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8
STUDIO
1.5
•
Problem solving
Problem solving is about the use of logic to address real-life situations and aid decision
making: it tests ability to understand, compare, use and analyse mathematical infor-
mation. This covers not only numerical data in the form of quantities and tables, but
also graphs, diagrams and spatial reasoning. Beyond the basic level of mathematics,
this requires a working knowledge of such things as simple algebraic equations and
probability.
The fundamental skills of problem solving are:
• selecting relevant information
: when presented with a mass of information, you should
be able to recognise which data or findings should be regarded as important and
useful and which should be put aside;
• recognising analogous cases
: by recognising when new information is similar to old in-
formation, and in which areas it differs, it is possible to use the new information in
more effective ways (discover cause and effect relationship in data, identify possible
reasons for patterns and variations and so on);
• finding and applying appropriate procedures
: in order to solve problems, different and
sometimes apparently unrelated pieces of data must be combined in appropriate
ways. The method of combining the data may require an informed search either
of the data or of the possible methods of using it. You have to ask yourself: what
information is needed to produce the answer? How can I calculate this from the
data I have?
Solving the problem generally requires a search: sometimes the required data are
easily findable from a large mass of information; in other cases, you may need to con-
sider many possible options so that it is difficult to be sure not to miss anything.
Alternatively, the search may be necessary to find the method of solution: in this case
it is not so easy to be systematic, but you must ensure that your method is leading to
the values you need.
1.5.1
•
Data analysis and inference
The skills described above have to be applied to handle and interpret larger amounts
of information: it is fundamental to select those pieces of data that are relevant to the
problem and analyse the writing, author’s interpretation, methods of data collection
and conclusions in a critical manner.
Data interpretation
requires you to draw additional meaning from the information
given, for example by obtaining values derived from the data or by considering possi-
ble causes for variation shown in data;
data analysis
consists in manipulating informa-
tion in order to highlight structure;
inference
and
deduction
are the final step to draw
conclusions from the information.