Although I am not a good student, I am an especially poor student of that
which does not work.
I have just been looking over some papers I found using a search on
the terms 'multi level reasoning'.  One which was the most interesting
concerned dealing with children who had difficulties with concrete learning.
But I also found another paper that used some of the same buzz words that I
would use and at first I was very interested.   As I read a little, I became
less interested.  I found that the author or authors used abstract notations
(like mathematical or functional notations) but I had an overwhelming sense
that there was something wrong with their use of formal notation. I finally
figured it out.  They were formalizing a system that was produced only
in their imagination.  Well, all good formal systems start with the
imagination, but here, they were not building a solution to a mathematical
problem or an explanation of some set of experiments and they were not using
formal notation to summarize their experiences using the methodology they
had thought up, they were formalizing something that they had never tried
with any actual experiments or with only the most nominal thought
experiments.

I have nothing against discussing your more imaginative ideas, but I really
wonder how useful it is to express yourself using formal notation as
if a fantasy constituted a mathematical proof or an apt description derived
from some number of actual computational experiments.  I think this is a
poor use of formal notation and it represents an immature understanding
of why formal notation can be so effective when used well.

Jim Bromer



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