I am posting your comments for my students. A frequent point I try to
make is to think big picture/concept and work down to a solution for the
issue at hand. Strong math students tend to be equation hunters. I try
to break them of the habit.
Thanks for the extra tool.
Paul Lulai
--JD--
Remark: There is quite a fundamental difference between [2,3] and
[4,5]. It involves a fundamentally different way of doing business.
Loosely speaking, [2,3] involves memorizing a rule, whereas [4,5]
involves rederiving the rule from first principles every time it
is needed. Don't get me wrong; I'm not saying that memorization
is always bad; there are some things that should be memorized and
some things that /must/ be memorized. I'm just saying memorization
shouldn't be carried too far. There are some cases where rederiving
the result is just plain easier -- and more reliable -- than trying
to memorize the corollary /with all the required provisos/.
-- --
We'll specifically discuss 1-4.
We've already 'worked' on (r x F_c) =/= work