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Problem Solving Approach to Mathematics, A (Recover), 10/E
Rick Billstein, University of Montana
Shlomo Libeskind, University of Oregon
Johnny W. Lott, University of Montana

ISBN-10: 0321570545
ISBN-13:  9780321570543

Publisher:  Pearson
Copyright:  2010
Format:  Cloth; 1128 pp
Published:  01/09/2009
Status: Instock


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Description

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.


To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit http://www.pearsonhighered.com/teachingmath.

 

 


Features

Professional Development

  • Actual school book pages show how mathematics is explained to K—8 pupils. Many activities and exercises involve the student pages, allowing students to see what is expected in elementary schools.
  • Research Notes in the margin highlight current research in mathematics and mathematics education as it relates to the content.
  • Historical Notes add context and humanize the mathematics.
  • NCTM Principles and Standards and NCTM Focal Points are referenced and discussed throughout the text.
  • Questions from the Classroom present questions collected from actual K-8 students.

 

Active Learning

  • NEW! The e-Manipulatives CD allows students to investigate, explore, and practice new concepts. This resource is referenced throughout the book and comes included with every new copy of the text.
  • The Activity Manual is more integrated with the main text, including references to specific activities in the Annotated Instructor’s Edition.
  • Brain Teasers add variety to the problem solving in the book and may be assigned or used by the teacher to challenge students. Solutions are located in the Annotated Instructor’s Edition.
  • Laboratory Activities are integrated throughout the book to provide hands-on learning exercises. A separate activities book is also available as a supplement.
  • Now Try This activities help students to become actively involved in their learning, to facilitate the development and improvement of their critical thinking and problem-solving skills, and to stimulate both in-class and out-of-class discussion. These activities appear throughout each chapter.
  • Technology Corners include use of spreadsheets, both graphing and scientific calculators, The Geometer’s Sketchpad, and computer activities to help students become proficient with the use of commonly used classroom technology.

 

Pedagogical Tools

  • Definitions, properties, and theorems are set apart from the main text to allow for quick review.
  • Problem-Solving Strategies are set apart from the text for easy reference, and Problem Solving boxes encourage students put these strategies to work.
  • End-of-chapter materials include a Chapter Outline and Chapter Reviews to help students study and test themselves in preparation for an in-class exam.

 

Assessment

  • Problem Sets are now more logically organized into Assessments A, B, and Mathematical Connections.
    • Assessment A problems have answers in the text so that students can check their work.
    • Assessment B contains problems similar to those in Assessment A, but no answers are given in the student text.
    • Mathematical Connections is divided into the following categories of problems: Communication, Open-Ended, Cooperative Learning, Questions from the Classroom, and Review.
    • Sample questions from both the TIMMS and NAEP exams allow future teachers to examine the types of questions that students are being asked on national and international exams.


New To This Edition

New Features:

  • Two new chapters have been added in accordance with the recommendations from the NCTM Focal Points documentation. Chapter 4, Algebraic Thinking and Chapter 8, Proportional Reasoning, Percents, and Applications are further described below.
  • Problem Sets are now more logically organized into Assessments A, B, and Mathematical Connections.
    • Assessment A problems have answers in the text so that students can check their work.
    • Assessment B contains problems similar to those in Assessment A, but no answers are given in the student text.
    • Mathematical Connections is divided into the following categories of problems: Communication, Open-Ended, Cooperative Learning, Questions from the Classroom, and Review.
    • Sample questions from both the TIMMS and NAEP exams allow future teachers to examine the types of questions that students are being asked on national and international exams.
  • An Annotated Instructor’s Edition is available for the first time. This special edition of the text displays answers to the text exercises on the page where they occur and includes answers to the Preliminary Problems, Now Try This activities, Laboratory Activities, Technology Corners, Brain Teasers, and Questions from the Classroom.
  • The e-Manipulatives CD allows students to investigate, explore, and practice new concepts. This resource is referenced throughout the book and comes included with every new copy of the text.
  • The Activity Manual is more integrated with the book with references to specific activities in the Annotated Instructor’s Edition.

  • The Technology Manual compiles the appendices found in the previous edition of A Problem Solving Approach to Mathematics for Elementary School Teachers into a convenient supplement for those who integrate technology into their course. Chapters offer tutorials for using spreadsheets, graphing calculator and geometry drawing utility software in the course. The manual can be shrink wrapped with the text at no additional cost.

     

     

New Content:

  • Chapter 1: An Introduction to Problem Solving
    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 are other additions as is a new section on Fibonacci sequences. The final section on reasoning and logic is included for those who wish to purse these topics in the course.
  • Chapter 2: Numeration Systems and Sets
    This chapter has been reorganized and shortened. The development of numeration systems is now the first section of this chapter. This section was placed first because of the historical development of the systems. The chapter includes all of the more traditional set concepts later.
  • Chapter 3: Whole Numbers and Their Operations
    This chapter explores whole numbers and operations on whole numbers. Various algorithms are investigated and explained in detail. Mental mathematics and estimation with whole numbers are prominently featured.
  • Chapter 4: Algebraic Thinking
    In response to greater emphasis on learning and teaching algebra throughout the elementary school curriculum, a new chapter on algebraic thinking has been incorporated. Only whole numbers are used, but in each subsequent chapter, algebraic thinking is reinforced when integers, rational numbers, and finally real numbers are introduced. Algebraic thinking is further reinforced in the chapter on probability and statistics as well as in the geometry chapters.
  • Chapter 5: Integers and Number Theory
    This chapter deals with integers and operations on integers. New models for operations and algorithms on integers are introduced with explanations. Divisibility and prime numbers are discussed along with explanation on why the divisibility rules work. Greatest common divisors and least common multiples are introduced. An optional section on clock and modular arithmetic in included for those who would like to examine how a different number system works.
  • Chapter 6: Rational Numbers at Fractions
    New examples in this chapter emphasize algebraic skills by simplifying algebraic expressions, and solving equations and word problems. The concept of division is enhanced with more thorough explanations and examples. Functions are revisited with the domain of rational numbers.
  • Chapter 7: Decimals and Real Numbers
    This chapter has been shortened with the introduction of Chapter 8. Many more student pages have been added and a new section on Using Real Numbers in Equations is a feature of this reorganized chapter.
  • Chapter 8: Proportional Reasoning, Percents, and Applications
    Because proportional reasoning and percents are so important in the middle school, an entire chapter is now devoted to the subject. The chapter includes a discussion of how the relationship between two ratios is multiplicative instead of additive and why this is important. Work with percents has been expanded to include percent bars and estimations involving percents. An optional section on computing interest is included to show an application of percents.
  • Chapter 9: Probability
    From the Preliminary Problem involving the artwork of Francois Morellet, there is a signal given that probability is used in the real world and in the world of students. Student pages are added to show how the concepts appear in the grades; more drawings, cartoons, and diagrams illustrate concepts.
  • Chapter 10: Data Analysis and Statistics: An Introduction
    An entire section, Section 10-4, is devoted to Designing Experiments and Collecting Data based on this GAISE Statistics Framework. Many new problems have been added, and algebraic notions are used in the development of the chapter.
  • Chapter 11: Introductory Geometry
    The various concepts are more thoroughly explained. More detailed treatment of interior and exterior angles in convex polygons is presented. Algebraic thinking is predominantly present throughout the chapter.
  • Chapter 12: Constructions, Congruence, and Similarity
    Discussion on congruence and non-congruence of triangles has been expanded to include the ambiguous SSA case, and congruence of quadrilaterals has been added. The discussion of systems of linear equations has been expanded to include an algebraic explanation of when a system of two equations with two unknowns has no solution and when it has infinitely many solutions.
  • Chapter 13: Concepts of Measurement
    This chapter includes work with both the English system and the metric system, along with conversion among and between systems. Linear, area, volume, mass and temperature measurements are included. Formulas for computing measurements are developed to show where they came from. The Pythagorean Theorem and Distance formulas are developed along with a new section on the equation of a circle.
  • Chapter 14: Motion Geometry and Tessellations
    Though most of the features of the ninth edition remain in the new edition of this chapter, there are many more drawings and more ties to student pages in this chapter than in the past. The authors have tried to build on what prospective teachers need to know, and that is more than their future students may need to know. This chapter gives a look at the fun and interest that can be seen in motion geometry.


Table of Contents

1. An Introduction to Problem Solving

1-1 Mathematics and Problem Solving

1-2 Explorations with Patterns

1-3 Reasoning and Logic: An Introduction

 

2. Numeration Systems and Sets

2-1 Numeration Systems

2-2 Describing Sets

2-3 Other Set Operations and Their Properties

 

3. Whole Numbers and Their Operations

3-1 Addition and Subtraction of Whole Numbers

3-2 Algorithms for Whole-Number Addition and Subtraction

3-3 Multiplication and Division of Whole Numbers

3-4 Algorithms for Whole-Number Multiplication and Division

3-5 Mental Mathematics and Estimation for Whole-Number Operations

 

4. Algebraic Thinking

4-1 Variables

4-2 Equations

4-3 Functions

 

5. Integers and Number Theory

5-1 Integers and the Operations of Addition and Subtraction

5-2 Multiplication and Division of Integers

5-3 Divisibility

5-4 Prime and Composite Numbers

5-5 Greatest Common Divisor and Least Common Multiple

5-6 *Clock and Modular Arithmetic

 

6. Rational Numbers as Fractions

6-1 The Set of Rational Numbers

6-2 Addition and Subtraction of Rational Numbers

6-3 Multiplication and Division of Rational Numbers

 

7. Decimals and Real Numbers

7-1 Introduction to Decimals

7-2 Operations on Decimals

7-3 Nonterminating Decimals

7-4 Real Numbers

7-5 Using Real Numbers in Equations

 

8. Proportional Reasoning, Percents and Applications

8-1 Ratios, Proportions and Proportional Reasoning

8-2 Percents

8-3 Computing Interest

 

9. Probability

9-1 How Probabilities are Determined

9-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities

9-3 Using Simulations in Probability

9-4 Odds, Conditional Probability, and Expected Value

9-5 Using Permutations and Combinations in Probability

 

10. Data Analysis/Statistics: An Introduction

10-1 Displaying Data: Part I

10-2 Displaying Data: Part II

10-3 Measures of Central Tendency and Variation

10-4 Abuses of Statistics

10-5 Designing Experiments/Collecting Data (found online on the catalog page under “Take a Closer Look”)

 

11. Introductory Geometry

11-1 Basic Notions

11-2 Polygons

11-3 More about Angles

11-4 Geometry in Three Dimensions

11-5 *Networks

 

12. Constructions, Congruence, and Similarity

12-1 Congruence through Constructions

12-2 Other Congruence Properties

12-3 Other Constructions

12-4 Similar Triangles and Similar Figures

12-5 Lines and Linear Equations in a Cartesian Coordinate System

12-6 *Trigonometry Ratios via Similarity  (found online on the catalog page under “Take a Closer Look”)

 

13. Concepts of Measurement

13-1 Linear Measure

13-2 Areas of Polygons and Circles

13-3 The Pythagorean Theorem, Distance Formula, and Equation of a Circle

13-4 Surface Areas

13-5 Volume, Mass, and Temperature

 

14. Motion Geometry and Tessellations

14-1 Translations and Rotations

14-2 Reflections and Glide Reflections

14-3 Size Transformations

14-4 Symmetries

14-5 Tessellations of the Plane

 

The Appendices are now full chapters to help students with specific technology tools: Using a Spreadsheet, Graphing Calculators, and Using a Geometry Drawing Utility. These chapters are available in the Technology Manual, which can be shrink-wrapped at no additional cost with the new textbook. See ‘Packages’ tab for ordering information. 

 

Answers to All/Selected Exercises

Index

Photo Acknowledgments

 

*Optional Sections


Previous Edition(s)

  • Problem Solving Approach to Mathematics, A (Recover), 9/E
    Billstein, Libeskind & Lott
    ©2007  |  Pearson  |  Cloth; 1056 pp  |  Out of Print
    ISBN-10: 0321375416  |  ISBN-13: 9780321375414
    Brief Description  |  More Info



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Author Bios

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.

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