Assessment of Authentic Performance in School Mathematics

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

pure mathematics activities (in which the symbols are concrete objects rather than abstract notation), whereas two of the three stages of our modeling approach focus on applied mathematics activities (which are explicitly based on children's' real-life experiences), even though all three stages are aimed at demonstrating the power of pure mathematical activities.

Our modeling approach to instruction is deliberately consistent with the way modern mathematicians think about their own activities in mathematics and mathematical modeling. Also, it was explicitly created to be consistent with three of the most basic principles of modern cognitive science, namely, (i) humans interpret their experiences by mapping them to internal models, (ii) these internal models must be constructed, and (iii) constructed models result in situated knowledge that is gradually extended and decontextualized to interpret other structurally similar situations. Moreover, our modeling approach to instruction is also consistent with a constructivist philosophy about how human knowledge develops.


REFERENCES

American Association for the Advancement of Science. ( 1989). Science for all Americans. Washington, D.C.: AAAS.

Bell, M., Fuson, K., and Lesh, K. ( 1976). Algebraic and arithmetic structures: A concrete approach: for elementary school teachers. New York: Free Press.

Brown, J. S., and Van K. Lehn ( 1980). "Repair theory: A generative theory of bugs in procedural skills". Cognitive Science, 4, 379-426.

Campione, J, Brown, A., and Connell, M. ( 1989). "Metacognition: On the importance of understanding what you are doing". In R. Charles and E. Silver (Eds.), The teaching and assessing of mathematical problem solving. Hillsdale, NJ: Lawrence Erlbaum Associates.

Carpenter, T. P., Moser, J., and Romberg, TA. (Eds.). ( 1982). Addition and subtraction: A cognitive perspective. Hillsdale, NJ: Lawrence Erlbaum Associates.

Carraher, T., Carraher, D., and Schliemann, A. D. ( 1985). "Mathematics in the streets and the schools". British Journal of Developmental Psychology, 3, 21-29.

Confrey, J. ( 1990, April). Origins, units, and rates: The construction of a splitting structure. A paper presented at the annual meeting of the American Educational Research Association. Boston.

Dienes, Z. ( 1957). Building up mathematics. London: Hutchinson Educational Ltd.

Ernest, P. ( 1991). The Philosophy of mathematics education. Bristol, PA: The Falmer Press, Taylor and Francis Inc.

Fuson, K. C. ( 1988). Children's counting and concepts of number. New York: Springer- Verlag.

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