Maths using images of real things

Young children do not think in an abstract manner. They like to think of things. This is called concrete thinking. When given a maths problem, for example 2 + 3, they don’t think of an abstract 2 and an abstract 3, they want to think of 2 things and add to them 3 things. This is why they count on their fingers. In primary schools the teachers tell the pupils not to count on their fingers. This is an attempt to force them to abandon concrete thinking and to embrace abstract thought. I believe that this is wrong. Children will start to think in an abstract manner as and when they are ready to do so. If they need their fingers to count on I think that they should use them. Certainly, teachers should hold up abstract thought as a target for the child to aim for, but don’t ban them from using concrete examples. Don’t ban children from counting on their fingers. After all teachers don’t ban children from moving their lips when they read, they let them do so, confident that as the child becomes more proficient at reading, they will cease; similarly, teachers should allow children to count on their fingers until such time that they are ready to count without the bother of using them. At Puppet Maths we encourage children to visualise numbers as sets of dots. They can then count the dots in their mind’s eye, then subsequently, by recognising the patterns formed by the dots, learn to do arithmetic without having to count out each time.