kitchen table math, the sequel: how to build a fast learner

Thursday, April 26, 2007

how to build a fast learner

I'm supposed to be writing a chapter of Temple's & my new book, so this will be quick. (I'll revise later.)

Some of you may remember last fall's posts about mastery learning and speed and mastery and IQ.

The jist of those posts is that while higher IQ means faster recall of new material, higher IQ doesn't give you a significant advantage in speed of relearning material that's been taught to mastery the first go-round.

Engelmann describes the same phenomenon, except Engelmann takes it a step further.

Engelmann observes that at some point slower learners get faster at learning new material, too:
[A]fter students have mastered a battery of skills and knowledge, the difference in rate of ascent for appropriately placed students is far less because all students tend to have enough skill to master the new material at around the same rate.

Student-Program Alignment and Teaching to Mastery (pdf file)
Siegfried Engelmann
In other words, at some point in a student's process of learning a subject, he gets faster.

Lots faster, it seems.

I'm certain this is true, because I've experienced it all my life.

And because I saw it last spring with Christopher.

Getting C. through the Phase 4 math course in 6th grade was a battle unto death, as faithful readers will recall.

Ed and I went back and forth on whether to bag the whole thing,* never quite reaching a conclusion for reasons having to do with stubbornness as much as anything else, no doubt.

Then suddenly, last spring, C. picked up the pace. Way picked up the pace. He'd come home from school having learned and remembered whatever it was they'd covered in math that day.

There wasn't any change beyond that. He wasn't understanding math better, or liking math better, or displaying greater motivation to learn math. (understatement)

The only difference was: he was faster. All of a sudden.

how do you build a faster learner?

So the question is: what has to happen to get a student to the tipping point?

I had been thinking that it must have to do with the learner (I can barely stand to type that word but I'm afraid I must) acquiring a schema of the field (or domain) he's learning.

Looks like I was right --
Schemas and Memory Consolidation
Dorothy Tse,1* Rosamund F. Langston,1* Masaki Kakeyama,2 Ingrid Bethus,1 Patrick A. Spooner,1 Emma R. Wood,1 Menno P. Witter,3 Richard G. M. Morris1

Memory encoding occurs rapidly, but the consolidation of memory in the neocortex has long been held to be a more gradual process. We now report, however, that systems consolidation can occur extremely quickly if an associative "schema" into which new information is incorporated has previously been created. In experiments using a hippocampal-dependent paired-associate task for rats, the memory of flavor-place associations became persistent over time as a putative neocortical schema gradually developed. New traces, trained for only one trial, then became assimilated and rapidly hippocampal-independent. Schemas also played a causal role in the creation of lasting associative memory representations during one-trial learning. [emphasis mine] The concept of neocortical schemas may unite psychological accounts of knowledge structures with neurobiological theories of systems memory consolidation.

April 6, 2007
Volume 316, no. 5821, pp. 76 - 82

One-trial learning is about as fast as it gets.

Here's the way Science News describes it (subscription required):
People call on a rich background [ed.: background knowledge!] of relevant experiences to organize and remember new material. Rats do the same, and with surprising speed, say Dorothy Tse of the University of Edinburgh and her coworkers.

Prior studies, which have focused on task learning unrelated to preexisting knowledge, indicate that a brain region called the hippocampus incorporates new facts and events into memory. The hippocampus gradually yields to another structure, the neocortex, as new memories become stronger. This process typically takes at least 1 month in rodents and a few years in people.

Tse's team trained groups of rats to associate six flavors, including banana and bacon, with six designated spots within a laboratory-test area.... The animals learned all six flavor-place associations in 1 month.

....[T]he animals had also developed a framework of knowledge about relations between places and flavors that enabled them to learn new pairings remarkably quickly. The rats remembered novel flavor-place associations after just one trial and retained this information for at least 2 weeks, the scientists report in the April 6 Science.

The rats' formation of a knowledge framework spurred the neocortex to integrate new information into memory in record time, the scientists propose. Surgical removal of the hippocampus 48 hours after the rats had rapidly learned new flavor-place associations left those memories intact, a sign that the neocortex had already taken charge of the material.

Rats take fast route to remembering
Science News
April 14, 2007 Vol 171, No. 15, p. 237
Bruce Bower

in a nutshell (t/k)

Note: the experimenters did not use a spiral curriculum.

These rats were taught to mastery.

Shouldn't we be asking whether schools have a moral imperative to teach students to mastery?

* Do the fastest learners get faster, too? They must, wouldn't you think?
how to build a fast learner
how to build a fast learner, part 2

* for newbies: "bag the whole thing," meaning move him out of accelerated math and into the regular track

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