Ways To Think About Mathematics: Activities And Investigation

Description: 'Ways to Think About Mathematics' will fill the gap between what the math teachers learned in college and what they are required to teach in today's classrooms. The book will be divided into five modules that focus on algebraic, geometric, and statistical ideas. The book uses immersion in content to help secondary mathematics teachers improve their knowledge and understanding of mathematical concepts. 'Ways to Think About Mathematics' gives teachers the opportunity to learn and understand the same math concepts and math problems that they will be teaching. This book can be used by individual teacher; whether preservice, novice teachers, or experienced teachers. This book can also be used in staff development workshops or faculty teams. It is also appropriate for teacher education courses in secondary mathematics. Review: 'This is a powerful teaching methodology that is bound to convey the spirit of problem-solving.' -- MAA Reviews, June 2006 20080807 Table of Contents: Preface About the Authors 1. What is Mathematical Investigation? 2. Dissections and Area 3. Linearity and Proportional Reasoning 4. Pythagoras and Cousins 5. Pascal's Revenge: Combinatorial Algebra 6. Problems for the Classroom Resource: Answers for Selected Problems Index Author Biography: E. Paul Goldenberg is a Senior Scientist and the Principal Investigator of three recent NSF-funded projects: Connecting with Mathematics, materials for teacher professional development programs; Problems with a Point,a Web-accessible, searchable database of orchestrated problem sets; and Math Workshop: A Comprehensive Elementary Curriculum for Skill, Mathematical Ability, and Real Thinking, a project that will develop materials for a K-5 comprehensive mathematics curriculum that promotes rather than requires professional development. He was previously PI on the Connected Geometry curriculum development project, and of a 3-year,NSF-funded research project into the nature of learning with geometry software. He has over 35 years of experience in elementary, secondary, and post-secondary teaching, teacher enhancement, and education research. He is widely published and has conducted workshops and seminars on a variety of topics in mathematics education. Nina P.Arshavsky is a Math Coach at Boston Public Schools, providing professional development to high school math teachers. She received her doctoral degree in educational psychology from the University of Wisconsin-Madison and taught mathematics in middle and high schools in both Russia and the US. Dr. Arshavsky worked on a variety of research, professional development, and curriculum development projects in the Center for Mathematics Education at EDC and is a co-author of Impact Mathematics: Algebra and More for the Middle Grades, a comprehensive 6-8 mathematics curriculum. She has published and presented numerous research papers, and has taught college courses in cognitive development and human development in infancy and early childhood. Eric E.Karnowski received both his BS and MS from the University of Tennessee, Knoxville, teaching high school for a year between undergraduate and graduate schools. He is currently project director for the Learning by Doing/Math Workshop K-5 curriculum project. Earlier work included editing mathematics textbooks (middle and high school),writing on-line teacher professional development courses for PBS Teacher Line,and writing for the Mathscape middle grades curriculum and the Problems with a Point database. Al Cuoco is Senior Scientist and Director of the Center for Mathematics Education at Education Development Center. Before coming to EDC, he taught high school mathematics for 24 years to a wide range of students in the Woburn, Massachusetts public schools. A student of Ralph Greenberg, Dr. Cuoco received his Ph.D. in mathematics from Brandeis; his mathematical interests and publications have been in algebraic number theory. His favorite publication is his 1991 article in the American Mathematical Monthly, described by his wife as 'an attempt to explain a number system no one understands with a picture no one can see.' Steven R. Benson is a senior research and development associate at Education Development Center, Inc. Before joining EDC in June 2000, he held mathematics faculty positions at St. Olaf College, Santa Clara University, University of New Hampshire, and University of Wisconsin-Oshkosh, and is currently a co-director of the Master of Science for Teachers program at the University of New Hampshire. At EDC, Benson has been involved in a wide variety of projects, most of which involve the development of curricula for mathematics students and teachers. He has also facilitated preservice and inservice teacher professional development workshops across the U.S., directed a research project investigating the genesis and development of mathematical talent in Mathematical Olympians, and edited the problem calendar section of the Mathematics Teacher journal published by the National Council of Teachers of Mathematics. He received his PhD from the University of Illinois, working under the direction of Leon McCulloh in algebraic number theory. Susan Addington is a professor of Mathematics at California State University,San Bernardino. Though her doctoral work was in arithmetic algebraic geometry (a ?eld that includes al-most every mathematical area except statistics),she now spends most of her time thinking about math education. Her educa-tional interests include teacher preparation (elementary through college), ethnomathematics, and the use of technology to teach traditionally difficult ideas. Susan is married to David Dennis, a math educator, historian of mathematics, jazz saxophonist, and virtuoso gardener.