Teaching Secondary Mathematics: Techniques and Enrichment Units (6th Edition) - Softcover

Posamentier, Alfred; Stepelman, Jay

Softcover

ISBN 10: 0130945145 ISBN 13: 9780130945143

Publisher: Prentice Hall, 2001

Synopsis

The revision of this book introduces the 2000 NCTM Principles and Standards and explains their use for teaching secondary school mathematics instruction. Unlike other books, it utilizes 125 enrichment units to provide the staples in preparing to teach mathematics. The authors provide step-by-step techniques on preparing lessons and tests, motivating students, designing assignments, and organizing the classroom. This valuable book also provides practical teaching methods for immediate use along with answers to typical questions readers have about teaching math. Chapter topics include the mathematics teacher today, long-range and short range planning, teaching more effective lessons, the role of problem solving in the mathematics classroom, using technology to enhance mathematics instruction, authentic assessment and grading strategies, enriching mathematics instruction, and extracurricular activities in mathematics. For mathematics teachers in secondary schools.

About this title

About the Author

Alfred S. Posamentier is Professor of Mathematics Education and Dean of the School of Education of The City College of the City University of New York. He is the author and co-author of many mathematics books for teachers and secondary school students. He believes that teachers should use methods and materials which build on their individual strengths, rather than on a prescribed "best way to teach" in general. This popular book is built on this philosophy, as is his book Tips for the Mathematics Teacher: Research-Based Strategies to Help Students Learn (Corwin Press, 1998), which complements this publication. Dr. Posamentier's recent book Problem Strategies for Efficient and Elegant Solutions: A Resource for the Mathematics Teacher (Corwin Press, 1998) elaborates on the chapter on problem solving, while his book 101 Great Ideas for Introducing Key Concepts in Mathematics (Corwin Press, 2001) provides a teacher with interesting alternatives to the traditional development of common topics and concepts in the curriculum.

After completing his A.B. degree in mathematics at Hunter College of the City University of New York, he took a position as a teacher of mathematics at Theodore Roosevelt High School in the Bronx (New York), where he focused his attention on the teaching process in general and the improvement of students' problem-solving skills in particular. He also developed the school's first mathematics teams (both at the junior and senior level) and established a special class whose primary focus was enrichment topics in mathematics and problem solving. He is currently involved in working with mathematics teachers both in the United States and internationally to help them better understand the ideas presented in this book, so that they can comfortably incorporate them into their regular instructional program.

After six years as a high school teacher, Dr. Posamentier joined the faculty of The City College (after having received his masters' degree there), and soon thereafter he began to develop inservice courses for secondary school mathematics teachers, focusing on practical classroom applications of educational research. In addition to the usual inservice offerings, these courses addressed such topics as the uses of new technology in mathematics instruction, efficient ways to teach weaker students, problem-solving strategies and the enrichment of mathematics through a variety of ways including, but not limited to, recreational mathematics.

Dr. Posamentier received his Ph.D. from Fordham University (New York) in mathematics education and since has extended his reputation to Europe. He is an Honorary Fellow at the South Bank University (London, England). He has been visiting professor at several European universities, including the Technical University of Vienna and the Humboldt University at Berlin, and a Fulbright Professor at the University of Vienna.

Dr. Posamentier is often cited for his outstanding teaching. He was named Educator of the Year ( I 993) by The City College Alumni Association and on May I , 1993 had a "Day" named in his honor by the City Council President of New York City. More recently, he was awarded the Grand Medal of Honor from the Federal Republic of Austria and the Medal of Distinction from the city of Vienna. In 1999 he was awarded the title of University Professor for Austrian Universities.

Now, after more than 32 years on the faculty of CCNY, he still exudes an ever-increasing energy and enthusiasm for mathematics and mathematics education. With his penchant for mathematics instruction, he has been especially concerned that during the recent years of mathematics teacher shortages, those who enter the classroom are as well prepared as possible. He enthusiastically believes that providing mathematics teachers with an appropriate knowledge base grid repertoire of teaching strategies enables them to fulfill an essential role in society: empowering our nation's youngsters to engage in the critical study of mathematics. This book is designed to provide the basis for this goal.

Jay Stepelman has had over twenty-five years of experience as a mathematics teacher and supervisor at George Washington High School and Yeshiva University High School in New York City. He is directly involved with on-the-job teacher training and curriculum development in a practical rather than a theoretical setting. His experience ranges from planning, supervising, and teaching regular, honors, and remedial mathematics programs to developing a unique, individualized algebra program that has found special success with inner-city students, pupils with emotional disabilities, youngsters with limited reading ability, and bilingual students.

He is currently teaching at Baruch College and New York City Technical College of the City University of New York.

Dr. Stepelman is the author of Milestones in Geometry (Macmillan, 1970) and the Algebra Tutor series for the Apple II family of computers (Learning Well, 1985). In addition, he is the author of Current Trends in Mathematics and State Mathematics Frameworks, published by Kraus International Publications' Curriculum Resource Handbook, 1993 edition. He has lectured at professional meetings of the National Council of Teachers of Mathematics, the Association of Teachers of Mathematics of New York State, and the New York City Mathematics Chairmen's Association. He has received numerous awards, including Exemplary Supervisory Service Award (New York City Division of High Schools), and has been named as the person most influential in the success of several Westinghouse Scholarship winners. He has also been honored by having many mathematics doctorate theses dedicated to him.

Dr. Stepelman has evaluated mathematics programs and teachers at various private schools. He has served with the Board of Examiners of the City of New York in the area of teacher certification. His academic training includes mathematics and education work at the City College of New York, Courant Institute of Mathematics, New York University, and Adelphi University.

Excerpt. © Reprinted by permission. All rights reserved.

Is teaching mathematics an art or a science? If it is an art, then only highly talented people will be successful teachers of mathematics. For an art, which is largely dependent on creativity, can be learned only to a limited extent; the rest must come intuitively. If mathematics teaching is a science, then anyone capable of learning to teach mathematics, regardless of talent, should be able to do it.

We consider the teaching of mathematics both an art and a science. One needs a certain amount of innate ability to teach successfully. With the rarest exceptions, this ability needs to be buttressed in varying amounts with sociological, psychological, philosophical, and common-sense principles. In this book, we provide the prospective and inservice teacher of mathematics a plethora of ideas covering all aspects of the profession, ideas that we believe will support the artist in everyone. In many cases we provide solid, experience-tested suggestions. One could possibly entitle the book Everything You Wanted to Know about Teaching Mathematics but Didn't Know Whom to Ask.

The first part of the book discusses methods of teaching mathematics, considering all aspects and responsibilities of the job. We begin with an overview of the history of mathematics education so that the teacher of mathematics today understands how the teaching of mathematics has evolved. After describing the rudiments of lesson planning, we discuss the aspects of teaching that make for effective instruction. Since one of the most important aspects of mathematics instruction is the students' ability to solve problems both inside and outside the classroom, we have devoted an entire chapter to this topic. We approach problem solving in a variety of ways: from its instructional underpinnings to its recreational and motivational aspects. One difficult issue is the rapidly changing world of technology. There are two problems. First, no sooner will this book be printed than there will likely be changes in the technology available to the mathematics instructional program. At the same time, there are many schools in the United States that are less fortunate than others and do not yet have the technology described here available for teacher use. We have attempted to address the issues and situations to cover the majority of today's schools.

Mathematics teachers have additional responsibilities beyond the regular instructional program. They must concern themselves with enriching instruction for gifted and not so gifted students, and ought to provide their more motivated students with extracurricular activities to further stretch their interest in mathematics. We conclude the first part of the book with a discussion of the professional responsibilities of mathematics teachers.

We make a conscious effort not to tell the teacher how to deal with every situation. Rather we attempt, as much as possible, to provide alternatives to allow the teachers to make professional judgments about their teaching performance. This is as it should be; no one method of teaching is suitable for all teachers. Personality differences among teachers dictate varying methods of instruction, and what works for one teacher may not work for another.

The second part of the book provides mathematics teachers with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum. Each unit states its objective(s), provides a means for pre-assessment, and then provides an in-depth description of the subject so that a reader unfamiliar with the topic can easily learn it. This development is accompanied by suggestions for teaching the topic to a secondary school class. A post-assessment is provided to help determine the level of learning (mastery) of the topic taught. There is a subject matter cross-index provided at the beginning of the section to enable teachers to select units by topic and grade level.

The National Council of Teachers of Mathematics 2000 Principles and Standards for School Mathematics (Standards) are referred to throughout the book. No one knows where the future emphases in the teaching of mathematics will be. Currently, the Standards are determining the agenda. Clearly, the significant technological advances we are seeing today, coupled with a decline in the cost of computers and calculators, will have a major impact on how mathematics is taught in the future. However, in many parts of the United States there is still uncertainty about the direction that mathematics education should take. We have therefore taken a forward-looking yet cautious approach to the teaching of mathematics, relying, when in doubt, on time-tested methods and ideas.

In effect the reader has within the covers of this book a complete resource on how to teach mathematics, including "the tricks of the trade:" Also provided here is an invaluable collection of enrichment material that can be easily adapted to classes of all levels, to enhance instruction and to motivate students to study mathematics with interest and enthusiasm.

The book is intended primarily for two audiences: for pre-service training of mathematics teachers for the secondary schools, and for inservice teachers of mathematics who are seeking to improve their teaching skills and increase their resources through formal coursework. The book should also be available to mathematics teachers who simply want to have a comprehensive resource at ready reference. This will provide them an opportunity to review their teaching performance and refer to the second part of the book to find ideas with which to enrich their instructional program.

Edition details

• Publisher: Prentice Hall
• Publication date: 2001
• Language: English
• ISBN 10: 0130945145
• ISBN 13: 9780130945143
• Binding: Paperback
• Edition number: 6
• Number of pages: 495