The aim of the present research was to explore the use of concept maps as an assessment tool. The research question posed was: can concept maps be used to quantitatively assess the learning of a physics topic in an engineering course? This paper describes a new approach to quantifying concept maps. The research was preceded by a pilot project that allowed the necessary processes for the proper conduct of the research to be developed. The sample comprised 47 first-year engineering students who were asked to construct a concept map about the content of electrostatic interactions. The concept maps the students prepared were valued quantitatively and qualitatively by an expert instructor. To validate the approach, an analysis of the relationship between the scores given in the three evaluation forms was made. A comparative statistical analysis of the multiple-choice examination data with the quantitative and the qualitative evaluations of the concept maps found not only that there were no significant differences between them in either case, but also that they were moderately, but significantly, correlated. These results suggest that we are on the right track to obtain an effective and easy-to-use tool to evaluate the students' learning results based on the quantitative assessment of the conceptual maps elaborated by them. Moreover, the analysis of the concept maps in the pilot stage allowed the difficulties that the students had during their learning to be detected, which led to the sequencing of the content of the electrostatic interactions topic being changed.