1. Introduction to Problem Solving

Skills at problem solving are very useful in life and in the workplace. The good news is that you can learn these skills. Problem solving should be at the heart of maths education. We present this resource to help you develop problem solving skills with your group. Try developing problem solving skills the Calmast way.

At the core of our system is practice and reflection

Why Problem Solving?

Problem solving has been cited by the National Research Council and PISA as an important skill for the workplace.

Students need to prepare for careers that require the ability to work effectively in groups and to apply their problem-solving skills in these social situations (Brannick and Prince, 1997; Griffin et al., 2011; National Research Council, 2011; Rosen and Rimor, 2012).

PISA explains that “today’s workplaces demand people who can solve problems in concert with others” and “employers are willing to pay higher wages for people with well-honed problem-solving and social skills”.  (Collaborative Problem Solving, PISA Results, Volume V, 2015, p.32).

Can we develop Problem Solving Skills?

Problem solving skills make us feel more comfortable when facing a new challenge. Developing our problem-solving skills means improving our strategic thinking, it helps us to find appropriate strategies and enables us to think of different ways to approach a problem. Such skills can be learned and improved through constantly challenging ourselves. The immediate feeling of success when having solved a problem is extremely rewarding. We become more confident and are encouraged to practise and tackle increasingly complex challenges.

However, if students are rewarded for quickly attaining the correct answer, and their effort and resilience is not acknowledged then this develops a fixed mindset and can hamper students’ progress later in life. A fixed mindset describes someone who believes that their level of intelligence cannot be changed. They are born with a certain limit on what they can achieve and nothing they do will change this. Somebody with a growth mindset believes that their intelligence can grow depending on the amount of effort they put in.

It is important to encourage a positive attitude towards maths/problem solving in the students, to nurture a ‘can do’ approach in an informal setting and to inspire them to develop strategies to solve maths problems and puzzles.

Working on a solution to a problem in a team is usually more effective: you support each other, you share ideas, you build on each other’s ideas and you are more likely to find a fast and simple / appropriate strategy to solve the problem you’re facing. This makes the project more fun and finding a solution together is a very motivating (but also challenging) experience that adds to everyone’s personal development.

Each problem may be solved by a unique strategy – but often several approaches can help to find a solution and many strategies can be applied to more than just one single problem. By practising and becoming more skilled in discovering these, we strengthen our strategic thinking. We also develop what is called lateral thinking: it becomes easier for us to see the problem in a different light, thus being able to solve it in a more creative way and using strategies that we may not have associated with a particular problem in the first place. We learn how to transfer problem solving strategies and by doing so become confident in new situations.

Next: Developing Problem Solving Skills
Encouraging Reflective Thinking
Problem Solving Skills Session