A Problem Solving Approach to Mathematics for Elementary School Teachers

by Billstein, Rick; Libeskind, Shlomo; Lott, Johnny W.

• ISBN13: 9780321570550
• ISBN10: 0321570553
• Additional ISBN(s): 9780135183885, 9780321331793
• Edition: 10th
• Format: Hardcover
• Copyright: 2009-01-12
• Publisher: Pearson
• More Book Details

Summary

The new edition of this best-selling text includes a new focus on active and collaborative learning, while maintaining its emphasis on developing skills and concepts. With a wealth of pedagogical tools, as well as relevant discussions of standard curricula and assessments, this book will be a valuable textbook and reference for future teachers. With this revision, two new chapters are included to address the needs of future middle school teachers, in accordance to the NCTM Focal Points document.

Author Biography

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 MATHThematics Phase II Project. Dr. Billstein has published articles in over 20 different journals, and has co-authored over 40 books, including ten 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.

 

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

An Introduction to Problem Solving

Mathematics and Problem Solving

Explorations with Patterns

Reasoning and Logic: An Introduction

Numeration Systems and Sets

Numeration Systems

Describing Sets

Other Set Operations and Their Properties

Whole Numbers and Their Operations

Addition and Subtraction of Whole Numbers

Algorithms for Whole-Number Addition and Subtraction

Multiplication and Division of Whole Numbers

Algorithms for Whole-Number Multiplication and Division

Mental Mathematics and Estimation for Whole-Number Operations

Algebraic Thinking

Variables

Equations

Functions

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

Rational Numbers as Fractions

The Set of Rational Numbers

Addition and Subtraction of Rational Numbers

Multiplication and Division of Rational Numbers

Decimals and Real Numbers

Introduction to Decimals

Operations on Decimals

Nonterminating Decimals

Real Numbers

Using Real Numbers in Equations

Proportional Reasoning, Percents and Applications

Ratios, Proportions and Proportional Reasoning

Percents

Computing Interest

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

Data Analysis/Statistics: An Introduction

Displaying Data: Part I

Displaying Data: Part II

Measures of Central Tendency and Variation

Designing Experiments/Collecting Data

Abuses of Statistics

Introductory Geometry

Basic Notions

Polygons

More about Angles

Geometry in Three Dimensions

Networks

Constructions, Congruence, and Sim

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