From: Peter2 on
This is my first post on this forum, and I've got to say I am a little intimidated by the apparent knowledge and sophistication displayed by the members of this forum on the threads I have read thus far. That being said, I hope I can render my thoughts as relevantly as those posted before me.
I am an elementary math teacher in Texas, teaching 5th grade math.
I want to share with William the new way we are teaching math in my district. Its called Reasoning Minds, sponsored for the most part by Exxon Mobil, as well as other trust funds that help.
The Reasoning Minds curriculum is an internet based program that allows the student to access the program from my classroom; which is set up with 24 pc's; also, the student can log in from home or a public library.
The curriculum is differentiated instruction. So, each student may work at their own pace as they navigate their way through the objectives of the accountability test.
The Reasoning Minds program really frees a teacher to give the struggling students the one on one they need without pulling the reins on the higher achieving students.
This year was our first to implement the program. We were late in getting it fully operational and missed the first 1 1/2 months of the year. Next year we will hit the track running , and I am really looking forward to having my best year of teaching yet. By the way, I have been teaching for ten years.
From: Frederick Williams on
"J. Clarke" wrote:

> However knowing how to fix a car does not help you to detect that a
> politician or lawyer's "proof" is anything but. Knowing what real proof
> looks like does.

That's irrelevant, lawyers are not required to prove things
mathematically.

--
I can't go on, I'll go on.
From: Jesse F. Hughes on
Peter2 <bhebert1957(a)yahoo.com> writes:

> This is my first post on this forum, and I've got to say I am a
> little intimidated by the apparent knowledge and sophistication
> displayed by the members of this forum on the threads I have read
> thus far. That being said, I hope I can render my thoughts as
> relevantly as those posted before me.

> I am an elementary math teacher in Texas, teaching 5th grade math.

There's no reason to be intimidated if the topic is elementary
mathematics education. I imagine I know a bit more about mathematics
than you do, but I'm also sure that I know much less about teaching
math to fifth graders!

Being able to do proofs is quite different than being able to teach
math to children.

--
"Not all features that are found on the Security tab are designed to
help make your documents and files more secure." --Microsoft on Office
security features (after it was pointed out by a third party that a
certain password setting is easily bypassed.)

From: J. Clarke on
On 5/3/2010 2:32 PM, Frederick Williams wrote:
> "J. Clarke" wrote:
>
>> However knowing how to fix a car does not help you to detect that a
>> politician or lawyer's "proof" is anything but. Knowing what real proof
>> looks like does.
>
> That's irrelevant, lawyers are not required to prove things
> mathematically.

So what? Are you saying that the public should be trained to be easily
bamboozled for the benefit of lawyers?


From: Transfer Principle on
On May 3, 9:23 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote:
> On 5/3/2010 11:15 AM, William Hughes wrote:
> > On May 3, 11:42 am, "J. Clarke"<jclarke.use...(a)cox.net>  wrote:
> >>>>     A balance is needed--students need to know how to prove theorems, but
> >>>> they also need to be able to solve problems, and knowing how to do one
> >>>> does not necessarily enable one to do the other.

This is the second thread I've seen on the topic in the past
few weeks about this topic. The other thread asked when most
American students learned about proofs, and the answer was
that while they were traditionally taught this in the
high school geometry class, this is now on the decline. One
would have to go to Asia to learn math fully rigorously.

> > Actually, I have grave doubts that this holds for most
> > people.
> Most people don't need any math beyond arithmetic anyway, so we aren't
> talking about "most people".

Bingo! There lies the dilemma. Since most people don't use
math beyond arithmetic, many people believe that math
shouldn't be taught past elementary school at all. In
particular, _no_ math should be required to graduate from
middle or high school or enter college. One should only
have to learn the bare minimum of math required to survive
in the real world and that's it.

Then whenever anyone asks why more math should be taught in
school and more rigorously, the answer inevitably goes back
to "Asia." Math classes need to be made more rigorous in
order to keep up with Asia, and the US will keep falling
behind unless the curriculum is changed.

So there are two philosophies on how much math should be
taught in school -- the minimalist idea that students need
only to learn as much math to survive in the real world and
not one iota more, and the competitive idea that one needs
to learn as much math as they do in Asia. And never the
twain shall meet.

An argument could be made that the status quo is in fact a
compromise between the two philosophies -- so one has to
learn more math than is needed in the real world in order to
get into college, but less math than Asians do.

The one question that I have never seen answered is why don't
the _Asians_ complain that they are required to learn more
math than is required in the real world. If Americans don't
like that the little math that they are forced to learn isn't
used in the real world, then Asians, who have to learn much
more math than Americans, have more right to complain -- and
yet we don't hear about such complaints. If Asians only had
to learn as much math as they need in the real world and not
one iota more, then there would no longer be a gap between the
math curricula of the two continents.