I normally wait until week two, but we had an opportunity that was too good to pass up. Andrew Grzadzielewski, who was a regular Brown Bagger until he left us for points east (way east--to wit, Wisconsin) will be in town briefly. While he was here, he tutored great multitudes of students taking almost all of our standard courses, and he has volunteered to share some of what he learned about how they do and don't learn. More specifically, he says: Math teachers have learned through experience (often their own) that explaining a solution to someone else will often help the one who explains it to retain the mathematical understanding gained by solving the problem. Often, a student with an incomplete understanding of a concept will have trouble explaining it, and many times the effort a student needs to put into a convincing explanation helps the student to clear up any confusion they may have had. Students often find that explaining their solution to others is much more difficult than they realize, and often shows exactly where their understanding is fragile or nonexistent. Given that, I want to share some techniques that I have used to try to encourage students to participate in sharing their thinking. Some ideas have worked well, and some I am still tinkering with. We will meet at 12:30 this Thursday (January 4) in the Math Lounge - come and join us! --