Showing posts with label implicit learning. Show all posts
Showing posts with label implicit learning. Show all posts
Tuesday, January 21, 2014
Should math students explain their answers in words?
Complex information, such as that required for motor skills, can be learned implicitly, without awareness.It's an article of faith, inside schools of education, that procedural learning is dumb.
[snip]
Imagine you are riding a bicycle, and you start falling to the right. How would you avoid the impending crash? Many cyclists say they would compensate by leaning towards the left, but that action would precipitate the fall. When responding to the same situation while actually riding a bicycle, these same cyclists would turn their handlebars in the direction of the fall. The example (from Ref. 1) highlights the distinction between implicit and explicit knowledge*. Implicit learning refers to the ability to learn complex information (e.g. skills such as bicycle riding) in the absence of explicit awareness. Anecdotes such as the bicycle example offer subjectively compelling demonstrations for the existence of implicit forms of knowledge that are distinct from (and possibly in conflict with) explicit knowledge, but the existence of such learning without awareness has been difficult to prove scientifically.
Implicit learning revealed by the method of opposition
Tim Curran
TRENDS in Cognitive Sciences Vol.5 No.12 December 2001
Having spent a great deal of time immersed in the literature on the basal ganglia, which handle procedural learning, I'm pretty sure that assumption is wrong. Possibly very wrong.
The emerging research on the intelligence of nonconscious learning and the cognitive unconscious hasn't surprised me at all, mainly because, years ago, I read Arthur Reber's Implicit Learning and Tacit Knowledge: An Essay on the Cognitive Unconscious. Reber's book was so world-altering that I have kept it on my desk ever since.
As I recall (it's time to re-read), Reber opens his book with the question of expertise: how to transmit expert knowledge from one generation to the next.
In other words, he opens with the question of education.
e.g.: We have, today, people who know how to perform open-heart surgery. We will need, tomorrow, people who also know how to perform open-heart surgery. Since the people who know how to perform open-heart surgery today will grow old and die, we need to transfer their knowledge to the next generation.
How?
People's first thought (again, I haven't read Reber's book in years, so take my summary with a grain of salt)…. People's first thought was that experts should simply tell novices how they do what they do.
Simple!
But that didn't work out.
The reason it didn't work out: experts don't know how they do what they do.
That fundamental insight into the nature of expertise has never left me.
Experts don't know how they do what they do.
The fact that experts don't know how they do what they do has made me highly skeptical of "explain your answer" questions as the sine qua non of math achievement and comprehension. As far as I can tell, adults who are really good at what they do have an enormous amount of nonconscious knowledge and comprehension, so shouldn't that also be the case with children who are good at math?
I don't think the second proposition necessarily follows from the first. Perhaps math students should be able to explain, in words, why they did what they did in order to arrive at a correct answer. However, anecdotally I do see "math kids" who "just get it" -- and, anecdotally, those kids always look like the good-at-math kids to me.
In any event, I was tickled to discover that people who know how to ride a bicycle not only don't know how they do what they do but in many cases consciously believe they do exactly the opposite of what they actually do.
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