First Problem of the Week

Last Tuesday, I brought in a talk that combined two previous talks that I've given. I started out preparing to discuss the idea of tolerance in measurements, which I discussed in Ms. Tran's geometry classes last year, and I decided to add on a section discussing nanotechnology at the beginning, which I talked about with Mr. Lancaster's class two years ago. I started by asking them what nanotechnology was and we broke it down into "nano" and "technology", and then we discussed some applications of nanotechnology in sports equipment, medical devices, and electronics. We then talked about how they are made, which requires an expensive clean room, and I discussed a company that I started as an undergrad that dealt with this. I thought that they would be interested in the fact that I started a company, but that wasn't really the case in the first class, so I cut it from the second class when I noticed that I already had low attention from the students. I then shifted the conversation to tolerance, and we talked about the use of decimal places and what they mean (e.g., what is the difference between 90 degrees and 90.0 degrees?). This led into the idea of "allowed error" or "tolerance": how much variation from the exact number we can tolerate in our design. I concluded by discussing the reasons for this and a few examples of products that have large or small tolerance.

This talk was not as successful as some previous talks. Two problems that I can identify are that I may have crammed too much into one talk (nanotechnology, startup business, and tolerance), and that I didn't have enough visual aids. Second hour (accelerated) was mostly attentive, but I could tell that there were several times when I was losing the students. Third hour was tougher, and I even skipped a few slides to get through it quicker. There were many students in third hour who were talking throughout or put their heads down. At one point, I went over toward two girls who were constantly chatting and said "can the two of you over here please be quiet?" which was followed by an exaggerated and sarcastic flinging up of the hands and, "of course, anything for you!" This is really hard to deal with - the students in this class really don't have the respect for me that some of the other classes do, and earning it back is proving to be a huge challenge. Fourth hour went better - fewer of them had their heads down, and it seemed like most of them paid attention for the whole talk. Sixth hour, as usual, went better than any of the others, and I felt like most of the students were attentive, although this talk still wasn't as exciting as some of the previous ones, so I didn't feel very much energy.

Today (Friday) I came in to make up for last week, when there was no school on Tuesday. This was our first attempt at a Problem of the Week, and Ms. Tran gave me between 20 and 40 minutes in each class to lead the students through the "Filling Glasses" problem from Drexel's Math Forum website. To start out, I passed out handouts for each table (two students in each table, and I wanted to conserve paper) that contained just the pictures associated with the problem: three glasses and four graphs, and i alos . I then went through the "think, pair, share" technique for noticing and wondering. Finally, after we had two nice lists of things that the students noticed and wondered, I posed the question: if the glasses were filled with water at a constant rate, how would the height of water in the glass change over time? Which graph corresponds to each glass? I again asked them to think, pair, share, this time giving them less time. Then, there was a bonus question, which was to draw a glass corresponding with the final graph, and at the end we reflected on what we did and how it's applicable to geometry.

In first hour, we ran out of time. We burned through 20 minutes very quickly, and while we had started discussing the answers, by the end I don't feel like the entire class was fully convinced of which answers were correct. I also didn't get to ask the bonus question (what kind of glass would correspond with the fourth graph?), nor did we get to reflect on how this technique is applicable to geometry. In third hour, the students actually participated a lot more than they normally do (there were still 2 or 3 students who put their heads down, but everyone else participated): we got through the answers to which graphs match up to each glass, and then we started to talk about what the fourth glass would look like. We didn't get to discuss that part, but a couple of people drew their guesses on the board - I took a picture of it with my cell phone so that next time we can remember what we were talking about. In fourth hour, we got through the entire problem, and they were actually quite involved throughout the activity. At the end, one of the students declared that this was the best presentation I've ever given, and many of the students agreed. It seems that this problem of the week was a great way to engage the students in the non-accelerated classes (3rd and 4th hours), which is a struggle I've had for a while. Sixth hour also went well, and I got the most active participation from them. We barely finished matching the graphs when the bell rang, so we still need to wrap up in that class next time. There was one student in the front of sixth hour who kept telling me: "I still think it's graph 4", when the rest of the class had concluded that the answer was graph 1. When I asked him to explain why, he'd say that he couldn't explain why, but he still thinks it's 4. I told him we'd talk about it later, but we ran out of time - I'm not sure if he's just busting my chops or if he legitimately doesn't understand what was going on and is afraid of talking in front of everyone, but I will try to talk to him alone next time and see what it is that he's thinking.

Over all, I think the problem of the week was a success, and I look forward to future sessions of POWs.