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.

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.

Logic and Programming

Last week I came in with a talk about programming in electronics, where we discussed some of the logical arguments that are embedded in the electronics that we use. I started off by saying that the conditional statements that we've talked about so far are things that we don't control, and I gave them a few examples of topics that we've discussed and other things that are relevant to the students. I then posed the question: "What if we had complete control?" My first example was the classic game of snake, which I chose because of its relative simplicity. I showed them a video that I shot where I played through the game and asked them to think about what happens under certain conditions, and afterward I wrote several of the conditional statements that they came up with on the board. I followed this with a more complex example of a program that I wrote over the summer, where selecting a button changed a picture that was displayed. Next, I showed them a piece of the actual code and asked the students what they noticed about it. When I asked them what it meant, they were able to figure a lot of it out, so I pointed out what was an "if" and what was a "then" and where variables were set. I mentioned that this is only a tiny piece of a code, and when you are looking to code bigger things like World of Warcraft or Halo or Super Mario Brothers, there are thousands and thousands of lines of code to deal with. I ended by asking the students to talk to their neighbor (their desks are in pairs) about conditional statements in some of the electronics they use - and I put up pictures of an xbox, a laptop, an iphone, and a digital camera for inspiration. This was kind of a "pair-share" activity. After 60 seconds, I asked them to share their discussions. Many of them came up with non-programming examples of if-thens, like "if I throw my xbox, then it will break," which wasn't exactly what I was looking for, but some of them did come up with good examples. Because of this and the large amount of time it took to get through the presentation in second hour, I took out the part about the program I wrote for third and fourth hours. I think this helped keep the students in those classes more focused and significantly cut down on time.

In the first two class periods, I wrote down the if-thens from the final discussion on the whiteboard, and I asked for volunteers. When I picked on non-volunteering students, they generally didn't have answers for me. So, in the fourth and sixth hours, I told them in advance that they should have something ready to share at the end, and we went through almost all of the table pairs. Third hour was rather disappointing with the amount of interaction I got, but fourth hour went surprisingly well, perhaps because of the changes I made and perhaps because of the tone I've set in those classes during my first 6 weeks. Sixth hour also went very well - I guess I am learning through my experiences in the earlier classes to improve on the later classes. During sixth hour, a student asked if they could see the simulation that I had run to make the program that I wrote, so I showed them a few example videos from that and was able to draw another parallel with the conditional statements. I think this was a good talk, and I am happy with how it went.

Today I came in prepared to do a Problem of the Week from the Drexel Math Forum, but Ms. Tran felt that the students would fall behind if I did. She was absent today, so she had a sub pass out some notes and a handout for the students to work on in class. The students had never learned the material before, so the notes were their only guide to completing this, along with me. Most of the students chose to ask me their questions rather than look them up in the notes, so in 3rd and 4th hours I talked through some of the main points on the whiteboard. In fourth hour in particular, many of the students refused to be quiet while I did this, so I asked the students who were going to listen to come up to the front, and we went through it with a group of 8 or so students. Of course, those who weren't in that group either didn't finish the assignment or had to ask me the same questions later, but I don't know what else to do. Fourth hour got extremely rowdy, to the point that the teacher next door came in and yelled at the students, then called Mr. Brown in to talk to the students as well. I try hard not to concern myself with discipline issues, but it is very hard to not get frustrated by students who feel the need to "rap" loudly throughout the entire class and insist that they are not doing anything wrong. I think a lot of today was a waste of time for many of the students, and I will talk to Ms. Tran about dealing with this situation in the future. In sixth hour, I got everyone's attention at the beginning of class and went over the important points of the notes before passing out the worksheet for about 3-5 minutes. The students listened, and I think as a result they all seemed to finish within 15 minutes, leaving the rest of the class period open for them to socialize.

More Problem-Solving

Last week I came in with a presentation prepared, but Ms. Tran wanted to spend the whole class period working through past homework and in-class problems to help them prepare for a quiz the next day. Toward the end of each class, there was about 10-15 minutes for an in-class worksheet on conditional statements and reasoning. The students in 2nd hour are the least awake and therefore the least likely to communicate a need for help, so I tried walking around and looking over their shoulders to see what they need help with, and there was only one student who had a question that I could address. Third hour was much different - before class even started, one of the students, A, told Ms. Tran that he didn't understand the homework. She was busy, so I went over to A and asked him what he needed help with. He seemed very enthused to have my help, and I helped him walk through the first two sections of the homework assignment. Later, when the students had an in-class worksheet to do, two of the students immediately got up and came to sit by me. It seemed like they just wanted the constant reassurance about what they were doing, and I sat with them as they went through it for the first half of the time allotted. I then decided to get up and answer a few questions on the other side of the room, just to be fair. I don't think any of the students in the non-accelerated classes were able to finish the worksheet in time, but I think that I was able to help a few of them understand what they were doing. I asked them to reference their notes frequently, and showed them where they could find the information they need... as they say, "teach a man to fish, he eats for a lifetime." In the other courses, I did feel like I was able to help out during the in-class problems, and I think that made those particular students trust me a bit more.

At the beginning of each class today, I gave a talk that drew off the previous one about problem solving in the case of hanging curtains. I started by showing some images from the last talk and asked for someone to summarize what we discussed. I then asked the students what we did to solve the problem, and inevitably someone would say that we tried a bunch of tools. In second hour someone actually used the term "trial & error," which brought me to my next point quite nicely, which was that we used the tools that we had (in the curtain case, screwdriver, hammer, pliers; in geometry, definitions, theorems, postulates) to solve the problem. I said that this class should actually be easier than other problems that they encounter in life because they KNOW that every problem in the book can be solved using the definitions, postulates, and theorems that they are learning. Next I showed them another example of a problem, where I was helping a friend of mine move his couch out of an apartment. After we tried many times unsuccessfully to get the couch out the door (and after tearing a big hole in the wall), we decided to modify our goal. Instead of trying the get the couch out of the apartment so that he could move it into his new place, we just needed the apartment to no longer have the couch in it. So, I proceeded to show them some entertaining photos of my friend and I beating his couch apart and ripping it into many pieces. I then asked them how this problem was like solving a math problem, and I wrote their responses on the board. They initially came up with some if-then statements, which were good, but not exactly what I was looking for. I was looking for the way that we used the tools that we had to solve the problem, and how we don't always know what the outcome will be, and how we used trial & error to come to a solution, and some students even made some analogies to variables, saying that we were solving for variables. Second and sixth hours (accelerated geometry) went very well, and students in both of those classes were attentive and able to guess my next moves. Third hour was more difficult, partially because several of them got up and left to get their school ID's made right before my talk. I had a couple of students put their heads down during the talk, which isn't too bothersome when there are 30 people in the class, but when we are down to 15 students, it makes the discussion circle and opinions that we can get much more limited. Fourth hour was actually more difficult than third. There was a full classroom, and it felt like even more of the students weren't paying attention. This indicates to me that this was a poor presentation for those audiences, as it clearly did not capture the audience like the previous talks have. Some of them were clearly entertained, but I think that they were a minority. I think a big part of where I lost them was at the beginning when I tried to bring in geometry parallels. It seems like that type of discussion equates to boredom for many students, and that causes them to zone out, thereby making my job of drawing entertaining parallels to geometry for them that much harder!

During my talk, several students asked the question about how my friend had gotten the couch into the apartment if we can't get it out, and I explained that the way the stairs and doorway were situated, he was able to use gravity to wiggle it down, but when we tried to reverse it, it just didn't work. A minute or two after I moved on from this part during fourth hour, a student, S, looked at me and said "how'd you get it in?" I chose to ignore S because (1) she didn't raise her hand, and (2) I had already answered that question at least twice. She noticed that I ignored her and said: "you gonna look at me and not answer my question?" I replied, "I already answered that question," and moved on as she put her head down for the rest of the class period. I guess I could have said: "who can answer S's question for me," and then she would have felt dumb when other people had to explain it to her. I feel bad for S, but I also think that she is an example of a very common student that has been frustrating me since I started here. This is the student who feels like she doesn't have to listen to anything until she has a question of her own, and then she can interrupt everything to rudely ask her question and expect an immediate answer. When responded to negatively, she feels like the world is out to get her and she gives up on school/math. I don't know what to do about these students, and trying to deal with them makes me angry, which then perpetuates the cycle of her feeling like the world is out to get her. Ugghh!