Final days at Ypsi High

I'm not good with goodbyes, so I'll just spit it out: this is my last post of the year. This academic year has had its ups and downs, but I certainly continue to learn a lot about teaching, about high school students, and about engaging non-technical audiences in interesting topics related to technical things. In my last two days I had the opportunity to do a design activity, which was bridge building out of candy (the same activity that I did with the students at the Expo in December), and I had a while to talk about my research on vehicle design optimization. These both went really well, and it was a great way to close out the year in these classes.

Last week I did the bridge building activity in the second and third hour classes. Since it was a short day, fourth and sixth hours didn't exist, so I suppose they missed out. I started with a brief slideshow talking about bridges with examples of good design and bad design, and showing them what a truss (triangular structure) is and why they are stronger than square structures. From here I gave them their task: to design and build a bridge (in teams of 3) using only gum drops and toothpicks which would span 11 inches. Ms. Tran helped them out by telling them that their participation would be graded, and winning any of the four awards would give them extra credit on their progress reports coming out the next day. The class was shorter than the activity was designed for, so we only had about 25-30 minutes to design, build, and test. I gave the students 5 minutes to just plan their designs and sketch them out before I even gave them the materials, and then they had about 15 minutes to build. Particularly in the first class, we were extremely pressed on time, and with less than 5 minutes left it was clear that they wouldn't finish, so I changed it from 11 to 6 inches. It turned out that 6 inches was way too easy! The students' bridges withstood all the pennies (weights) that I brought and even went through most of Ms. Tran's change. They did a nice job though, even though we ran out of time during testing. In third hour we were able to get through everything, this time with 8 inch bridges. For the most part, the students got very into this activity, and the group sizes of 3 were good to make sure everyone was able to contribute. I'd do this again.

Today I wanted to finally talk about my research, since I haven't directly shared it with the students yet. I started out by telling them that when I'm not in their classroom, I'm at U of M working on computers running simulations and analyzing data for my research. I used this opportunity to remind them that as a graduate student I'm getting paid to do this research, so it's sort of like a real job. I started out with some videos of the crash and blast simulations that I've been running, just to give them something interesting to look at and grab their attention. I then introduced the phrase "design optimization" and asked them to define it. I'm still surprised at how few students know the term "optimal" or "optimize", but there was always some student that could give us the gist. I then asked what the "optimal" or "best" car would be? Is it the safest car? most fuel efficient? best looking? least costly? fastest? The students often replied that it should be all five, but I suggested that this isn't the case and cited examples of vehicles that are among the best in certain categories, but seriously lacking in others. Next I explained that in order to evaluate cars on these criteria, we have to be able to quantify each of the objectives, and I gave the example that we quantify fuel efficiency using miles-per-gallon (mpg), but in other places they use gallons per mile or liters per kilometer. Next I actually gave them some time to think about how to quantify the other four objectives, and asked them to talk in pairs about them. Most students seemed to actually spend the minute or two that I gave them to discuss this (which I considered a huge success), and in the end they were able to give some good ideas on how to quantify these things. I explained in the end that this is the most important and perhaps hardest part: formulating problems mathematically with numbers. I then continued to talk broadly about some of my research in both the commercial vehicle sector and military vehicle design, discussing the problems as well as some of the things that I've found in my studies. I closed out and asked if they had any final questions for me.

One of my challenges with this talk was in keeping it simple enough for the students to understand and follow, yet still showing something meaningful. In the end I showed less meaningful things, but brought up some interesting discussion topics that the students were able to participate in. I think the think-pair-share activity was useful in that it gave those who were interested an opportunity to think about the questions I posed, and we got more participation this way than normally. Second hour was very receptive in general, and one of the students asked what he should do if he wants to get into vehicle design for a career - I think he was already interested in this area, but my presence might have strengthened that interest, which I consider a success. Third and fourth hours were slightly less engaged in the latter part of the presentation where I discussed my research, but they were still polite and receptive to me. Sixth hour, as usual, was rowdy but respectful, and many of the students contributed to the discussion and asked questions. All in all, I think this was a great way to close out the year, which lets me leave with a fairly positive attitude toward my students and my contributions at YHS. Thank you to everyone who made this experience possible!

Reduce, Reuse, Recycle

No, this post isn't about environmental friendliness. In the last two weeks I gave presentations that I "recycled" from last year, both of which went pretty well once again. Since I used them both last year and they both went well, I allowed myself to be lazy and only made a few minor changes from the old slides. As a result, I can say that they both went well, though not exceptionally so. As is often the case, many of the students checked out early and quietly ignored me for both talks, but I did feel like there were a good number of students who stayed with me and as a result learned a few things.

Last week's talk was about the angles that are important when steering a car. I started out by showing a video that had a Corvette driving along a curvy road before spinning out because of driving too fast and taking the curve too hard. So I posed the question: why do cars spin out? Most of the answers revolved around poor driving or poor car maintenance, so I pushed them to continue brainstorming and come up with the more specific cause: the tires of the car slip against the surface of the road. So then I asked the students whether the wheels of the car turn at the same angle as the steering wheel, and usually got a resounding "no", which is good. Power steering makes it so that we can turn the steering wheel almost a full turn while the wheels only rotate 20 or 30 degrees. Next I asked whether both front wheels turn at the same angle, and most people thought the answer was yes. I spent the next couple of slides showing them why the tires should turn at different angles - the inside wheel (with respect to the turn) needs to turn a little bit steeper because it's revolving around a tighter turning radius than the outside wheel. We then talked briefly about handling and how at high speeds, the tires of a car slip on the road, and if there is too much weight in the back of the car, that might cause spinning out to occur more easily. This was a fairly quick talk (less than 15 minutes), and I did get the impression that the students were engaged and many of them learned a few things or at least will think a bit differently next time they are in a car.

This week I talked about flight. I started out with a cool, somewhat funny video that showed some early attempts at flying and mostly how some elaborate machines broke down after they started moving. We then talked about some of the reasons that we fly (we can go really fast, avoid obstacles, it's safe, it gives the military more options), and then we went through the three main types of aircraft that we see: blimps, airplanes, and helicopters. With blimps, we fill it with a gas that is lighter than air (I showed a periodic table to illustrate what gases are lighter than air), and heat it up or cool it down to make it lift or lower the weight in the cabin. With airplanes, there are a lot of complex forces going on, but the important force is lift, which is controlled by the speed of the aircraft along with the angle that the wings hit the air. I spent a little bit of time discussing those angles, but tried not to talk too long for fear of losing students. I ended by briefly discussing how helicopters work, and how the speed and the angles of the main rotor affect the lift of the vehicle. I think on the whole it was valuable and I think that some of the students gained some higher understanding of the challenges and current methods in flying work.

Explosives & Scaling

Two weeks ago, I came in with an updated version of my talk on explosives, and I was very pleased with the response I got in all of the classes. I start out with a short video clip that shows two military vehicles driving on a dirt road, and a land mine detonating between the vehicles, which does a great job in grabbing the students' attention. I then pose the question: what if the humvee had been directly above the explosion? What would happen to the vehicle? What would happen to the occupants? The students are actually very good at coming up with responses - usually at first someone says, "the vehicle will explode," but when I push them harder to be more specific they'll say something about the vehicle being thrown into the air and possibly deform. I then pose a question regarding how we would learn about the effects of explosives on vehicles so that we can design safer vehicles, and get them to say something about physical or virtual testing. Everyone agrees that physical tests are expensive, so we talk about scaled-down testing, which is something that I did as an undergrad while at the University of Maryland. This is also something that ties in directly to their current classwork, which is on proportions and ratios. So, I show them how I scaled down my tests, and what the relevant proportions are, and hopefully everyone is able to see how scaling can be useful in real life. At the end, I ask a question about what other professions might use scaling/proportions, and the students were able to respond really well with examples about architects, rollercoaster designers, maps, etc. Second hour (accelerated) went fairly well, though the morning classes are less responsive since it's so early. Third hour (non-accelerated) was also very attentive and respectful, and we went all the way until the bell rang. Fourth hour (non-accelerated and usually my toughest crowd) actually seemed to really like it. The students actually sat through the dismissal bell while I continued talking, which both Ms. Tran and I were extremely impressed with - that may be my most successful moment so far with this group of students.

Today is the day before the students' Chapter 8 test, and so I came in to help the students with their in-class practice tests. I don't have anything eventful to talk about, but I did get a feeling that many of the students are more comfortable with me than they have been, and asking questions of me wasn't so bad. It seemed like there were enough questions to occupy me throughout the three class periods that I was there for, so I consider that a meaningful three-hours' work.

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.