As happens so often these days, I find myself either taking part in or following various discussions online about the nature of the teaching of my subject, that a few days later begin to tie together in my mind as I reflect on how I approach the teaching of Mathematics and the learning I want to see happening in my classroom.
The Secret Teacher article in the Guardian a while ago bemoaned the majority of the content in the Mathematics GCSE, complaining that so much of it will “never be used again.” Indeed “When am I going to use this, Sir?” is an all-too familiar refrain in Maths classrooms across the country, and I would imagine the world. In some cases, it is very easy to provide an answer, and with functional Mathematics, we can easily provide an answer to these problems – percentages are placed easily into contexts surrounding interest rates, discounts, margins etc, Pythagoras’ Theorem can be used to prove right-angles in carpentry, and so on. However, I don’t believe that we should feel as though we have to justify everything we teach with a concrete context for everything we teach.
It dismays me that articles are being written by teachers who work in classrooms that seem to echo the argument of a disinterested, apathetic 14 year old student. My response to reading this article is therefore the exact same argument my students get when they ask what the point is of a learning particular topic; the point of a wide–ranging curriculum is to equip those leaving to follow whatever path they follow after their education or career, ready to take their understanding to the next level, and adapted to the ways in which it needs to be applied for this path – whether that’s working in actuarial offices, architectural work, or in astronomical physics. While those who argue passionately against grammar schools quite correctly suggest that it is very wrong to decide on the future of a human being at the age of 11, by deciding what to teach based on some idea of what will be “useful and relevant” to these pupils in the future we run the risk of doing exactly the same thing. The paths of our future are not mapped out when we are 11, 12, 13 or 14 – it is incredibly important to keep those doors open.
As I mentioned at the beginning, and as Greg Ashman points out, the use of contexts often serves only to justify why we bother studying each individual aspect of Maths, rather than serving to illustrate what a fantastically interesting subject Mathematics is in its own right. I don’t enjoy Mathematics when I’m using it in the mundane, everyday situations that crop up when I’m applying for a mortgage, or figuring out whether I can afford my next guitar. I enjoy it most when I’m solving problems involving proofs, or geometric diagrams, that require me to think and struggle. Whilst I understand the naiveté of expecting all students to find the same enjoyment in ‘pointless’ Mathematical tasks, or ‘Maths for Leisure,’ I believe that the more we attempt to shoehorn in contexts to justify our existence as Secondary Mathematics teachers, we devalue to richness and beauty that provides us with the enjoyment in the subject we love to teach.
I can see a creeping ‘fetishisation’ of the explicit teaching of “Problem Solving,” mainly as a result of the new GCSE. However, the problem I have with this phrase is that it somehow seems to detach the application of Mathematics from the concepts learned, and is heavily tied in with the ‘contextualisation’ of the Mathematics we teach. “Problem Solving” therefore becomes conflated with real-life application, which I think misses the point of what and why we are teaching Mathematics.
Furthermore, we end up with what Dan Meyer refers to as “pseudo-contexts”; contextually applied problems within situations that bear no real semblance to every day life. The much maligned “Hannah’s sweets” question from the Edexcel GCSE Paper in 2014 is a perfect example of a probability question that is mathematically sound, but is trying so hard to exist as a “real-life” application that it ends up being anything but. In fact, I believe that this obsession with contexts and functionality serves only to devalue Mathematics as a subject, as it reduces it merely to a set of tools. Furthermore, having spent so long trying to justify every topic that you teach, it will be a genuinely struggle to pull back a class when you struggle to find to find that ‘real-world application’ for a particular topic.
This devaluation of our subjects was the central theme in a conversation I found myself in with a number of Twitter users recently, including Barry Smith of the fashionable-to-malign Michela School in Brent, known for, and proud of, its no-fad, traditional teaching methods and expectations. As we talked about the way in which teaching has slipped further and further towards an expectation of ‘edutainment,’ it became increasingly clear that I want the positive feelings in my classroom to come from a sense of accomplishment in students finally getting their heads round a concept that until that point had made little sense, or breaking through a problem that had seemed previously insurmountable. I want my classroom to be one where knowledge and understanding is not only valued, but actively sought, rather than hidden behind a series of games.
This is where it all tied together for me. Maths is an incredible subject, without trying to shoehorn it into contexts that in reality serve only to further demotivation and a lack of interest. It doesn’t need to be hidden behind pseudo-contexts or fads in the name of “engagement” or ‘functional problem-solving.” Understanding and successful application need to be considered rewards in themselves, and this needs to be modeled and communicated to students. Think of those moments in your Maths teaching life, and previously, where something has just worked, and made you feel either quietly proud, or caused you to gasp in excitement. Now imagine if the 180 students that you teach each week saw that as the main aim of anything they are taught by you. Embrace Mathematics, and the amazing feeling of things clicking into place.
I try to make sure my students receive this impression, and it was lovely to hear from the parent of a Year 7 this week that her daughter is really enjoying Maths with me so far – “she thinks you’re really enthusiastic!” Enthusiasm for me doesn’t come from delivery of mundane, utilitarian concepts – it comes from sharing my knowledge and understanding of a subject that I think can enrich and create critical thinkers and problem solvers of our students if we don’t reduce it to merely a tool needed to get by.