Reconceptualizing Mathematics for Elementary School Teachers 3rd edition

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Judith Sowder, Larry Sowder, and Susan Nickerson
Publisher: W. H. Freeman

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  • Chapter 1: Reasoning About Quantities
    • 1.1: Ways of Thinking About Solving Story Problems
    • 1.2: Quantitative Analysis (4)
    • 1.3: Problem Solving (3)
    • 1.4: Issues for Learning: Ways of Illustrating Story Problems (4)
    • 1.5: Check Yourself

  • Chapter 2: Numeration Systems
    • 2.1: Ways of Expressing Values of Quantities (3)
    • 2.2: Place Value (3)
    • 2.3: Bases Other Than Ten (4)
    • 2.4: Operations in Different Bases (2)
    • 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)
    • 3.2: Children's Ways of Adding and Subtracting (2)
    • 3.3: Ways of Thinking About Multiplication (3)
    • 3.4: Ways of Thinking About Division (2)
    • 3.5: Children Find Products and Quotients (1)
    • 3.6: Issues for Learning: Developing Number Sense (2)
    • 3.7: Check Yourself

  • Chapter 4: Some Conventional Ways of Computing
    • 4.1: Operating on Whole Numbers and Decimal Numbers (12)
    • 4.2: Issues for Learning: The Role of Algorithms
    • 4.3: Check Yourself

  • Chapter 5: Using Numbers in Sensible Ways
    • 5.1: Mental Computation (3)
    • 5.2: Computational Estimation (3)
    • 5.3: Estimating Values of Quantities (3)
    • 5.4: Using Scientific Notation for Estimating Values of Very Large and Very Small Quantities (3)
    • 5.5: Issues for Learning: Mental Computation
    • 5.6: Check Yourself

  • Chapter 6: Meanings for Fractions
    • 6.1: Understanding the Meanings of ab (6)
    • 6.2: Comparing Fractions (4)
    • 6.3: Equivalent (Equal) Fractions (6)
    • 6.4: Relating Fractions, Decimals, and Percents (5)
    • 6.5: Issues for Learning: Understanding Fractions and Decimals
    • 6.6: Check Yourself

  • Chapter 7: Computing with Fractions
    • 7.1: Adding and Subtracting Fractions (3)
    • 7.2: Multiplying by a Fraction (4)
    • 7.3: Dividing by a Fraction (3)
    • 7.4: Issues for Learning: Teaching Calculation with Fractions (3)
    • 7.5: Check Yourself

  • Chapter 8: Multiplicative Comparisons and Multiplicative Reasoning
    • 8.1: Quantitative Analysis of Multiplicative Situations (3)
    • 8.2: Fractions in Multiplicative Comparisons (9)
    • 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 (2)
    • 9.2: Comparing Ratios (3)
    • 9.3: Percents in Comparisons and Changes (8)
    • 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 (2)
    • 10.2: Children's Ways of Reasoning About Signed Numbers (1)
    • 10.3: Other Models for Signed Numbers (1)
    • 10.4: Operations with Signed Numbers (2)
    • 10.5: Multiplying and Dividing Signed Numbers (2)
    • 10.6: Number Systems (2)
    • 10.7: Issues for Learning: Open Number Sentences
    • 10.8: Check Yourself

  • Chapter 11: Number Theory
    • 11.1: Factors and Multiples, Primes and Composites (4)
    • 11.2: Prime Factorization (3)
    • 11.3: Divisibility Tests to Determine Whether a Number is Prime (3)
    • 11.4: Greatest Common Factor, Least Common Multiple (2)
    • 11.5: Issues for Learning: Understanding the Unique Factorization Theorem (1)
    • 11.6: Check Yourself

  • Chapter 12: What Is Algebra?
    • 12.1: Algebraic Reasoning in Elementary School (2)
    • 12.2: Numerical Patterns and Algebra (2)
    • 12.3: Functions and Algebra (2)
    • 12.4: Algebra as Generalized Arithmetic (2)
    • 12.5: Algebraic Reasoning About Quantities (2)
    • 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 (4)
    • 13.2: Understanding Slope: Making Connections Across Quantitative Situations, Graphs, and Algebraic Equations (2)
    • 13.3: Linear Functions and Proportional Relationships (2)
    • 13.4: Nonlinear Functions (2)
    • 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 (1)
    • 14.2: Using Motion Detectors (1)
    • 14.3: Graphs of Speed Against Time (1)
    • 14.4: Interpreting Graphs (2)
    • 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 (1)
    • 15.2: Solving Two Linear Equations in Two Variables (1)
    • 15.3: Different Approaches to Problems (1)
    • 15.4: Average Speed and Weighted Averages (1)
    • 15.5: More About Functions (1)
    • 15.6: Issues for Learning: Topics in Algebra (1)
    • 15.7: Check Yourself

  • Chapter 16: Polygons
    • 16.1: Review of Polygon Vocabulary (3)
    • 16.2: Organizing Shapes (2)
    • 16.3: Triangles and Quadrilaterals (2)
    • 16.4: A Focus on Problem-Solving Strategies (2)
    • 16.5: Issues for Learning: Some Research on Two-Dimensional Shapes (1)
    • 16.6: Check Yourself

  • Chapter 17: Polyhedra
    • 17.1: Shoeboxes Have Faces and Nets! (1)
    • 17.2: Introduction to Polyhedra (3)
    • 17.3: Representing and Visualizing Polyhedra (3)
    • 17.4: Congruent Polyhedra (1)
    • 17.5: Some Special Polyhedra (3)
    • 17.6: Issues for Learning: Dealing with 3D Shapes
    • 17.7: Check Yourself

  • Chapter 18: Symmetry
    • 18.1: Symmetry of Shapes in a Plane (3)
    • 18.2: Symmetry of Polyhedra (3)
    • 18.3: Issues for Learning: What Is Geometry in the Pre-K–8 Curriculum?
    • 18.4: Check Yourself

  • Chapter 19: Tessellations
    • 19.1: Tessellating the Plane (2)
    • 19.2: Tessellating Space (3)
    • 19.3: Check Yourself

  • Chapter 20: Similarity
    • 20.1: Similarity and Dilations in Planar Figures (4)
    • 20.2: More About Similar Figures (2)
    • 20.3: Similarity in 3D Figures (4)
    • 20.4: Issues for Learning: Similarity and Proportional Reasoning (1)
    • 20.5: Check Yourself

  • Chapter 21: Curves, Constructions, and Curved Surfaces
    • 21.1: Planar Curves and Constructions (6)
    • 21.2: Curves Surfaces (5)
    • 21.3: Issues for Learning: Standards for Mathematical Practice
    • 21.4: Check Yourself

  • Chapter 22: Transformation Geometry
    • 22.1: Some Types of Rigid Motions (2)
    • 22.2: Finding Images for Rigid Motions (2)
    • 22.3: A Closer Look at Some Rigid Motions (2)
    • 22.4: Composition of Rigid Motions (2)
    • 22.5: Transformations and Earlier Topics (2)
    • 22.6: Issues for Learning: Promoting Visualization in the Curriculum (1)
    • 22.7: Check Yourself

  • Chapter 23: Measurement Basics
    • 23.1: Key Ideas of Measurement (4)
    • 23.2: Length and Angle Size (4)
    • 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 (4)
    • 24.2: Volume (4)
    • 24.3: Issues for Learning: Measurement of Area and Volume (1)
    • 24.4: Check Yourself

  • Chapter 25: Counting Units Fast: Measurement Formulas
    • 25.1: Circumference, Area, and Surface Area Formulas (5)
    • 25.2: Volume Formulas (5)
    • 25.3: Issues for Learning: What Measurement Topics Are in the Curriculum?
    • 25.4: Check Yourself

  • Chapter 26: Special Topics in Measurement
    • 26.1: The Pythagorean Theorem (4)
    • 26.2: Some Other Kinds of Measurements (4)
    • 26.3: Check Yourself

  • Chapter 27: Quantifying Uncertainty
    • 27.1: Understanding Chance Events (1)
    • 27.2: Methods of Assigning Probabilities (3)
    • 27.3: Simulating Probabilistic Situations (1)
    • 27.4: Issues for Learning: Research on the Understanding of Probability
    • 27.5: Check Yourself

  • Chapter 28: Determining More Complicated Probabilities
    • 28.1: Tree Diagrams and Lists for Multistep Experiments (1)
    • 28.2: Probability of One Event or Another Event (1)
    • 28.3: Probability of One Event and Another Event (1)
    • 28.4: Conditional Probability (1)
    • 28.5: Probability and Problem Solving (1)
    • 28.6: Check Yourself

  • Chapter 29: Introduction to Statistics and Sampling
    • 29.1: What Are Statistics? (1)
    • 29.2: Sampling: The Why and the How (2)
    • 29.3: Simulating Random Sampling (1)
    • 29.4: Types of Data (1)
    • 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 (1)
    • 30.2: Representing and Interpreting Measurement Data (1)
    • 30.3: Examining the Spread of Data (1)
    • 30.4: Measures of Center (1)
    • 30.5: Deviations from the Mean as Measures of Spread (1)
    • 30.6: Examining Distributions (1)
    • 30.7: Issues for Learning: Understanding the Mean (1)
    • 30.8: Check Yourself

  • Chapter 31: Dealing with Multiple Data Sets or with Multiple Variables
    • 31.1: Comparing Data Sets (2)
    • 31.2: Lines of Best Fit and Correlation (2)
    • 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 (2)
    • 32.2: Confidence Intervals (1)
    • 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 (1)
    • 33.2: Permutations and Combinations (2)
    • 33.3: Issues for Learning: Children Finding Permutations
    • 33.4: Check Yourself


Available July 2017

Reconceptualizing Mathematics for Elementary School Teachers, 3rd Edition, by Judith Sowder, Larry Sowder, and Susan Nickerson is founded on many years' research and studies of learning processes and mathematics education. Reconceptualizing Mathematics is designed for use in classrooms in which students take an active part in learning mathematics. This team of esteemed authors 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 in a way that teaches students to understand the elements present in the situation and how they relate to each other.

Macmillan Learning and WebAssign have partnered to deliver 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, Reconceptualizing Mathematics extends and enhances the classroom experience for instructors and students.

Features:
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  • Detailed, worked-out solutions for all questions are available to students at your discretion.
  • Instructor resources include Lecture, Image, and iClicker PowerPoint Slides, Test Bank links, an Instructor's Guide, an Instructor Resource Manual, and an Instructor Solutions Manual.
  • Student resources include Practice Quizzes, a Student Solutions Manual, Learning Curve links, Data Sets, MathClips Video links, Printable & Electronic Manipulatives, Suggested Websites, Tables, and Web Appendices.

Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

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Group Quantity Questions
Chapter 1: Reasoning About Quantities
1.2 4 002 005 007 008
1.3 3 004 005 008
1.4 4 002 003 006 008
Chapter 2: Numeration Systems
2.1 3 004 005 006
2.2 3 005 006 008
2.3 4 002 013 018 021
2.4 2 003 004
Chapter 3: Understanding Whole Number Operations
3.1 3 003 006 009
3.2 2 002 005
3.3 3 008 010 014
3.4 2 005 006
3.5 1 S.003
3.6 2 004 005
Chapter 4: Some Conventional Ways of Computing
4.1 12 S.001 S.008 S.011 001 002 005 007 008 010 011 012 013
Chapter 5: Using Numbers in Sensible Ways
5.1 3 001 003 006
5.2 3 006 007 008
5.3 3 S.001 S.003 002
5.4 3 001 003 008
Chapter 6: Meanings for Fractions
6.1 6 003 006 013 016 018 023
6.2 4 S.002 004 006 011
6.3 6 003 005 006 008 011 012
6.4 5 001 002 008 013 014
Chapter 7: Computing with Fractions
7.1 3 003 005 016
7.2 4 004 012 017 020
7.3 3 002 013 014
7.4 3 002 004 008
Chapter 8: Multiplicative Comparisons and Multiplicative Reasoning
8.1 3 001 003 006
8.2 9 S.001 S.003 S.004 S.006 S.009 001 007 009 012
Chapter 9: Ratios, Rates, Proportions, and Percents
9.1 2 003 007
9.2 3 005 010 020
9.3 8 CS.003 CS.013 CS.020 004 009 011 013 027
Chapter 10: Integers and Other Number Systems
10.1 2 004 007
10.2 1 001
10.3 1 003
10.4 2 002 009
10.5 2 003 006
10.6 2 002 010
Chapter 11: Number Theory
11.1 4 002 008 011 016
11.2 3 007 012 013
11.3 3 004 011 021
11.4 2 005 013
11.5 1 002
Chapter 12: What Is Algebra?
12.1 2 001 009
12.2 2 001 005
12.3 2 010 012
12.4 2 002 016
12.5 2 004 013
Chapter 13: A Quantitative Approach to Algebra and Graphing
13.1 4 003 005 006 008
13.2 2 001 008
13.3 2 006 008
13.4 2 001 004
Chapter 14: Understanding Change: Relationships Among Time, Distance, and Rate
14.1 1 007
14.2 1 001
14.3 1 005
14.4 2 006 007
Chapter 15: Further Topics in Algebra and Change
15.1 1 020
15.2 1 023
15.3 1 001
15.4 1 013
15.5 1 002
15.6 1 005
Chapter 16: Polygons
16.1 3 001 011 013
16.2 2 002 003
16.3 2 002 006
16.4 2 006 008
16.5 1 003
Chapter 17: Polyhedra
17.1 1 003
17.2 3 001 003 010
17.3 3 005 016 018
17.4 1 003
17.5 3 001 007 009
Chapter 18: Symmetry
18.1 3 S.001 004 008
18.2 3 S.001 005 009
Chapter 19: Tessellations
19.1 2 005 009
19.2 3 S.001-008 002 003
Chapter 20: Similarity
20.1 4 008 016 023 028
20.2 2 004 008
20.3 4 005 011 015 023
20.4 1 002
Chapter 21: Curves, Constructions, and Curved Surfaces
21.1 6 S.001 S.005 001 006 012 013
21.2 5 S.004 001 003 007 008
Chapter 22: Transformation Geometry
22.1 2 003 004
22.2 2 005 010
22.3 2 S.003 006
22.4 2 002 008
22.5 2 007 009
22.6 1 001
Chapter 23: Measurement Basics
23.1 4 001 016 018 020
23.2 4 012 016 024 043
Chapter 24: Area, Surface Area, and Volume
24.1 4 006 012 014 025
24.2 4 001 009 014 020
24.3 1 002
Chapter 25: Counting Units Fast: Measurement Formulas
25.1 5 002 007 009 018 025
25.2 5 002 009 011 014 018
Chapter 26: Special Topics in Measurement
26.1 4 003 013 016 020
26.2 4 010 012 014 024
Chapter 27: Quantifying Uncertainty
27.1 1 001
27.2 3 013 014 021
27.3 1 S.003
Chapter 28: Determining More Complicated Probabilities
28.1 1 007
28.2 1 002
28.3 1 007
28.4 1 009
28.5 1 001
Chapter 29: Introduction to Statistics and Sampling
29.1 1 002
29.2 2 006 008
29.3 1 001
29.4 1 001
Chapter 30: Representing and Interpreting Data with One Variable
30.1 1 002
30.2 1 003
30.3 1 017
30.4 1 017
30.5 1 003
30.6 1 011
30.7 1 002
Chapter 31: Dealing with Multiple Data Sets or with Multiple Variables
31.1 2 009 013
31.2 2 S.001 001
Chapter 32: Variability in Samples
32.1 2 002 010
32.2 1 005
Chapter 33: Special Topics in Probability
33.1 1 003
33.2 2 002 010
Total 305