This book contains supplementary learning resources for students taking or preparing to take a post-secondary “mathematics for elementary teachers” course. The resources focus on how to solve many of the basic arithmetic problems typically encountered in elementary school.

Please contact the author, Iain Pardoe, if you notice any typos or errors.

Many post-secondary institutions in British Columbia offer a “mathematics for elementary teachers” course designed for students intending to pursue a career as an elementary school teacher. Example courses include Math 1900/1901: Principles of Mathematics for Teachers at Thompson Rivers University, Math 190: Principles of Mathematics for Teachers at Simon Fraser University, and Math 105: Math for the Elementary School Teacher at University of the Fraser Valley. These courses emphasize conceptual understanding of elementary mathematical techniques and ideas. Topics include numbers, operations, proportional reasoning, number theory, algebra, geometry, measurement, data analysis, and probability. These courses cover *elementary mathematics content* rather than *teaching methods* (such as mathematical content delivery, instructional strategies, and practice teaching).

Despite a wealth of learning resources included in these courses, many students struggle with particular topics, and some fail the course because they do not achieve sufficient mastery of the material to pass a final exam. Frequently, students enter the course with very limited understanding of how to solve basic math problems (e.g., adding fractions or calculating percentages) and it is difficult to achieve a successful course outcome without this understanding. The course is designed to take a basic understanding of “how” to solve specific problems and explore “why” the problem-solving techniques work. The goal is that with this deeper understanding, students will be better equipped to teach mathematics effectively to elementary students. However, students that continue to struggle with the “how” can find it extremely challenging to also master the “why.” Without this deeper level of understanding, it is difficult to achieve a successful course outcome. The purpose of this book is to provide open learning resources to help these students master the “how” so that they can more easily master the “why” in the course itself.

The learning resources included in this book include:

- Notes that explain in simple language the techniques covered in “mathematics for elementary education” courses and how to solve related problems;
- Short instructional videos with tips on applying the techniques and solving problems;
- Practice exercises for each technique that provide immediate feedback.

The book is organized into ten parts:

- Numbers
- Addition and Subtraction
- Multiplication
- Division
- Proportional Reasoning
- Number Theory
- Algebraic Thinking
- Sequences and Functions
- Geometry and Measurement
- Data Analysis and Probability

Many of the ideas and methods used in this book are adapted from Beckmann, S. (2022). *Mathematics for elementary and middle school teachers with activities* (6th ed.). Pearson Education, Inc.