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I feel this goes unrecgognized by many teachers. The problem is somewhat
greater than that, however. A couple of years ago I taught a mechanics
course at second-year level in which I discovered *after my own teaching
of the material* that, while the students knew and could apply Newton's
second law of motion mathematically
-> -> They did not believe it! <- <-
It was a shock to me, a naive fellow who had been teaching for a bit
less than three decades.
I discovered this by setting up a simple demonstration and asking the
students to predict what would happen. They pretty much all failed to do
so correctly, and the demonstration was a revelation to them. It is
somewhat unsettling to realize that I (and my colleagues) must have been
turning out nonbelievers as physics graduates for all that time.