Older teenagers and young adults are able to improve their fundamental maths skills and reasoning abilities more rapidly than younger teens, according to research that overturns longstanding assumptions about children’s learning.

The research, published by academics from University College London’s Institute of Cognitive Neuroscience, also upends ideas that tests used in grammar school selection can be made “tutor-proof” to assess potential.

In particular, the research found that older adolescents significantly improved their performance in maths skills after training – suggesting that older teenagers could reveal further potential even after sitting GCSE exams at the age of 16.

“We find that these cognitive skills, which are related to mathematics performance, show greater training effects in late adolescence than earlier in adolescence,” said Lisa Knoll, one of the authors of the research.

“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.”

The research – the first of its kind to compare the effects of training between age groups – gave tests in one of three formats to more than 600 children, teenagers and adults aged 11 to 33. After completing 20 days of training through brief online sessions, they were retested to measure improvement.

While one of the three formats – face recognition – showed no improvement after training, the other two tests, of non-verbal reasoning and number judgments, showed distinct differences between age groups, with those at the older end of the age scale developing more rapidly after training.

The tests were repeated six months later and showed little difference in outcome.

The non-verbal reasoning test involved looking at a grid of shapes, with the final square left blank. Participants had to choose the correct shape to complete the pattern, and the shapes could vary by colour, size, shape and position.

In another test, described as “numerosity discrimination”, participants were shown two groups of different coloured dots in quick succession and had to judge which group had the most dots.

Prof Sarah-Jayne Blakemore, senior author of the study, said that while older teens did better following training in non-verbal reasoning, the tests showed that younger teens aged 11-13 could also advance rapidly after being given brief online training sessions for three weeks.

“This calls into question the claim that entry tests for selective schools that include non-verbal reasoning [can] assess the true potential of every child,” Blakemore said.

In the recent debate over the revival of grammar schools, supporters have claimed that “tutor-proof” tests using non-verbal reasoning could be used to judge academic potential in 11 year-olds. The claim has been challenged by experts including Prof Robert Coe at Durham University, who argues that all such tests are vulnerable to coaching.

The UCL paper, published in the journal Psychological Science, concludes that “complex cognitive skills relevant to maths education, particularly relational reasoning, show larger training effects in late adolescence than earlier in adolescence”.

It notes: “The fact that relational reasoning can be trained in all age groups tested here, and is particularly amenable to training in late adolescence, does not support the notion that matrix reasoning gives an indication of some kind of innate, fixed ability. This has implications for education because matrix reasoning is commonly used in IQ tests and school entrance exams.”