On Rote Memory

The question has come up, what should teachers ask students to memorize, and the answers seem to differ.  But I suspect the answers are not really as different as all that, because the word "memorize" tends to take on different meanings in different people's minds.  Should one memorize the Pythagorean Theorem, for example?  One person will say one should, rather, understand it, and be able to use it, and maybe even be able to prove it.  Well, of course, but how does this say it shouldn't be memorized?  Well, says that person, we don't want kids standing up in four straight rows and reciting thesquareofthehypotenuse..., and calling that the lesson for the day.  The other guy says, no, that's not what he meant when he said kids should memorize the theorem. He did mean it should be known.  He meant that when someone shows the kid a diagram in which there is some right triangle two of whose side lengths are somehow known, perhaps from other considerations, that kid should be able to calculate, on demand, the length of the other side.  And he calls this "memorizing".

Indeed I do, nor can I see how “understanding” and being able to use the theorem can be divorced from the use of our memory, even for professional mathematicians who have known and used the theorem all their lives.  But it is conceivable that someone could memorize the statement of the theorem, and to recite it without thinking about what it is saying, or how to use the theorem.  So the phrase "rote memory" has been invented to describe such fruitless memorization, something we all do not want in the use of memory.

But this, too, is tricky.  I have "rote-memorized" the fact that 7X8=56, in the sense that I don't draw a 7 by 8 rectangle and count squares every time I need that particular product.  I have it by rote as surely as if I were taught a Chinese song (I don't know any Chinese language at all).  In the case of 7X8 I do know how to arrive at the result, so that the "56" is not the only thing I know about it, while in the Chinese song I would be able to exhibit nothing analogous, but this doesn't mean that my memorization of 56 as the answer has any fault.  Indeed, it is valuable to know such things "by heart" --- meaning, without further use of the head --- and we all know that.  So why all the dispute about rote memory?

The trouble mainly is that we don't have terminology to distinguish the kind of "memorization" that can be replaced by a crib sheet on an exam from the "memorization" that cannot.  And so we argue about a word, rather than about the two distinct ideas that generally are conveyed by that same word in two distinct contexts.  And yet the distinction is not really something to worry about.

Generally speaking, I have never been sorry to have memorized anything, from snatches of poetry to the wording of theorems.  To put the matter even more strongly, I have never learned anything, anything at all, that I was later sorry to have learned.  Why should others be so fearful of knowledge?  They make it a virtue to avoid teaching facts, for fear they will be memorized without understanding. Yes, that does happen, but shall the best forever be the enemy of the good?

Ralph A. Raimi

Revised 12 April 2005