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Thu, 07 Jun 2012

Beginners and Experts

An article published in Make Magazine and as a blog post Zen and the Art of Making comparing the beginner and expert approaches to things made me think learning and teaching.

Phillip Torrone says, I've been thinking about how much fun it is when you're a beginner at something as opposed to being an "expert."

Seeing math and most subjects as a beginner sees it keeps it fun. Kids aren't generally worried about "getting it" as long as they still enjoy making progress. Kids are satisfied with doing a job well enough, but mainly don't concern themselves with a refined product. If the plane flies, they are happy. Most kids don't obsess that the plane isn't an exact replica of the WWII Spitfire, down to the precise location of the painted red-white-blue roundel (I should point out that I knew the emblem was a circle, but had to look up on line to find out what the emblem is called: "roundel".) An expert might know that. A kid doesn't know or care. How often, as students, did we give an answer like that only to be upgraded (not necessarily upbraided) by the teacher who said the emblem was called a roundel? Teachers are experts, insofar as they know much more than their students.

Teaching can be a process of enticement, but it is also possible to "be the expert", to give the answers, to know the shortcuts that save time. Classroom efficiency is potentially a problem. Children, left to discover some important concept will not be efficient. They will stumble around a problem. They will build concepts the same way they build models or buildings from blocks. Even they wouldn't want to move into the block building as a house, but they'd be really proud if they built a treehouse with their friends, even if the boards didn't meet precisely at the corners every time.

That poses a big conflict, especially in math. Math is as close as we get to perfection in abstract thought, especially before concepts like chaos or fuzzy logic enter the discussion. Perfection isn't intrinsically part of the world of childlike exploration.

When 2+2 is 4, there's no wiggle room. If I say "five" to the teacher's example on the board, I'm not congratulated for coming closer than if I had said "fifteen." Math isn't usually explored, it is explained. That's not the same thing, is it?

Efficiency trumps exploration. Aren't we gradually moving algebra down the curriculum tree? Once it was advanced math. I took it as a high school freshman. I know it has been taught in grade 8. How soon before some expert says we should teach it in third grade?

A version of this post was sent to Mathfuture mailing list June 7, 2012



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