For those who think I have no life...
This is the second night in a row that I've spent working. Well, kind of working, and kind of playing around on the internet and listening to music while pretending to work. I did get my printer fixed, a 12-week-plan for robotics written, and several 6th grade lesson plans written. (Last night I fell asleep on the couch midway through the 7th grade quizzes - it's a miracle I didn't have nightmares, let me tell you).
But this post is really about numbers, and it should be titled,
Where has all the wonder gone?
Maybe I was just lucky, or maybe the times, they are a-changin', or maybe I just don't pay close enough attention to what the kiddies are doing in their math classes (a definite possibility), but it seems like number theory has sort of disappeared from middle school math. Jonathan's comments below reminded me of the golden ratio, something I'd completely forgotten about, and about how you can use consecutive Fibonacci numbers to create more aesthetically pleasing rectangles, and about that episode of "Mathnet"** where the two math-detectives solve a mystery using the Fibonnacci sequence... I loved numbers in middle school. And I wasn't the only one; I think most of the kids in my math class understood that numbers could be mysterious, fascinating, even beautiful, at times. I liked numbers for their own sake,* prime numbers, imaginary numbers, being able to add & multiply & square in my head. I don't remember all of the details (I don't think I could tell you what an imaginary number actually is...)*** but I remember that both my father and a couple of influential math teachers fostered a sense of appreciation of the ways numbers turned up in unusual places and unusual forms and the patterns and tricks that were cool to know and to trade with others.
Math scores are low, and math is treated like a crisis, and I can't argue with the kids' dire need to be able to manipulate fractions and decimals. But where's the beauty, the playfulness, the gee-whiz?
And now, the footnotes that ramble on longer than the post itself. That's what you get at 1 am on a Sunday morning.
*Actually, I liked them more for their own sake than for their usefulness, as it was "practical applications" that turned me off of calculus a few years later. Then again, these practical applications that were supposed to motivate me to understand and value calculus tended to be stuff like different sized pipes filling swimming pools or sand falling into a conical pile, and, um, are any high school kids really motivated by piles of sand?? Hello? Later, in college, after I'd stopped taking math classes, a biology professor used a curve to show how even if you didn't know the exact population of a fishery, you could determine a safe harvesting-rate that would ensure population growth no matter what. If you fished on the higher end of the curve, you were almost guaranteed to overfish and drive the population towards extinction, but if you fished on the lower end, you could ensure that even if your population estimate was significantly off of the real number, you'd still fish at safe levels. It was both practical and beautiful, and so simple. It was like putting on new glasses and realizing how much you hadn't been seeing - suddenly, a new tool for looking at the world became available.
**Please tell me I'm not the only one out there who lived for "Mathnet", the ten-minute mathematical mystery series at the end of the PBS show "Square One TV." The fan website is hilarious, by the way, definitely read the confessionals. I think my mom had to delay dinnertime because no one in my family was going to budge from in front of the TV until after Pat Tuesday and George Frankly had cracked the code or tracked down the thief. Sometimes she would run in while stuff was cooking to catch the clues... I mean, I remember these episodes vividly: there was the Fibonnaci one, which took place in a mansion, and the clue was that what looked like a boring abstract painting on the wall turned out to contain the key to cracking the code, which was embedded in bricks on the wall, all in Fibonacci numbers of course; there was the one where George himself was accused of a crime, but he proved that according to wind speed & an airplane's velocity, he could not have flown back from his island vacation in time to commit the crime; there was one that had to do with cars getting towed away illegally, and George nearly got squished at the end, I forget the math part of that one, though...
***Is it the square root of a negative number or something like that? It is! ...Googling... Yay! i is the square root of negative one.