Rote learning versus thinking.

Should children learn facts by rote, or should they they be taught to think? In maths which should be teach? The answer is both. I spent a significant period of my life as a quality manager in the medical devices industry. My job was to stop people thinking. When you do something without thinking you don’t make mistakes (and in the medical devices industry mistakes aren’t acceptable). It is only when you think about an activity that you get things wrong. As an example consider when drivers change gear. On a manual shift car, drivers change gear without thinking routinely, and they do so without encountering a problem. However, when they think about changing gear, they get it wrong and grind the gearbox cogs together. Had they done it automatically they would probably have got it right. So lesson for maths is that for basic routines, which people will use often and repeatedly, the best strategy is to train people to do them automatically, to do them without thinking, to know the method and just apply it. This is where rote learning, and repeated practice is important.
However, before we can solve a maths puzzle using standard routines, we have to convert the problem to a standard form which is tractable to a solution using them. This is where thinking is required. If all one can do is manipulate the standard routines, then one is destined to be nothing more than a calculator. So it is important to teach children how to interpret problems and using logic rearrange them into a form which can then be solved using the standard routines. This is where pupils need imagination and insight. This is the fun part of maths. So many children are put off maths because all they are ever expected to do is practice the standard routines, and then as a consequence they find the subject boring. At Puppet Maths we teach pupils to think and use their imagination when solving maths puzzles, but we also, by using puppets introduce an imaginative element to the activity of practicing the standard routines and alleviate the boredom that so many pupils experience when learning them.

Next in a sequence

Here is a maths puzzle. What is the next in the sequence?
3,5,7...
well it could be 9 (series of odd numbers), or it could be 11 (series of prime numbers)... or it could be anything. The series might be 3,5,7,301,303,305,307,601. You cannot tell the next number in a series from the preceeding numbers. If it were possible, and I knew how it were done, then I'd have made my fortune on the stock market already and retired. But spotting patterns and rules is an important skill, for many processes in life follow relatively simple rules. So we ask pupils to predict the next number in the series. Therein lies the mistake. We should be asking the pupils to determine the next possible numbers in the series, and to explain the rules that would cause those numbers to appear in the sequence. That transforms the process from a right/wrong answer to one of exploration and inventiveness. Therein lies one of the great problems with maths as it is taught in our schools. It is taught as a subject of boundaries and rules which are there to constrain the pupil rather than an opportunity for exploration and for the pupil to show how clever they are. Boys are particularly disposed to getting one over on those around them. They want to show how clever they are by tricking or outsmarting others, but they are often the most alienated from maths. At Puppet Maths we give our pupils the opportunity to show off how clever they are, we provide them with open ended questioning that allows them to think beyond the parameters of a narrow maths question and get one over on the teacher.

How to approach a problem.

Life is full of difficulties. That is its nature, even without governments producing their best efforts! How to overocme these difficulties? To do so we must plot our way through to a solution, which involves the steps of understanding the problem, understanding the solution we wish to attain, and the use of logic and reasoning to get us from the start to the finish. Maths should be teaching us these steps. Maths is not just about performing sterile manipulation of numbers, it is about solving problems. It should teach us a robust methodology for approaching problems. Unfortunately, all to often in schools it fails to do that. Judging by the sales of puzzle books, people like to solve problems, but would the same people who buy these books say that they like maths? In many cases the answer would be a resounding "No". This has much to do with the way maths is taught at school. On the other hand Puppet Maths puts the fun back into maths. It makes maths immaginative so that the exercises become maths puzzles rather than maths problems.