Addison-Wesley / Prentice Hall

Mathematics

Browse available resources for Mathematics:



Problem Solving Approach to Mathematics for Elementary School Teachers, A, 9/E
Rick Billstein, University of Montana
Shlomo Libeskind, University of Oregon
Johnny W. Lott, University of Mississippi

ISBN-10: 0321331796
ISBN-13: 9780321331793

Publisher: Addison-Wesley
Copyright: 2007
Format: Cloth; 1056 pp
Published: 01/19/2006

Suggested retail price: $134.67
Buy from myPearsonStore



This best-selling text continues as a comprehensive, skills-based resource for future teachers. In this edition, students will benefit from additional emphasis on active and collaborative learning. Revised and updated content will better prepare your students for the day when they will be teachers with students of their own.

  • NCTM Principles and Standards for School Mathematics are fully integrated throughout the text.
  • Problem-solving strategies are integrated throughout the text and reinforce the strong problem-solving theme introduced in Chapter One.
  • A Preliminary Problem begins each chapter to get students interested in the topics to be discussed.
  • 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.
  • Technology Corners include spreadsheets, both graphing and scientific calculators, Geometer's Sketchpad, and computer activities.
  • Now Try This problems appear throughout each chapter. This feature helps students become actively involved in their learning, develop problem-solving skills, and stimulate discussion.

 

  • Algebraic Reasoning: This revision includes an increase in the coverage of algebraic reasoning which is woven throughout the text.
  • Data Analysis and Statistical Thinking: This material has been expanded to include more content on populations, sampling, and surveys.
  • Research Notes: Margin notes have been added to highlight current research in mathematics and mathematics education as it relates to the content.
  • Problem Sets: New exercises have been added from the Trends in International Mathematics and Science Study (TIMSS) and the National Assessment of Educational Progress (NAEP). In addition, 20% of the existing exercises have been revised. We have retained the six different types of problems: (1) ongoing assessment, (2) communication, (3) open-ended, (4) cooperative learning, (5) technology, and (6) review.

  • Content Changes are as follows:

    • Chapter 1: The reorganization of this chapter puts mathematics and problem solving first, followed by an expanded section on exploration with patterns. New problems and new student pages have been added as well as a new section on Fibonacci sequences. In the algebra section, there is increased coverage of solving equations using pan balances.
    • Chapter 2: New problems and student pages have been included, as well as new models to better explain computations involving whole numbers. Work with algebraic reasoning has been expanded.
    • Chapter 3: Many examples, problems in the Ongoing Assessments, and student pages have been added. The improved exposition includes much more on algebraic thinking, with examples and problems on algebraic computations analogous to their respective arithmetic computations. In addition, greater emphasis has been placed on the division algorithm, both in the text and in Ongoing Assessments.
    • Chapter 4: This chapter contains many new problems and a greater emphasis on algebraic thinking, including functions and absolute value functions.
    • Chapter 5: This chapter has a new discussion of fractions relating parts to the whole. Models for computations involving fractions are another addition, and the section on proportional reasoning has been expanded.
    • Chapter 6: In this chapter, an increased emphasis on the use of number lines to order decimals incorporates both fractions and decimals, and further ties them together. The reordered sections introduce real numbers before applications of decimals as percents. Each section contains many new problems and references, and geometric sequences are incorporated as a tool used to approach repeating decimals. Fraction bars or percent bars help in thinking about percentage problems.
    • Chapter 8: This chapter contains references to the American Statistical Association’s latest draft document on recommended data analysis and probability to be studied in grades K-12. An examination of categorical and numerical data and different treatments of these data is included, with graphical material reorganized to follow these different treatments. Following the ASA’s recommendations, the language is updated, and the fact that mode is not really a measure of central tendency is explained. Continuous and discrete data are also distinguished. Mean absolute deviation is introduced as an alternative to standard deviation, and the need to report mean with standard deviation or mean absolute deviation is acknowledged. Additional work on abuses of statistics, more examples, and more problems are also present in this chapter.
    • Chapter 9: Greater emphasis has been placed on algebraic thinking, and the Questions from the Classroom feature is expanded.
    • Chapter 10: This chapter contains more challenging problems, more emphasis on tying slope and similar triangles together, and the addition of applications of coordinate geometry.
    • Chapter 11: More challenging problems are now presented in this chapter. The topic of measurement is slightly reorganized with more alternative solutions in converting measures given.
    • Chapter 12: This chapter places greater emphasis on transformations with coordinate geometry.

Chapter 1    An Introduction to Problem Solving

                        1-1 Mathematics and Problem Solving

                        1-2 Explorations with Patterns

                        1-3 Algebraic Thinking

                        1-4 Logic: An Introduction

 

Chapter 2    Sets, Whole Numbers, and Functions

                        2-1 Describing Sets

                        2-2 Other Set Operations and Their Properties

                        2-3 Addition and Subtraction of Whole Numbers

                        2-4 Multiplication and Division of Whole Numbers

                        2-5 Functions

 

Chapter 3    Numeration Systems and Whole-Number Computation

                        3-1 Numeration Systems

                        3-2 Algorithms for Whole-Number Addition and Subtraction

                        3-3 Algorithms for Whole-Number Multiplication and Division

                        3-4 Mental Mathematics and Estimation for Whole-Number Operations

 

Chapter 4    Integers and Number Theory

                        4-1 Integers and the Operations of Addition and Subtraction

                        4-2 Multiplication and Division of Integers

                        4-3 Divisibility

                        4-4 Prime and Composite Numbers

                        4-5 Greatest Common Divisor and Least Common Multiple

                        4-6 Clock and Modular Arithmetic

 

Chapter 5   Rational Numbers as Fractions

                        5-1 The Set of Rational Numbers

                        5-2 Addition and Subtraction of Rational Numbers

                        5-3 Multiplication and Division of Rational Numbers

                        5-4 Proportional Reasoning

   

Chapter 6    Decimals, Percents, and Real Numbers

                        6-1 Introduction to Decimals

                        6-2 Operations on Decimals

                        6-3 Nonterminating Decimals

                        6-4 Real Numbers

                        6-5 Percents

                        6-6 Computing Interest

 

Chapter 7    Probability

                        7-1 How Probabilities Are Determined

                        7-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities

                        7-3 Using Simulations in Probability

                        7-4 Odds, Conditional Probability, and Expected Value

                        7-5 Using Permutations and Combinations in Probability

 

Chapter 8    Data Analysis/ Statistics: An Introduction

                        8-1 Statistical Graphs of Categorical and Numerical Data

                        8-2 Measures of Central Tendency and Variation

                        8-3 Abuses of Statistics

 

Chapter 9    Introductory Geometry

                        9-1 Basic Notions

                        9-2 Polygons

                        9-3 More About Angles

                        9-4 Geometry in Three Dimensions

                        9-5 Networks

           

Chapter 10  Constructions, Congruence, and Similarity

                        10-1 Congruence Through Constructions

                        10-2 Other Congruence Properties

                        10-3 Other Constructions

                        10-4 Similar Triangles and Similar Figures

                        10-5 Trigonometry Ratios via Similarity

                        10-6 Lines in a Cartesian Coordinate System

 

Chapter 11    Concepts of Measurement

                        11-1 Linear Measure

                        11-2 Areas of Polygons and Circles

                        11-3 The Pythagorean Theorem and the Distance Formula

                        11-4 Surface Areas

                        11-5 Volume, Mass & Temperature

           

Chapter 12  Motion Geometry and Tessellations

                        12-1 Translations and Rotations

                        12-2 Reflections and Glide Reflections

                        12-3 Size Transformations

                        12-4 Symmetries

                        12-5 Tesselations of the Plane

 

 

Appendix I: Using a Spreadsheet

Appendix II: Graphing Calculators

Appendix III: Using a Geometry Drawing Utility

Rick Billstein is a Professor of Mathematics at the University of Montana. He has worked in mathematics teacher education at this university for 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 and also is 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 an NSF grant called 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 co-authored 24 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 has also presented at the International Conferences on Mathematics Education (ICME).

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 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 in grade schools in Montana while at 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, has been a member of its Board of Directors, and was its president from April 2002-April 2004. In the Department of Mathematical Sciences at The University of Montana, Dr. Lott was a full professor and served as department chair. He is currently the Director of the Center for Teaching Excellence at the University.  His doctorate is in mathematics education from Georgia State University.

View a Sample Chapter PDF:

For Math for Future Elementary Teachers


Give your students a choice! PearsonChoices products are designed to give your students more value and flexibility by letting them choose from a variety of text and media formats to best match their learning style and their budget.

Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students, see the Packages tab.

Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students, browse our available packages below, or contact your Pearson Higher Education representative to create your own package.