On 16 January I attended the Shard Conference of the Mathematics Resilience Group led by Sue Johnston-Wilder (Warwick University) and Clare Lee (Open University).
It was held in the Warwick University Business Centre, which occupies most of the 17th floor. The view is superb. The main Conference Area looks across directly at all the iconic totem poles of capitalism thrusting skywards in the City. Just below is the massive building site of the London Bridge Station development.
Mathematics Resilience is a hard sell because it is profoundly counter-intuitive. It argues that the adults and children of the western world, and especially the UK, are gripped by a destructive, deep rooted anxiety about maths. And not just hard maths, but also numeracy at the most basic level.
Fine so far, who would argue with that?
But Mathematics Resilience argues that the solution is not to break down the teaching of maths into a progression of even more small, easily accessible, shallow steps, for which pupils can be rewarded with success as they mount each stage, but to deliberately and methodically confront them with stuff that makes their brains hurt because they can't readily understand it.
The argument is that maths anxiety is the inevitable consequence of being forced to participate in a world of numbers, in maths classrooms and elsewhere, that is a complete mystery in terms of understanding, and that being trained through repetition and memory exercises to 'get sums right' just increases the anxiety because, just as you thought you could it do it, along comes a vaguely similar but slightly different problem that you haven't a clue how to tackle. And often you don't even understand the question.
So the problem is not primarily a lack of knowledge but that the knowledge, and even successfully taught calculation skills, are floating about like detritus in a cognitive ocean of disconnected misunderstandings.
Now comes the anti common sense part. The solution is to give pupils harder, not easier problems. And to especially praise them when they get the wrong answers!
Followers of Vygotsky (who else) will see where this is heading: yes, to the pedagogic principle of the Zone of Proximal Development (ZPD) and the necessity of cognitive struggle for the process of gaining understanding.
We mustn't forget Piaget either, because the understandings gained are never specific to the problem that was the context for the particular cognitive struggle. The resulting cognitive gains are general. The pupil can then not only understand different sorts of maths problems for the first time, but can now tackle harder stuff in all subjects and in real word situations. A developmental, stage-related progression in personal cognitive function has resulted.
Of course none of this will work if the learner is left to drown without support in an ocean of misunderstanding. Such support involves the following features that have all been proven to facilitate successful developmental learning.
1. A teacher that understands the pedagogy and is sufficiently skilled to apply it. There is therefore a training need.
2. Pupils that are familiar with the personal cognitive processes of metacognition, and who readily practise it.
3. Unselfconscious and uninhibited peer to peer discussion about the problem in question and how it might be solved. This is Vygotsky's 'social plane learning'.
4. The cultural expectation of mental struggle. Guy Claxton refers to this as developing 'a positive learning disposition' that expects dead ends and wrong answers. This might be called having a 'good mental character', almost in the VIctorian sense.
5. The need to consciously engage Daniel Kahneman's 'System 2 thinking
' as a mental habit.
6. The explicit absence of external incentives and competition.
So how did the day go?
Pretty well. I am sure all the delegates left feeling much the wiser and more energised. Here are some of my personal highlights.
The contribution of Mike Ellicock of 'National Numeracy
"Being numerate goes beyond simply ‘doing sums’. It means having the confidence and competence to use numbers and think mathematically in everyday life, for example being able to make estimates, identify possibilities, weigh up different options, decide which is most appropriate and choose the correct skills to tackle and solve the problem or situation."
A debate about why maths anxiety is largely absent in China, Singapore and South Korea
As might be expected this was inconclusive, but I was very interested in Sue Johnston-Wilder's analysis of the teaching of one of China's 'superstar status', high earning, private maths coaches. She said that she was particularly impressed by the amount of time spent developing conceptual understanding. The example she gave was in relation to 'fractions'. The coach clearly recognised the cognitive struggle involved in the understanding of the concept of 'parts of things' and spent a great deal of time on it prior to the teaching of how to 'do sums with fractions'. She also talked about the growing interest from the high achieving far east education systems in the 'mathematical resilience' movement here.
A debate about the importance of parental support
I was a bit worried about this. The speaker talked about 'parental engagement' and support being more important as a learning outcome indicator than 'FSM' and 'social class'.
These latter are 'proxy indicators'. It is 'cognitive ability that counts', as I am always banging on about.
I wondered how parents might react to a teacher telling them that their children 'didn't make enough mistakes'. If the principles of learning resilience are a hard sell to teachers, then how can we get parents on board?
I reflected on being told by a Hackney insider that Mossbourne Academy's SEN provision is superb, largely because of the time and money spent on doing all the things in school that are necessary to ensure that all pupils get what they need, regardless of parental support. Isn't this what the pupil premium is for?
The relevance of my book, 'Learning Matters'
Part 5 is a summary of the important work of many of those that share the basic principles of 'Mathematics Resilience'. These include the following.
5.2 Shayer and Adey - The 'Cognitive Acceleration' programmes
5.3 Mortimer and Scott - The importance of pupil talk - CLIS at Leeds
5.4 Johnston-Wilder and Lee - Mathematical Resilience
5.5 Claxton - Developing Learning Capacity and Resilience
5.6 Kahneman - Thinking Fast and Slow
5.8 The Rev Dawes - Kings Somborne School 1837-1860
There are others not included, especially Mike Grenier and the 'Slow Education
This latter is a serious omission
There is clearly a lot of excellent work going on.
I would like to see more of a common front. This is mainstream 21st century pedagogy. It needs to be promoted as such by all involved pushing forward together on as many fronts as possible.