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@terra.com.br>
>> To: mstram <mstramba@sympatico.ca>
>> CC: squeakland@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@squeakland.org
>>>
http://squeakland.org/mailman/listinfo/squeakland
>>>
>
>
>
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