Tasks and Rubrics for Balanced Mathematics Assessment in Primary and Elementary Grades

Judah L. Schwartz is currently Visiting Professor of Education and Research Professor of Physics and Astronomy at Tufts University where he directs a large NSF-supported project on science education for middle-school and elementary school teachers. He is also Emeritus Professor of Engineering Science and Education at the Massachusetts Institute of Technology and Emeritus Professor of Education at the Harvard Graduate School of Education. He was trained in theoretical physics and mathematics and did research for some years in the area of atomic physics. In the course of that research, he and his colleagues developed a variety of computer graphics techniques that proved to be useful in the teaching of mathematics and science. His current research interests include the design of microcomputer software environments to improve the teaching and learning of science and mathematics and the application of cognitive science techniques to the study of mathematics and science education. He has been a visiting Professor at universities in France, Italy and Israel, has consulted and lectured widely in this country and abroad and has published extensively in the area of educational technology. He is the author or co-author of many software environments including The Semantic Calculator, The Algebraic Proposer, M-SS-NG L-NKS: A Game of Letters & Language, What Do You Do With A Broken Calculator?, The Geometric Supposer, Calculus Unlimited, Sir Isaac Newton′s Games, and The Newtonian Sandbox. Judah has a long standing interest in alternative modes of assessment and has edited reports entitled "The Prices of Secrecy: The Social, Intellectual and Psychological Costs of Current Assessment Practice" and " Assessing Mathematics Understanding & Skills Effectively". Recent publications include a book-length case study of educational reform entitled "The Geometric Supposer; What Is It A Case Of?" and "Software Goes to School: Teaching for Understanding in the Age of Technology". Judah may be contacted by e-mail at judah@gse.harvard.edu.Joan M. Kenney’s professional career has encompassed a wide variety of experiences in the field of mathematics. She has worked as a research scientist, specializing in operations analysis and risk management; taught mathematics at the secondary and college level; and performed task modeling and pedagogical intervention in elementary and middle school classrooms. Joan served as the national evaluator for the NSF-sponsored Assessment Community of Teachers and Connecting with Mathematics projects, the Instructional Leadership Academy sponsored by the Council for Basic Education, and the Digi-Block program. She has delivered keynote addresses at several national and international conferences, and has written extensively about mathematics education reform and assessment. Joan recently retired from the Harvard Graduate School of Education, where for 10 years she was the Project Coordinator and Co-director of the Balanced Assessment Program. During that time she was involved in assessment task design, student performance evaluation, and outreach to community stake-holders; she also served on the Mathematics Task Force of the Massachusetts Board of Higher Education, and on the original design committee for the Massachusetts Comprehensive Assessment System (MCAS). She continues to consult with school districts on issues of mathematics curriculum and classroom practice, and to provide professional development for teachers and administrators in the areas of mathematics content and assessment. Her book, Literacy Strategies for Improving Mathematics Instruction, was recently published by ASCD. Joan may be contacted by e-mail at Joan_Kenney@post.harvard.edu.

"The authors show a remarkable talent for embedding important and substantive mathematics in charming yet authentic tasks. A rare talent."

• PrefaceAcknowledgmentsAbout the Authors1. Introduction to Balanced Assessment2. Number and QuantityPrimaryAdd-RingsBirthday CupcakesTV ShowsA Very Long HallwayDot to DotMeasuring the MarigoldsTable TalkLeopard’s LeapAdd ‘Em UpElementaryMultiplication RingsFermi FourBroken CalculatorsTrouble With TablesBroken MeasuresCounting OffNetwork NewsPiece of String3. Shape and SpacePrimaryGrassy ParksStickersShirts in the MirrorElementaryDoes It Fit?Mirror, MirrorGardens of Delight4. Pattern and FunctionPrimaryWall DesignCalendar MovesElementaryMake a MapCoding the Alphabet5. Chance and DataPrimaryBeach DayWe Scream for Ice CreamElementaryMixed Up SocksMeasure Me6. ArrangementPrimaryPostal PuzzlesSharesElementaryValentine HeartsMillie & Mel’sReferencesIndex