Types of problem solving
Here you can find out about the three types of activities, given on page 48 of the 5-14 Guidelines, which represent problem solving in its widest sense. These are; adopting an investigative approach to learning concepts, facts and techniques; working on tasks designed specifically to highlight the merits of certain approaches to mathematical thinking; using their mathematics in an enquiry that could be part of a cross-curricular study.
There is also a section on thinking skills. A number of schools are running planned and structured programmes to develop thinking skills, which are seen as complementary to mathematical problem solving activities.
At secondary level, teachers from two schools describe the work they are doing with the Cognitive Acceleration in Mathematics Education (CAME) materials.
Investigative approaches
Here you will see examples of pupils working at different stages, from P1 to S1, using an investigative approach.
Strategy or process problems
Referred to obliquely in the 5-14 Guidelines as ‘tasks designed specifically to highlight the merits of certain approaches to mathematical thinking’, these are what many think of as ‘problems’. They are non-routine, self-standing questions for which there is one correct solution, which can often be arrived at using a variety of strategies or processes. You can see examples of pupils working on this type of problem and teachers talking about them.
Open-ended or cross-curricular investigations
This section gives examples of enquiries that are open-ended in the sense that there is not always a clearly defined solution. These can arise naturally from work going on in the class, perhaps related to projects or outings, and may not necessarily be mathematical in origin.
Thinking skills
Teachers discuss and speak highly of the benefits of thinking skills programmes. Although this aspect of problem solving is not mentioned in the 5-14 Guidelines, many schools are following a thinking skills programme designed to develop pupils’ abilities to think in a critical, analytical and investigative manner.