Re: [Phys-l] a different kind of math background quiz

[Stefan Jeglinski <jeglin@4pi.com>]

> The following does *not* answer the question that was
> asked ... but list members may find it amusing and/or
> useful anyway.

I found it amusing, and perhaps it would indeed be helpful in trying 
to judge the core competency of students coming into a class, hence 
useful.

> There are several easy ways of doing step (3).  Often
> folks who are pleased to accomplish step (3) drop the
> ball on step (4).

In fact, I did drop that ball :-)

After decoding your scheme, I muttered to myself "well yes, of 
course, don't bother me with trivialities," but the point is 
well-taken.


> For one thing, I fantasize about showing it to the math
> teachers and saying it would be nice if the students
> could answer all these questions ... answer them them
> easily, in less time than it takes to ask the questions
> ... but often they can't.

To answer the questions at all is a sensible goal. Who cares of the 
comparison between the time to ask and the time to solve, much the 
"ease." Even in the "real world," this should rarely be a criterion 
for success or knowledge, although I acknowledge the practicality of 
clear quick thinking. Looked at another way, if students were already 
educated/skilled, why the need to teach? After learning the skills 
gained from these exercises, *then* it might be appropriate to expect 
more speed/insight toward similar or new problems.

As to the question "Is there anything we can do about this?": Perhaps 
I am cynical; I'm not even a teacher, so I may not even have standing 
to attempt an answer, but it was not the case for me, nor have I met 
many of my ilk who would disagree, that I learned most if not all of 
my "important" math as a part of taking the physics classes. If I may 
advance an [inappropriate] analogy, the Taliban will never attempt a 
conventional war because they know better; they are quite happy, if 
not successful, mounting a guerilla insurgency.

Be all that as it may, is there a name of the class of problem or 
formulation posed in question 7? I would like to read an expanded 
critique (history perhaps, etc). I was surprised that I came to the 
answer as quickly as I did, having sometimes struggled with seemingly 
simple problems of that sort. But further noodling led me to the 
question/result of what happens when one replaces the 6s with 0s (or 
more appropriately, epsilons -> 0s). There appears to be an 
interesting twist (perhaps only to me!) that I would like to read 
more about at the feet of those who know more than me, but I couldn't 
figure out how to google for it :-)


Stefan Jeglinski