1.3 Solutions not problems 13
Some people do not like the word ‘problem’;
they say, ‘We don’t have problems, we only
have solutions.’ The word ‘problem’ is used in
different ways. It can mean something that is
causing us a difficulty. The word ‘problematical’
implies a situation where we cannot see an easy
solution to something. However, not all
problems are like this. In some cases we may
enjoy problems and solve them for fun: for
example, when reading a puzzle book or doing a
crossword. Most people have some sorts of
problem in their lives and many of these may
be solved with a little careful thought. The
problem solving we are talking about here is
based on logic; it is often related to
mathematics, in the sense of shape or number,
but does not require a high level of formal
mathematics to solve. It is largely based upon
the real world and is not abstract like much of
mathematics. Many people, from carpenters to
architects, from darts players to lawyers, use this
type of problem solving in their everyday lives.
On the face of it, critical thinking and
problem solving might appear as quite
separate disciplines. Most critical thinking
questions are primarily textual whilst many
problem-solving questions contain numerical
information. However, the skills used,
especially in the application of logic, are
quite similar and certainly complementary.
Scientists, politicians and lawyers will
frequently use both verbal and numerical
data in proposing and advancing an
argument and in drawing conclusions.
One of the reasons why the two disciplines
may be thought of as separate is in the nature
of thinking skills examination papers, which
often present the tests with clear divisions
between critical thinking (CT) and problem
1.3 Solutions not problems
solving (PS). Some of this is due to the nature
of short multiple-choice questions which
mainly deal with testing sub-skills rather than
looking at the full real-world application of
thinking skills. However, there are areas where
a more rounded evaluation is carried out,
such as the Cambridge A2 papers, BMAT data
analysis and inference, and in Unit 2 of the
AQA syllabus. Some of the questions in both
disciplines will be seen to be ‘hybrid’ where,
for example, you may be asked to draw a
conclusion or asked about further evidence
when presented with a set of numerical data.
Although many of the skills used in problem
solving in the real world are mathematical in
nature, much of this mathematics is at a
relatively elementary level, and needs little
more than the basic arithmetical operations
taught at elementary school. In fact, many
problem-solving tasks do not need arithmetic
at all. The origins of problem solving as part of
a thinking skills examination lie in the
processes used by scientists to investigate and
analyse. These were originally defined by
Robert J. Sternberg (Beyond IQ: A Triarchic Theory
of Human Intelligence, Cambridge University
Press, 1985) and can be summarised as:
• relevant selection: the ability to identify
what is important in a mass of data, and
thus to recognise what is important in
solving the problem in hand
• finding procedures: the ability to put
together pieces of information in an
appropriate way and thus to discover the
route to a solution of a problem
• identifying similarity: the ability to
recognise when new information is similar
to old information and thus to be able to
understand it better and more quickly.