Mathematical Reasoning For Elementary Teachers by Calvin LongMathematical Reasoning For Elementary Teachers by Calvin Long

Mathematical Reasoning For Elementary Teachers

byCalvin Long, Duane Detemple, Richard Millman

Hardcover | January 9, 2014

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Long/DeTemple/Millman’s Mathematical Reasoning for Elementary Teachers presents the mathematical content needed for teaching within the context of the elementary classroom, giving future teachers the motivation they need while also showing them the bigger picture of when they will use and teach the concepts. The program endeavors to answer the frequently-asked question “Why are we learning this?” by going beyond skill explanations and showing the ways that these concepts are implemented in the future classroom and what types of questions children may ask. Now updated to include the Common Core State Standards for Mathematics, the text imparts mathematical reasoning skills, a deep conceptual understanding, and a positive attitude to those who aspire to be elementary or middle school teachers.


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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 throu...
Title:Mathematical Reasoning For Elementary TeachersFormat:HardcoverDimensions:864 pages, 11 × 8.7 × 1.4 inPublished:January 9, 2014Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0321900995

ISBN - 13:9780321900999


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