An unsupervised quantitative method to analyse students' answering strategies to a questionnaire

Questionnaires are perhaps the most widely used instruments to assess conceptual learning in physics as well as in mathematics. In the field of physics and mathematics education research it is surely interesting to be able to use a questionnaire as a “diagnostic instrument,” i.e., to know details about relationships among student answers to the different questions. In recent years several research works focused on this goal by using different quantitative methodologies, like Factor, Model and Cluster Analyses. However, very few research works deepened the theoretical aspects of the Cluster Analysis. In this contribution, we discuss two Cluster Analysis methods with respect to this issue. By means of an example of application on real data, groups of students homogeneous with respect to the ways students answer a questionnaire are identified. Each of these groups is identified without any prior knowledge of what form those groups would take (unsupervised classification) and can be characterised by means of the answering strategies the students deploy when facing the questionnaire. Each characterisation allowed us to infer the students’ lines of reasoning. Finally, we show to what extent the two clustering methods are coherent with each other.