You could go a step further and ask how many teachers used
really different methods of teaching exponents or other math
concepts. Did they try manipulatives along with writing the
information in various ways? What were the visuals like - just
numbers written on the board 3 x 3 x 3 = 3^3? Some kids really
need math to be hands on and visual, but there are few truly
hands on math programs used in classrooms. And if they are, it
is rarely by all teachers for different groups of students.

So, I guess my point is, you CAN say it is the student if you
expect that all should be able to learn by various explanations
not different methods, but the reality is that not all students
learn math that way and few teachers use manipulatives or good
visuals after the first few years (if at all depending on the
school). So, I would be more pressed to say it is the TEACHING
(not saying bad, uncaring teacher - just not enough training in
a system not designed to teach all students) not the student in
many cases. But what is seen by the time the kids reach middle
to upper grades is that they are woefully confused and many have
given up trying to understand because it is futile and they are
blamed for their failure (not trying hard enough).

On 6/22/09, algie2 wrote:
> Going out on a limb here, but I think we as teachers place far
> too much blame on teaching methods when trying to figure out
> why true learning hasn't taken place.
>
> I had a couple of really low high school classes this year.
> They were all taught Order of Ops with P E MD AS. They all had
> trouble with it. We spent tons of time on not just the what
> but the how and why of P E MD AS. They were bored beyond
> belief. We've been doing this since middle school! When do we
> get to Algebra! But they still had trouble. As a class they
> couldn't consistently evaluate an arithmetic expression
> accurately. Some were very defensive about it -- but I did it
> this way...(hmm, what is it about "order" that you don't get).
> There were a few in this group that simply could *not* get the
> hang of exponents no matter how many times (and ways)it was
> explained and broken down for them.
>
> When we did get to algebra, they had mountains of trouble
> "undoing" Order of Ops. No, you can't isolate 3x by subtracting
> 3 -- let's relook at P E MD AS. (What, again? But we've been
> doing this since middle school...)
>
> While at the beginning of the year I may have thought their
> prior teachers did a poor job of teaching Ord of Ops, by the
> end of the year I realized that it didn't much matter -- these
> kids just were not going to master it. Meanwhile, other
> students (college prep or honors level) were taught the acronym
> the very same way by the very same prior teachers and fully
> mastered Order of Ops. The variable is the students.
>
>

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