Mrs Paxton was a maths teacher, and later the head teacher, at Heathcroft High School.
As a maths teacher
Mrs Paxton was teaching maths at the school at the time when Noughts were first allowed into the school. She was noted for being one of the more liberal teachers, and one of the few Crosses who actually wanted Noughts in the school. When Noughts were isolated by the Crosses, she argued with the head teacher, Mr Costa, about the situation, saying that something needed to be done. She formed a bond with Callum over his enthusiasm for maths. When Callum was bullied by Mr Jason, Mrs Paxton confided to Callum that Mr Jason couldn't be against Callum, as his mother was a Nought.
As the head teacher
By the time that Callie Rose joined the school, Mrs Paxton had become the head teacher. This was apparently one of the main reasons that Sephy wanted Callie Rose to attend the school, as she remembered Mrs Paxton from her own school days. By Callie Rose's time, the school is a lot more inclusive than when her parents attended, presumably as a result of Mrs Paxton's efforts. Mrs Paxton is apparently very strict, but also fair.