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Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi DOUGLAS H. CLEMENTS University at Buffalo, State University of New York Buffalo, New York Part 1: Elementary School Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 MICHELLE STEPHAN Purdue University Calumet Hammond, Indiana JOANNE MENDIOLA Herman Badillo Bilingual Academy 76 Buffalo, New York 1. Linear, Area, and Time Measurement in Prekindergarten to . . . . . . . . 3 Grade 2 MICHELLE STEPHAN Purdue University Calumet Hammond, Indiana DOUGLAS H. CLEMENTS University at Buffalo, State University of New York Buffalo, New York 2. Understanding Children’s Developing Strategies and Concepts for Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 JEFFREY E. BARRETT Illinois State University Normal, Illinois GRAHAM JONES Illinois State University Normal, Illinois CAROL THORNTON Illinois State University Normal, Illinois SANDRA DICKSON Parkside Elementary School Normal, Illinois vi CONTENTS 3. Making Connections with Powerful Ideas in the Measurement of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 NICOLA YELLAND RMIT University Bundoora, Victoria, Australia 4. Developing the Building Blocks of Measurement with Young Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 THERESA J. GRANT Western Michigan University Kalamazoo, Michigan KATE KLINE Western Michigan University Kalamazoo, Michigan 5. Benchmarks as Tools for Developing Measurement Sense . . . . . . . . . 57 ELANA JORAM University of Northern Iowa Cedar Falls, Iowa 6. Assessing and Developing Measurement with Young Children . . . . . 68 DOUG CLARKE Australian Catholic University Melbourne, Victoria, Australia JILL CHEESEMAN Australian Catholic University Melbourne, Victoria, Australia ANDREA MCDONOUGH Australian Catholic University Melbourne, Victoria, Australia BARBARA CLARK Monash University Melbourne, Victoria, Australia 7. Count Me into Measurement: A Program for the Early Elementary School. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 LYNNE OUTHRED Macquarie University Sydney, New South Wales, Australia MICHAEL MITCHELMORE Australian Centre for Educational Studies Sydney, New South Wales, Australia DIANE MCPHAIL Department of Education and Training Ryde, New South Wales, Australia PETER GOULD Department of Education and Training Ryde, New South Wales, Australia vii CONTENTS 8. Developing an Understanding of Measurement in the Elementary Grades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 RICHARD LEHRER University of Wisconsin—Madison Madison, Wisconsin LINDA JASLOW Ed and Verma Pastor Elementary School Phoenix, Arizona CARMEN L. CURTIS Country View Elementary School Verona, Wisconsin 9. Understanding Students’ Thinking about Area and Volume Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 MICHAEL T. BATTISTA Kent State University Kent, Ohio 10. Structuring a Rectangle: Teachers Write to Learn about Their Students’ Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 DEBORAH SCHIFTER Educational Development Center Newton, Massachusetts JANICE SZYMASZEK Smith College Campus School Northampton, Massachusetts 11. About Students’ Understanding and Learning the Concept of Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 CINZIA BONOTTO University of Padua Padua, Italy 12. The Measurement of Time: Transitivity, Unit Iteration, and Conservation of Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 CONSTANCE K. KAMII University of Alabama—Birmingham Birmingham, Alabama KATHY LONG University of California at Berkeley Berkeley, California 13. Bridging Yup’ik Ways of Measuring to Western Mathematics . . . . . 181 JERRY LIPKA University of Alaska Fairbanks Fairbanks, Alaska TOD SHOCKEY Mesa State College Grand Junction, Colorado BARBARA ADAMS University of Alaska Fairbanks Fairbanks, Alaska Part 2: Secondary School Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 VERONICA MEEKS Western Hills High School Fort Worth, Texas ROBERT F. WHEELER Northern Illinois University DeKalb, Illinois 14. What Students Know about Measurement: Perspectives from the NAEP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 MARILYN E. STRUTCHENS Auburn University Auburn, Alabama W. GARY MARTIN Auburn University Auburn, Alabama PATRICIA ANN KENNEY University of Michigan—Ann Arbor Ann Arbor, Michigan 15. Providing Opportunities for Students and Teachers to “Measure Up”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 MELISSA BOSTON University of Pittsburgh Pittsburgh, Pennsylvania MARGARET SMITH University of Pittsburgh Pittsburgh, Pennsylvania viii CONTENTS ix 16. Measuring Montana: An Episode in Estimation . . . . . . . . . . . . . . . . . 221 TED HODGSON Montana State University—Bozeman Bozeman, Montana LINDA SIMONSEN Montana State University—Bozeman Bozeman, Montana JENNIFER LUBEK Montana State University—Bozeman Bozeman, Montana LYLE ANDERSON Montana State University—Bozeman Bozeman, Montana 17. Estimation at Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 THOMASENIA LOTT ADAMS University of Florida Gainesville, Florida GREGORY HARRELL Valdosta State University Valdosta, Georgia 18. Exploring Measurement Concepts through Literature: Natural Links across Disciplines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 RICHARD AUSTIN University of South Florida Tampa, Florida DENISSE THOMPSON University of South Florida Tampa, Florida CHARLENE BECKMANN Grand Valley State University Allendale, Michigan 19. Using the Geoboard to Enhance Measurement Instruction in the Secondary School Mathematics Classroom . . . . . . . . . . . . . . . . . 258 BARBARA A. BURNS Canisius College Buffalo, New York GAIL A. BRADE University at Buffalo, State University of New York Buffalo, New York 20. Using Measurement to Develop Mathematical Reasoning at the Middle and High School Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 MARY C. ENDERSON Middle Tennessee State University Murfreesboro, Tennessee CONTENTS x 21. Is Our Teaching Measuring Up? Race-, SES-, and Gender-Related Gaps in Measurement Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 SARAH T. LUBIENSKI Iowa State University Ames, Iowa 22. Measurement, Representation, and Computer Models of Motion. . 293 CHRISTOPHER HARTMANN University of Wisconsin—Madison Madison, Wisconsin JEFFREY CHOPPIN University of Wisconsin—Madison Madison, Wisconsin 23. Measuring the Unmeasurable: Using Technology to Study the Irrational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 MAURICE BURKE Montana State University—Bozeman Bozeman, Montana 24. Measurement in Adult Education: Starting with Students’ Understandings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 MYRIAM STEINBACK TERC Cambridge, Massachusetts MARY JANE SCHMITT TERC Cambridge, Massachusetts MARTHA MERSON TERC Cambridge, Massachusetts ESTHER LEONELLI Notre Dame Education Center South Boston, Massachusetts CONTENTS

Measurement can develop in the earliest years from children's experience, and it readily lends itself to real-world application. Focusing on research and practice, NCTM's 2003 Yearbook presents current thinking about the learning and teaching of measurement, including students' understanding, the mathematics of measurement, estimation and approximation, connections, and pedagogy. The companion booklet, which not only illustrates some of the issues from the yearbook but also contains activities that go beyond the content, contains teaching notes and ready-to-use handouts.