Assessment of Authentic Performance in School Mathematics

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

A Unified Conceptual Framework

Learning can be enhanced by a unified conceptual framework for instruction, testing, and reporting, because in such a framework coherent feedback loops can be constructed. This chapter has focused on the educational measurement aspect of a system built on this premise. The recent introduction of measurement models built around states of understanding, and of inferential techniques to connect such pieces into networks that describe domains of school learning, provide a foundation for improved educational practice.


NOTES AND REFERENCES
1.
A particularly interesting special case occurs when the universe of student models can be expressed as performance models ( Clancey, 1986). A performance model consists of a knowledge base and manipulation rules that can be run on problems in a domain of interest. A particular model can contain both knowledge and production rules that are incorrect or incomplete; the solutions it produces will be correct or incorrect in identifiable ways. Here the parameter specifies features of performance models.
2.
Advocates of student modeling emphasize the qualitative aspects of student models. Our approach is compatible with this view as it is possible to build universes of qualitative models, indexed by parameters that distinguish their features. Our knowledge about a particular student's model is imperfect, however. It can be expressed in terms of probabilities expressing the plausibility of various models, given what has been observed. Probabilities are quantitative and admit to a calculus of manipulation. We might thus employ a quantitative model for our (imperfect) knowledge about qualitative student models.
3.
The ESPRIT team has generalized the application to address clusters of interrelated muscles in a network containing over a thousand nodes.
4.
This model assumes that the five states are exhaustive and mutually exclusive. Alternative models, such as those of Tatsuoka and Yamamoto mentioned earlier, could be used to relax these restrictions.

Andreassen, S., Woldbye, M., Falck, B., and Andersen, S. K. ( 1987). "MUNIN: A causal probabilistic network for interpretation of electromyographic findings". Proceedings of the 10th International Joint Conference on Artificial Intelligence. Milan, Italy.

Biggs, J. B., and Collis, K. F. ( 1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.

Bock, R. D. and Aitkin, M. ( 1981). "Marginal maximum likelihood estimation ofitem parameters: An application of an EM algorithm"

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