HIERARCHICAL AND NON-HIERARCHICAL CLUSTERING METHODS TO ANALYSE AN OPEN-ENDED QUESTIONNAIRE ON ALGEBRAIC THINKING

In recent years, some papers have tried to develop detailed models of the reasoning competences of the student populations tested, or to subdivide a sample of students into intellectually similar subgroups, by using quantitative or qualitative analysis methods. It is worth noting that research papers using quantitative analysis methods to study student responses to open-ended questionnaire can be found in Science and Physics education (Springuel et al., 2007), but the same cannot be said for research in Mathematics education. In this paper we focus on the application of hierarchical and non-hierarchical clustering methods referred to dendrograms and k-means approaches (Everitt, et al., 2011…