Johnstone (1998) proposes a useful classification of problem types. If the
data are given, the methods to apply familiar and the goals clear, students can
apply their knowledge without much analysis and thought. These are
characteristics of ‘structured problems’,
If the data are given but the method is not strictly familiar or if students
have to choose from different data, a non-routine problem arises. Students have
to look for parallels between their acquired knowledgeand the problem. The
goal state (the correct answer) is clear, but there is more than one way to arrive
at the answer. The aim of this kind of problem is to learn how to analyse a
problem situation and decide what information is needed to solve it. The
problems are semi-structured and the student has to analyse and select from the
given information or to adapt known methods in order to go from the problem
state to the goal state.
Johnstone (1998) also describes the characteristics of open problems
where the goal is open-ended and the data are superfluous or the methods
unfamiliar. These are unstructured problems. The aim of such problems is to
prepare students for real-life situations in which the problem itself has to be
further developed to turn it into a solvable problem and where there are many
ways to solve a problem and several solutions.