The academics looked at the test scores of more than 10,000 eight- and nine-year-olds, and compared them with the scores parents had given when asked to estimate their children's academic ability and achievement.
"Ensuring that parents are knowledgeable about their children's academic skills is important if parents are to effectively assist their children at home with schoolwork," the researchers say in the report. "Parents who are more knowledgeable about their children's abilities interact more sensitively with their children, and provide more appropriate learning environments."
The study finds that parents form impressions of their children's abilities in a range of ways. Some work with their offspring at home or meet teachers on a regular basis to discuss progress. Others offer to work as classroom assistants, in order to see first-hand how their children and others perform.
The study shows that, on average, parents' ratings of their children's abilities are only moderately related to actual test scores. Sixty-seven per cent think their children are higher-achieving than their peers in reading and maths, which would be statistically impossible.
"These findings suggest a need to improve parents' knowledge of their children's academic competencies, in order that they may more effectively assist their children," the researchers say.
Students from higher-income families are more likely to have parents with a clear idea of their academic ability, the study shows. Parents with lower incomes are less likely to be actively involved with schoolwork at home or in the classroom. As a result, they have a limited sense of their children's ability.
But parents who regularly speak to teachers have a much better idea of their children's true skills than those who merely help them with schoolwork at home. Those who work as classroom assistants are particularly well-informed.
"In the classroom, parents can see instructional processes, see their children's performance relative to others and get suggestions from teachers," the academics say. "Parents may need more explicit guidance when interacting at home to infer correct information about their children's academic skills."
But Russell Hobby, general secretary of the NAHT headteachers' union in the UK, does not believe there will be a huge rush of parental applications for teaching assistant posts.
"I don't think many parents have the time to do that," he said. "And I don't think many schools have the money to afford it. But schools do need to get better at thinking about how they communicate pupils' achievements to parents - getting people in for extended conversations. There are other ways you can get parents to see what's happening."