From a young age, people develop perceptions about their own intelligence and what they are “good” and “bad” at.

In a competitive school environment, they measure themselves against their peers and listen to their elders for confirmation of their abilities. But it's far from clear that academic talents are innate, says Eabhnat Ní Fhloinn, director of the DCU's Maths Learning Centre. And for an example of how teachers can get it wrong, look no further than John Gurdon, who won the 2012 Nobel prize for physiology despite being written off by his schoolmaster as "a sheer waste of time" and incapable of learning "simple biological facts".

Ní Fhloinn challenges the idea that mathematical ability is a "gift" that you either have or don't have. Drawing on the work of Stanford University psychologist Carol Dweck, she says people tend to approach learning with one of two mindsets: 'growth' or 'fixed'. "Those with a growth mindset believe that their intelligence can be developed, while a fixed mindset reflects the belief that intelligence is unchanging."

In a number of research papers, Dweck has shown that students with a growth mindset do better in the long term academically, while also developing the sort of virtues – like perseverance and humility – that are a great help in work and life.

For today’s ‘Unthinkable’, Ní Fhloinn explains the implications of Dweck’s research, endorsing her advice: “If parents want to give their children a gift, the best thing they can do is to teach their children to love challenges, be intrigued by mistakes, enjoy effort, and keep on learning.”

What is a mathematical mindset? Is it something only a select group of people have?

Eabhnat Ní Fhloinn: “Your mathematical mindset is your perception of your mathematical ability, and as such, everyone has a mathematical mindset. People’s mindsets can vary in relation to different areas, but Dweck found that students tended to have a more fixed view of mathematical skills than other intellectual skills.

“The idea that people are ‘good’ or ‘bad’ at mathematics is deeply ingrained in popular culture, leading to a general acceptance of people self-identifying at being ‘useless’ at maths and avoiding further engagement with the subject whenever possible.

"Dr Jo Boaler brought out a book last year called Mathematical Mindsets, which focused on providing teachers and parents with practical advice and sample teaching materials in order to help them to foster growth mindsets in children in relation to mathematics."

What sort of lessons are there for parents and teachers from Dweck and Boaler’s research?

“In terms of education, the major significance of Dweck’s work is that students with a growth mindset learn more effectively and are more resilient when faced with failure in a mathematical task. Students with a fixed mindset tend to give up more easily and gravitate towards easier tasks which they know they can perform well, rather than challenging themselves with more difficult ones.

“Dweck also showed that it is possible to change a student’s mindset from fixed to growth and that this change then results in higher achievement levels for the student.

“One simple change that both Dweck and Boaler advise is in terms of our approach to praising children, with both advocating praising the process rather than either the child or the outcome of their work. So while we might naturally tend to tell a child how smart they are or praise a correct numerical solution to a mathematical problem, they instead suggest focusing the praise on how a child might have tried a number of ways to get to the right answer.

“Dweck, however, counsels against praising effort alone, stating that ‘the growth mindset was intended to help close achievement gaps, not hide them’. Therefore, she suggests an approach where teachers may praise the efforts a child has made so far but follow this immediately by saying something like ‘Let’s talk about what you’ve tried, and what you can try next’. This avoids praising a child who is repeatedly attempting the same approach to a problem and ignoring the evidence that suggests a different approach is needed.

“Another aspect of encouraging a growth mindset in relation to mathematics is in terms of our reaction to mistakes – instead of these being seen as a sign of failure, they should be valued as a way of learning. By educating ourselves, and our children, about the recent research in brain plasticity and how new synapses fire in the brain when we make a mistake, helping us to learn, we can present mistakes as an integral and important part of learning.

“If children are afraid of making mistakes, they will not attempt more challenging problems in mathematics but will stick with those that are familiar and safe.”

How does a mathematical mindset change, or enrich, your view of the world?

“Perhaps the biggest impact of a growth mindset over a fixed one, in terms of your view of the world, is that it leads to a passion for learning rather than a need to seek approval or validation. In terms of mathematics, this results in a desire to understand and explore difficult problems, along with the tenacity to stick with a problem through numerous failed attempts.

“People with a growth mathematical mindset are far more likely to maximise their potential, as they believe it is possible to do so with hard work and effort.”

--------

Ask a sage:

Q. My child is no good at sums, what should I do?

Johann Wolfgang von Goethe replies: "If you treat an individual as he is, he will remain how he is. But if you treat him as if he were what he ought to be and could be, he will become what he ought to be and could be."