[IAEP] versus, not

[Edward Cherlin]

On Thu, May 7, 2009 at 2:55 AM, Albert Cahalan <acahalan at gmail.com> 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.

It is in China, and used to be in the Soviet Union.

> Music class isn't expected to create pop stars.

I have observed in an arts and music school in China where all of the
third-graders are competent to perform in public. I am told that every
child in the Netherlands learns to play recorder and read music.
Zoltan Kodaly's reforms of music education in Hungary long ago
resulted in so many pro-level musicians that most had to leave the
country to find work in orchestras all over Europe and beyond.

> Native language
> class isn't expected to create a J. K. Rowling, Shakespeare,
> or Tom Clancy.

Enough! Compare the level of literacy of Civil War soldiers shown in
their letters home with the traffic on the Internet. It is not the
quantity of reading or writing, but the fact that they were required
to read as though they meant it. You remind me of a friend whose
school report read, "He sets himself the lowest possible standards,
and falls far short of them."

> Math isn't any different.

That's true. It is no different. Children can learn to understand
math, not just manipulate symbols to get approved right answers.

> 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.

The principal reason that I am aware of for US schoolchildren not
learning calculus is that it would show up the teachers as
incompetents.

> 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,

All.

> followed by statistics with calculus.
> Maybe one could throw in a tiny bit about game theory or aliasing.

Now you are just guessing. It doesn't help your case.

> 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.

Every child can appreciate some of Euler's real work. V-E+F=2. We
could teach that in kindergarten, in the form V+F=E+2, with
appropriately colored models. For a tetrahedron, it comes out to
4+4=6+2. No trouble. Cube: 8+6=12+2.

-- 
Silent Thunder (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) is my name
And Children are my nation.
The Cosmos is my dwelling place, The Truth my destination.
http://earthtreasury.org/worknet (Edward Mokurai Cherlin)