Optimal counterexamples expectation based method for knowledge space construction

In this paper a novel method for knowledge space construction is proposed. The method is based on the optimization of the counterexamples expectation in students' responses. Firstly, the parameters of binomial distribution of the correct/incorrect responses are estimated using maximum likelihood estimation. Then, the obtained parameters are used for calculating optimal estimations of probabilities for careless mistakes and lucky guesses in a multiple choice test, whereby a knowledge space is constructed.