When I was a wee lad, I wanted, no, I needed a calculator. And my dad, in his infinite wisdom, said that he didn’t have a problem with me using a calculator.
If I didn’t need one.
So I memorized multiplication tables, played with numbers, developed a whole brain toolbox around how to play with numbers and get them right. I even developed the pattern of seeing two possible ways to get to an answer and making sure they lead to the same answer. For instance, if “x squared” is 144, I knew the multiplication table and can see 12×12 on one side of my inner vision, and on the other I knew that 12×2 was 24 and 12×10 was 120, so I could add those together and get the same numbers. Or on a multiple choice test, I could use one of those two ways to quickly get into the right range, and the test answers were usually pretty far off from one other, I could quickly narrow down the options.
Eventually I didn’t need that calculator although it was still faster, so I used it. Especially for things like adding up long sequences of numbers. And then I hit algebra and geometry and algebra 2 and even calculus. I spent hours — yes hours on pretty graphs for my solutions, finding the best answer, making hyperbole graphs, drawing sin(x)*tan(x) graphs. I probably used the most colored pencils of anyone in my high school who was not in the Art program.
You remember those days. Well, pretend that you do, ok?
Ms B had to take a statistics course for nursing. And for that, she needed a graphing calculator. You plugged in the numbers and it drew out your graph on its little LCD screen. Fascinating! A ten minute graph now took ten seconds. Well, at least she knew how to do the graphing, right? But her math wasn’t my responsibility and whoa, that little calculator was pretty neat too. She could look at the black on grey output and compare it to her paper and see that she had the right idea.
And now I’m reading The Talent Code and learning about focused practice, repetition, ironing out the errors, and myelin, and how long myelin takes to wrap around a “brain circuit,” and how that wrapping affects what we see as talent. Which is about a 10,000 foot view, sure, but you can see that I did a bunch of math practice, then people claimed I was talented at math. A direct relationship as it were between practice and talent.
I want to share this with my kids. And I considered putting Octave on the computers so they could see the glory of these cool graphs that equations make, but only after they build a few hundred themselves. I want them to have the practice behind the glory that is math. I tried to describe the formula of conversion from Celsius to Fahrenheit as a graph line to Miss B the other day but I’m pretty sure she tuned me out. (Yeah yeah, the slope is 5/9 and it’s offset by 32 blah blah blah). (Actually what I was trying to do was show her how to answer the question from her current knowledge… 0C=32F,100C=212F so what is 80F in C?).
But, like my dad, I could filter their tools by their practice level.
And then, because of a silly post on reddit.com, I stumble across wolfram alpha. Goddamn, wolfram alpha. You want to see the graph for Celsius to Fahrenheit? Here ya go:
actually this is F to C but you see the line?
Oh, and did you want a sine wave?
Neat. How about three dimensions ?
(note: I had a hard time building an ellipse because Wolfram kept changing the X axis so my ellipse would be circular. She’ll have to watch that.)
And here I was worried about the girls searching for porn? Porn is tame compared to the damage they could do with this — why bother to learn something hard if goddamn wolfram alpha (and I think I’m going to add that adjective to it every time I say that) will just jump in and do pretty graphs for the girls.
What do you do to filter this out of their possibilities? Look — you can e’en do this on your iphone!!
(ps: here’s the link I followed to G.W.A. )