End of Fall

So I have been a bit remiss in my blogging updates, so I will try to catch up right now. I have given two more talks since my last post, and they have centered on examples that demonstrate geometric concepts seen in everyday designs. The students were assigned an end-of-term project that involved creating a "winter-themed" holiday ornament to hang from the ceiling of the classroom, and for the project they had to discuss ten geometric concepts that are evident in their ornaments. So, my talks were about some interesting design projects that I am familiar with, and at the end we listed and discussed at least 10 concepts from geometry that we could tie in.

The first of these talks discussed Humvees, which is a familiar topic that most of the students could understand. I opened up by talking about the characteristics of a Hummer, the commercial version of the military Humvee, and they all seemed to be familiar with the vehicle and many of them mentioned its low fuel economy. I then moved the discussion to the original military vehicle, the Humvee, and discussed its purposes and some of the considerations that designers must take into account. From here, I was able to transition into some research that I did as an undergraduate, of which the aim was to design for safety against buried land mines. The research I did involved experimenting with explosives, which seemed to catch the interest of a lot of the students, and I was able to even talk a little bit about my results without all of them losing interest. After this, I then asked them where they saw geometry in the Humvee, and they were able to come up with most of what I had thought of on their own, which was encouraging. The fifth hour class, as usual, was a little less attentive on the whole, but there was one student in the front who actively participated this time (who normally does not), which was nice.

The second talk was about the Solar Decathlon project that many of my peers at the University of Maryland participated in. This is a project where teams of university students work together to design and build a completely solar-powered house, and they compete against other universities in ten different categories. I began this talk by going back and referencing a previous talk I gave that discussed wind turbines as an alternative source of energy. I then asked what the other big source of renewable energy was, and most of the classes were able to come up with solar as the source. From here, we talked about the technologies that currently help us to harness solar energy, mainly through photovoltaic (PV) cells and rooftop water heating, and I introduced the project. I stressed the interdisciplinary nature of this project and discussed all of the university departments at Maryland that were involved, since I know not all of the students want to be engineers. This was interesting for them, and I got a lot of questions about the technology and the Solar Decathlon in general. As with the previous discussion, I ended by asking the students where they see concepts from geometry in the solar house, and they were able to easily come up with ten concepts.

I had been under the impression that I would only be with Ms. Tran's classes for the Fall term, and these would be some of my last discussions with the class; however, soon after the talk about the Solar Decathlon I was informed that I would be working with Ms. Tran's class for the entire year. I decided that if this is the case, I should try to get to know the students better, so my last class periods were spent helping the students on an individual-by-individual basis with their practice quizzes and homework assignments. I enjoyed this, and I think the students appreciated my help. Many of them are reluctant to raise their hands, but when I come around they will ask questions. Still more are reluctant to even attempt their homework without me standing over their shoulder and telling them that what they are doing is correct - this is a habit that I intend to break during the course of next term. The fifth-hour students responded fairly well to this, and most of them got through the assignment with the exception of three guys who refused to even look at the questions. I will continue to push them through the next couple of weeks in January, but unfortunately the fifth-hour students will not be back with Ms. Tran when they start their new semester, so I won't have much more time to work with them.

Overall, I think this was a successful semester. I feel like I got a good start as I presented the students with some interesting topics and showed them some of examples of what engineering is; however, it may have been beneficial to get involved with them on a more personal basis earlier. Next term I will try to strike a better balance between engaging them with discussions and assisting them with their individual coursework assignments.

Decimals and Transformations

I have been very pleased with the last two discussions that I've led. Last time I came in with a presentation that introduced the concept of tolerance in measurements. We started out by discussing significant figures and why we sometimes write 90.0 instead of 90 when specifying a degree measurement. I explained to them that it is more specific to say 90.0, because that covers a small range from 89.95 to 90.05 whereas saying 90 covers the larger range of 89.5 to 90.5. We all agreed that a lower tolerance (higher accuracy) will result in a higher-quality product, but a higher tolerance will be cheaper. We then discussed the purpose of tolerance and how we can never produce something with 100% accuracy. To end the discussion, I gave some examples of things that might be designed, and we talked about whether we'd want a high or a low tolerance in their designs. While this didn't pertain specifically to the curriculum, I think it added something to their understanding of why we use decimals sometimes. The classes were engaged, and I think they are still interested in the things I have to say.

Since I had some serious problems with the fifth hour class in the past, I started out in that class by reminding them why I'm there. I just wanted them to realize that I'm taking time and making an effort to talk to them about interesting things, and I let them know that I'm open to feedback. That was fairly successful, and they were respectful and mostly attentive for the entire talk.

Today I came in with a talk that supplemented last week's class lesson on rotations and next week's curriculum on transformations. The discussion centered on electricity generation, which is something that I really enjoy talking about. The talk was a little bit longer than I had planned, and a lot more of the focus was on electricity generation and renewable power; although this isn't the main goal of the class, I think it's educational and the students were attentive and interested. So I introduced electricity and talked about the different sources and their pros and cons (fossil fuel causing air pollution, nuclear power creating radioactive waste, and renewable versus nonrenewable sources). We then got into a discussion on wind turbines and how turbines work. I had a 3D CAD drawing of a wind farm, and we discussed how that drawing would be built - the main take-home was that you can save a lot of time by using rotations and translations to create an accurate and robust CAD model. I ended by asking an open-ended question about where else in design we might use transformations, and got some good responses.

Overall, this went much better than I had expected. Because energy is such a hot field right now, the students understood its applicability to their lives, and there were lots of questions in each class. As usual, third hour was the most engaged, and I think that's because they are awake enough at 10:00 to mostly be able to listen to what we talk about. Fifth hour was also more engaged than they have been in the past, which was great.

Applying Geometry to Vehicle and Rollercoaster Design...

The last two classes have gone fairly well, and Ms. Tran and her class seem to be accepting my weekly presence and my discussions. Last week I was feeling ambitious, and I prepared a talk centered around convex sets, which Ms. Tran had introduced the previous week. I wanted to introduce to them the concept of design optimization, and finding the minimum of a curve. I used an example from my previous talk about car safety, which I think was a good transition from the week before. This talk was very high-level, and we discussed design spaces. To show its usefulness, I brought up the idea of multiple variables and dimensions, and brought up the fact that we cannot visualize curves in more than three dimensions. This all circled around to drive home my point about the usefulness of having convex sets.

I knew coming into this that it wouldn't be easy to explain, and I think the first class got a bit lost during my talk (it didn't help that they had an assignment to work on during the talk). As I got more comfortable with presenting it and learned from the first class, I think the second and third classes were more able to follow what I was saying. For the fifth-hour class, the non-accelerated geometry class, I chose not to give the same talk, since it wasn't relevant to their work and we didn't think they would be interested. I decided instead to talk to them about triangles and trusses, and I brought in some very crude 3-D models of a square and a triangle, showing the strength of the triangle over the weakness of a square in a structure. I didn't prepare as much for this talk, and without the visual structure of a powerpoint presentation, I don't think they took it as seriously. This did not go as well as I had hoped.

Today I came in with an improved version of my fifth hour talk from last week, to be given to all of the classes. I set up a powerpoint presentation that talked about rollercoasters, picking out one in particular from Cedar Point. We discussed reasons for designing rollercoasters, safety factors and concerns, and the truss structure of the rollercoaster. I then used the 3-D models to show the importance of triangles in a stable design, and I explained how useful it is to know when triangles and angles are congruent. This was pretty successful in the accelerated classes. They asked a lot of relevant questions and seemed to have some genuine interest in the topic.

Today's fifth hour class was very hard to handle. The school was doing "hall sweeps", which means the teachers were locking their doors after the bell rang, leaving late students in the halls to be collected and disciplined. Fifth hour was at about half capacity, with only 7 students. The students that were locked out were being very disruptive (banging on the door and yelling through the window), and it was tough for me to get through that. I don't think more than one or two of the students actually followed my discussion all the way through, which was disappointing and disheartening. I try very hard to make these interesting and relevant, but I need to find another way to get through to this class. I will try harder in the future, and hope that these external distractions will calm down.

First 2 weeks

So this year I am working in Ms. Tran's geometry classes, going in on Mondays for 1st through 5th hours. The first three classes are an accelerated course, which moves a little bit quicker; the fourth is not accelerated, so the material being covered is different, which should make me work harder to accommodate everyone. It's almost a full day, but we have a nice hour and a half break in the middle for lunch and planning, so it should be nice to have some time to discuss the lessons with Ms. Tran and plan for the following week. I was a little bit worried that geometry would be more difficult to find engineering connections with (unlike algebra last year, which was very easy to connect to), but so far I haven't had any trouble. After the first two weeks in class, it is pretty clear that the fundamentals of geometry are all over mechanical engineering.

The first day I went in with a powerpoint prepared to introduce myself and discuss who I am and what I do. Unfortunately, we didn't have a projector, so I just had to ad lib without the slides. I introduced myself and told them about my background, where I'm from, where I went to college, and that I'm in grad school at U of M. Next, I asked them all about their aspirations - what they want to be when they grew up. I was surprised that many of them are very ambitious, and most of them will need to go to graduate school to get to where they want to be. I then discussed what I want to be when I grow up - an engineer. We talked about what engineering is and what I do within the field. Very few of them actually knew what engineering was (which is not surprising as I didn't know either as a sophomore in high school), so I hope that I will be able to influence some of them to consider it as a career. Overall, I think it was effective and much of the class was engaged; however, visual aids would have been nice to spice the discussion up a bit.

I went back yesterday, and was happy to find that Ms. Tran had arranged for an LCD projector. I brought in some powerpoint slides that built off a topic that I had heard the previous week - networks of nodes. I introduced the class to the concept of finite element models (FEM) - we discussed what it is, and I showed some screen shots of a car FE model that I use in my research. I asked them why the model might be useful, and all of the classes came up with testing for safety after a few guesses (which is what I was looking for). I then showed them a video that I made of the car model crashing into a wall, and we talked about car safety and how I might use FEM models to design safer cars. The classes got very into the discussion, and it took around 20 minutes in each class. Even though the fourth (non-accelerated) class hadn't studied node networks, they actually responded pretty well to the discussion and were fairly engaged. Ms. Tran seemed to like the discussion as well, at least enough to ask me to stay and give the talk with her 6th hour!

After my talks, Ms. Tran gives the class lesson/notes on the overhead, and then they have the rest of the time to do their homework. The students don't ask me questions during the homework time, but I hope that I can make it clear in the future that I am there to answer questions and help them during that time.

I'm very happy with how my discussions going so far, and I hope that I can continue to make connections with the course material and engage the class in interesting discussions. My strategy of asking lots of questions to try and get them to bring up the important points of the talk seems to be working well so far, and I think they appreciate my energy and the extra presence in the classroom.