I saw this blog from Tom Bennett on tes and it really caught my interest. I’m a firm believer in the idea that the best teachers have the best subject knowledge, I can’t accept the idea that someone who doesn’t have excellent subject knowledge can truly inspire a top set in their subject.
My route into maths teaching was straight from completion of a four year undergraduate masters in maths, onto a secondary maths PGCE. My subject knowledge is excellent, this may sound somewhat arrogant but I’d question any teacher who couldn’t say the same, as a minimum every teacher should have good sound subject knowledge.
I quickly managed to get a reputation in my current department as a super maths geek, and I love it, I play on it constantly and wear it with pride. I wouldn’t change this opinion of me that my colleagues and the students as well have, I don’t get why a teacher wouldn’t want to be known to be passionate about their subject.
Similarly to Tom’s blog however, the assumption was clear on my PGCE that subject knowledge wasn’t something that would actively be scrutinised. Clearly any inadequacies would be identified, but that was it and only through observations, there was the expectation that placement schools would identify and sort out subject knowledge. A simple subject knowledge check was done by the university, but it had no real substance and looking back I can see how little it actually meant. Same goes for teaching once you are qualified, except in a few 20-30 minute snapshot observations, when was your subject knowledge actually checked?
Having spent a number of years teaching I have come to realise the importance of real subject knowledge in maths, especially for the top set and the most able. The idea of a teacher being “one page ahead” is a somewhat frightening concept for someone teaching the best students.
Take my year 10 top set for example, so far this year we have covered vectors, quadratic formula/completing the square, sine/cosine rules, transformations of graphs and algebraic proof. These are some of the most challenging topics on the GCSE yet I know that a select few of my students will find most of that fairly straightforward were I to use typical exam questions as the end game. To stretch them I needed to go beyond what an exam would typically examine and if I didn’t possess subject knowledge beyond the GCSE specification this wouldn’t be possible.
Every topic in maths links to almost everything else as you take topics further and the beauty in maths is that the best will start to see this and unlock even more, I take my hat off to William Emeny for producing this masterpiece of visualisation.
To unlock this a teacher must know how every topic starts from the basics up to and above what is required at each level. The progression through each topic is key to leading students from start to finish in each topic, particularly when the end game is the very top.
You need to approach a top set with almost limitless ambition for them; these are the best kids and they are the ones you should be looking to inspire to take your subject further. In maths they will make leaps you can’t predict and if given the chance will surprise the hell out of you with their ability, some will seem to just absorb skills and understanding like a sponge.
Anyone who is trying to stay a few steps ahead of a class in maths will get found out. Quickly with able students. The real challenge for the most able shouldn’t be how quickly they can get through material and how far they can get, the challenge should be how deeply can students understand what they are doing. For a teacher to really excel with the best students they need to know their stuff inside out, back to front and well beyond what the specification requires.
For maths this doesn’t come from endlessly repeating and analysing topics; there is limited benefit to true subject knowledge in maths by repeated study of a topic. It may prepare you for any exam question that may be asked, but does that actually mean anything?
To really understand a topic in maths I believe you need to go (much) further and then drop back down to truly appreciate what a topic is all about. I found this during almost every module at university, and looking further back applied to A-level modules as well.
A significant proportion of the PGCE students in my cohort came through a subject knowledge booster course the previous year. Are these people ideally suited to teaching the best students? Debatable. Quite a lot very perfectly capable at GCSE level maths, but A-level was another matter.
When it came to finding a job for the following year we inevitably shared interview experiences and not one mentioned a subject knowledge question. I asked for advice from the head of maths at the school I was placed in and he said he would always ask a subject knowledge question and actually get the candidates to answer it. Why is subject knowledge normally assumed to be sound?
For those who are lucky enough to teach the very best at maths, I’m sure you have encountered that student who possesses more natural ability than you do, or at least possess a seemingly limitless ability to absorb knowledge. For anyone who isn’t equipped with subject knowledge above and beyond what is normally called for will fail that student. An A* is a grade, not a true indication of a students understanding of a subject. Some students will not find reaching the A* standard challenging in maths.
What to do
Putting a teacher’s subject knowledge to the test is simple: test them. How many members of your department actually do the exam papers that you set students? Now consider what they would actually get, how many would ace the exam? How many could?
Any maths teacher who can’t complete a GCSE higher paper easily under an hour and with almost zero mistakes doesn’t have good enough subject knowledge.
With the advent of the new GCSEs this brings subject knowledge to the fore; particularly for anyone who only teaches 11-16 as they potentially haven’t taught some topics at all. How many of your department would ace the new specification sample papers without needing to look anything up?
When they were released I sat down and did them, and I know quite a few others I follow on twitter did the same. I was surprised by some questions and really quite enjoyed doing them (really helping my maths geek tag I know). What I did learn though was that there was a lot to be gained by doing these as a department as a learning experience and I’m waiting to see how well this goes down in the near future.
How can a teacher be expected to teach something they can’t do themselves (with ease I might add)?