Some eleven plus mathematics questions are indisputably of a practical or concrete nature. 101 – 35 can be performed by the great majority of eleven plus pupils in the months leading up to the examination. Some children will even be able to perform the operation in their heads. 101 – 35 can be called a mechanical procedure.
Some questions, however, seem to be of a more abstract phenomena.
It can be argued that there is a preliminary or groping stage – where the child can arrive at the answer through playful and exploring means. Children gain insight into the answer by assembling various stages and consolidating the thoughts.
The next stage is probably a little more structured. Where rules are developed and awareness and more direction seem to be taking place. These various activities appear to build to an eventual moment of insight.
Then comes a stage that eleven plus parents will recognise with some considerable relief. This is where the eleven plus child wants to use the insight and work through more examples. Your child will want to actually practice. Oh my word! This is an exciting step!
Your child is trying to anchor the concepts so that they can be retrieved and used at some later date. But how do you know when this stage has been reached? It may well be when your child does not ask you: “Do I add or multiply?”
Numbers are really quite abstract. Take a simple exercise. You are going on holiday with your family. Your ten year old has responsibility for packing his bag to take on the aeroplane. He is an avid reader – he is going to be given a Kindle on his next birthday – but for the moment he has to take the books he wants to read with him in his bag. The family are flying on a budget airline – and only 15 kilograms can be taken on the plane. Your son’s bag weighs 2.5 kilograms. The clothes – even the ones he selects – only come to 8 kilograms. He wants to take several books, however, and needs to be able to work out how many books he can take. He will need to leave some books behind. You sneak a quick look into his semi packed bag and see that he has left some staple clothes out of the bag.
Do you remind your son that he will need extra pairs of shorts and shirts or do you leave him to take responsibility for his actions?
Do you slip the additional clothes into his bag – and hide three books to keep the weight down?
Do you ask him to weigh the shirts and shorts that he `forgot’ to pack, weigh the books and come up with a compromise and a solution?
As he is an `eleven plus candidate’ do you simply suggest that he `sorts himself out’?
At what stage does the problem turn from simple meanderings around the potential problem to your child formulating rules and then coming up with a solution?