Money for counting

What do young children understand? They understand what money is for. Money can buy them sweets and toys, it’s also used for other things as well, but they are not as important. Most young children can count out money to pay for their purchases. Some, however, do not work out the change they are due, they will pay with a £1 coin, or with a 50p piece, and accept that the change they are given is right. When I was young the shop assistants used to count out the change by counting up. If the purchase cost 33p and you paid with a £1 coin, then the shop assistant would count money into my hand starting at the value of the purchase (33p) and then add pennies “34p, 35p” then add a 5p piece “40p” then a 10p piece “50p” and finally a 50p piece “£1”. This way I knew that the change I was getting was right and incidentally I learnt how to work out the amount of change I was due from observation. But today, the electronic tills tell the shop assistant what change is due, they no longer have to count it up. A learning opportunity is lost, gone forever. At Puppet Maths we want to teach children these old techniques of handling numbers, because they’re useful and proven, tested throughout time. We provide relevance to our maths by associating it with money. Young children are concrete thinkers and they find it easier to imagine coins rather than handle abstract numbers, so we use money as a vehicle to allow children to achieve success in their arithmetic.

Over testing in schools

There is a great concern regarding the hyper-accountability of the school system. Pupils are tested almost to destruction, and schools are held accountable for their results. The upshot of this is that teachers teach to the exam, rather than provide the pupils with an education. This failing permeates all school subjects and is just one reason why so many parents have chosen to teach their children at home. Home education / home schooling allow parents to educate their children rather than cram them for an exam. Cramming in schools has reduced mathematics from an imaginative subject, which teaches pupils how to solve problems, to one in which pupils just follow routines for no particular purpose. Success at maths has become the result on a good memory. Pupils who can remember the routines and how to use them are good at maths, those that cannot, aren’t. Many teachers recognise this problem, but they are part of a system which they are powerless to change, and upon which their livelihood depends, so they are reluctant to rock the boat, they simply go along in the direction which their line manager directs them, and they do their best. Puppet Maths sprang out of my disillusion with maths teaching in schools. I wanted to reintroduce imagination into the subject, and make it fun for the pupil. I want to make maths education something that children will enjoy and a subject that they will succeed at.

Home education, a sense of community.

We teach children in the classroom rather than give them books to read and leave them to get on with it. Why? Children are usually not motivated to spend a long time studying, especially when the learning gets challenging, when it is so much more congenial to give up and do something else, so social pressure to keep on task is one reason. Another reason is the provision of feedback. Pupil’s learning needs to be assessed and their strengths and weaknesses identified, so that they don’t remain in their comfort zone repeatedly doing things that they know they can do well and ignoring those things at which they need more practice. But also there is the element of human interaction. The human animal is designed to learn from other humans by social interaction. This is where the internet tends to fall down. There is plenty of information on the internet, some of it text, some audio, some video, but outside of chat rooms and social media sites, where individuals online communicate in real time, there is little social interaction. Puppet Maths intends to address this aspect of learning when it teaches maths. Children often have imaginary friends, or they often relate to a comic character or a fictional character from film or TV. Reality is not a barrier to them in this respect… but it is a character that they relate to. When we at Puppet Maths teach maths we put a lot of effort into characterisation. Each puppet has its own character, so that the child can imagine that they are a participant in the classroom along with the puppets, they can learn from the puppets and even feel superior that they could solve a problem that a puppet struggled with, giving them a sense of achievement. This is especially valuable to children that are being home educated / home schooled, who, however content they may be learning in the family environment, can still feel isolated.

Home Education

Parents turn to home education / home schooling and teach their children at home for a variety of reasons. These range from religious beliefs, to problems with their child’s health or problems of bullying within the school, to a lack of confidence in the ability of the school system to teach effectively. Parents who teach their children at home cannot be expert in all the subjects that are covered by the curriculum. The internet provides a lifeline allowing them to access the information and teaching materials that they need. Puppet Maths is a resource that home education / home schooling parents can access to help them teach maths to their children. As a maths teacher of many years standing, I have learnt a lot about teaching maths on the job. Time and again I have revised my method in the light of experience. Pupils experience problems and misunderstandings that, until I witnessed them, I could not have guessed at. It has been my job to help them overcome these problems, and in my teaching, I try to address these problems in passing to ensure that my pupils do not develop a mental block regarding some subject or other. Home education / home schooling parents do not generally have this experience, and they don’t have the time to learn from their mistakes in finding the best ways of explaining a topic… they want their children to succeed academically. Puppet Maths brings them the benefit of my experience in teaching maths and in avoiding many of the mental blocks that can be introduced in a child’s mind when they don’t understand some aspect of mathematics.

Concrete Thinking

If abstract thinking is a sign of maturity, then it follows that young children prefer concrete thinking, thinking about actual things rather than ideas. When children start to add and subtract they use their fingers to count on. This is a perfectly legitimate way for them to aid their counting. Unfortunately, it can be slow, and it introduces a limit in their minds that it is easy to add on any number up to 5, but that it's hard to add a bigger one - an impression created solely by the need to put down their pencil to use both hands to counnt on, and having no free hand to point to the fingers while counting.
To encourge children to move on and do their sums without using their fingers, pupils are told not to count on their fingers. Many children, at this point, think that they are expected to add and subtract numbers without using any sort of framework to count up/down the numbers. They can remember the first few like 2+3 which they know add up to 5, but they do not remember bigger ones like 7+8 (which was more than hard enough when they were using their fingers to count on). "How on Earth,"? they ask themselves, "do I add these big nummbers?". What's more, numbers go on up for ever and ever, and the child, quite sensibly, realises that they won't be able to learn all the combinations of all of them. And they give up.

Children need to be given some other way of counting something concrete, which they can do in their mind's eye (or on a scrap of paper) that will enable them to add/subbtract numbers up to 9. Because of the way the number system has been built, addition and subtraction only requires manipulation of numbers up to 19, another fact that isn't immediately apparent to the child. At Puppet Maths, by using puppets, we tap into the children's imagination, we get them to use that part of their brain which is so important when they're doing maths.