Robots & Lecturing On My Own

One of my students has suggested multiple times that I talk about robots, so two weeks ago I came in with a presentation on robots, trying to link them in with geometry by discussing how all robots have rotating parts (tying into the degrees of freedom talk the previous week) and they all use logical arguments in sensing and responding to their environments (tying into the conditional statements talk from the beginning of the year). I began with a screenshot from the movie "I, Robot", and asked them if it was realistic for the world to be that way in 2035. Most of them said "no", and I reminded them that the book was written 60 years ago, and that's what some people expected would happen. I then asked them their thoughts on what defines a robot, what robots are useful for, and what they have in common. I concluded by showing several examples of existing robots including the roomba vacuum cleaner, toy robot dogs, auto-manufacturing robots, the military packbot, and the mars rover. I tried to emphasize the if-then statements that are programmed into these examples, and talked some about the degrees of freedom and the motion of each. I hope that this showed them that some really cool and useful things can come out of applied geometry. The student from second hour who had requested a talk on robots, D, said at the end that he wanted to hear more about "realistic" robots. Apparently he was referring to human-like robots, which are really not used in practical applications at this point. I tried to explain that what I showed really are realistic robots that are in use right now, but it seems that he was disappointed that I didn't talk about any prototype android robots that are under development. The classes all responded fairly well to the talk, and it seemed to arouse more interest in fourth hour than I've been able to do all year (though there was still a lot of chatter, it seemed to be on-topic), which was terrific. Sixth hour again asked lots of questions, and Ms. Tran and I cut them off after a while.

Last week, Ms. Tran was out, and I had the opportunity to teach two days' worth of lessons. She left me the notes, and my job was to teach the students from those notes, and have them work on an in-class worksheet as we went through the material. On the first day, I used the ELMO projector, which projects anything (paper, calculator, book) onto the wall, so I simply used her notes and talked through them with the students. Some students had trouble keeping up, and the writing was a bit too small for many, but in general we were able to get through the notes in every class. On the second day I used the traditional transparency overhead projector, and I wrote out the notes along with the classes, so I was able to write bigger and write at the same pace as them. This went much better, as most of the students kept up with me and were able to listen to my explanations. I was surprised at how long it took to get through a mere two and half pages of handwritten notes, and it took most of the hour to do so. Fourth hour was again problematic for me - many of the students sat in the back and just talked constantly. I know that this is distracting for the few students that actually wanted to take notes and learn the material, but as hard as I tried to ask them to show some respect, it never seemed to hit home for at least half of the class. I am again at a loss for how to deal with this group of students.

Transformations in Shaun White and Tetris

Two weeks ago I had a bad cold and didn't come in for my normal Tuesday appearance in Ms. Tran's class. I came in the following week, and I was surprised to receive a "get well soon" card from my 2nd hour class, which was really nice. It feels good to know that I was missed by at least a few of the students to take the initiative to do something like this. I had no prepared presentation last week, so when the students had 10-15 minutes for in-class problems at the end, I walked around the room and helped them with their work. I was planning to come in yesterday to make up for the missed week, but when I woke up I had a beautiful email from Ms. Tran informing me that it was a snow day in Ypsilanti! Snow days are awesome, and the great University of Michigan should start having them - it was a wonderful day until I realized that I'm still responsible for doing research, so I went into (my) school anyway. I'll make up my missed day in two weeks (barring any more distractions).

Today I came in with a discussion on degrees of freedom in design, which I think was crafted quite well and fit in with their unit on tranformations. I was planning to open up by talking about the game of Tetris, but I got an email yesterday about Engineers' Week, which gave a fun fact about snowboarding that I thought was more exciting. So I opened my talk with the video of Shaun White's victory run in Vancouver from last Friday, which was awesome. A lot of the students had already seen this, which was good because I think it drew them into paying attention as the talk was about something interesting, and for those who hadn't seen it, they got exposed to an exciting and quasi-important international event. After we watched the clip, I shared with them a bit about the history of the snowboard (straight from the E-week email), stressing the engineering effort and genius that has gone into the modern snowboard. I then went back to my original talk and brought up a screenshot of a Tetris game. Fortunately, almost all of the students had seen this game (I wasn't sure if it was too outdated, but apparently not), and I was able to get someone from each class to explain what the game was about. I was able to get it out of them that the player actually ROTATES and TRANSLATES the pieces into the desired position. I then asked how this might relate to something that people do in real life, and in second hour a student actually replied with the word "packing", which was exactly what I was looking for. So I showed them a picture of a moving truck packed with boxes and a car trunk packed with suitcases, and almost everyone was able to relate to either moving or packing a trunk for a trip. We talked about how you have to rotate the boxes and suitcases in all different directions and translate them to different locations so that everything fits. I told them that this is a problem that people are studying and talked about how a guy in my research group is working on optimization algorithms to do just that: find the optimal way to pack items of different geometries, particularly all the stuff under the hood of a car. From here, I introduced the idea of "degrees of freedom", and after explaining what they are I gave them a few examples and asked them to tell me how many degrees of freedom each object has: an elbow, a cd, a car on the road, and an airplane in the sky. This brought about some good discussions, and I helped them get to the right answers in the end. I concluded by asking them how many degrees Shaun White has on a snowboard, which we pretty much agreed was the most he could possibly had at 6.

The talk went really well in second hour. There were no significant distractions, the students seemed fairly engaged and attentive, I had students participating that don't always participate, and the examples at the end got them more into it. Third hour also went very well, and there weren't any instances where I asked a question and got no response (which is sometimes the case in third and fourth hours). In fourth hour, which is always the most difficult, Ms. Tran had a talk with the students about respect and listening right before I started my presentation, which I think had a slight positive effect on their behavior. The students were fairly responsive to my questions, and they come up with some good answers, though it still got out of hand with the talking a few times. Sixth hour was also a bit chatty today, and they asked a lot of questions - to the point that it became obvious that they were just trying to waste time so that they couldn't get to the lesson. Ms. Tran eventually cut them off, but I probably should have cut them off sooner. I need to make it clear next time with sixth hour that I am not here to waste anyone's time, and that those types of questions are disrespectful. Despite this, I think that this was an overall successful exercise with a very clear link to what they are currently studying in geometry, and I'm happy with how it went.

The MShoe, Take 3

Yesterday, I came into my geometry classes with a tried-and-true talk that I've given for the past two years on a project that I did in grad school to develop a running shoe that generates power. This discussion is usually a hit with the students, as they seem to really understand this application of science to their lives. I used a model that worked last year, using fewer slides (a shorter version of the powerpoint) for the nonaccelerated students. I start out by explaining that I was working on a graduate school course project, and my team was trying to design a product that would power an iPod through running. Before discussing the product itself, though, I like to talk about energy first - what it is and where it comes from, and why we chose to take it from running. I conclude by describing the project, walking through a quick calculation that we had to do to ensure that there would be enough power, showing the prototype, and passing it around while answering questions about it.

Second hour (accelerated) seemed to enjoy the talk, and it went on for a lot longer than I had planned (probably about 25 minutes). There were a lot of questions from the students, and they were able to point out a lot of our issues that we came across (e.g., waterproofing, too many wires/cables). Third hour (non-accelerated) had some new faces, as this is my first class of the new semester, so I briefly introduced myself to them and gave the abbreviated version of the shoe talk. While they seemed attentive, they weren't responsive to my questions, which makes me feel like they weren't very interested. As a result of the low response, this talk probably only lasted about ten minutes or so. In fourth hour, which is historically less engaged and in which Ms. Tran wanted more time for lecture notes, I dropped the powerpoint altogether and just told them about the project with the prop. This actually seemed to work well, and when I told them what we did, many of them expressed that it was a cool idea and design. I think the brevity and the props helped. I wish that I could do this with fourth hour all the time, but unfortunately I don't have any other cool projects that I can easily bring in to show the students. Sixth hour (accelerated again) also went well, although at times they were unresponsive. Perhaps I over-talked the energy issue and should have stuck to the meat of the presentation (the product), but I always like to make sure that they have some background information and tidbits of knowledge.

Two Minor Victories

This Tuesday, I came in without a presentation and was able to help students with their in-class work. They are reviewing for their final next week, and they had the entire class period to work on a worksheet, and it really should have taken them almost the entire time to finish it. As is often the case, many students simply ignored the worksheet, less so in the accelerated classes, but there were always students who just didn't care to do the work. Of those who did attempt the worksheet, they often moved very slowly because they were socializing instead of focusing on their work. I tried to nudge those students to focus, and it did help some of them keep on track, but there were still a lot of students who didn't get past the first four questions (out of maybe 30). I spent most of the time walking around the room and looking over shoulders to see if the students were doing the problems correctly, as well as answering questions when they arose.

Fourth hour is always particularly difficult for me, as my relationship with these students is still rather tense. There is a particular student, we'll call him J, who simply ignores me most of the time. Often he just walks around the room silently, but today he was sitting with a group of friends playing with a pair of dice. There was no money gambling going on, but he tried to make a bet with me: he said, "if I roll a 7, you have to do my worksheet." So I asked him what was in it for me if he didn't roll a 7, and he said that he would do it himself. While the odds were in my favor and I really wanted him to actually do the worksheet, I couldn't take the chance that I'd lose and do his classwork for him. So, I declined. He rolled anyway, and it wasn't a 7, and I told him that the odds were really in my favor. He didn't know why, so I explained how there are 36 possible outcomes with a roll of two dice, and 6 of them (which I wrote out on the whiteboard) would result in a 7. That would mean he has a 6/36 or 1 in 6 chance of winning. By this point, several students were interested and listening, so I talked a bit more about rolling other numbers (like a 7 or 11, which is used in craps) and how to calculate odds. Little did they know that they were actually learning about probability! Ha! Point: Steven.

There was one more incident of note on Tuesday, and that was in 6th hour. One of the students, I'll call R, who frequently asks for help, was struggling with getting started. I talked him through how to do the first problem, and then continued in my "rounds" walking around the classroom. When I was almost back to him, he crumpled up his paper and threw it in the recycling bin and said "I'm done." I went and got it, smoothed it out, and said "no, you're not." It turns out that he was on the right track, he had just made an error by confusing multiplication and addition. I made sure that he knew what to do, and for the rest of the period, he actually did work quietly on his worksheet. He works very slowly, and he didn't come close to finishing, but I was still happy to see him working for the entire class period. Steven: 2 points, Class: (well, they win when I win, they just don't know it, so) 2 points.

Back-to-School Car Talk

This week, the first week back after the holiday break, I've had the opportunity to spend three full days in the classroom. Ms. Tran is out of town for the week, so I filled in for her on Monday, Tuesday, and Friday. She left worksheets for the students to work on each day, but I wanted to also bring in a technology discussion for the geometry classes. So, I prepared a talk about "the future of cars", as I thought it was appropriate to our location near Detroit, the recent big changes in the auto industry, and the fact that it's now 2010 and all of my friends back home were asking me on New Years where their flying cars are.

I started by discussing hybrid cars and their benefits and how they work, then moved on to electric cars. With that, we briefly discussed where the electrical energy actually comes from, realizing that most of it comes from fossil fuels anyway and thus it isn't all that much "cleaner" than conventional gasoline cars. I then went on and showed them the UM solar car and talked about the interdisciplinary project and the 2500 mile competition. Many students commented on the safety of this car, which is a huge drawback and reason why we don't see things like that on the road - so I compared the solar car to a Ford Taurus just to show some of the important differences that make a Taurus much more practical than the UM solar car. I ended with a slide each on fuel cells and flying cars - I had found a new article discussing the US military's recent interest in flying cars, so we talked about the benefits and practicalities of the concept of flying cars. This was a rather long discussion, so I split it across Monday and Tuesday.

Second, third, and sixth hours all did very well with this discussion, and they were respectful and listening for almost the entire time. Fourth hour, however, had problems. I had even prefaced it on Monday by asking them whether they would rather have a discussion on cars or just start the classwork, and the consensus seemed to be that they wanted to hear the talk. Since I gave them the option, I figured that they would be respectful of me, but that just wasn't the case, and there were several conversations going throughout the class. I tried to ignore them and I tried stopping and giving "the look" until they stopped, but as soon I started talking again it was like I opened a floodgate to talking again. So, after this happened a couple of times, I just stopped. I said, "Okay, I can't do this. You can work on the classwork for the rest of the hour." After some initial protests, it actually seemed to suit all but one of the students fine (although several of the students didn't even touch the worksheet and just socialized for the entire class period). I didn't even try to resume the discussion with this class on Tuesday, and I'm not sure that I want to even try with this class in the future. They have always given me a hard time, and with all of the different approaches I've tried, I just can't find a way to get through to them. Perhaps my efforts will be more efficiently spent just helping these students with classwork and homework.

On Friday I didn't have a talk prepared, so I gave them the hour to work on their classwork, while I walked around and answered questions. I asked at the beginning of 2nd hour whether they thought the car talk from Monday and Tuesday was interesting. Only two people responded - one with a quick "no" and another with a "somewhat." This surprised me, because they seemed interested and almost all of them paid attention for the two twenty-minute-ish sessions. So I asked them what they'd like to hear about in the future, and the only response I got was "bombs" (which I do plan to talk about, as I did research on explosives as an undergrad). Sixth hour had several people say that it was interesting, but still at least one said "no." They gave me a couple of suggestions, and I'll try to address their interests in the future, but I'm realizing that I can't please everyone simultaneously (and there are some people that it seems like I can't please at all!).

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.