This paper proposes a novel application of knowledge space theory for identifying discrepancies between the knowledge structure that experts expect students to have and the real knowledge structure that students demonstrate on tests. The proposed approach combines two methods of constructing knowledge spaces. The expected knowledge space is constructed by analysing the problem-solving process, while the real knowledge space is identified by applying a data-analytic method. These two knowledge spaces are compared for graph difference and the discrepancies between the two are analysed. In this paper, the proposed approach is applied to the domain of stoichiometry. Although there was a decent agreement between expected and real knowledge spaces, a number of relations that were not present in the expected one appeared in the real knowledge space. The obtained results led to a general conclusion for teaching stoichiometry and pointed to some potential improvements in the existing methods for evaluating cognitive complexity.