Mathematics for Elementary School Teachers

by O'Daffer, Phares; Charles, Randall; Cooney, Thomas; Dossey, John; Schielack, Jane

• ISBN13: 9780201699517
• ISBN10: 0201699516
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-09-01
• Publisher: Pearson College Div

Summary

Future elementary and middle school teachers need a clear, coherent presentation of the mathematical concepts, procedures, and processes they will be called upon to teach. This text uniquely balances "what" they will teach (concepts and content) with "how" to teach (processes and communication). As a result, students using "Mathematics for Elementary School Teachers" leave the course knowing more than basic math skills; they develop a deep understanding of concepts that enables them to effectively teach others. This Fourth Edition features an increased focus on the ' big ideas' of mathematics, as well as the individual skills upon which those ideas are built.

Table of Contents

Preface	ix
Viewing Mathematics	1	(57)
Mathematics as Communication	1	(13)
Views and Attitudes about Mathematics
Communicating Mathematically
Using Technology to Communicate Mathematically
Mathematics as Reasoning	14	(23)
Types of Reasoning
Inductive Reasoning and Patterns
Deductive Reasoning
Proportional Reasoning
Spatial Reasoning
Importance of Reasoning Processes
Mathematics as Problem Solving	37	(11)
The Role of Problem Solving
A Problem-Solving Model
Problem-Solving Strategies
Importance of Problem Solving
A Connected, Balanced View of Mathematics	48	(10)
Importance of a Connected View of Mathematics
Importance of a Balanced View of Mathematics
Developing a Connected, Balanced View of Mathematics
Chapter Summary	53	(2)
Chapter Review	55	(3)
Sets and Whole-Number Operations and Properties	58	(64)
Sets and Whole Numbers	59	(14)
Connecting Sets to Whole-Number Ideas
Using Sets to Define Whole Numbers
Using Sets to Compare and Order Whole Numbers
Important Subsets of Whole Numbers
Addition and Subtraction of Whole Numbers	73	(15)
Using Models and Sets to Define Addition
Basic Properties of Addition
Modeling Subtraction
Using Addition to Define Subtraction
Comparing Subtraction to Addition
Multiplication and Division of Whole Numbers	88	(15)
Using Models and Sets to Define Multiplication
Properties of Multiplication
Modeling Division
Using Multiplication to Define Division
Comparing Division to Multiplication
The Division Algorithm for Whole Numbers
Numeration	103	(19)
Numeration Systems
The Hindu-Arabic Place-Value Numeration System
Other Early Numeration Systems
Comparing Numeration Systems
Chapter Summary	118	(2)
Chapter Review	120	(2)
Estimation and Computation	122	(66)
Strategies and Procedures for Mental Computation	123	(12)
When to Use Mental Computation
Mental Computation Techniques
Strategies and Procedures for Estimation	135	(10)
Computational Estimation Techniques
Choosing an Estimation Technique
Algorithms for Addition and Subtraction	145	(19)
Developing Algorithms for Addition
Developing Algorithms for Subtraction
Calculator Techniques for Addition and Subtraction
Algorithms for Multiplication and Division	164	(24)
Developing Algorithms for Multiplication
Calculator Techniques for Multiplication
Developing Algorithms for Division
Using a Calculator to Evaluate Multiplication and Division Expressions
Chapter Summary	184	(2)
Chapter Review	186	(2)
Number Theory	188	(42)
Factors and Divisibility	189	(17)
Connecting Factors and Multiples
Defining Divisibility
Techniques for Determining Divisibility
Using Factors to Classify Natural Numbers
Prime and Composite Numbers	206	(24)
Defining Prime and Composite Numbers
Techniques for Finding Prime Numbers
The Role of Prime Numbers in Mathematics
Greatest Common Factor and Least Common Multiple
Prime and Composite Numbers and Relationships
Chapter Summary	227	(1)
Chapter Review	228	(2)
Understanding Integer Operations and Properties	230	(46)
Addition, Subtraction, and Order Properties of Integers	231	(24)
Integer Uses and Basic Ideas
Modeling Integer Addition
Properties of Integer Addition
Modeling Integer Subtraction
Applications of Integer Addition and Subtraction
Comparing and Ordering Integers
Multiplication, Division, and Other Properties of Integers	255	(21)
Modeling Integer Multiplication
Applications of Integer Multiplication
Properties of Integer Multiplication
Explaining Integer Division
More Properties of Integer Multiplication and Division
Chapter Summary	273	(1)
Chapter Review	274	(2)
Rational Number Operations and Properties	276	(68)
Rational Number Ideas and Symbols	277	(18)
Modeling Rational Numbers
Defining Rational Numbers
Using Fractions to Represent Rational Numbers
Properties of Fractions
Using Decimals to Represent Rational Numbers
Connecting Rational Numbers to Whole Numbers, Integers, and Other Numbers
Adding and Subtracting Rational Numbers	295	(11)
Modeling Addition and Subtraction of Rational Numbers
Adding and Subtracting Rational Numbers in Fraction Form
Properties of Rational Number Addition and Subtraction
Adding and Subtracting Rational Numbers in Decimal Form
Estimation Strategies
Multiplying Rational Numbers	306	(13)
Modeling Rational Number Multiplication
Multiplying Rational Numbers in Fraction Form
Properties of Rational Number Multiplication
Multiplying Rational Numbers in Decimal Form
Estimation Strategies
Dividing, Comparing, and Ordering Rational Numbers	319	(25)
Modeling Rational Number Division
Defining Rational Number Division
Dividing Rational Numbers in Fraction Form
Dividing Rational Numbers in Decimal Form
Estimation Strategies
Comparing Rational Numbers
Other Characteristics of Rational Numbers
Chapter Summary	339	(3)
Chapter Review	342	(2)
Proportional Reasoning	344	(46)
The Concept of Ratio	345	(6)
Meaning of Ratio
Uses of Ratio
Ratios in Decimal Form
Proportional Variation and Solving Proportions	351	(17)
Recognizing Proportional Variation
Characteristics of Quantities That Vary Proportionally
Proportional Variation in Geometry
Properties of Proportions
Solving Proportional Problems
Solving Percent Problems	368	(22)
Definition of Percent
Connecting Percents, Ratios, and Decimals
Types of Percent Problems
Solving Percent Problems
Percent Increase or Decrease
Simple and Compound Interest
Estimating the Percent of a Number
Chapter Summary	386	(1)
Chapter Review	387	(3)
Analyzing Data	390	(62)
Types of Data Displays	391	(18)
Common Forms of Data Display
Representing Frequency and Distribution of Data
Representing Variation and Comparing Data
Representing Part-to-Whole Relationships in Data
Data Displays That Show Relationships	409	(11)
Displaying Two-Variable Data
Scatterplots and Trend Lines
Describing the Average and Spread of Data	420	(13)
Different Types of Averages
Numerical Descriptions of the Spread and Distribution of Data
Graphical Descriptions of the Spread and Distribution of Data
Additional Ways to Describe the Spread and Distribution of Data
Decision Making with Data	433	(19)
Evaluating Data Collection Procedures
Making Valid Conclusions from Data
Misleading Conclusions from Graphs
Evaluating a Data-Based Conclusion
Connecting Data Analysis and Problem Solving
Chapter Summary	446	(2)
Chapter Review	448	(4)
Probability	452	(50)
Understanding Probability	453	(11)
Defining Probability
Identifying Sample Spaces
The Addition Property of Probability
Connecting Probability to Models and Counting	464	(9)
Representing and Counting Experimental Outcomes
Probabilities of Independent Events
Conditional Probability
Simulations	473	(8)
Approximating Probabilities with Simulations
Creating Simulations with Technology
Odds and Long-Term Behavior	481	(6)
Odds in Favor and Odds Against
Expected Value
Connecting Expected Value and Odds to Fairness
Permutations and Combinations	487	(15)
Listing Permutations
Solving Permutations Problems
Counting Combinations
Chapter Summary	497	(2)
Chapter Review	499	(3)
Introducing Geometry	502	(82)
Basic Ideas of Geometry	503	(22)
Seeing Geometry in the World
Modeling and Defining Basic Geometric Ideas
Solving Problems in Geometry	525	(16)
Point and Line Problems
Segment, Angle, and Triangle Problems
Quadrilateral, Polygon, and Circle Problems
More about Angles	541	(14)
Angles in Intersecting Lines
Angles in Polygons
Angles in Regular Polygons
Angles in Circles
More about Triangles	555	(15)
Congruent Triangles
The Pythagorean Theorem
Special Right Triangles
More about Quadrilaterals	570	(14)
Properties of Quadrilaterals
Quadrilaterals and Geometric Constructions
What-If Questions about Quadrilaterals
Chapter Summary	579	(3)
Chapter Review	582	(2)
Extending Geometry	584	(62)
Transformations	585	(17)
Translations, Rotations, and Reflections
Connecting Transformations and Symmetry
Transformations That Change Size
Transformations That Change Both Size and Shape
Geometric Patterns	602	(14)
Geometric Patterns and Tessellations Polygons That Tessellate
Combinations of Regular Polygons That Tessellate
Other Ways to Generate Tessellations
Tessellations with Irregular or Curved Sides
Special Polygons	616	(10)
Golden Triangles and Rectangles
Star Polygons
Star-Shaped Polygons
Three-Dimensional Figures	626	(20)
The Regular Polyhedra
Prisms and Pyramids
Cylinders, Cones, and Spheres
Symmetry in Three Dimensions
Visualizing Three-Dimensional Figures
Chapter Summary	642	(2)
Chapter Review	644	(2)
Measurement	646	(56)
The Concept of Measurement	647	(12)
The Measurement Process
Types of Measures and Units Used
Nonstandard Units of Measure
Standard Units of Measure
Measuring Time and Temperature
Measuring the Perimeter and Area of Polygons	659	(19)
Perimeters of Common Polygons
Areas of Common Polygons
Circumference and Area of Circles
Comparing Perimeters and Areas of Similar Polygons
Measuring the Surface Area and Volume of Solids	678	(24)
Surface Areas of Solids
Volumes of Solids
Comparing Surface Areas and Volumes of Similar Solids
Chapter Summary	697	(2)
Chapter Review	699	(3)
Exploring Ideas of Algebra and Coordinate Geometry	702	(69)
Variables, Expressions, and Equations	703	(16)
Understanding How Letters Are Used in Mathematics
Understanding Numerical and Algebraic Expressions
Understanding Equations
Analyzing Different Types of Equations
Solving Equations	719	(17)
Understanding the Meaning of a Solution to an Equation
Developing Ways to Solve Linear and Quadratic Equations
Exploring Graphs of Linear Equations	736	(8)
Developing Techniques for Graphing Linear Equations
Understanding How Graphs and Equations Are Related
Understanding How Slope Is Related to Horizontal and Vertical Lines
Connecting Algebra and Geometry	744	(27)
Finding the Midpoint of a Line Segment
Finding the Distance Between Two Points
Finding the Equation of a Line
Using Coordinate Geometry to Verify Geometric Conjectures
Developing the Equation of a Circle
Describing Transformations Using Coordinate Geometry
Chapter Summary	767	(2)
Chapter Review	769	(2)
Appendix A Graphing Calculator	771	(11)
Appendix B Geometry Exploration Software	782	(12)
Appendix C Glossary of Geometric Terms	794	(3)
Appendix D Constructions	797	(10)
References	807
Selected Answers	1	(1)
Index	1