A comprehensive school’s approach three years on…
I very rarely blog about mathematics teaching but we’ve had numerous visits asking about mastery teaching recently so I thought perhaps people may like to see what it looks like in our school and what our journey has looked like along the way. There are much better people in our department to talk about this like our Acting HOD or our Mastery Coordinator (@MrMoMaths), as well as many other contributors like @MrHayhurstMaths but they tell me they’re way too busy to blog so you’re stuck with me! Here are some of the most important things to consider if you’re thinking of developing teaching for mastery at your school.
1. Mastery teaching is not a quick fix
If you’re looking to rapidly improve your GCSE results this year then stop reading now. We are over three years into our work on mastery and we know that we’ll only see the results as scores on doors with current Year 9 (& 10 to an extent) but we know that it’s having an impact on developing our students as mathematicians.
2. Mastery is an ideology not a scheme of work
When it was suggested that we start looking at mastery nearly five years ago, our then KS 3 Coordinator went with our Lead for T&L to the White Rose Maths Hub (a superb place to start). He came back bursting with excitement (and free resources), deciding that he was going to implement the SOW he had been given the next day. Our Lead for T&L was not as convinced. He was more experienced in both teaching and leading people and he knew that trying to take something off the shelf from another school and place it into a different setting was a recipe for disaster. It was. Things went pear shaped very quickly and our KS 3 Coordinator wanted to throw it out as quickly as he’d put it in. We knew mastery teaching was right for the journey we were on as a school so we sat down together reflected and did more research, tweaking a few things to better suit our students’ needs. Staffing changes gave us the opportunity to appoint a Mastery Coordinator – someone with experience of seeing mastery teaching in another setting. This time the whole department began to look in depth at SOWs and resources together, they began to spend a lot of time discussing approaches to teaching and key subject pedagogy.
3. Don’t assume teachers understand
We have an extremely talented group of teachers at our school, the majority of whom are also brilliant mathematicians. However, it is an error to assume that because someone looks good in a classroom that they completely understand the pedagogical approaches to teaching. Subject knowledge is an over-riding factor here but even that doesn’t automatically translate into good explanations and learning in the classroom. The best example of this I can give is using myself. In my previous setting, I was considered to be an “outstanding practitioner” (whatever that means) because students behaved and did well relative to other colleagues. I used to teach expanding brackets using claw methods. Every year I’d religiously teach this way, if students got it then great, if they didn’t then they were doing something wrong. I never considered that there could be a different approach because other colleagues assumed I knew these other approaches whilst I myself didn’t know what I didn’t know. In schools where behaviour is an issue or where there are copious amounts of unnecessary systems in place subject pedagogy discussions are often overlooked. The team I work with now are always talking about pedagogical approaches so teachers are armed with a variety of approaches and an understanding which underpins them. There are many aspects of teaching for mastery which need to be discussed, clarified and reviewed – this can only happen if opportunities for continual dialogue are in place. If you talk to a group of maths teachers about bar modelling for example, they’ll nod in agreement. Chances are 5% will fully understand and use in their day-to-day practice, 30% will have come across this concept before and use it to a limited extent, a further 20% will have heard of it and the rest will be nodding so as not to look stupid. The truth is, 95% of maths teachers (not just the biased sample we see on Twitter and social media) will need the time and conversation to develop understanding and practice. Don’t assume that just because you (or your best teachers) are doing/getting it, that everyone is.
4. Agree some minimum expectations
I know this goes without saying but as a team you need to decide what you’re all going to set out to do, and you need to continually revisit it to review planned versus enacted curriculum. There is no blanket one size fits all approach to teaching in our school but all maths lessons have a similar feel to them, not because we all use the same resources, textbooks or teaching styles but because everyone tries to include key features of good teaching in their lessons. These include:
- Repetition and drill to develop fluency
- Direct instruction to introduce concepts/topics
- Strategies to reduce cognitive load when working with novice learners
- Deliberate intelligent practice
- Deliberate incremental practice
- Standard and non-standard examples
- Exposure to concepts across settings and revisiting them at every opportunity
- An emphasis on strong questioning
- An appreciation of multiple approaches to teaching a concept (teachers who are experts)
- Interleaving of topics
- Spaced retrieval as an integral part of homework
- Feedback which is minimal but diagnostic and specific
- Expectation of high effort from students with extended periods of silent, independent work in lessons
This isn’t exhaustive and it doesn’t happen every lesson, in every classroom, every day of the week but teachers are working on improving their own approaches to improve learning in the classroom.
5. Be brave
When you first introduce anything, there’s always a degree of resistance. It might be from staff, students, parents or leadership so it’s important to have given it full consideration and have a clear understanding of why you’re doing what you’re doing. Mastery take 1 was introduced in a hurry – without thought, at a time when the department’s results weren’t great; the fallout from this was resistance from staff and students but mainly from parents. I was asked to step in and line-manage the team from an SLT perspective at this time and was met with a whole host of fire-fighting. We did a lot of work with parents to explain our rationale behind teaching for mastery (once we’d talked at great length as a department and agreed why we would continue with it). We explained the difference between learning versus performance and we used evidence to support our argument – most of the complaints were from parents who felt that their children were repeating work they’d done in Year 6 but when we showed them internal tests and the diagnostics which accompanied them they began to understand. We communicated effectively and explained that this was something which we believed in and it wasn’t going away. Very quickly they saw that generally teaching was improving as was the confidence and attitude of students with regard to maths. This was the case with reluctant staff too (of which there were very few).
6. Organisation is very important
Thankfully, we have a lot of organised people in the Mathematics department. As students have to “pass” a module to move on, coordinating testing and grouping is quite a job! This is where you need to consider staffing (and over-staffing – a luxury I know) to make it work. We’ve spent three years now tweaking as we go to achieve a structure which works for us but it’s important to think what will work in your setting and what the constraints are, some of these you’ll only find out as you implement it.
7. Testing, toughness and knowing when to call it a day
We are selective about testing, we encourage formative testing throughout but students’ progress is primarily based on our assessments at the end of each module and their end of year tests. We place an emphasis on the importance of preparation for tests and that if students don’t meet a minimum expectation they will revisit a module again. Here you have to be tough and objective. I found that teacher bias (both positive and negative) is often damaging to children’s learning. How often have we kept the nice, quiet student in our group because we want to save them when perhaps they’d have been better supported elsewhere? So we set an expectation and we stick to it (on the whole) and this means that sometimes we have to be cruel to be kind. Surprisingly we’ve found it has had a positive impact in terms of student confidence, achievement and esteem, we’ve also found that students are more determined to succeed. One school of thought towards mastery in mathematics in its purest sense is not to move on until everyone has fully “mastered” a concept. We don’t subscribe to this both on a philosophical and practical level, which will create quite a stir with the puritans out there. The team don’t apologise for this as we agree that it’s a balancing act. We give groups who don’t pass two attempts at a module (which can equate to about 16 weeks covering the same content) and then if they still don’t pass we move on (very few students don’t pass on the second attempt). Teachers who have students who don’t pass work with those students outside of maths lessons to intervene in areas where those students are struggling, since our teaching and assessment is very diagnostic, teachers know exactly where to plug the gaps. Students then have to sit the resits when they are ready whilst continuing with new content in class. Intervention at KS 3 is much more effective than fire-fighting at KS 4 in my opinion.
8. Look outside your own setting
There’s some amazing stuff out there on mastery teaching so don’t just be tempted to buy a SOW and a load of textbooks without looking at what Mark McCourt has to say on the matter here or seeing what lots of great contributors like White Rose Maths on TES have to offer for free. Although these guys differ in ideology to one another, both have brilliant contributions to make. Also, if you’re intent on buying off the shelf SOWs and textbooks, proceed with caution. Approaches to teaching for mastery are still evolving so talk to schools who are using your prospective purchase and maybe order some sample copies before rushing in spending money which schools don’t have much of these days. Visit schools like ours and see what it looks like in practice. We are not a perfect example by any means but we are keen to collaborate and help colleagues along the way so ask your SLT for a couple of days in another school (cheaper than an external course and a much more sound investment than £10000 on textbooks and SOW which might be ineffective).
9. Create a coherent and continuous curriculum
Something that the Acting HOD and myself constantly revisit (often provoked by the naive should we adopt the mastery curriculum for KS 4 debate which comes up every now and then both inside and beyond the department) is this idea of mastery versus teaching for mastery. This comes back to philosophy. If you look at mastery superficially as a scheme of work or the latest fix in mathematics education you’ll never really fully understand its purpose. Our curriculum in the mathematics is a 9 year journey – we look at what is going on in primary schools (specifically Year 5 and 6) and we ask ourselves what do we want a student leaving our 6th Form to look like? We think about the most able mathematicians who will hopefully go on to study mathematics at a higher level, we consider the least able mathematicians who need a certain level of mathematics to get by and we think about everyone in between – which I think is the beauty of an 11 -18 school with great links with their feeder primaries. We do follow our Mastery SOW at KS 3 but we make sure our KS 4 curriculum dovetails into it and then builds on the skills that students have acquired whilst forming a solid basis for KS 5. We aren’t constantly looking at the GCSE examinations, instead we focus on planning rich curricula which teach knowledge, enact this in a focused and deliberate way, test what students have learned and what has stuck (changes in long-term memory) whilst developing their ability to communicate this in an articulate and fluent way. This means a continual dialogue between the staff responsible for leading the department and the teachers within it, with our Lead for T&L supporting teachers’ understanding of what it looks like in practice along the way – the time investment is worth it. Teaching for mastery is about understanding and empowering teachers to support students learning of mathematics in a deep and concrete way.
10. Whatever you do, do it well
Finally, I want to leave you with a couple of thoughts from Daisy Christodoulou and Mark McCourt. At ResearchEd last year Daisy talked about assessment and grades in isolation (available here), she explained that a grade on its own tells us very little about what a child can and can’t do, additionally when we focus of grades as targets for measures (e.g. the old 5 A* – C measures) we lose sense of what learning is all about. We have a duty of care to teach children not just so that they can pass a test to achieve a certain grade but so that within the grade they have a level of understanding and competency to build on. We must develop students who understand, can articulate and retain knowledge, not just ones who pass tests then forget. And in Mark’s recent blog on setting versus mixed ability (here) he suggests that it doesn’t matter what approach you choose to take as long as you do it well, I wholeheartedly agree with this and would echo his sentiments entirely. Whatever approach you take with regard to your planned and enacted curriculum do your research, think it through thoroughly, develop it collaboratively and review regularly but most of all deliver it well with clarity.