What does teacher collaboration look like in practice?


Over the last few weeks I have had the privilege of meeting a range of primary school maths leaders who are in the process of adapting their maths teaching to a mastery approach. This post is not so much about what mastery teaching and learning looks like but more about how teachers work with each other to improve their teaching.

This year I will be working with these schools to develop TRGs (Teacher Research Groups) under the auspices of the Maths Hub programme. The impetus initially came from looking at all things Shanghai. However, the context there is so very different (e.g. 20-25% contact time vs. 80-90% in UK and specialist Maths teachers in Primary) that it is hard to see that on the topic of teacher collaboration we can “lift” very much from this particular school system.  I have written before on my issues with a focus on the “South Asian method” and no doubt I will again, however I want to focus here on some good practice that I have observed so far in the UK.

I will use the label TRG, but you could call co-planning, teacher collaboration, lesson study, action research, INSET or CPD.  Ideally it should be all of those things.  With increasing pressures on budgets and many teachers feeling highly time-constrained, there is an imperative that any time out of the classroom is time well spent.  My measure of any good INSET/CPD is that it is directly relevant to me, and that at some point over the next week, it will either improve my teaching or save me time, or both. Ideally I would like to spend some time during each INSET session planning a lesson such that I have one thing less to do when I leave.

Last year, I was involved in a TRG for teaching our Year 7 maths classes and this year I have already seen a wide range of approaches to TRGs in Primary.  Here are some of my early thoughts, which I will add to as I see more during the year.

Observe it in practise

At one end, a TRG can literally just be a traditional-style INSET where teachers gather and listen to the presentation from the “expert” and then have some form of discussion. However, this misses the opportunity to see some teaching taking place and see how different teachers do it.  The key to any peer-observation of teaching is that nobody is there to judge how good a teacher you are, nobody should be passing such judgements and nobody should be feeling that that is what will happen.  The legacy of Ofsted grading of lessons and teachers being evaluated in this way still means that many teachers feel that being observed by others will result in a grade.  We need to move on from this, to work together as professionals to support each other in our development as teachers.  What can work well is that you observe a teacher who is NOT the Maths lead or the person running the TRG.  This can mean that conversation is more fluid.

It might take some planning, but you should try to do the whole thing in one sitting, i.e. some introduction, followed by observing a lesson, followed immediately by discussion on that lesson.

Chose a focus / theme

This might be something that you all agree at your first meeting for each session that you have throughout the year.  The purpose of our primary TRGs this year is to embed a mastery approach so for us, we can pick a theme of mastery, e.g. variation, fluency, CPA, use of a specific text book, whole-class discussion / questioning, etc. The lesson would be planned to incorporate that theme and there could be a short discussion before the lesson is taught to explain how it was incorporated and what to look out for.  Alternatively, your focus might simply be a topic, e.g. Year 7 fractions.

Facilitate the Discussion

It needs one person to take the lead in setting up the session and asking the questions if the conversation “runs out of steam”  But this person is not there as the expert, they are there to keep the conversation moving.  Everyone brings a diverse range of professional experience to the TRG and it is this range that should come out in the discussion.


Share out the planning

This might not work in all scenarios but it worked really well for us in Year 7 as there were 6 teachers with a class each following the same scheme of work. In terms of actually preparing lesson resources, each teacher therefore only had to do one in every six lessons, but the value was in the richness of discussion that went on when these lesson resources were presented to the group.  Any resource / slide is only as good as its presentation to students so it was vital that we all felt confident in utilising other teachers’ work. For me, this is what the discussion achieved.




Use your words!

Here’s a piece of subject knowledge that I have seen used in some primary schools but I would bet that most secondary school maths teachers don’t know.


The terms highlighted in blue are those required by KS1&2 curriculum and the red ones are those used in secondary maths.

But the question is, do we need to teach pupils these terms?  Clearly some of the concepts behind them, namely that addition and multiplication are commutative whereas subtraction and division are not. But does having knowledge of the words themselves help?

I’d love to hear from anyone who teaches these terms and the rationale behind that decision.

Sum of Consecutive Numbers, a multi-layered investigtion

One of those classic investigations that gets forgotten about all too easily.  So much scope for generalising at different levels.

The fact that all odd numbers can be expressed as sum of two consecutive numbers is probably the first thing that will be established.  But why is this the case? And can students express this as a generalisation, first in the form of concise words and then algebraically?

The beauty of this is that there are then many other layers of things to discover, right down to a generalisation explaining which numbers cannot be expressed as a sum of consecutive numbers.  And maybe even a proof.

This nRich page gives away some of the answers.

Thanks to Alan Parr for reminding me about it with this excellent blog post:

The All I Can Throwers – Sessions with Den and Jenna. #1 – Consecutive Numbers