kitchen table math, the sequel: an hour a day

Saturday, March 3, 2007

an hour a day



in the sports supplement to today's TIMES (subscription required):

K. Anders Ericsson, who has devoted much of his life to studying phenomena like Dementieva and Spartak. Ericsson, a native of Sweden and a professor of psychology at Florida State University, is co-editor of “The Cambridge Handbook of Expertise and Expert Performance,” published in 2006. If talented people can be thought of as a singular species, then Ericsson is its John J. Audubon, and the handbook is his painstakingly annotated field guide.

The handbook runs to 901 pages, so, in the interest of time, allow me to sum up. Every talent, according to Ericsson, is the result of a single process: deliberate practice, which he defines as “individuals engaging in a practice activity (typically designed by teachers) with full concentration on improving some aspect of their performance.” In a moment of towering simplification, “The Handbook” distills its lesson to a formula known as the Power Law of Learning: T = a P-b . (Don’t ask.) A slightly more useful translation: Deliberate practice means working on technique, seeking constant critical feedback and focusing ruthlessly on improving weaknesses.

“It feels like you’re constantly stretching yourself into an uncomfortable area beyond what you can quite do,” Ericsson told me. It’s hard to sustain deliberate practice for long periods of time, which may help explain why players like Jimmy Connors succeeded with seemingly paltry amounts of practice while their competitors were hitting thousands of balls each day. As the tennis commentator Mary Carillo told me, “He barely practiced an hour a day, but it was the most intense hour of your life.”

Ericsson also discusses the Ten-Year Rule, an intriguing finding dating to 1899, which shows that even the most talented individual requires a decade of committed practice before reaching world-class level. (Even a prodigy like the chess player Bobby Fischer put in nine hard years before achieving his grandmaster status at age 16.) While this rule is often used to backdate the ideal start of training (in tennis, girls peak physically at around 17, so they ought to start by 7; boys peak later, so 9 is O.K.), the Ten-Year Rule has more universal implications. Namely, it implies that all skills are built using the same fundamental mechanism, and that the mechanism makes physiological demands from which no one is exempt.

I think this jibes with instructivist's philosophy of teaching:


My own favored teaching/learning model is one I dubbed the Optimal Electrode Gap model, or OEG model (somehow I feel I must turn this into an acronym. Acronyms lend legitimacy even to screwball ideas. Not that I consider the OEG model to be a screwball idea).

The analogy is taken from physics. When relatively high voltage is applied to electrodes, three things can occur depending on the electrode gap:

a) no sparks fly if the electrodes are too far apart

b) a short-circuit is created if the electrodes touch each other

and c) sparks begin flying if the gap is just right.

This technical bit lends itself beautifully as an analogy and even metaphor for education where it has major implications for teaching and learning. The flying sparks are a metaphor for true learning and understanding. The electrode gap stands for the kind of pupil/teacher interaction. Finding the right gap is at the heart of a teacher's teaching ability and skill.

If a teacher talks above the head of the pupil without connecting with the pupil's prior knowledge, then the gap is set too wide and no sparks fly. If the teacher tells the student (who may not be paying attention as is most often the case) everything without allowing for creative tension and some student struggle, then we have a short-circuit (the electrodes touch each other) and the voltage is for nought.

On the other hand, finding the right gap prevents pupil frustration on the one hand and wasted energy on the other, and can lead to student excitement and enthusiasm, and a real sense of accomplishment.

This is my teaching philosophy in a nutshell. I am not sure how all of this ties in with prevailing theories, but I suspect it incorporates elements from a variety of philosophies.

Years ago, when Jimmy was 5 or 6 years old, he had a teacher who taught only material that was miles over his head.

He was learning nothing.

Not one thing.

We had a meeting with the teacher who said that, yes, she was teaching material that was over his head.

"I like to challenge students," she said.

For newbies: Jimmy was then and is today severely autistic.

There was no challenging going on in that classroom.

There was 6 hours of nothing going on.

5 comments:

SteveH said...

“It feels like you’re constantly stretching yourself into an uncomfortable area beyond what you can quite do,”

My son's summer piano teacher liked to have him learn new pieces very slowly, using both hands and getting all of the fingering, dynamics, and articulation correct starting from the first time he played the piece. Talk about having your brain hurt. She said that's when you know you're practicing correctly.

Catherine Johnson said...

Talk about having your brain hurt. She said that's when you know you're practicing correctly.

That's fascinating.

I realize that I have no idea what "deliberate practice" is.

One hour a day??

Jimmy Connors??

Amazing.

Tracy said...

If the teacher tells the student (who may not be paying attention as is most often the case) everything without allowing for creative tension and some student struggle...

Hmmm - this contradicts with the DI method, which is that kids should be presented with everything necessary to make the next connections.

(Of course there is a lower level, where you only tell a student things they already know perfectly well, which is a waste of time).

Instructivist said...

"Hmmm - this contradicts with the DI method, which is that kids should be presented with everything necessary to make the next connections."

It's modified DI. You try prompts to facilitate the connection but ultimately you don't leave them dangling if they don't get it. Then you tell them. Alternatively, you model first (tell all), then apply the Socratic method to reinforce. It's a flexible approach geared to the needs of each case.

Catherine Johnson said...

My experience of direct instruction, small caps, jibes with Tracy's observation: the goal is to give you everything you need to take the next step.

"baby steps"

We've got different variables here: expertise versus "learning the basics."

Ericsson is talking about people at the very top of their fields - or people who are trying to get there.

As I'm learning math, I'm not attempting to reach the top of any mathematical field. I'm trying to become proficient in high school algebra and geometry.

Once I become proficient in high school geometry & algebra I'll work my way through Saxon's physics & calculus texts.

At some point I'm going to need a teacher and a class, but until then I can teach myself using the Saxon books because Saxon has broken the material down into very small, logical component parts which he teaches incrementally with lots of distributed practice.