Saturday, January 3, 2015

Favorite comments of '14: Barry Garelick and Niels Henrik Abel

On Puzzle Math, II: abstract pattern recognition:

Barry Garelick said...
The "math is about patterns" meme is usually limited to IQ test type problems that depend on inductive (rather than deductive) reasoning. Supposedly this is to develop the "habits of mind" of algebraic thinking outside of the algebra class (like in 6th grade). In real math, the appropriate habits of mind are developed simply by doing the work. The fluency and the skill in recognizing key "patterns" comes from continual exposure to the material and a grounding in appropriate tools of the trade, like subject content, experience, knowledge and skill.So it's one thing to say "math is about patterns" but you still need the subject content and skill to know where to look and what to do with what you find.

By working from routine problems, students can then progress to non-routine problems and beyond. See also this article.

Niels Henrik Abel said...
Unfortunately, a lot of students have trouble with these kinds of exercises. The ones I run across tutoring get stumped with problems that look like #1, which is really rather easy if you know your stuff. The latter ones (e.g., with the radicals) would not even be attempted by such students, I'm sure ~

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