Noticing Things

This is what I wanted to say when I was talking about Kim's Game!  But I got sidetracked.  (Happens every few hours.)

Thinking back to my teaching days (i.e, before 2017), I realize that I missed a lot of good opportunities.  One of the basic tricks (it's not really a trick, but kids pay attention if you call it a trick) is: to notice things. 

One of the major things I taught was techniques of integration.  If you don't know what integration is, it's a little like being a doctor.  You have an integration problem (which is a math problem that has to be solved), which is your patient.  You first have to assess what kind of integration it is, because what you do next depends on that assessment.  It's like a diagnosis, get it?  You need to find out which way to go.  In math (unlike in medicine) if you go the wrong way, nobody gets sick or dies; you just have to back up, and start again in a different direction. 

Classifying your problem--- the diagnosis--- depends on noticing various little things, just as in medical diagnostics.  Once the doctor notices one thing, there are other related things he or she could look for.  It's exactly the same in mathematics!  Is there a radical of a certain sort?  Is there a logarithm?  An exponential?  A fraction?  A simple substitution you could do?

The good students are already hot on the trail of these critters.  At the time I was teaching, I was so annoyed with the typical students, that I thought: oh let them go screw themselves; they should have picked up a lot of this in Grade 10.

But a lot of things could have gone wrong in Grade 10: athletics---even if the kid was hopeless at it; hormones; a marginal high school teacher; a home environment where there was nobody to help with studying; all sorts of problems.  If I had gone just a tiny bit outside my lane, and helped my students with the FOIL rule, for instance,  which is something they learn in 6th or 7th Grade, they might have kissed the ground I walked on!  Well, that's going too far; I walked on some pretty dirty ground.

When I was thinking about this post, I wondered whether the whole concept of noticing things might be a pretty universal performance aid.  Does critical reading require noticing certain things?  Does debugging faulty code in a program involve noticing certain things?  It seem to me that even getting the benefit of a video clip a teacher shows a class requires noticing things.  This is huge. 

Notice things, young people.  No pressure. 

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