On 07 May 2009, at 11:55 , Albert Cahalan wrote:
Maria Droujkova writes:
I think it may be useful to distinguish tracks, and destinations to
which they lead. The real deal destinations are to make mathematics:
coin definitions and refine them, pose problems, form conjectures,
construct example spaces, create models and so on. Activities with
real deal destinations invite students to make mathematics; this is
the part where I get pretty "religious" and I suspect Tim does, as
well.
I don't think this is a proper expectation.
Gym class isn't expected to create pro or Olympic athletes.
Music class isn't expected to create pop stars. Native language
class isn't expected to create a J. K. Rowling, Shakespeare,
or Tom Clancy.
Math isn't any different.
A student who is **solidly** prepared for calculus is doing well.
This would include word problems with a minimum of 4 steps,
some algebra, geometry, trigonometry, etc.
Here in the USA, most students get nowhere near that level.
For the very best students we may hope for completing calculus early
enough to use it for physics, followed by statistics with calculus.
Maybe one could throw in a tiny bit about game theory or aliasing.
A desire to have students "make mathematics" can't be allowed to
get in the way of ensuring that non-ideal students learn the existing
math that they need. Math isn't just for people like Euler.
I agree 100% with that statement Albert. It would be irresponsible in
the extreme. In fact, probably, such a policy decision would likely
destroy civil society.
I might take a bit of an issue with the use of the term "non-ideal"
but this is a silly detail not worth quibbling about because we all
know which students we are talking about.
My question for everyone is, can we come to agree that not only is
Albert's statement true, but the following statement is at the same
time also true:
"A desire to have students learn the existing math they need can't be
allowed to get in the way of nurturing those students who aspire to
become mathematicians one day."
Yes ?
Great !
So now we all agree there is a critical need to make sure that, even
if we have to move heaven and earth to do it, we must all make friends
with each other and work together so that the learning system can
support both kind of student!
Because if we don't... we're all going to still be stuck with our
existing system when we revisit this argument next year, and the next
year, and the year after that.
And we must all agree that this is very important because this
existing learning system of ours... this system is really great
because it manages to at the same time, simultaneously:
* Produce students who are NOT able to do the elementary mathematics
needed to thrive in our complex society.
AND
* Produce students who are NOT getting access to critical
instruction during the years they are most likely to integrate the
math at a level allowing them to produce the work of an Euler one day
instead of wasting their talents & postdoctoral qualifications helping
the management at Lehman Brothers et al accidently the entire economy.
Wow!
If Phys Ed teachers are able to help the non-ideal kids like me learn
to throw a ball and still support the kids who will pitch major league
one day surely it can't be that hard ?
On this note I'll sit down now and let Rabbi Eliezer lead the class in
prayer:
http://lesswrong.com/lw/3h/why_our_kind_cant_cooperate/
- antoine
--
http://7degrees.co.za
"Libré software for human education."
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