Teaching Secondary Mathematics

Teaching Secondary Mathematics

Teaching Secondary Mathematics

Teaching Secondary Mathematics


This book--a primary text for secondary mathematics methods students--is grounded in the NCTM standards and informed by up-to-date research and theory in mathematics education. The book is organized in three parts: General Fundamentals (a broad overview of education, curriculum, learning theory, discipline, planning, and adolescent behavior); Mathematics Education Fundamentals (technology, problem solving, discovery, and proof); and Content and Strategies (Algebra I, Geometry, Algebra II with Trigonometry, Pre-Calculus, and Calculus).

To motivate students to become effective teachers of mathematics, the text engages them in a variety of stimulating activities such as reflective thought questions, mathematical challenges, and student life-based applications. Throughout the text, emphasis is given to:

Technology as a teaching tool. Many examples for secondary classrooms are included.

Development of teaching professionals who are self motivated, life-long learners. Students are encouraged to do a variety of problems; once they have done the problem, the setting is extended through discussion and reflection.

Connectivity. Concepts that are traditionally covered in one area are mapped into related areas; discussions focus on how an idea used in one environment can be used in a different environment.


This book is the result of the urging of former students, teachers, colleagues, and friends of Doug Brumbaugh to put his Secondary Mathematics Methods course into print. It is designed to make you, a future teacher of mathematics, think. We have used an informal writing style in order to maintain an informal dialogue with you. We want to be talking with you, not to or at you. We assume you will think about and do the problems as you read through this book. Our intent is to have you begin thinking about your classroom now. We do not expect you to accept all of our ideas, but we do anticipate that you will react to them and, in the process, begin formulating your own teaching style.

As we created this book, several undergraduate mathematics education majors voluntarily read the manuscript. We incorporated their suggestions. They liked the style and practical approach. They appreciated the fact that they could see a variety of theoretical bases revealed throughout the text. We opted to take an eclectic approach to the learning theories as opposed to stressing any single one. Our assumption is that your teacher will emphasize an approach of preference. Between your teacher and this text, you should be more able to make an informed decision about the approach you will use as you embark on your professional teaching career.

We assume that you will have had some prior exposure to general learning theory and educational methods. This text is designed to build on those, coupled with experiences, specializations, and preferences of your teacher. This text provides a collection of examples in a variety of environments. They are designed to furnish you with a broad base of ideas that will stimulate the formative development of thoughts and models you will employ in your classroom.

The text is organized into three parts: General Fundamentals, Mathematics Education Fundamentals, and Content and Strategies. The General Fundamentals (chapters 1-4) assume some formal background in courses designed to provide a broad overview of education, curriculum, learning theory, discipline, planning, and adolescent behavior. Our chapters are intended to refresh your memories, provide a basis for discussion that will lead into specifics related to the teaching of mathematics, and motivate you to begin thinking about how you can become an effective teacher of mathematics at the secondary level.

The Mathematics Education Fundamentals (chapters 5-8) are designed to be more specific. Here we begin dealing more directly with topics out of the general education environment. Each chapter deals with a subject that will permeate your instruction. We encourage you to plan thoroughly, long before you cover any topic with your class. As you plan, you need to think of how you will incorporate technology, problem solving, discovery, and proof into your lesson.

The Content and Strategies section (chapters 9-14) builds on the General Fundamentals and the Mathematics Education Fundamentals. We assume you will discuss these issues in the class using this . . .

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