## Description

Test Bank For Reconceptualizing Mathematics for Elementary School Teachers 3rd Edition| ©2017 by Sowder

Test Bank For Reconceptualizing Mathematics for Elementary School Teachers 3rd Edition| ©2017 by Judith Sowder,Larry Sowder,Susan Nickerson,ISBN:9781319101824

This new edition further prepares future teachers to impact students’ mathematical understanding.

Reconceptualizing Mathematics, founded on research and studies of learning and mathematics teaching for many years, is designed for use in classrooms in which students take an active part in learning and experience doing math. The esteemed author team has written the only textbook of its kind to both incorporate aspects of student-centered learning into lessons and model the teaching that will be expected of their students. To this end, the authors provide worthwhile tasks, activities, and support for facilitating discussions.

Quantitative reasoning and problem solving are recurring themes in Reconceptualizing Mathematics. The authors approach problem solving that teaches students to understand the quantities embedded in the situation and how they relate to each other.

Maximize Teaching and Learning with WebAssign Premium

Macmillan Learning and WebAssign have partnered to deliver WebAssign Premium – a comprehensive and flexible suite of resources for your math for teachers course. Combining the most widely used online homework platform with authoritative textbook content and Macmillan’s esteemed Mathtools, WebAssign Premium extends and enhances the classroom experience for instructors and students. Preview course content and sample assignments at www.webassign.net/whfreeman.

Table of Contents

PART I: REASONING ABOUT NUMBERS AND QUANTITIES

Chapter 1: Reasoning About Quantities

1.1 Ways of Thinking About Solving Story Problems

1.2 Quantitative Analysis

1.3 Problem Solving

1.4 Issues for Learning: Ways of Illustrating Story Problems

1.5 Check Yourself

Chapter 2: Numeration Systems

2.1 Ways of Expressing Values of Quantities

2.2 Place Value

2.3 Bases Other Than Ten

2.4 Operations in Different Bases

2.5 Issues for Learning: Understanding Place Value

2.6 Check Yourself

Chapter 3: Understanding Whole Number Operations

3.1 Ways of Thinking About Addition and Subtraction

3.2 Children’s Ways of Adding and Subtracting

3.3 Ways of Thinking About Multiplication

3.4 Ways of Thinking About Division

3.5 Children Find Products and Quotients

3.6 Issues for Learning: Developing Number Sense

3.7 Check Yourself

Chapter 4: Some Conventional Ways of Computing

4.1 Operating on Whole Numbers and Decimal Numbers

4.2 Issues for Learning: The Role of Algorithms

4.3 Check Yourself

Chapter 5: Using Numbers in Sensible Ways

5.1 Mental Computation

5.2 Computational Estimation

5.3 Estimating Values of Quantities

5.4 Using Scientific Notation for Estimating Values of Very Large and Very Small Quantities

5.5 Issues for Learning: Mental Computation

5.6 Check Yourself

Chapter 6: Meanings for Fractions

6.1 Understanding the Meanings of a/b

6.2 Comparing Fractions

6.3 Equivalent (Equal) Fractions

6.4 Relating Fractions, Decimals, and Percents

6.5 Issues for Learning: Understanding Fractions and Decimals

6.6 Check Yourself

Chapter 7: Computing with Fractions

7.1 Adding and Subtracting Fractions

7.2 Multiplying by a Fraction

7.3 Dividing by a Fraction

7.4 Issues for Learning: Teaching Calculation with Fractions

7.5 Check Yourself

Chapter 8: Multiplicative Comparisons and Multiplicative Reasoning

8.1 Quantitative Analysis of Multiplicative Situations

8.2 Fractions in Multiplicative Comparisons

8.3 Issues for Learning: Standards for Learning

8.4 Check Yourself

Chapter 9: Ratios, Rates, Proportions, and Percents

9.1 Ratio as a Measure

9.2 Comparing Ratios

9.3 Percents in Comparisons and Changes

9.4 Issues for Learning: Developing Proportional Reasoning

9.5 Check Yourself

Chapter 10: Integers and Other Number Systems

10.1 Big Ideas About Signed Numbers

10.2 Children’s Ways of Reasoning About Signed Numbers

10.3 Other Models for Signed Numbers

10.4 Operations with Signed Numbers

10.5 Multiplying and Dividing Signed Numbers

10.6 Number Systems

10.7 Issues for Learning: Open Number Sentences

10.8 Check Yourself

Chapter 11: Number Theory

11.1 Factors and Multiples, Primes and Composites

11.2 Prime Factorization

11.3 Divisibility Tests to Determine Whether a Number is Prime

11.4 Greatest Common Factor, Least Common Multiple

11.5 Issues for Learning: Understanding the Unique Factorization Theorem

11.6 Check Yourself

PART II: REASONING ABOUT ALGEBRA AND CHANGE

Chapter 12: What is Algebra?

12.1 Algebraic Reasoning in Elementary School

12.2 Numerical Patterns and Algebra

12.3 Functions and Algebra

12.4 Algebra as Generalized Arithmetic

12.5 Algebraic Reasoning About Quantities

12.6 Issues for Learning: The National Assessment of Educational Progress and Achievement in Algebra

12.7 Check Yourself

Chapter 13: A Quantitative Approach to Algebra and Graphing

13.1 Using Graphs and Algebra to Show Quantitative Relationships

13.2 Understanding Slope: Making Connections Across Quantitative Situations, Graphs, and Algebraic Equations

13.3 Linear Functions and Proportional Relationships

13.4 Nonlinear Functions

13.5 Issues for Learning: Algebra in the Elementary Grades

13.6 Check Yourself

Chapter 14: Understanding Change: Relationships Among Time, Distance, and Rate

14.1 Distance-Time and Position-Time Graphs

14.2 Using Motion Detectors

14.3 Graphs of Speed Against Time

14.4 Interpreting Graphs

14.5 Issues for Learning: Common Graphing Errors

14.6 Check Yourself

Chapter 15: Further Topics in Algebra and Change

15.1 Finding Linear Equations

15.2 Solving Two Linear Equations in Two Variables

15.3 Different Approaches to Problems

15.4 Average Speed and Weighted Averages

15.5 More About Functions

15.6 Issues for Learning: Topics in Algebra

15.7 Check Yourself

PART III: REASONING ABOUT SHAPES AND MEASUREMENT

Chapter 16: Polygons

16.1 Review of Polygon Vocabulary

16.2 Organizing Shapes

16.3 Triangles and Quadrilaterals

16.4 A Focus on Problem-Solving Strategies

16.5 Issues for Learning: Some Research on Two-Dimensional Shapes

16.6 Check Yourself

Chapter 17: Polyhedra

17.1 Shoeboxes Have Faces and Nets!

17.2 Introduction to Polyhedra

17.3 Representing and Visualizing Polyhedra

17.4 Congruent Polyhedra

17.5 Some Special Polyhedra

17.6 Issues for Learning: Dealing with 3D Shapes

17.7 Check Yourself

Chapter 18: Symmetry

18.1 Symmetry of Shapes in a Plane

18.2 Symmetry of Polyhedra

18.3 Issues for Learning: What Geometry Is in the Pre-K-8 Curriculum?

18.4 Check Yourself

Chapter 19: Tessellations

19.1 Tessellating the Plane

19.2 Tessellating Space

19.3 Check Yourself

Chapter 20: Similarity

20.1 Similarity and Dilations in Planar Figures

20.2 More About Similar Figures

20.3 Similarity in Space Figures

20.4 Issues for Learning: Similarity and Proportional Reasoning

20.5 Check Yourself

Chapter 21: Curves, Constructions, and Curved Surfaces

21.1 Planar Curves and Constructions

21.2 Curved Surfaces

21.3 Issues for Learning: Standards for Mathematical Practice

21.4 Check Yourself

Chapter 22: Transformation Geometry

22.1 Some Types of Rigid Motions

22.2 Finding Images for Rigid Motions

22.3 A Closer Look at Some Rigid Motions

22.4 Composition of Rigid Motions

22.5 Transformations and Earlier Topics

22.6 Issues for Learning: Promoting Visualization in the Curriculum

22.7 Check Yourself

Chapter 23: Measurement Basics

23.1 Key Ideas of Measurement

23.2 Length and Angle Size

23.3 Issues for Learning: Measurement of Length and Angle Size

23.4 Check Yourself

Chapter 24: Area, Surface Area, and Volume

24.1 Area and Surface Area

24.2 Volume

24.3 Issues for Learning: Measurement of Area and Volume

24.4 Check Yourself

Chapter 25: Counting Units Fast: Measurement Formulas

25.1 Circumference, Area, and Surface Area Formulas

25.2 Volume Formulas

25.3 Issues for Learning: What Measurement is in the Curriculum?

25.4 Check Yourself

Chapter 26: Special Topics in Measurement

26.1 The Pythagorean Theorem

26.2 Some Other Kinds of Measurements

26.3 Check Yourself

PART IV: REASONING ABOUT CHANCE AND DATA

Chapter 27: Quantifying Uncertainty

27.1 Understanding Chance Events

27.2 Methods of Assigning Probabilities

27.3 Simulating Probabilistic Situations

27.4 Issues for Learning: Research on the Learning of Probability

27.5 Check Yourself

Chapter 28: Determining More Complicated Probabilities

28.1 Tree Diagrams and Lists for Multistep Experiments

28.2 Probability of One Event or Another Event

28.3 Probability of One Event and Another Event

28.4 Conditional Probability

28.5 Probability and Problem Solving

28.6 Check Yourself

Chapter 29: Introduction to Statistics and Sampling

29.1 What Are Statistics?

29.2 Sampling: The Why and the How

29.3 Simulating Random Sampling

29.4 Types of Data

29.5 Conducting a Survey

29.6 Issues for Learning: Sampling

29.7 Check Yourself

Chapter 30: Representing and Interpreting Data with One Variable

30.1 Representing Categorical Data

30.2 Representing and Interpreting Measurement Data

30.3 Examining the Spread of Data

30.4 Measures of Center

30.5 Deviations from the Mean as Measures of Spread

30.6 Examining Distributions

30.7 Issues for Learning: Understanding the Mean

30.8 Check Yourself

Chapter 31: Dealing with Multiple Data Sets or with Multiple Variables

31.1 Comparing Data Sets

31.2 Lines of Best Fit and Correlation

31.3 Issues for Learning: More Than One Variable

31.4 Check Yourself

Chapter 32: Variability in Samples

32.1 Having Confidence in a Sample Statistic

32.2 Confidence Intervals

32.3 Issues for Learning: What Probability and Statistics Should Be in the Curriculum?

32.4 Check Yourself

Chapter 33: Special Topics in Probability

33.1 Expected Value

33.2 Permutations and Combinations

33.3 Issues for Learning: Children Finding Permutations

33.4 Check Yourself

Appendix A: Video Clips Illustrating Children’s Mathematical Thinking

Appendix B: Summary of Formulas

Appendix C: Using the Table of Randomly Selected Digits (TRSD)

Appendix D: Data Sets in Printed Form

Master for Nets

Available Online or In Print via Custom

Appendix E: About the Geogebra Lessons

Appendix F: A Review of Some Rules

Appendix G: Using a Protractor to Measure Angle Size

Appendix H: Using the TI-73

Appendix I: Using Excel

Appendix J: Using the Illuminations Website

Masters for Base Materials, Pattern Blocks, and Dot Paper