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!

Persistence Persistence Persistence Persistence

Maybe it is a bit inappropriate to reference Sisyphus when describing my work with the students at YHS, but it is somewhat unavoidable. Some days progress seems slow and halting and is inevitably followed by an equally large backslide. In light of my difficulties with the most recent problem of the week, I've decided to write a separate, but connected, piece.

Opposite to my tragic Greek brother's (after)life, a motif of 'lack of persistence' appears in many of my discussions with Mrs. Porter. In contrast to many that I know from college, the students in our classes find even the most modest challenges to be discouraging and disheartening. An equation that is slightly different than the one before is enough to render the student incapable of absorbing any information for the rest of class. All but a few are unwilling to acknowledge any difficulty, and in the worst cases, those confused turn to distracting the people around them. Most will disregard any words of encouragement and genuinely believe themselves incapable of solving certain problems. In these cases, I try to lead the student through a few example problems and have them tackle the remainder using those cases, but often they refuse to do any work independently. I've had several students throw their work to the floor as soon as it became apparent that I wasn't going to provide them with the answers followed by accusations of unfair treatment.

To their credit, many of the students are being asked to operate at a level much higher than they've ever experienced before. A large number have assessment scores which place them at elementary school levels, and yet we demand that they learn algebra. To make things worse, Mrs. Porter tells me that many have never had to do homework or take notes before, and must be taught the importance of both. Finally, each class is interrupted by futile writing/reading assignments that provide the students no feedback whatsoever. It is rather difficult to ask the students to do work that you yourself don't believe is useful or helpful. These factors contribute to a class whose content is pretty simple from a conceptual standpoint, but moves at such a fast rate through different assignments and subjects that few students can keep up.

The other day, Mrs. Porter asked me what it would take to properly teach the students. For many of the students in my class I believe that year-round school, with longer days and approximately half of the students per class are all requirements (there are many reasons for these, but they are out of the scope of this entry and for another time). Of course, there isn't a person in this world that could convince all the necessary parties to accept these changes, but for the current crop of students each step seems like a battle. I find myself wondering if any of what's being taught is retained. Most importantly, I ask how to convince the students that persistence pays off, because lacking that they'll be average in their achievements at best. Certainly, the concept isn't new to them, too many play sports or participate in other competitive events, but none of it is applied to their school work, or at least to math.

Fractional Learning

Over the past months, I've noticed that there is a severe deficit in the students' understanding of fractions and it has not been improving. Realizing that they're shorthand for division, how to reduce, reciprocals; each class I get a question about one of these subjects. In an effort to cement their understanding of fractions, I chose to do the PotW #5260, "Fraction Debate", over a period of two days. Usually, Mrs. Porter and I have attempted to finish problems within a single class period over the course of twenty minutes. However, this doesn't provide enough time for the students to produce a whole lot of work on their own. Spreading the problem out over multiple days is an obvious solution, but my days at YHS are not consecutive. By the time I return to the classroom, the students will have either lost the problem sheet, lost their notes, or forgotten about the problem entirely. In this case, we started on Friday, and I returned on Monday to complete the problem, as the students were off after Tuesday for Thanksgiving break.

At the start of the problem I broke the first class up into groups of three and the second class into groups of two. I attempted to choose groups whose students' strengths would be complementary. In addition, I tried to avoid placing the most talkative students together. This step alone proved to be exceptionally problematic in the first class. Every student wanted to work with their best friend and would outright refuse to work with anyone else. Regardless of any encouragement on my part, they just would not work together and kept on trying to establish their own groups. In the second class, I had the students work with the person to their left as Mrs. Porter's seating assignments had done most of the work in keeping problematic students apart. This session went much better, and the students seemed much more obliged to work together (though there were still a number that didn't try particularly hard).

The problem at hand is particularly interesting because it uses fractions, inequalities, and (I believe) a great introduction to proofs. For this reason, I started by explaining the difference between definitions and theorems. Definitions being the most basic rules of math that we accept as true without proof and theorems being the subsequent rules built by applying definitions. I then had several students read the scenario out loud. While some students dislike being put on the spot and having to read, there a fair number that are excited to participate and I think that more students pay attention when one of their classmates is doing the talking. We then proceeded to Noticing and Wondering as has been done in the past. This section appeared to work much better than before, the students seemed more apt to work together in generating ideas than by themselves. After giving them about five minutes to compile some ideas, I started asking them for their observations and proceeded to write them on the board. Their willingness to provide feedback has increased compared to the first problem I did with them, and I got several good suggestions. However, I found that both classes concentrated on the numbers in the example pictured above rather than key phrases in the scenarion; "any proper positive fraction," "add 1 to the numerator," "add 1 to the denominator," etc. In addition, I had notable difficulty in convincing the class that 4/5 > 3/4. Even after putting the decimal equivalent on the board, some were reticent to accept the statement.

In light of the progress made on the first day, I was very excited to have them work on the proof. I thought it would be optimistic if one or two students figured out how to complete the problem, but I hoped that they would be able to start work on it and write the comparison in algebraic form. I ran into timing issues in the first class that prevent me from giving the students time to work on their own. Instead, I tried to turn the problem into a class exercise with me guiding them through the problem. I lost the class almost immediately when I wrote the comparison of the two fractions with two variables and few numbers. Despite having already gone through an entire chapter on solving equations, the students do not seem to have developed a lot of flexibility in their ability to solve problems. The inequalities alone seemed to confuse most of the students and several didn't even know why variables were being used. The concept of a "general solution" was much more difficult to grasp than I initially expected, and only the students I spoke with individually seemed to see the point. There were several different ways of solving the problem and I had wanted to show the ones that I had found to the students so that they might see there was more than one way of approaching things. Unfortunately, it was difficult enough to get them through the first solution, let alone the subsequent ones. As has become common, there were maybe 5 or 6 students altogether that had genuine interest in understanding the problem, but their classmates proved to be too effective at distractions.

Engage!

Here's a short article on the gender gap between girls and boys in science education. It highlights some interesting results, unfortunately, the paper does not provide much insight as to why girls are not as engaged in these settings.

Studying the science gender gap at the high school level

Miscellany

A few brief notes:

After receiving some complaints of the comment system not working, I've changed the settings to allow anyone to comment. If problems persist, please contact me and I'll see what I can do.

The hip new thing on the internet these days is Google Wave. I've been playing around with it and I think it may be a useful place to discuss class specific topics. For example, I've created a "wave" with the word problem I plan to do this Friday. If you'd like access (even if it isn't necessarily for the TF program), I have several invites remaining, send me an email and I'll set you up.