Edited by Alan H. Schoenfeld
University of California, Berkeley
Testing matters! It can determine kids’ and schools’ futures. In a conference at the Mathematical Sciences Research Institute, mathematicians, maths 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 and a demonstration of what interviews (versus standardized tests) can reveal.
• Offers examples of very different ways to understand what students know in mathematics • A ‘live’ interview with a student and what it reveals about understanding • Reveals what testing does and does not tell you and can tell you
Preface Alan H. Schoenfeld; Part I. The Big Picture: 1. Issues and tensions in the assessment of mathematical proficiency Alan H. Schoenfeld; 2. Crucial contemporary social, political, and cultural issues in mathematical assessment in the United States Judith Ramaley; 3. Crucial contemporary social, political, and cultural issues in mathematical assessment in the United States Susan Sclafani; Part II. Perspectives on Mathematical Proficiency: 4. What is mathematical proficiency? R. James Milgram; 5. What is mathematical proficiency (and how can it be assessed)? Alan H. Schoenfeld; Part III. What Does Assessment Assess? Issues and Examples: 6. Assessing mathematical proficiency: what is important? Hugh Burkhardt; 7. Aspects of the art of assessment design Jan de Lange; 8. Mathematical proficiency for citizenship Bernard Madison; 9. Learning from assessment Richard Askey; 10. Using assessment to design professional development David Foster; Part IV. The Case of Algebra: 11. Context and learning: an assessment of ‘real world’ mathematics tasks Ann Shannon; 12. Making meaning in algebra: examining students’ understandings and misconceptions David Foster; 13. Assessing the strands of student proficiency in elementary algebra William McCallum; Part V. What Do Different Assessments Assess?: 14. Learning about fractions from assessment Linda Fisher; 15. Brandon interview and commentary, plus CD of interview Deborah Ball; Part VI. The Importance of Context: 16. Assessment of mathematics learning in France Michele Artigue; 17. Assessment to improve learning in mathematics: the BEAR assessment system Mark Wilson and Claus Carstensen; 18. English learners and math learning: language issues for the math educators to consider Lily W. Fillmore; 19. Beyond words to mathematical content: assessing English language learners in the mathematics classroom Judit Moschkovich; 20. Assessment in the real world: the case of New York city Elizabeth Taleporos; 21. Perspectives on state assessments in California Elizabeth Stage; Part VII. What Do We Need To Know?: 22. Research agenda emerging from the conference.
Andrew Smith (University of Canterbury), Derek James (University of Oxford), Peter Thomas (University of Durham)
Alan H. Schoenfeld, Judith Ramaley, Susan Sclafani, R. James Milgram, Hugh Burkhardt, Jan de Lange, Bernard Madison, Richard Askey, David Foster, Ann Shannon, William McCallum, Linda Fisher, Deborah Ball, Michele Artigue, Mark Wilson, Claus Carstensen, Lily W. Fillmore, Judit Moschkovich, Elizabeth Taleporos, Elizabeth Stage