Using modern graph analysis techniques on mind maps to help quantify learning

In this work, we use a graph analysis tool to measure how student-created mind maps reflect learning. Mind maps consist of words and connections between words, and this visual tool helps illustrate how an individual understands how these words connect together in a field. From an analysis standpoint, mind maps are graphs consisting of nodes connected by edges. In the fall of 2011, students created three mind maps over the duration of a digital system design course, and at each of the three intervals, these mind maps were created with the same 20 terms that were introduced throughout the course. Each student´s mind maps were then digitally encoded and analyzed using a modern graph analysis tool called GraphCrunch II. Our results show that a simple analysis of graph density is a poor indicator of learning since this metric does not capture a graph´s structure, and it is this structure that reflects meaning and understanding by the learner. Instead, a metric called relative graphlet frequency distance (RGF-distance), which is calculated by comparing a golden mind map (expert created mind map) to each of the students mind maps, is used to analyze each students understanding of how these words relate. Our results show that learner´s mind maps decrease in RGF-distance over the period of the course, and this means that the students are building graphs more similar to that of the golden model. We, also, see that the RGF-distance over the set of students compared to their grades on an exam or overall grade in the course has some correlation, meaning that these mind maps relate to grades in terms of the learners understanding of vocabulary, but the correlation is not strong. The ultimate goal of these tools is to provide the learners with a method of getting automatic feedback on their understanding as well as learning progress in particular topics.