start by undoing a lot of what they had
previously been taught, such as
that PI was EXACTLY 22/7 ! (half a century ago, in elementary school, I
got into "big trouble" for telling a teacher that PI was NOT 22/7 !)
Aarrghh!! Is that what they teach in American schools?? That is *evil*.
I was perhaps unlucky in that i had a string of clueless maths and
physics teachers.... I remember one related incident.
The teacher had just proved exp(i*pi) + 1 = 0 .
ARD : OK so I assume I can say exp(i*pi) = -1
Teacher : Of course
ARD : Can I now take natural logs of both sides and say that ln(-1) = i*pi
Theacher : No. There are no logs of negative numbers
[A bit later I discovered the true version. exp(3*i*pi) = -1,
exp(5*i*pi)=-1, etc too. And thus ln(-1) = (2n+1)*i*pi. But i*pi is
taken as the principal value of ln(-1). To claim that 'logs of negative
nmumbers do not exist' is plain wrong]
My mother once had a teacher who when his pupils were
bad, told them to
behave, otherwise he would teach them wrong. In his opinion that was the
worst punishment he could think of.
That would not work in the UK any more. In fact I think it would only
work with students who want to learn, and such students are unlikely to
mishehave in the first place (unless you count 'asking difficult but
relevant questions; as misbehaving).
-tony