# Decagons inside decagons inside…

Two ways to make decagons inside decagons.

# A response to ‘secret teacher’

I sighed, once again, when I opened my laptop this morning and found this new article from ‘secret teacher’ (a blog from various teachers wanting to bemoan the state of UK education each week under a veil of anonymity). This week it’s about how maths is useless, and how students will never use it, and how mean it is to put them through such awful stress and… and Pythagoras?! Who needs that, right? Who’s with me! (*cheers from the masses*).

Well, here’s the thing:

I’ll never use this in my life

Probably correct. And by pretending otherwise you’re being a fool. Any maths teacher who is still relying on the “oh but you might need algebra when you’re in the supermarket… and if you need to rearrange your furniture you could use Pythagoras” is completely missing the point of mathematics, and is completely confusing being numerate (which is, let’s be honest, quite important and you probably rely on numeracy skills every day)  with being a mathematician. Whilst the article points out numeracy is important, the author doesn’t quite make the connection that mathematics isn’t numeracy and isn’t intended to be. Numeracy is a pre-requisite, like having a p.e. kit to do p.e.

Furthermore, you’re convincing no-one with these terrible examples of ‘real maths’, because what you’re saying simply isn’t true and you know it. It’ll only make people think the subject is even more useless than before, because you can’t convince them otherwise.

This is not a unique argument for mathematics. Far, far from it. Have I ever needed to talk about tectonic plates in my life? Noop. Have I ever needed to discuss the history of castles or the victorians since I was 14? Hmm, also… no. Have I ever discussed the composition of language in a critical essay about Shakespeare in the last 20 years? Yes! All the time. No wait, I mean no. No I haven’t. I could go on, but I’m pretty sure I haven’t used almost all the explicit facts I learned at school since I left, apart from the specific things that apply to the job I pursued, and the key skills underlying the things I studied. Do I feel angry about learning the other things? No. Why? Well, ask yourself what the alternative is.

I need to learn things that are relevant

Don’t you see how problematic that is? Define relevant. Now get the person sat next to you (come on, let’s have a group activity! They work well) to define it in their terms. Do you get the same answer? Probably not. Hmm, let’s fix this and send each of you into two different classes so that you can get your bespoke curriculum taught to you individually. Oh there’s 30 of you. M’kay, we’ll just get some more teachers in. Oh you want to change your future career now, 4 years into your bespoke curriculum? Oh dear, we didn’t plan for that. The curriculum is intended to be broad. It is intended to accomodate a little bit of everyone’s interests, and keep the doors open. It isn’t intended to be a tick-list of everyday skills we need. The curriculum carries more cultural weight than that. Tom Bennett explains the crux of the argument very clearly:

“we teach because we are helping children to inherit their intellectual heritage, the pearls and rubies of science, art, the humanities.”

And yes, maths is very relevant to some careers

Not your career? No problem. Move along, but don’t forget to say thankyou to your teachers and school for enabling you to decide upon a career path, rather than carve one or two options out for you from the age of eleven.

Why always me?

Every time this debate rises up from the ashes like a sulky teenage phoenix, it inevitably involves mathematics rather than any other subject. Mathematics is difficult and abstract, so it’s great fun to poke it with a stick. Funnily enough, I find the students who struggle with maths to be the ones who declare it as useless and pointless. Shocker. Art teachers find the students who can’t draw well don’t like their subject either. PE teachers find the students who don’t exercise dislike their subject too. Mathematics is at the front of the bashing line because it’s hard, and sadly it’s often taught procedurally, without allowing time to disect why things work to make sense of it all (as Ofsted and Nick Gibb are often so keen to remind us).

This leads onto the points made in the Guardian article that are actually interesting and worth pursuing, but get lost in the stupid:

Mathematics is compulsory

Does it need to be? If we take away politics, and assume everyone is numerate by 11 or 12, do we need everyone to study it? Why? Why are certain subjects compulsory and others not? That’s an interesting debate to be had.

Mathematics results are “important”

More so than any other subject bar English. Why is that? How has that come about and what would the implications be if the setup was different? That’s an interesting debate to be had.

Mathematics is swamping the curriculum

With increased emphasis on maths, it is inevitably taking up more curriculum time at the expense of other subjects. There’s an interesting debate to be had there too.

I’m going to go and eat some toast now.

If a student asks you “what’s the point in studying maths?”, don’t patronise them with nonsense about supermarkets and taxes. Have a real discussion about it if you want, but it boils down to this: “I’m making you smarter”.

# An interview

I recently was invited to be interviewed for Craig Barton’s maths podcast (Craig is the maths adviser for the TES). We covered lots about how I teach maths to my students, and my approaches to training maths teachers.

You can listen to the interview here.

# Why anecdotal evidence matters

I’ve recently had a couple of conversations with a few people about the need to take anecdotal evidence in teaching a little more seriously. I thought I’d share my reasoning here.There are a lot of buzz words and fads in education. Flipped learning, thinking hats, learning styles, the unforgivably aggresive red marking pen, educating the ‘whole child’, and so forth.

A lot of the fads that catch on often stem from published research – as you’d probably expect. Someone somewhere investigates something, finds a valuable insight / result, and shares it with the world. Growth mindset for example, has some pretty solid research behind it, and (cruicially) has had similar results from different researchers. However, as with all things education, the idea behind it seems to get whittled down to an actionable 5 word poster “the power of not yet” or some such, which detracts from the ways in which growth mindset is most effective – as part of an ensemble of approaches that fundamentally includes good teaching and formative assessment, alongside psychological motivation strategies.

On the other hand, often fairly poor research gets through the net, and ends up being picked up and hung on the mantlepiece as gospel. Thinking hats for example, are built upon a kind of ‘inside job’ research, and the outcomes conveniently benefit the research stakeholders. Group work research almost always includes caveats about how to make it work ‘best’ such as having pre-trained the students several times over, or comparing the outcome with that of a class where a feral dog has been let loose (“the results showed a marked improvement … it was the group work… not the dog”).

Often research is based around a tiny sample of just a single class (or half a class!).

An extreme example is this awful nonsense:

inspired by this ‘sound research

which upon close inspection reveals painfully poor practice:

Yes, six participants informed an entire legacy of bullshit strategy for learning times tables, which continues to make money. The researcher was a masters student. I could go on.

Anyway, back to anecdotal evidence. If you ask teachers about how successful group work (for example) has been for them, many will tell you it sucks. Many will tell you that it works badly most of the time, and that it relies on too many variables to be successful. This is anecdotal evidence. It’s not founded on any academic research, but it is voiced by many people ‘on the ground’, doing the job.

Who would you side with? The research into a handful of groups, or a few hundred teachers who each have 7 or 8 classes several times a week, year after year? Follow blogs, listen to teachers who are still teaching the dreaded 5 back-to-back lessons a day. They’re the ones who will help you survive teaching and its fads. They’re the ones who can put research to the test. Scrutinise what you’re told. Some research is excellent, and should be persued with an open mind. Some isn’t, and should be buried in the dirt.