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RE: How one math problem changed the way I saw math
Good story. Upvoted and resteemed for you.
The truth is, most primary teachers who teach maths don't understand it either and mess up millions of kids. I wish they'd just stop and have a separate maths/science teacher. Once in secondary, the damage is done!
!-=o0o=-!
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There's a more subtle problem too. Very often people chosen as dedicated math teachers (and chemistry teachers, in my experience) find the introductory levels of their subject almost instinctive. They have a hard time understanding why others struggle with the concepts, so they don't know how to help the students struggle through to comprehension.
I can't tell you how many times my college-level biology students come into class complaining about how hard it is to understand the concepts in the math class they've just come from. If I have a few minutes before class, I'll go over how the quadratic equation came to make sense to me, or how multiplication of fractions came to make sense, or how integral calculus or polar coordinates ...or any of a number of other concepts. Usually after my explanation of how I struggled through to a very practical, non-abstract way of looking at those concepts, my biology students' mouths are open in a big "O" of realization... and they get excited again about understanding math.
We need more math and science teachers who struggled with the subject themselves and came to an understanding that can be related to ordinary students.
Two different issues it seems. At university, many lecturers are not required to be trained teachers and so can easily develop poor pedagogy. I taught one term of differential equations to engineers, as their usual maths lecturer was away on some sabbatical. As a former physicist I thought I had a good idea of the engineering attitude to this. So I gave them the ready-made worksheets but taught it completely differently. I showed them how the equations related to the final waveforms and how those were described by the formulas and then finally linked the diff eqns to the solution techniques. They seemed pretty pleased with themselves!!
But I don't see that as the problem in primary; they are just required to teach everything and are just not good enough at everything and - most worrying - transmit their fears and incomprehension to their students. I make sure I teach my own daughter at home!
One last thing, I'd like to include your post in the next math-trail compilation, but need your permission first. Is that OK?
Yes be my guest!