By Ralph A. Raimi (1924-2017)

Dr. Raimi grew up in Detroit, Michigan, and received his B.S. in physics and M.S. and Ph.D. in mathematics from the University of Michigan. He joined the faculty of the University of Rochester in 1952 as a teaching fellow, ultimately becoming a full professor in 1966. After being named emeritus in 1995, he became active in the movement to reform K-12 math education, and was a consultant on curriculum matters for several states. 

Today's guest post is a little different in that it is a reblog of a piece by an author who is no longer with us. A few months ago, Yana published a blog post called "In Defense of Memory", where she discussed all the different ways that memory is used throughout our lives. Our external expert Richard P. Phelps read that post and commented that it reminded him of this piece by Raimi. It fits perfectly, and we have reblogged it here. Since we cannot obtain permission to reblog the piece from the author, and not knowing the copyright license under which he published it, we are reproducing the whole piece here as a long direct quotation.

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.

Ralph A. Raimi

Revised 12 April 2005

Retrieved from http://web.math.rochester.edu/people/faculty/rarm/rote-mem.html