VALIDATION AND EXTENSION OF THE MATHEMATICAL EXPRESSION RESPONSE TYPE: APPLICATIONS OF SCHEMA THEORY TO AUTOMATIC SCORING AND ITEM GENERATION IN MATHEMATICS

Abstract

In this report, we describe the development of general, accurate, cost-effective, and immediately usable automatic analysis routines that dichotomously score rational expressions of arbitrary complexity. This development has led to the new Mathematical Expression (ME) response type, which may appear operationally in the new GRE Mathematical Reasoning test scheduled for deployment in 1999. We detail work confirming the accuracy of these scoring routines and then describe extensions to the existing capability based on schema theory. We show how schema theory can be applied not only to the scoring of more complex test responses but also to the automatic generation of items and intelligent tutoring.