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The process of problem solving                          7/1

The big Picture

The
goal
Our goal is to be able to solve problems reliably in all areas in which mathematics can be used effectively.
Problem
solving
is a
natural
process
An important step in achieving this goal is to recognize that all living things exhibit innate problem solving abilities and all solve problems in basically the same way albeit, using different tools appropriate to the situation. Problem solving is a natural process.

A plant in need of energy turns its leaves toward the sun. A paramecium will travel in the direction toward nutrients or preferred temperature. Ants will leave pheneromes that mark the path from food to nest. Many examples of responding to a need to produce a result can be identified.

A problem may be characterized by the need to accomplish a goal. Accomplishing the goal is effected by using tools appropriate to the situation. The existence of appropriate tools in the situations cited is the result of eons of evolution.

But we
are
different
Human beings share the innate problem solving abilities of other living things. We respond to a need to produce a result.

However, the tools available to us for responding far exceed those available to other living things. This is a consequence of our ability to create tools and improve the tools we have already created.

Distributed
cognition
The importance of tool making is dwarfed by our ability to pass on the tools we have created and how to use them to successive generations. Our libraries, for example are an important repository for knowledge..

Our extensive educational systems are remarkably successful in making the tools and their use available. The results of the store of accumulated knowledge, the methods of dissemination, and use of this knowledge attest to the power of the process intellegent life has created.

It is this jointly held knowledge, distributed cognition, that defines intelligent life.

Physical tools
and
intellectual tools
The idea of tools goes far beyond physical tools. It includes the many intellectual tools that have evolved over several millenia. Examples are language, mathematics, social sciences and physics. To become educated means leaning how to make use of this huge font of knowledge. It is not physically possible, or even desirable, to understand all of this knowledge in depth. The goal of becoming educated is to be able to learn enough about topics as needed and to use them effectively for the task at hand. It is a matter of learning to learn.
It's
AMAZING
!!!!!
Access to the huge font of knowledge that exists and continues to expand is increasingly available to everyone. Our schools, librarys, communication systems, including the internet, gives rise to an intellecutualy connected society that can reasonabley desribed as a global brain. See The Social Superorganism and its Global Brain by Francis Heylighen. (1996, 1997)
WHAT
to do
vs
HOW
to do it
The problem solving process, Request-Response-Result is straightforward, easily understood and efficient use of these resources in problem solving. It I easy to know what to do. Indeed the process TELLS you what to do. Being able to find a resource and to do what you are instructed to do is a different matter. This involves learning to use the tools and resources appropriate to the situation at hand. This requires experience and training. This is just as true in mathematical problem solving as it is in performing ballet, ice skating, understanding history, writing an essay or playing football. Do not confuse problem solving with learning to use tools and resources.

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