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Mathematical Reasoning for Elementary Teachers (5TH 09 - Old Edition)


Mathematical Reasoning for Elementary Teachers (5TH 09 - Old Edition) Cover


Synopses & Reviews

Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.

Publisher Comments:

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.


Provides detailed, worked-out solutions to all exercises that are answered in the back of the student text.

About the Author

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

Chapter 1 Thinking Critically

Activity 1 When You Don't Know What to Do

Activity 2 Pictoral Patterns

Activity 3 Number Patterns

Activity 4 What's the Rule?

Activity 5 Polygons and Diagonals

Activity 6 Ten People in a Canoe

Activity 7 Fascinating Fibonacci

Activity 8 Magic Number Tricks

Activity 9 An Ancient Game

Activity 10 Attribute Elimination

Activity 11 Missing Persons Report

Activity 12 Who Dunit?

Activity 13 What's the Number?

Activity 14 Eliminate the Impossible

Activity 15 Candies, Couples and a Quiz

Activity 16 What's the Last Card?

Chapter Summary


Chapter 2 Sets and Whole Numbers

Activity 1 What's in the Loop?

Activity 2 Loop de Loops

 Activity 3 Odd and Even Patterns

Activity 4 Multiplication Arrays

Activity 5 Finding the Missing Factor

Activity 6 How Many Cookies?

Activity 7 Paper Powers

Activity 8 The King's Problem

Chapter Summary


Chapter 3 Numeration and Computation

Activity 1 Regrouping Numbers

Activity 2 Find the Missing Numbers

Activity 3 A Visit to Fouria

Activity 4 It All Adds Up

Activity 5 What's the Difference?

Activity 6 Multi-digit Multiplication

Activity 7 Multi-digit Division

Activity 8 Division Array

Activity 9 Target Number

Activity 10 Least and Greatest

Chapter Summary


Chapter 4 Number Theory

Activity 1 A Square Experiment

Activity 2 A Sieve of Another Sort

Activity 3 Great Divide Game

Activity 4 The Factor Game

Activity 5 How Many Factors?

Activity 6 Interesting Numbers

Activity 7 Tiling with Squares

Activity 8 Pool Factors

Chapter Summary


Chapter 5 Integers

Activity 1 Charged Particles

Activity 2 Coin Counters

Activity 3 Addition Patterns

Activity 4 Subtracting Integers

Activity 5 A Clown on a Tightrope

Activity 6 Subtraction Patterns

Activity 7 Multiplication and Division Patterns

Activity 8 Integer × and ÷ Contig


Chapter 6 Fractions and Rational Numbers

Activity 1 What Is a Fraction?

Activity 2 Equivalent Fractions

Activity 3 How Big Is It?

Activity 4 Fraction War

Activity 5 What Comes First?

Activity 6 Square Fractions

Activity 7 Adding and Subtracting Fractions

Activity 8 Multiplying Fractions

Activity 9 Dividing Fractions

Chapter Summary


Chapter 7 Decimals, Real Numbers, and Proportional Reasoning

Activity 1 What's My Name?

Activity 2 Who's First?

Activity 3 Repeating Decimals

Activity 4 Race for the Flat

Activity 5 Empty the Board

Activity 6 Decimal Arrays

Activity 7 Decimal Multiplication

 Activity 8 Target Number Revisited

Activity 9 People Proportions

Activity 10 A Call to the Border

Activity 11 What is Percent?

Activity 12 What Does It Mean?

Activity 13 Flex-it

Chapter Summary


Chapter 8 Algebraic Reasoning and Representation

Activity 1 Regular Polygons in a Row

Activity 2 Patterns and Expressions

Activity 3 The Function Machine

Activity 4 What's My Function?

Activity 5 Exploring Linear Functions

Activity 6 Graphing Rectangles

Activity 7 Graphs and Stories

Chapter Summary


Chapter 9 Statistics: The Interpretation of Data

Activity 1 Graphing m&m's

Activity 2 Gaps and Clusters

Activity 3 Grouped Data

Activity 4 What's the Average?

 Activity 5 Finger-Snapping Time

Activity 6 The Weather Report

Activity 7 To Change or Not to Change

Activity 8 What's in the Bag?

Activity 9 Populations and Samples

Chapter Summary


Chapter 10 Probability

Activity 1 What Are the Chances?

Activity 2 The Spinner GameActivity 3 Numbers That Predict

Activity 4 Paper-Scissors-Rock

Activity 5 Simulate It

Activity 6 How Many Arrangements?

Activity 7 Theoretical Probability

Activity 8 It's in the Bag

Activity 9 Pascal's Probabilities

Activity 10 The Mystery Cube

Chapter Summary


Chapter 11 Geometric Figures

Activity 1 What's the Angle?

Activity 2 Triangle Properties- Angles

Activity 3 Inside or Outside?

Activity 4 Angles on Pattern Blocks

Activity 5 Sum of Interior/Exterior Angles

Activity 6 Name that Polygon

Activity 7 Mysterious Midpoints

Activity 8 Spatial Visualization

Activity 9 A View from the Top

Activity 10 Map Coloring

Chapter Summary


Chapter 12 Measurement: Length, Area, and Volume

Activity 1 Units of Measure

Activity 2 What's My Area?

Activity 3 Areas of Polygons

Activity 4 From Rectangles to Parallelograms

Activity 5 From Parallelograms to Triangles

Activity 6 From Parallelograms to Trapezoids

Activity 7 Pythagorean Puzzles

Activity 8 Right or Not?

Activity 9 Now You See It, Now You Don't

Activity 10 Surface Area

Activity 11 Volume of a Rectangular Solid

Activity 12 Pyramids and Cones

Chapter Summary


Chapter 13 Transformation, Symmetries, and Tilings

 Activity 1 Slides, Flips, and Turns

Activity 2 How Did You Do It?

Activity 3 Double Flips

Activity 4 Reflections

Activity 5 Translations

Activity 6 Rotations

Activity 7 Glide Reflections

 Activity 8 Transforgeo

Activity 9 Dilations

Activity 10 Cut It Out

Activity 11 Draw It

Activity 12 Tessellations

Chapter Summary


Chapter 14 Congruence, Constructions, and Similarity

Activity 1 Triangle Properties- Sides

Activity 2 To Be or Not to Be Congruent?

Activity 3 Paper Folding Construction

Activity 4 Pattern Block Similarity

Activity 5 Similar Triangles

Activity 6 Outdoor Geometry

Activity 7 Side Splitter Theorem

Chapter Summary




Product Details

Long, Calvin T.
Williamson, James C.
Detemple, Duane W.
Dolan, Dan
Cram101 Textbook Reviews
Millman, Richard
Muri, Mari
Long, Calvin T.
Millman, R.
Williamson, James
Teaching Methods & Materials - Mathematics
Study and teaching (elementary)
Mathematics -- Study and teaching (Elementary)
Edition Description:
Trade paper
Mathxl Tutorials on CD
Publication Date:
December 2007
Grade Level:
College/higher education:
10.3 x 8.2 x 1.6 in 2186 gr

Related Subjects

Education » Teaching » Math and Science
History and Social Science » World History » General

Mathematical Reasoning for Elementary Teachers (5TH 09 - Old Edition) Used Hardcover
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Product details 1120 pages Addison Wesley Longman - English 9780321460844 Reviews:
"Synopsis" by , Provides detailed, worked-out solutions to all exercises that are answered in the back of the student text.
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