It’s taken awhile but I’ve concluded school mathematics comes at problem solving from arithmetic/algebra. The subject of problems for most of us is not mathematics, that’s just a tool to evaluate expressions we formulate in terms of the elements of the problem itself. It is this front-end of problem solving that is creative and difficult. I suggest an approach to solution expression formulation in recent posts to my blog.

From what I can tell school mathematics is pretty much a world unto itself; the rewards for teaching it must come from within the system itself. It is easy to understand frustration felt by those seeking to make a difference for students in the world beyond school. I have two suggestions: (1) Make connections with the problem solving world, and look beyond the mathematicians and cognitive scientists; it’s the subject matter not the methodology. (2) Look for ways problem solving can help you teach. How can you expect students to see any good in what you teach them when you haven’t?. This is not a teach-by-the-numbers thing; it is using quantitative thinking to get at what you want your teaching to be.

Math has it tough as a subject because it straddles both worlds, the creative and the applicable. I suppose this is true about every subject to some degree. But with math, the divide is more apparent because the two ends of the spectrum are so far apart: there is little more creative or useful as mathematics.

So, do we teach math like we do art, or do we teach it like we do physics? I struggle with this often. I suppose others do, too, even if its subconsciously. Personally I sit on the ‘pure’ end of the spectrum. I see relevance in the beauty of math without needing any application for it. If I’m not careful, my math class turns into something more like an art class. I have to make a conscious effort to bring in the applications to show math is useful for things.

There really should be two synergistic strands of math class. That’s hard to do with one teacher and one course though. Instead we tend to find one blend and sit there …and its often at our comfort level or personal preference.

While I certainly use social justice aspects in my classroom (we’re doing a concussion study today using angular velocity, and later this year I have planned a density lesson using neighborhood segregation) I feel uncomfortable with the standpoint that math has no inherent social justice in itself.

It does, and I might recommend the book _Radical Equations_ which is the first place I learned of the standpoint that algebra in itself is social justice. That is, providing stronger mathematical background opens opportunities, and denying that opportunity (deciding that perhaps they don’t need to learn the Pythagorean Theorem, say) passes some judgement about what they are capable of in life.

Once forced to do something, I am with you on asking why it should be this or that and not something else. However, it is also the case that applications or uses of mathematics in socially relevant contexts tends to dwell in arithmetic, and not to encounter mathematics.

For example, as a customer, you want to know what something will cost. But as an entrepreneur you need to have a policy so that different customers are treated fairly. Such a policy is essentially algebra. it is a statement of generality.

For example, if you want people to be able to challenge what politicians say and do, you need to instantiate their generalities and ask yourself whether they are reasonable, equitable, etc. This involves specialising or instantiating generalities.

If you want people to be able to think coherently about proposals (such as the EU, but also such as building houses, a high speed rail link, a new football stadium etc.) then they ned to be able to challenge the modelling assumptions. This requires being aware of structural relationships, which is what mathematics can offer (as does physics, but in a mathematical way).

I am particularly concerned that the EU debate is content free; people simply assert things and then claim the other side’s assertions are wrong. This shows tremendous disrespect for voters.

So working on socially relevant issues is valuable. But ‘relevance to me’ means, ‘real to me’, and as the RMP project has shown, well as it has confirmed what has been known for ever such a long time, what can be real to someone has to do with what they can imagine, can grow to imagine, and is not confined to what they already do every day.

So the weakness in your stance is, I think, that while promoting social awareness of inequality etc., that your language can be taken to mean ‘relevance’ is what people already do day by day, and that, I think, will condemn people to not discovering ways of thinking that open up possibilities for them, whether through social critique or through finding fulfilling work.

But I would argue that these skills are not specific to maths, and could be gained whilst also studying something more directly relevant to the majority of the lives our students will live.

I don’t think that there is a great deal of value for many people in many of the mathematical concepts we teach at school. I could write a long list of irrelevant-unless-you-want-to-be-a-scientist subjects that every child must study until they leave school. Pythagoras Theorem – why? Simultaneous equations – why? Prime numbers – why? Is it enough to say ‘because they are interesting/beautiful?’ I don’t think so. Is it enough to say because they allow us to puzzle and become resilient? I don’t think so – other more relevant endeavours could fulfil these criteria.

If everyone really has to study maths to 16/18 (but again, I ask why?), then at least *try* to demonstrate how it might be meaningful when placed in context. Can we not at least *try* to place it in contexts that will at least have some impact on children’s lives – and yes, I am talking exactly about what you mention: social justice, racism, sexism, poverty, inequality, psychology, … – contributing to our children’s awareness of the society they live in.

So what if children don’t learn Pythagoras’ Theorem if they learn instead how to analyse the data that tells us that people in the UK lost £5bn gambling in 2015, and that they majority of those who gamble, and the majority of betting shops, are in the poorest areas. And so what if they can’t reproduce this knowledge in an exam because they got too interested in the context?

So what if they don’t learn how to solve simultaneous equations if they learn how to interpret the graph that shows that the UK government is reducing the living standards for the poorest people in the UK and improving the living standards for the richest 10%?

This is not to say that I don’t think maths-in-itself is not valuable, or interesting *for some*. I just don’t think we should expect all students to be interested in maths-in-itself – we should accept that it is only for some (me and you?), and allow others to opt out if they wish.

And why is it *not* OK to be *not* a maths person? Why does everyone have to be a maths person? This is very odd – it seems OK that people are allowed to not be sociologist people, or philosopher people, or even be politically aware, but every child should be maths person…?? I say we as maths educators should either accept that maths is not for everyone, or try a bit harder to make it more relevant.

To piggy back on @michael’s comment (#6) reasoning, perseverance, problem solving and student’s opinion about their abilities to engage in these activities are socially important. These abilities and students opinions about them do not exist in a vacuum separate from the student’s conception of their self. I’m not saying that every student needs to pursue an advanced math degree and become a research mathematician, but if we could rid students of the ‘I-am-not-a-math-person’ mentality and give them the confidence to reason and engage in mathematical activities a little bit at a time, then the work has importance to the student when they leave our room.