Thursday, September 1, 2016

Algebra Redux

This is my fourth semester teaching Algebra 1, and I am a well oiled machine.  My lectures notes are all written, I have a large stock of old exams for revision, and I know the material so well that I can cover it twice as fast!

Oops.

As convenient as it is to teach the same course again, I find that there are some drawbacks to familiarity.  For the most part, my presentation is smoother and I'm more likely to focus on what's really important instead of getting sidetracked, but there is an increasing disconnect between how new the material feels to me and to my students.  I think good teaching requires some imagination on the part of the lecturer: you have to simultaneously understand the material and also understand what it's like to be confused by it.  In a calculus class, the exercise in duality was always clearly necessary, so I put some effort into maintaining both perspectives.  For upper level classes, it hasn't required as much effort, but apparently traipsing through group theory for the fourth time (sixth, if you count Stanford) changes that.

(Btw, if you're in Algebra 1 and reading this, we're only going about 10% faster, so don't panic!)

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