Assessment of Authentic Performance in School Mathematics

By Richard Lesh; Susan J. Lamon | Go to book overview

NOTES AND REFERENCES
1.
The procedure of making examinations publicly available after administration is not unknown in the United States. The New York State Regents examinations are regularly published in their entirety after they are administered. Generations of high school students and teachers in New York have used these published tests as curricular materials. On the other hand, there are truth-in-testing laws in several states that require that testing companies make available to test-takers, for a fee, the questions and answers on the test they have taken. These laws have not produced an avalanche of interested test-takers eager to see what the testers were and were not asking and what they thought the answers were. I believe that it would be wrong to infer from this experience that the publication, after administration, of a test is of little value. Contrast this case with the Regents' examinations cited above.
2.
The most notorious of the rote procedures that are ill understood by students (and teachers) are long division and division of fractions. The computation of logarithms and the procedure for extracting square roots, now almost never taught, were rarely understood.
3.
A way to solve this problem without actually carrying out the subtractions is to construct a string of equivalent subtractions. For example: 7102 - 4595; 6102 - 3595; 6202 - 3695; 6242 - 3735; 6241 - 3734; and so on. Thus, the first of the original problems, 7102 - 4595, is equivalent to the problem 6241 - 3734. This is to be compared to the second of the original problems, 6241 - 3976. Even if we limit ourselves to integers, there are more than two hundred problems of the form 6241 - (some number) that can be made up to correctly answer the question. Moreover, a modest amount of reflection will probably persuade the reader that there are an infinite number of incorrect answers to the problem as well.

Schwartz, J. L., and Viator, K. A. (Eds.) ( 1990). The social, intellectual, and "pychological costs of current assessment practices. Cambridge, MA: Educational Technology Center, Harvard Graduate School of Education.

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