Today my son was working on graphing. He wanted to know how to create an equation that would result in a horizontal line. We went through several options but to save a bit of paper; I grabbed the online graphing calculator (click the free calculator link). After we figured out the horizontal line (y=0x; add something to it to move it above the base X line so you can see it better); Dude wanted to explore the different buttons. So we tried 'abs'. I was smart enough to figure out that meant 'absolute value' which is a fancy way of saying it can't be negative. (Dude has seen that as a pair of straight bars around the number) It makes a pretty V graph.
Then we also tried 'sin', 'cos', 'tan', and 'e'. I honestly for the life of me could not recall just what those were! I mean I know sin and such, are trig functions that end up in some sort of wave, but as to what it does to X, or why anyone could care to do so.....I really have no clue!
The first thing I noticed was my son happily changing the equation with no real concern for the total explanation. He was content to see what differences were between the three trig functions (e was a boring line). We spent a few minutes testing 'sin(60X)', and sin(X+4) and the like. All without him knowing just why the graph changed.
Maybe it was better for him to play, than for me to explain it all. Maybe if I let him play for a long time like I let Baby girl play with shapes, and counters he will one day understand the Trig functions as simply and easily as he crunches numbers. Or at least better than I do.
We once borrowed a computer game from the library. It had some sort of 'game' that involved choosing numbers and watching a ball, of size determined by the numbers, move based on those numbers. The first thing I wanted was an explanation. I wanted to know just how the numbers effected the ball, so I could know what I was doing before I put anything down.
Dude on the other hand just plugged in some numbers and noticed patterns. It took him quite some time, he was having a blast long after I grew bored. I am not sure he ever determined all the rules, but I know he was willing and able to determine something based on old fashioned testing. (not EOG testing, but actually try something and see what happens)
The wonderful patience and curiosity of children never ceases to amaze me. Not all my children are willing to test all things, they are of course unique. But they all are far more interested in testing and exploring than I am. Only since beginning to teach, or better still learn with the kids have I gained some of my thirst for knowledge back.
When Dude decides he wants details I hope to be ready (thank goodness for a father who remembers all this math! -and has the patience to keep trying to explain it me.....) But I also hope Dude has a plenty of chances to play and see some connections on his own.
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