Re: LOGO-L> Re: Total Turtle Trip

[mikedoyle@cix.compulink.co.uk (Mike Doyle)]

In-Reply-To: <v03007808b074865622f3@[139.132.40.201]>
John Gough <jugh@deakin.edu.au>, in his reply to me remarked:

> We need to be careful arguing from history.

A comment with which I heartily concur. And, indeed, I avoided so doing. I 
simply described the instruments used to represent (construct) shapes in 
Euclidean geometry - the same instruments that engineering draughtsmen 
used until the very recent advent of CAD. 

The problem with computers and mathematics is that all mathematical 
thought and ideas are historical. They are based on mental processes aided 
by to passive representational media. The computer is a fundamentally 
different medium in that it can represent processes actively.

Thus, the procedure:

to polygon :sides :sidelength
repeat :sides [forward :sidelength right :side]
end

is a description of the *process* of drawing a regular polygon. 

NB the 'repeat' in the procedure tends to hide the fact that the procedure 
prescribes a *sequence* of actions. One explanation of why children prefer 
to write out each step in a sequence is that they want to be able to 
follow every individual action, as if they were drawing it themselves by 
hand. I.e. they want to record the process. 

The procedure defines a polygon through the process by which one might be 
constructed. This process is fundamentally different from the process of 
constructing a circle. Andy diSessa was groping at this idea when he 
talked of procedural definitions being 'intrinsic'. Unfortunately, the 
weight of mathematical history he carried with him, and which we all 
carry, seems to have blinded him to the real point of divergence of the 
procedure from a classic formal definition. A procedure defines in terms 
of processes. A classic definition defines in terms of formal 
relationships.

School mathematics still focuses on formal rather than process 
descriptions. Thus, we ask children to use Logo to draw a train and give 
it polygonal wheels which they perceive to be, and which we call, 
circular. We pull out procedures for shapes as we pull out shapes from the 
box to draw round. We do not ask children to attend to the sequence of 
operations required - which leads straight to the classic 'house' bug.

Perhaps we need rather more thought about what the *computer* does and a 
little less about what children do for their teachers and what historical 
figures did with minds and hands. 

Michael Doyle (aka Micheal O Duill)
37 Bright Street
SKIPTON BD23 1QQ UK
Tel/fax: +44 (0)1756 794601
Email: mikedoyle@cix.co.uk

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