Teaching Students to Prove Theorems

For the last several summers I have had the pleasure of presenting a workshop on "Teaching Students to Prove Theorems " to the Project NExT fellows. Here are the resources used in the presentation I gave at Mathfest in Knoxville, August 2006.

• Teaching Students to Prove Theorems ---This powerpoint presentation was used to make static slides. There are no "special effects." They can be printed out, as shown, with no loss of information.
• Handouts
• Exploring Conjugation with GAP---this exploration was written by Judy Holdener, Associate Professor of Mathematics at Kenyon College. Click here to see a copy. Judy has other interesting GAP projects in her classes. The complete set can be found here.
• Equivalence Relations and Partitions---This link is only to an introductory page. The main portion of the handout was an excerpt from the book Chapter Zero---Fundamental Notions of Abstract Mathematics, 2e by Carol Schumacher. (Addison-Wesley, 2001). Mathematics faculty members interested in the book may obtain an examination copy here.
• Discovering Trees---This is a discrete math activity that I wrote to introduce the concept of a tree. (The "short" form of the assignment that I gave as a handout is here.)
• Sequence Convergence in Real Analysis---In-class activity to help students make sense of the first limiting process ("epsilonics" definition) in a real analysis course.
• Problems and Scenarios---This handout is a duplicate of the last part of the Powerpoint slides. It presents 5 common (but tricky) classroom scenarios. The workshop participants are challenged to come up with practical solutions for their students.
Several people who attended Project NExT workshop expressed an interest in the instructor's companion to Chapter Zero. The first half of the Instructor's Resource Guide describes the pedagogical philosophy and class procedures that Carol Schumacher uses when she teaches a course out of the book This portion of the guide may be of interest to anyone who is teaching a course in which students are asked to prove theorems, particularly when the students do not have a great deal of prior experience in abstract mathematics. The second half of the guide more specifically addresses the nuts and bolts issues associated with the book itself and will be less interesting to those who are teaching from a different text.

Click here for the most up to date set of known errors in the book Chapter Zero.

E-mail:  schumacherc@kenyon.edu