What is the permissibility regarding a woman teaching a primary school class of 10-11 year old boys in an Islamic primary school?

The class is a mixed class of girls and boys aged 10 to 11.

If it isn't permissible for the male and female children to mix, what is it that makes it permissible for a female teacher to mix with the male students?

Please note there will not be a screen.

To the best of my knowledge there is nothing wrong with a female teacher teaching males provided the principles and guidelines of the Shari’ah are observed. Some of the great scholars had female teachers and in that list I believe there is Imaam Maalik.

The mixing of the boys and girls is not permitted as the fitnah which results from that is greater. Since it is an Islamic school they should separate the boys from the girls.

As for the second part of your question, the important requirement is the observance of the hijab and the Islamic etiquettes. If that is present then it is not called mixing. If these requirements are missing then it won’t be permissible. The male and female children are not to mix because they are of the same age and there is a high risk for fitnah and this is a bit different if there is one teacher and a group of students who are of the same gender.[1]

Reference:

[1] http://islamqa.info/en/1200