Math Skills versus Math Concepts (Pt. 2)

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The previous post was about the value of learning conceptually before you start practicing for skill.

There is an alternative argument that argues for the opposite. Many pedagogues try to plead the case that first you must teach the “basics” (meaning the basic skills, like the “multiplication facts”) before you can expect a child to acquire any meaning about it.

First, a short digression:
I HATE it when they call them the this-or-that “facts.” Firstly because it implies that anything outside the stupid, limited chart they are pushing are not “facts.” Is 84.5 * 63 = 5,323.5 somehow not a fact? And secondly because the way they use the word “facts” somehow implies that the fact is “outside driven.” By that I mean that it is a random kind of thing that you just have to memorize, instead of something that you can experience and learn from conceptualizing. Okay, back to our theme…

There is some validity to those pedagogues argument. Or at least there would be if some conditions were fulfilled first. But they almost never are in any public school system, which renders them pitifully invalid. Before I rip their into little girlie-man shreds, let me present the kind of case where their arguments would be valid:

“… wax on - wax off …”

Maybe you remember the cool seventies flick, “The Karate Kid.” (If you haven’t seen it, you should. It will illustrate several important points about teaching - and it’s a fun flick.) In it, the kid wants to learn Karate, and somehow convinces the somewhat reluctant Mr. Miyagi to teach him martial arts.

Mr. Miyagi ends up having the kid paint his house, wax his car, etc. Even worse, Miyagi is apparently a control-freak, and insists the kid do those chores with certain arm movements.

After a few weeks of this, the kid gets impatient, and asks about when Mr. Miyagi finally will teach him some self-defense. Mr. Miyagi pretends to try to slap the kid, and the kid blocks the slap perfectly. The kid is totally astounded that he could even do that.

It turns out that the arm movements that Miyagi Sensei was so obsessive-compulsive about are exactly the arm movements you need to learn for those basic blocking moves.

There was a perfect example of learning the skill mindlessly, by rote first, and then grasping the concept later.

This may actually be the best way for many things, including basic math facts. But certain conditions must be fulfilled in order for them to work.

What condition our condition is in

The first condition, is that the teacher must not only be a master practitioner, but a master teacher of his art. And it must be an art, in a deep sense.

I have only met one teacher in my lifetime in a public school (university) who met these conditions. He is a decorated and brilliant retired theoretical physicist and professor emeritus, and the founder of “Eduction” (or “Edux“). (More on Edux at some later date.)

How many teachers or parents out there want to try to fulfill those conditions? When you do, you’ll have nothing but my admiration. But until any of us do, we’d be well advised to teaching the concepts first, I think.

So if you’re short of being a Zen Master of your art, the next best thing seems to be being a thoughtful teacher, who doesn’t insist on teaching with a style that you can’t really fulfill, but will do the best with what is within your capacity.

There is a tendency to demand certain things from students without providing the means for them to attain those things. We “raise standards” and enact a cruel and, well, basically retarded “No Child Left Behind” act. Then we don’t fund it. We demand “accountability” (one of those words from this hypocritical era in American history that will go down in infamy) with “standardized testing,” yet we don’t give teachers the kind of training, the time, and the resources that they need to do their jobs. Then we blame them for it. And we blame kids for failing. You can’t load thirty kids into a class, undermine the teacher’s ability with some random “standards,” and then expect any meaningful outcome.

Those pedagogues who have the “lofty” Ideas, but not the means to make them work, are only going to confuse more and more children, and make sure no one wants to remain or become a teacher. It’s one thing to be an academic, with your head stuck firmly up your butt, and it’s another thing to try to stick innocent young kid’s heads up there with it.

“You vill do it first, und zen you vill undershtant it!”

If you are interested in reading some interesting thoughts about how to learn something to a degree of meaning that most of us might otherwise never dream of, consider getting a copy of “Zen in the Art of Archery” by Eugen Herrigal. It is a classic, and I don’t believe I can think of any other book that has a greater right to be on everyone’s bookshelf (and read).

If you’ll allow me another digression:

The archer in the animated movie below was scanned from the cover of my original copy of “Zen in the Art of Archery.”
Please enable Javascript and Flash to view this Flash video.
This was one of the first “flash” animations I ever made. Please excuse the soundtrack if you speak Japanese. I don’t speak much Japanese (Suimasen watashi wa Nihongo hanesamasen), so when I chose the soundtrack, I chose it for the actual sounds, not the meaning. The sentences came from the soundtracks of old Japanese movies, and I have no Idea what they mean. If you are Japanese, you are either rolling on the floor laughing your ass off, or are pissed at me. Please forgive me. I meant no disrespect. Much to the contrary.

A lesson from contemporary China

I have been corresponding with a student at Beijing University who put up a video on YouTube. It is of him rolling a coin over his fingers and doing other magician’s “flourishes” with coins. The kid is amazing. The coin-roll is one of my specialties in magic (I am a semi-retired professional magician), and this kid’s coin-rolling skills just blow mine away. So I wrote to him to express my admiration, and we began corresponding to exchange Ideas about magic, performance, skill, philosophy, etc.

In one of his e-mails he mentioned this wonderful thought: “… and as in a old saying in China ‘Interest is the best teacher.’”

Tao, I couldn’t agree more.

Here is Tao jamming with coins:

BTW, as you watch this one, crank your speakers. The soundtrack is by Jeong-Hyun Lim, a Korean kid who recorded this at home. His youtube video was featured on these Chronicles on this post.

If you’d like to see an old (1991) video of yours truly rolling two coins at once, check out the video below.

Afterthoughts:

As you watch those young Korean and Chinese kids perform those intricate, creative and absolutely astounding feats, you might ask yourself why many of us in the US set such wussified standards for our own kids. What will our kids accomplish when they are their age? More important, what will turn them on?


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