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.

A gRAPh

I saw this site about a year ago, but forgot about it until now. Maybe half of the graphs are appropriate for a high school setting, but they might be a neat way of explaining how to interpret visual data. It doesn't hurt that many of them are pretty hilarious.

rap represented in mathematical graphs and charts

Sixty Symbols

While looking for videos of Chladni plates for my presentation on sound, I came across a site with a lot of well produced videos on common physics topics. Called Sixty Symbols, it is a series from the University of Nottingham physics department. Most run from 7-9 minutes long and usually feature a demonstration of some sort. Like the PheT site, some of the videos are better than others and a few of the professors they talk to seem ill-prepared. Other videos are much more intriguing, my favorite so far is the one on Schrodinger's Cat. The level of the talks seem a tad high for my 9th graders, but may fit well in a science class.

Sound Principles

Today I gave my first large presentation to my two classes. On an earlier occasion I did a short talk on the LCROSS mission and had the class do basic calculations. That didn’t go over so well because I think many of them don’t share quite the same enthusiasm for space as I do. A few weeks ago I handed out a small piece of paper asking the students to write down a topic that they’d like me to talk about. I left the field open to any subject as I didn’t anticipate having any trouble finding math in even the most obscure suggestions. One of the most frequent suggestions was music; though many simply wrote ‘rap’, there were others that mentioned music, and how to build instruments. I decided that a presentation that covered the basic principles of sound and how it can be described mathematically would be the best place to start.

I used a few principles to guide how I put together the material. I decided on two “acts” in the talk. The first was rather basic and tried to imbue a qualitative understanding of the necessary principles. The second act used those principles as a foundation for real world topics that are difficult to analyze without an advanced degree, but would hopefully be understood intuitively. I also tried a form of multimedia blitzkrieg; almost every slide had a visual and audio component with several short videos near the end. It was my hope that this would keep the students’ attention much better than a straightforward, dry lecture.

My talk began with a discussion of what exactly sound waves are and some of their properties. I made a conscious effort to avoid words like transverse and longitudinal, but instead demonstrated the concept using a Slinky. By hooking my laptop up to the overhead speakers, I then played back various sine waves and combinations thereof. I did my best to show them how sines could be manipulated in much the same way as regular numbers.  I mentioned how the simple ideas behind superposition could be used for tuning instruments or for noise-cancelling headphones. These examples helped a fair amount in grabbing the attention of the students. I ended this first act with mentioning how combining a sufficient number of sine waves could added in such a way as to make any sound imaginable. This was a natural precursor to drum machines and electronic music which in turn led to music in general.

In the application portion of my talk, I went over many subjects. The first one was on turntablism. Here I used a microscopic view of record grooves to explain why scratching sounds like it does. I also used a video of an oscilloscope output to show how music is really just a collection of sine waves. My next target was how to use speaker response curves to select a good speaker. This slide did not go as smoothly as the turntablism one, probably because I did a poor job of discussing why a flat response curve is a good one and many found the topic as an excuse to discuss what speakers systems they wanted for cars. I also used a slow motion video of guitar strings vibrating to discuss how stringed instruments make noise and why many of them have large resonant bodies. I wrapped up the discussion with a slightly tangential video, but one that the students really enjoyed. I chose the collapse of the Tacoma Narrows bridge as an example of waves gone wrong. Like the resonation in a guitar body, I showed them how the bridge resonantly reacted to the winds.

Overall, the talk went very well. While there were a number of kids that got distracted, talked out of turn, or passed notes, many seemed genuinely interested. The best part of my day was when several told me how interesting the presentation was at the end of class. One student who is usually hostile and taciturn was very engaged by the talk, listened to me and volunteered answers. I was nonplussed. My only regret is not having a more interactive presentation; I’ve been meaning to make an ultra toriton for a long time and it would’ve been a perfect accompaniment to the talk. I’m planning to do my next talk on football which will likely be a bit more challenging to put together, but I’m hopeful. In the mean time, anyone who would like to look at my slides, can be download them  here (careful it’s nearly 20 MB).