Many
studies in mathematics education research occur with a nonrepresentative sample
and are never replicated. To challenge this paradigm, the author designed a
large-scale study evaluating student conceptions in group theory that surveyed
a national, representative sample of students. The author illustrates the
potential of replication studies to refine theory and theoretical propositions
in 3 ways: by offering alternate interpretations of student responses, by
challenging previous pedagogical implications, and by reevaluating connections
between theories.