Functional roles are of considerable interest in research of joint mental activity. For many years it has been the purpose of investigating to classify functional roles. Few researchers have considered the problem from the point of internal cognitive processes. Most of the research has been focused only on the exposed side of the process. This paper considers functional roles in joint mental activity by using cognitive maps of its participants. The results allow describing internal thinking process of participants in the joint activity who perform various functional roles. The obtained data can be used to analyze the reasons for success and failure in joint mental activity.