ENDNOTES

1  

For examples of such matrices, see Edward G. Begle and James W. Wilson, "Evaluation of Mathematics Programs," in Edward G. Begle, ed., Mathematics Education, 69th Yearbook of the National Society for the Study of Education, pt. 1 (Chicago, IL: University of Chicago Press, 1970), 367-404; for a critique of this approach to content, see Thomas A. Romberg, E. Anne Zarinnia, and Kevin F. Collis, "A New World View of Assessment in Mathematics," in Gerald Kulm, ed., Assessing Higher Order Thinking in Mathematics (Washington, D.C.: American Association for the Advancement of Science, 1990), 24-27.

2  

Edward A. Silver, Patricia Ann Kenney, and Leslie Salmon-Cox, The Content and Curricular Validity of the 1990 NAEP Mathematics Items; A Retrospective Analysis (Pittsburgh, PA: Learning Research and Development Center, University of Pittsburgh, 1991).

3  

Edward Haertel and David E. Wiley, "Representations of Ability Structures: Implications for Testing," in Norman Fredericksen, Robert J. Mislevy, and Isaac I. Bejar, eds., Test Theory for a New Generation of Tests (Hillsdale, NJ: Lawrence Erlbaum Associates, 1992).

4  

John Dossey, personal communication, 24 June 1993.

5  

Alan H. Schoenfeld, Balanced Assessment for the Mathematics Curriculum: Progress Report to the National Science Foundation (Berkeley, CA: University of California, June 1993).

6  

See also Suzanne P. Lajoie, "A Framework for Authentic Assessment in Mathematics," in Thomas A. Romberg, ed., Reform in School Mathematics and Authentic Assessment, in press.

7  

California Department of Education, Mathematics Framework for California Public Schools: Kindergarten Through Grade 12 (Sacramento, CA: Author, 1992), 20.

8  

E. Anne Zarinnia and Thomas A. Romberg, "A Framework for the California Assessment Program to Report Students' Achievement in Mathematics," in Thomas A. Romberg, ed., Mathematics Assessment and Evaluation: imperatives for Mathematics Education (Albany, NY: State University of New York Press, 1992), 242-284.

9  

Lauren B. Resnick and Daniel P. Resnick, "Assessing the Thinking Curriculum: New Tools for Educational Reform," in Bernard R. Gifford and Mary Catherine O'Connor, eds., Changing Assessments: Alternative Views of Aptitude, Achievement and Instruction (Boston, MA: Kluwer Academic Publishers, 1992), 37-75.

10  

National Research Council, Mathematical Sciences Education Board, Measuring Up: Prototypes for Mathematics Assessment (Washington, D.C.: National Academy Press, 1993), 117-119.

11  

John S. Brown, Allan Collins, and P. Duguid, "Situated Cognition and the Culture of Learning," Educational Researcher 18:1 (1989), 32-42; Ralph T. Putnam, Magdalene Lampert, and Penelope Peterson, "Alternative Perspectives on Knowing Mathematics in Elementary Schools," Review of Research in Education 16 (1990):57-150; James G. Greeno, "A Perspective on Thinking," American Psychologist 44:2 (1989), 134-141; James Hiebert and Thomas P. Carpenter, "Learning and Teaching with Understanding," in Douglas A. Grouws, ed., Handbook of Research on Mathematics Teaching and Learning (New York, NY: Macmillan Publishing Company, 1992), 65-97.



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