*know*that what they are saying is true. I see it every day when I teach trig to a desperately bored class. I

*feel*that students have missed the point when they are pleased that they can now apply the quadratic formula properly.

Now don't get me wrong, I try to remedy this, and (I hope) I'm improving my teaching towards this end all the time. I don't just tell pupils about mean, median and mode and expect them to remember. I give them problems like this one, that lend themselves to the different averages and play around with the numbers. We create a need for more than one average. I love the WCYDWT model for its multiple entry points, which is a neat way to give interesting problems to people not in the top set. However, I have never felt that I can stray too far from the standard teaching model or the standard curriculum. Why? Well this is what the school, my head of department, parents and pupils expect from me. They want 'exam readiness', they want regular standardised tests, etc. Maybe I just feel insecure as a first-year teacher, but I honestly don't think I could keep my job if I tried to teach maths differently. In fact, I've never been in a school that I think would employ a teacher like this.

All this when so much in my school is ripe for this style. For one, this is the first school I've been to where the maths teachers actually enjoy doing maths. We regularly have discussions about UKMT maths challenge questions, project euler, or interesting textbook questions (yes they do exist, though you have to do the further maths A level to get to them). We have books like 'What is mathematics' lying around that are actually read. Also, our pupils are bright and I mean

*really*bright. Their grasp of language alone is so good that most can make fairly convincing arguments in their first year.

So here are the questions that will be going round in my head for God knows how long:

- Will I ever be able to teach my pupils in this way, without meaningless definitions and magic formulas? How?
- How can I convince others that this is a good idea?
- How can I become good at it without really being able to practice and have no other experience than reading about it online?