Re: Programming languages for the very young

From: Darius (ddarius_at_hotpop.com)
Date: 01/20/04 

Date: Mon, 19 Jan 2004 18:02:07 -0500

On Mon, 19 Jan 2004 17:58:45 +0000
Tim Haynes <usenet-20040119@stirfried.vegetable.org.uk> wrote:

> Samuel Walters <swalters_usenet@yahoo.com> writes:
>
> > | Tim Haynes said |
> >> Yes, there is a balance between both - I'm not advocating
> >abandoning> knowing a few times-tables, but saying folks will come
> >from both angles.> I'm no teacher, so however you handle that is out
> >of my scope. :)
>
> > Neither am I advocating abandoning them. Sublimation, the process of
> > learning a process so well that the original mechanism can become
> > obscured from self-awareness, is *very* important so that one can
> > concentrate on the form of an equation, rather than the numbers of
> > it.
>
> Aha, this is exactly what we're talking about.
>
> >> Possibly. But how did I just calculate 12*8 in my head other than
> >by> saying "10*8 is easy enough, add on 2*8 afterwards"? Dad taught
> >me to do> that sort of thing way way back, so I've been applying
> >elementary> algebra in my arithmetic ever since :)

The way you learn to find vertices of parabolas in Algebra is a pain. I
could never (readily) remember the way to rearrange the equation so
that it's "obvious". It's much easier to take the derivative and solve
the linear equation. ;)

> > Let me cast what you did in a different light. First, you picture,
> > however briefly or inaccurately, a pile of 80 things in your head.
> > Then, you mentally took a pile of 16 and merged them together. You
> > didn't have to count them, but the process of building one pile of
> > two piles is the intuition I'm discussing.
>
> Well, the details of the visualization are significantly different.
> The transformation "split it into two easy things and add" was almost
> pictured, but not in terms of countable bricks, rather more like `(10
> 8)' .... `(2 8)'. I saw the sub-expressions, not piles of bricks.
> Still, there's only one of me, be forever glad... :)

Yes, my (admittedly smartass but true) mental response was: I saw two
piles alright, one had 10 & 8 in it the other had 2 & 8 in it, in fact
they looked a little like (10*8)+(2*8).