I can relate to your frustrations, and I wish I had the answer. I,
too, worked with very low students last year. I taught Geometry and
had sophomores and juniors who still could not solve for x, and they
couldn't get an equation into slope-intercept form unless I AGAIN
walked them through every step. I was very frustrated. I think the
whole "balancing the equation" just never clicked for them. The
frustrating part was that I needed to teach Geometry, not go back and
re-teach Algebra I.

I did not blame their Algebra I teacher. I know she taught them, but
like you said, even if they are taught, they don't really have a true
understanding of what they are doing or why. Something didn't click
for them at some point in their math education, and I fear that it
never will. They will have trouble passing their exit level TAKS (I
teach in Texas)
The very basic concepts they could understand, and believe me I kept
it basic...such as transformations...they got that at the most
fundamental level, but anything more than what each transformation
was, they complete lost it. When they had to find the transformed
coordinates, they were confounded. 8th grade Geometry is all these
students needed. Higher level Geometry was wasted on them. Even
plugging the numbers into formulas..total surface area, lateral
surface area, volume, etc, they would screw up. I discovered that
they were trying to do everything on their calculator and NOT have to
write anything down. I finally made them start writing the formula
down and going from there.

Well, now I'm just venting, but it goes back to order of operations
with those formulas. They would get the wrong answer because they
didn't know their order of operations, or would try to square
everything clustered with the radius instead of just the radius...for
ex. 2pir^2...they would multiply 2 x pi x r and then square the
product. Argh.

I was exhausted by the end of the year. I felt like a special ed
teacher.
I think there is a limit to what some students are able to learn,
process and apply. If Rene Descartes himself had been my teacher he
would be saying the same thing about me!

On 6/22/09, algie2 wrote:
> 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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