I finally get it — you don’t have to worry about memorizing a bunch of formulas if you just understand where they come from. You can always figure them out again.

— unidentified student in Doug’s class

from the comments on Kate’s post Formulas? What Formulas?

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Awesome and inspiring quote! I love it when my students really “get it.” Thanks for the link

Exactly. I was in calculus II before I realized my professor hadn’t memorized some things, e.g., derivatives of trig functions other than for sine and cosine. Later realized myself that I didn’t need to know the double angle formulas for sine and cosine, since they fell out of the angle sum formulas. Of course, some things are easier to recreate/derive than others, but in the real world, no one puts a gun to your head and says, “No books, no internet, just your memory.”

Why we make kids think math is all about memorizing meaningless rules and procedures is beyond me.

On the other hand, when I’m reading higher math, I really do struggle with all the new terminology, notation, etc., and it gets worse when there’s no consistency from text to text with the latter. Abstract algebra authors seem to love not using the same notation as each other, and even with some simple things like set inclusion, there’s no consistency about terminology or notation between authors. Frankly, this makes me more than a little frustrated.

We don’t have to *make* kids believe math is all about meaningless rules. Natural laziness does that on its own: “Just tell me what to do, and don’t make me think!”

But it is a shame that many teachers (especially at the elementary level) never got beyond that way of looking at math themselves, and so they don’t know how to push their students beyond it, or even realize that a better way is possible.

I’m trying(to teach them the hows and whys of math- not just memorizing)! This year my goal was to make math fun- that is it! I’m still having a hard time because they are having to THINK about things in a different way. I am loving the posts here- they give me inspiration and continued hope!

So here I was going through my RSS feeds the morning after being off on vacation for a week when I saw this post and thought “That sounds like something someone said in class two weeks ago.” Yes, it was a great moment.

One of my assignments at the beginning of the year asks the students to explain what they think math is all about. Several students, usually sophomores or freshmen in my geometry class, always write something about memorizing formulas. I’m usually happy if a couple of those students say something about moving beyond that view of the subject in their end-of-the-year reflections.