Their anxieties are laid out in a new report from the psychology department of Dundee University.
Suzanne Zeedyk, lecturer in charge of the Quality Contact programme which has worked with children, parents and teachers in the Charleston district of the city, said: "Making the move from primary to secondary is regarded as one of the most difficult . . . and success in navigating it can affect not only children's academic performance but their general sense of well-being and mental health."
The most frequently expressed concern was over bullying. But at least 10 per cent of both primary and secondary pupils singled out relationships with peers, getting lost and handling the workload. Less predictable anxieties included forgetting things, ability at sports and vaccinations. But the survey also found that a third of primary pupils identified no concerns at all. The report comments: "This may represent a show of bravado, given that a much lower proportion - 8 per cent - of secondary students endorsed that view."
The Quality Contact programme's work on primary-secondary transfer is one of few practical long-term studies made worldwide. "While teachers identified relationships with classmates and fears of bullying they made no mention of pupils' other concerns ranging from getting lost to worries about vaccinations," Dr Zeedyk said.
She added: "If even a few pupils worry about an issue it should be included in the support programmes which many high schools already run to ease the transition."
Dr Zeedyk was concerned to find that teachers in the survey rarely referred to a wide range of personal skills such as listening, talking and accepting criticism which pupils and their parents felt were important. "Does this indicate that teachers are less likely to think in terms of developing children's own coping skills than in making them conform to existing school structures?"
Marjie Henderson, Quality Contact development officer, said: "It is important that children are themselves empowered to cope with stress, so that they have a greater sense of control over their own lives and experiences."
Parents and pupils wanted familiarisation visits to secondary schools to take place throughout the whole of primary 7 rather than as at present generally lasting only a single day.
Dr Zeedyk concluded: "Although it is encouraging that two-thirds of secondary pupils state that high school is better than they expected, a majority still experience some degree of concern well into first year. This anxiety needs to be taken seriously. Transition programmes need to be flexible to ensure individual concerns can be discovered and dealt with."