In my maths department we are starting on a journey of building a new curriculum based on the principles of mastery. To find out what mastery is, read Mark McCourt. Implementing something different comes with all sorts of challenges but, if it’s a good thing to do, it brings benefits too. One of the benefits I am finding this year is the liberation from the compulsion to produce a three- (or four- or five-) part lesson with objectives and mini-plenaries and some kind of forced activity to (falsely) demonstrate the “progress” my students have made over the course of an hour. By having a curriculum with clear aims and (hopefully) coherent thinking underpinning every aspect I feel more confident to teach the way I feel will be most effective rather than making my lessons a conflation of lots of “best practice” techniques in order to satisfy a checklist.

I am hoping that we can spend quite a bit of department time this year discussing the best way to build our curriculum, and we have already been working on things like what we want from assessments and the difficulties of resourcing a mastery curriculum from scratch. One of the first things we talked about was lesson planning and the idea of planning in sequences rather than thinking about lessons as discrete units of time.

I start a unit with a list of its objectives, then drill down into what I want students to think about most, what I want them to practise most, what is the best order to teach things, and how I want to assess them as I go along.

As an example, let’s take rearranging formulae. There is so much to cover:

- one-step (four operations),
- two-step (four operations),
- multi-step, including brackets (four operations),
- subject appearing in the denominator,
- all the above with powers and roots,
- isolating the subject by factorising,
- all the above with non-integer coefficients,

and more (we haven’t even considered, for instance, quadratic formulae such as *s* = *ut* + 1/2*at*^{2}).

This becomes a series of examples and practice questions, and when students are sufficiently practised in the procedures we can look at contextual and more complex problems. Examples need to be extensive so that students have seen lots modelled by the teacher. They need to be sufficiently varied to allow students access to as many different thought processes as possible. My planning becomes identifying these examples and the best source of practice for students. I don’t waste time making presentations (although I haven’t done that for years) and lessons flow one to the next rather than being standalone. I integrate different types of activities (whole-class, individual, competitions, etc) when they are appropriate and I feel provide the best way to help the students learn, not because they are engaging or different, or because I’m supposed to change what we do every 15 or 20 minutes.

Allowing a number of weeks on the unit enables me to address everything in a logical sequence and allows the students plenty of time to get to grips with the maths properly. What I don’t expect is that in lesson 1 we will achieve x, then in lesson 2 we will move onto y. We move on when we are ready to. That might be halfway through a lesson, but that’s fine – I am trying not to be constrained by the end of an hour always being the cut-off.

I also have no problem in devoting lesson time to recapping previous content, distributing practice is important to give students chance to remember what they’ve learnt. Previously, spending lesson time on old content would have been contrary to the principle of “rapid and sustained progress” and therefore frowned upon.

It’s not rocket science, and many people will be reading this thinking, “but that’s obvious”. The point is the atmosphere has changed. Ofsted-induced pressure to perform a certain way has dissipated and I feel like I can teach the way I see fit without needing to change it when someone’s watching. Couple that with the explicit curriculum aim of taking as much time as we need (which, incidentally, is a topic of interesting discussion in the department at the moment) and the expectation of teaching the old Ofsted way is gone. Now we can try and make our curriculum really work.

I think many teachers wanting to work like this are hampered by senior management observations that are still looking to tick (inappropriate) boxes. How have you managed to persuade your management to change (or abandon?) their checklists?

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Good question. I am fortunate. They abandoned grading lessons a while back and now focus on giving constructive feedback. I’ve yet to have an observation teaching like this, but I do feel confident that I can explain and justify my methods to whoever watches. Also, they are fully behind our attempt to implement a mastery curriculum, so they trust me to do what I think is best.

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Hi Jemma, thanks for these great posts. I’m looking to move my science lessons to a mastery approach, and I’m just struggling a bit with lesson logistics. When you give extension to pupils who have mastered the current topic, how long do you spend explaining it to them? What are the other pupils doing while you do this? Do you arrange your room so that those who have mastered are all in one area?

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For me, the key is that extension is within the current topic, work that gets them to think in more depth. That way you don’t have to explain a lot. I also structure my lessons so that we are working on normally one small concept at a time. I have found that most students actually need more practice than you think they do.

I don’t group students into “mastered/not-mastered”, partly because I don’t like to use “mastered” as a descriptor: no-one’s ever mastered something, there is always more depth/more to know. I am not a huge fan of group work, although we do have paired discussions and whole-class discussions when it’s appropriate, so I don’t really feel the need to group students anyway.

When considering the mastery approach it’s really important to get the curriculum design right – sequence topics properly and make sure you build in plenty of time to revisit/revise old work. I know nothing about science teaching, but I would suggest that a good activity for a lesson is one that gives plenty of practice at the essentials (more than just a cursory glance) and then provides lots of questions to delve much deeper. Those who are able to move quicker can spend more time on the deeper questions, but those who can’t still have sufficient practice at what you consider to be the absolute essentials.

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Great, thanks – lots to think about! I haven’t given much thought to topic sequence but will do so now. I agree on the need for lots and lots of questions at different levels, I’ve been making these and I find it’s easy to make them for calculations, and easy to think of extension questions, but when it comes to the more descriptive areas I have found it really hard to write extension questions- I’m not even sure if it’s really possible or appropriate some of the time… Anyway thanks for your help, love your blog!

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Reblogged this on The Echo Chamber.

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[…] Jem Maths on mastery https://jemmaths.wordpress.com/2016/12/18/adventures-in-mastery-4-lesson-sequences/ […]

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[…] Sherwood describes how her maths department is applying the mastery model: ”I start a unit with a list of its […]

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