Automatic Stepwise Correctness Assessment of Constructed Mathematical Response Schemes

Computer-aided free-response mathematics assessments are becoming increasingly important vehicles in supporting the notion of “learning through assessment”. Hence, having a marking engine that is able to assess each step in a scheme of constructed responses (or working scheme) is a vital requirement for a mathematics computer-aided system that offers free-response assessments. Existing computational solutions for assessing the correctness of intermediate steps do so by limiting the responses to be entered stepwise, and not all at once, with the delivery of qualitative feedbacks to steps that are incorrect. In this paper, we propose our marking engine that is able to execute a stepwise assessment of responses in a working scheme that closely emulates the marking practices of a typical human. The marking engine delivers quantitative feedbacks in the form of numeric scores that indicate the degree of correctness of the responses in a working scheme and of the working scheme as well. The results of the reliability analysis on the automated correctness scores suggest that the scores are reliable indicators of responses correctness as well as working schemes correctness.