Alfred S. Posamentier - 100 Commonly Asked Questions in Math Class: Answers That Promote Mathematical Understanding, Grades 6-12

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Library of Congress Cataloging-in-Publication Data

Posamentier, Alfred S.

100 commonly asked questions in math class : answers that promote mathematical understanding, grades 612 / Alfred S. Posamentier, William Farber, Terri L. Germain-Williams, Elaine Paris, Bernd Thaller, Ingmar Lehmann.

pages cm
Includes bibliographical references and index.

ISBN 978-1-4522-4308-5 (acid-free paper)

1. MathematicsStudy and teaching (Middle school)
2. MathematicsStudy and teaching (Secondary)
3. MathematicsProblems, exercises, etc. I. Title. II. Title:
One hundred commonly asked questions in math class.
III. Title: Hundred commonly asked questions in math class.

QA139.P65 2013
510.712dc23 2013022103

This book is printed on acid-free paper.

13 14 15 16 17 10 9 8 7 6 5 4 3 2 1

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Contents

About the Authors

Alfred S. Posamentier is Dean of the School of Education and Professor of Mathematics Education at Mercy College, New York. Previously, he held these same positions for 40 years at The City Collegeof The City University of New York. He began his professional career as a high school mathematics teacher for six years in New York City. He is the author and coauthor of more than 55 mathematics books for teachers, students, and the general readership. He is also a frequent commentator in newspapers on topics relating to education.

Dr. Posamentier has extended his reputation in mathematics education to Europe. He has been visiting professor at several European universities in Austria, England, Germany, and Poland, and at the University of Vienna, he was Fulbright Professor in 1990.

William Farber is an Associate Professor of Mathematics Education at Mercy College in New York. He presently serves as Director of the Graduate Level Clinically Rich Teacher Preparation Pilot Program, which was awarded to the School of Education of Mercy College to establish an ongoing partnership with participating high-need schools in the Yonkers School District. His professional experiences include serving as K12 Mathematics Specialist for the New York City Department of Educations Department of Mathematics, Director of the Dr. Charlotte K. Frank Mathematics Education Center at The City College of New York, and a teacher of secondary school mathematics in the Bronx. He is the author and coordinator of many grant awards involving innovative professional development programs in mathematics education.

Terri L. Germain-Williams is an Assistant Professor of Mathematics Education at Mercy College. Prior to accepting the position with Mercy College Graduate School of Education, GermainWilliams worked as an Achievement Manager with the New York City Department of Education, supporting more than 25 K12 schools in the areas of instruction, strategic planning, professional development, federal and state data and accountability, scheduling/programming, and student services. She has taught Grades 812 mathematics and served the New York City Department of Education as a high school Assistant Principal.

Elaine Paris holds BS and MA degrees in mathematics from Brooklyn College, CUNY, and a doctorate in mathematics education from Teachers College, Columbia University.

She began her teaching career at Erasmus Hall High School in Brooklyn as a math teacher. Later, Dr. Paris began teaching mathematics and computer programming at Mercy College. She coauthored the first computer manual used at Mercy College and published several math and computer texts and articles.

She has been a professor in the Department of Mathematics and Computer Information Sciences for more than 30 years, Assistant Chair and Chair, as well as the Director of the U.S. Department of Education federal grant McNair Post-Baccalaureate Scholar Program. Dr. Paris recently retired and holds the rank of Professor Emerita.

Bernd Thaller is a mathematical physicist and Associate Professor at the University of Graz, Austria, who has made contributions to quantum mechanical spectral and scattering theory. He has written several books on quantum mechanics, introducing and applying new visualization methods for quantum wave functions. In recent years, his focus has shifted toward educational math. He was coordinator of a European Community project for teaching math in secondary high schools between 2005 and 2008. In 2008, he founded and is currently the head of a regional educational competence center for mathematics and geometry, whose main task is the coordination of activities of the math teacher training institutions in the region.

Ingmar Lehmann is retired from the mathematics faculty at Humboldt University in Berlin. For many years, he led the Berlin Mathematics Student Society for gifted secondary school students, an organization with which he is still closely engaged today.