Archive for January, 2008
Computers in math education
I’ve made a decision this semester that I want to try to keep all my notes in digital form, which has a number of advantages: I can search them much more easily, I don’t have to carry around a bunch of notebooks, and it makes it easy for me to keep a copy of my homework even after I pass it in. It also makes them easy to archive and back up.
This was working nicely for me until I went to do my first assignment for Network Fundamentals, my only class this semester with a fair amount of math in it. There isn’t any calculus, certainly nothing beyond some algebra, summations, and basic statistical method, at least so far. I sat down to take a crack at it and realized in about five seconds that my plain-text methods were not going to work nicely. It’s very hard to keep your thought process going without being able to see equations written out in familiar symbols and layouts. For summations especially, plain text fails miserably.
So I conceded that I would have to use something that could lay out problems in more readable formats. My first instinct was to reach for Microsoft Word, which I knew to have an equation editor that I had never used before. After installing it, I set about trying to set up my equation. After about twenty minutes of fooling with the toolbar (that conveniently has no words on it), I had managed to set up something resembling a fraction with summations on both the top and bottom. I was finally ready to begin to solve the problem, when I realized that I would have to go through that process again for each step through the solution. Not only that, but I had had to invest so much attention and energy into formatting the formula that I forgotten what the original problem even was!
The tool was getting in my way. How can I focus on the math problem when I have to spend so much of my energy just to write down one step? As it turns out, I gave up on Word and went back to good old pencil and paper. The number of digital advantages I lose by doing that pains me, but I just couldn’t see any other efficient way of solving the problems. The freedom and familiarity of the pencil (and eraser!) let me focus on the problem at hand, rather than the pencil itself.
This problem interests me particularly, as someone who has always been into math and who chose to go into programming. To write my homework on a sheet of paper means to have only one copy, which I have to pass in. Of course, I can photocopy it if I don’t mind spending a few cents or using the ink. But as a programmer, this strikes me as a violation of the Don’t Repeat Yourself (DRY) principle. My data should be in one place and one place only so that if I change it once, all its representations change. This, to me, is one of the major disadvantages of paper.
This made me think about all the other computer programs I’ve ever tried to do math on. To me, all merely supplemented pencil and paper, never replaced it. Can we ever have a math program that allows that level of free thinking? I can imagine that tablet PCs may be able to reach that level, but they are a long way from general adoption. Data would be difficult to edit without that very specialized hardware and, in any case, your data would be no more than some kind of image file, gaining you none of the searching advantages of digital text, nor much (if anything) in the way of automated calculations.
The bottom line is that, while there are a lot of programs out there that are good for displaying finished calculations, I’ve yet to find one that is as good as pencil and paper for actually doing math.
2 commentsRock Band
So Ethan and Tellef and I finally broke down and bought Rock Band on Sunday, and it is awesome. The drum set is a bit bulky for our living room, but well worth it considering the entertainment value the whole thing gets us. We spent pretty much all of Sunday and Monday (huzzah for well-timed snow days) playing it with Lauren, Pat, Dave, and Walsh. Here’s the way things are looking for our band (“The Keltons”) right now:
Me – Guitar, vocals
Ethan – A little of everything
Tellef – Drums
Pat – Guitar, vocals, 4/5 drums
Lauren – Vocals, some guitar
Dave – Guitar
Walsh – 1/5 drums (Pat’s dedicated bass pedalist)
With such talent available, it’s no surprise that we were rocking for pretty much two days straight. Lauren pulls us through most vocal tracks, to say nothing of her obvious talent on the cowbell/tambourine. Ethan can hold his own on pretty much any instrument and has a better voice than perhaps he ever told anybody. Tellef holds down the drum set, without a doubt the toughest instrument, except perhaps for some particularly evil vocal tracks. Dave’s smooth upright style is perfect for the bass, and whether out of pure smoothiness or laziness he uses it for the lead too. Pat showed us all how you’re supposed to sing with stunning renditions of “Epic” and “Timmy & the Lords of the Underworld.” And let’s not forget Walsh, the bass-pedal-pushing specialist for those of us who can’t make more than two limbs cooperate at the same time.
Unfortunately, our band remains incomplete. The Rock Band box only comes with one guitar controller, and the game is completely incompatible with all guitar controllers made previously. Although it’s depressing that we can’t use the Guitar Hero controllers we invested in, Rock Band is so much fun that Ethan offered to make the investment into another guitar. And so we set out to Best Buy today to find one.
We should have done some research first. Apparently, despite the fact that the game has been out for two months, there are still no individual instruments available for purchase. From anyone. They don’t hit shelves until February 4, despite the piles of Rock Bands waiting to be bought, each containing a precious guitar controller. Considering that the game is made specifically to be played with four people, this is just wrong. It’s one thing to have inventory issues if you are marketing a game that can be for four players, for instance, running out of controllers when (if?) Super Smash Bros comes out. But when you make a game that begs for four players so obviously as Rock Band does, it is your sacred duty to make sure that four players can play a little bit sooner than three months after the game is released. Right now the only way to play four player Rock Band is to buy another box set for $170 and use its guitar controller. Not nice, Harmonix.
That said, the game is ridiculously fun. I only wish that I had less homework so I could spend more time playing it.
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