Education reformists abhor the word “memorization,” especially if it is qualified with another abhorred word, “rote.” The word is so much detested that it now has acquired the status of a (long) four-letter word in certain educational circles. If you want to do away with an educational practice among some reformists, point to its emphasis on memorization. That is why the Common Core State Standards for math uses “know from memory” instead of “memorize.”
What is memorization and why has it obtained such an ugly reputation among some educators? There are at least two meanings associated with the word: one is storing facts in the memory for the sole purpose of regurgitating it later. I’ll call this mode of memorization rote memorization. The other is storing facts along with steps, rules, and arguments that lead to that fact from other, more basic, facts. Parrots are very good at rote memorizing sounds; they are great examples of memorization of the first kind.
The second kind of memorization is best illustrated by the Pythagorean theorem. A student who can recite the theorem, and has memorized (yes, memorized) the ingenious tricks of drawing appropriate squares, rectangles, and triangles to prove it, is truly understanding the theorem. And if (s)he wants to be a mathematician, (s)he has to make a habit of memorizing the proof of every theorem (s)he comes across. I have to emphasize:
Memorization is necessary for learning proofs, but not sufficient. It is conceivable that a student (perhaps with a photographic memory) could rote memorize the proof of a theorem!
Poets can write new poems only because they have memorized hundreds of poems by other poets; and we don’t discourage memorization in our teaching of poetry based on the assumption that our pupils will not be poets. Composers create new music only because they have memorized hundreds of pieces of music by other composers; and we don’t tell our piano students not to memorize piano pieces unless they want to be composers. Writers write new novels only because they have read and memorized excerpts of dozens of novels by other writers; and we teach literature the same way whether or not our students turn out to be writers. Chess masters create new game strategies only because they have memorized hundreds of moves by other masters; and we teach novices as if they were becoming chess masters. Then why is it so outrageous to say that
Mathematicians discover new theorems only because they have memorized dozens of existing theorems, and we should teach mathematics the same way whether our students turn out to be mathematicians or not.