Posted to sci.physics and sci.math, October, 2000
I ask for comments on the role of memorization in physics, math, or any other subject that requires understanding concepts. I define the process of understanding to be the process of articulating relationships among various parts to form a "whole." In physics and math this means articulating relationships among various facts/concepts (i.e., the parts, just to keep the discussion free of complications). If you don't agree with my definition of "understanding" that's fine, but if you contest it, then please offer your own alternative definition. If you don't know the parts, you can't articulate relationships among them. And anyone who says that they understand something but can't state that something from memory, has a funny notion of "understanding" to me.
I define "having something in memory" as being able to correctly state that something from memory at will. Just HOW things get memorized is not the issue to me. The issue to me is just to get things memorized. Then the process of understanding can begin. I have no problem personally with lots of rote memorization, though initially it took some getting used to. My rule of thumb is this: Memorization comes before understanding! So I see the rote memorization I do as profitable to me. If someone had to memorize without the benefit of believing the effort was worth it, then of course it would be psychologically harder for him or her. Part of the problem is our cultural attitude against memorization of "boring" facts.
My goal for myself is to really understand the deep concepts, not just to memorize end results or formulas. But to accomplish this, I voraciously memorize parts to always be ready to articulate relationships among them until deep understanding occurs. This process seems much more efficient than any other I've tried.
For years I tutored one-on-one many high school and college students in physics and math. I tutored students at all levels of competency. One thing about them impressed me tremendously: The poorer students did not memorize current material before I tutored them and they lost precious time during the session (trying to) familiarizing themselves with basic information -- the result of this usually was that they would easily get lost and have a definite non feel good experience with education. On the other hand, the best students always had the basic material memorized before I arrived for the session. They tended to get my explanations and have a good feeling about their educational experience. But I don't believe the difference is simply that the better students were intrinsically more "intelligent" than the poorer students. Mostly, the better students were just better prepared, and that included more memorization of the basics. That observation said something to me. I believe in the "he who hesitates is lost" theory of learning.
I believe that rote memorization is wrongly tied to the so-called "rote learning" concept, which itself is tied to the educational curricular philosophy of dumbing down material to reach the lowest common denominator of today's students. It is a philosophy that sacrifices understanding concepts in favor of learning a few end formulas and rigid problem solving strategies. But that's NOT what I'm advocating. I'm advocating lots of memorization of parts to get ready to understand the deep concepts, and then a period of context-rich learning (with analogies, demonstrations, experiments, examples, proofs, models, pictures, graphs, heuristics, etc) until understanding occurs.
One obvious but under-appreciated fact about highly successful intellectuals is that not only do they "understand" more than most others, they also know more than most others, too. That is, they have more raw information in memory than most others. I also believe as Pasteur once said, that chance favors the prepared mind, so prepare your mind with facts.
Patrick
Links to Memorization Sites