The question is: If you don't teach by rules, what will you use?

In the Elementary Statistics course I used to teach, I had several different
objectives.
1) Students should develop arithmetic reliability.
2) Students should learn how they can be tricked by statistical wizardry.
3) Students should learn how to understand what is written by responsible
statisticians.

In the Applied Statistics course, my objectives were different.
1) Students should learn to read and evaluate the professional literature in
their discipline.
2) Students should learn to apply the basic ideas of statistical description
and inference: estimation, simple hypothesis testing, regression, etc.
3) Students should learn that their experience is limited and gain the
confidence to consult a professional statistician.

In the Mathematical Statistics course, my objectives were primarily
mathematical, not statistical. Statistics was seen as a technology built on
the foundations of the infinitesimal and finite difference calculus.

Different strokes for different folks!

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