ABSTRACT
In this chapter, we attempt to show how schema theory can be applied to the automatic generation of items, the scoring of more complex test responses, and to intelligent tutoring. When attempting to develop algorithms for automatic item generation in mathematics, one necessarily learns a lot about the underlying structure of the problems. This knowledge of problem structure is indispensable to making progress in item generation, but it may also be useful for other applications. In particular, it may be useful for either assigning partial credit scores or offering remediation in instructional settings. We report here on a particular theory of problem structure, schema theory. Schema theory is applied to the automatic generation and variation of items, the analysis of multiple-line solutions, and the delivery of instruction.
