In this paper, we distinguish between two ways that an individual can construct a formal
proof. We define a syntactic proof production to occur when the prover draws inferences by …

How do undergraduate students cope with abstract algebra concepts? How should we go
about researching this question? Based on interviews with undergraduate students and on …

In this paper I describe a local instructional theory for supporting the guided reinvention of
the group and isomorphism concepts. This instructional theory takes the form of a sequence …

Group isomorphism and homomorphism are topics central to abstract algebra, yet research
on instructors' views of these concepts is limited. Based on interviews from two instructors as …

This paper reports on a continuing development of an abstract algebra course that was first
implemented in the summer of 1990. This course was designed to address discrepancies …

This paper is one in a series of studies by members of the “Research in Undergraduate
Mathematics Education Community,” orRUMEC, concerning the nature and development of …

Many studies in mathematics education research occur with a nonrepresentative sample
and are never replicated. To challenge this paradigm, I designed a large-scale study …

The purpose of this paper is to describe the process by which a pair of undergraduate
students, participating in a teaching experiment, reinvented (with guidance) the concepts of …

Well, if you were inclined to answer in the negative, then you are up for some surprises, just
like we were. As it turned out, our students did find a connection. In fact, 20 students out of …

This research aimed at determining student errors in completing abstract algebra tasks. This
study can be catagorized as descriptive research involving 31 college students of …