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Mathematical Reasoning for Elementary Teachers (5TH 09 - Old Edition)by Calvin T. Long
Synopses & ReviewsPlease note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the 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 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 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 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 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 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 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 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 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 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 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 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 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
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