It's time to put an end to 'cognitive abuse'
Maths teaching in many secondary schools is tantamount to abuse, creating anxiety and fear among pupils, according to researchers from leading universities.
But changing these methods, and focusing instead on the development of "mathematical resilience", could transform the way in which pupils perceive the subject.
Sue Johnston-Wilder of the University of Warwick and Clare Lee of the Open University believe many people find maths problems so difficult that they develop a phobia of any situation or task that may require mathematical reasoning.
"The way that mathematics is often taught in English classrooms is an unwitting form of cognitive abuse," they say.
Ways of working that they believe "seem calculated to cause anxiety" include asking pupils "to memorise formulae without understanding in classrooms where the mathematics is divorced from the reality". Teachers also often use a "restricted practice" that involves explaining a single technique, followed by exercises that allow pupils to practise that technique.
This creates a belief among pupils that they are either good at maths or have no mathematical ability at all. "Acting in such a way that many people are made to feel anxious, concerned or fearful seems to us to be acting in an abusive way," the academics say.
They identify a quality they refer to as "mathematical resilience". This, they say, will enable pupils to persevere when faced with mathematical difficulty.
"There will not be competitions to see who can recite memorised answers most quickly," the researchers explain. "Mathematical resilience can be developed when the school encourages people to see that learning takes effort, but that effort will result in improvement."
Pupils thus learn to talk like mathematicians, possessing the language necessary to express their understanding - or lack thereof - of any given topic. The more they talk like mathematicians, the more they will feel that they are capable of understanding maths.
The researchers were invited into a school to demonstrate their methods. The inner-city school, with many disadvantaged pupils, was unable to recruit a sufficient number of qualified maths teachers. The staff's main concern was to achieve acceptable GCSE grades in the subject.
The academics worked with a Year 9 class, asking pupils to write and direct a short film to explain new mathematical concepts. "Placing pupils in the position of having to communicate what they are learning is at the core of increasing ... resilience and ... thinking," they say.
Pupils discussed how to use mathematical language to explain their ideas. They described having to "double-check that we'd got it right". One pupil said: "With teachers, people normally just say, 'Oh yeah, I understand that.' But, with your friends, you'll just say if you don't understand it."
In particular, the students appreciated the independence that the project allowed them. "You can get on with your own work and figure it out for yourself," one teenager said. "So you're not bored."
Another added: "We actually wanted to do it. In normal maths lessons, it's just a bit boring, so we don't really want to learn." And her friend said: "We're not having to sit there and listen to someone explain something. We're doing it ourselves and we're learning from our own abilities."
The researchers stop short of concluding that pupils became more mathematically resilient purely as a result of a single activity. However, the proportion of pupils at the school receiving an A*-C grade in maths GCSE rose to 47 per cent - an increase of 12 per cent over the year before.
"Mathematical resilience is about ... confidence in what is understood and knowledge about what to do if you do not understand," the researchers say. "Pupils' confidence increased and ... they felt supported in answering a challenging task and knew what to do to overcome any barriers that they encountered."
Johnston-Wilder, S. and Lee, C. Developing Mathematical Resilience. A paper given at the 2010 British Educational Research Association annual conference.
Sue Johnston-Wilder, University of Warwick.
Clare Lee, the Open University.
School staff are often as lacking in mathematical resilience as their pupils.
There were not enough qualified maths teachers at the inner-city school where the researchers trialled their approach. So they suggested that teachers from other departments and non-teaching staff become "Maths Angels" and act as coaches, helping pupils to confront their mathematical demons.
However, it transpired that the Angels themselves were sorely lacking in resilience. Only four of the 15 initial volunteers attended a training meeting and one Angel became so distressed by the maths involved that the meeting had to stop.
"The feelings of anxiety and fear that we knew to be widespread were so embedded in the staff ... that they seemed to be unable to help the students," the researchers say. They believe that further training is necessary to change the way that maths is perceived within the school.