Assessing Mathematical Proficiency

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Overview

Testing matters! It can determine kids' and schools' futures. In a conference at the Mathematical Sciences Research Institute, mathematicians, math education researchers, teachers, test developers, and policymakers gathered to work through critical issues related to mathematics assessment. They examined: the challenges of assessing student learning in ways that support instructional improvement; ethical issues related to assessment, including the impact of testing on urban and high-poverty schools; the different (and sometimes conflicting) needs of the different groups; and, different frameworks, tools, and methods for assessment, comparing the kinds of information they offer about students' mathematical proficiency.

This volume presents the results of the discussions. It highlights the kinds of information that different assessments can offer, including many examples of some of the best mathematics assessments worldwide. A special feature is an interview with a student about his knowledge of fractions, demonstrating what interviews (versus standardized tests) can reveal.

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Editorial Reviews

From the Publisher
"Anyone interested in the current state of assessment in mathematics education will find this book relevant."
Scott A. Fellows, Mathematics Teacher

"The book... is though provoking. The authors succeed in showing the complexity of the problem of assessing mathematical proficiency and the difference, sometimes dramatic, in the perception of this issue by various stakeholders. The majority of them convincingly argue in favor of tasks and procedures that would go beyond simple computational or operational abilities."
Alex Kozulin, American Journal of Psychology

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Product Details

Meet the Author

Alan Schoenfeld is the Elizabeth and Edward Conner Professor of Education and Affiliated Professor of Mathematics at the University of California at Berkeley.

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Table of Contents


Preface     ix
Acknowledgments     xix
The Big Picture     1
Issues and Tensions in the Assessment of Mathematical Proficiency   Alan H. Schoenfeld     3
Aims of Mathematics Education   Judith A. Ramaley     17
The No Child Left Behind Act: Political Context and National Goals   Susan Sclafani     23
Perspectives on Mathematical Proficiency     29
What Is Mathematical Proficiency?   R. James Milgram     31
What Is Mathematical Proficiency and How Can It Be Assessed?   Alan H. Schoenfeld     59
What Docs Assessment Assess? Issues and Examples     75
Mathematical Proficiency: What Is Important? How Can It Be Measured?   Hugh Burkhardt     77
Aspects of the Art of Assessment Design   Jan de Lange     99
Mathematical Proficiency for Citizenship   Bernard L. Madison     113
Learning from Assessment   Richard Askey     125
When Assessment Guides Instruction: Silicon Valley's Mathematics Assessment Collaborative   David Foster   Pendred Noyce   Sara Spiegel     137
The Case of Algebra     155
Assessing the Strands of Student Proficiency in Elementary Algebra   William G. McCallum     157
Making Meaning in Algebra: Examining Students' Understandings and Misconceptions   David Foster     163
Task Context and Assessment   Ann Shannon     177
What Do Assessments Assess? The Case of Fractions     193
Learning About Fractions from Assessment   Linda Fisher     195
Assessing a Student's Mathematical Knowledge by Way of Interview$dDeborah Loewenberg Ball with Brandon Peoples     213
Reflections on an Assessment Interview: What a Close Look at Student Understanding Can Reveal   Alan H. Schoenfeld     269
The Importance of Societal Context     279
Assessment in France   Michele Artigue     283
Assessment to Improve Learning in Mathematics: The BEAR Assessment System   Mark Wilson   Claus Carstensen     311
English Learners and Mathematics Learning: Language Issues to Consider   Lily Wong Fillmore     333
Beyond Words to Mathematical Content: Assessing English Learners in the Mathematics Classroom   Judit Moschkovich     345
Assessment in the Real World: The Case of New York City   Elizabeth Taleporos     353
Perspectives on State Assessments in California: What You Release Is What Teachers Get   Elizabeth K. Stage      357
Epilogue: What Do We Need to Know? Items for a Research Agenda     365
About the Authors     369
Subject Index     381
Author Index     385
Task Index     389
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