A Problem Solving Approach to Mathematics for Elementary and Middle School Teachers, 14th edition

Published by Pearson (May 6, 2025) © 2026
  • Rick Billstein
  • Barbara Boschmans
  • Shlomo Libeskind
  • Johnny Lott
  • Brian Beaudrie

Title overview

For courses in Math for Future Elementary Teachers.

Promote discovery and active learning

A Problem Solving Approach to Mathematics for Elementary and Middle School Teachers prepares future educators with a concept-rich, skill-based approach. It aims not only to help them learn the math, but to contextualize it within the elementary and middle school classrooms. 

The 14th Edition has been revised to prepare students more effectively for their own classrooms; material is reorganized throughout to better reflect the topics that students will likely be teaching. Expanded and updated content is informed by recent Standards for Mathematical practice. A new “Illustrative Mathematics K-8 Student Tasks” feature shows real examples of what is expected of K-8 students. Chapter-opening problems are revised throughout for enhanced relevance, exercise sets are updated and reorganized in every chapter, and more.

Hallmark features of this title

  • Connecting Mathematics to the Classroom exercises require interpretation and analysis of the thinking of typical K-8 students.
  • Now Try This exercises follow key examples to help students in their learning, develop critical-thinking and problem-solving skills, and stimulate discussion.
  • Common Core State Standards (CCSS) are cited in sections to focus student attention and provide a springboard for discussion.
  • Extensive Problem Sets are organized into 3 categories for maximum instructor flexibility when assigning homework that address the standards.

New and updated features of this title

  • REVISED: The reorganized table of contents better reflects the topics that students will likely be teaching in K-8 classrooms. Content within many of the chapters has been updated, with new examples, updated discussions, and new material.
  • NEW: Illustrative Mathematics K-8 Student Tasks feature replaces the previous School Book Pages. Elements of the content from this K-12 series, which is open and freely available online, are pulled into the text.
    • Students will be able to experience the content that elementary and middle school students are actually seeing in their classrooms.
    • Each section with this new feature will also have a block of exercises within the Mathematical Connections portions of the exercise sets that ask students related questions.
  • REVISED: Updated Chapter Opener Problems are more relevant and engaging.
  • REVISED: Updated and reorganized exercise sets: Assessments A and B for each section more closely match each other. The flow of exercises also better matches how the content was covered in the sections.
  • REVISED: A completely new Activity Manual includes classroom-tested activities, letting instructors include as much or as little active learning as they’d prefer. The Annotated Instructor's Edition includes a link to the Activity Manual. 

Key features

Features of MyLab Math for the 14th Edition

  • REVISED: A fully updated Activity Manual includes classroom-tested activities, letting instructors include as much or as little active learning as they’d prefer. The Annotated Instructor's Edition includes a link to the Activity Manual. 
  • REVISED: Updated section lecture videos incorporate the various resources found in the MyLab Math course, such as animations and IMAP videos. Videos are broken down to the objective level and offer a modern, engaging approach that incorporate animations, applets, and StatCrunch.
  • Animations let students interact with the math in a visual, tangible way. These interactive figures, powered by GeoGebra, allow students to explore and manipulate mathematical concepts, leading to more durable understanding. They can also be used by instructors in the classroom to enhance instruction.
  • E-Manipulatives online tools model physical manipulatives, which enable students to investigate, explore, and practice new concepts while solving specific problems that will help them develop a conceptual understanding of key ideas.
  • StatCrunch, a statistical analysis tool that allows users to interact with data, is integrated into the MyLab Math course and accompanying eText as an aid to learning.
  • Mindset videos and assignable, open-ended exercises foster a growth mindset in students. This material encourages them to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities.

Table of contents

1. Problem Solving

  • 1-1 Mathematics and Problem Solving
  • 1-2 Explorations with Patterns
  • Chapter 1 Review

2. Introduction to Logic and Sets

  • 2-1 Reasoning and Logic: An Introduction
  • 2-2 Describing Sets 2-3 Other Set Operations
  • Chapter 2 Review

3. Numeration Systems and Whole Number Operations

  • 3-1 Numeration Systems
  • 3-2 Addition of Whole Numbers
  • 3-3 Subtraction of Whole Numbers
  • 3-4 Multiplication of Whole Numbers
  • 3-5 Division of Whole Numbers
  • Chapter 3 Review

4. Number Theory

  • 4-1 Divisibility
  • 4-2 Prime and Composite Numbers
  • 4-3 Greatest Common Divisor and Least Common Multiple
  • Chapter 4 Review

5. Integers

  • 5-1 Addition and Subtraction of Integers
  • 5-2 Multiplication and Division of Integers
  • Chapter 5 Review

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, Division, and Estimation with Rational Numbers
  • 6-4 Proportional Reasoning
  • Chapter 6 Review

7. Decimals, Percents, and Real Numbers

  • 7-1 Terminating Decimals
  • 7-2 Operations on Decimals
  • 7-3 Repeating Decimals
  • 7-4 Percents
  • 7-5 Real Numbers
  • Chapter 7 Review

8. Algebraic Thinking

  • 8-1 Expressions and Equations
  • 8-2 Solving Equations and Inequalities with One Variable
  • 8-3 Functions and Graphing Equations
  • 8-4 Solving Systems of Equations and Inequalities with Two Variables
  • Chapter 8 Review

9. Introductory Geometry

  • 9-1 Basic Notions
  • 9-2 Curves, Polygons, and Symmetry
  • 9-3 More About Angles
  • 9-4 Geometry in Three Dimensions
  • Chapter 11 Review

10. Congruence and Similarity

  • 10-1 Congruency Through Constructions
  • 10-2 Additional Congruence Theorems
  • 10-3 Additional Constructions
  • 10-4 Similarity
  • Chapter 10 Review

11. Measurement

  • 11-1 Linear Measure
  • 11-2 Concept of Area and the Pythagorean Theorem
  • 11-3 Areas of Polygons and Circles
  • 11-4 Surface Areas
  • 11-5 Volume and Mass
  • Chapter 11 Review
  • Technology Modules

12. Transformations

  • 12-1 Translations, Rotations, and Tessellations
  • 12-2 Reflections and Glide Reflections
  • 12-3 Dilations 935
  • Chapter 12 Review

13. Data Science and Statistics

  • 13-1 The Statistical Problem-Solving Process
  • 13-2 Visualizing Univariate Data
  • 13-3 Visualizing Bivariate Data
  • 13-4 Measures of Central Tendency and Variation
  • Chapter 13 Review

14. Probability

  • 14-1 Determining Probabilities
  • 14-2 Multistage Experiments and Modeling Games
  • 14-3 Simulations and Applications in Probability
  • 14-4 Permutations and Combinations in Probability
  • Chapter 14 Review

Modules (online)

  • Module A: Clock and Modular Arithmetic
  • Module B: Using Real Numbers in Equations
  • Module C: Networks
  • Module D: Trigonometry Ratios via Similarity
  • Module E: Spreadsheets
  • Module F: Graphing Calculators
  • Module G: GeoGebra

Credits

Answers to Select Problems (Student Edition only)

Additional Instructor Answers (Annotated Instructor’s Edition only)

Index

Author bios

About our authors

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 MATH Thematics Phase II Project.

Dr. Billstein has published articles in over 20 different journals and has co-authored over 40 books, including 10 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.

Dr. Barbara Boschmans teaches in the Department of Mathematics and Statistics at Northern Arizona University. She received her BsEd (1995), MAT (1997), and EdD (2003) in Mathematics Education from Northern Arizona University. She has taught at Arizona State University (AZ), Plymouth State University (NH), and Northern Arizona University (AZ). Dr. Boschmans has taught a variety of mathematics and mathematics education courses. She has been a frequent speaker at local, state, national, and international conferences. She has been a board member of the New Hampshire Teachers of Mathematics and the Arizona Association of Teachers of Mathematics. Dr. Boschmans is interested in bringing a joy and appreciation of mathematics to preservice and inservice elementary teachers, and changing non-STEM students' fixed mindset to a growth mindset.

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 1 year at the Westminster Schools, grades 9-12, and 1 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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