The study, based on detailed questioning of 238 children in two Kent primary schools, found that girls had formed these attitudes by the time they were in reception year and that they held on to them throughout primary school.
Boys' opinions were split from reception to year two, but by the age of eight, the boys appeared to agree, saying that girls were more likely to have the right qualities to do well at school.
Children of both sexes thought that, in general, adults believe that girls do better at school than boys.
For the study, which was presented at the British Educational Research Association, children aged between four and ten were presented with a series of statements and scenarios.
These included, 'This child is really clever', 'This child always finishes their work' and 'The teacher is taking the register in class and this child sits very quietly, waiting for their name to be called out.' The children were then asked to point to a picture, in silhouette, of a boy or a girl.
The children were also asked a series of more direct questions, such as, 'Who do you think is cleverer?' and 'Who is better behaved?'
The findings highlight some difficulties that teachers may face in trying to close the gap in academic achievement between boys and girls.
Bonny Hartley, postgraduate researcher at the University of Kent's School of Psychology, who presented the research, said, 'By seven or eight years old, children of both genders believe that boys are less focused, able and successful than girls, and think that adults endorse this stereotype.
'There are signs that these expectations have the potential to become self-fulfilling in influencing children's actual conduct and achievement.'