Mathematical Reasoning for Elementary Teachers

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  • Edition: 5th
  • Format: Hardcover
  • Copyright: 2007-12-28
  • Publisher: Pearson
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The Fifth Edition of Mathematical Reasoning for Elementary Teachers,with new co-author Richard Millman,;focuses on ;mathematical knowledge needed for teaching demonstrating why future teachers are learning math content as well as when they will use it in the classroom. One of the most important aspects of teaching is being able to explain why students; methods and ideas are either right or wrong. Imparting this skill to future teachers the emphasis of this fantastic text.

Author Biography

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 over one hundred 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 two books and is the sole author of a text in number theory. In addition, he has authored over ninety articles on mathematics and mathematics education, and also served as a frequent reviewer for both 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, Dr. Long enjoys listening to, singing, and directing classical music, reading, fly fishing, camping, and back packing.




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 joined the faculty at Washington State University, where he is now Professor of Mathematics. He has been extensively involved with teacher preparation and professional development at both the elementary and secondary levels. Professor DeTemple has been a frequent consultant to projects sponsored by the Washington State Office of the Superintendent of Public Instruction, the Higher Education Coordinating Board, and other boards and agencies.


Dr. DeTemple has co-authored three other books and over 80 articles on mathematics or mathematics materials for the classroom. He is a member of the Washington State University President’s Teaching Academy, and in 2007 was the recipient of the WSU Sahlin Faculty Excellence Award for Instruction and the Distinguished Teaching Award of the Pacific Northwest Section of the Mathematical Association of America.


In addition to mathematics teaching and research, Duane enjoys reading, listening to and playing music, hiking, biking, canoeing, traveling, and playing tennis.




Richard Millman received a B.S. from the Massachusetts Institute of Technology and a Ph.D. from Cornell University in Mathematics. He is the Outreach Professor of Mathematics at the University of Kentucky, which supports pre-service and in-service teacher training for PreK-12 mathematics teachers. He is Principal Investigator and Project Director for ALGEBRA CUBED, a grant from the National Science Foundation to improve algebra education in rural Kentucky.


Dr. Millman has co-authored three books in mathematics, co-edited two others, and received nine peer reviewed grants. He has published over 40 articles about mathematics or mathematics education and has taught a wide variety of mathematics and mathematics education courses throughout the undergraduate and graduate curriculum, including those for preservice teachers.    He received, with a former student, an Excel Prize for Expository Writing for an article in The Mathematics Teacher.


Rich enjoys traveling, writing about mathematics, losing golf balls, listening to music, and going to plays and movies. He also loves and is enormously proud of his grandchildren with whom he enjoys discussing the conceptual basis of mathematics, among other topics.

Table of Contents

Thinking Critically
An Introduction to Problem Solving
Poacute;lya's Problem-Solving Principles
More Problem-Solving Strategies
Algebra as Problem-Solving Strategy
Additional Problem-Solving Strategies
Reasoning Mathematically
Sets and Whole Numbers
Sets and Operations on Sets
Sets, Counting, and the Whole Numbers
Addition and Subtraction of Whole Numbers
Multiplication and Division of Whole Numbers
Numeration and Computation
Numeration Systems Past and Present
Nondecimal Positional Systems
Algorithms for Adding and Subtracting Whole Numbers
Algorithms for Multiplication and Division of Whole Numbers
Mental Arithmetic and Estimation
Getting the Most Out of Your Calculator
Number Theory
Divisibility of Natural Numbers
Tests for Divisibility
Greatest Common Divisors and Least Common Multiples
Codes and Credit Card Numbers: Connections to Number Theory
Representations of Integers
Addition and Subtraction of Integers
Multiplication and Division of Integers
Fractions and Rational Numbers
The Basic Concepts of Fractions and Rational Numbers
Addition and Subtraction of Fractions
Multiplication and Division of Fractions
Properties and Applications of Rational Numbers
Decimals, Real Numbers, and Proportional Reasoning
Decimals and Real Numbers
Computations with Decimals
Proportional Reasoning
Algebraic Reasoning
Expressions, Functions, and Equations
Graphing Functions in the Cartesian Plane
Statistics: The Interpretation of Data
Graphical Representation of Data
Measures of Central Tendency and Variability
Statistical Inference and Sampling
Empirical Probability
Principles of Counting
Permutations and Combinations
Theoretical Probability
Geometric Figures
Figures in the Plane
Curves and Polygons in the Plane
Figures in Space
The Measurement Process
Area and Perimeter
The Pythagorean Theorem
Surface Area and Volume
Transformations, Symmetries, and Tilings
Rigid Motions and Similarity Transformations
Patterns and Symmetries
Tilings and Escher-like Design
Congruence, Constructions, and Similarities
Congruent Triangles
Constructing Geometric Figures
Similar Triangles nbsp;

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