Analysing the conceptions on modelling of engineering undergraduate students: A case study using cluster analysis

The problem of taking a set of data and separating it into subgroups where the elements of each subgroup are more similar to each other than they are to elements not in the subgroup has been extensively studied through the statistical method of Cluster Analysis. This method can be conveniently used to separate students into groups that can be recognized and characterized by common traits in their answers, without any prior knowledge of what form those groups would take (unsupervised classification). In the last years many studies examined the consistency of students’ answers in a variety of situations. Some of these papers have tried to develop more detailed models of the consistency of students’ reasoning, or to subdivide a sample of students into intellectually similar subgroups by using Cluster Analysis techniques. In this paper we start from a description of the data coding needed in Cluster Analysis, in order to discuss the meanings and the limits of the interpretation of quantitative results. Then a method commonly used in Cluster Analysis is described and the variables and parameters involved are outlined and criticized. Section 3 deals with the application of this method to the analysis of data from an open-ended questionnaire administered to a sample of university students, and discusses the quantitative results. Finally, some considerations about the relevance of this method in Physics Education Research are drawn