Learning To Teach Maths
- What I learnt from working with very frustrated children
(who might have been be described as “gifted” )

By Jenny Newland

Sometimes, one comes across children who seem to learn very fast indeed, who appear to stumble effortlessly upon successful ways of doing things and who think so fast they barely know that they are doing it and those around them (adults included) just can’t keep up with them.

Children like this are often described as being “gifted” - a label that explains little and often does more harm than good in the long run (Mindshift 2015). However, in the absence of a better way to refer to them I shall use the term ‘gifted’ here to describe these particular children, though ultimately, what I have to say applies to all learners.

It all began when I was working one-to-one with a couple of children who could be described as gifted but they were both, in their different ways, struggling with formal maths education. At that time, I couldn’t understand why these two highly numerate and intelligent children were experiencing such difficulties and such intense frustration with maths.

I am very grateful to these two young people as , by giving me the challenge of helping them with their frustrations, they unwittingly taught me a lot and were the beginnings of a journey that caused me to turn everything I knew about teaching and learning maths upside down.

Now my experience of maths as a child learner in school was that if you were obedient and attentive, you could learn how to follow the teachers method and if you did the same as they did, you would get the right answer. That worked up to a point, though it never seemed to be enough to bridge the gap between those who could get by in maths (like me) and those who seemed to be brilliant at it. There were several ingredients that I now know about such as creativity, curiosity, flexibility with numbers …. and many more, which at that time eluded me completely. But, that is how I learned and how many of us learn. I became acceptably good at maths, I passed my ‘O’ level (back in the days of ‘O‘ levels) and my ‘A’ level though I never felt that I was particularly good at maths and I had no idea that creativity in maths might be possible or even desirable.

Working with these two children, I found 2 key things that they did that began to explain why they were experiencing such intense frustration.

 

1) They could process information very very fast!

 

2) They were highly creative in their approaches!

 

So what are the implications of these two behaviours ?

 

It seemed that being taught mathematical “methods” generally made no sense to them. From close observation, I discovered that the reason for this was that they had done two things, often before the explanation of the method was even complete. Firstly, they had devised a method of their own and secondly, they had used it. . . and . . . they had achieved both of these things without even realising that that is what they had done!

 

So, this is what seems to happen that creates the first stages of frustration.

1) - Because they have invented their own method, they don't see the point of the 'prescribed' one.

 

and

 

2) - Because their brains process information so fast, they can do things in their heads with numbers very fast, that many of us struggle to do.

 

They don't need as many simplification steps as most of us do to get an answer, in fact they can often experience anothers attempt to simplify things as an insult.  And thus they become confused by prescribed methods.

An example of this can be found in long division. Long division involves working through several stages before an answer is arrived at. The stages a supposed to make something that is generally thought of as being quite difficult into steps that are more manageable.

However, when working with these particular children, I have found that they often do half of the stages in their head without knowing it. This means that when someone steps in to ‘help’ by showing them how to do it, it makes no sense to them. They find the steps confusing and irrelevant – they can already process several steps very fast.

Frequently, the methods they come up with themselves may be convoluted and complicated. They are not necessarily the quickest methods and almost certainly not the easiest. Some of the time, they don't work and some of the time they do. But actually, that doesn't matter! What matters is that these methods are precious. Their way of working involves very impressive creativity and real mathematics going on – what they are doing is what mathematicians do! Sadly, this creativity can often go unnoticed or, in the worst case scenario, be thwarted altogether.

In fact it is interesting to note that doing things the hard way has been identified as one of 5 activities that can improve cognitive ability or 'fluid intelligence' (Kuszewski 2011). So these children are frequently opting to take the path that will increase their own intelligence. A choice that I believe should be respected and encouraged.

As a result of noticing these things happening, my task has become about helping all my pupils (‘gifted’ or otherwise) to understand their own processing. I have found that through encouraging them to pay more attention to their thinking and to begin to articulate their ideas, they gradually develop a greater awareness of what they are doing. Their thinking and creativity are validated and this in turn lessens their feelings of frustration. They start to feel good about themselves and are able to move on and progress.

It is often a case of finding out what learners have done – helping them to separate out their own thoughts so that they can see what it is they have come up with and how, what assumptions they are making and, if an error has occurred, where along the line it happened. I have found that learners tend to be very quick to self correct when their thinking is scrutinized in this way.

I have also found it tremendously instructive to find out what children have come up with on their own. When I get them to teach me their methods, I can get a great deal of insight into their level of knowledge and their way of understanding the material. This enables me to see what is happening when they attempt a maths activity and if they trip up along the way, they can then be helped to see something they might not have seen before. Sometimes, I even learn a new way to do it and it makes for smooth and amiable learning.

The fact is that in maths, there are many options for how to go about things – many of us have grown up thinking that there is only one ‘correct’ way to do things in maths when in reality, this just isn’t true. Comparing notes with people who learned in different parts of the world or in different eras will confirm this.

Research has shown that those who are ultimately the best at maths are those who can be very flexible about the methods they use and are not restricted to using just one. The maths of professional mathematicians is all about problem solving which requires creative versatile thinking. And it is the development and honing of these creative and problem solving skills that leads to that elusive brilliance in maths as well as improvements in many other aspects of learning (Boaler 2009).

 

References

Jo Boaler (2009) The Elephant in the Classroom: Helping Children learn and Love Maths, London, Souvenir Press Ltd

Andrea Kuszewski (2011) You can increase your intelligence: 5 ways to maximize your cognitive potential. Blog, March 7, Scientific American.

http://blogs.scientificamerican.com/guest-blog/you-can-increase-your-intelligence-5-ways-to-maximize-your-cognitive-potential/

Students Share The Downside Of Being Labeled 'Gifted' by Mindshift (November 2017)

https://www.kqed.org/mindshift/49653/students-share-the-downside-of-being-labeled-gifted