The Nuclear Option

For me, this will mark my final entry for the year. Many things have changed in my classes during the last few weeks. Molly had to leave for the remainder of the year due to medical issues, and a substitute teacher, Mr. Mustapha, has taken over. While I always felt that Molly and I had different ways of approaching the students, Mr. Mustapha seems to share much of my philosophy. He has been more willing to write referrals and tries to be as fair and consistent as possible. Nevertheless, the students still realize that they're basically on a boat without a captain, and Mr. Flowers has started delivering the lecture for half of each class. It is in this environment that I gave my final presentation, one that I had been thinking about for quite some time.

As the year has progressed, my presentations have become more simple with each time. Part of this may be attributed to time constraints on myself, but there's a more overriding reason for it. Previously I had tried to fit into the curriculum as best I could, making math the first priority and application secondary. While there is no reason a priori that this could not work, I found that my talks ended up becoming rather dry in spite of the best intentions. This time, I focused almost entirely on the application with few equations and only a very broad overview of how math was related. For this reason, my usual slideshow was cut down to about 7 slides that complemented the talk rather than led it. This change was also inspired by some interesting notes made by Edward Tufte on the subject of slideshows. For this reason, I will briefly outline the talk below.

Slide One: The Gadget
I began by informing the students that this would be my last day with them. I had planned on being a bit more subtle about the affair, but Molly's sudden departure proved rather disruptive. I mentioned that I would be going to Cleveland to work with NASA for about 10 weeks on my research. I brought up that I'd be shifting from a math oriented approach to one that focused on the application but assured them that math governed each aspect of the talk. Afterward, I asked the students what kind of engineer I was and reiterated common perceptions about the word "nuclear". I then drew their attention to the slide and told them that it was a recreation of the first nuclear bomb ever detonated, The Gadget. For some historical background, I mentioned the Manhattan Project, its duration and some of the people involved.

Slide Two: Ivy Mike
After mentioning that the first nuclear test occurred in July 1945, I projected a rendition of the Ivy Mike test. I used my hands to indicate the approximate scale of the picture. I mentioned the TNT-equivalent of the first nuclear test and tried to describe the sheer magnitude of the event.

Slide Three: Uranium
I told the students that we were getting a bit ahead of ourselves, and really had started at the end of a long story. After probing them for their knowledge about atoms, I also attempted to convey the size scale of an atom. I also described the basic subatomic components along with a qualitative description of radioactive decay. In particular, that uranium is always a bit unstable, but that  it can take around 100 million years on average for a single atom to decay.

Slide Four: Fission
This was an excellent segue into how adding a single neutron could disrupt the balance of the atom and cause it to split apart. Because the image of smaller nuclei being flung away from and fissile atom inherently implies kinetic energy, it was simple to describe the reaction as exothermic without resorting to the concept of mass difference. I also indicated that on average two or so additional neutrons were generated for every fission. When asking what would happen if I grouped together a large number of uranium nuclei, it became pretty clear that there would be a large growth in energy and neutrons.

Slide Five: Hiroshima
After building up to the excitement of understanding the bomb, I shifted toward its effects. I mentioned what happens immediately after a blast and the resulting effects on the people below. I tried to emphasize the human aspect of the situation and expressed my dismay that one of the greatest scientific achievements was also immediately used to kill hundreds of thousands of people. That the event also signified the beginning of my field made it especially relevant.

Slide Six: Atoms for Peace
The idea of an uncontrolled chain reaction was pretty well developed by this point, so I introduced the concept of a neutron absorber and moderator. Using a clever combination of the two, one can create a device where the number of neutrons is always constant as is the energy output. I mentioned that the energy output could be used to heat water, run a turbine and generate electricity. As a side note, I gave a brief description of Cherenkov radiation, in terms of the wake following a boat in water. Following all the advantages of nuclear fission plants, I also discussed the fact that every method of generating energy produces and undesirable byproduct, in this case nuclear waste.

Slide Seven: The Z Machine
This led to the concept of a nuclear reactor with a less objectionable byproduct. I mentioned that energy could also be produced by joining small nuclei together, and that the natural deuterium found in the water could provide the Earth with power for millions of years. The only byproduct being helium (I neglected to mention the low-level activation of reactor materials). This led to the question of why fusion isn't being used for all power, at which point I expressed how the reactions require an environment that's hotter than the sun. I briefly described several approaches; the magnetic bottle, inertial confinement fusion (both NIF and the Z Machine). I ended by describing how this was the material that had captured my imagination and got me into the discipline I chose. I thanked the students for letting me work with them throughout the year, and said goodbye.

The reactions were different in my two classes, but more students were engaged than ever before. I got a lot of strange questions ranging from superpowers, to nuclear guns, to how bombs are actually built, and more all of which were entertaining and interesting. Third hour still suffered from several students that couldn't keep from talking loudly and interrupting me (including one that was eventually sent away by referral). After being instructed to stop talking to their friends another student harassed me with the poorly veiled sarcastic remarks before asking how science had anything to do with math. If the dear reader will recall, I have gotten this question almost every time I have given a presentation and always from this student. I asked the student to stop interrupting me and that the issue had already been explained to them several times, including at the very beginning of the talk. This of course drew accusations that I was being rude and dismissive. I barely managed to eke out the end of my talk about how I had learned about communicating technical principles from them and doubt that many heard it anyway.

Fourth hour was generally more receptive and those that didn't care had the decency to just fall asleep. Several seemed genuinely interested and appeared to get a lot out of the talk. It also helped that many of the students that are usually disruptive just didn't bother showing up. I had a great time with the talk and feel like this talk was the first unequivocal success for me this year. Afterward when I thanked the students they began to clap for me, and that was about it.

In respect to the TF program, this year has been a bit of a rollercoaster. I'd feel exhausted whenever I left YHS, but always managed to rebuild my eagerness for the next week in the hope that things would progress. With the end of the school year in sight, I think it is fair to say that some students did progress, but a large number simply remained stagnant. While the behavior has greatly improved, there is still a large margin between where the students are now and what is acceptable. If the final grades are a true reflection of how much the students understand algebra, I would be surprised if more than 60% were moved on to geometry. I was in the district for a limited time, and understand it much less than those that work there day in and day out, but my impression is that instead of trying to bring the students to the expectations, the expectations are brought to the students. In addition, my discussions with students and teachers indicate that many parents' involvement in the education of their children is minimal. On top of it all, many of the students have an air of entitlement about them; that the teacher and myself were there to serve them. The combination of all these factors is a bit frightening.

While my exposure to the politics of YHS was small, the tension between the faculty of YHS and the White House was palpable. How the school is reorganized under its new principal during the summer will be indicative of how the school will evolve over the next few years. There is a lot of mistrust floating around, and while everyone agrees that something is wrong, no one can agree on what it is. Hell, no one even knows what missing the AYP requirements again would mean. At the very least Mr. Moore must prove himself a charismatic leader that is capable of convincing others in his plans. There is a still a lot of loyalty and respect for Mr. Brown, and many don't seem to understand his departure. To make a long post longer, below is a compilation of some changes that I think should be implemented.

• Return to the old grading system: Basically, the current system assures that the student cannot receive below a 50 on assignment so that poor performance on a single assignment is not overwhelmingly discouraging and an enormous setback. While this is an admirable goal, the reality is that this policy artificially inflates grades and gives the appearance of improved performance. It has become quite difficult to fail a class (though some students still manage) and I can guarantee that many students will be moving on to sophomore level classes without adequate understanding. In addition, if a class has enough grades, then a single bad grade will not doom a student anyway. Stop lying to yourselves.
• Intervene for recurring absences: There are some students that miss almost every day of class, a formula for failure (or moving on without understanding the material). While parents are notified of each absence, there appears to be little effort to alter the situation or any efforts are inadequate. While the Program of Study lays out an extensive policy, I cannot help but wonder at its implementation. At the very least, I notice that it promises in-school suspension for recurring cases, but there is no such thing available. I have heard of students missing over 100 classes in just this semester or around 1 out of 5 days of school. This is just plain embarassing.
• Confiscation of electronic devices: Look, all this pussyfooting about liability is dust under the rug. If students are listening to music or text messaging the only option for teachers is to remove them from their classroom. This reduces instruction time and helps no one. That no one seems to have come up with a better solution is scary.
• Comprehensive school-wide behavior policy: There has been some effort to produce something similar to this, but it's limited to a small set of rules posted on everyone's doors. A group of teachers, students, and parents should be assembled to develop a single document on expectations and rights of students as well as appropriate reactions if expectations are not met. Once approved by the administration, the document would be signed by all parties to signify that they understand the document and promise to abide by it. A necessary corollary is that the document is fully and consistently enforced.
• Get parental buy-in: While Molly seems to be calling parents incessantly, I have rarely seen the phone calls result in any significant change in behavior. Parents have enormous flexibility in correcting the behavior of their children, while teachers are much more limited. It is reasonable to expect then that the parents provide the brunt of corrective action. If there is a better partnership between teachers and parents, then I believe that the school would be much more effective. Of course, this is one of the more difficult suggestions to incorporate.

I'd like to make my gratitude toward Molly public. She's been a great help in learning about how to communicate with students and the working with her has been a pleasure. I wish her and her students the best in the coming years, and hope that others will take a chance to get involved in the TF program.

The Full Monty

Last Friday I gave a presentation that I had been rather excited about. After seeing kids shoot dice incessantly, I decided that I'd do a talk on probability. I hoped that when I had finished, everyone would understand dice and never want to play the lottery. I planned for the talk to go for about fifteen minutes, and I think that I finally had my timing down. As dictated by Moore's Law, Molly was out sick and I was suddenly faced with the class all by myself.

The beginning the class went much like most classes did when run by Molly. We covered the starter, answers, and went over the homework. However the students were terrifically more difficult to settle down. Several refused to pay attention and found that they liked wandering around the classroom better. I always had pity for substitute teachers, but I must say that this reinforced that sympathy by a few orders of magnitude. I tried reprimanding the worst students, but waiting quietly until everyone realized I had stopped talking seemed to have a more profound effect. In particular I was grateful to the several students that actually took to encouraging their classmates to pay attention. I had the pleasure of stopping a near fight, and by the time class had ended I was completely worn out.

Before beginning the talk I gave the students their homework and asked that they either follow the talk or quietly complete their homework. Another TF had tried something similar with his class and it seemed to work very well. I forgot that in his case he had physically separated the two groups of students, in my case I left them in their seats which was a bit disconcerting. Disappointingly few seemed to care about what I had to say with only about 3 in each class giving the talk much thought.

The presentation began with an explanation of probability and a simple example, then moved on to the slightly more complex case of two die (including a quick MATLAB simulation). Afterward, I explained independent probability and showed how the odds for the lottery were calculated. Then I presented an oddly morbid list of things more likely than winning the lottery, and ended with the Monty Hall problem. This presentation was deliberately shorter and less complicated than my previous ones. I had very little writing on the slides, and made an effort to reserve them for visualizing the talk. In that sense, the lecture went much more smoothly than before. The Monty Hall problem was particularly fascinating for the students, though by the time I got to it most of the students had tuned out or settled in on their homework. I probably would have been better served by starting with it instead of ending with it.

While I have tried to aid Molly in meting out reprimands, I did not have the authority or the mental preparation to go it alone. After suffering through the question dozens of times I can understand her impatience with students asking to use the bathroom (though I still believe the school policy of locking them during lunch hours is absurd). The presentation also likely suffered from not being directly related to the class material, but I had made the decision to consciously break from it. In the past having to track the curriculum with my presentations always felt rather limiting and I saw a chance to try something different. In any case, I intend on doing one more presentation on my final day at the end of this month. The subject will still be somewhat distinct from class lessons, but I hope to use some of the other lessons from Friday to better inform this one.

See below for the presentation and MATLAB code:
Presentation
Dice Code

Lillian's Lines

On the suggestion of Max over at the MathForum, I recently did a Problem of the Week called Lillian's Lines (#5180). In our discussions, we found that some of the problems I had done in the past were a bit abstract for the students to really get a hold of. In contrast, this one had a very straightforward solution (provided active participation and understanding of the rules), and several more in-depth solutions.

Simply put, the problem presents a square grid that is 36 by 28 squares. One takes a ruler and starts in the upper left corner, then draws a line at 45 degrees to the outer edge. Here, the line "bounces" at 45 degrees and continues on to the next outer edge. This process is repeated until the line ends up at a corner. The question asked is how many squares did the line cross through to get to the corner. The scale of the problem is large enough to make even the simple solution require some time to get. In addition, several examples were provided that hinted at patterns in the lines that could be used to reduce the magnitude of the problem.

I began by providing each student a print out of the problem statement (minus the question), a sheet of graphing paper, and a ruler. In each class I had two students read through the problem and then conducted my simplified version of Noticing and Wondering. As previously detailed, this involved asking the students to point out what they thought was important in the problem statement, I'd then highlight the relevant passage on the overhead. Quite a few noticed the recurrence of what they called the "fish" pattern and the "upside down heart" pattern. I then presented the question to them, and asked that they try and work through the problem themselves. With about 5 minutes left in my discussion, I called the students' attention back to the front in order to discuss their solutions.

The simplified Noticing and Wondering worked about as well as I could have hoped with several students providing input. Usually singling students out to provide some kind of response is asking for the silent treatment, but in this case most were glad to respond. Even with some modest guidance and hints no one appeared to make the connection that the larger problem could be simplified. As usual, there were minor issues as I struggled to write on the board and projector simultaneously, but this will hopefully be solved with further practice on my part. While I understand the great value in group work, past experience suggested I'd have more results if I asked the students to work individually and Molly agreed in this respect. Mary Beth had come along to observe the class, but got swept up with Molly and I as we walked around and helped the students work on the problem. Surprisingly few were able to follow the rules in the problem statement, and only one or two came up with the final solution. Many had problems understanding the importance of making each line precisely 45 degrees. I made an effort to highlight this fact in the second class with an additional diagram, but I still noticed many students were being a bit impulsive in drawing their lines.

It was interesting to note here that the two classes acted very differently when set off on their own. The first class worked quietly for a few minutes before devolving into commotion and tangential discussion. A few continued their work in spite of the disturbance, but at this point the class appears irretrievable. The second class worked for almost the entire allotted time, and those that didn't work quietly minded their own business. In both cases it took a while to get the students started, but the fact that the problem could readily be solved with some effort definitely appeared to have some appeal.

I wanted to allow the students long enough to reach the solution, but unfortunately my time was limited to 20-25 minutes in both classes. There were no moans of inadequate time when I called the attention back to the front, but I do think that they might've felt cheated. I walked each class through the solution by reducing the problem slowly, and at each step asked the students careful questions so they could lead the way forward. I never did make it to some of the other more interesting solutions, but I felt like those that listened at least had a good starting point.

Ultimately, the problem was a mixed success much like each one before. It is apparent that the patience and work ethic of the students has improved by leaps and bounds over the beginning of the year. At the same time I feel like they do not have a lot of the intuition necessary to solve even the simple problems. In my preparation for the lecture, I hadn't even considered that they would have such trouble drawing 45 degree lines. Mary Beth noted that there didn't seem to be enough time to work the problem out properly. I don't necessarily agree with that characterization. The time was limited for the second class because the majority were actually engaged in solving the problem, but the time allotted was far too long for the first class that lacked the discipline to put more than a passing moment's effort into the work. I had hoped that scheduling my days for Thursday and Friday would help to alleviate the problem of cramming an entire complex problem into twenty minutes, but the scheduling issues have proved to be greater than anticipated. I'm more convinced that the original vision of doing the problems on a day to day basis is the right approach, despite the interruption in continuity but in my position I'm simply not around to make this happen.

This very well may be the last Math Forum problem I do this year so I'd like to make a few notes on the overall experience. The library of problems is immensely useful and well-organized though some have more support materials than others. While most are rooted in real-life applications of math, they still seem a bit off the mark for the students. That is, the students may like football, but that doesn't mean they'll necessarily enjoy a math problem about football. At this point, I think that outright trickery and deception is required to teach mathematics. The problem solving process that went along with the Math Forum problems is very logically set out, but seems better suited to classes with superior behavioral characteristics than mine. Only a small subset of students would engage in Noticing and Wondering, and many times the students seemed to be unclear about the point of the whole exercise. I admit that some of the issues lie with the instructor rather than the students. I could have been more clear in my explanations and instructions to the students. Of particular note, my time management could be greatly improved. While I think there is potential for the program, it really should be implemented on a daily basis and ergo by the primary teacher.