I recently withdrew from a maths PhD to focus on other career options, and one of them that I'm very keen on is mathematics teaching.
I applied for a college A-level maths lecturer role (teaching students aged 16-18), in which I had to do a 20 minute micro-teach session, some exam questions and answer some interview questions about my general attitude and ethos to teaching. I wasn't offered the job but I was offered a very appealing teacher training opportunity which would allow me to train with the college and get a PGCE/CertEd at heavily reduced costs, a generous government bursary, and take part in guaranteed hours of teaching the A-levels partially due to needing to cover for a teacher who is going on maternity leave.
In the education system in the UK, students are very heavily tested and so there is a large tendency for teachers to get students through exams, more so than actually teaching the subject in a more general context. I know that as a college teacher I won't be able to reinvent the wheel with the education system in this country, and I may be pressured into solely focusing on getting good marks out of the students, but I would like to take steps in order to make my maths lessons engaging, rigorous and fulfilling.
Can someone suggest some ways in which I can teach a standard A-level course in a way that allows students to succeed in their exams, but also making it unique and exciting, and without diluting on the mathematical rigour?