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In the last years many studies examined the consistency of students' answersin a variety of contexts. Some of these papers tried to develop more detailedmodels of the consistency of students' reasoning, or to subdivide a sample ofstudents into intellectually similar subgroups. The problem of taking a set ofdata and separating it into subgroups where the elements of each subgroup aremore similar to each other than they are to elements not in the subgroup hasbeen extensively studied through the methods of Cluster Analysis. This methodcan separate students into groups that can be recognized and characterized bycommon traits in their answers, without any prior knowledge of what form thosegroups would take (unbiased classification). In this paper we start from adetailed analysis of the data coding needed in Cluster Analysis, in order todiscuss the meaning and the limits of the interpretation of quantitativeresults. Then two methods commonly used in Cluster Analysis are described andthe variables and parameters involved are outlined and criticized. Section IIIdeals with the application of these methods to the analysis of data from anopen-ended questionnaire administered to a sample of university students, andthe quantitative results are discussed. Finally, the quantitative results arerelated to student answers and compared with previous results reported in theliterature, by pointing out the new insights resulting from the application ofsuch new methods.

Cluster Analysis of Educational Data: an Example of Quantitative Study on the answers to an Open-Ended Questionnaire