Children as young as six feel fear, rage and despair as a result of "mathematics anxiety", a condition which can cause physical symptoms and behaviour problems in class, according to a study.

Pupils in both primary and secondary school can find themselves locked in a cycle of despair, suffering from anxiety which harms their maths performance, which in turn leads to increased anxiety.

Researchers say maths anxiety should be treated as a "real concern" because of the damage it does to a child's learning. They also point out it may be contributing to a growing maths crisis in the UK, where the level of adult numeracy is relatively low and getting worse.

According to the Nuffield Foundation report, Understanding Mathematics Anxiety, the proportion of adults with functional maths skills equivalent to a GCSE grade C has fallen from 26% in 2003 to 22% in 2011. In contrast, functional literacy skills are steadily increasing, with 57% of working-age adults gaining the equivalent level.

Researchers from the faculty of education and the centre for neuroscience in education at Cambridge University worked with 2,700 primary and secondary students in the UK and Italy – including detailed one-to-one interviews – to explore maths anxiety and its causes.

The children they interviewed provided graphic descriptions of their fears about maths. "I felt very unwell and I was really scared," said one primary school student, describing his reaction during a lesson about equivalent fractions. "Because my table's in the corner I kind of tried not to be in the lesson."

The co-author Dr Ros McLellan, who led the interview research, said: "Maths anxiety is very much an emotional reaction. Younger kids won't want to go to school when they have maths classes; they get tearful and upset.

"We had some young people saying: 'I get so frustrated, I end up hitting the desk,' and then they get themselves into bother. If we know what is at the bottom of the problem rather than addressing the symptoms we can address the root cause."

Researchers found there was a general sense that maths was hard compared with other subjects, which led to a loss of confidence, yet the study points out that most children with high levels of maths anxiety are normal to high achievers in the subject.

Key triggers for anxiety included poor marks, test pressures, teasing by fellow pupils and a confusing mix of teaching methods. National Sats tests taken in the final year of primary school were a cause of anxiety for some, while the transition to secondary school was challenging for others.

The children's emotional reactions included feelings of apprehension, tension, frustration or fear, while physical symptoms included butterflies, a racing heart or struggling to catch breath.

"The experiences of maths anxiety are multifaceted, with students expressing emotions from rage to despair," the report says. "Students often reported overwhelming negative emotions which in some cases led them to act out in class and be removed from the classroom, or to become tearful. Others reported that they dreaded their mathematics lessons or that physical symptoms had an impact on their ability to flourish."

It warns teachers and parents that their own anxieties about maths might have a negative influence and so urges them to tackle these first. It also urges policymakers to be conscious that emotional blocks can affect learning potential.