Welcome to the third volume of Research in Collegiate Mathematics Education
(RCME III). For an introduction to the series of volumes see the preface to
RCME J, which appeared in this CBMS series in 1994; for a general introduction
to the field of research in undergraduate mathematics education see the first
chapter in that volume, by Alan Schoenfeld. In this preface we focus on providing
brief introductions to the papers that appear in this volume.
In the three years since we began this enterprise, we have tried to have these
volumes grow with the field, reflecting the broad spectrum of work done by
researchers concerned with collegiate mathematics education. In journal-like
fashion, we consider papers independently and publish those that we think reflect
or advance the state of the art. Nevertheless, it still makes sense to structure
the collection of papers that have been accepted, for purposes of coherence and
to introduce the content and methodological issues they deal with.
In Volumes I and II we established the tradition of bringing each volume to a
close with an article focusing on open questions in the field and/or suggestions
for future research. Volume I presented Lynn Steen's "Twenty Questions for
Research on Undergraduate Mathematics Education," an attempt to "define the
challenge and frame the debate" concerning the role of education research in the
mathematics enterprise. In Volume II we printed a list of 18 questions raised
at the first Oberwolfach conference in Undergraduate Mathematics Education
that was held in the Fall of 1995. These are a combination of 18 research and
curriculum questions that have no special status other than that after several
hours of discussion 24 people at a conference agreed that they are important. In
this volume we close with a paper by Annie and John Selden that presents a set of
questions that arose during the first annual Conference on Research in Collegiate
Mathematics Education held at Central Michigan University, September 5-8,
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