Mathematics for Secondary School Teachers

Elizabeth George Bremigan, Ralph J. Bremigan, John D. Lorch

• Publisher: American Mathematical Society
• Year: 2011
• Topic: Mathematics
• eBook ISBN:
  9780883859803
• Subtopic: Mathematics General
• Index: Mathematics

Mathematics for Secondary School Teachers discusses topics of central importance in the secondary school mathematics curriculum, including functions, polynomials, trigonometry, exponential and logarithmic functions, number and operation, and measurement. Acknowledging diversity in the mathematical backgrounds of pre-service teachers and in the goals of teacher preparation programs, the authors have written a flexible text through which instructors can emphasize any of the following: Basics: exploration of key pre-college topics from intuitive and rigorous points of view; Connections: exploration of relationships among topics, using tools from college-level mathematics; Extensions: exploration of college-level mathematical topics that have a compelling relationship to pre-college mathematics. Mathematics for Secondary School Teachers provides a balance of discovery learning and direct instruction. Activities and exercises address the range of learning objectives appropriate for future teachers. Beyond the obvious goals of conceptual understanding and computational fluency, readers are invited to devise mathematical explanations and arguments, create examples and visual representations, remediate typical student errors and misconceptions, and analyze student work. Introductory discussion questions encourage prospective teachers to take stock of their knowledge of pre-college topics. A rich collection of exercises of widely varying degrees of difficulty is integrated with the text. Activities and exercises are easily adapted to the settings of individual assignments, group projects, and classroom discussions. Mathematics for Secondary School Teachers is primarily intended as the text for a bridge or capstone course for pre-service secondary school mathematics teachers. It can also be used in alternative licensure programs, as a supplement to a mathematics methods course, as the text for a graduate course for in-service teachers, and as a resource and reference for in-service faculty development.

Table of contents

• front cover
• copyright page
• title page
• Contents
• 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 Systems
• 7.1 Addition and Subtraction in Number Systems
• 7.2 Multiplication in Number Systems
• 7.3 Division in Number Systems
• 7.4 Algebraic Properties in Number Systems: An Intuitive View
• 7.5 Algebraic Properties in Number Systems: A Survey of Some RigorousArguments
• 7.6 Complex Numbers
• 8 Topics in Number Systems
• 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
• About the Authors
• Back cover