*Mathematics for Secondary School Teachers*, which is intended for prospective educators in middle and high school, balances discovery learning with direct instruction.

Written to develop a deeper understanding of the mathematics that will be taught, the book presents topics of central importance in the secondary school mathematics curriculum, notably, functions, polynomials, trigonometry, exponential and logarithmic functions, numbers and operations, and measurements.

Beyond the goals of conceptual understanding and computational fluency, readers of the book can devise their own mathematical explanations and arguments; create examples and visual representations; remediate typical student errors and misconceptions; and analyze students’ work.

A broad collection of exercises of varying degrees of difficulty is integrated with the text. Instructors are able to emphasize the following:

- Basics: The exploration of key precollege topics from intuitive and rigorous points of view;
- Connections: The exploration of relationships among topics, using tools from college-level mathematics;
- Extensions: The exploration of college-level mathematical topics that have a compelling relationship to precollege mathematics.

By taking into account the diverse mathematical backgrounds of preservice teachers and the varied goals of teacher preparation programs, the authors have written a textbook whose subject matter addresses a wide range of learning objectives appropriate for future teachers.

*Mathematics for Secondary School Teachers* can also be used in licensing programs; as a supplement to mathematics methods courses; as a text for graduate courses for in-service teachers; and as a resource for faculty development.

Preface

To the Student

To the Instructor

1. Functions

2. Lines in the Plane

3. Quadratic Polynomials

4. Trigonometry

5. Hyperbolic Trigonometry

6. Numbers

7. Operations in Number Theory

8. Topics in Number Theory

9. Exponentiation

10. Exponential and Logarithmic Functions: History, Computation, and Application

11. Transcendental Functions and Complex Numbers

12. Beyond Quadratics: Higher Degree Polynomials

13. Measurement

Appendix A: Log Tables

Index

The word trigon refers to a three-sided figure, while metry means measurement. Thus trigonometry is the measurement of triangles, which is tantamount to studying the measurement of the relationships among side-lengths and angles. There is no doubt that trigonometry is useful. Human beings have been using triangles to make measurements (e.g., the height of Everest, the circumference of the earth, the distance of from the earth to the sun) for thousands of years. But why is trigonometry nontrivial? After all, we know how to measure angles and line segments, so what can be so hard about trigonometry?

Elizabeth Bremigan, Ralph Bremigan, and John Lorch are faculty members at Ball State University. They are also members of the MAA.

As the authors state early on, this book is intended in part as a response to the 2001 report from the Conference Board of the Mathematical Sciences on the mathematical education of future teachers.

There is a very definite need for books like this one. While courses and textbooks on mathematics for elementary teachers are common across America, few schools offer a course for which this book would be a good fit, and that’s probably regrettable. There is a good argument to be made for offering prospective secondary teachers the same kind of course — in which they consider the math they expect to teach from an advanced perspective and with some attention to how to teach it — that we routinely require of prospective elementary teachers. Continued...