Welcome to My Blog!

This blog highlights the work that I did during my graduate studies as part of a partnership between the University of Michigan College of Engineering and the Ypsilanti Public School District from January 2008 through April 2011.  During the first two and a half years (Jan 2008 - May 2010) I assisted high school math classes by introducing engineering concepts and applications to the students, which involved weekly interactions with students in four separate classes.  In the final year (September 2010 - April 2011) I was involved in middle school science classes, planning and facilitating laboratory activities on earth science topics.

I hope you enjoy my reflections from my time at Ypsilanti High School and Ypsilanti Middle School, which you'll find in the earlier entries of this blog.  If you have any comments or questions for me, please don't hesitate to contact me!  You can find more information about me as well as contact information at my personal website: www.stevenhoffenson.com.

Water Filters

During the last two weeks, we did a lab where the students designed and built water filters. To me, this lab seemed much more successful than the earthquake lab, and I usually left the school at the end of the day feeling good about what we did. This lab was designed to take less time than the previous one, and the students' tasks were simpler than in the earthquake lab (thanks to experience and some tips from Lucie Howell). I also completely cut out the powerpoint, which I think was a good move with this age group. This was again a two-day lab, and I spend Monday and Tuesday of last week with Mrs. Buckwalter's classes and Monday of Tuesday of this week with Mrs. Karalash's classes.

Day 1 began with me starting a discussion with the class about drinking water. I asked "who drinks water?" and usually everyone raised their hands, so I followed it up with "where does that water come from?" I got a variety of answers to this question (which was what I was hoping), with answers ranging from "the ocean", "the lake", "wells", "rain", "the faucet", and "the Ypsilanti Community Utilities Authority." Regardless of this, I tried to get it all back to the fact that our water in Michigan typically comes from the Great Lakes, which are the largest source of fresh water in the world. I then transitioned the conversation toward the water cycle (precipitation, evaporation, condensation), which I drew on the board. We talked about how nature cleans water through evaporation and how the dirtiest part of the water cycle (runoff and rivers/lakes) is where we get our water, which means we need a good way to clean water.

Usually around this point I would pass out the Day 1 worksheets, which had 3 questions on them that we answered together and space for two drawings of filter designs. We then passed out the materials, which were a two-liter bottle with the bottom cut off, gravel, sand, cotton balls, rubber bands, cheesecloth, coffee filters, and masking tape. In Mrs. Buckwalter's classes we didn't have the sand, and in Mrs. Karalash's classes we didn't have rubber bands. The students were asked to draw and label two different ideas for filter designs, and then as a team of 3-4 students pick one and build it. I passed out some dirty water (manufactured with water and potting soil) for the students to experiment with for the rest of the hour (usually around 15-20 minutes), and at the end of the hour they packed up their materials and put them away for Day 2.

Day 2 started out with the students retrieving their materials and having about 15 minutes to rebuild their best design and make a detailed drawing of that design. Once the students were ready, we tested the filters, and one at a time the teams came up, explained their designs, and I poured dirty water in and we watched the cleaner water come out. At the end, all of the cups of "clean" water were lined up, and we decided who had the cleanest water. If there was a tie, we went with the team that had the most water won (since they all had thirty seconds with the exact same amount of water). We congratulated the winning team, and we talked a little bit about what seemed to work about their filter. Mrs. Buckwalter asked her classes to vote on which material they thought was the best filtering device, which I thought was a nice idea, but must've forgotten for Mrs. Karalash's classes. We then had the students clean up their filters, throwing everything away except for the bottles, which they cleaned up for me for later use. When there was time at the end, we showed the students some videos. Mrs. Buckwalter had found a video about the Central African Republic that highlighted some of the problems with water shortages and their health impacts in that country. In Mrs. Karalash's classes, I brought in a couple of videos about engineering solutions to help regions with water shortages, one of which was from U of M (the Wheelo) and the other from a competition called "Innovate or Die" (the Aquaduct). The students were surprisingly engaged in watching these, and I was really happy with that.

Overall, I think this was a successful activity for the seventh grade students. It was simple, we didn't bore them too much, and they got a chance to build and experiment on their own. The competition didn't really have any real prize (we gave the winners a certificate), but the students still wanted to win. Naturally, there were always a few students who didn't seem to care or who disagreed with their teams, and there were several students who would wander around the room and see what other teams were doing; surprisingly, most of these side conversations were still about the project, which I thought was great. I would recommend this lab activity for this age group in the future.

Earthquake!

For the last two weeks, I got to do my first lab in the seventh grade science classes. Last week I went in on Wednesday and Thursday for Mrs. Karalash's classes, and this week I was in Mrs. Buckwalter's classes on Tuesday and Thursday (Wednesday was a field trip day). The lab was about designing and building earthquake-proof buildings, which is an activity that has many different versions all over the internet. None of these versions seemed to fit our purpose well, so I created my own version of a two-day lab, where Day 1 was about brainstorming and designing and Day 2 was about building and testing.

I started Day 1 with a three-part powerpoint-based discussion that was only supposed to take up 15-20 minutes before leaving the students with 25-30 minutes for brainstorming, designing, and selection of a final design. The first part of the discussion was about engineering design, which began as 12 slides in Mrs. Karalash's first class and ended as 3 slides in Mrs. Buckwalter's classes. The point of this was to introduce the students to the engineering design process, using a lot of the slides that I presented to some high-schoolers a few weeks ago on campus. This seemed to be way too much, as the students' attention waned very quickly (prompting the gradual removal of 75% of the slides). The second part of the discussion was on earthquakes in general, and I showed a news clip video that talked about a company that retrofits buildings for earthquake-resistance. I followed this up by discussing some ways (from their textbooks) that buildings can be designed to minimize earthquake damage. We also used this time to answer the pre-lab questions that were on their worksheets: What happens during an earthquake? Can we predict where and when they will occur? What dangers do earthquakes pose to people? How can we as designers and engineers prevent some of these dangers? In Mrs. Karalash's class, we answered all of these questions together as a class, and we basically told the students exactly what to write on their worksheets (though some still neglected it); in Mrs. Buckwalter's class, we let the students come up with their own answers (and gave them some time to do so).

The third and final part of the powerpoint introduced the design activity - to redesign the Port-au-Prince (Haiti's capital) City Hall, which was destroyed during the earthquake back in January. In Mrs. Karalash's classes, I explained that the student teams were design firms competing for the contract against the other "firms" in the class, and we listed 4 or 5 design criteria that they will be evaluated on (earthquake-resistance, appearance, functionality, cost/environmental friendliness). This seemed to go over their heads, so in Mrs. Buckwalter's classes I simplified it and just said that their job was to design the new City Hall. From here, I explained that their assignment for the rest of the class was to brainstorm and draw at least 5 different building ideas, and then as a team to agree on one final design to start building the following day. Depending on the class, the students typically had between 10 to 20 minutes for this part, which didn't seem like enough time. We also had to continually remind the students of what they were tasked to do, as they seemed to have a lot of listening problems. The goal was for them to have detailed drawings of what they planned to build so that they could come in the next day and immediately start building. Unfortunately, this didn't happen for the majority of the teams.

Day 2 was all about building and testing, which had varying degrees of success in each class. Before we gave the students materials, we made them finalize their designs on paper ("measure twice, cut once"), and depending on when they did that, they had 10-25 minutes for building. After they finished building, we weighed, measured, presented, and tested the buildings. This went very differently in Mrs. Karalash's classroom than in Mrs. Buckwalter's classes, partly because of the classes themselves and partly because we had a chance to learn from the earlier classes to improve the later class experiences. In Mrs. Karalash's classes, we typically needed 15 minutes or so for the students to finalize their designs before they could get the materials, and then we gave the students 10-20 minutes to build. The students didn't know how to use the scales, so we set up a "height-measuring station" where Mrs. Karalash used a meter-stick to see how high the buildings were. Then they came over to the "weight-measuring station" where I weighed them using the balance scale. After that, the students had a chance to present (and many of them got very shy or had nothing to say) and then we shook it. Unfortunately, about 4 buildings into the first class, the shaker fell apart. There were several problems with it, and I tried to fix it before realizing that I didn't have the materials, which frustrated me through the end of the hour. For the rest of the day, I settled on just holding the motor down by hand and adjusting the rotating arm between each test. Because of this three-stage process of testing, we were always rushing to finish on time, and we never had time for the reflection questions, which was unfortunate. In Mrs. Buckwalater's classes, we let the students weigh and measure their own buildings during the "build" phase. This meant that when we started testing, all we had to do was present (and the students had fewer problems speaking in front of the class) and test it with the shaker. It helped that the shaker had fewer problems, though I still had to find something heavy to weigh down the top of the shaker table and adjust the rotating arm between tests. Still, we were able to get through this stage much more quickly, and we actually had time to let the students answer the reflection questions and turn in their lab worksheets.

There are some more major differences that I noticed between these 7th grade classes and my high school algebra and geometry classes that I worked with for the previous two and a half years. One of them is that the teachers tend to step up and take charge a lot more than in the high school. I was expecting to lead the entire two days by myself, but in both classes the teachers tended to take over and help lead the activity. This was somewhat a relief to me, because I'm not sure if I'd be able to settle down some of these classes by myself. In the high school (at least with the teachers I worked with), the teachers were all too happy to hand over the floor to me, and often took the opportunity to catch up on work, leaving me relatively alone to deal with any distractions and keep the students' attention. The other thing is just the maturity levels of the students, which is much lower than what I saw in my high-school students that were typically 2 years older.

Welcome to Middle School

My first days in the middle school gave me a chance to introduce myself to the students and to get to know them a bit better. Over the course of three days, I visited 8 seventh-grade classes (4 of Mrs. Buckwalter's and 4 of Mrs. Karalash's) and used up between 25 and 40 minutes to discuss myself and the general concepts of engineering. I started out by telling the students a little bit about where I'm from and discussed what I'm doing in their classroom, and then I went into trying to define engineering. After I discussed what engineers do and what kinds of jobs engineers have, we played a little game called "Stump the Engineer." This involved me challenging the students to come up with a product that did not involve an engineer. Some of them came up with good examples (fruits, vegetables, and pets were the best in my opinion), but I was always able to come up with a way that engineers helped us get those products (harvesting, transportation, storage, etc.). I think this was good in showing the students that engineers touch our daily lives in ways that we don't typically think about. We concluded by talking a bit about my research on vehicle safety, and in some classes I was able to talk about the MShoe, which was a project I did to design a shoe that would generate electricity to charge an iPod.

For the most part I thought the talks went well, but I didn't quite anticipate the number of questions that middle school students would ask, and I ended up taking up more time than I had hoped. Both teachers were very supportive of me and were surprisingly okay with me taking up most of the class periods. Similarly to high school, typically 10-20% of the class is active in asking and answering questions, and the other portion of the class only speaks up when I happen upon a special interest of theirs. So, my goal for when we start doing labs should be to take special care to engage those students who don't speak up as much. As I experienced in the high school over the last two and a half years, each class sort of has its own personality, and some are very quiet (making it difficult to ask questions and have interesting conversations) while others are very energetic (making it difficult to settle the students down when an exciting topic comes up).

The biggest difference from high school that I noticed was in the maturity level of the students. When I told the students that it was okay to ask questions throughout the talk, I ended up getting a lot of comments and questions that were totally off topic. I liked the enthusiasm and the way the students were willing to be open with me, but I'd like to see that energy in a more directed manner.

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.

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!

The Finite Element Method and Problem Solving in Geometry

The last two weeks have gone well in Ms. Tran's classroom, and I am starting to feel like the students appreciate my presence. Yesterday, there were students in both of the first two classes who looked around for me at the beginning of the day to see if I was there. A highlight occurred yesterday in fourth hour just before my talk, when a student came up to me and said: "You would make a good teacher." That made me feel like I am doing good things in this classroom, and that I am getting through to at least some of the students. Last week I came in with a talk about nodal networks and finite element models, for which I recycled much of a powerpoint slideshow that I used last year, with an iteration of improvement. This week I came in with a new discussion on problem-solving, showing them an example of a real-life problem that I encountered just a few weeks ago. This will be the basis of the students' first project of the year, which I helped Ms. Tran formulate.

My talk last week was pretty successful. I had been talking with Ms. Tran the week before and asked her what topics would be good to cover. She actually remembered the talk that I gave last year around this time, which discussed nodal networks, which was something that they covered in class last year. This year, the curriculum changed, so they did not talk about nodal networks, so that was my opportunity to give them their only exposure that to the topic that they'll likely get during high school. My title slide included a figure from their assignment the previous week, which had a bunch of points connected by lines, and I told them that it was a network of nodes. I then asked them what they knew about networks of nodes, and most of them knew very little, so I broke it down into the words "node" and "network." In all of the classes, at least one person knew what a node was or could guess based on my intro slide; most of the students were able to define what a network is, and I asked them for examples of networks. Many of them came up with the phone company's definition of your "in" network, the internet, and facebook. This was great, so in each case I asked them what the nodes would be in their network; respectively, those were the individual cell phones, the computers and servers on the web, and people's profiles on facebook. I then showed them a few more examples of what I view as nodal networks, including rollercoaster truss structures, the human circulatory system, and an ipod's circuitry. I then introduced the students to finite element models, where we again broke the phrase down into individual words and then brought them together to define the phrase. I showed them an example of a Ford Taurus model with over a million elements, or nodes, and showed them how the network of nodes is useful for crash test simulations with a quick video animation. We wrapped up with a discussion on the purpose of models and why we simulate them. I thought this went fairly well - most of the students were attentive, and I noticed more students answering questions that had in the previous talk.

During Ms. Tran's lesson after my talk, there was some time for in-class problems, and for most of the classes I was able to go around and help students work through the problems. I was rather disappointed that some of the students (particularly in the non-accelerated classes) don't seem to know basic algebra, which is technically a prerequisite for this course. Not knowing how to solve problems of the form (3x+1)/2 = 5 is a real problem, and I have a feeling that the students who don't get it now will have a hard time getting it in the future, when they're fully expected to know it. Being able to get a variable by itself is so important, and it seems to me that the root of the problem is not understanding multiplication and division. There were at least two students that I was trying to help, and when time was up I still didn't feel like they understood what we were doing. I want to help them, but I get such little time with them that it is difficult to make any lasting impact. I spoke with Ms. Tran about this yesterday during the planning period, and she said that some students in the regular geometry classes actually failed algebra, and there weren't enough spots in the algebra classes, so they were placed in her geometry class. I told her that I will let her know who these students are so that she can push them to seek help outside of class, but I am still concerned about these students.

Yesterday I came in expecting time in class to help the students with in-class problems, but there was a change in plans and Ms. Tran gave a test yesterday. She told me when I came in yesterday morning that I could present for the last 15-20 minutes of each class, so I prepared my slides while the first class took their test. We had discussed this topic beforehand, when at the beginning of the year Ms. Tran asked me to help her come up with a project for the first half of the first term. I thought about it for a while, and I came up with an idea while I was helping a friend move into her new apartment. After hanging a curtain rod, we spent maybe 20 minutes trying to solve a problem that we had with a protruding bracket, and when we finally fixed it, I had a real sense of satisfaction from solving the problem. We went through several steps before finally fixing it, and I thought of this as a good example of real-life problem solving that students don't often think about during math class. I also thought that there was a good way to link this with geometry "logic," which mostly revolves around conditional statements. So I proposed to Ms. Tran that the project be to find an example of a real-life problem and discuss the steps and methods for solving it; then, the students could write 5-10 "if-then" conditional statements about the problem solving process, such as "IF this method doesn't work, THEN try this other idea."

So it wasn't a huge surprise when she asked me to do it yesterday morning, and I already had a bunch of photos prepared for it, so I sat in the back of the room and put together my powerpoint while the first class took the test. The slide show started out by defining what problem solving is and asking the students if they've ever had a problem or ever solved a problem (I may or may not have mentioned that Jay-Z had 99 problems). I also posed a question here about how problem solving relates to math, and I had an opportunity to discuss how math is really just a language that we can translate real problems into so that we can solve them. I then presented the curtain-hanging scenario, and walked the students through the three ideas that we tried before finally solving the problem, at each stage asking them for suggestions on how to fix it - they almost always came up with the same ideas that we did. I concluded by asking them to come up with some if-then statements about what I just did, and then I put a few examples up on the board. The classes got a little bit rowdy because many of my pictures were cheesy and kind of goofy, but I think because of this, more people paid attention. My first time through it, in second hour (accelerated), took a lot longer than I expected (maybe twenty minutes), but the students seemed engaged for the most part. One of the students actually gave a really good conditional statement that I hadn't thought of, and I later added to the slides: "If I don't solve the problem, then my friend is unhappy." Third hour (non-accelerated) is shorter than the others, and I only had 10 minutes to breeze through it, which rushed me quite a bit. The bell rang right before I got to the conditional statements part, but we told them to hang on one minute so I could get through it - the downside of being rushed was that I wasn't able to ask as many questions and give them time to respond. Fourth hour (non-accelerated) seemed to really get it, and I was impressed that most of them were engaged throughout and had really good answers to my questions. This was the only class where a student guessed where I was going with it before I got to the "if-then" slide, which made it go a lot quicker (too bad this didn't happen in third hour when I was rushed!). Sixth hour hadn't yet been exposed to conditional statements, so I felt like the part at the end didn't get as much feedback or response. Overall, I think this was an excellent exercise, and I'm looking forward to seeing what kinds of projects the students come up with.

First Two Weeks 09-10

This semester, Ms. Tran and I decided that it would be best if I come into four classes one day a week, and I chose Tuesdays to fit my schedule best. She has Geometry classes 3rd and 4th periods and Accelerated Geometry classes 2nd and 6th periods, so I come in for 2nd through 6th.

My first day was last Tuesday, and I came into all four classes with a quick presentation to introduce myself and explain to them what I am doing in their classroom. I began by introducing myself, and then I showed four video clips to start it off. I asked them to think about what these things have in common - they were of a rollercoaster (Millenium Force at Cedar Point), a crash test between two cars, windmills in a field, and a land mine explosion in Iraq. Much of the responses were something like "they're all fast", but I think in one class someone said "technology". Anyway, I told the classes that they are all things that I'm interested in and that I might be talking with them about throughout the semester. I then continued by introducing to them where I am from, what I do as a graduate student (many of them were shocked when I told them that I'm starting my seventh year of post-high school school, but when I told them that I got paid to go to school, that quelled many of their fears), and why I am here. I told them that I am here because I use math frequently, I want to help them understand math and problem solving, and I want to share some interesting application of geometry with them. I then introduced the field of engineering, and showed some pictures of some technological devices that I think of as fine examples of engineering. For most of the classes, I quickly introduced my research area. When I finished, I opened the floor for questions about me or about anything I talked about. Most of the questions were irrelevant to engineering and math, but I responded to all of them so to build some comfort and a free atmosphere.

I ended a little differently this time, taking a tip from a previous TF who had asked the students to write down what they want to be when they grow up and pass them up. So I told the classes: "Now I want to learn something about you," and I passed out index cards and asked them to answer the following:

1. Class period
2. Name (what you want to be called)
3. How do you feel about math?
4. What technologies interest you?
5. What do you want to be when you "grow up"?

The responses varied, and I think many of them were quite honest, which was my goal. Regarding question number three, many of them said "I hate math", but even more said "I love math", and I categorized them all and was surprised with the results: there are 22 students who dislike math, 36 students who are iffy or indifferent about math, and 41 students who like math. I always expected that most people don't like math, but I really do think they were honest, and this indicates that most of the students are here with the right intentions, which is quite encouraging. There is a wide range of professional dreams, including tattoo artists, rappers, and athletes, but also many doctors, engineers, and lawyers. I'm not quite sure how I'll use this information, but I think it can help me to make more applicable presentations and have more meaningful conversations with the students.

This week, Ms. Tran emailed me to tell me that there would be a sub, and she was just going to assign a worksheet for them to do, and I would be able to walk around and help students do the problems. I decided to forgo a powerpoint talk in order to have more time to work with the students on problems, and I will give the talk I was planning next week. So, I came into class, and the substitute actually spent about 35-40 minutes doing practice problems from the worksheet on the whiteboard. Unfortunately, that only left me with 10-15 minutes at the end of class to walk around and help students, and by that point, many of them were done or were copying others' work. In the latter case, I asked the copier which problems he/she was having problems with, and they would usually tell me and we'd walk through them together. There were a few students in each class still working on the worksheet by the end of Mr. R's (the sub) whiteboarding, and I think I was able to give those students some valuable help. However, fourth hour (non-accelerated) just completely stopped working on it, put the worksheet away, and began socializing as soon as the formal discussion ended. I don't feel like it's my place to tell the students that they need to get their homework back out and do it in front of me, nor will that facilitate the type of relationship that I want with the students, so I didn't do anything after it came to that point (I did do a lap around the class to help the few students who still had it out for an extra 5 minutes, but for the last 15 minutes of class, it was a social melee). Anyway, this day wasn't as constructive as I hoped, but I think I did what I could with the situation.

5/4 talks

Ms. Tran was out today, and we had a substitute teacher in the class. I still came in to give my talk, and after the talk the students watched the beginning of the movie "Stand and Deliver." I basically swapped two of the successful talks from previous weeks to the classes that had not heard them yet, so I gave the shoe talk to the Geometry classes and the explosives talk to the Algebra classes. First and second hour went very well. The students were respectful and engaged in hearing about the running shoe that my team built last year to power an iPod. Third hour is always more talkative because it's later in the day, and while they were talkative, most of them seemed interested in the talk and we got through it without much trouble.

Fifth hour (the students who are re-taking Algebra I) was a different story, and it has really become frustrating for me. I showed a video of a land mine exploding in Iraq (which was extremely successful at drawing the attention of the geometry classes), and it got the attention of a few of the guys in the class, and we talked about the research I did on explosives back at Maryland. Despite everything I tried to get their attention, there were always about 5 side conversations going on throughout the talk. These students seem to simply not care about how incredibly rude and disrespectful they are being. One student who was actively involved in a side conversation started to butt into my talk with a "question" - while I normally welcome questions, I was really bothered by her disrespect and told her that it was very rude of her to do that. As usual, she started to give excuses and claim innocence, which really just shows me how little some students understand about respect and manners. I have tried so hard with this class and sometimes it feels impossible. I don't know what I can do in the two days I have left to make a positive impact on these students, but I will think more about it once I've cooled off from this incident. Anyway, I pressed through the talk and focused on the 4 or 5 students who were actually interested in what I was talking about, and then turned them over to the sub and the movie.