[FOM] Teaching with original historical sources

Guram Bezhanishvili gbezhani at nmsu.edu
Mon Nov 20 19:07:36 EST 2006

A team of mathematicians and computer scientists at New Mexico State
University and Colorado State University at Pueblo has developed an innovative
pedagogical technique for teaching material in discrete mathematics,
combinatorics, logic, and computer science, with National Science Foundation
support for a pilot project. Topics are introduced and studied via primary
historical sources, allowing students to participate in the sense of
discovery, and to appreciate and gain motivation from the context in which
concepts were developed.

For example, we have authored classroom modules in which students learn
mathematical induction from Pascal's "Treatise on the Arithmetical Triangle,"
written in the 1660's. Another module develops the short recursion relation for
the Catalan numbers from a seminal paper of G. Lame in 1838 (based on a
start by Euler!!) We also have authored modules on binary arithmetic, based
on the original historical sources by Leibniz and von Neumann; on 
infinite sets,
based on original historical sources by Cantor; and on Turing machines, and
Church's Thesis, based on original historical sources by Goedel, Church,
Turing, and Kleene.

We have authored 18 modules so far; all these modules and more information
can be found at www.math.nmsu.edu/hist_projects/.  The modules will appear
in a chapter of a forthcoming MAA resource book for teaching discrete
mathematics. We found that 65% of the students who completed a course with
these historical projects performed equally well or better than the mean GPA
in subsequent mathematics and computer science courses.

We are seeking to expand our pilot program with further major support from
the National Science Foundation to create a full book with a comprehensive
collection of classroom projects based on historical sources. We would like
to invite any instructors of mathematics or computer science courses to
agree to site test future projects in related courses in discrete
mathematics, combinatorics, logic, or computer science, or perhaps even to
design your own projects. We hope to be able to provide a little NSF
support as travel and/or consulting for site testers.

If you think that you (or a colleague) would be interested in teaching with a
project during 2008-2011, we would like to hear from you.  We plan to finalize
our new NSF proposal by mid-December, and would like to attach a brief letter
of support from you if you are interested.  It would be nice if it 
indicated the
institution, the course, nature of students, rough timeframe, why you think
it would be good for your students, and possible choice of projects for your

Contact persons:
Guram Bezhanishvili (gbezhani at nmsu.edu)
Jerry Lodder (jlodder at nmsu.edu)
David Pengelley (davidp at nmsu.edu)

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