[IAEP] 40 maths shapes challenges

[Edward Cherlin]

On Fri, Sep 4, 2009 at 5:12 PM, Alan Kay<alan.nemo at yahoo.com> wrote:
> Well, much of the version of calculus that is used in the physical sciences
> is adapted from Gauss' differential geometry of vectors,

In particular, the standard textbook on General Relativity (Gravity,
by Misner, Thorne, and Wheeler) uses differential geometry, that is,
the geometry of the tangent vectors at a point, throughout. The reason
is that General Relativity in curved spacetime coordinates reduces to
point-at-a-time Special Relativity, but with smoothly varying flat
inertial frames at each point.

I you didn't understand that, I hope you will take comfort from an
incident described by Richard Feynman at his Nobel Prize banquet. A
Swedish princess said to him, "You're a physicist. We can't talk about
that because nobody knows anything about it." Feynman replied, "No,
actually it's because somebody _does_ know something about it that we
can't discuss it. We can only talk about things like the weather that
nobody really knows anything about." He commented that he had heard of
people's faces turning to ice, but had never seen it before.

>and that is the
> math that Seymour adapted for Logo (in part because DGofV uses the same
> "from where I am" coordinate system that children have built in).

Einstein heartily approved of childlike thinking, particularly "the
holy curiosity of childhood". It got him into more trouble than
Feynman created for himself later on. But then, Einstein described
himself as autistic, while Feynman was no worse than severe Attention
Deficit. (More so than mine.)

> So the real problem is to convince school folks (most of whom are innocent
> of mathematics) that Logo is actually more like the real deal than what they
> have gotten into the habit of teaching. This "innocence" was (I believe) one
> of the main factors for Logo not catching on in the early 80s (or now).
>
> And, by the way, the circle as the limit of a polygon whose side count gets
> unboundedly larger with the side lengths approaching zero is the way
> Archimedes thought of circles, and the way he was able to get the first
> really good approximation to pi.
>
> I.e. don't worry about Logo, let's worry about the school systems ...
>
> Cheers,
>
> Alan
>
> ________________________________
> From: Bill Kerr <billkerr at gmail.com>
> To: Maria Droujkova <droujkova at gmail.com>
> Cc: iaep <iaep at lists.sugarlabs.org>
> Sent: Friday, September 4, 2009 4:27:26 PM
> Subject: Re: [IAEP] 40 maths shapes challenges
>
> On Sat, Sep 5, 2009 at 2:12 AM, Maria Droujkova <droujkova at gmail.com> wrote:
>>
>> Circle is one of the hardest in Scratch. Unless I am missing a command.
>
> move a little turn a little lots of times
>
> repeat 360 [move 1 turn 1]
>
> that is a classic discussion arising from Papert
> does this prepare students for calculus?
> an honest child's version of sophisticated maths?
> or are the conventions of calculus so different from body syntonic logo
> maths that the learning does not transfer?
> good one to discuss
>
>
>
>>
>> Cheers,
>> Maria Droujkova
>> http://www.naturalmath.com
>>
>> Make math your own, to make your own math.
>>
>>
>>
>>
>> On Mon, Aug 31, 2009 at 7:19 AM, Bill Kerr <billkerr at gmail.com> wrote:
>>>
>>> Image attached
>>> Forty shapes to make in Scratch or some other version of logo, such
>>> as Turtle Art. It's hard to see the thumbnail but click on it for a larger
>>> view.
>>>
>>> This is one of the best sheets ever for teaching maths (designed by Barry
>>> Newell):
>>>
>>> the logo turtle or scratch cat acts as a transitional object between the
>>> concrete maths shape and the abstraction of the script that makes the shape
>>> the sheet includes both simple and complex shapes, increasing in order of
>>> complexity, there is a challenge there for everyone
>>> many of the more complex shapes are made up of combinations of the
>>> simpler shapes
>>>
>>> Source: Barry Newell's Turtle Confusion (1988)
>>> _______________________________________________
>>> IAEP -- It's An Education Project (not a laptop project!)
>>> IAEP at lists.sugarlabs.org
>>> http://lists.sugarlabs.org/listinfo/iaep
>>
>
>
>
>
> _______________________________________________
> IAEP -- It's An Education Project (not a laptop project!)
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>



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