Maths should not be torture

What makes anyone succeed at anything? What is it that made David Beckham a superb footballer? What is it that made Bill Gates a great computer programmer? The answer is practice. According to Malcolm Gladwell’s book “Outliers” it is 10000 hours of practice. Would these people have spent so much time practicing their skills in their respective areas if they had not enjoyed doing so? Of course not. Children are capable of speaking English, which has rules that are much more complex than those of mathematics, because they practice it. They enjoy doing so because language is what gets them the things they want. But where is the incentive for undertaking maths? So often, maths is not fun. For many children, maths is incomprehensible and therefore boring. For many children, maths is something that makes them feel powerless and only serves to provide an opportunity for them to earn criticism. I remember myself, aged 7, hiding the fact that I couldn’t do some mathematical calculation or other. During the subsequent lesson, the teacher required us to continue on with the same type of calculations and I had to pretend to be busy and be working diligently even though I was doing nothing. All the time I was under the stress of being found out and getting told off. Worse still, the teacher continued with the exercise during the next lesson - another period of having to hide my weakness! At the end of this third session, the teacher wanted to see my work. Agony. What work? I’d done none! I had to come clean, and admit that I couldn’t do the sums. I expected to be told off. I wasn’t, the teacher didn’t seem to care. I was amazed. As an adult I can see that the teacher was simply happy to know which of her pupils could do the work and which couldn’t, and wasn’t about to punish those who still needed to learn. But the point of view of the young child is so different. I endured the fear of failure at maths for 3 lessons. Other pupils endured it each day and every day. For them maths was nothing less than a daily torture, whose purpose was to expose them as inadequate. At Puppet Maths we want to banish such terrors from the minds of our pupils. We want maths to be unthreatening. We want maths to be fun, so that children will want to practice it, and through practice will become good at it. We want to make maths somewhere where children can feel safe, somewhere where they can feel at home.

Use your imagination to be good at maths

Although younger children can confuse the two, older children know the difference between the world of their imagination and reality. At what age does a child start to distinguish between them? At what age does a child compartmentalise the two? This may well be a reason why children, who are to go on and fail at maths, start to do so around the ages of 8 and 9. Maths being a subject studied at school, where you get praised for getting your sums right, and get told off for getting them wrong is clearly part of the real world. So children compartmentalise maths as being in the real world. But this is not helpful. Maths is all about the imagination, though this is a point missed by most people. I well remember an episode of “The News Quiz” on BBC Radio 4, where the chairman Barry Took made a joke about the comment passed by an academic regarding one of his post graduate students, who had subsequently become eminent in another field, “He didn’t have the imagination to be a good mathematician”. This observation was thought by Mr. Took, his scriptwriters and the audience of the show to be an absolute hoot, but I believe that they were all missing a vital point. Mathematics is all about the imagination. That so many people could find the academic’s comment ridiculous demonstrates how sterile and dry the mainstream manner of teaching maths is. We at Puppet Maths are committed to redressing this failing in maths education. Through the use of puppets to teach maths, we put mathematics firmly in the realm of the imaginative realm of a child’s life. When children are working with puppets they know that they have entered an imaginary world. The imaginative areas of their brains become active, and they become susceptible to learning. We tap into children’s imaginations while we teach, because we know that that is how they learn best.

Maths as puzzle solving

Stan Raimes’s third rule for solving differential equations, like his second rule, also had general applicability. Raimes’s third rule was “if you don’t know the answer, find it by hook or by crook”. Here again we get good advice. This rule tells us clearly that we are to think about our maths problems, and we are to use our imaginations to arrive at a solution. It tells us that there is not necessarily a path already plotted, an algorithm that we can simply slot our numbers into, which will yield us the answer we desire. Because at the start of their maths education, when pupils are still learning the equivalent of the maths alphabet, they are taught to learn set methods to arrive at the correct answers, and they pick up the idea that maths is not about inventiveness, or cunning, or lateral thought, but that it is about mindlessly following rules that they have learnt by rote or repetition. This does them a disservice, and although helpful in the short term, it acts as a block to later success in the subject. At Puppet Maths, we recognise this mental block, and we aim to avoid it by teaching our pupils to approach maths from the perspective of puzzle solving rather than maths problem solving. This is also the approach taken by Singapore Maths, so we feel that we are in good company in our approach.

Manipulating maths problems

As an undergraduate at Imperial College, I was one of the many thousands who were taught maths by the great Stan Raimes. As part of his teaching, he taught us “Raimes’s Rules”. These 3 rules were, as it happens, rules for solving differential equations, but apart from rule 1, they had much more general applicability. In this article I wish to consider the second rule. Rule 2 stated “If you already know the answer, you don’t have to work it out”. The point of this rule is that maths is not about just doing a calculation (as so many pupils think it is), it is about manipulating a problem until it is in a soluble form. This is the first bit of solving any maths problem. However, it is the bit that many pupils just don’t get. They look at a maths problem and they can’t see how to solve it immediately and give up. “I can’t do this,” they tell themselves. The part they are missing is an essential part of solving maths problems. It is at this stage that they need to use logic and imagination to convert the problem into an equivalent one that they know how to solve. But, unfortunately, so often, they do not do this. At Puppet Maths we inculcate our pupils with the concept of manipulating the maths problems they get into a form that they can recognise, so that they can solve them. We teach them the process of how to approach maths as well of how to accomplish the mechanics of calculation.

Thinking in pictures

There are persons, autistic persons, known as savants, who can do complex calculations in their heads at a fantastic speed. This shows us just what the human brain is capable of. Most of us cannot compete at mathematical ability with such people. But these people, as autistics, have difficulty communicating. Can it be that the data processing our brains undertake to communicate inhibits our ability to perform maths? Well we have seen that the names we give to numbers affects our ability to do mental arithmetic, why would the way we think about numbers, in verbal, descriptive terms, not also affect our ability? This is why Puppet Maths teaches its pupils to think in pictures when doing maths. A picture says a thousand words. Thinking in pictures helps pupils perform mathematics. Those who stumble upon this technique go on to succeed at the subject, those that do not are handicapped. At Puppet Maths we want introduce all pupils to the techniques that help them succeed.

Fear of failure

Maths is part of the real world. It is taught in schools. Children doing well get praised for it. Children doing badly get to feel that they aren’t good enough. This latter is true however supportive the teacher. The child who has got a sum wrong feels diminished in spite of the teacher saying, “Never mind, this is how you do it, try again”. Why? Because, until adolescence, children are programmed to try and please adults. Also they are very self centred. So instead of taking notice of what adults expect of them, they decide for themselves what would please an adult. These expectations generally start off high, children imagine themselves doing the most ambitious things, and very often the most unrealistically ambitious things. So when they fail to achieve at something that falls well short of their ambitions, when they if they fail to meet something much less than their own expectations (which are way above anything any adult expects of them) they feel failure. Puppet Maths aims to avoid these feelings by taking adults out of the experience of maths. Children know that puppets are an inferior species to themselves. Children have no illusions about trying to impress their toys with their brilliance, they know that their toys are already in awe of them. In this world they are persons of importance, and they know that the puppets know it, so in this world, children are not inhibited by the need to put up a front, to appear confident and capable even when they’re not. They can admit their weaknesses and failings and learn how to address them without losing face. Because puppets are not authority figures, but things which are unthreatening, they make ideal companions for children to learn from. At Puppet Maths we harness this effect to enable children to achieve at maths, and get them home and dry as far as the subject of maths is concerned.

Why it's so hard to learn statistics

The purpose of maths is to help us understand what is happening in the world around us. It starts with the pupil learning arithmetic. This can easily be related to everyday life. The concept of what constitutes a “three” or a “five” is relatively easy to convey. Arithmetic is a precise discipline, and naturally emphasis that is put on accuracy when children learn it, however this is unhelpful when children come to learn statistics. Statistics have no precise “right” answers. The subject is all about getting an idea about what is going on. The metrics that are used in statistics only mean something once you’ve used them and “got a feel for them”. Before one has grasped the concepts one just doesn’t know what they mean. Learning statistics involves the pupil “getting their feet wet”, wading in and engaging with the subject before the pupil knows what it all means. This is hard for them to do when statistics is taught by a maths teacher in a maths lesson, because they’ve already been conditioned to think of maths as being all about precision, and nothing to do with gaining a gut feeling of what the data is “sort of” telling us. At Puppet Maths, because the maths is taught by puppets, who are not strict disciplinarians, pupils find it easier to accept the transition from the precision of arithmetic to the overall appreciation that is embodied in the study of statistics.

Story telling

I haven’t posted on this blog for a couple of months now, so it’s time I started again. The reason for this gap is that I spent Christmas helping one of my daughters, Julia, move home. She was in a flat with other people who just wanted to party, but she had to get up early in the mornings to go to work in the hospital and she didn’t appreciated being kept awake at 3 am.
Then in the middle of January I moved to New Zealand. It’s a lovely country and I’m looking forward to the start of the school year, and getting back into the classroom to teach maths.
As a result of these diversions, I’m afraid that the blog went by the board.

Nevertheless back to business.

Storytelling is integral to human beings. We have evolved to learn from stories. Once this was a matter of survival, the way that the human animal discovered that things were good or dangerous without having to experiment for themselves.

In recent years, since the widespread availability of recorded video, pupil studying English literature have spend ever more time watching the plays they study rather than reading the script. Why, because its simply easier to remember the story and the dialogue from experiencing the story than from reading the script. I myself was at one time an expert in Shakespeare’s King Henry IV (part 2) because when school enacted it, I was on stage for just over half of the production... I played a dead body, but that was good as it allowed me to relax and be a spectator of the play. Without effort I learnt everybody’s part. When my children were young, they loved nothing more than watching Disney videos over and over again. They knew them word perfect as well. They learnt it all without effort. That is why, at Puppet Maths, we dramatise maths. We put maths in the context of a story, and enact that story for children to enjoy. As a by product children learn to do maths without fear and without effort.