APPLYING CLUSTER ANALYSIS TO PHYSICS EDUCATION

One major thrust of PER is the identification of student ideas about specific
physics concepts, both correct ideas and those that differ from the expert consensus.
Typically the research process of eliciting the spectrum of student ideas involves
the administration of specially designed questions to students. One major analysis
task in PER is the sorting of these student responses into thematically coherent
groups. This process is one which has previously been done by eye in PER. This
thesis explores the possibility of using cluster analysis to perform the task in a more
rigorous and less time-intensive fashion while making fewer assumptions about what
the students are doing. Since this technique has not previously been used in PER,
a summary of the various kinds of cluster analysis is included as well as a discussion
of which might be appropriate for the task of sorting student responses into groups.
Two example data sets (one based on the FMCE the other looking at A2D are examined
in depth to demonstrate how cluster analysis can be applied to PER data and
the various considerations which must be taken into account when doing so. In both
cases, the techniques described in this thesis found 5 groups which contained about
90% of the students in the data set. The results of this application are compared
to previous research on the topics covered by the two examples to demonstrate that
cluster analysis can effectively uncover the same patterns in student responses that
have already been identified.