Grading, talking, and experimenting

For a change of pace today, instead of doing the warm-up at the beginning of class, I graded quizzes while Mrs. Colwell gave the lecture. I made sure the students knew I'd be happy to answer questions during class, but only a couple came over to chat. One conversation was about math, and in the other I had a trickier problem. Tricky problem first:

• student: "someone stole my backpack"
• me: "uhh... wow. that sucks. you should get it back."
• s: "but I don't know who took it! I had my friend watch it on Monday, but she left it there and when I came back it was gone. It had four books. I didn't even tell my mom. She would be so mad"
• me: "uhh... you have no leads as to whom might have it?"
• student: "well... I think I know. This boy on tuesday said 'where is your backpack?' and I was like 'how did you know it was missing' and he was with my friend who I left it with on Monday."
• me: "so it sounds like he has it."
• s: "but I don't want to accuse him of having it."
• me: "Actually, a couple of weeks ago, my bike was stolen. It made me really mad, because it is my primary mode of transportation. You know who took it? My friend that I work with. I felt really bad accusing him, but I just knew it was him. Still... I didn't say anything and I called the police first. Sure enough, it was him and the police made a trip out to my place for no reason. You should ask this boy if he has your bag."
• s: "but what if he doesn't? he will be mad"
• me: "ask him if he can help you find it."
• s: "oooooh. that may work."
  

Boy was I glad that that advice seemed to be sufficient. What do you tell someone who has lost everything they use on a day-to-day basis? I felt almost as helpless as she must. Needless to say, the math question was relatively simple compared to that.

Grading quizzes today, it was good to see a lot of high scores for my first class. Our genius friend mentioned before didn't perform as well as I think he can, but we did get a chance to talk about one of my favorite "math" games: Nim. In Nim, there are three piles of stones. On your turn, you can take any number of stones from one pile. Your opponent then does the same. Whomever takes the last stone wins. In a standard game, the piles begin with 3, 5, and 7 stones each.

The great thing about Nim is how easy it is to pick up and how quickly patterns start to emerge. For example, after you've played a few games, you realize that if, after you move, there are two piles of the same size, you can always win. Another pattern is that if there are piles of 1, 2, and 3 stones you can always win. Generalizing, there is a really neat trick you can use to figure out if you can force a win, but we'll save that for later. I showed a few students this game when they had a few spare moments and told them to play it a lot, hinting that "like tic-tac-toe, you should be able to figure out who is going to win." The students seemed really interested and excited, so we'll see if they've figured any tricks out later.

Mrs. Colwell really seemed to appreciate the grading, and I can understand. With so much homework (daily), so many quizzes (weekly or so), and so many tests (every few weeks) and so many students (most of these classes are around 30 students each), there's a lot of grading to do. Mrs. Colwell says sometimes she grades until 9 before she has a chance to do anything else. Talk about long hours!! Grading today was actually pretty fun. After stumbling over the first few, it became easier to explain the trick for a given problem to a student right on the test. Hopefully they are able to decipher my chicken-scratch handwriting and it's useful. It was also good to see that a number of students were able to get the really hard problems and were only getting tripped up by a silly reading mistake. I always thought that was the hardest part of math: translating sentences into symbols. Some students seem to have the same problem, while other continue to struggle with symbol manipulation.

During lunch today, Mrs. Colwell and I sat down and discussed our goals for the semester. Mine are pretty straightforward: be as helpful to Mrs. Colwell and the students as I can, while trying new things, without causing trouble. Mrs. Colwell's included:

• increasing student achievement using her teaching fellow
• maximizing utility of the extra teaching fellow body
• having some interesting presentation (~10 minutes) related to lecture and including engineering applications

While I agree that this program (the UM-YPSI partnership) should do a good job advertising engineering to potential engineers, my focus is less on selling engineering as a career choice as showing the beauty of math. This may seem antithetical, as I am an engineer and it is only natural to validate one's career choice by pushing other towards it, but I strongly believe that a stable math education is accessible to all (including those not engineering-inclined), should be enjoyable, and is fundamentally more important than knowing what it's good for.

In the area of testing out new things, tomorrow Mrs. Colwell has given me the go-ahead to try out a new format. In this first experiment, we're going to see if it's possible to keep everyone interested, teach a subject, and do all the normal stuff we do (collect homework, grade homework, pass back homework, give new homework assignment, etc) all at the same time. In tomorrow's experiment, the plan is to go something like this:

• Split the students into small groups (3-6 ppl/group)
• Put some problems on the board for students to work on in teams
• While doing all this, be collecting/grading/passing back homework (I really do like parallel processing. In case you don't believe me, check this out.)
• Collect a sheet of answers from each group, possibly for use as extra credit.

My hope in the future is to randomly select students from groups to answer questions, with the extra credit for the entire group depending on a correct answer (giving an incentive to make sure everyone understands the material), but tomorrow's experiment is just to probe the waters to see what we have to work with, and if anything sticks out as great or horrible. As I may have mentioned previously, I have some big hopes for group work with the following rationale:

• Bored over-achievers will have an opportunity to share their knowledge
• Attention-seeking students will have more people to ask questions of
• Questions common to all groups will pop up, allowing these to be addressed with the whole class
• Mrs. Colwell and I will have an opportunity to devote more personal attention to those that request it
• The format is superficially less quiz-like or test-like, while helping promote quiz taking strategies in a different way:
• What does this problem mean?
• How do other people solve it?
• What ways work best for me? etc.

One concern that Mrs. Colwell expressed is that time may be an issue: what if we're unable to cover the material we want to cover with these new activities? My goal is to not only not fall behind, but to eventually work up to covering more than one chapter in a day. I suspect some will find this unrealistic, but I am confident we at least will be able to keep the regular pace. Lofty goals are good ones. That, or the motivational posters that tile the Ypsi high walls are lying.