It was my privilege to spend a week in Shanghai at the start of November with Debbie Morgan, the NCETM’s Director for Primary School Mathematics, and 70 English primary school teachers (all NCETM-trained primary maths teaching for Mastery Specialists, two from each Maths Hub), on the first leg of the NCETM’s latest China-England teacher exchange. This is the third exchange visit the NCETM has run with teachers from Shanghai. For the return leg, 70 Shanghai teachers are coming to England for two weeks in two waves, the first half in November/December, and the second half in January 2017.

As with the previous exchanges, our Chinese hosts were hugely welcoming, both at Shanghai Normal University, which trains the vast majority of Shanghai primary maths teachers, and in the many schools involved in the exchange. There was a real spirit of sharing ideas and learning from one another. We were all thrilled to attend a lecture by the eminent Chinese mathematics educationalist, Professor Gu, whose work on variation theory was familiar to all of the Mastery Specialists. Over the last year I have been articulating what it means to ‘master’ an aspect of mathematics by saying that a piece of mathematics has been ‘mastered’ when a student can use it as a basis on which to build further mathematical learning. I was very pleased to hear Professor Gu say that the philosophy of their mathematics teaching is ‘to move forward from a solid starting point consistently’, which seems consistent with my view.

Two key aspects of this trip really stand out for me: 1) The impact it had on our primary Mastery Specialists and 2) how it further deepened my own understanding of maths teaching for mastery.

I first visited Shanghai in February 2014 and reported on my experience in a blog post on my return. On the evidence of that visit, the first China-England exchange was organised in the autumn term of 2014, involving almost 70 teachers from primary schools from the then newly-formed Maths Hubs across England. That exchange was a huge success and has had a profound impact on the NCETM’s work on maths teaching for mastery, which is now influencing mathematics teaching in primary schools across the country. The following year we ran a second exchange, this time taking secondary school teachers, to look at Shanghai maths teaching Key Stage 3. Again the exchange was very successful and the Maths Hubs are now working with secondary schools across England to investigate how best to implement what we have learnt.

So, what’s different about this year’s exchange? The key difference is that the 70 teachers are drawn from the 140 that the NCETM trained last year as the first cohort of Mastery Specialists, so they have already received training in Shanghai-style mathematics teaching, but had not yet experienced it first-hand. For both of the previous exchanges, I was intrigued (and a little apprehensive) to see how our teachers would react to the Shanghai teaching. Each time I was hugely relieved that they were as impressed by the Shanghai maths teaching as I was, and felt that they could learn from it to improve their teaching. This year I wondered how our trained specialists would react; would they gain as much from it as a complete novice? I needn’t have worried. If anything, they have gained even more than the previous exchange cohorts. I think this is because they have already done so much thinking about maths teaching for mastery over the past year, and have been trying to establish and embed it in their own schools. They found it exciting to see the things they had learnt about being put into practice. They marvelled at how the carefully designed lessons, which are delivered with both simplicity and depth to the whole class, worked to develop the understanding of every pupil.

In my conversations with our Mastery Specialists in Shanghai, a key point they emphasised was the fast ‘pace’ of the lessons they were observing. This is an interesting perception because, in England, we tend to associate ‘pace’ with ‘covering’ a lot of material. The Shanghai lessons do indeed seem ‘pacey’, but this is pace not associated with rushing through the curriculum. Instead, it reflects the level of engagement with the mathematics that takes place in the Shanghai lessons. Purposeful work takes place throughout the lessons and that work focuses on ensuring depth of understanding, so that pupils properly master the mathematics - not just ‘getting the answer’, but really exploring the structure of the mathematics they are studying. This is best explained by an example:

I observed the following lesson in Shanghai Huangpu District No.1 Central Primary School on Wednesday 9 November. The object of the lesson was to explore adding single digit numbers to give totals up to 20. The pupils were in Chinese grade 2, equivalent to our Year 3. The lesson started with games to revise number bonds to 10: 1 + 9 = 10, 2 + 8 = 10, 3 + 7 = 10, etc. After about five minutes the teacher moved on to holding up cards with sums such as ‘7 + 3 + 4 =  ’ written on them, giving all the pupils a few seconds to think about their answers, then asking individual pupils for responses. Pupils were expected to give their answers in full in a standard form: ‘seven plus three equals ten, then ten plus four equals fourteen’. The key point, strongly emphasised by the teacher, was making 10 first. After about 10 minutes, the teacher moved on to adding two numbers that would give a total between 11 and 20. The teacher began with an example using manipulatives fixed to the blackboard, using red and blue counters on two ‘10s grids’ to look at the sum 9 + 5. The children had the same manipulatives on their desks. These PowerPoint slides show what the teacher did at the board and how the lesson then developed.

A fundamental point about this lesson is that most, if not all, of the pupils could have answered the sums correctly straightaway, without needing to use the tens grids. However, being able to get simple addition sums right was not the purpose of the lesson. The purpose of the lesson was to explore the mathematical structure of the sums and to understand how ‘making 10’ could be used to obtain the solutions. The lesson was designed to develop deep understanding of number and the ‘10’ place value. Compared to a typical lesson in England, in terms of curriculum coverage the pace was slow, but in terms of pupil and teacher activity, because of the constant teacher-pupil interaction and continual engagement in mathematical thinking, the lesson appeared pacey. There was no acceleration, but the lesson achieved real depth and all the pupils in the class experienced the same lesson content. When addition and associated written methods are developed further in future lessons, this understanding will be invaluable. 7 + 6 = 13, understood deeply through the 10s grid, will lead easily to 17 + 6 = 23 and, later, to 36 + 27 = 63, etc.

There was significant repetition of key phrases and processes in the lesson. However, this wasn’t the mindless repetition associated with rote learning. Things were only repeated when children had gained a sense of the meaning through their manipulation of counters to expose the structure of the mathematics and had reinforced their understanding through interaction with each other and with the teacher. I like the phrase the teacher used “let’s rehearse the process”. The repetition highlighted and reinforced key aspects of learning.

After the lesson we attended a ‘teacher research group’ (TRG) discussion with the teacher who had given the lesson and other maths teachers from the school, to analyse the lesson in detail. Thinking about how such a lesson might be criticised in England, I asked whether pupils or their parents ever complained that such lessons were too easy, because the pupils could already add single digit numbers accurately. The Chinese teachers were surprised by the question. The answer was an emphatic ‘No!’. Parents had been taught in the same way and know it works. Pupils are not bored because they are engaging deeply with the mathematics and are developing their understanding.

This lesson epitomises the Shanghai approach. There are still a few who dismiss Shanghai maths teaching as ‘learning by rote’, or claim that ‘cultural differences’ mean it is not relevant to maths teaching in England. But Shanghai teaching is the antithesis of rote learning, and teachers who have seen it at first hand are inspired by it, and convinced we can learn from it to improve maths teaching in England.

Teacher Research Groups (TRGs) are a standard aspect of a Shanghai maths teacher’s work. Shanghai maths teachers are involved in a TRG on a weekly basis and it is routine for them to observe one another teaching (many classrooms are set up to facilitate this) and discuss one another’s lessons. In Shanghai, being observed teaching is seen as constructive, rather than threatening. In England, lesson observation is often viewed as a means of measuring teacher performance and causes fear and defensiveness. Our Mastery Specialists are already trying to emulate TRGs in England. Several of our specialists have already been involved in constructive, Shanghai style, lesson observation in England and are planning to develop this further during this school year. When you see it happening, it is obvious that teachers watching one another teach and then discussing what worked and what didn’t and how the lesson could be adjusted to improve pupils’ learning is a really effective way to improve teaching.

As well as observing more Shanghai teaching, my trip also enabled me to have detailed conversations with several of our specialists. I was greatly impressed. They were already deeply committed and enthusiastic about the teaching for mastery approach before they went to Shanghai, particularly since it is already starting to have a positive impact on the children they teach in their own schools, and their experiences in Shanghai have strengthened their commitment. Over the next four years, the NCETM will be training 140 new primary Mastery Specialists each year, four per Maths Hub. Once trained, each specialist supports six primary schools each year that wish to establish maths teaching for mastery (the specialists’ schools are paid for them to have 30 days off timetable to do this, and the six schools also receive funding to subsidise supply cover to work with the mastery specialist). In this way, by 2020, the NCETM plans to have trained 700 mastery specialists and supported them in working with over 8000 primary schools across England. The Mastery Specialists who’ve just got back from Shanghai are in the vanguard of this programme to improve mathematics education in England and they have the knowledge and know-how to do so.

It will be a huge challenge to establish maths teaching for mastery in primary schools across England, but my recent experiences in Shanghai have boosted my confidence and resolve. A further challenge will be how to ensure the continuity of the teaching for mastery approach for pupils moving on to KS3. I am more convinced than ever that learning from Shanghai-style maths teaching can bring about significant improvements to English maths education and that, through the Mastery Specialists, the NCETM and the Maths Hubs, our schools can use it to improve their maths teaching and the maths education outcomes for our pupils.