As a team we kicked off the week by exploring problem solving strategies to solve maths puzzles. The room was filled with cubes, bead strings, number cards, scissors, coloured pens, paper and whiteboards and there was a sense of excitement as everyone discussed how to tackle the problem.
“How should we start?”, “What does that mean?”, “Can we try it this way?”, “What would happen if…?”
Each of us used different strategies and ways of recording when solving the same problems and, although some of our answers were different, through our explanations we could see that they were still all correct. This got us thinking about what problem solving really is and the skills and strategies learners need to explore and develop.
We identified the following problem solving strategies used by us as learners which should be modelled and encouraged by us as teachers.
- Trial and improvement – Make a guess using the information given in a problem and check this against the criteria in the problem. This process may be repeated again and again until a correct solution is found.
- Use organised list or diagram – Using a systematic approach to listing the different possibilities. This can be an efficient method for keeping a record of the possibilities tried and can help pupils to see connections.
- Work backwards – Sometimes a problem is posed where learners are required to start at the end point and work backwards to find the solution. They need to be able to unpick each step systematically.
- Use logical reasoning – Often there can be more than one right answer to a problem. When solving a problem, learners may hypothesise a rule after working through examples. Learners use logical reasoning to draw a conclusion based on that rule. Through this process, learners need to explore and whilst applying what they already know to solve an unfamiliar problem.
Many pupils will apply more than one problem solving strategy which may include some of the strategies mentioned above. Just as we did, pupils may even change which strategy they are using part way through a problem. By giving opportunities for collaboration, contemplation, forming hypothesis and analysing problems, you develop pupils’ thinking, conceptual understanding and mathematical language.
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