For young children problem solving is very much based on practical situations around them where children make choices, and have the opportunity to reason and arrive at decisions. In these situations, children will bring to the problem the knowledge and skills they have, but in the attempt at solving it they may achieve greater understanding. When working with young children our role is to provide them with challenges that arouse their curiosity, and stimulate them to resolve a problem.
Problem solving involves a range of thinking skills: predicting, talking the problem through, making connections, reasoning, spotting patterns, generalising, and seeking solutions. This is also what mathematicians do, and most of the mathematical activity that young children engage in should be embedded in problems. Young children will spend a little time in rehearsing facts they know about numbers and shapes, but mostly they will be tackling problems. Our role is to supply children with problems, and contexts for problems, in each of the areas of mathematics that they are learning: counting, measuring, comparing, ordering, adding, subtracting or partitioning objects.
We can involve children in everyday organisational problems such as making sure that everyone has a turn, checking that none of the scissors is missing, deciding whether the book box will fit in the space behind the door. We can also provide children with activities that are intrinsically problem to solve, such as puzzles and computer games. Most importantly, though, we can make sure that the mathematical activities we organise for children daily are open-ended and challenging:
The slot machine only takes 1p and 2p coins. How can we buy something for 5p?
I don’t think this pack of 1-20 cards is complete. Can you find out the numbers that are missing?
Can you pack these two bags with these groceries so the two bags weigh the same?
We need to encourage children to predict, with questions such as ‘I wonder what happens if we try another number’. We can encourage reflection by presenting misunderstandings and errors in playful contexts, such as helping teddy who has got into a muddle. We can model thinking by thinking aloud: ‘I wonder whether I need one more or two more to make it the same’. We can also discuss problems and use mathematical language: ‘Look, Amy’s managed to fill in this space with two triangles, and together they form a square’.
To ensure real mathematical problem solving takes place, we need to create an atmosphere [conjecturing atmosphere] where experimenting, trying things out and seeing what happens is celebrated. Children can be encouraged to try different approaches to solving a particular problem rather than steering them to one solution. Discussion can be promoted so that children can decide what way worked best. We can support children to work in pairs or in a team, and plan ways in which they can all contribute to their team’s success [Talk in pairs].
Young children benefit from us identifying their particular skill or part in the solution ‘I saw Ruby measuring the space really carefully’, ‘I’m glad Billy counted all of the conkers – that must have been useful in getting a solution’. Encourage the group to reflect on what they did that worked well and to say something supportive about their fellow problem solvers. As practitioners it is helpful if we identify for the children when we notice them being systematic ‘That was a really good idea to try each one of the shapes in turn, that way you know you’ve tried them all’.
Progression in problem-solving for young learners
Begins to use mathematical skills and knowledge: Knows how to find out which pot of scissors has more in, and can stack wooden blocks in rows.
Becomes more thorough and systematic: Checks that there is the right number of scissors in each pot, and notices that the numbers on the washing line are in the wrong order.
Begins to use more complex mathematical skills and knowledge: Uses a tally mark to show that everyone has had a turn, and suggests a method for sharing the fruit pieces between members of the group.
Is confident to try new activities, initiate ideas and speak in a familiar group: Compares their tower with their friend’s and says ‘I need four more blocks to make mine the same’.
Solves harder problems and relates them to others they’ve solved: Works out that to have ten pairs of scissors in the pot they need to find another three pairs, and uses a computer programme to make a repeating pattern.
Begins to relate a problem to others they’ve solved: Suggests a method for sharing the fruit between members of the group.
Uses a range of strategies: Plays a game, and works out how many more counters they need to make 10.
Sustains involvement and perseveres: Makes as many different sticks of four cubes as possible, using just two colours.