Hypothesis: Proving trig identities unteaches functions.
After all, thinking of these as functions really just gets in the way, so all of our sensible students just treat these functions like variables.
(Thanks, Tina!)
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Hypothesis: Proving trig identities unteaches functions.
After all, thinking of these as functions really just gets in the way, so all of our sensible students just treat these functions like variables.
(Thanks, Tina!)
4 replies on “Trig Identities Unteach Functions”
I think it has to do with the convention of placing the exponent applied after the trig function evaluation before the parameter list. It violates the temporal order of the operations. Hell, it confused the crap out of me when I was a kid, and I was considered apt in math.
Treating functions like variables is just fine with me. In fact, I wish more students would substitute S for sin(x) do some simplification that way. Forgetting that you can’t cancel over addition when faced with complicated looking equations is the issue. Or that (a+b)^2 == a^2+b^2. It’s amazing the issues that appear when things look scary and kids are hoping for an easy way out of the mess.
isn’t that an application of structure?
When it comes to establishing identities, it isn’t uncommon for students to use ‘wishful thinking.’ Hey, if this cancels like that then were done!