EIGHT
WAYS OF THINKING ABOUT PROBLEM SOLVING
Alex
H Johnstone
Problem solving is what you do
when you do not know what to do. Much of
what is called Problem Solving is algorithmic and not problem solving at
all. Any problem consists of three
parts:
a) What you start with (The Data).
b) What you want to achieve (The Goal).
c) The Method by
which you link a) and b).
For a real problem to exist, at least one
of a), b) or c) must be unfamiliar or incomplete. If all he starting material is complete, if
the goal is clear and the method is familiar we have an algorithmic exercise,
merely substituting numbers in a well known equation. It may be a useful drill for certain routine
purposes, but it is NOT Problem Solving.
Let us set out the possible
forms of problem and the illustrate them with
examples.
Type

Data 
Method 
Goal/Outcome 
1 
Given 
Familiar 
Given 
2 
Given 
Unfamiliar 
Given 
3 
Incomplete 
Familiar 
Given 
4 
Incomplete 
Unfamiliar 
Given 
5 
Given 
Familiar 
Open 
6 
Given 
Unfamiliar 
Open 
7 
Incomplete 
Familiar 
Open 
8 
Incomplete 
Unfamiliar 
Open 
As we have already said, Type
1 is not really a problem, although it is the commonest form we find in
examination papers.
Type 2 is a genuine form of
problem, but once the student has done two or three examples of it, it becomes
Type 1, because the method becomes familiar.
Type 3 brings us into real
problems. For example: "How many
copper atoms are there in this ‘copper’ coin?" The goal is quite clear, but a lot of data is
missing. The problem lies in the
student’s ability to find or ask for the data.
"What is the percentage composition of he coin?"
"What is its mass?"
"What is the Atomic Weight of copper?"
"What is Avogadro’s Number?"
This is the thinking
part. Once the student has gathered
these data, the rest of the problem is automatic application of simple
arithmetic. Learning how to recognise
what data are needed is an important skill for a scientist to acquire.
Type 4 would be the above
question given to a nonscientist.
Type 5 lends itself well to
chemical situations. For example:
"Tell me all you can about the complex Ni(NH_{3})_{4}Cl_{2}_{.}"
The student would have to
reach into various parts of his knowledge network to answer this completely.
Percentage composition
Molecular weight
Name of elements, ligands and
complex
Structure and isomerism
Colour
Possible reactions
Etc
Type 6 could be the same
problem given to a schoolboy who might not have met complexes, but could do
elementary things with the formula
Type 7 An
example might be "How much work can be obtained from 10g of sodium
bicarbonate, NaHCO_{3}, given excess HCl?" The reaction is familiar, but the goal is
unclear and much more data will be needed.
Some might do it from thermodynamic tables via Free Energy, some might
devise some simple machine such as syringe with a mass on its piston and
measure the distance moved by the mass.
There are many possibilities and no one answer!
Type 8 seems to be impossible,
but it is in fact the most common type of problem in real life. "Where shall I go on vacation this
year?" is a problem with a lack of data.
The procedures may be unfamiliar and the goal is not clear to begin
with. However we solve the problem and
go on vacation. Chemists in industrial
situations are confronted with such problems daily.