Next in a sequence

Here is a maths puzzle. What is the next in the sequence?
3,5,7...
well it could be 9 (series of odd numbers), or it could be 11 (series of prime numbers)... or it could be anything. The series might be 3,5,7,301,303,305,307,601. You cannot tell the next number in a series from the preceeding numbers. If it were possible, and I knew how it were done, then I'd have made my fortune on the stock market already and retired. But spotting patterns and rules is an important skill, for many processes in life follow relatively simple rules. So we ask pupils to predict the next number in the series. Therein lies the mistake. We should be asking the pupils to determine the next possible numbers in the series, and to explain the rules that would cause those numbers to appear in the sequence. That transforms the process from a right/wrong answer to one of exploration and inventiveness. Therein lies one of the great problems with maths as it is taught in our schools. It is taught as a subject of boundaries and rules which are there to constrain the pupil rather than an opportunity for exploration and for the pupil to show how clever they are. Boys are particularly disposed to getting one over on those around them. They want to show how clever they are by tricking or outsmarting others, but they are often the most alienated from maths. At Puppet Maths we give our pupils the opportunity to show off how clever they are, we provide them with open ended questioning that allows them to think beyond the parameters of a narrow maths question and get one over on the teacher.