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Mathematics

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Mathematics for Elementary Teachers plus Activities Manual, 2/E
Sybilla Beckmann, University of Georgia

ISBN-10: 0321447174
ISBN-13: 9780321447173

Publisher: Addison-Wesley
Copyright: 2008
Format: Cloth Package; 912 pp
Published: 02/05/2007

Suggested retail price: $120.00
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Elementary school classrooms are increasingly relying on a discovery method for the teaching of mathematics. Mathematics for Elementary Teachers thoroughly prepares preservice teachers to use this approach as it has been proven to increase their depth of understanding of mathematics. In this text, topics are organized by operation, rather than number type, and time is spent explaining why the math works, rather than just on the mechanics of how it works. Fully integrated activities are found in the book and in an accompanying Activities Manual. As a result, students engage, explore, discuss, and ultimately reach true understanding of the approach and of mathematics.


  • The table of contents is organized according to operation instead of by number type, making the learning process more intuitive and easier.
  • Class Activities are integral to learning and are designed to be done in class or in small groups outside of class. They promote critical thinking, discussion, and give students depth of understanding and perspective on the concepts.
  • Practice Problems are an opportunity for students to work through problems with solutions immediately following. This prompt feedback prepares them for homework questions that count.
  • Problems are opportunities for practice without available solutions, typically assigned as homework. Answers appear in the Instructor's Solutions Manual and can be provided online for students at the discretion of the instructor.
  • Unique content in Chapter 13: Functions and Algebra introduces U.S. teachers to the impressive diagrammatic method presented in grade 3 - 6 math texts used in Singapore, where children score top in the world in math. This method helps students make sense of, and solve, a variety of algebra and other word problems without using variables. The text helps students see the relationship between the Singaporean diagrammatic method and standard algebraic problem solving methods.

  • This Second Edition offers clarity and enhanced readability. The new design, including new graphs and mathematical art, improves the visual pedagogy and makes it a more effective learning tool.
  • Updated examples offer current, fresh illustrations of core concepts. Introductory examples are simplified to better highlight key ideas.
  • Exercise and activity categories, Essential or Extension, make it easier for instructors to assign homework or activities.
  • New chapter summaries review and reinforce key chapter ideas, helping students to prepare for exams.
  • An improved Instructor's Manual, an invaluable resource, includes suggestions for discussing problem solving, highlights areas where students typically struggle, and provides alternative teaching strategies for difficult concepts.
  • A full set of electronic manipulatives for use in conjunction with select book activities is now available on CD-ROM. For instructors who prefer hands-on manipulatives to electronic, a kit containing centimeter cubes, overhead color tiles, overhead pattern blocks, and overhead fraction tiles is available separately from Addison-Wesley.

Chapter 1 Problem Solving

1.1  Solving Problems

1.2  Explaining Solutions

 

Chapter 2 Numbers and the Decimal System

2.1 Overview of the Number Standards

2.2 The Decimal System and Place Value

2.3 Representing Decimal Numbers

2.4 Comparing Decimal Numbers

2.5 Rounding Decimal Numbers

 

Chapter 3 Fractions

3.1 The Meaning of Fractions

3.2 Fractions as Numbers

3.3 Equivalent Fractions

3.4 Comparing Fractions

3.5 Percent

           

Chapter 4 Addition and Subtraction

4.1 Interpretations of Addition and Subtraction

4.2 Why the Standard Algorithms for Adding and Subtracting Decimal Numbers Work

4.3 Adding and Subtracting Fractions

4.4 When Do We Add Percentages?

4.5 Percent Increase and Percent Decrease

4.6 The Commutative and Associative Properties of Addition and Mental Math

 

Chapter 5 Multiplication

5.1 The Meaning of Multiplication and Ways to Show Multiplication

5.2 Why Multiplying Decimal Numbers by 10 is Easy

5.3 The Commutative Property of Multiplication and Areas of Rectangles

5.4 The Associative Property of Multiplication and Volumes of Boxes

5.5 The Distributive Property

5.6 Mental Math, Properties of Arithmetic, and Algebra

5.7 Why the Procedure for Multiplying Whole Numbers Works

 

Chapter 6 Multiplication of Fractions, Decimals, and Negative Numbers

6.1 Multiplying Fractions

6.2 Multiplying Decimals

6.3 Multiplying Negative Numbers

6.4 Scientific Notation

 

Chapter 7 Division

7.1 The Meaning of Division

7.2 Understanding Long Division

7.3 Fractions and Division

7.4 Dividing Fractions

7.5 Dividing Decimals

7.6 Ratio and Proportion

 

Chapter 8 Geometry

8.1 Visualization

8.2 Angles

8.3 Circles and Spheres

8.4 Triangles, Quadrilaterals, and Other Polygons

8.5 Constructions with Straightedge and Compass

8.6 Polyhedra and Other Solid Shapes

 

Chapter 9 Geometry of Motion and Change

9.1 Reflections, Translations, and Rotations

9.2 Symmetry

9.3 Congruence

9.4 Similarity

 

Chapter 10 Measurement

10.1 Fundamentals of Measurement

10.2 Length, Area, Volume, and Dimension

10.3 Calculating Perimeters of Polygons, Areas of Rectangles, and Volumes of Boxes

10.4 Error and Accuracy in Measurements

10.5 Converting from One Unit of Measurement to Another

 

Chapter 11 More About Area and Volume

11.1 The Moving and Additivity Principles About Area

11.2 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem

11.3 Areas of Triangles

11.4 Areas of Parallelograms

11.5 Cavalieri’s Principle About Shearing and Area

11.6 Areas of Circles and the Number Pi

11.7 Approximating Areas of Irregular Shapes

11.8 Relating the Perimeter and Area of a Shape

11.9 Principles for Determining Volumes

11.10 Volumes of Prisms, Cylinders, Pyramids, and Cones

11.11 Areas, Volumes, and Scaling

 

Chapter 12 Number Theory

12.1 Factors and Multiples

12.2 Greatest Common Factor and Least Common Multiple

12.3 Prime Numbers

12.4 Even and Odd

12.5 Divisibility Tests

12.6 Rational and Irrational Numbers

 

Chapter 13 Functions and Algebra

13.1 Mathematical Expressions, Formulas, and Equations

13.2 Solving Equations Using Number Sense, Strip Diagrams, and Algebra

13.3 Sequences

13.4 Series

13.5 Functions

13.6 Linear Functions

 

Chapter 14 Statistics

14.1 Formulating Questions, Designing Investigations, and Gathering Data

14.2 Displaying Data and Interpreting Data Displays

14.3 The Center of Data: Mean, Median, and Mode

14.4 Percentiles and the Distribution of Data

 

Chapter 15 Probability

15.1 Basic Principles and Calculation Methods of Probability

15.2 Using Fraction Arithmetic to Calculate Probabilities

 

Sybilla Beckmann earned an undergraduate degree in mathematics from Brown University and a PhD in mathematics from the University of Pennsylvania. She taught and did research in mathematics at Yale University for two years. Since then, she has been at the University of Georgia. When she had children, she became very interested in helping prospective teachers understand and appreciate the mathematics they will teach. This interest led to her book. She enjoys playing the piano, weaving, attending classical music concerts, and traveling with her family.

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For Math for Future Elementary Teachers


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