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From: kerrb@magill.unisa.edu.au
Newsgroups: comp.lang.logo
Subject: Planners v. Tinkerers
Message-ID: <1994Jan25.180028.104@magill.unisa.edu.au>
Date: 25 Jan 94 18:00:28 +1030
Organization: University of South Australia - Magill
Lines: 114

Posted with permission from Augusto.

From:	IN%"augusto@itd.ge.cnr.it"  5-JAN-1994 04:53:52.78
To:	IN%"kerrb@Magill.Magill.UniSA.edu.au"
Subj:	Planners vs Thinkerers and the poly microworld


Dear Mr. Kerr,
I'm sending this message directly to you since I read comp.lang.logo via
a gopher gateway, but I have no direct access to USENET so I can't
send messages to newsgroups.

You raised the question of direct manipulation style interfaces to Logo.
In many way Logo is still confined to the teletype interface.  The
more interesting evolution of Logo, in my opinion, is Boxer.  I wish
Andy di Sessa would contribute directly to the discussion, otherwise
I could send you references on his work.

UCBLogo is not innovative with regard to user interface issue, and I
think Brian Harvey would agree with this statement.  One interesting
innovation in UCBLogo is the extension of simbolic manipulation
capabilities and the introduction of macro.

On the commercial side, Microworlds from LCSI is an interesting
product addressing the user inteface weakness of previous Logo. I've
only seen a demo at a conference and in the process of ordering a
copy in Canada, no Italian distributors!

Now let me turn to your point about turtle graphics being easy and intuitive.
on one side this is true, but you can have seriuos problems with
learners if you cannot offer assistance once you start exploring
mathematical ideas using the turtle.

I will pick up your own example to discuss on a concrete base:

>Meaningful and powerful turtle graphics microworlds can be created fairly
>easily. 
>to poly :angle
> fd 50
> rt :angle
> if heading = 0 [stop]
> poly :angle
>end
>
>This can be explained concretely. eg. by a role play.

If you try to draw an 11 sides regular poligon

        poly 360/11

the poly procedure will not stop as expected.

There is no conceptual bug, the math is OK.  Unfortunatelly th
turtle on the screen deals with floating point representation of
numbers and the round off error will defeat the equality test.  When
I was introduced to programming with FORTRAN (it was 1979, and
physicist still use it) I learned quickly not to use zero equality
test when floating point numbers where involved.  Again you need a
mental model of your tool to understand its behaviour; if you fail
to grasp what's happening you are lost.
I don't like it and think that would not be wise to explain this
machine working to learners while at the same time that we are
trying to explore the poly microworld.

Here is an attempt to avoid this problem (the code is in UCBLogo):

to poligon :angle
forward 50
right :angle
if zero.heading? [stop]
poligon :angle
end

to zero.heading?
local "tollerance
make "tollerance 0.0001
output or (lessp heading :tollerance) ; almost zero ~
          (lessp (360 - heading) :tollerance) ; almost 360
end

The zero.heading? could be provide to learner as a fix to the
earlier problem, this does not neceserally implies that it should be
fully mastered to be used.

Once we have a good behaving poly procedure let's start exploring;
how many different 11 edges poligon can be drawn using poly?

Hint:
        poly 360/n      describes regular poligons
        poly 360*2/n    describes star poligons if is odd

so we can experiment with:
        poly 360*3/n etc.

once we have some pattern coming out of our exploration of 11 edges poligons
and we have concrete examples we can start exploring the nice math
of the poly microworld. (Chapter II of Turtle Geometry is all about
this).

The point of all this is that teachers need to know more about Logo
to assist learners in eploring math (or another subject).  This will
not be solved by advances in user interfaces.  In the era of the
global village I hope that tools like comp.lang.log and the
community that use it will help to create Seymour Papert Mathland.

Sincerely,
                Augusto


/// Augusto Chioccariello
/// Istituto Tecnologie Didattiche, C.N.R.      Genova - ITALY
/// E-mail: augusto@itd.ge.cnr.it