3.1 What do we mean by a ‘problem’? 79
What do we mean by
a ‘problem’?
3.1
Unit 3 Problem solving: basic skills
Consider the action of making a cup of instant
coffee. If you analyse the processes you need to
go through, they are quite complicated. Just
the list of items you need is quite long: a cup, a
teaspoon, a jar of coffee, a kettle, water, and
milk and sugar if you take them. Having found
all these items, you fill the kettle and boil it;
use the teaspoon to put coffee into the cup;
pour the boiling water into the cup, just to the
right level; stir; add milk and sugar; then put
all the things you used away again. In fact one
could break this down even more: we didn’t
really go into very great detail on, for example,
how you boil the kettle.
Although this is complicated, it is an
everyday task that you do without thinking.
However, if you encounter something new,
which may be no more complicated, the
processes required to achieve the task may
need considerable thought and planning.
Most of such planning is a matter of
proceeding in a logical manner, but it can also
require mathematical tasks, often very simple,
such as choosing which stamps to put on a
letter. This thought and planning is what
constitutes problem solving.
Solving most problems requires some sort
of strategy – a method of proceeding from the
beginning which may be systematic or may
involve trial and error. This development of
strategies is the heart of problem solving.
Imagine, for example, trying to fit a number
of rectangular packages into a large box. There
are two ways of starting. You can measure the
large box and the small packages, and
calculate the best way of fitting them in. You
may make some initial assumptions about the
best orientation for the packages, which may
turn out later to be wrong. Alternatively, you
may do it by trial and error. If you have some
left over at the end that are the wrong shape to
fit into the spaces left, you may have to start
again with a different arrangement. Either
way, you will have to be systematic and need
some sort of strategy.
With some problems the method of finding
an answer might be quite clear. With others
there may be no systematic method and you
might have to use trial and error from the start.
Some will require a combination of both
methods or can be solved in more than one way.
The words ‘problem solving’ are also used in
a mathematical sense, where the solution
sought is the proof of a proposition. ‘Problem-
solving’ as tested in thinking skills
examinations does not ask for formal proofs,
but rather asks for a solution, which may be a
calculated value or a way of doing something.
Although many of the problems we shall look
at here use numbers and require numerical
solutions, the mathematics is usually very
simple – much of it is normally learned in
elementary education. Many problems do not
use numbers at all.
As we saw in Chapter 1.3, there are three
clearly defined processes that we may use
when solving problems:• identifying which pieces of data are
relevant when faced with a mass of data,
most of which is irrelevant
• combining pieces of information that
may not appear to be related to give new
information