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Problem Solving Approach to Mathematics, A (Recover)

by ; ;
Edition:
10th
ISBN13:

9780321570543

ISBN10:
0321570545
Format:
Hardcover
Pub. Date:
1/9/2009
Publisher(s):
Pearson

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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
Table of Contents provided by Publisher. All Rights Reserved.

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