More than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts-it also provides an invaluable reference to future teachers by including professional development features and discussions of today's standards.
The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments. The Annotated Instructor's Edition offers new Integrating Mathematics and Pedagogy (IMAP) video annotations, in addition to activity manual and e-manipulative CD annotations, to make it easier to incorporate active learning into your course. MyMathLab® is available to offer auto-graded exercises, course management, and classroom resources for future teachers.
To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit www.pearsonhighered.com/teachingmath
Active learning helps future teachers develop their understanding of key skills and concepts, and it helps them prepare for their future classrooms.
- A Preliminary Problem encourages active learning from the start by opening every chapter with a thought-provoking question that sets the tone and prepares students for the material ahead.
- Now Try This examples help students become actively involved in their learning. These alternate examples facilitate the development of critical thinking and problem-solving skills, and stimulate class discussion. Answers are in both the Annotated Instructor's Edition and student text.
- E-Manipulatives accompany the text, and are available on both the CD-ROM bound into the back of each text, and in MyMathLab.
- 21 Flash-based manipulatives allow students to investigate, explore, and practice new concepts and solve specific problems. These build a conceptual understanding of key ideas.
- The e-manipulatives icon appears in the margin of the text, so students know when to reference them.
- NEW! MyMathLab® includes a new question type that relates to the e-manipulatives, making them easier to assign.
- Updated! The Activity Manual has been redesigned for this edition, streamlining the contents and including a new pouch of perforated, printed color manipulatives.
- Activity Manual annotations in the Annotated Instructor's Edition clarify when specific activities can be used for each lesson, making it easier to teach a more hands-on course.
- This manual is available as a valuepack option with the text.Ask your Pearson representative for details.
- Brain Teasers provide a more challenging avenue for problem solving. Solutions are in both the Annotated Instructor's Edition and student edition.
Extensive support and practice opportunities help students build their problem-solving skills and master the concepts.
- Updated, streamlined focus on content keeps students concentrating on what's important when learning each new concept.
- Problem-Solving Strategies are highlighted in italics, and Problem Solving Boxes help students put these strategies to work.
- NEW! Chapter Summaries are organized in a student-friendly chart format, for easy exam preparation. These summaries also provide specific pages references for additional help on individual concepts.
- Extensive Problem Sets are organized into three categories for maximum instructor flexibility when assigning homework.
- Assessment A has problems with answers in the text, so that students can check their work.
- Assessment B contains parallel problems to those in Assessment A, but answers are not given in the student text.
- Mathematical Connections problems include the following categories: Communication, Open-Ended, Cooperative Learning, Questions from the Classroom, GSP/GeoGebra (where appropriate), Trends in Mathematics and Science Study (TIMSS), National Assessment of Educational Progress (NAEP), and Review.
- Chapter Review questions allow students to test themselves when preparing for an exam.
Professional Development: the authors help students to stay motivated by showing the relevance of each topic to future teachers, and by including discussions of modern classroom standards.
- Updated, relevant discussions from theCommon Core State Standards (CCSS), and Curriculum Focal Points are incorporated throughout the text to provide a context for the material and to supplement the discussions of the Principles and Standards of School Mathematics (PSSM).
- NEW! Integrating Mathematics and Pedagogy (IMAP) videos, now available in MyMathLab, provide an opportunity for valuable classroom discussion regarding the knowledge of student understanding needed to teach mathematical concepts.
- NEW! IMAP annotations in the Annotated Instructor's Edition make it easier for instructors to integrate these videos into their course.
- NEW! A new MyMathLab exercise type asks students to watch a video and answer a related question.
- NEW! A guide for instructors in MyMathLab helps integrate these video clips into your course. The guide contains how & why you might want to integrate the videos, along with some discussion questions.
- Questions from the Classroom present questions as they might be posed by K-8 students. More of these questions have been added to the Eleventh Edition in the Mathematical Connections exercise sets.
- School Book Pages are included to show how the mathematics is introduced to the K-8 pupil. Referenced throughout the text, an icon shows where discussion is related to an upcoming School Book Page. Students are asked to complete many of the activities on the student pages so they can see what is expected in elementary school.
- NEW! In addition to the online Geometer's Sketchpad module, an online GeoGebra module is now available, providing introduction to GeoGebra along with labs to work on. References to the online module problems and lab activities are included in the Mathematical Connections section of the assessments under the heading GSP/GeoGebra.
- Historical Notes add context and humanize the mathematics.
New to this Edition
Updated, streamlined focus on content keeps students concentrating on what's important when learning each new concept. Updated, relevant discussions from theCommon Core State Standards (CCSS), and Curriculum Focal Points are incorporated throughout the text to provide a context for the material and to supplement the discussions of the Principles and Standards of School Mathematics (PSSM). Integrating Mathematics and Pedagogy (IMAP) videos, now available in MyMathLab, provide an opportunity for valuable classroom discussion regarding the knowledge of student understanding needed to teach mathematical concepts.
Chapter Summaries are organized in a student-friendly chart format, for easy exam preparation. These summaries also provide specific page references for additional help on individual concepts. The Activity Manual has been redesigned for this edition, streamlining the contents and including a new pouch of perforated, printed color manipulatives.
- IMAP annotations in the Annotated Instructor's Edition make it easier for instructors to integrate these videos into their course.
- A new MyMathLab exercise type asks students to watch a video and answer a related question.
- A guide for instructors in MyMathLab helps integrate these video clips into your course. The guide contains how & why you might want to integrate the videos, along with some discussion questions.
Greater emphasis on algebra is found in the early chapters, which build upon previous knowledge, and in Chapter 8 (Real Numbers and Algebraic Thinking) which offers a more intensive focus. Algebraic thinking is still at the forefront of mathematics in the early grades and must be in the thinking of prospective teachers. Several chapters are reorganized to better reflect today's courses.
- Activity Manual annotations in the Annotated Instructor's Edition clarify when specific activities can be used for each lesson, making it is easier to teach a more hands-on course.
- This manual is available as a valuepack option with the text. Ask your Pearson representative for details.
Geometry chapters offer more technology support to develop the students' understanding and keep them engaged.
- Integers and number theory are separated into two different chapters, based on user feedback, and now appear as Chapter 4 (Number Theory), and Chapter 5 (Integers).
- Because proportional reasoning is so closely connected to irrational numbers, these topics are the basis of Chapter 6 (Rational Numbers and Proportional Reasoning).
- Additional technology problems appear in the Mathematical Connections section, using Geometer's Sketchpad and GeoGebra.
- An online GeoGebra module is available, in addition to the online module for Geometer's Sketchpad. References to the online module problems and lab activities are included in the Mathematical Connections section of the assessments under the heading GSP/GeoGebra.
- Chapter 1 (An Introduction to Problem Solving): This chapter has been reorganized and shortened to make it more student-friendly. Much of the detail work on series has been moved to later chapters, enabling students to learn problem-solving techniques with less algebraic manipulation at this stage.
- Chapter 2 (Numeration Systems and Sets): This chapter includes a historical development of numeration systems to explore how various cultures handled concepts and computations. Different number bases are used to help students understand the base-ten system and to address issues students have when learning the Hindu-Arabic system. Set theory and set operations with properties are introduced as a basis for learning whole-number concepts.
- Chapter 3 (Whole Numbers and Their Operations): This chapter models addition and subtraction of whole numbers. It emphasizes the missing-addend model, the definition of subtraction in terms of addition, and discusses various algorithms for addition and subtraction including algorithms in different bases. Models for multiplication and division of whole numbers, properties of these operations with emphasis on the distributive property of multiplication over addition, and a variety of algorithms follow. Mental mathematics and estimation with whole numbers feature prominently.
- Chapter 4 (Number Theory): In the new edition, a separate chapter on number theory does not depend on integers, which are introduced in Chapter 5 (Integers). Concepts of divisibility with divisibility tests are discovered. Prime numbers, prime factorization, greatest common divisor and least common multiple, as well as Euclidean Algorithm, are explored with many new problems added. A module on Clock Arithmetic is available online. (Online modules are available at www.pearsonhighered.com/mathstatsresources).
- Chapter 5 (Integers): Significantly streamlined for this revision, this chapter concentrates only on integers, their operations, and properties.
- Chapter 6 (Rational Numbers and Proportional Reasoning): This chapter has been revised to follow many recommendations in the Common Core State Standards. Videos showing elementary students learning fraction concepts are now included so that future teachers can observe how students absorb what is taught and how they work with those concepts. Proportional reasoning, one of the most important concepts taught in middle school mathematics, is covered in great depth in its natural setting.
- Chapter 7 (Decimals: Rational Numbers and Percent): This chapter has been reorganized to focus on decimal representation of rational numbers. Discussion on percent includes the computing of simple and compound interest, as well as estimation involving percents.
- Chapter 8 (Real Numbers and Algebraic Thinking): With an introduction to real numbers in the opening sections, the chapter combines knowledge of real numbers with algebraic skills to provide a review of algebra needed to teach in K-8. This includes work in the coordinate plane and with spreadsheets. A module on Using Real Numbers in Equations is available online. (Online modules are available at www.pearsonhighered.com/mathstatsresources).
- Chapter 9 (Probability): Material has been reorganized, with many new problems and student pages added. Common Core Standards have been addressed with content that compliments these standards. The use of permutations and combinations in probability is included in this chapter.
- Chapter 10 (Data Analysis/Statistics: An Introduction): Chapter 10 opens with Designing Experiments/Collecting Data, a section based on Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A preK-12 Curriculum Framework by the American Statistical Association (2005). Aligned with the Common Core Standards, this section focuses on designing studies and surveys. In the following sections, data, graphs, examples, and assessment problems have been updated and new material added.
- Chapter 11 (Introductory Geometry): This chapter has been reorganized so that students may explore some of the ramifications of different definitions in mathematics used in schools. Linear measure is introduced in this chapter to emphasize its importance in the curriculum. Symmetries are now introduced as an early concept that could be used to form geometrical definitions. The Networks module is now offered online. (Online modules are available at www.pearsonhighered.com/mathstatsresources).
- Chapter 12 (Congruence and Similarity with Constructions): The congruence and constructions sections have been expanded to allow more exploration of circles and quadrilaterals. The concept of similarity is used to reintroduce slope of a line and its properties. Many new problems have been added. A module on Trigonometric Rations via Similarity is available online. (Online modules are available at www.pearsonhighered.com/mathstatsresources).
- Chapter 13 (Congruence and Similarity with Transformations): To align with the prominence on motion geometry in the Common Core Standards, this chapter appears earlier among the geometry sections. It focuses on connections among transformations and dilations in congruence and similarity.
- Chapter 14 (Area, Pythagorean Theorem, and Volume): Chapter 14 continues a reorganization of the geometry chapters. Geometry in three dimensions is included with the topics of area, the Pythagorean theorem, and volume. Many topics have been shifted and new material added: for example, the subsection on Comparing Measurements of Similar Figures. Assessment sets and examples have been updated.
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. Number Theory
4-2 Prime and Composite Numbers
4-3 Greatest Common Divisor and Least Common Multiple
Online Module: Clock & Modular Arithmetic
5-1 Integers and the Operations of Addition and Subtraction
5-2 Multiplication and Division of Integers
6. Rational Numbers and Proportional Reasoning
6-1 The Set of Rational Numbers
6-2 Addition, Subtraction, and Estimation with Rational Numbers
6-3 Multiplication and Division of Rational Numbers
6-4 Ratios, Proportions, and Proportional Reasoning
7. Decimals: Rational Numbers and Percent
7-1 Introduction to Decimals
7-2 Operations on Decimals
7-3 Nonterminating Decimals
7-4 Percents and Interest
8. Real Numbers and Algebraic Thinking
8-1 Real Numbers
8-5 Equations in a Cartesian Coordinate System
Online Module: Using Real Numbers in Equations
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 Designing Experiments/Collecting Data
10-2 Displaying Data: Part I
10-3 Displaying Data: Part II
10-4 Measures of Central Tendency and Variation
10-5 Abuses of Statistics
11. Introductory Geometry
11-1 Basic Notions
11-2 Linear Measure
11-3 Curves, Polygons, and Symmetry
11-4 More About Angles
Online Module: Networks
12. Congruence and Similarity with Constructions
12-1 Congruence through Constructions
12-2 Other Congruence Properties
12-3 Other Constructions
12-4 Similar Triangles and Similar Figures
Online Module: Trigonometry Ratios via Similarity
13. Congruence and Similarity with Transformations
13-1 Translations and Rotations
13-2 Reflections and Glide Reflections
13-4 Tessellations of the Plane
14. Area, Pythagorean Theorem, and Volume
14-1 Areas of Polygons and Circles
14-2 The Pythagorean Theorem, Distance Formula, and Equation of a Circle
14-3 Geometry in Three Dimensions
14-4 Surface Areas
14-5 Volume, Mass, and Temperature
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 ofA 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.