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What We Know About Mathematics Teaching and Learning DOCUMENT RESUME ED 465 514 SE 066 094 AUTHOR Sutton, John, Ed.; Krueger, Alice, Ed. TITLE EDThoughts: What We Know about Mathematics Teaching and Learning. INSTITUTION National Network of Eisenhower Regional Consortia and National Clearinghouse.; Association of State Supervisors of Mathematics.; Mid-Continent Research for Education and Learning, Aurora, CO . SPONS AGENCY Office of Educational Research and Improvement (ED), Washington, DC. ISBN ISBN-1-893476-02-2 PUB DATE 2002-00-00 NOTE 126p. CONTRACT R168R950025-00 AVAILABLE FROM Mid-continent Research for Education and Learning, 2550 S. Parker Road, Suite 500, Aurora, CO 80014-1678 ($11). Tel: 303-337-0990;Web site: http://www.mcrel.org. PUB TYPE Guides - Non-Classroom (055) -- Reports - Descriptive (141) EDRS PRICE MFOl/PCO6 Plus Postage. DESCRIPTORS Cognitive Style; Elementary Secondary Education; *Mathematics Education; Teaching Methods ABSTRACT This volume, part of the EDThoughts series, was authored by mathematics education specialists from across the United States. It addresses approximately 50 questions of interest to mathematics educators, including IIHow does integrated instruction in mathematics affect teaching and learning?" and "What factors contribute most strongly to students' success in learning mathematics?Il Teaching mathematics with technology, characteristics of appropriate homework, benefits of active learning, and communicating with the public about the importance of mathematics also are discussed. The purpose of the book is to support standards-based reform of mathematics education. For each question addressed, background is provided from the perspectives of research and best practices, followed by implications for improving classroom instruction. (Contains 209 references.) (MM) Reproductions supplied by EDRS are the best that can be made from the original document. U.S. DEPARTMENT OF EDUCATION 01 Educational Research and Improvement ATIONAL RESOURCES INFORMATION CENTER (ERIC) 0 This document has been reproduced as received lrom the person or organization originating it. 0 Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERl position or policy. WENEED YOUR HELP IN IMPROVING THIS BOOK - AND WE’LL REWARD YOU FOR HELPING If you are willing to complete a brief survey about this book several weeks from now, we will use your input to create additional materials reflecting your comments and provide you a free copy. Name Home Address Home Phone E-mail Address I am reading this book in my role as: Ci K-12 Teacher D Administrator D Parent Cl Post-secondary Educator D Student D Other Where did you get this copy? Date Card Filled Out Note to the Reader: In fillin out and returning this card, ou a ee to articipate in a mailed survey about this book. Your respomes to the survey whhelp shape the updating ofibTkughPand the development of supporting materials. Yourpersonal infonation will not be used in any other manner. 3 A collaborative fiublication porn mEL EISENHOWER REGIONAL CONSORTIUM FOR nn*E*mC, AND ICIE*CI and ASSM Association of State Supervisors of Mathematics The National Network of Association of State Supervisors Eisenhower Regional Consortia of Mathematics and Clearinghouse Published by Midcontinent Research for Education and Leaxning 2550 S. Parker Road, Suite 500 Aurora, CO 80014-1678 (303) 337-0990 www.mcrel.org Fractal image on front cover courtesy of Paul W. Carlson. The program that created the fractal image on the front cover is available on a CD along with 730 fractal images. A school site license costs $30. No previous knowledge of fractals or mathematics is required. For Windows 95/98/ME/2OOO/NT4/Xp. For more information, visit http://www.mbfractals.com 0 2002 McREL ISBN NO. 1-893476-02-2 This book was produced in whole or in part with funds from the US.Department of Education National Eisenhower Mathematics and Science Programs Office of Educational Research and Improvement (OERI), under grant R168R950025-00. The content does not necessarily reflect the position or policy of OEM or the Department of Education or any other agency of the federal government. 6 Acknowledgements Centr'ibuting,4Qthers k.ibrLriLqs Gary Appel, NCREL Linda Brannan, McREL Malcolm Butler, SERVE Norma Brown, McREL Anne Collins, Massachusetts, ASSM Terry Young, McREL Ella-Mae Daniel, SERVE Elaine DeBassige D'Amato, McREL Judy Florian, McREL Graphics and Layout Fred Gross, TERC Dawn McGill, McREL Jodean Grunow, Wisconsin, ASSM Molly Drew, McREL Carol Hanley, Kentucky, CSSS Clare Heidema, McREL Bill Hopkins, Texas, ASSM Indexing Deb Jordan, McREL James Sucha, McREL Mozell Lang, Michigan, CSSS Arlene Mitchell, McREL Brett Moulding, Utah, CSSS Randi Peterson, McREL Gwen Pollock, Illinois, CSSS Linda Schoen, South Carolina, CSSS Sharon Stenglein, Minnesota, ASSM Jan Tuomi, McREL Jim Woodland, Nebraska, CSSS Editors Jim Harper, RBS Barbara Hicks, AEL Nancy Kellogg Carolyn Richbart Lynn Richbart Vicki Urquhart, McREL Janie Zimmer, RBS 7 ~ Dear EdThoughts Reader, Many good intentions have gone into ambitious education reform goals, including those ratified by the U.S. Congress in 1985. But the year 2000 deadline has passed, and our nation has not made measurable progress toward the goal of becoming “first in the world in mathematics and science education.” In international comparisons, our students’ overall mathematics and science achievement is mediocre. The Third International Mathematics and Science Study (TIMSS) from 1995 showed our 3rd- and 4th-graders scoring above the international average but our 12th-graders scoring well below. The TIMSS-Repeat results released in 2000 do not show significant improvement. What can we do to make a difference? EDThoughts provides a place to start. The mathematics and science EDThoughts books summarize educational research and surveys of best classroom practices, and they offer implications for improved teaching and learning. Classroom teachers and K-12 administrators will find these books useful for their own professional development; teacher educators can use them to inspire their students, and parents and the public can read about the intended and achieved results of educational practices. Effective reforms in mathematics and science education practice and policy will require the collaboration of all of these stakeholder groups. They will need a common understanding of the current status of mathematics and science education and of the direction that research and best practice indicate for improvement as well as how they can help accomplish reform. We hope that this book provides a foundation for greater understanding and reflection. Please take a moment to fill out and return the postcard enclosed in this volume. You then will be sent a short survey that will help us to design useful supporting materials and products and to keep this document fresh. Your participation is sincerely appreciated. John Sutton Alice Krueger Kim Gattis McREL McREL ASSM Table of Contents t I Dear EDThoughts Reader ............................................................................................ i Questions Addressed in Each Section .................................................................. iv .. Preface .....................................,....................................,..,............................................vll About the EDThoughts Books .................................................................................. ix Mathematics For All .................................................................................................... 1 Teaching Mathematics .............i ................................................................................ 11 Assessment in Mathematics .................................................................................... 33 Mathematics Curriculum ........................................................................................ 43 Instructional Technology in Mathematics .......................................................... 61 Learning Mathematics ............................................................................................ 73 References .................................................................................................................. 101 Index............................................................................................................................ 111 9 iii Questions Addressed in Each Section Mathematics For All 0 What is equity and how is it evident in mathematics classrooms? What are the impacts of ability grouping and tracking on student learning? What can schools do to facilitate students’ opportunity to learn mathematics? How can different learning styles be addressed with consistent expectations? Teaching Mathematics what instructional methods support mathematical reasoning and problem solving? How is mathematical thinking addressed in the mathematics classroom? What role does teacher questioning play in learning mathematics? How can teachers motivate students to enjoy and want to learn mathematics? What instructional strategies make mathematics teaching more learner-centered? How does linking instruction and classroom assessment impact student learning? How does teacher content knowledge impact instruction? How does teacher pedagogical knowledge impact instruction? How do teacher attitudes about mathematics learning impact student achievement? What are the characteristics of effective professional development
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