On 6/26/09, Old Fogey, sort of wrote:
> Not sure if I'll express this adequately, but here goes...
>
> I've been wondering lately what has changed, in say the
> last 30 years, in math learning and education? I worry
> each day about how to teach more effectively so my students
> will grasp math concepts with true and deep understanding.
>
> I don't think my math teachers worried too much about that
> when I was growing up...or at least I don't remember. Were
> there just as many students "left behind" 20-30 yrs. ago as
> there are today in their understanding of math?
>
> I hear some of my friends say, "Well, I was never good in
> math", or "I can't help my own kids with all the new
> math". I would like to do some type of retrospective, or
> read something (anyone have any recommendations?) about the
> change in math education in this country from about 1950
> until now. I grew up in th e 60's and 70's and it seems
> like we just did math, no big deal. Now there's this BIG
> focus on it...like EVERYONE has to be a whiz in math.
> Well, that's just not realistic.
>
> What I'd like to do is find some of my old math
> teachers..if they're not dead...and ask them.

The 2 biggest factors, IMO are 1) widening the curriculum to
the famous mile wide, and 2) diluting the curriculum to the
famous inch deep. Except among the top students the basics are
not learned to a mastery level, largely because the width of
the curriculum leaves insufficient time. As math is a
foundational subject, building concept on concept, a failure to
learn basics to a mastery level leaves the student unprepared
for the next step. And since the next step is actually 37
steps, since that curriculum is so wide, they are basically sunk.

When I get 8th grade students who not only cannot add 6+3
without using their fingers but don't have the number sense to
realize that when counting on their fingers it is easier to
start with 6 and count 3 more than to start with 3 and count 6
more then I am in big trouble if my task is to teach them
algebra. And the very sad truth is that except in the most
exceptional cases there is essentially no chance that
remediation is going to bridge the gap in any really meaningful
way.

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