Multiplication – the privilege of mathematical thinking

7 min read

I love John Mason. It is always a pleasure to listen to him as he takes you with him through his exploration of mathematical thinking and learning: “sit there and close your eyes and imagine a number line…” He takes you on a journey of ideas, connections and new understandings of the relationships between concepts and ideas in mathematics.

This evening we explored multiplication in the Faculty of Education.

But it is not the wonderful session that I want to talk about. It is my theme of not Mathematics Education (nME). A kind of meta- hyper- mathematics education. I mentioned to John that I was interested in nMEHe looked puzzled, but not dismissive, John is always interested in thinking. I talked about how we had been through a period of relative stability in mathematics education research (I was talking about neo-liberalism). It is the liberalism that it is important in mathematics education research, it allows the freedom of thought and builds on the constructivism following Piaget and Vygotsky: constructing worlds of meaning and mathematical imaginaries as part of the process of learning (and doing) mathematics. It is the neo– in neo-liberalism that has contributed to deepening inequality in the last forty years.

Neo-liberalism, while it indulges some in this kind of constructivist thinking, it is for those, primarily, who have the time and luxury to indulge. If you want a sense of the mathematical indulgence that is associated with social class read G H Hardy’s Mathematician’s Apology. It is an apology for the fact that his position, wealth and privilege gave him access to think about pure mathematics. Wonderful things ensue, of course – the contribution of pure mathematics is without any doubt. Hardy explains how the pursuit of mathematics for its own sake and without purpose often leads to useful applications. It is the pursuit for no particular purpose that makes pure mathematics productive. But it is, in the context of liberal economics with its implicit utilitarianism, limited to a selected elite.

“Ah!” You say, “mathematics is meritocratic, it is blind to socio-economic status, class or even background.”

Well, no it isn’t, the fact that some children from disadvantaged backgrounds get to study mathematics at top universities insufficient to support this claim. Disadvantage children who progress to study mathematics in leading universities generally have a combination of talent, some luck and often or not a great deal of support. Sadly, there is often an unspoken appeal to competition or even social Darwinism: surely it is a fitting way to select the best. Probably not: the top universities’ mathematics departments are by-and-large filled with students who are from middle class or privileged backgrounds.

Let me explain why this (and I can go back to John Mason’s talk for this). Clear your minds – imagine a number line. Now imagine that number line is an elastic band. Stretch it out to three times its length, on what number would the original ‘4’ be. This is the basis of mathematics learning – of rich deep and agile mathematical thinking in which we explore concepts and relationships.

Now imagine that you are 13 years-old, you have one parent. They may be in precarious, low paid work, they may be struggling with their mental health because of debts. They may be struggling with alcohol, they might be worrying about paying the rent or getting evicted. You might live on a road where families face all sorts of difficulties in work and in keeping a roof over their heads. A community working and living precariously. You might have been pushed out of the shiny academy because you are distracted and can’t follow the strict and daunting behaviour policy. Your school is facing problems because there are lots of kids like you facing challenges, the teachers are tired and stressed. They haven’t got the patience for the kind of stuff John is doing. They love it, they love what he does. But they are so so tired. Even if they can, there is lots going on in your head, even your loving parent can’t shield you from their own or even the community’s anxiety and deepening sense of hopelessness.

Now tell me how you are going to shut all this out  – this noise – and imagine your number line, even if you have a patient, thoughtful, energetic teacher. How do you stand a real chance? You don’t, it is a lottery for those from disadvantaged backgrounds.

Just before John began his talk, he mentioned the work he had been doing with Cambridge Maths, an initiative run by Cambridge Assessment to develop curriculum. There is no doubt that they are doing wonderful things. I reminded John of Cambridge Assessment’s primary purpose as an arm of the University of Cambridge, in a political and economic climate where the University can’t rely on public funding. Cambridge Assessment is about making money and it follows that Cambridge Maths will have to contribute at some stage. John agreed but argued that any opportunity to develop mathematics education must be taken. He was about to start his wonderful talk and I couldn’t make the following and my final point.

If we really want to make mathematics universal and allow all to indulge in the rich thinking that the study of mathematics promotes, then we have to – we must – start to think critically about it. That is ‘critically’ in the sense of what is driving the agenda: things that are not Mathematics Education – things like political economy. We cannot (must not) put mathematics education in a bubble insulated from political economy. Neo-liberalism fabricates and manufactures consent for economic scarcity (reducing public sector deficits). The consequence is that mathematics education research and development necessarily has to rely on markets and private finance. It is not any-port-in-a-storm to sustain research and development projects; by not resisting we are complicit in the political economy of neoliberalism. If we want universal access to mathematical thinking and a mathematics education for all, then we need to fight for public investment in research and education. We need to campaign against the meanness of economic policy that has marginalised so many and left them without the basic quality of life that creates barriers to the wonderful mathematical journeys that John Mason takes us on.



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