But the 53-year-old decided against quitting teaching altogether when the injury made his old job impossible two years ago.
Instead he began teaching maths and has now become one of the first to be accepted on to an intensive "conversion" course for teachers without maths as a specialism.
The Mathematics Development Programme for Teachers was introduced as a response to the 2004 Adrian Smith review, which highlighted the dearth of quality maths teachers.
Mr Bills-Brown, of Bridgnorth endowed school in Shropshire, said he hoped the course would improve his ability to teach using technology. "I dreaded the thought of not teaching PE at first, but realised maths was another subject I could enjoy teaching," he said.
"I did maths at A-level and studied it alongside PE for my degree, but ICT is an area I feel I could improve on and it is such a big thing in maths teaching now. I'm really enjoying the challenge and looking forward to the training."
Government targets for recruitment on to maths PGCEs have not been met for the past 10 years.
Brighton, Liverpool Hope and Wolverhampton universities are recruiting for the conversion scheme, which will start in June and July. Recruiters are sifting through applications from teachers from a wide range of backgrounds.
From October, the Training and Development Agency for Schools will offer similar courses for non-specialist teachers of physics and chemistry.
Mr Bills-Brown will attend a five-day assessment in June and the course will then be structured to his needs. Depending on subject knowledge and teaching skills, participants will attend up to 40 days over the course of a year. If the scheme goes well, the TDA said it could be introduced nationally in 2009.