Mathematical Reasoning for Elementary Teachers, Media Update (7^th Ed.)

For courses in Mathematics for Teachers or Mathematics for Future Elementary Teachers.

Fosters reasoning skills, deep conceptual understanding, and a positive attitude to aspiring elementary or middle school teachers

Mathematical Reasoning for Elementary Teachers presents the mathematical content needed for teaching within the context of the elementary classroom. The authors endeavor to answer the frequently asked question ?Why are we learning this?? by going beyond skill explanations to show how these concepts are implemented in the future classroom, and what types of questions children may ask. The Common Core State Standards for Mathematics are included.

This Media Update for the 7th Edition features:

• Education Insights video program adapted from teacher education videos, produced with assessment questions, worksheets, and an implementation guide
  
• Common Core in Action videos with assessment questions
  
• Common Core Assessment Analysis questions
  
• GeoGebra animations with assessment questions
  
• Assessment questions for lecture videos
  
• MindSet material.
  

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Package consists of:

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Table of Contents

1. Thinking Critically
   • 1.1 An Introduction to Problem Solving
   • 1.2 Polya’s Problem-Solving Principles and the Standards for Mathematical Practice of the Common Core State Standards for Mathematics
   • 1.3 More Problem-Solving Strategies
   • 1.4 Algebra as a Problem-Solving Strategy
   • 1.5 Additional Problem-Solving Strategies
   • 1.6 Reasoning Mathematically
2. Sets and Whole Numbers
   • 2.1 Sets and Operations on Sets
   • 2.2 Sets, Counting, and the Whole Numbers
   • 2.3 Addition and Subtraction of Whole Numbers
   • 2.4 Multiplication and Division of Whole Numbers
3. Numeration and Computation
   • 3.1 Numeration Systems Past and Present
   • 3.2 Algorithms for Addition and Subtraction of Whole Numbers
   • 3.3 Algorithms for Multiplication and Division of Whole Numbers
   • 3.4 Mental Arithmetic and Estimation
   • 3.5 Nondecimal Positional Systems
4. Number Theory
   • 4.1 Divisibility of Natural Numbers
   • 4.2 Tests for Divisibility
   • 4.3 Greatest Common Divisors and Least Common Multiples
5. Integers
   • 5.1 Representation of Integers
   • 5.2 Addition and Subtraction of Integers
   • 5.3 Multiplication and Division of Integers
6. Fractions and Rational Numbers
   • 6.1 The Basic Concepts of Fractions and Rational Numbers
   • 6.2 Addition and Subtraction of Fractions
   • 6.3 Multiplication and Division of Fractions
   • 6.4 The Rational Number System
7. Decimals, Real Numbers, and Proportional Reasoning
   • 7.1 Decimals and Real Numbers
   • 7.2 Computations with Decimals
   • 7.3 Proportional Reasoning
   • 7.4 Percent
8. Algebraic Reasoning, Graphing, and Connections with Geometry
   • 8.1 Variables, Algebraic Expressions, and Functions
   • 8.2 Graphing Points, Lines, and Elementary Functions
   • 8.3 Connections between Algebra and Geometry
9. Geometric Figures
   • 9.1 Figures in the Plane
   • 9.2 Curves and Polygons in the Plane
   • 9.3 Figures in Space
10. Measurement: Length, Area, and Volume
    • 10.1 The Measurement Process
    • 10.2 Area and Perimeter
    • 10.3 The Pythagorean Theorem
    • 10.4 Volume
    • 10.5 Surface Area
11. Transformations, Symmetries, and Tilings
    • 11.1 Rigid Motions and Similarity Transformations
    • 11.2 Patterns and Symmetries
    • 11.3 Tilings and Escher-like Designs
12. Congruence, Constructions, and Similarity
    • 12.1 Congruent Triangles
    • 12.2 Constructing Geometric Figures
    • 12.3 Similar Triangles
13. Statistics: The Interpretation of Data
    • 13.1 Organizing and Representing Data
    • 13.2 Measuring the Center and Variation of Data
    • 13.3 Statistical Inference
14. Probability
    • 14.1 The Basics of Probability
    • 14.2 Applications of Counting Principles to Probability
    • 14.3 Permutations and Combinations
    • 14.4 Odds, Expected Values, Geometric Probability, and Simulations

About our authors

Calvin Long received his B.S. in Mathematics from the University of Idaho. Following M.S. and Ph.D. degrees in Mathematics from the University of Oregon, he worked briefly as an analyst for the National Security Agency and then joined the faculty at Washington State University. His teaching ran the gamut from elementary algebra through graduate courses and included frequently teaching the content courses for prospective elementary school teachers.

His other professional activities include serving on numerous committees of the National Council of Teachers of Mathematics and the Mathematical Association of America, and holding various leadership positions in those organizations. Professor Long has also been heavily engaged in directing and instructing in-service workshops and institutes for teachers at all levels, has given more than 100 presentations at national and regional meetings of NCTM and its affiliated groups, and has presented invited lectures on mathematics education abroad.

Professor Long has co-authored 2 books and is the sole author of a text on number theory. In addition, he has authored over 90 articles on mathematics and mathematics education, and served as a frequent reviewer for mathematics journals including The Arithmetic Teacher and The Mathematics Teacher. In 1986 he received the Faculty Excellence Award in Teaching from Washington State University, and in 1991 he received a Certificate for Meritorious Service to the Mathematical Association of America.

Aside from his professional activities, Cal enjoys listening to, singing and directing classical music, reading, fly fishing, camping and backpacking.

Duane DeTemple received his B.S. with majors in Applied Science and Mathematics from Portland State College. Following his Ph.D. in Mathematics from Stanford University, he was a faculty member at Washington State University, where he is now a Professor Emeritus