Teachers As Scholars (Steven J Miller: sjm1 AT williams.edu)

"A-ha!" Moments in Mathematics and the Sciences

Monday January 13 and Monday February 3, 2014
Harvard Hillel, 52 Mount Auburn Street, Rabb Hall (1st Floor)

Videos and Links for Topics: Below are the videos of the main items I presented at the sessions, as well as some links and supporting materials by myself and the class; discussions among participants was not recorded. Feel free to share these resources with anyone you wish. These are meant to be just quick summaries to remind you of what we discussed; if there are items I can add to make these more useful, just let me know. I'm happy to work with you on creating units for your students (and if that means having me do new lectures and record and upload them from Williams, I'm happy to do that).

Description: There are many stages and approaches to solving a problem. Before trying to find a solution, it's often a good idea to determine if one exists, as if it doesn't our search will be fruitless! If we're fortunate enough to know there is a solution, the next step is to find it. Oftentimes we can solve a problem through brute force approaches, but these are inelegant, give us no greater understanding of the problem or why the solution works, and frequently cannot be generalized to related problems. The goal of this seminar is to introduce you to alternatives to brute force. There are many examples throughout mathematics and science where, if you look at the problem the right way, what was originally a long, involved calculation evaporates into a wonderful `A-ha!' moment! We'll draw examples from problems that can be solved by tedious, long computation as well as quick arguments if viewed the right way.

Probable topics, comments and reading:

Math Riddles
I also maintain a math riddles page. Please feel free to share these riddles with your colleagues and your students, and let me know if there is anything I can do to make the site more useful for you and your classes. The goal is to continuing expanding the student / teacher's corner to facilitate using these in classrooms. If you or any of your students are interested in helping (a great item for the CV!), or want updates on the progress, let me know.