Ways to Think about Mathematics Activities and Investigations for Grade 6-12 Teachers

ISBN-10: 0761931058

ISBN-13: 9780761931058

Edition: 2004

List price: $41.95 Buy it from $11.10
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Description:

Engaging in mathematical investigations yourself will help you be a better mathematics teacher! National, state, and local curriculum requirements and recommendations increasingly emphasize active student involvement in exploratory investigations. Teachers now face new demands when they field unexpected student discoveries, determine when some open-ended activity has played out its usefulness or is just on the verge of paying off in a major way, and judge which student-initiated directionsnbsp;are likely to lead to development of important mathematical ideas and which are dead ends. These pedagogical judgments depend heavily on deep mathematical knowledge. Ways to Think About Mathematics uses immersion experiences in algebra, geometry, and statistics to help mathematics teachers improve their knowledge and understanding of mathematical concepts. By experiencing open-ended problems, making and checking conjectures, and evaluating problem solving strategies, every math teacher can become better prepared to deal with day-to-day classroom decisions. Funded by the National Science Foundation and successfully field-tested in a wide variety of professional development and preservice settings, the materials in this book integrate mathematical thinking, effective teaching practices, and explicit connections to exemplary curricula. Because it is aligned with the principles and standards of the National Council of Teachers of Mathematics but is not fixed to any single curriculum, the materials in this book can be aligned with any state or district standards. Emphasizing all components of mathematical investigation, this accessible volume focuses on: Mathematical ways of thinking Discovering connections between mathematical ideas Posing and analyzing problems Making, modifying, testing, and proving conjectures Linking higher level mathematics to the content of grade 6-12 classrooms Ways to Think About Mathematics gives teachers the opportunity to grow as learners and teachers of mathematics by including problems for teachers to explore as well as selected "Problems for the Classroom" for the classes they teach.
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Book details

List price: $41.95
Copyright year: 2004
Publisher: Corwin Press
Publication date: 10/5/2004
Binding: Paperback
Pages: 264
Size: 8.25" wide x 10.50" long x 0.50" tall
Weight: 1.364

Steven R. Benson is an Associate Professor of Mathematics at Lesley University in Cambridge, Massachusetts, where he teaches a variety of mathematics content courses for traditional undergraduate students and in-service mathematics teachers. Before joining the Lesley faculty, Dr. Benson was a Research Scientist at Education Development Center, Inc., where he was involved in a wide variety of projects, most of which involved the development of curricula for mathematics students and teachers. He has also facilitated preservice and in-service teacher professional development workshops across the U.S. and internationally (including serving as consultant to the Ministry of Education in Azerbaijan), 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. Prior to joining the EDC staff 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. He received his PhD from the University of Illinois, working under the direction of Leon McCulloh in algebraic number theory.

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.

Preface
About the Authors
What is Mathematical Investigation?
Dissections and Area
Linearity and Proportional Reasoning
Pythagoras and Cousins
Pascal's Revenge: Combinatorial Algebra
Problems for the Classroom
Resource: Answers for Selected Problems
Index
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