Concept networks in learning: finding key concepts in learners' representations of the interlinked structure of scientific knowledge

Students' understanding of scientific conceptual knowledge is often represented as an interlinked web of concepts, principles, laws and models. A long-standing problem in educational research is identifying the key concepts that are central in producing cohesion and contingency in such a web. Here we use network analysis to examine students' representations of the relatedness of physics concepts in the form of concept maps, and suggest how key concepts can be identified. The concept maps are analysed as weighted networks, where nodes are concepts or other conceptual elements and links represent different types of epistemically justified connections between concepts. The importance of concepts in providing cohesion is operationalized through subgraph centrality ${{\rm SC}}$, while their importance in providing contingency is operationalized through communicability betweenness centrality ${{\rm BC}}$. Key concepts are identified through importance ranking ${{\rm IR}}$, which is the geometric mean of ${{\rm SC}}$ and ${{\rm BC}}$, suitably normalized. We show that ${{\rm IR}}$ is able to reliably identify a set of nodes that are the most important in all networks. In order to effect a more detailed comparison of different concept networks, a similarity measure is developed, which pays attention to subtle but important differences in the importance rankings of concepts in different concept networks.