Demands for educated labor force with well-integrated cognitive structures call for necessity to use in educational institutions appropriate teaching and knowledge assessment methods directed towards fine development and assessment of students’ conceptual understanding. Concept maps as a kind of mental models have great potential in knowledge assessment due to several significant advantages. However, a taxonomy of possible concept mapping tasks has not been developed yet. The paper considers the problem of extending a set of concept mapping tasks in the already developed concept map based knowledge assessment system. The possible types of tasks are investigated from the point of view of the degree of directedness. As a result, a taxonomy of concept mapping tasks directly related to externalization of students’ knowledge structures are given and explained in detail.