A smart friend (whose permission I have not asked) read an article of mine that will be published in Mathematics Teaching in the Middle School sometime soon. The article is based on my NCTM talk last spring, titled “They’ll Need It for Calculus”.
This friend asked by email:
For clarification: are you arguing that the sorts of problems that you point to will help students better understand calculus, or that these sorts of problems will help students do better in their calculus classes?
I was pretty sure that you were making the first argument, but not the second.
My reply, which I stand by, is this:
That these two things are different from each other is a pretty damning critique of the whole affair, is it not?
You know what will help them do well in their calculus classes? Memorizing about 20 of these:
Overthinking my teaching 
I’m looking forward to your article.
I’m also frustrated that “understanding the concepts of calculus class” is something that is sometimes not taught in a calculus class. 😦
Sorry, I don’t get it. Is that snake supposed to be the integral sign?
Yes. The snake is the integral sign.
We were having fun on Twitter with mnemonic devices and questioning their usefulness for learning number facts. This stuff was way beyond “six and eight go on a date; when they come back they’re forty-eight.” You can click through the link in the main piece to find the discussion.
So I thought it might be interesting to demonstrate how profoundly different memorizing a silly mnemonic device is from learning the content.
Griffin has memorized the mnemonic device (as has Tabitha—7 years old). Are we prepared to say that he knows the Fundamental Theorem of Calculus? Of course not.
So are we prepared to say that students know their multiplication tables if they memorized a bunch of disconnected rhymes?