If the maths curriculum was a big stick of rock you'd find the words "problem solving" running through the cylindrical cross-section. Despite occupying such a central position, problem solving can often be ignored because it is surrounded by a thick syrup of objectives. Problem solving is reduced to a treat for a Friday afternoon, which is not long enough.
Everything in maths should be coated in problem solving and continually maintained throughout the year. So where do you start? Undercoating children's thinking with open-ended problems helps prepare the way and also assists us in gauging the level at which our pupils are achieving.
In looking at open-ended problems, children become skilled at answering in more than one way. For example, if a rectangle has an area of 24 centimetres squared, what might the length of its sides be? This could produce a range of answers from 1cm x 24cm to 3.2cm x 7.5cm. Asking children to write 20 numbers between 6.8 and 6.9 could similarly bring a variety of responses.
Open-ended problems are an ideal foundation for children to then create their own. Problem solving is rich in reasoning and we should be doing it every day
John Dabell is a numeracy consultant and teacher trainer