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# Secondary Magazine - Issue 140: Teaching for Mastery in Secondary Schools

Created on 31 January 2017 by ncetm_administrator
Updated on 07 February 2017 by ncetm_administrator

## Teaching for Mastery in Secondary Schools

“Teaching for mastery”… what does it mean to you? Something fluttering around at the edge of your consciousness, or something you are trying to implement in every lesson? Most secondary teachers are somewhere between these two extremes, but it’s fair to say we are a way behind some of our primary colleagues.

Due to a substantial national programme, aiming to reach 8400 primary schools by summer 2020, many primary schools are well advanced in introducing an approach known as ‘teaching for mastery’. Taking transferable elements from high-performing jurisdictions in the Far East, teaching for mastery promotes deep, connected and secure understanding, by extending the time spent learning each topic and by breaking concepts down so that mathematical structure is exposed. Conceptual understanding and procedural fluency are developed hand in hand.

In secondary maths departments, time is often spent wondering if we have sufficiently good understanding to teach that tricky GCSE topic well, or whether we can really find ways to help our Foundation students to understand trigonometry. How much time do we spend interrogating our own (or our students’) understanding of fundamental concepts? For example:

• Why does the ‘bus-stop’ algorithm for division, start on the left-hand side when all the other standard algorithms for the four operations, start on the right? And why does the algorithm work?

• What are we doing when we ‘borrow’ to subtract, and why don’t we pay it back?

• Why would almost all of us, when faced with the question:

Which is larger $\inline \dpi{80} \fn_jvn \frac{3}{7}$ or $\inline \dpi{80} \fn_jvn \frac{1}{6}$ ?

immediately begin finding a common denominator rather than a common numerator (ie $\inline \dpi{80} \fn_jvn \frac{1}{6}= \frac{3}{18}$ so, $\inline \dpi{80} \fn_jvn \frac{3}{7}> \frac{3}{18}$)?

We often appreciate that it is an insecure understanding of basic concepts that holds our students back, but little of our attention is focused on how to teach these concepts to students that haven’t managed to understand them in primary school.

A Mastery Specialists Programme for Secondary

Following the success of the Primary Mastery Specialists Programme in 2015/16, where 140 primary teachers participated in a series of three residential professional development courses run by the NCETM, there was a swell of enthusiasm to provide something similar for the secondary sector. While the primary programme was driven from above, the secondary programme was the product of grassroots pressure and initiative from the Maths Hubs – particularly from those teachers that had been involved in visiting Chinese maths classrooms in autumn 2015.

The programme, which started in autumn 2016 (jointly designed and led by the NCETM and three Maths Hub Leads) describes itself as a “collaborative effort to define teaching for mastery at secondary”. This is clear acknowledgement of the new territory being explored in this country, an invitation to participants to try things out and take an active role in ascertaining what seems to work in their classrooms and what doesn’t, and allowing this to contribute to a building definition of teaching for mastery in the UK.

Each of the 35 Maths Hubs has up to four secondary teachers attending the residentials. Each of these teachers is expected to engage with and support colleagues in their department with trying out different features of teaching for mastery. Later in the programme they will be asked to share their learning more widely with interested colleagues in neighbouring schools.

At Residential 1, in the first term of 2016/17, participants spent time discussing what they understood by ‘teaching for mastery’ and then looking at how it could be used to support coherent and connected learning of mathematical concepts. An early session addressed the co-dependent requirements of conceptual understanding, and procedural fluency:

There was a session on ‘variation theory’ and how these ideas could be used to choose or construct examples and exercises to focus pupils’ attention on specific structural features of the mathematics:

Connecting directly to the thorny area of algebra was a session using plenty of geometric imagery to expose the structure of algebraic algorithms:

Among the teachers on the Secondary Mastery Specialists Programme, the range of experience of teaching for mastery is enormous. Some are from academy chains that have already adopted a mastery approach, written a scheme of work with supporting materials, and established strong patterns of collaborative professional learning to support the changes. Others are lone heads of department, interested in the approach and wondering about how to implement it in their own schools.

I applied because I think the new GCSE, with the problem-solving element has highlighted that we have very bright students but they are not able to see the bigger picture and link things together. They don’t always have those connections that you would think they should have, with able students. So to me that’s a failing on our part. It needed us to rethink what we did. And mastery seemed to address that – looking deeper, with more breadth, and the connections element was key. It could be challenging for my staff because they tend to think, because we have bright kids, we should push them along, but I definitely see with the students when they get to A level, that they’ve got gaps (Head of Department at a grammar school in Cumbria).

I’m here because my head of department recognised that this is how I teach anyway, and I want to enhance this and talk to other people who value this way of teaching. I’m very visual, so concrete and pictorial is where I start. I’ll invite students to use algorithms but I want them to understand what is going on. Rounding to ten for example – I see the two numbers, and then we decide where it is in terms of halfway – we don’t have a procedure of ‘do this, then this, then the answer’s this’ (teacher of 17 years' experience, Oldham).

Finding Out More

As the Maths Hubs have made clear, it won’t be long before secondary teachers begin to encounter Y7s who have had an increasingly significant diet of maths taught using ‘teaching for mastery’ principles. Hopefully they will be impressed by the depth of understanding the Y7s bring, and the way that this allows them to manipulate numbers in a confident and efficient way to solve problems. As this begins to happen, more and more secondary teachers will be looking for ‘teaching for mastery’ approaches to secondary maths topics. Contact your local Maths Hub to find out about ‘teaching for mastery’ events and professional development in your area.

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13 February 2017 13:17
Thanks for your comments Rogerjob and andrewdeamer. I think your points echo the concerns of many regarding the introduction of a ‘Teaching for Mastery’ approach. The Maths Hubs are beginning to find their way with this and are looking at what we can learn from these approaches when used in our secondary schools: What works well? How can we ensure that all students are engaged and challenged at the same time as developing a deep understanding? All aspects to be explored and we will keep teachers updated through regular articles in this magazine.
10 February 2017 09:22
The final true test of the change to Mastery comes in 4 years time when the first Mastery educated students complete their GCSE 9-1 maths exams. I look forward to the examination results.
10 February 2017 08:27
If the focus of the ncetm & maths hubs was to try and copy Shanghai methods and simply parachute strategies these into our schools this endeavour would be doomed to failure. However it appears to me that the way forward is to enter into a dialogue with teachers both locally and internationally, exploring what pedagogies work and why.

If learners aren't challenged and inspired then I suspect a mis-interpretation of teaching for mastery is being applied.