 1

1.1 The Problem Solving Process and Strategies 3

1.2 Three Additional Strategies 20

2 Sets, Whole Numbers, and Numeration 43

2.1 Sets as a Basis for Whole Numbers 45

2.2 Whole Numbers and Numeration 59

2.3 The Hindu–Arabic System 70

2.4 Relations and Functions 82

3 Whole Numbers: Operations and Properties 107

3.1 Addition and Subtraction 109

3.2 Multiplication and Division 123

3.3 Ordering and Exponents 140

4 Whole Number Computation—Mental, Electronic,

and Written 155

4.1 Mental Math, Estimation, and Calculators 157

4.2 Written Algorithms for Whole-Number Operations 171

4.3 Algorithms in Other Bases 192

5 Number Theory 203

5.1 Primes, Composites, and Tests for Divisibility 205

5.2 Counting Factors, Greatest Common Factor, and Least Common Multiple 219

6 Fractions 237

6.1 The Sets of Fractions 239

6.2 Fractions: Addition and Subtraction 255

6.3 Fractions: Multiplication and Division 266

7 Decimals, Ratio, Proportion, and Percent 285

7.1 Decimals 287

7.2 Operations with Decimals 297

7.3 Ratios and Proportion 310

7.4 Percent 320

8 Integers 341

8.1 Addition and Subtraction 343

8.2 Multiplication, Division, and Order

9 Rational Numbers, Real Numbers, and Algebra 379

9.1 The Rational Numbers 381

9.2 The Real Numbers 399

9.3 Functions and Their Graphs 417

10 Statistics 439

10.1 Organizing and Picturing Information 441

10.2 Misleading Graphs and Statistics 464

10.3 Analyzing Data 484

11 Probability 513

11.1 Probability and Simple Experiments 515

11.2 Probability and Complex Experiments 532

11.3 Additional Counting Techniques 549

11.4 Simulation, Expected Value, Odds, and Conditional Probability 560

12 Geometric Shapes 581

12.1 Recognizing Geometric Shapes 583

12.2 Analyzing Shapes 600

12.3 Properties of Geometric Shapes: Lines and Angles 615

12.4 Regular Polygons and Tessellations 628

12.5 Describing Three-Dimensional Shapes 640

13 Measurement 665

13.1 Measurement with Nonstandard and Standard Units 667

13.2 Length and Area 686

13.3 Surface Area 707

13.4 Volume 717

14 Geometry Using Triangle Congruence

and Similarity 739

14.1 Congruence of Triangles 741

14.2 Similarity of Triangles 752

14.3 Basic Euclidean Constructions 765

14.4 Additional Euclidean Constructions 777

14.5 Geometric Problem Solving Using Triangle Congruence and Similarity 790

15 Geometry Using Coordinates 807

15.1 Distance and Slope in the Coordinate Plane 809

15.2 Equations and Coordinates 822

15.3 Geometric Problem Solving Using Coordinates 834

16 Geometry Using Transformations 849

16.1 Transformations 851

16.2 Congruence and Similarity Using Transformations 875

16.3 Geometric Problem Solving Using Transformations 893

Epilogue: An Eclectic Approach to Geometry 909

Topic 1. Elementary Logic 912

Topic 2. Clock Arithmetic: A Mathematical System 923

Answers to Exercise/Problem Sets—Part A, Chapter Tests,

and Topics A1

Photograph Credits P1

Index I1

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