How open ended can maths be?

What is the most effective way of helping children to understand and solve open-ended maths problems?

At the heart of most problem solving there is the technique of breaking down what may seem an almost intractable situation into its elements, while looking for rules and patterns, which in turn lead to a solution.

And where children are able to undertake such work on a regular basis, they not only come to understand more about how numbers interact with each other, but also begin to see the role maths can play in problem-solving.  

In short, they start to learn problem-solving strategies which will help them not just in their maths, but in all aspects of life.

This approach to maths is particularly helpful when there are different ways in which questions can be answered, and indeed different answers to each question.  For this approach enables children to see each other’s solutions, and reflect on the fact that in the outside world there is often more than one way of solving a problem.

Additionally, children will learn that not all problems involving numbers are most readily solved by writing out the maths.  Sometimes the drawing of pictures or a plan can help us see where the problem lies and what the best solution is.

This approach can involve a physical problem, as with a matchstick puzzle of the “remove four matches to leave five squares” type.  Or it might involve a puzzle such as the making of a maze in which there is only one route to the centre.

Through such work children quickly begin to realise that problem solving is what life is all about, for the techniques found here can be used in number, money, measurement, space, matters of chance, patterns and the use of algebra.

You can see examples of how “Open-ended Maths Investigations” can encourage pupils to apply mathematical strategies creatively and effectively through these links.

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