Actually, I did use hands on manipulatives along with chalkboard
explanations. I already told you the reaction: but we've been doing
this since middle school!

I agree that there are a vast variety of learning styles. I agree
that some kids are so frustrated with math by the time they get to
high school that they just turn off. However, I disagree that every
high school age kid out there can achieve mastery. I'm not saying
it's always the fault of the student. Some are trying very hard but
they may not be developmentally ready or they may just lack the
innate math intelligence.

Just as I have taken skiing lessons every winter for decades and can
hardly call myself a skier, some people (especially adolescents) will
not *master* this stuff at this time no matter how you teach them.
Sure, they may understand the hands-on lesson while you are doing it
but it doesn't "click" to the point that they can then apply what
they have learned.

So my point is we shouldn't denigrate a particular teaching strategy
(the acronym P E MD AS for example) just because it doesn't work for
some kids.

And do we really have a whole population of crumbling math students?
This suggests that students had better math foundation in the past.
But past math teaching relied much much more on "chalk and talk"
followed by paper and pencil practice and rarely on hand-on
manipulation.

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