Thinking Skills: Critical Thinking and Problem Solving

3.5 Finding methods of solution 93

3.5 Finding methods of solution

The previous chapter dealt with problems for
which the method of solution was relatively
easy to find. In this chapter we are looking at
problems where the primary skill in solving
them is to develop a method of solution. The
way of proceeding to an answer in some
problems may not be clear:

a either because it is necessary to find an

intermediate solution first,

b or because we need to work

simultaneously forward from the data

(to identify what can be calculated) and

backwards from the required answer (to

identify what needs to be calculated).

Having a strategy for approaching such
problems is important. In particular, it can be
very useful if you have seen a problem of a
similar sort before, which you know how to
approach – this is where experience in tackling
problem-solving questions can be invaluable.
Sometimes it may be necessary to try different
ways of approaching the problem; it is
important to realise quickly if your line of
attack is being unsuccessful.
One strategy that can help to solve
problems when you are not clear how to
proceed is to analyse the problem:

• organise the information you are given
• write down or underline those pieces of
information which you feel are important
• simplify (reject unimportant information)

•   look at the question and decide what

pieces of information could lead to the

answer

•   make a sketch, list or table.

Sometimes, intermediate answers are

necessary in order to proceed to the complete

solution. This may be regarded as similar to

the identifying of intermediate conclusions

in Chapter 2.6. The solution of a problem can

be like an argument that first leads to one

conclusion, which then, possibly using

further information, proceeds to the final

conclusion.

This may be illustrated as in the diagram

below. Here, the calculation steps are

represented by the arrows. Not all these

processes are used in all problem solutions.

A problem that may be solved using an

intermediate result is given in the example

on the following page. This is similar to the

question in the previous chapter in that it

involves distances, speeds and times but,

because of the nature of the question, the

method of proceeding is less obvious.

Answer required Information required

Data

Intermediate

result Solution