[IAEP] versus, not

[Edward Cherlin]

On Thu, May 7, 2009 at 6:30 AM, Alan Kay <alan.nemo at yahoo.com> wrote:
> I would agree with Albert if notions could only be divided into two parts
> (and the unsophisticated human brain loves this kinds of "either-or"
> distinctions).

+1
> I was careful to identify at least three divisions in my initial post. The
> two of interest are "fluent, but not pro" and the one that Albert mentioned
> "pro".
>
> I'm interested in the first of these "fluent, but not pro", because this is
> where learners are doing the "real deal" and not any other kind of deal.
>
> This is the level that is necessary for a Jeffersonian democracy in which
> "the ultimate repository of the powers of the society lie in the hands of
> the people" and "if their discretion is not sufficient, the remedy is not to
> take these powers from them but to better inform their discretion through
> education".

+1

> An analogy that is not too strained is that people made things with bricks
> for thousands of years before the arch was invented -- there was almost no
> route via "brick thinking" to the arch, despite that arches can be made from
> bricks.

I am planning a module on conic sections with applications to
perspective drawing and gravity. One of the essential points is that
the Greeks had all of the math that they needed to do both, but never
started either. In particular, none of them ever noticed that a
fountain of water has a parabolic shape (an ellipse with a focus at
the center of the Earth, if you want to get real picky, but there was
no way they could have measured the difference). Leonardo da Vinci
noticed parabolas (late 1400s), and figured out the law for uniform
acceleration more than a century before Galileo (early 1600s), but
could not publish any of his work in physics.

> Best wishes,
>
> Alan
> ________________________________
> From: Albert Cahalan <acahalan at gmail.com>
> To: droujkova at gmail.com; iaep <iaep at lists.sugarlabs.org>
> Sent: Thursday, May 7, 2009 2:55:09 AM
> Subject: Re: [IAEP] versus, not
>
> 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.

To notice patterns, which is useful in every subject. Not just
patterns of numbers or shapes.

>> 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.
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>
> _______________________________________________
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-- 
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And Children are my nation.
The Cosmos is my dwelling place, The Truth my destination.
http://earthtreasury.org/worknet (Edward Mokurai Cherlin)