Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:

If you understand the concepts, you can do this.
If you could compute perfectly in your head, you
could do no better.

Again, that very much depends, particularly
if you're still arguing that one never forgets concepts.
I had lots of probability and statistics. For a while, I
used it regularly. It's been quite a few years since then.
I do not retain enough to properly formulate anything but
relatively simple statistical problems. To do more, I would
have to go back and study.

Did you have the basic concepts? I very much regret
that probability is not taught without having the concepts
of measure and integral (one does not need calculus for
this) first, and in fact it is hidden. Also, attempts
to define probability are misleading, and the overuse
of "equally likely" makes things harder to learn. Again,
it is not about computing answers to simple problems, but
knowing how to formulate.

Yes, I had plenty of probability and stats (and
calculus, and formal logic, and "modern algebra," and
so on and so forth). I got it. I simply have forgotten
much of it, thanks to disuse. I have also forgotten
enough Latin that I can't sit down and read Ceasar easily,
enough music theory that I can no longer easily take
dictation for more complicated chord progressions, and
enough accounting & finance that I'd need to brush up before
attempting any serious valuation of a business. It's
use it or lose it for most of us.

As for statistics, the basic principle of statistical
decision making is

It is necessary to consider all consequences
of the proposed action in all states of nature.

If you remember what was taught in the methods courses
you probably took, you can show that most of them violate
that one sentence on very simple grounds.

Of course they do. Living in the real world, however,
one does not expect that most, if any, real life studies will
achieve that lofty goal. One does the best one can, and then
one attempts to recognize the limitations on any results imposed
by the failure to achieve perfect methods.

Well, I can hardly speak to any of that, as
I seem not to have met any of these "educationists"
you keep speaking of. Certainly, none of my children's
teachers have thought that it was ok for them not
to understand concepts or do problems mechanically,
incorrectly, or without any understanding.

I strongly question whether any of your children's
teachers understand the basic concepts of mathematics.

Feel free to question. I have felt quite
comfortable with most of their approaches, and feel
quite comfortable with my children's resulting achievements
in math. Do they all have a background identical to yours?
Probably not, but I don't find that to have been an
impediment. Most of my math teachers in elementary
school didn't have that background either, and it didn't
seem to lead to any serious issues in my learning (or
applying) math either. So, I must say, I'm not terribly
concerned about my children's future at the moment. Now,
I realize that we are blessed with good schools here,
so I'm not suggesting the scenario is as rosy everywhere,
but my experience at this point doesn't really lead me
to put a lot of faith in the notion that the strategies
you advocate are required to teach mathematics.

Best wishes,
Ericka