Through others we become ourselves.

Lev S. Vygotsky

This is a post that follows up on fmaths’ great post on CPD. Here’s my thoughts.

**The Dark Arts**

I talked, in a previous post, about Mathematics being a language of odd symbols, the ultimate subjective truth in a sense. Because it is so subjective, it needs treating differently, a la the Dark Arts in Harry Potter.

I can’t believe I made a Harry Potter reference in my writing. I absolutely hate the whole Harry Potter concept. It’s in the same false-picture-painting-of-Britain twaddle as a Richard Curtis rom-com. All RP accents, nuclear families and knowing upper middle-classness, trust fund supported ‘finding myself’ trips and general pratting round

pretendingto be adults. SOME OF US IN BRITAIN GREW UP WEARING CLOTHES THE COUNCIL GAVE US, YEAH? Anyway, I digress…

Both John Hattie and The Sutton Trust, amongst many others, recognise the importance of CPD being provided externally by experts in the teaching and learning of that subject. This is especially the case of Mathematics which, because of the abstract nature of the subject, needs people who understand the subject and the demands it places on student thinking.

However, there is a trend for schools presently to run CPD in-house. The premise is that (rightly) there is a great deal of expertise in schools, and that because “we know our students better than anyone else”, it’ll have greater impact. However, this is simply hubris. There is a lot of expertise in schools, and it deserves an opportunity to be shared. But keeping CPD purely within schools is akin to royal intermarriage: the gene pool doesn’t diversify, hereditary problems exacerbate and you’ll end up with a Prince Phillip at some point.

Instead, schools need to be outward facing. Now many schools claim to be exactly that. However, they’re not willing to put up the funding or the time to support that claim, which is a shame, because if there’s any lesson that schools need to learn it’s that to survive and succeed, you need to adapt; you need to diversify the gene pool.

**The Black Sheep**

Now, inward facing schools will argue that this gene pool can be diversified by sharing practice between departments – but quite simply this isn’t fair, because – and yes, you know what I’m going to say – Mathematics is different from other subjects generally. A few people reading this will sigh, and say that all subjects can learn off each other. But, remember this…

Mathematics is the most objective study there is. It has a purity of method and reasoning that no other – no other – subject has.

Therefore, we need a CPD system that needs to appreciate this. Schools generally cannot achieve themselves this because – and forgive me for the generalisation – school leaders don’t tend to be Mathematics teachers themselves. Most of the time they’re from the Humanities. Now this is no slight – those who have studied or taught Humanities tend to be better at the rhetorical methods that are required of a leader of a school, but they often lack the deeper understanding of Mathematics that is required to teach it well, and therefore aren’t in a position to determine what CPD will have the biggest impact on teaching and learning in our subject. Again, let me be clear – this is not a slight on such people’s capability as leaders; it’s placing emphasis on the fact that there is a separation between the skill set and understanding that many leaders have and the requirements needed to plan out effective CPD for Mathematics teachers.

**There Has To Be A Better Way**

So how do we rectify this situation? I have few ideas.

- Accept that the best Mathematics CPD provision is usually offered by external organisations. It will have to be paid for – unless the LEA or Academy Chain will fund it – and it will almost certainly require time out of school for staff.
- SLT members should be open to the idea of participating in such CPD themselves. This will open their eyes to the particular challenges that we as Maths teachers face. I would go as far as to say that it might be worthwhile them taking the Maths GCSE themselves!
- Understand that some school policies might need to be adapted to suit Mathematics – as long as the adapted policy is used consistently. I mean this in the context that as a study, GCSE Mathematics in particular is an accumulative subject – you can’t necessarily take a piece of work – say for example finding the exterior angle of a polygon – and consistently develop and build on that particular skill until it’s at a A* grade standard. The only way that one can build the difficulty in this topic is to attach more Mathematics (either through detail or connections to other topics) to it! This is not the case in English, where a piece of writing can be extended and embellished to a point where it’s moved from an E grade quality to an A* grade quality in a relatively straightforward fashion.

I am not saying that Maths should be treated completely differently, I am saying that there are fundamental differences between our subject and others than any CPD programme should appreciate.

I am aware I’m talking in a general sense. So let’s talk specifics. In my experience, there are some key strands in Mathematics teaching and learning that are trying out for good CPD.

*Quality of Instruction*: It still strikes me how many teachers use tricks and acronyms to teach Mathematics. This has to stop. Tricks, acronyms and shortcuts are revision tools. They are not mathematically sound, and as such place student knowledge on very shaky ground. Also such methods ignore the interconnectivity of methods in Mathematics. One example ‘change side, change sign’ approach to solving equations. It’s a shortcut. It ignores the whole concept of algebra being a method of balance, which is important for all equations!*Curriculum Design*: Stop relying on textbooks, or exam board supplied schemes of work. Who are we serving? Publishers, exam boards (or in the case of Pearson/Edexcel – both) or students? Know your students, know how they’re going to be assessed, and work from there. Don’t just work through a ticklist of topics. How are you going to embed Cockcroft’s three key principles of developing Knowledge, Skills and Understanding in your curriculum? When are you going to do it?*Sharing Pedagogical Practice*: I’ll put my house on the fact that within Mathematics departments different teachers use (slightly or very) different ways of teaching topics. Teachers have their own style, and if it works for them in their own bubble, then that’s fine, yeah? But actually what happens is when a student moves to a different teacher, then there’s a clash of methods, and confusion abounds. Mathematics departments need an agreed set of teaching principles for topics across the curriculum, particularly things like solving equations, calculating with fractions, mensuration and the like, where (and this connects to an earlier point) where shortcuts and tricks pervade in teacher pedagogy.

There’s plenty of other issues that we face in Mathematics teaching. But dealing with the three above, for me, will have the greater positive impact on student progress in classrooms – trust me.

**Weaving It All Together**

The only way CPD can have a measure of quality is if it is outward facing, especially for Mathematics, which needs treating not completely differently, but with a consideration for the objective nature of the subject. There are ways in which this can be done, and through these ways we should be able to tackle some common problems of Mathematics teaching presently. Let’s stop doing a one-size fits all strategy of CPD, as it de-personalises and alienates. Specificity and quality will make the biggest difference, and staff will consequently value the efforts to develop their practice. Easy? No. Crucial? Certainly.

Reblogged this on The Echo Chamber.

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