I'm lucky. I teach in a great department in a great school. We have a fantastic head of department who loves maths and encourages us all to share our passion for the subject with the pupils we teach. Lessons are dynamic, engaging and purposeful: we have licence to experiment and try new ideas in the classroom. On the odd occasion that things don't go as expected, we dust ourselves off, learn from our mistakes and carry on, secure in the knowledge that it is better to have tried and failed than never to have tried at all.
Our students also know that trying and failing is fine. In fact, it's more than fine, it's essential. It is only through making mistakes that we learn, make progress and achieve.
As a staff, we share great ideas: in our weekly department meeting one of us is called upon to deliver a three-minute briefing, sharing and showcasing a new resource, idea or strategy to enhance the teaching of maths. Everyone buys in to the philosophy and everyone teaches great lessons. It's a wonderful place to work and, although the students may have many things to say about the subject, "boring" is an adjective that is rarely used.
A numbers game
Picture the scene: with two weeks until the end of the Easter term, my upper-sixth class is desperately trying to complete a module before the break so they can start revising in the holidays. This is a class that works hard but for whom maths (or A-level maths at least) does not come easily. A few students aspire to a grade C; with hard work and a following wind, they may achieve it. Some of the class are just hoping to avoid a U. They are all retaking two modules from last year and so, with exams around the corner, they are doubly busy. But it is time to teach them implicit differentiation.
I love my job, I love my department and I love its philosophy. And yet.I make a decision. I am honest about this decision and I share it with my students.
"For once, please," I ask of them, "just accept what I am going to tell you. I'm going to show you how to do something, but not explain how it works or why it works. Just do as I do and you'll be able to solve these problems in your exams, even if you don't know why."
There is a palpable sense of relief and a few students nod in agreement. This is a pragmatic bunch. They recognise that their maths A-level is a stepping stone to the next chapter of their lives. I smile back at them, happy that they have made the right decision, and suppress a pang of guilt. I am cheating them out of understanding at the expense of exam success.
We crack on and I show them how to differentiate implicitly. Soon they can all do it, tackling past exam questions and coming out on top. They are able to correctly answer the questions by adopting a formulaic approach: "First I do this, then I do that and I end up with the correct solution." The reward is the satisfaction of completing a problem - a rather difficult-looking problem - and being a step closer to a good mark.
Pragmatism v principles
When the chips were down, I abandoned my principles. I dropped my engaging and entertaining lessons and said "Do as I do". And it worked. So, does rote learning trump other approaches when needs must?
Not exactly. I did what I did out of necessity. We owe it to our students to do the very best for them; at that point, the best thing I could do was to help them achieve the very best grades. For other classes, the best thing I can do is to give them a solid understanding of the subject and hopefully share my excitement about it.
However, an interesting thing happened with that A-level class. As they encountered more implicit differentiation questions, a few of them began to formulate an understanding of why my solution worked; they asked me questions and began to grasp the reasoning behind the method. Throughout their mathematical education at this school, they have been encouraged to explore and think about the subject. This is what they did, even when they didn't need to.
As a maths teacher, I blame the English language. Unlike my subject, language is vague and open to interpretation. I think the problem lies with the word "fun".
"Maths needs to be fun!" many of its detractors cry. No, it doesn't. I'm not saying it can't be - it often is - but every lesson doesn't have to be fun. Fun then becomes the goal at the expense of the mathematics.
Maths doesn't need to be fun, it needs to be interesting. But interesting doesn't necessarily mean practical or related to the real world. Maths needs to draw pupils in and engage them. Lessons need to be purposeful: often the purpose will be to achieve the lofty goal of making pupils love maths, but sometimes the purpose will just be to help them through whatever is in front of them. Sometimes learning by rote can be the extra shove to help them over that hurdle.
As a maths teacher, I see fun lessons and rote learning as two ends of the same spectrum. Both are equally valid and both should be used when appropriate, but neither is the only way. Teaching is not black and white and there is no one-size-fits-all solution. We are professionals and every day we make professional judgements: some days that will be to teach a fun lesson, on others it will be to learn by rote, but every day should be a purposeful day. That is the way to get results.
Jeff Peabody teaches maths at Millfield School in Somerset and blogs at www.amathsteacherwrites.co.uk