Computational model of stepwise quantitative assessment of equations correctness / Nuru’l - ‘Izzah Othman

Existing computational solutions for stepwise correctness checking of free-response solution schemes consisting of equations only consider providing qualitative feedbacks. Hence, this research intends to propose a computational model of a typical stepwise correctness checking of a scheme of student-constructed responses normally (usually) performed by a human examiner with the provision of quantitative feedbacks. The responses are worked solutions on solving linear algebraic equations in one variable. The proposed computational model comprises of computational techniques of key marking processes, and has enabled a marking engine prototype, which has been developed based on the model, to perform stepwise correctness checking and scoring of the response of each step in a working scheme and of the working scheme as well. The assigned numeric score of each step, or analytical score, serves as a quantitative feedback to inform students on the degree of correctness of the response of a particular step. The numeric score of the working scheme, or overall score, indicates the degree of correctness of the whole working scheme. Existing computational solutions that are currently available determine response correctness based on mathematical equivalence of expressions. In this research, the degree of correctness of an equation is based on the structural identicalness of the constituting mathtokens, which is evaluated using a correctness measure formulated in this research. The experimental verification shows that the evaluation of correctness by the correctness measure is comparable to human judgment on correctness. The computational model is formalized mathematically by basic concepts from Multiset Theory, while the process framework is supported by basic techniques and processes from the field of textual information retrieval that have been adapted to suit the problem of this research…