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October 14, 2008

Memory: The Forgotten Art

Nick Diaz

Ah, Mnemosyne, daughter of Gaia and Uranus, and mother, by Zeus, of all the Muses! Poets and kings reputedly receive their gifts and powers of authoritative speech from their personal relationship with Mnemosyne. How precious is the gift of memory – yet how maligned it has become over the past 30 years, especially by trendy math educationists.


The word "memory" seemed to have been transmogrified into one beginning with 'R' – "rote-memory" – at least in the world of education. To me, this negative attitude has associated the new syllable to the name of the Goddess.


Without memory there is no knowledge, regardless of how many encyclopedias and computers one might own, or even be able to carry around. Certainly all of us have met someone with what psychologists – and like-minded nerds – call an eidetic (photographic) memory, a gift that comes in quite handy while in school (and during Christmas season).


In college I had a classmate, Tim, who could recall the proper page of the textbook where a given formula or historical fact was located. He would remember not only the correct page, but the exact location on the page where the necessary fact or formula was located. Even, if occasionally, Tim would not know such things at once, he would leaf through the textbook and, in a few seconds, would find what he needed. He went on to attend law school, where this eidetic memory continued to serve him well.


There were times 40 years ago when I wished I possessed the gift of Mnemosyne. How many hours of laborious study and reviewing I would have saved? During finals time, Tim would often dwell at the local watering holes that surrounded the University of Dayton campus – and still graduated cum laude. Tim was, and still is, my model. I wanted to be like Tim, (not like Mike).


So, in the past 40 years I’ve trained myself to remember things, to put them in order. Ask me who was President of The United States in 1872 and I’ll tell you – not from my eidetic memory, (because it isn’t that powerful), but from my “random-access memory,” by association – “mnemonic” devices. A little etymology lesson here never hurt anyone…


These days, encyclopedias are found on CD’s and are more convenient than they used to be; and the calculator is much better, quicker and more accurate, than the log tables or slide rule. Anyone rich enough can buy a computer and encyclopedia, and even a copy of Shakespeare, and thereby have a lot of knowledge around the house. However, if he knows nothing, or what he can look up on demand, he is what I call “ignorant.”


His ability to use this stuff via the "understanding" he might have learned – or 'developed', as they say – in a course in literary criticism or mathematics, is zero – if  he has no part of this material already in his accessible memory. For otherwise, what will he know to look up, or why, or when?


Practically all states nowadays offer mandatory performance assessments that public school students must pass in order to graduate. Math, along with English and a couple of content areas, form an important part of such tests and assessments. Maryland, of course, is no exception.


I can imagine the discussions the test preparers must have among themselves prior to the final edition.


 – Should calculators be available, and what sort is admissible.


 – Should there be multiple-guess questions, and how many.


 – How many questions should there be altogether.


 – What fraction of the test should be “contextual,” involving a real-world situation.


The results will be unimportant to the present discussion of memory, however, except for one matter:


 – Should there be a “formula page” for the students’ use?


The SAT and many other aptitude and achievement tests nowadays have a formula page. If you’re as old as I am, you’ll probably agree with me that having such a formula page is ridiculous. Do students really need to be reminded of the formula for the area of a rectangle, or triangle, or circle? Or that a student can’t, or won’t, memorize the Pythagorean relationship, or the basic triples that go with it, in order to solve simple contextual problems?


I’m distressed at the attitude displayed toward memorization these days. The presence of a formula page probably doesn’t matter much to the results of the exam; it does, however, allegedly matter to the “morale” of the test-takers, according to modern educators, and to the “morale” of teachers as well. It seems to be expected that, if students were not assured of having these formulas printed there with the exam, they would spend months in drill during preparation for the exams, wasting time on mere memorization that they now have free for conceptual learning. Nonsense, I say!


My own view is that it is the more honorable of the math educators who believe as I do, and that the less honorable simply want to make things as easy as the public will let them get away with, so as to get higher scores and be seen, thereby, to be doing their jobs.


To the degree the honorable educators are right, and that depriving students of the comfort of knowing that these things need not be memorized, I must say the nation has come to have an altogether diseased notion of the function of memory. And, while this is only part of a larger disease concerning education in general, we shall have enough to do attacking the particular problem of the place of memory in mathematical education.


The public at large should strive to restore memory to the position of respect it had up to about 100 years ago, when school children memorized orations of Abraham Lincoln, scenes from Shakespeare, The Wreck of the Hesperus and Casey at the Bat, not to mention the procedures of arithmetic.


The fact that some teachers drilled children in routines that were not given sense does not mean that drill as such creates a vacuum in the brain. I have known of actors who memorized scenes from Shakespeare and also knew what they were about. I have known scientists who knew the size of the dihedral angle in a regular tetrahedron and understood organic chemistry, too.


There is no harm in knowing things, and much value. Some of the actors who memorize their parts in Shakespeare do not, in fact, understand much of what they were saying during the first few read-throughs, but would never have gotten on to their characters if they hadn't first had the words in their minds and ready to their tongues.


Why is a technique thousands of years old, and still considered valid in the teaching of music and theater, reviled in school mathematics?


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