T – 530 Assessing Mathematical Attainment
This course is intended for those interested in the assessment of individual student mathematical performance or the evaluation of the effectiveness of mathematics instructional programs. The course will focus on alternatives to current assessment practice. Topics to be covered include the intellectual structure of the subject, what can/should be expected of students at different grade levels, the design of tasks and scoring rubrics, reporting performance to diverse audiences, sampling for the purposes of program evaluation, the role(s) of technology, and issue of secrecy vs. openness of assessment. Extensive use will be made of the Balanced Assessment Task Data Base produced at the HGSE Educational Technology Center.
There will be a single weekly class meeting on Wednesday from 12 to 2 in the afternoon. In addition, students are expected to meet in small groups to work on the design of assessment tasks. Students, working in small groups, are expected to complete a term project which involves the design and, if feasible, field-test of a collection of tasks appropriate to any one of the following courses; algebra I, geometry, algebra II, pre-calculus, or calculus. Alternative term projects include the design of the mathematics portion of an admissions examination to an elite high school, a teacher education program or a recruitment examination for an entry level position in a commercial establishment.
I am happy to meet individually with students by appointment. I am always reachable by email at
JUDAH_SCHWARTZ@HARVARD.EDUThis course not offered in the 2001-02 academic year
Outline of Class Sessions
What is mathematics about? Why is it taught?
What are the purposes of assessment?
What can/should be expected of students at different levels?
Task design for the elementary grades I
Task design for the elementary grades II
Task design for the secondary grades I
Task design for the secondary grades II
Task design for the secondary grades III
Writing scoring rubrics
Scoring and interpreting student work
Clinical interviews
Portfolios
Public Task Data Bases
Student presentations
Student presentations
Selected Assessment Bibliography
Here are some of the published works that I have found useful. I do not include much of the general literature on assessment and the need for reform, but focus rather on assessing mathematics performance. It should be noted that the published literature is thin when it comes to the question of assessing secondary and post-secondary mathematical attainment.
Baxter, Gail P., Richard J. Shavelson, Sally J. Herman, Katherine A. Brown, and James R. Valadez. "Mathematics Performance Assessment: Technical Quality and Diverse Student Impact." Journal for Research in Mathematics Education, 24, 3, (1993): pp. 190-216.
Cain, Ralph W. and Patricia A. Kenney, "A Joint Vision for Classroom Assessment." The Mathematics Teacher 85, 8, (1992): pp. 612-615.
Charles, Randall I., and Edward A. Silver, eds. Research Agenda for Mathematics Education: The Teaching and Assessing of Mathematical Problem Solving. Hillsdale NJ: Lawrence Erlbaum Associates, 1988.
Kulm, Gerald. Assessing Higher Order Thinking in Mathematics. Washington DC: American Association for the Advancement of Science, 1990.
Kulm, Gerald. Mathematics Assessment: What Works in the Classroom. San Francisco CA: Jossey-Bass, 1994.
Leder, Gilah, ed. Assessment and Learning of Mathematics. Victoria, Australian Council for Educational Research, 1992.
Lesh, Richard and Susan J. Lamon, eds. Assessment of Authentic Performance in School Mathematics. Washington DC: American Association for the Advancement of Science, 1992.
Lester, Frank K. and Diana L. Kroll. "Evaluation: A New Vision." The Mathematics Teacher 84, 4, (1991): pp. 276-283.
Mathematical Sciences Education Board. Measuring What Counts: A Conceptual Guide for Mathematics Assessment. Washington DC: National Academy Press, 1993.
Mathematical Sciences Education Board. For Good Measure: Principles and Goals for Mathematics Assessment. Washington, DC: National Academy Press, 1991.
Office of Technology Assessment. Testing in American Schools: Asking the Right Questions. Washington DC: Office of Technology Assessment, 1992.
Petit, Marge. Getting Started: Vermont Mathematics Portfolio — Learning How to Show Your Best!. Cabot VT: Cabot School, 1992.
Resnick, Lauren B. and Daniel P. Resnick. "Assessing the Thinking Curriculum: New Tools for Educational Reform" in Changing Assessments: Alternative Views of Aptitude, Achievement and Instruction. edited by Bernard R. Gifford and Mary C. O’Connor, Boston MA: Kluwer Academic Publishers, 1992.
Romberg, Thomas A., ed. Mathematics Assessment and Evaluation: Imperatives for Mathematics Educators. Albany NY: State University of New York Press, 1992.
Rothman, Robert. Measuring Up: Standards, Assessment and School Reform. San Francisco CA: Jossey-Bass, 1995.
Schwartz, Judah L. and Katherine A. Viator, eds. The Prices of Secrecy: The Social, Intellectual and Psychological Costs of Current Assessment Practice, Cambridge MA: Educational Technology Center, Harvard University, .1990.
Webb, Norman L. "Assessment of Students’ Knowledge of Mathematics: Steps Toward a Theory" in Handbook of Research on Mathematics and Learning, edited by Doulas A. Grouws, New York NY: Macmillan, 1992.
Webb, Norman L. and Arthur F. Coxford, eds. Assessment in the Mathematics Classroom. 1993 Yearbook, Reston VA: National Council of Teachers of Mathematics, 1993.
Wiggins, Grant P., Assessing Student Performance: Exploring the Purpose and Limits of Testing. San Francisco CA: Jossey-Bass, 1993.