Teaching problem solving

Teaching problem solving

In this section you can see video clips of lessons and interviews with headteachers, teachers and pupils about various aspects of teaching problem solving. Some relate to an understanding of different types of problem solving activities and others look at planning, organisational approaches, resources, recording, reporting and assessment. In addition, pupils of different ages share their views and experiences of problem solving. The ‘Points to consider’ can be used for staff development purposes, to generate discussion amongst groups of teachers or pupils or to inspire thinking at an individual level.

Types of problem solving

The three aspects of the problem solving outcome as articulated in the 5-14 Guidelines in Mathematics are discussed and illustrated. They are:

investigative approaches
strategy type problems
open-ended or cross-curricular investigations.

Programmes to develop pupils’ thinking skills are also described.

Planning

You can find out about whole-school and individual teachers’ planning for problem solving. Many schools have designed their own progressive cumulative programmes of strategy development. Others teach all strategies at all stages, whilst some local authorities have produced one template for all their schools to follow. Using these, teachers draw up their own year or term plans for covering strategies and within these they include open-ended investigations.

Approaches

You can find out about a range of organisational structures used by teachers. Whole-class, group, paired or individual models of working are described and justified in a variety of contexts. You can also see examples of collaborative group work and the accompanying group-building exercises.

Strategies

This section looks at how problem solving strategies are taught. Some teachers argue that strategies should be taught explicitly while others believe that strategies should be learned by an implicit experiential process. Many teachers use a mixture of both approaches. You can see examples of strategies being used at different levels; these include some strategies that are not referred to in the 5-14 Guidelines.

Pupils' comments

Here pupils talk about problem solving, how it differs from other maths and what happens when they get 'stuck’. They also give their views on working in groups and identify some beneficial outcomes that result from solving problems.

Assessment

Here you can find out about different schools’ approaches and the uses to which their assessment results are put. Most assessment is seen as informal, observational and for formative purposes. Many teachers take note of problem solving behaviour and attitudes as well as problem solving skills.

Recording

In this section, teachers discuss their recording procedures. Some record their pupils’ work in pupil files or in teachers’ records. Others use more innovative methods of recording, such as photographic records. Many teachers increasingly encourage pupils to keep their own records of work where appropriate - in jotters, folders or on solution boards. These records can be used for self-assessment and self-evaluation purposes.

Reporting

In this section you can find out how teachers are encouraging their pupils to report on their problem solving processes. Reporting can be oral (delivered verbally to colleagues, groups or to the whole class) and/or written. Teachers describe sharing responsibility for reporting amongst group members and discuss the personal benefits for pupils of reporting publicly.

Resources

In this section, examples are given of some of the most commonly used and popular resources and of ways in which resources are organised. Teachers describe how packs, files or folders of problems can be arranged by level and strategy - either within the class or on a whole-school basis.