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.