Passer Rating

Yesterday I finished grading the worksheets I had handed out to accompany my talk. Even being very generous with the points, I believe the average was somewhere around 70%. I have come to expect such averages on exams in classes on complex topics, but not in a situation where the students are almost handed the answers. In fact, I am not convinced that I could have made it easier. One question required that they answer with "zero"; maybe they took me too literally when I said that the answer was "zero". For all the trouble I had in the first class, they actually had better grades on the worksheet, but not by much. As before, the situation just makes me question whether my instruction is that bad or if the students just don't see or don't care about an opportunity for an easy grade. Maybe it was so easy that it was demeaning.

Stemming the Tide

While not entirely relevant to high school learning, there was recently a House panel on STEM education at the college level. The participants were informative and offered suggestions on improving the declining fields.

Fixing US STEM education is possible, but will take money

In particular, I was pleased that there someone else noticed the lack of teaching preparation for graduate students. It always boggled my mind that there are stringent requirements for teacher specific education when it comes to primary and secondary schooling, but none at the collegiate level. Part of the reason I decided to participate in the TF outreach program was to become a better instructor and communicator, but I could have just as easily completed my degree with no experience in teaching whatsoever.

While it was not the focus of the panel, it is unfortunate that the article didn't place a little more emphasis on improving STEM outreach in K-12. I agree that there is a great import to retaining students at higher levels, but the Boeing representative is correct in singling out the perception of engineers by youth. I do not believe that the instruction quality in college could change appreciably in the last 40 years and yet the number of STEM degrees relative to total degrees has been falling. Something to think about.

Collisions

As a much delayed followup to my presentation on sound, today I gave a presentation on how math fits in to football. I worked on the presentation quite a bit which included several videos, an accompanying worksheet, and two live demonstrations. Molly and I discussed having the presentation run for the entire class which is the reason for the ambitious composition. I practiced the talk with some less physics-inclined friends and went to class feeling like there was some chance the subject would go over better than previous ones. Of course, everyone knows what's said about the best laid plans...

 If you'd like to see the presentation and worksheet, they're available at the following two links:

Football Presentation
Football Worksheet

Let's start our playback of today's presentation by stating that I probably bit off more than I could chew. I knew there would be problems getting students to concentrate on a single subject for more than 20 minutes (see previous talks and the field trip tours), but thought that the variety in the presentation would be enough to keep them under my thumb. Turns out that I was wrong about that. I did not get through the talk with the first class, and after some last minute changes, only eked through the second. Part of the reason for this was the prevalence of troublesome students another is that there was too much material. I got so worried about having enough material to cover the lecture that the opposite happened.

The Presentation
Whenever discussing physics or other science subjects I always hear the question, "but what does this have to do with math?" Well, usually it's not a question and is worded a bit more aggressively, but you get the point. I tried to short-circuit this sentiment by explaining that physics was simply how we use math to model the world around us. A bit general, but at least some of the students nodded their heads. To drive the point home, I described a couple of famous equations that described physical phenomena. From here I transitioned to some of the important kinematic equations that physics students first learn. I defined what each term meant and provided a written description on the back of their worksheets. We went over examples of potential and kinetic energy. Finally, I asked them to write examples of how kinematics could be related to football and then presented four examples of my own that would be the body of my talk.

The first question (one football player tackling another) was a chance to explain the conservation of moment. I began by showing them a head-on collision of two steam engines. Like all of the later video clips, it was one of the more popular parts of the talk. I made an analogy between the trains and two colliding football players, but indicated that the mass and velocities of the players would not necessarily be the same. In the first class, I attempted to lead them through the process of solving how fast one player must be going to stop another (in one dimension). In the second class, I skipped this section in an effort to save time and address the more important points of the talk. After the situation was presented, I showed them a clip of two such players colliding and asked them to make connections between the math and reality.

We next talked about conservation of energy, in the form of a car colliding with a concrete wall. I pointed out that the car had energy before the collision and asked the students to discuss and describe where that energy went afterward. At this point I ran out of time with the first class. In the second class, I continued on to described how the kinetic energy of two colliding football players could cause one to clip into the air. I had planned on calculating a specific height however, as before, the numerical part was skipped for time and clarity. Again, I included a video of a real football player getting flipped into the air.

Next up was a question on how one could throw a football as far as possible for a given amount of effort. Here, I wanted to show that while the math could be very difficult, we could use a simple experiment to approximate the result. To begin, I showed them the result of the actual derivation for range as a function of angle. This was followed by a discussion on how to model how a football player throws a ball. Eventually, with the help of several students I used a ball launcher to create a plot of range versus angle. I then showed them a plot of the functional relation derived earlier so that they could see the differences and similarities between the experiment and model.

As the talk progressed, I allowed the material to become progressively qualitative so that more advanced concepts could be addressed. I ended by trying to explain to them why spin on a football is important. Several of the students knew that a football would wobble or tumble if thrown without spin, but didn't know why it occurred. I gave a phenomenological explanation of angular momentum and some common examples. I had several students help me conduct the common demonstration of this by using a spinning bicycle wheel.

I ended by emphasizing some of the points that I thought were the most important and intentionally focused more on the basic concepts than the specific use of math or algebra.

Commentary
Talking, texting, dice throwing, and other thrown objects were a handful of all the distractions that ran throughout the talk. One student even thought it was appropriate to say "this is boring," on the start of every single slide. Molly and I did our best to contain these problems, but I tried to push on with the talk in order to cover each individual topic. On one hand, having to stop the presentation every three minutes to reprimand a student is not useful at all, but on the other if they're permitted to continue talking or doing whatever else it interrupts everyone anyway. I have some other thoughts about this issue that I'll put in a separate post, but it was a significant problem.

While I thought that the slide on the relation between physics and math would be useful, several students obviously did not pay attention or did not pay attention. I was asked about how any of the presentation was related to math on several later occasions, which was quite disappointing to hear. I tried to reiterate my initial point and while the students cared enough to comment on it, they did not care enough to hear my response.

The part addressing kinetic and potential energy went much better than I had hoped and most of the students participated readily. There was some confusion between the two, but in this case the students were mostly self-correcting. Momentum was a little less successful and I spent less time than I should have giving them a physical explanation of it. On the worksheet, I gave an example of 1 newton second being about as much "power" in a tennis ball traveling 40 miles per hour, but no one bothered to read it. I also cheated a bit by not explaining the difference between speed and velocity which I thought might have confused the issue more than it was already. The kinematic equations were accepted and the students did recognize the standard rate equation.

Most of the examples of kinematics in football were ones that the students recognized on their own. At this point, everyone was still on the same page and things were moving relatively smoothly. Conserving momentum was a little bit more difficult to get across, again because I do not think many of the students had a feel for what it is. The example dragged along painfully in the first class, especially the part about using algebra to calculate the required speed of one football player to stop another. As is good practice, I carried my variables through to the end of the calculation, but the students found it prohibitively hard to follow them. Among other problems, the students began to argue some of my points from experience. I did not have enough time to convince them that when they "dig in" they are describing a situation that's different from the model. I did try to explain that physicists use models of the world that aren't always accurate in every way so that they can first understand the principles of the system.

Conservation of energy went a little bit better, but I was still recovering from the bad experience with the momentum slides. I was relatively brief, and the topic wasn't as interesting without calculating how high a player would flip. For those looking at the slides, I included a fudge factor of 1/5 in the calculations on the slide. This is to account for other energy losses and the fact that I didn't run through an actual conservation of momentum, otherwise the returner would be flipped 20-some feet into the air.

The prelude to the best throwing angle went alright. Although, I was a bit annoyed when one student loudly accused me of showboating by displaying the derivation. The experiment was one of the highlights of the morning as several students were able to participate and almost every student was paying attention. Not only that, but the data matched my predictions quite well which provided me the opportunity to discuss modeling. The spin slides went fine and response to the demo was lukewarm. Everyone appeared to be tired by this point and I admit I was ready to be done as well.

Conclusion
I prepared too much material and glossed over some finer points in kinematics that should have been explained with more depth. I'm not sure if it is the way I present the material or if certain students lack the ability to be respectful and pay attention, but the number and magnitude of interruptions clearly aggravated confusion may have made much of what I said worthless. The students were extremely receptive to the live demonstration, but shut down soon afterward. Even now I'm frustrated with the challenge of teaching some of the students, but there were still bright spots and students that conducted themselves well.

Physical Links

I'm finishing up my presentation on physics in football and have come across a few interesting links that I thought might be nice to share.



The Naked Scientists - A large collection of podcasts, videos, and kitchen experiments that demonstrate many different scientific principles. They're put together by "media-savvy" scientists and researchers from Cambridge University. Personally, I got a kick out of the "Science Experiments from the Sporran" series, but the innuendo would be best left to more mature audiences. One experiment I quite liked was how to use buttered bread and a microwave to measure the speed of light. Overall, the site is quite well-produced and has (generally) safe and accessible experiments.



Phun and Algodoo - Both are 2D physics simulators for computers developed as side projects by a student of Umea University. The first is the more simple of the two and focuses on mechanics while the second includes more functions for fluids and the addition of light/lenses. Algodoo is also oriented toward teaching physics to students and has been optimized for Intel's classmate PC and supposedly works well with the SMART board that is in each YHS classroom. I haven't tried Algodoo yet, but Phun was extremely addictive even if the interface wasn't as intuitive as one could have hoped. It may work well as a computer lab for physics students, though I imagine one would have to assume that the students would play around with it quite a bit.

The Longest Journey

Sorry for the lack of updates in recent weeks. Thursdays and Fridays have been very popular for teacher development days, wisdom teeth extraction, and (upcoming) Winter Break. On the bright side, this gave me a chance to work with Mike on putting together a field trip for our students. Coming in to this month we already had some ideas for where to go, but there was a lot of effort put into hashing out the details. This is something of a post-mortem on the trip, including some lessons learned.

The students arrived at the North Campus of the University of Michigan around 9:30am. There were about 24 students who were chaperoned by Carol, Mary Beth, Mike and myself. Everyone was a bit groggy in the morning, but we all had directions and maps of where we were going which made it much easier. The students were split into four groups: two for algebra students and two for calculus students. We then started on the labs...

Engineering Research Center for Reconfigurable Manufacturing Systems (ERC/RMS)
The RMS is an NSF funded research center that focuses on anticipating future manufacturing techniques. Before even hitting the floor, our guide took us to the conference room to discuss what he'd be showing us. He wrote Newton's second law on the board and tried to explain it to the students. I'm not sure they really got what he was trying to explain, but they definitely remembered the equation as several wrote it on their surveys after the trip. At the very least, the students were able to see that there were equations underlying the demonstration. After the short lecture, we were taken to the water jet cutter, a system that uses a high velocity water stream combined with some sand to cut through almost anything. The tech had set the sytem up to cut out a small, and rather detailed, 'M'. Though there wasn't a lot to see during the cutting, I think many of the students were mesmerized by watching the computer controlled machine produce a perfect replica of the image on the screen.

Structural Engineering Laboratory
Next up, Matt led us through the Civil Engineering department's largest lab. Holding up small samples of concrete, he explained how adding tiny wires could significantly strengthen the largest of structures. The point sort of hit home when he pointed to the shattered concrete pillar behind him that was nearly 15 feet tall and at least a foot thick. He explained how the large hydraulic arms could slowly stress any attached sample, or how others could put up to 100 klbs of force on a small block. He also showed the results of his personal research; a hollow rectangular beam with 1" thick walls that had buckled and broken. Several students asked to see a test in action, however Matt pointed out that many of the tests could take hours to complete and the failure modes were rarely as explosive as the students hoped. Other subjects such as foundation stability, and how bridges affect the flow of water were also brought up.

Wilson Student Center
We then headed over to the College of Engineering's building for student projects. The building houses everything from solar car, to baja racing, human-powered submarine, concrete canoe, steel bridge, etc. Our guide, Michael, took some time to explain the origins of the project center and to emphasize that almost every single thing in the building was run by students. We later walked back to the cages to see some examples of the projects. Michael discussed how each team had a certain set of goals they were required to meet and again mentioned that everything from calculations, design, and manufacturing was student-run. The trial runs for the Formula One team, how to build a cargo-carrying glider, the dangers of being in a human-powered submarine and catastrophic bridge failure were all mentioned.

Subsonic Wind Tunnel
Chris took us on our final tour, this time of the subsonic wind tunnel. He explained some of the operating principles to the students, though the mention of Bernoulli's principle and settling chambers was probably a little much. More exciting, he put a model of a truck into the tunnel and showed the formation of streamlines. He then explained how the air collapse behind moving objects causes drag and some of the ways aerospace engineers try to minimize the effect. One thing that he got to mention was how valuable research experience is in finding a job, and while the students may not understand the magnitude of this right now, I think it was a great thing to mention. He also showed off a device that looked like a shuttlecock (surprisingly, no giggles) that was actually the receiver for a mid-air refueling tanker. Also unlike the other tours, he actually mentioned the amount of money such research can generate.

Student Panel
I'll admit, I was more focused on my lunch and finally getting a break during this section. We had four YHS alum come in to discuss how they got in to college and what the transition was like. Most of the questions were written out by the students beforehand which made it easy to answer in quick succession, but I think that it also removed any kind of interactive elements from the talk. Nevertheless, several of the questions and responses were very insightful. In particular, some of the comments about study habits were very well-thought out and hopefully made some impression on the students. I don't know if it was more encouraging or discouraging when the panelists listed their GPAs and each was > 3.9 (hell, I wasn't even close to that). Out of the whole process, I am just glad that it may have gotten some of my algebra students to start thinking about what it takes to get in to college.

Plasmadynamics & Electric Propulsion Laboratory
The final tour was given by my cohort, Mike. The tour circled around a 6m x 9m vacuum chamber which is used to simulate conditions in outer space. Mike and some of his labmates went over the principles of propulsion, what plasmas are, the costs involved in a research lab, free-fall, and other sci-fi-esque subjects. The students even got to see a rather unique thruster currently in testing; a first for myself as well and I even work in the field. I was surprised out how outgoing and positive the response was, even if the students were beginning to show signs of weariness. The tour ended with a bit of extra time so I had a chance to talk to some of the students one-on-one and also answer some of their additional questions about propulsion. And tell one to stop hitting the Pyrex window on the vacuum chamber.

Overall, the students behaved themselves very well. One problem was the nagging complaints about not enough time spent sitting which I didn't consider when planning. As the tour drew on, more and more students felt compelled to hold personal discussions and ignore whoever else was talking, but this was still a very small number. One of my biggest disappointments occurred when one of the more advanced students in my class was outright derogatory about the whole experience and refused to believe that math played any part in engineering. This was countered by some unexpected compliments about the trip from the students and their surprising amount of concentration. Carol sent the results of a survey she conducted afterward and almost every comment was positive about the trip.

Lessons Learned

• 20 minutes is a good length for a tour, but 15 minutes might be better. Most of our tours started losing steam around the last couple minutes.
• Walk your route beforehand, and walk like a high schooler (slower than molasses). This will help with timing the trip. Aside from a few hiccups, we did not run in to any time constraints.
• Make the trip take less than 4 hours; we took as much time as was available to us, but it might have been too much. While the schedule worked perfectly, most of the algebra students were beginning to lose it by the end.
• High schoolers really like Jimmy John's
• High schoolers also really like explosions or at least hearing about them.
• The trip may have been better with some more hands-on activities. While the students got to handle several samples from some of the labs, I think they'd really get enjoy building stuff. And souvenirs, give them souvenirs.
• Hammer the date and time of the trip into the minds of the attendees, tattoo it on their foreheads if necessary.
• Try to avoid bringing students that are just trying to cut class, they really take away from the rest of the trip and make it miserable for everyone around them.
• Bring a camera so you can remember what happened.
• Triple check the date with Mary Beth.
• Contact any labs that you'd like to tour with at least a week in advance, if not two.
• You can try talking while walking, but it didn't work very well for me.
• According to Molly, many of the students (and herself) didn't realize how physical engineering is; this would be a good thing to emphasize.

Acknowledgements
These are the people that made the trip possible. While my blog may not have the same prestige as a plaque, I think it's important to note that there were a lot of people who worked with Mike and I to put this on.

• Mary Beth, Carol and her husband for chaperoning students to labs that they themselves had never seen before.
• Tonya (and all the RMS students), Michael, Chris, and Matt for the wonderful tours and taking my constant harassment.
• Mike for putting together half of this field trip.
• The Outreach office for covering the costs of the trip, food, and other important financial concerns.

When in the course of human events...

it becomes necessary to tell a student "Alex!* Get your hands out of your pants," you begin to wonder if self-discipline is something of a problem. Don't worry, the situation wasn't quite as lewd as the wording would suggest (he had gym shorts on underneath and was trying to hide his phone while texting), but the phrase caused a ruckus nonetheless.

In other news, Bonnie* was being disruptive during a class today and got moved to the back of the room (isolated from other students). The student then accused the teacher of reviving the practice of making African Americans sit in the back of buses back in the 60s, asked if the teacher was racist, and just generally made the event into a drawn out scene. Ironically, the same student frequently disparages the Chinese and asks me questions like "do you know martial arts," "do you eat Chinese food every day," etc. While my responses generally range from sarcastic to very direct, I don't think the student knows why the questions bother me. I feel like this is going to require a personal discussion at some point, a discussion that I do not look forward to having.

Race is a recurring conversation topic and appears in all different contexts. In another instance today, two students today were making comparisons between being told not to talk during a test and being slaves. Very early in the year, I was accused of being racist for forgetting a student's name. I do not want to avoid the subject, but I have admittedly not mentioned it before, despite its prevalence. At some point in the future, I will write a more fully developed post on the matter, but for now I thought it important to at least acknowledge.

* Names changed to protect the guilty, taken from the list of hurricane names for 2010.

Madder 'n Hell

Actually, I'm not mad at all, but it fits in with the word problem for this week. As mentioned in a previous post, I had decided to do the Math Forum problem #3340 with the students. It was the first word problem I've done since returning from break, and had quite varied success with. I also assumed that the students would be less interested in charity donations, so the problem was altered to be about the Madden video game. The rewritten version can be found here.

In both classes, I decided not to go through the explicit process of Noticing & Wondering. The students did not really seem to buy into it. I replaced it with a nearly equivalent process where I projected the problem statement on the board. I then had the students prompt me to circle what they thought was important. The process more closely emulates what they might do on a homework assignment or test, and reduces the amount they have to write which lead to a noticeable improvement in participation. On the flip side, if they're not writing are they still learning?

After the last attempt at encouraging the students to work out a solution themselves, I did not feel that allowing them to work together would be fruitful. Instead, I tried to lead the entire class to a solution. I accomplished this in different ways for each class, and the results were similarly different.

During third hour, with a total of 10 students, I threw them into the deep end without floaties. After having them read the problem statement, I immediately tried to convince them that the number of donors and total budget represented a coordinate point. I found the step to be logical, but if anything, I've learned that you can't force students to reach a result. Instead, you have to leave a trail of breadcrumbs and let them arrive to the result themselves. As soon as I talked about replacing the x-y plane with a donors-budget plane, I had lost nearly everyone. Trying to connect the problem to y = mx + b, was also futile. Usually, the quicker students can help to pull the class along, but most of them were missing on this day. It got to the point where I asked one student a simple question and he ignored me. For several uncomfortable minutes. Last year I taught a lab class at the undergrad level, and the NCRTL told us that you just have to wait it out. I don't think they considered a case where you only have 15 minutes to make your point. I pushed ahead, but had lost any momentum that I had started with.

Determined to correct my mistakes in third hour, I spent the lunch break rethinking my approach to the problem. This time, I deliberately ignored the linear relation. Instead, I had them rewrite the statement,

The company started by setting aside  a  certain  amount  of  money  to  produce  the  game.  To  encourage  their 60  richest  fans  to make  individual contributions, the company pledged to also provide an additional fixed amount for each fan who made a personal donation to the budget.

in the form of an equation. We ultimately ended up at something like B = FA+C, where B represented the company's part of the budget and F was the number of fans who donated. All it took to convince them that this was the same as a line was writing the slope-intercept form directly beneath it. Despite the success in this initial portion, I still think many of the students had difficult thinking of the data in as coordinate points. However, there were definitely several students that grasped the concept and helped move the class forward. While we were able to find A, time ran out right before we could finish the calculation for C. Nevertheless, change in the students' attitudes was palpable.

Who explained working hard may help you maintain

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Return to the Fold

Well, at least the students remembered who I am, and some even seemed excited to have me back. I just started a new term and will now be going in to class on Thursdays and Fridays. I hope that the consecutive days will provide more flexibility in doing problem solving with the students. Instead of try to wedge everything into a single day (or two disconnected ones), I'll be able to continuously engage the class. Come this Thursday I will be doing my first word problem of the term, provisionally #3340 (with some minor alterations to encourage interest).

Though class was out for nearly two weeks, it seems that no one has lost their vim or vigor. In fact, several of the students appear especially stressed. This may be related to threats that they'll have to repeat the first term material if they fail to pass their midterms, or maybe it's just the return to school. I am usually content with letting Molly handle the discipline and restricting myself to instructional efforts, but trends have convinced me to be more confrontational with the students about their actions. In particular, several students use talking out, throwing things, and harassing other students as a means of demanding constant attention. It is no surprise that these actions are detrimental to the entire class (whether one chooses to ignore them or cater to their whims), but I've come across no good solutions. In many cases the parents are not involved enough to care, and removing them from the classroom simply puts them farther behind (which worsens their behavior in later classes). Mentioning that proficiency in algebra is a requirement for graduation merely elicits shrugs.

This suggests several, equally displeasing, possibilities:

• They do not believe that they are capable of passing high school.
• They do not care about passing high school.
• They believe that the issue will simply disappear.
• They do not understand the word 'required'.

The first issue is, perhaps, the most difficult to deal with. Its presence is obviously rooted in (lack of) self-confidence. Though not a universal truth, I feel that most if not all of my students have the necessary faculties to complete high school if they so choose. The solution is then one of how to convince the students that they have such abilities. Any solution that would work on one student is not likely to work on another. Ideally, imparting motivation to the student would not be the responsibility of a single teacher, but rather the responsibility of every person the student interacts with.

The second issue strikes a bit closer to home for me. One of my primary duties in the classroom is to impart a physical appreciation for math and learning in general. This is done with the understanding that if the students perceive a usefulness for education, then they'll desire it. Either this assumption is wrong or I have been inadequate in my description of mathematical applications. Again, it would be a cheery world if everyone participated in demonstrating the usefulness of education, but I believe (with no evidence) that it should only take one or two particularly compelling subjects to carry a student through high school.

As for the third issue; much like when I ask the students to share their work with me, they may believe that the best approach to an obstacle is not acknowledging that it exists. In this case, it's instructive to quote an already over-quoted text (and perhaps convince them that not every adult's memory is short),

"A towel, it says, is about the most massively useful thing an interstellar hitchhiker can have. Partly it has great practical value. You can [...] wrap it round your head to ward off noxious fumes or avoid the gaze of the Ravenous Bugblatter Beast of Traal (such a mind-boggingly stupid animal, it assumes that if you can't see it, it can't see you)."

As for the final bullet point; there are several students that fall into this category and the school's opinion is that full immersion is the best approach to learning a language. I question the wisdom of using a math class to teach language, but such issues are beyond my pay grade.

Uncanny Valley

I have a love/hate relationship with Wolfram. For example, Wolfram Alpha is a wonderful resource for online calculations, but it's coupled with a very restrictive user agreement. Likewise, Mathematica has tremendous functionality, but I always hated its notation. Well, I now have a reason to both be afraid of Wolfram, and be scared for the future of high school homework. I present to you, dear reader,

Step-by-Step Math

The short of it? Wolfram Alpha can now solve most equations that have analytic solutions and can provide you with the proper steps to arrive at the solution. Oh woe!