Monday, October 15, 2007

feigned facetiousness

Our school is having a 'sports day' on Saturday, which naturally means that we just received an all-staff email informing us that a large number of children will be missing class on Tuesday, Wednesday, and Thursday, in order to participate in so-called pre-determined events, such as javelin, which is supposedly a huge sport here. On the annual sports day, I mean. And by 'the annual sports day', I really mean during school on the Tuesday preceding the annual sports day.

The annual sports day is the biggest and best track meet of the year here, which means merely that it is bigger and better than the other track meet of the year, inter-house sports day. We take the kids down to the field, hand them a giant metal ball that they do not know how to safely throw and say, "Throw this," and the shot put event has begun. We line up the hurdles and explain, "You jump over them, climb over them, kick them over, anything to get to the end. It is best if you can clear them by about a foot so they don't bite you. The harder you fall, the tougher your friends will think you are." Then we give them medals and the season is over as quickly as it began.

I am currently battling the temptation to send an all-staff email of my own:

Please excuse my math students from 'extra-curricular' activities which take place during my math classes for the week of October 15. They have all qualified for participation in our current units on two-variable data, applications of differentiation, and number concepts. This is a unique learning experience, and it will not interrupt their regularly scheduled class. They will not be needing a bus ride or shiny jackets.

Some questions about "Sports" "Day" that I would ask if I thought there was an answer:

If so many of the events are "pre-determined", why do students have to participate in them?

If they have not thrown a javelin since the last "Sports" "Day", why is it worthwhile for us to bus them around the city to show off their skills? Are they really export quality?

If the sports are "extra-curricular", why do they all take place during class?

Why are 6 of the 16 kids on Academic "Probation" missing class to represent our school at these events?

Friday, October 12, 2007

prevention & blame

So another school shooting. The headline I see is "Lesson of shootings: Schools act too late". I am always amazed to hear bad news accompanied by accusations like that.

After the Virginia Tech shooting, the finger pointing began and it was decided that the university officials should have responded to early signs of a student's mental trouble. How? By sharing concerns with the kid's parents? The school would have been sued for violating his privacy. By jeopardizing his place in school just because he was a demented rascal? That would be stifling his freedom of expression. If we got rid of all the demented rascals, where would they go? Who would get to decide which people fell into that category? How many people display some level of mental distress, and what kind of society could effectively regard them as future mass-killers?

Who gets the blame for a hurricane? The federal government. Until we find out that the local government actually did receive federal funds for a levee project that never happened. So we blame the local government. Then we might blame the people who knew that living in a swamp near a boisterous gulf could lead to problems. We have to blame somebody, because a hurricane doesn't just happen. It was probably global warming, so we should blame the auto-makers.

After the fact, people act like these events were foretold and they blame the lack of prevention. If the prevention had been in place, they would have resented the insinuation that evil thoughts lead to evil deeds. They would have resented the insinuation that they could not stay in their home, and against government orders, they would have stayed. They would have resented the insinuation that Koreans could put themselves and others in danger by travelling to a warring nation full of political strife. Any congratulations to the Korean government for telling them not to go? Of course not. Instead we blame whatever army has been antagonizing those peaceful terrorists.

The accusations really imply that all organizations of every color, shape, and size should have a well-rehearsed plan in place to deal with pandemonium. There is a need for a scapegoat capable enough to foresee everything and protect us from it. But how much of our resources should be dedicated to dealing with astronomically rare disasters? How paranoid can we afford to be? Should we be so paranoid that we want to prohibit school kids from being part of a cult? Apparently not. Should we be so paranoid that we want to take away a nation's ability to wage nuclear war if that nation supports terrorism? Apparently not.

The need for a scapegoat to deal with societal problems that nobody really affords to prevent is universal. This is because we each are secretly devastated as we fearfully fathom our own personal depths of guilt. If we could only agree to pin it on someone... because the only way to really live this life is to know that my sins are gone.

Thursday, October 4, 2007

joys of calculus

I have had a number of mathematical epiphanies lately in calculus. A few years back, when I was hacking my way through calculus at the U of M, I never imagined that the derivative of a parametrically defined function would ever make sense to me. I also never found implicit differentiation to be all that exciting. I figured out how to move the numbers and get the answers, but there was no beauty to it. I guess both of those topics seemed like untidy little loose ends that were clumsily dealt with by the big-haired math guys from days of yore. Boy was I wrong. I now feel like I can understand the necessities and the mechanisms for each of these concepts, and I really can appreciate the utter inspiration.

Here's what had been missing: In both cases, we are able to find a derivative dy/dx in spite of the fact that there is not the traditional relationship between independent and dependent variables. In the case of parametric functions, x and y are both dependent variables defined in terms of t, the parameter. In the case of relationships which are implicitly defined, there is not a proper arrangement between independent and dependent variables. In both cases, the graphs of the functions, the patterns of ordered pairs that satisfy the equations, exist on the x-y plane and therefore have slopes which are defined as the change in y compared to the change in x, or dy/dx. The ways in which this quantity is obtained are remarkably clever.

Anyway, most of the people who read this will be the more grateful to be finished with math forever. The rest of them will wonder how I never figured this out until now.

Today for two of my calculus sections, I delivered (with relish) the third installment of the power rule for differentiation. We are now justified in using the rule when the exponent is rational. For my efforts, I got a bunch of unimpressed stares and one "that's the same result we got the first time". Of course it's the same result, isn't that great? But now we have shown that it works for rational numbers. The first time, we were only able to algebraically show that the rule worked whenever the exponent was a positive integer, and our proof made no sense for other powers. After that, we used the quotient rule along with the positive power result to show that negative integer powers give the same rule. Now we have used implicit differentiation and both previous results to show that the exponent can be any rational number! Next class we'll prove it for the reals!

Uhhh... Mr. Burchell, why didn't you just tell us the real number thing at the beginning?

From my point of view, we are using our elementary tools to construct bigger and better tools, creating the amazing structure of Calculus from simplicity itself. Some of the students wonder why we don't just start with the awesomest tools. Because if we did, it would not be awesome.