> -----Original Message-----
> From: Alan Kay [mailto:Alan.Kay at squeakland.org]
> Sent: maandag 30 juli 2001 19:06
> To: squeak-dev at lists.squeakfoundation.org
> Subject: RE: The goal of K-12 CS education
> 
> 
> For a minute let's not worry about satisfying official school 
> systems, and worry just about teaching "real math" and "real 
> science". (I use these terms because in the US "math" and "science" 
> have been "colonized" to actually mean "fake math" and "fake 
> science". And let's suppose we are interested in having the children 
> actually learn a strong combination of the two.
> 
> There are some very interesting implications that arise from these 
> goals. One is that we should try to help children develop "uncommon 
> sense" (instead of the 80,000 year old common sense that most 
> cultures bestow). We especially would like the uncommon sense to 
> include both the epistemological stance of science towards knowledge 
> and knowing, and also a large toolbox of modern heuristic methods for 
> thinking, having ideas, and colliding theories.
>
How deep and how early this adaptation to common sense math takes place:
- Ask a child that starts with math: " 3 melons and 2 melons makes..?"
- the child will answer 5
- Then ask the same child again: " 3 million and 2 million makes..?
- The child will answer: "I don't have learned that yet.."
- you can in an endless loop repeat these questions an get the same answers.
You can even play an adapted form of this context-game with math-teachers: 
- Ask them on wich age children learn 2 + 3?
- Ask them then the learning age of 2 + . = 5
- Ask them if you may replace the dot with a flower and if this does change
the age
- Ask them then if you may replace it with a bucket? age does not change.
- Then ask them if you may replace it by any other thing and if that would
affect age.. No..
- Then propose 2 + x = 5 
- O NO... that is algebra, that is secondary school stuff?
- Why, you say x is just a container to hold a digit like x is...
(depending of their teacher training you can convince them.

> If we could come up with a "new math" that included them (a) new math 
> of complex internally interacting systems, and (b) a new math for 
> differential vector geometry and quasi-linear relationships, whose 
> foundations can be taught to children as play, then we might be able 
> to make some progress.
>
In the seventies we had in Holland a movement called the critical teachers,
as a spin-off it did end in The Freudenthal-Math-institute. They try for
years to change Dutch-math in the direction you whish, the even sold there
products to the US. Acceptance for their real-life-and-also-fun-maths does
still not reach all schools.
 
  
> Simply put: objects in relationship is a nice way to do (a), and 
> turtle geometry with costumes is a nice way to do (b).
>
I think that especially the direct visual feedback does the work..
 
> Where the play gets applied and transferred is in the gradual 
> escalation of the systems that can be modeled. Just the simple car 
> with "car forward 5, car turn 5" is the differential vector geometry 
> expression of a circle (as can easily be seen if the pen of the car 
> is dropped). Each constant differential vector is added (the loop 
> acts the part of the integral sign) and the result is an expression 
> for constant curvature (a circle) whose derivative, the change in 
> curvature, is 0.
> 
We had ots of discussions about LOGO in the 80-s. A difficult one about
Vartesian was that LOGO works well for symetric forms, but doing the same
for more irregular forms took away all this repeat and recusive power... it
seemed easier in a cartesian frame...

> Now the few children who even get to calculus do not usually learn 
> this in the US because the pathway is Cartesian coordinate, numeric 
> and algebraic. What Papert proposed to do years ago was to simply 
> start the kids off on the precursors for modern mathematical thinking 
> in science.
>
Yes I remeber that feeling of magic in numbers: changing numbers in these
drawing formula's did create marvellous drwaings, others did not, children
where looking for patterns in numbers... I think that was a level to high.
 
> When the child hooks the steering wheel into the car (via dragging 
> the "steer's heading" tile into the "car turn by 5" tile) they are 
> painlessly learning about variables and why variables are a great 
> idea.
>
What I like in your explanation on the list about the wrong speed and the
introduction of a gear was that you did show how subtile the tuning of these
learning-settings really is.
After years of working on learning environments of all kind, I got the
feeling that what teachers are looking for is a tool they can tune for THEIR
children in THEIR class in THAT specific year.

I did call this new approach to muy colleguaes, with an apology of misusing
a computer-concept: late-binding-educational-software. Can you imagine how
thrilled I was that you, mister dynabook himself, did use the term
ExtremeLateBinding in the book of Mark I am reading now in my holiday. From
now on I cite Your XLP-idea, without any apology.
(I am also realistic about teachers, even on a university, so I (let) design
tools that support their bad habits, so they like it and use it... and then
- little by little, using for example cues in fill-in forms that support
their habits, I try to reorganize the flow of their habits.. no longer
fighting them from the baricades of IT-innovation.)

> When the child makes the car into a robot car that can follow a track 
> by itself, they are learning the powerful idea of feedback that is so 
> central to animal and mechanical controls systems that don't have 
> complete knowledge. The next stage of this is to make a gradient 
> follower and now they can model what salmon, clownfish, and ants do 
> in critical phases of their existence.
>
Who organizes for them this learning-path in your approach?
In the Netherlands we had a lonesome professor van Pareren, preaching for
many many years the Russian Learning theory of Vygotsky: the learning-zones
nearest to a childs deveopment.
(The man did die lonesome, recently we have this revival of the look-alike:
constructivism)   

> The combination of science (trying to understand cause and effect 
> "out there") and math (trying to model useful and interesting 
> relationships) is extremely powerful.
> 
> So the possibilities for transfer are both large and successful if 
> the further curriculum is also in accord with modern math/science. 
> (We have been doing this for 30 years now and have seen much 
> convincing evidence.) The difficulty with getting this stuff going in 
> the US has primarily been the lack of any kind of math preparation on 
> the part of K-8 teachers. (Also, for political reasons the math and 
> science groups do NOT cooperate in the US very much.) This is a huge 
> problem.
>
I have a background in psycholgie. When I enterde the faculty of educational
technology I did discover that these people, even on the subject of
psychologie did read other books and did have other heroes than we the as
psycholgists... So it does not sound so strange to me.
 
> In any case, those who are interested in this stuff will find quite a 
> bit in the current Squeak to this end.
> 
Yes, that is the fun I did rediscover. Now I only have to convince all these
university colleguas. For a start I decide to learn Squeak (and Swiki) for
myself in freetime, then I will construct some prototypes - tackling UML,
XML, IMS on the fly - and then...
O my, I think that I need at least an educational leave or so for that.  

> Cheers,
> 
> Alan
> 
> At 4:08 PM +0200 7/30/01, G.J.Tielemans at dinkel.utwente.nl wrote:
> >-----Original Message-----
> >From: Alan Kay [mailto:Alan.Kay at squeakland.org]
> >Sent: maandag 30 juli 2001 16:12
> >To: squeak-dev at lists.squeakfoundation.org
> >Subject: Re: The goal of K-12 CS education
> >
> >
> >Do you folks realize that every Player (the automatic wrapping of a
> >morph for kids) in Squeak is a turtle?  Get the handles by cmd-click,
> >then click on the blue eye to see the viewer, then look in the
> >category called "pen use". Change pen down to true.
> >
> >Cheers,
> >
> >Alan
> >
> >>  OK Alan, the problem of transfer: Suppose I learn in 
> Squeakland to build a
> >car and automatic run a track with the color-under-command. 
> Where can I
> >apply this knowledge outsite track-racing or other kinds of 
> mazes (like the
> >moving robot.) What can help me to come to better transfer from this
> >knowledge-molecule?
> 
> 
> -- 
> 
>