The YouGov survey of 603 children aged eight to 11 shows 51% of boys believe they are better behaved with a male teacher - and 42% say they work harder.
At present, a large majority of teachers in England's primary schools are women with only 16% being men.
The TDA, which recruits and trains teachers, wants to see a more balanced workforce in primary schools - providing both male and female authority figures.
Currently one in 12 pupils will have gone through primary school without ever having been taught by a man.
The survey suggests male teachers can provide a positive role model for boys at primary school - and that a large majority of boys would like to have both male and female teachers in their schools.
There were indications that having male teachers could help boys' overall experience of school - with 44% agreeing that male teachers "help them to enjoy school more" and 37% of boys saying it made them feel more self-confident.
More than a quarter of boys agreed that male teachers "understand them better" and could be "relied upon for good advice".
There has been a rise in applications from men wanting to enter teacher training for primary school - up to 19% of applications - but the training agency would like to see a further increase.
