A Problem Solving Approach to Mathematics for Elementary School Teachers

For courses in Math for Future Elementary Teachers.

A concept-rich, skill-based approach to preparing outstanding elementary math teachers

A Problem Solving Approach to Mathematics for Elementary School Teachers not only helps students learn the math – it provides an invaluable reference to future teachers by including professional development features and discussions of today’s standards. 

Revised throughout to prepare students more effectively for their own classrooms, the 13th Edition gives instructors a variety of approaches to teaching, and encourages discussion and collaboration among students and with their instructors. The MyLab™ Math course for this revision is updated extensively with new resources and features.

The Common Core Standards are used in the text to highlight concepts. The National Council of Teachers of Mathematics (NCTM) publications, Principles and Standards of School Mathematics (2000) and Principles to Actions: Ensuring Mathematical Success for All (2014) are reflected throughout.

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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 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.

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 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.

1. An Introduction to 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

* Module A: Clock and Modular Arithmetic–online

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 Variables

8-2 Equals Relation and Equations

8-3 Functions

8-4 Equations in a Cartesian Coordinate System

* Module B: Using Real Numbers in Equations–online

Chapter 8 Review

9. Probability

9-1 Determining Probabilities

9-2 Multistage Experiments and Modeling Games

9-3 Simulations and Applications in Probability

9-4 Permutations and Combinations in Probability

Chapter 9 Review

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

Chapter 10 Review

11. Introductory Geometry

11-1 Basic Notions

11-2 Curves, Polygons, and Symmetry

11-3 More About Angles

11-4 Geometry in Three Dimensions

* Module C: Networks–online

Chapter 11 Review

12. Congruence and Similarity with Constructions

12-1 Congruence Through Constructions

12-2 Additional Congruence Theorems

12-3 Additional Constructions

12-4 Similar Triangles and Other Similar Figures

* Module D: Trigonometry Ratios via Similarity–online

Chapter 12 Review

13. Area, Pythagorean Theorem, and Volume

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

Chapter 13 Review 890

Technology Modules

* Module E: Spreadsheets–online

* Module F: Graphing Calculators–online

* Module H: GeoGebra–online

14. Transformations

14-1 Translations, Rotations, and Tessellations 

14-2 Reflections and Glide Reflections 

14-3 Dilations 935

Chapter 14 Review

Credits

Answers to Problems

Additional Instructor Answers (Annotated Instructor’s Edition only)

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