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.

Teaching by stimulating the child's mind

When I was at school, there were still 12 pennies in a shilling (and 20 shillings in a £) so from the age of seven I was expected to count in bases 12 and 20 in addition to base 10. How did I do it? I imagined a big pile of pennies, which, when they reached the height of 12 got turned into a shiny silver shilling (not that I often saw a shilling, they didn’t circulate, they were kept aside for use in electricity meters). As I did my calculations I imagined pennies being put on or taken off the pile.

Any child who didn’t use their imagination in this way that must have been an enormous disadvantage. They must have faced enormous difficulties counting in 3 bases (10, 12 and 20). Later, when I was 8 we were expected to count in bases 14 and 16 (there being 16 ounces in a pound, and 14 pounds in a stone). Then at age 9 we were asked to count in bases 22, and 8, there being 22 yards in a chain and 8 furlongs in a mile (The chain was actually a decimal unit, as there were 100 links in a chain, and 10 chains in a furlong). We were expected to count in all these different bases before we reached the age of ten years! And we did. Why? Because we rose to meet what was expected of us. This is why it is so important not to dumb down maths.
At Puppet Maths we believe in academic excellence. We will not dumb anything down. We believe in making academic ideas and concepts accessible to the young mind, and we have found the use of puppets to be the ideal vehicle to achieve this.
Puppets stimulate children’s imaginations, and once they are imagining then they can see piles of pennies, or lines of numbers, or patterns in their mind’s eye.

Children love animation

Children have vivid imaginations. Maths is not often taught in a manner that allows the child to use their imagination. Maths is considered to be far too serious a subject to let children harness their imagination. What sort of answers would a child come up with if it used its imagination when doing maths?
Q. “What’s 1 + 1?”
A. “Pink bunnies”.
But is this the case? Children want to please the adults in their lives. They know when it is appropriate to be serious and when to be frivolous. They might use frivolity as an excuse to avoid work, but they know exactly what they’re doing, when they do it. The aim of Puppet Maths is to harness children’s imagination to make maths fun. And Maths should be fun, without having to dumb it down.
Children love animation, it simply catches their imagination. The use of puppets immediately propels a child to start using the imaginative part of their mind. When they’re doing this, the child’s mind is open for learning. This is why Puppet Maths is so effective at teaching maths, it engages children’s open minds.

Many ways to solve a maths problem

It is a humbling experience for any maths teacher when a pupil comes up with a better way to solve the problem than that used by the teacher himself. Naturally, the teacher teaches the standard method, and when faced with a maths problem, as a matter of routine, launches into a solution based on applying that standard method. This saves the teacher from having to think about the problem. Then along comes a pupil who has thought about the problem, and using imagination reframes it in terms that are significantly simpler. This allows the pupil to shortcut the route to the answer. This ability to think about a problem and reframe it with simplicity is the mark of a good mathematician. Unfortunately, this is not a skill that is taught in most school maths classes. At Puppet Maths, we think about how maths problems should be approached, and we encourage our pupils to think about how they might be solved. We present our pupils with a number of different ways to view the same data, and a number of different ways to manipulate that data to arrive at an answer. By this means we show our pupils that there is more than one way of considering a maths problem and that there is more than one method reaching a satisfactory answer. We want our pupils to be aware of this diversity, so that they can use their imaginations to arrive at the best path to a solution. We, at Puppet Maths, want to lead children away from the idea that the way that teacher does it is the only good way of doing it, and that it must only be done by that method. Whether at home or at school, we want pupils to develop insight and, yes, cunning into their relationship with numbers.

Don't judge students

An unhappy thing happened today, the connector to my external hard drive got torn from the printed circuit board that it’s mounted on. It needs 9 solder joints to reattach it, but its a surface mount component, so it’ll be hard to get at with a soldering iron. If I had a reflow oven then soldering it would be straightforward, except the disk drive would have to be removed from the circuit board, and no doubt that would require unsoldering. Not so simple. At least maths is easier.
Maths can be solved in your head, no fiddling around with hot tools. The nastiest material you come across with maths is ink (that is unless you think that paper is more offensive). It’s one of the reasons that I gave up semiconductor engineering to teach maths, there’s no hydrofluoric acid or arsene involved in doing sums. When viewed from this perspective, maths really is easy.
If maths is such a good option, why do so many children hate it? My theory is that it’s because, the subject of maths forms a pyramid. Every new thing that a pupil learns depends upon them knowing the preceding stuff. If there is something that they “don’t get”, then from there on, they are at sea. Young children can be very shy of pointing out that they don’t understand something, they’ll pretend that they do, and go to great lengths to hide the fact that they don’t. In this way they act against their own best interests, but, of course, they don’t understand it that way, because they don’t see the bigger picture. This has a lot to do with their status within their peer group, and not being seen as being weaker than the others around them, weaker than those who they are competing with. This is where Puppet Maths helps. Children know that they are superior to puppets, and so are more inclined to admit their inability to do something, because it carries no social stigma. They know they are not going to be picked on by the puppets; they know they are not going to be judged by the puppets.

Pupils should develop confidence in their own abilities

Perseverance is a quality that is not prized as much as it should be. Today, we live in a society that seeks instant gratification. If something can’t be completed immediately it’s not worth doing, it should be abandoned, in favour of something that can. Another word that isn’t used as commonly as heretofore, is “endeavour”. In our culture of immediacy, why should anyone be expected to struggle on to achieve a long term goal? This is what has bred the cult of television talent and reality TV shows. Why strive when one can gain celebrity and fortune by appearing on the television. Why learn maths, when all you have to do is learn to sing (not necessarily particularly well) or behave outrageously? In life, two of the keys to success are persistence and endeavour, but these are not properly acknowledged either in popular culture or at school. In English schools the government has placed a timetable that says what should be taught by what age, and the schools are running to keep up with the timetable, for should they fail to do so they are adjudged to be failing. This forced pace at which the topics within maths must be covered, removes the time required to allow pupils to practice persistence, for them to learn that they can master a maths topic themselves by repeated application. It also removes the opportunity for pupils to practice endeavour, for their teachers, fearful of criticism themselves and the consequences that such criticism might have on their careers and livelihoods, meet their targets by spoon feeding their pupils rather than by requiring them to think for themselves. At Puppet Maths, we encourage children to think for themselves. We want them to find new ways to approach problems, to learn by trial and error, to succeed by their own efforts so that they learn confidence in their own abilities to succeed at maths.

Don't be put off by the vocabulary

The use of words gets in the way of doing maths. In one study, they found that children could not do calculations based on Pythagoras’s Theorem, but they could do calculations using “three, four, five”. Apparently, children were frightened off by the word “Pythagoras”. For young children, it is a long and a strange word. They try to remember it, and fail because it is such a strange word. They think that because the name of the theorem is hard to pronounce and remember, that what the theorem says must be hard to follow (and what is a theorem anyway, anything that is a “Theorem” must be hard). The phrase “three, four, five” comes from the building industry. Naturally, when bricklayers are building buildings they need to get the corners at 90°. To do this they have a loop of string marked into 12 equal sections. They are taught that they if they peg a length three long to the ground, and then take hold of the string at the point where there are four sections on one side and five on the other, and pull it tight, they will get a right angle where the pegged three sections meet the four sections they are holding. When pupils are taught about “three, four, five”, three words that they recognise and aren’t intimidated by, they find no difficulty with the concept embodied in Pythagoras’s Theorem. Once again we observe how the use of words gets in the way of maths. At Puppet Maths, our puppets introduce our pupils to strange words like “theorem” in a fun and non-threatening way. As a result they come to accept these words as just another word in their vocabulary. They are not put off or intimidated by them anymore and as a result they can focus on the important thing - the underlying maths. This way, we help them succeed rather than be distracted and put off by nomenclature.