🚀 go-pugleaf

I've been sending this explanation one week ago and I have not confirmation
about the distribution to the list. I don't know why, but I have really
bad luck.

Thank you, Helen, for your interest and your reference for J.Novak work.
Could you send me the title?. Is a book or a paper?. Sorry, I don't know
nothing about psychology. If you would like, e-mail me directly to
fdr@halfter.tid.es.

I am going to explain the expression "mental maps of mathematical
concepts". I am on the basis that students of mathematics must develop a
"map of concepts" in their minds. This map consist in several levels
with different concepts on it and with multiple connections between. Grafically
it seems something like this:



            /                          /
           /   C(n)1--------> C(n)3   /
          /       \         |        /      <-------   level n
         /         \        C(n)4   /
        /           \C(n)2         /
       /            /             /
      /         C(n)k            /
     ---------------------------
         /                 C(n-1)2   /      <-------   level (n-1)
        /   C(n-1)1                 /
       -----------------------------
         /                 C(n-2)2   /      <-------   level (n-2)
        /   C(n-2)1                 /                  :
       -----------------------------                   :
                                                       :
         /                 C(1)2     /      <-------   level 1
        /   C(1)1                   /
       -----------------------------


In level n there are k concepts (c(n)1, c(n)2,...., c(n)k) and possibly it will
be related between it not exhaustively. The relations are like these:

if (concept c(n)1) then OBTAIN (concept c(n)2) and/or (concept c(n)3)
if (concept c(n)3) then CALCULATE (concept c(n)4)

Of course, the number of levels it depends on the system purpose, high or low
skill.

for example: Context ---> plain/line relative positions

if (S is a CRAMER system) then OBTAIN/AFFIRM that (S is compatible) &
                                                  (S is determined)

of course it might be relations between levels, for example:

if (alpha is a plain) & (beta is a plain) & (r=alpha intersection beta)
then (the system S: alpha
                    beta
                    r       is compatible)

With this rule I mean than concepts like plain or line are in a map with higher
level than concepts like compatible, determined, parametric equations,
vectorial equations, etc.

My work hypothesis is that students must have such a kind of this maps
on her/his mind. We can help them with a Computer Supervisor of their
knowledge. The students have to learn with the classical methods and,
afterwords, they could use the Supervisor for check if their knowledge is
coherent with the system one (correctly implemented).

I don't know how develop this kind of system, therefore I am thinking
in use SOAR architecture because I think this architecture represents
well the human mind and behaviour, but I am open to any suggestions about
this. For somebody who want knows something about SOAR, could find information
in WWW, URL:http://www.isi.edu/

I hope that this explanation will be enough, but if don't, please let me know,
I'll try again.


        Fernando Diez
        Telefonica I+D   (Madrid - Spain)
        e-mail: fdr@halfter.tid.es