Replying to LO26744 --
Dear Organlearners,
Greetings to all you fellow learners,
My reply to Leo Minnigh's <l.d.minnigh@library.tudelft.nl>
7 Steps Problem Solving Skill LO26744
may be somewhat frank (in the sense of taste), although I intended it to
be frank (in the sense of ingenuity).
I have used "the" in stead of "a" deliberately. With this I invite all of
you to a LO-dialogue on what is typical of all problems. In other words,
how will we be able to know "This is THE problem!"? When will we know that
we have become aware of THE problem? What is THE essence of all problems?
I will try to avoid describing any procedure to solve some problems.
However, I am shooting myself in the foot here because I am now pretty
sure that the first step in problem-solving is to know "This is THE
problem". In other words, I am actually concerned with the first step to
solve ANY problem. Hence, if you want to extend this topic to all the
steps needed to find a solution, feel free to explore these steps also.
As I wrote to Leo, I created systematically over several years a powerful
algorithm for solving problems. I thought that this algorithm would help
all my students with problem-solving. However, I never expected that the
students would begin to use it like a fixed recipe because of its power!
Thus this algorithm (not the students!) began to horrify me and likewise
my enthusiasm for refining it dwindled away.
I began to teach them in a different way how to solve problems. I created
carefully problems which would afford the students, through solving these
problems, the tacit knowing how to solve other problems. I began to call
these problems by the strange (for you) name MonCat problems.
I also had another reason for doing it. My researching into and teaching
of problem-solving began thirty years ago. I was then, as a South African,
a somewhat lone figure in doing it. But by the time I got disillusioned by
my own algorithm, many students had already been taught as pupils in
school how to solve problems. So many had their own recipe and did not
need my "recipe" too.
As my own skill in creating MonCat problems improved, so did the horror of
my students when getting such a MonCat problem to solve. They became
disillusioned with the recipes which they had been taught! What happens in
a MonCat problem is this. An initial set of data is given and the first
problem is solved. The solution contains further data (i.e generated data
rather than originally given data) for a second problem. So the second
problem has to be solved. Its solution generates the third problem and so
fourth.
Afterwards, when studying the work of Maturana and Varella, I realised
that these MonCat problems could also have been called Autopoiesis
Problems ("auto"=self, "poiesis"=make). Likewise these MonCat problems
could also have been called irreversible self-organising problems. Perhaps
the chaos facet of entropy is telling in the next story.
One day I became aware that most students, even though solving these
MonCat problems and thus acquiring tacitly skill in problem-solving, were
obvlivious to the autopoietic nature of these MonCat problems. So one day
I decided to do a little experiment. I created once again a MonCat problem
to make sure how far it would generate its own problems. But rather
generating these problems for the students, I wiped all of them out,
including the first problem. I gave the students only the set of initial
data.
What consternation followed. There were many bright students among
these some 150 students, the "cream of the nation" as some would say.
The wording was simple.
Solve the problem, given ...... as data.
But I did not tell them what the problem was. I only gave them the data
and expected from them to identify self one the possible initial problems,
then solve it and thereafter do the same for every subsequent problem. In
other words, I expected from them to show their own skill in creating
MonCat problems and then solve them.
To understand what I mean by the consternation, here is a simple (and
thus not a good MonCat) example.
. Solve the problem, given three apples and the
. price of pears is 50 cents each.
(I wish you knew more chemistry so that I could give you an actual example
rather than this apples, pears and price thing.) What would your reaction be?
* This is not a problem.
* The problem is a joke.
* The problem is not clear.
* The problem cannot be solved.
* What is the problem?
These are the kinds of reactions which I got from the students. However,
not even one student offered a solution in even the tiniest sense. Some
came to my office and asked me to give them more information. I did not.
The outcome of this experiment stunned me. Problem-solving involves far
more than what a teacher ever can articulate with even the most powerful
problem-solving procedure. I will say no more. I rather want you fellow
learners to say more.
I think that Michael Polanyi, should he have lived today, would have came
across this LO-list and became a member of it. So let me introduce him to
our dialogue with the following, even though he wrote it 35 years ago in
"The Tacit Dimension" (pp21-22):
. "It is commonplace that all research must start from
. a problem. Research can be successful only if the
. problem is good; it can be original only of the problem
. is original. But how can one see a problem, any problem,
. let alone a good and original problem? For to see a
. problem is to see something that is hidden. It is to have
. an intimation of the coherence of hithertho not
. comprehended particulars. The problem is good if this
. intimation is true; it is original if no one else can see
. the possibilities of the comprehension that we are
. anticipating. To see a problem is not just to see
. something hidden, but to see something which the rest
. of humanity cannot have even an inkling. All this is a
. commonplace; we take it for granted without noticing the
. clash of self-contradiction entailed in it. Yet Plato has
. pointed out this contradiction in the "Meno". He says
. that to search for the solution of a problem is an
. absurdity; for either you know what you are looking for,
. and then there is no problem; or you do not know what
. you are looking for, and then you cannot expect to find
. anything."
Michael's solution to the paradox was to use his own insight:
. "We can know more than we can tell."
Can you solve the paradox too?
Michael also became aware that the awareness to any problem originates
from the tacit level of knowledge. Thus it is impossible to tell for an
orginal problem what is the first step in its solution. For, should we do
that, we have transformed this tacit knowledge into formal knowledge.
Furthermore, this transformation is indeed possible. He argues this from
p29 to p52 under the heading "Emergence"
But as a result of this emergence, our remaining tacit knowledge will see
another original problem which the rest of humanity cannot even have an
inkling. Should we not understand this, we will forever be buying into
novel procedures for solving original problems, procedures which became
obsolete the moment they have been formulated.
Add to this the tragedy which I have discovered that a novel procedure may
soon become corrupted into a rote procedure. This brings me to my main
point which I want to make -- what is THE problem. Please let us create a
thorough LO-dialogue on it. We are a society of explorers, are we not?
With care and best wishes
--At de Lange <amdelange@gold.up.ac.za> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa
[Host' Note: In assoc w/Amazon.com...
Tacit Dimension by Michael Polanyi http://www.amazon.com/exec/obidos/ASIN/0844659991/learningorg
I have found Polanyi's books extremely stimulating! ..Rick]
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