[Squeakland] Weird Heading numbers

[Alan Kay]

Yes -- thanks Paulo.

Logo uses all child centric references such as 
right and left with the reference being up = N. 
One of the experiments early on in Etoys was to 
see how well + and - could be used in place of 
right and left with ~ 7 year olds. This was going 
to be part of a whole vectorized cuisinaire rods 
approach to numbers (that used some results we 
got in the Vivarium) that were unified with the 
number line way of thinking of + and - as 
directions (also right and left) of one dimensional vectors.

When the Etoys demo started being used in schools 
(instead of the home as originally planned) we 
found that grades 4-5-6 were a better fit with 
the tradeoffs between what children can do and 
what adults want to learn. So we never carried 
through the concrete number representations originally planned.

(However, now we are going to because the OLPC XO 
needs to have a K-12 range. This actually 
requires a somewhat different approach to Etoys 
than the demo version we have now, and we are 
working on it, which supporting current Etoys for the various XO builds.)

Most adult conventions and forms have huge QWERTY 
components which make learning more difficult for 
children. However, eventually the conventions 
need to be added in. It's imperative to start 
children thinking in the strongest and most 
intuitive way -- then we can figure out how to 
merge in the somewhat ad hoc conventions that 
adults have devised. Various ways of thinking 
about numbers, lengths, directions, magnitudes 
etc is a ideal way to eventually get to some of 
these conventions. But, e.g. trying to get 
children started into real numeracy with 
positional notation is really bad, even though it 
is a mainstream convention ... the general result 
in America is that children don't get numerate, 
even though they are forced to learn how to parrot a few of the conventions.

Cheers,

Alan

At 09:21 PM 5/25/2007, Paulo Drummond wrote:

>On May 25, 2007, at 11:57 PM, Mike Stramba wrote:
>
> > Compasses, GPS, Aircraft, Marine Vessels all use "real headings".
>
>Ok. Try explain to a 8-year child that 0 = 360.
>
> >
> > I've never heard of any other use for them (before playing with
> > Etoys ;)  )
>
>It's Geometry, in its very roots. I bet starting with this negativity
>of angles, relativity of things, one who learned with this principles
>in mind can understand the real basic Geometry (Euclidian, Cartesian,
>Vector Space etc) much better, much earlier.
>
>cheers,
>Paulo
>
> >
> > Mike
> >
> >
> >> From: Paulo Drummond <ptdrumm at terra.com.br>
> >> To: mstram <mstramba at sympatico.ca>
> >> CC: squeakland at squeakland.org
> >> Subject: Re: [Squeakland] Weird Heading numbers
> >> Date: Fri, 25 May 2007 23:50:47 -0300
> >>
> >> Imho, there is no such thing as "real headings". Geometry, as its
> >> mother Mathematics is a wonderful symbolical language to provide
> >> us  all means of mapping the physical world as we see it.
> >>
> >> The use of semi-circular geometrical convention helps (among
> >> other  things) in:
> >> 1) give the sense of "negative" when the object passes "downward"
> >> or  "to the other side" of an 2-D axis (another convention);
> >> 2) the coming back rationally to zero instead of jumping from
> >> 359º59'59" to it.
> >>
> >> cheers,
> >> Paulo
> >>
> >> On May 25, 2007, at 7:19 PM, mstram wrote:
> >>
> >>>
> >>> While playing with the Etoys, I've noticed the "weird" heading
> >>> numbers.
> >>>
> >>> By that I mean when the object's heading passes 180 degrees,
> >>> instead of
> >>> continuing on to 190 ... 270 .. 360, we get the negative numbers.
> >>>
> >>> Why was this convention adopted ?
> >>>
> >>> I think if kids ... and some us "older" kids are going to be
> >>> using  headings
> >>> it would be more educational and instructive to use "real" headings.
> >>>
> >>> Maybe an option / preference could be setup on which heading
> >>> numbering
> >>> system to use.
> >>>
> >>> The only minor problem I can see is whether it should be "0" or
> >>> "360" to
> >>> begin with.
> >>>
> >>> Just for the fun of it, I'm digging in and seeing if I can
> >>> construct my own
> >>> subclass to use the "360" system.   I have an idea for an ATC
> >>> simulation I'd
> >>> like to do and "real" headings .. or at least converted for
> >>> input  and output
> >>> would be a must.
> >>>
> >>> Mike
> >>> --
> >>> View this message in context: http://www.nabble.com/Weird-
> >>> Heading- numbers-tf3818581.html#a10811065
> >>> Sent from the SqueakLand mailing list archive at Nabble.com.
> >>>
> >>> _______________________________________________
> >>> Squeakland mailing list
> >>> Squeakland at squeakland.org
> >>> http://squeakland.org/mailman/listinfo/squeakland
> >>>
> >
> >
> >
>
>
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