Addison-Wesley / Prentice Hall

Mathematics

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Problem Solving Approach to Mathematics for Elementary School Teachers, A, 8/E
Rick Billstein, University of Montana
Shlomo Libeskind, University of Oregon
Johnny W. Lott, University of Mississippi

ISBN-10: 0321156803
ISBN-13: 9780321156808

Publisher: Addison-Wesley
Copyright: 2004
Format: Cloth; 912 pp
Status: Out of Print


This best-selling text emphasizes solid mathematics content, problem-solving skills, and analytical techniques. The eighth edition focuses on the National Council of Teachers of Mathematics (NCTM) Principles and Standards 2000. The text allows for a variety of approaches to teaching, encourages discussion and collaboration among students and with their instructors, allows for the integration of projects into the curriculum, and promotes discovery and active learning. Students using this text will receive solid preparation in mathematics, develop confidence in their math skills and benefit from teaching and learning techniques that really work.

  • NCTM Principles and Standards for School Mathematics fully integrated throughout the text.
  • Chapter One is devoted to problem-solving with an added emphasis on inductive versus deductive reasoning.
  • Problem Solving Strategies are integrated throughout the text and reinforce the strong problem solving theme introduced in Chapter One.
  • There is an increased focus on algebraic thinking throughout the whole text.
  • A Preliminary Problem begins each chapter to get students interested in the topics about to be discussed. These have all been updated in this edition.
  • Applications of Mathematics are integrated throughout the text.
  • Laboratory Activities are integrated throughout the book to provide hands-on learning exercises. A separate activities manual is also available.
  • Questions from the Classroom present questions posed by actual students in K-8 classrooms.
  • Student Pages are included to show how the mathematics is actually introduced to the K-8 student and are referenced throughout the text.
  • Problem Sets contain six different types of problems (1) on-going assessment, (2) communication, (3) open-ended, (4) cooperative learning, (5) technology, and (6) review. Communication, open-ended, and cooperative learning problem sections are included to conform with the major Standards' processes. A major focus of the revision was to make the exercise sets more even with regard to level.
  • Technology Corners include spreadsheets, both graphing and scientific calculators, Geometer's Sketchpad, and computer activities.
  • Now Try This appears throughout each chapter. This feature helps students become actively involved in their learning, develops problem-solving skills and stimulates discussion.
  • Appendix: Geometer's Sketchpad offers information on using this geometry manipulation software in the classroom and at home.
  • Updated supplements package now includes MathXL and MyMathLab.



1. An Introduction to Problem Solving.

Explorations with Patterns.

Mathematics and Problem Solving.

Algebraic Thinking.

*Logic: An Introduction.



2. Sets, Whole Numbers, and Functions.

Describing Sets.

Other Set Operations and Their Properties.

Addition and Subtraction of Whole-Numbers.

Multiplication and Division of Whole-Numbers.

Functions.



3. Numeration Systems and Whole Number Computation.

Numeration Systems.

Algorithms for Whole-Number Addition and Subtraction.

Algorithms for Whole-Number Multiplication and Division.

Mental Mathematics and Estimation for Whole-Number Operations.



4. Integers and Number Theory.

Integers and the Operations of Addition and Subtraction.

Multiplication and Division of Integers.

Divisibility.

Prime and Composite Numbers.

Greatest Common Divisor and Least Common Multiple.

*Clock and Modular Arithmetic.



5. Rational Numbers as Fractions.

The Set of Rational Numbers.

Addition and Subtraction of Rational Numbers.

Multiplication and Division of Rational Numbers.

Proportional Reasoning.



6. Decimals, Percents, and Real Numbers.

Introduction to Decimals.

Operations on Decimals.

Nonterminating Decimals.

Percents.

*Computing Interest.

Real Numbers.



7. Probability.

How Probabilities Are Determined.

Multistage Experiments with Tree Diagrams and Geometric Probabilities.

Using Simulations in Probability.

Odds, Conditional Probability, and Expected Value.

Using Permutations and Combinations in Probability.



8. Data Analysis/Statistics: An Introduction.

Statistical Graphs.

Measures of Central Tendency and Variation.

Abuses of Statistics.



9. Introductory Geometry.

Basic Notions.

Polygons.

More About Angles.

Geometry in Three Dimensions.

*Networks.



10. Constructions, Congruence, and Similarity.

Congruence Through Constructions.

Other Congruence Properties.

Other Constructions.

Similar Triangles and Similar Figures.

Trigonometry Rations via Similarity

Lines in a Cartesian Coordinate System.



11. Concepts of Measurement.

Linear Measure.

Areas of Polygons and Circles.

The Pythagorean Theorem.

Surface Areas.

Volume, Mass, and Temperature.



12. Motion Geometry and Tessellations.

Translations and Rotations.

Reflections and Glide Reflections.

Size Transformations.

Symmetries.

*Tessellations of the Plane.



Appendix I. Using a Spreadsheet.


Appendix II. Graphing Calculators.


Appendix III. Using a Geometry Drawing Utility.


Answers to Selected Problems.


Index.

Rick Billstein is a Professor of Mathematics at the University of Montana. He is currently working half time in the Mathematics Department teaching courses for future teachers and half time on the Show-Me Project, a NSF-funded project supporting dissemination and implementation of standards-based middle grades mathematics curricula. He has worked in mathematics teacher education at the University of Montana for 30 years and his current research is in the areas of curriculum development and mathematics teacher education. He has served on the Board of Directors of the Montana Council of Teachers of Mathematics and has served and chaired the National Council of Teachers of Mathematics (NCTM) Instructional Issues Advisory Committee. Dr. Billstein has co-authored 18 books including eight editions of A Problem Solving Approach to Mathematics for Elementary Teachers . He typically does about 25 regional and national presentations per year and has traveled to Thailand to work with the international schools there. He also presented at the Fourth International Conference on Mathematics Education in Chicago and served as an organizer and presenter for the ICME-9 conference in Tokyo.

Shlomo Libeskind is a professor in the mathematics department at the University of Oregon in Eugene, Oregon. He is responsible for the "pre-college" teaching major in the department and has continuously been teaching and advising preservice and inservice teachers. Dr. Libeskind has extensive writing experience (books, articles, and workshop materials) as well as experience in directing mathematics education projects. Libeskind is an active member of Oregon Mathematics Council (OMEC) and has been involved in reviewing materials for the state of Oregon's new standards for college admission.

Johnny W. Lott began his teaching career in the public schools of DeKalb County, Georgia, outside Atlanta. There he taught mathematics in grades 8-12. He also taught one year at the Westminster Schools, grades 9-12, and one year in the Pelican, Alaska, school, grades 6-12. In addition, he has taught part-time in grade schools in Montana and at Georgia State University and The University of Montana. Johnny has been co-author of several books and has written numerous articles and other essays in the "Arithmetic Teacher", "Teaching Children Mathematics", "the Mathematics Teacher", "School Science and Mathematics", "Student Math Notes", and "Mathematics Education Dialogues". He has been the Project Manager for the "Figure This!" publications and website developed by the National Council of Teachers of Mathematics (NCTM) and was project co-director of the State Systemic Initiative for Montana Mathematics and Science (SIMMS) Project. He has served on many NCTM committees and has been a member of its Board of Directors. In the Department of Mathematical Sciences at The University of Montana, Dr. Lott is a full professor and has served as department chair. His doctorate is in mathematics education from Georgia State University. Dr. Lott�s hobbies include quilting, reading, and writing short stories. In April 2002, Dr. Lott will become President of NCTM.

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For Math for Future Elementary Teachers


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