A new psychological study has cast doubt both on the saying “you can’t teach an old dog new tricks” and claims that entrance exams for selective schools can accurately determine a child’s “true potential”.

The researchers tested more than 550 school pupils aged 11 to 18 and more than 100 adults on various skills such as “non-verbal reasoning”, a process involved in maths.

And they found that children aged 11 to 13 – older than the age when children typically take entrance exams – were able to improve their performance by 10 percentage points in just three weeks.

They also found a greater effect of training on older adolescents than on their younger counterparts, according to a paper in the journal Psychological Science.

Professor Sarah-Jayne Blakemore, of University College London, who led the research, said: “Although adults and older adolescents benefited most from training in non-verbal reasoning, the average test score for adolescents aged 11-13 improved from 60 per cent to 70 per cent following three weeks of ten-minute online training sessions.

“This calls into question the claim that entry tests for selective schools that include non-verbal reasoning ‘assess the true potential of every child’.”

In the non-verbal reasoning test, participants were shown a grid of different shapes and colours with one space left blank. They then had to work out the correct shape to complete the pattern.

Another test, which measured “numerosity discrimination”, they were shown two groups of different coloured dots in quick succession and had to judge which group had the most dots.

“We find that these cognitive skills, which are related to mathematics performance, show greater training effects in late adolescence than earlier in adolescence,” said Dr Lisa Knoll, who co-wrote the paper.

“These findings highlight the relevance of this late developmental stage for education and challenge the assumption that earlier is always better for learning.

“We find that fundamental cognitive skills related to mathematics can be significantly trained in late adolescence.”

Delia Fuhrmann, another of the researchers, stressed there were limits to what could be claimed about good performance in such tests.

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“Some ‘brain training’ apps claim to improve your IQ by getting you to practise a specific task such as the non-verbal reasoning task we used in our experiment,” she said.

“However, there is no evidence that this leads to an improvement in overall cognitive ability. All we can say for sure is that training to spot patterns in a three-by-three grid of abstract shapes improves your ability to spot patterns in a three-by-three grid of abstract shapes.