I love Desmos, I love graphing packages. I even *like *TI-8x graphic calculators (Even the old, old TI-82s with dodgy screen contrast).

But sometimes it needs to be graphed by hand. Sharp pencils. Accurate marks. Slow, deliberate, calculation of points.

Why?

Because there’s something about realising that when you plot sin(x) and cos(x) they have the same value at x=45 that comes from *actually drawing it*. Or that something *horrible* and *frightening *and *wonderful *is happening as you approach tan(90). Or that cosec(x) and sec(x) look totally weird but make sense when you try to make a table of values and compare to sin(x) and cos(x).

Because in the end, if you haven’t drawn it accurately and had your hand try to make the shape, what hope do you have of sketching or visualising?

Because in the end, ‘I drew it on my graphic calculator’ won’t earn you marks.

Maybe it’s blasphemy. But tomorrow we will sharpen our pencils, fire up our scientific calculators and draw some goddamn trig functions. And, since I’m in a bit of a mood and I haven’t finished my tea, I’ll fight anyone who tells me I’m wrong.

Enjoy the smell of pencil shavings.

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I agree. There are plusses and minuses to having graphs so readily available. I think we sometimes lose the beauty of mathematics and the ways of thinking developed over the centuries because we have graphs easily accessible. Graphs used to be harder to make so the first response wasn’t to graph it. On the other hand, I also think that having graphs available does make the concepts much more tangible to students.

Thanks Mike, I think its a fine balance to strike, you want to help develop students’ graphsense, and sometimes graphing packages make that easier, sometimes they just act as a crutch. Room for both I think 🙂

Reblogged this on The Echo Chamber.