EIGHT WAYS OF THINKING ABOUT PROBLEM SOLVING

 

Alex H Johnstone

University of Glasgow, Glasgow G12 8QQ, UK

alexj@chem.gla.ac.uk

 

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 non-scientist.

 

Type 5 lends itself well to chemical situations.  For example: "Tell me all you can about the complex Ni(NH3)4Cl2."

 

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, NaHCO3, 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.