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.