Dr Carter has devised four groups displaying similar traits as a guide for teachers: "worriers", "butterflies", "self-confident professionals" and "socialites".
The worriers tend to be girls, she said, who panic about getting their work finished. In contrast, the butterflies are predominantly male, middle-class pupils who lack concentration and fail to finish set tasks.
She says the worriers should be reassured and praised. The butterflies should be set work in small groups to aid concentration and be given small, achievable tasks.
The self-confident professionals are generally highly motivated and know what to do and how to do it. But Dr Carter warns that they are the best at undermining a teacher's confidence and need rich stimuli in lessons to keep them busy. They need to have their complacency challenged, she said.
Finally, the socialites are, as their name suggests, the pupils who regard school chiefly as somewhere to meet their friends. "They are the ones who come back to school even after you have excluded them," Dr Carter said.
"They think lessons get in the way of their real purpose for being there."
Dr Carter, who admits she was a worrier as a pupil, insists that the categories are not designed to make teachers stereotype their students.
Instead, she says, they can help teachers adapt their styles. "It's a matter of recognising that able pupils are not a homogeneous group, but diverse in nature and personality," she said.
The academic's theories met with raised eyebrows when she outlined them to heads at a conference of the National Grammar Schools Association last month.
But Diane Woods, head of Queen Mary's high school in Walsall, said she felt the categories were accurate. "All schools have their socialites, for whom lessons are an unwelcome distraction from their social lives," she said.