People must often understand how complex systems work to successfully interact with them. To assess whether these mental representations of system functioning are accurate, different methods are available. One is concept maps – graphs that connect concepts (e.g., system goals, functions, components, characteristics) via labeled links to specify their relationships. However, people may not be able to express their actual understanding of system functioning using this abstract method, compared to when they can simply explain it verbally. Therefore, the present study examined how concept maps as representations of system functioning depended on the method used to elicit them (i.e., graphical construction or verbal description). Participants received instructions on how to explain system functioning via functional abstraction hierarchies and on how to construct concept maps. Subsequently, they explained two everyday systems (bike ride, washing dishes), one by constructing a graphical concept map and one verbally. In both conditions, a set of pre-defined concepts was provided. From the verbal descriptions, the authors subsequently constructed concept maps. Both types of maps were evaluated using a master map that correctly represented the functional abstraction hierarchy. Compared to the verbal condition, maps from the graphical condition contained fewer redundant and more functional relationships. They also took over three times longer to complete, but this drawback seems acceptable in light of the other results. While training is needed to construct accurate and useful concept maps, the present study shows people can describe system functioning more accurately when using concept maps compared to verbal descriptions.