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From: bh@anarres.CS.Berkeley.EDU (Brian Harvey)
Newsgroups: comp.lang.logo
Subject: Re: Evolution of logo
Date: 1 Jan 1994 05:48:23 GMT
Organization: University of California, Berkeley
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Message-ID: <2g32r7$nih@agate.berkeley.edu>
References: <1993Dec24.194331.91@magill.unisa.edu.au> <2ff56r$l29@agate.berkeley.edu> <1994Jan1.140735.97@magill.unisa.edu.au>
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kerrb@magill.unisa.edu.au writes:
> [...]
>Hence it is desirable for logo to evolve further in its design using visual
>and OOPs features to accomodate half the population. This is more likely to
>work than exhortations to teachers about the one and only true way. I don't
>believe there is one true way. It is more an artifact of the cultural 
>dominance of one particular style in present computing cultures.

I don't think there's "one true way."  I believe, in fact, that the way
real creative mathematicians work is a synthesis of tinkering and formal
reasoning.  New mathematical ideas are not invented formally; they're
invented precisely by tinkering.  But formal thinking comes in in two
ways.  One is that *after* the new idea is created, formal language is
used to communicate it to other people.  The other is that if you want
to be able to invent new ideas beyond the simplest level, you have to
understand the supporting ideas through and through, and that means both
an intuitive and a formal understanding.

>I thought the whole ideas of logo was to transform traditional subjects like
>maths to better fit the learner. ie. epistemology is about the evolution of
>learning structures in our mind. Logo is about making it more natural, not
>imposing traditional formal methods.

Well, "traditional" and "formal" are two different things.  Turtle geometry
is (among other things) a nontraditional formalism.

In his new book, Seymour seems to be saying that he used to think the goal
was to get to formal thinking, but now he thinks that informal thinking is
valuable throughout life.  I agree with that.  But I don't think he's
saying (and if he is, then I disagree) that one can get by with *only*
informal thinking.

Certainly our job as teachers is to meet our students where they are, and
that includes their preferred learning styles.  But I think we also must
get students into a broader intellectual world.  It's not a question of
which style is better, as you seem to think I think.  When I'm dealing with
some of my computer science students who are *only* comfortable with formal
ways of thinking, I try to introduce them to a broader intellectual world
too.  For example, I prefer the psychoanalytic view of the human mind to
the cognitive psychology view, in which people are understood as being
a lot like computers.

But I do think that if you want to be an *expert* programmer, you have to
be able to do the formal stuff.  I don't think OOP or graphical interfaces
will change that at all; those things will expand the range of tasks that
non-experts can perform, but I don't apologize for the ultimately formal
nature of technical work, any more than a novelist should apologize for
the ultimately non-formal nature of that kind of work.

Not everyone has to be an expert programmer.  But the point I was trying
to argue earlier was that if you're a Logo teacher, it seems to me clearly
better if you can think *both* in the formal and in the informal mode,
rather than either one without the other.  Jung talks about personality
types, and his view is that, on the one hand, you should know and use your
own strengths, and that you'll probably always be best at the same kinds 
of things you start out best at, but on the other hand, that you should also
try to develop your weaker sides.

So, I have to work harder at understanding informal thinkers, and informal
thinkers have to work harder at formalism.  I think.

P.S.  I don't like to use the word "tinkerer" as meaning something opposite
to formal thinker, because I like to think of myself as a tinkerer also;
when my dishwasher stopped working the other month, I took it apart and
fixed it, even though I had no prior knowledge of how the thing worked.
Nevertheless, there is something else, neither formal reasoning nor
tinkering, that I'm not so good at.