Last day of 2009

I went in on Friday, the last day of school before the winter break, and we had a half-day with only 2nd (accelerated) and 3rd (non-accelerated) hours. I wanted to try another problem of the week (POW), and I tried the "congruent rectangles" problem that was featured in the training session with the Math Forum folks. This problem definitely looks like a math problem, so I wanted to spice it up a bit, and I began by talking about money, and then about foreign money. We briefly discussed the European Union and the Euro, and then I showed the graphic, which I superimposed 5-euro notes onto. So instead of asking the dimensions of random rectangles, I was talking about the dimensions of money. The main reason I didn't use American money was because the shape was better (or more, the students aren't familiar with the shape of Euros, so I could stretch them to make them work), but I think it also gave some valuable side information - "fun facts" to break up the math tedium.

The talk about money and Europe was actually pretty good, and the students participated and were interested. When we got to the actual problem though, the students struggled. As usual, I gave them time to notice and wonder, and some of the observations included the fact that four sideways bills are the same length as three horizontal bills - which is a very important observation for setting up the problem mathematically. After listing and discussing the noticings and wonderings, I then presented the problem and asked them to see if they could solve it. The students in both classes struggled with this. They seem to not grasp the concept of area, which is something I really expected them to understand by now. So, in both classes, I ended up walking them through how to solve it, but it was more of me doing the problem and a handful of the students paying attention and following, which is not really the goal of the POWs. I sent Annie from the Math Forum an email about this issue last week, and hopefully she'll have some insights about how to make these POWs work better for our classes.

Second POW and Rollercoaster Discussions

Last Tuesday, I came in with a three-part slideshow. The first part was to complete the "Filling Glasses" activity from last week, in which some of the classes were further along than others. The second part was a two-slide discussion on computer viruses - one of the students mentioned last week that he was interested in learning more about viruses, so I wanted to oblige him. I first discussed biological viruses and what they are and how they work, and then moved on and talked about a few different types of computer viruses. I only intended it to take a few minutes, but this discussion lasted upwards of 10 minutes in most classes. Finally, I had the "Adding Areas" problem of the week for the classes that had time left over. Second hour is shorter because of math intervention, and they had a lot to finish covering with the first POW, and so we just finished the talk on viruses when the bell rang. In third and fourth hours (non-accelerated geometry), we started the new problem of the week. They seemed attentive for the talk on viruses, but it seems like I lost them with the problems of the week. It felt less like they were doing the problem and more like I was explaining the answer to them, and this is not the goal of the problems of the week. In fourth hour I pretty much had to tell them exactly how to do this, which is exactly what the problem of the week tries to avoid. I had even put up all of the necessary equations, so it was just an algebra problem. I feel like they just aren't taking this seriously, and many of them just sit there and do no thinking or talking during the activity. It was extremely frustrating. Sixth hour went well, but we only had about 15 minutes for the POW, so we had to rush through it, and since I don't plan on returning to this problem, I essentially showed them how to do it.

This problem of the week was not nearly as successful as the first one, and I suspect is because of a combination of several factors: (1) it's not as interesting-looking as the filling glasses problem, (2) it looks like a math problem that the students might find in a textbook, and (3) I didn't relate it to anything practical that the students might see in real life. I tried very had to find an interesting problem in the POW database that relates to geometry, and this one just wasn't interesting enough to keep the students engaged.

This Tuesday, I came in a with a discussion about rollercoaster design. As I've given similar talks in the past, I started out by asking why we have rollercoasters and what designers should consider. Next, I showed a picture of the Millennium Force at Cedar Point (which showed the big hill at the very beginning, particularly the structure that holds the hill up), and I asked them what they noticed and wondered about the picture or the rollercoaster in general. As I hoped, they all mentioned something about the structure holding it up and how it's composed of many bars. I then talked about triangles and why the angles in the structure matter to the safety analysis of the rollercoaster. I then drew a part of the truss structure that consisted of six congruent triangles, and tried to walk them through how we know the triangles are congruent and how congruent triangles are helpful to the designers.

Second hour went very well, and the students were attentive and able to respond with interesting and entertaining responses. It felt like we were having a fun conversation. When I got to the talk about the congruent triangles, some of the students were able to quickly give the answers to why they were congruent. Third hour was different. Most of them seemed interested at the beginning when we were talking about rollercoasters and why we have them and cool tidbits about the rollercoasters they've been on, but once I started talking about triangles and angles, many of them zoned out. When I asked questions about why two angles are congruent, which should be very easy for them if they are following the class material, they really struggled to get the correct answers, and many more continued to drop out of being interested. Fourth hour (which is also the non-accelerated version) was actually great - there were several students who contributed and responded to my questions, and I didn't lose them quite like I lost the third-hour students when I started talking about lines and angles. I can't think of anything that I did differently, so even though they are both in the same level of geometry, there seems to be a stark difference in the way they respond to me, and I need to figure out a way to adjust accordingly. Sixth hour also went well, as the students seemed engaged and were responsive. This is a discussion that I would be very confident repeating in the future with high school students.