A friend of mine once told of an experience in school (I don't remember what grade it was), in which a math teacher told the students that the shape of a polygon was uniquely determined by the angles. Some of the students knew that this was only true for triangles, and some of them proceeded to produce counterexamples (rectangles, hexagons with every other edge elongated, etc.) The teacher was unable to explain the counterexamples, but nevertheless maintained that the original statement was correct. Finally one of the parents had to tell the teacher, or the math department, to cease and desist. Your tax dollars at work! Tom Dan Asimov writes:
I'm a very good mathematics tutor.
A classroom can be much trickier with students of varying
a) abilities,
b) background knowledge,
and
c) communications skills (reading, listening, articulateness both orally and in writing).
But I love classroom teaching as well.
But one on one, I think the key is to initially figure out where the student is coming from with respect to a), b), c). That's important to assess initially just by interacting with the student.
Then just go on from there, expressing things in language the student will understand — at once in speech and writing — going only as fast as the student can follow, and getting copious feedback from them on their expressed comprehension, both oral and written as they tackle problems. Concrete examples are indispensable.
I've always enjoyed teaching the smartest students at the highest levels, but found teaching motivated students at any level to also be amazingly gratifying. My favorite tutoring experience came recently with 3 siblings in grades 1, 3, and 6, each with their own shtick, but all eager to learn.
As for the ones who have no interest in learning and cannot be wheedled, coaxed, cajoled, persuaded, or bribed to feel otherwise: meh.
—Dan
On Apr 26, 2016, at 12:07 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
I don't think anyone knows very much about the psychology of math. There's no easy pathway to the circuits and programming of it.
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