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Thanks for the thoughtful answer.
I remain sceptical.
It's all about communication. A communication is never complete
until the recipient has repeated the communication ("Roger, bogey 10
O'clock high").
My own frustration is with the student who is unable to repeat any
part of yesterday's lecture. Once, in a calculus class I spent a week
trying to teach induction - the proposition is true for n=1, assume true
for n and show that truth for n+1 is thereby implied. The attempt was a
total failure, as I learned from asking the students to apply the process
to some simple cases.
I liken teaching to experimental physics. The experimenter tests
a theory by trying to prove it wrong. We need to test our students by
letting them show that they did not learn what we were trying to teach.
I no longer try to teach induction to first year students in local
colleges. Maybe the reequisite prefrontal cortex ain't there yet.