Problem Solving Approach to Mathematics for Elementary School Teachers / Edition 13

by Rick Billstein

Overview

This best-selling text emphasizes solid mathematics content, problem-solving skills, and analytical techniques. The seventh 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. For mathematics teachers.

Product Details

ISBN-13:	2900135183884
Publication date:	01/02/2019
Pages:	1056
Product dimensions:	6.50(w) x 1.50(h) x 9.50(d)

About the Author

Rick Billstein is a Professor of Mathematics at the University of Montana. He has worked in mathematics teacher education at this university for over 40 years and his current research is in the areas of curriculum development and mathematics teacher education. He teaches courses for future teachers in the Mathematics Department. He served as the site director for the Show-Me Project, an NSF-funded project supporting the dissemination and implementation of standards-based middle grades mathematics curricula. He worked on the NSF grant Tinker Plots to develop new data analysis software and he serves on the Advisory Boards for several other national projects. From 1992-1997, he directed the NSF-funded Six Through Eight Mathematics (STEM) middle school mathematics curriculum project and is now directing the Middle Grades MATH Thematics Phase II Project. Dr. Billstein has published articles in over 20 different journals and has co-authored over 40 books, including 10 editions of A Problem Solving Approach to Mathematics for Elementary Teachers. He typically does about 25 regional and national presentations per year and has worked in mathematics education at the international level. He presently serves on the Editorial Board of NCTM’s Mathematics Teaching in the Middle School. Dr. Billstein was recently awarded the George M. Dennison Presidential Faculty Award for Distinguished Accomplishment at the University of Montana.

Dr. Barbara Boschmans teaches in the Department of Mathematics and Statistics at Northern Arizona University. She received her BsEd (1995), MAT (1997), and EdD (2003) in Mathematics Education from Northern Arizona University. She has taught at Arizona State University (AZ), Plymouth State University (NH), and Northern Arizona University (AZ). Dr. Boschmans has taught a variety of mathematics and mathematics education courses. She has been a frequent speaker at local, state, national, and international conferences. She has been a board member of the New Hampshire Teachers of Mathematics and the Arizona Association of Teachers of Mathematics. Dr. Boschmans is interested in bringing a joy and appreciation of mathematics to preservice and inservice elementary teachers, and changing non-STEM students’ fixed mindset to a growth mindset.

Shlomo Libeskind is a professor in the mathematics department at the University of Oregon in Eugene, Oregon, and has been responsible there for the mathematics teaching major since 1986. In addition to teaching and advising pre-service and in-service teachers, Dr. Libeskind has extensive writing experience (books, articles, and workshop materials) as well as in directing mathematics education projects. In teaching and in writing, Dr. Libeskind uses a heuristic approach to problem solving and proof; in this approach the reasonableness of each step in a solution or proof is emphasized along with a discussion on why one direction might be more promising than another. As part of his focus on the improvement of the teaching of mathematics, Dr. Libeskind is also involved at many levels locally, nationally and worldwide in the evaluation of mathematics teacher preparation programs. In his home state he is actively involved in schools and councils, as well as in reviewing materials for the state standards for college admission. Most recently (spring 2008) he visited teacher colleges in Israel as a Fulbright Fellow. During this visit he conducted observations and critiques of the preparation of mathematics teachers at several colleges in Northern Israel. Dr. Libeskind received his Bachelor’s and Master’s Degrees in Mathematics at the Technion (Israel Institute of Technology) and his PhD in Mathematics at the University of Wisconsin, Madison.

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. Johnny is the 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 was 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, has been a member of its Board of Directors, and was its president from April 2002-April 2004. Dr. Lott is Professor Emeritus from the Department of Mathematical Sciences at The University of Montana, having been a full professor. He is currently the Director of the Center for Excellence in Teaching and Learning, Professor of Mathematics, and Professor of Education at the University of Mississippi. Additionally, he is on the Steering Committee of the Park City Mathematics Institute, works with the International Seminar, the Designing and Delivering Professional Development Seminar, and is editor for its high school publications. His doctorate is in mathematics education from Georgia State University.

Table of Contents

(Each chapter begins with a "Preliminary Problem" and concludes with a "Hint for Solution to the Preliminary Problem," "Questions from the Classroom," "Chapter Outline," "Chapter Review," and a "Selected Biography.")

(*indicates optional section.)
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. 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 and Expected Value.
Methods of Counting.

8. 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.
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. Logo Turtle Graphics.
Appendix II. Graphing Calculators.
Appendix III. Using a Geometry Drawing Utility.
Appendix IV. Using a Spreadsheet.
Answers to Selected Problems.
Index.