A few annoyances with Maths education in the UK, that I would like to change, wherever possible if I were a Head of Department or higher.
The biggest annoyance is the amount of tricks that are taught in place of proper understanding. “But two negatives make a positive sir!” “To divide by a fraction, leave, change, flip.” Unfortunately, I was guilty of this earlier in my career, as I wanted the students to remember methods by any means possible. Perhaps this is down to the lack of Maths specialists at primary level, but I see no solution to that when there is a recruitment and retention crisis for Maths teachers at secondary level. I am now teaching these topics completely differently to how I once did, and using the statements above as a plenary of when, how and why do they work.
All these tricks come as a bi-product of a bizarre system where we teach lots of topics with discrete methods. I believe that we should be looking for more links, teaching fewer methods and a better understanding of how these methods can be used in different situations. A few examples of this are multiplicative reasoning for all areas of proportion. We can use the same method for percentages, direct proportion, ratio, converting between units, compound units etc. (Thanks to the excellent Don Steward for that one). Prime factorisation for cancelling fractions, and possibly division, can also help when moving on to algebraic fractions. Teach dividing fractions as the inverse of multiplying fractions, rather than a trick that works but doesn’t make complete sense to learners.
So what shapes the way new teachers teach? Their ITT mentors, teachers in their training schools and teachers in their department. How many come in with their own vision? How many come in thinking about how they are going to teach negative numbers in a way that pupils are going to understand? How many are influenced by teachers who themselves are willing to do these things? Where is the innovation coming from if they are recycling the ideas and thoughts of established teachers. I think that it can be even worse for new teachers now, as the extra pressures of results because of performance related pay lead to more short-term thinking.
This brilliant article by Matthew Syed should be read by all teachers, particularly new teachers. If I was a Head of Department or higher, this would be my starting point for all discussions with staff. Do you want to get good results or make good mathematicians? Surely if more energy is focused on making good mathematicians, the results will come naturally.