This is an interesting project: teach discrete mathematics not from a textbook, but using the historical papers that first dealt with the topics taught. A bunch of mathematicians and computer scientists at New Mexico State are doing that, and they’re asking for your help: try it out in your courses, write them letters of support for NSF funding. They have two modules on logic: one on set theory (Cantor), and one on computability (Turing’s 1936 paper). Here’s their email that came over FOM yesterday.
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 testing.
Guram Bezhanishvili (email@example.com)
Jerry Lodder (firstname.lastname@example.org)
David Pengelley (email@example.com)
2 thoughts on “Teaching Logic from Historical Sources”
The understanding is NOT all in the proof. Think, by definition-theorem-proof style lectures – even if they are very well explained – a lot of understanding is lost. Perhaps this kind of teaching can uncover sth of this ‘deeper understanding’ here. ( … hmm – so is that all, then?) Posted by markus
This seems like a great idea. When I took recursion theory, we had to write a largely exegetical paper on some big result in the field. Some of the suggested papers were the classics, like Turing’s or Church’s. I chose Turing’s On Computable Numbers. Working through his essay and a commentary on it were quite helpful in seeing the development of the ideas of computability. At least it made it much clearer why the primitive functions were chosen as they were. It is definitely a worthwhile project. Posted by Shawn