" I had expected rote learning, but instead saw teaching that emphasised deep conceptual understanding "

Charlie's Angles

Thoughts on topical issues of mathematics education from the NCETM’s Director, Charlie Stripp

12 March 2014: Shanghai Surprise!

At the end of February, at the DfE’s invitation, I visited China to spend four days finding out about Chinese mathematics teaching at first hand. I was able to observe mathematics teaching in two Chinese cities; Shanghai, a mega-city of 24 million that is the highest scoring jurisdiction in PISA’s international comparison of mathematics scores for 15-year olds, and Wuhan, a less glamorous city of over 10 million people that is a ninety minute flight west of Shanghai. What I present here are some overall impressions, having had a week to reflect on what I saw.

So, what was the surprise? What I saw completely overturned my pre-conceptions about what mathematics teaching would be like in China. I had expected rote learning, but instead saw teaching that emphasised deep conceptual understanding; I had expected an oppressive classroom atmosphere, but instead saw pupils engaging enthusiastically with learning and doing maths. In fact, what I saw is what I would describe as very good mathematics teaching, wherever I saw it.

I had also wondered whether mathematics teaching in other parts of China measured up to Shanghai. From my trip I can say that the mathematics teaching I saw in Wuhan was equally impressive, though I cannot, of course, comment on what it might be like in other Chinese cities, or in rural China.

I had been expecting large classes, and classes were large; the smallest I saw had 45 children, the largest 60. However, classroom management did not seem to be an issue. Classes were not organised into sets by ability, but teaching was pitched at a very high level (by age 14 what I saw was two years beyond what I’d expect to see in England). Expectations are very high and the pupils seemed to rise to them. The teachers I saw were completely confident about the mathematics they were teaching, and about how to teach it. The primary-age classes I saw involved children developing fluency with numbers, including group work and a game to help them develop number bonds, and using a ‘standard formal written method’ for – you guessed it! – long division. The secondary-age children seemed completely fluent in dealing with basic number work, so that lack of facility with basic skills in no way impeded their progress with more sophisticated mathematics, as it so often does in England.

All lessons (generally 45 minutes long) were sharply focused, with clear progression; no time was wasted. A typical teaching pattern was a short introduction and explanation (less than 5 minutes), followed by pupils working on questions in carefully constructed exercises (pupils put their hand up to indicate when they have finished), followed by class questioning (this included pupils coming up to the board to present their solutions to the class). This cycle was repeated three or four times during the lessons. Pupils were encouraged to discuss work with their neighbours, or to work in small groups for some tasks. It was notable that far more of each lesson was spent with the pupils working on problems – doing maths - than with pupils listening to teacher exposition.

Teachers have much less class contact time than teachers in England (two 45 minute lessons per day seemed typical), so they have far more time to reflect on their classes and refine their planning (they refer to this time as ‘research’), and more time to mark work and provide rapid feedback – either on the day the work is handed in or the next day.

A theme that shone through is that education, especially mathematics education, is very highly valued by the Chinese, and this is reflected in the enthusiasm and diligence of the pupils and in the confidence of the teachers.

A question set at the end of a lesson for 13-year olds (literally in the last five minutes) highlighted the differences between mathematics education in China and in England – it was clearly set partly for the benefit of the delegation of English education experts sat at the back of the classroom:

Ben Nevis is the highest mountain in England (!!). On a summer’s day, the temperature at the base of Ben Nevis is 24 degrees Centigrade and at the summit the temperature is 13.25 degrees Centigrade. If the temperature falls by 0.8 degrees Centigrade per 100m of altitude, how high is Ben Nevis?

I set to work on this question at the same time as the pupils. They (and I) were working without calculators. They (and I!) calculated the answer correctly, but a large proportion of them did the calculation faster than I did, giving an exact answer (1343.75m). However, there was no discussion that the question concerned a mathematical model (the 0.8 degrees per 100m rule) and that therefore the ‘answer’ would only be an approximation. Their ability to do the right calculation (the theme of the lesson was rational division), and to do the calculation quickly and accurately was extremely impressive. We could and should aspire to our 13 year olds developing the same facility. I took some (but not much) consolation from the thought that in an English classroom there would have been some discussion about what degree of accuracy was appropriate for the answer!

So, no shortage of moments where I simply applauded what I saw.

However, a short trip that enabled me to visit five schools in China and speak to Chinese education academics, mainly through interpreters, in two regions, could not answer all my lingering questions, such as:

How representative are the schools, teachers and pupils we saw?

How exactly do teachers give feedback to pupils?

What happens to pupils who can’t keep up?

What exactly are the teachers doing when they are not teaching?

How does formative assessment work in China?

[These questions were asked, through interpreters, but the answers were not clear and the limited time meant there was no opportunity for first-hand observation]

My conclusion from the trip is that, despite the obvious cultural differences, there are definitely things we can learn from the way mathematics is taught in China. We need to find out more about the details, and try out some ideas. I’m convinced it will be worth doing. For example, if we taught maths in England in significantly larger classes, thus freeing up teacher time for planning and feedback, would that make our mathematics teaching more effective? We’ll never know unless we try!

24 March 2014 10:30 I was educated in Pakistan and reading this article made me remind my own classroom, about 17 years ago. I still remember the days when I used to crack on my homework as soon as I arrived home after school. No phones or video games. Alot of practice of statistical and mathematical exercises every day during the week. I think it is mainly the practice which would make British perfect and fluent in mathematical operations - also a balance between being on the phones and studies ....

I have just come back from 2 years working in an experimental primary school in Shanghai. I was the Head of English but worked closely with other departments. I speak fluent Mandarin and thus was able to participate in Maths team meetings, and support some Maths lessons.

To answer a few questions, all of the Maths teachers I knew were massively overworked. Yes, they had fewer classes per day but every child was set an expected 20-40 minutes of homework per night which was then marked before the first class of the day and any misconceptions were corrected in class or during breaks and lunchtime. If children were struggling with the content of lessons, parents were quickly informed, extra support was put in place and the teachers worked until the child met the expected level.

Whilst the lessons you describe sound representative of a typical lesson, these types of lessons were taught only a few times a week. The rest of the classes were homework correction, testing and feedback from tests. Formative assessment was done through tasks that all children in the year-group undertook, feedback was immediate and extra support was put in for children or classes who struggled with the content.

In two years I was never able to pin-down a formal curriculum, but the local government provides text books and homework books which the teachers follow for the formal lessons. Each year-group had a Maths coordinator who attended weekly meetings with the Maths coordinator. There are also Maths advisors (former heads and local government advisors) who oversee lessons, prepare tests and encourage enrichment activities. Thus, with so much support, the individual teachers did not have to prepare new material for each class and could spend their time focusing upon marking and feedback.

Whilst the teaching I witnessed was amazing, it has to be put in the context of China, where the only subjects that parents feel are important are maths and language. Parental support is a major factor that ensured no children were left behind and made the children appreciate the value of maths lessons.

19 March 2014 22:51 "It's not all about rote learning and drills"

Hi Charlie

I was fortunate to visit Shanghai in January. Your article is spot on - the rich variety of questions and problems used was impressive.

Since being back, it took me three presentations to appreciate the need to dispel the myths and pre-conceptions about rote learnng and drills from the outset for future presentations. Your opening quote really helps to set the scene.

Once we are clear that the emphasis in Shanghai is on conceptual understanding, and the threat of ongoing rote learning and drills have been banished, everybody has been much more receptive to the transferable elements. The rich variety of questions and the reduction in transitions have led to fascinating discussions. The "transition" debate includes the transition of having a different teacher for Maths each year, even if it is in the same school.

In England, many pupils have 10 or more different teachers for Maths up to the age of 16. In Shanghai, pupils are likely to have much greater continuity, and may have as few as 2 different teachers for Maths up to the age of 16.

Collaborative planning supports this approach, so that the weakest teachers are always delivering lessons which have been planned with excellent practitioners. Likewise, regular CPD opportunities and confident subject knowledge help to reduce variation in the quality between teachers.

If we can support less confident teachers with collaborative planning and regular CPD, as happens in Shanghai, it will give schools greater confidence to reduce the number of transitions for children.

much of my own research, curriculum development and creation of ICT teaching resources has focused on those hard-to-teach, difficult concepts as defined in numerous research papers and GCSE examiners reports e.g. geometry, transformations, vectors, surds, writing & solving equations, ratio & proportion, sequences in shapes, trigonometry, experimental probability etc.

Understanding how Chinese teachers meet the needs of their pupils and deliver engaging interactive lessons to accomplish these topic objectives would be of great interest, especially if they ensure, as we UK maths teachers aspire to, that they address the needs of pupils who may be Visual, Auditory, and/or Kinesthetic learners. I would suggest that UK pupils have a greater spread of these 3 styles and the lack of presence of their preferred learning style in lessons may lead to much of their initial difficulty with these topics. Do Chinese teachers ensure that these VAK elements are featured in their lessons and content is differentiated for ability, outcome and the innate learning characteristics of individual pupils?

13 March 2014 21:31 Having heard the initial media reports on this issue, my intial reaction was the predictable one of "How is that every going to work here" etc. But I have decided to approach the issue with a open mind and came here to read what Charlie had found out. It certainly raises some interesting questions, although I still have several questions and concerns.

I am intersted in the idae of large class sizes, presumably to free up more time for teachers, but I fear that the politicians will cherry pick the idea of larger classes to save money and quietly dismiss the reduced contact time. I am also struggling to see how I would even physically fit 45 students into any of our classrooms - I am guessing that a resurection of "building Schools for the Future" isn't on the cards.

It is gratifying to read that mathematics education is so highly valued, but making that happen here is beyond the control of schools. Everywhere in the media, feelings of inadequacy in mathematics are worn as a badge of honour - combating this would be a prerequisite to any changes, yet we seem as far away from this as ever.

It would also be interesting to know how Chinese schools approach the use of ICT in the classroom, how they make use of problem solving activities and how discipline problems are either dealt with or avoided.

Some interestng ideas, but the devil, as always will be in the detail, and I fear that The Goves of this world will select what they like and brush the rest under the carpet.

I read your blog regarding your Chinese teaching experience. I'm lucky enough to work with a partnership school in Shanghai and go there every October for 10 days. It would be really worth catching up to swap experiences as I have spent a fair amount of time looking at assessment, consolidation, homework and pupil progress in what is deemed to be a really good Shanghai Experimental school.

13 March 2014 11:57 Your reference to how much time and energy the Chinese teachers spent reflecting and planning is interesting. Sounds like the kind of thing Liping Ma (Knowing and Teaching Elementary Mathematics - Teachers' understanding of fundamental mathematics in China and the US, 1999) talks about. She suggested that the Chines teachers were - on paper - often less well educated than their US counterparts, but that their approach to maths and to teaching, and the scope they have for discussion with colleagues, means that they think more deeply about the ideas they're teaching. The Chinese teachers were also less likely to say (I'm paraphrasing) "I can't remember, I'll go and look that up", more likely to say "I'll think about that, and will discuss it with colleagues; meanwhile let's make a start on puzzling it out now" when something mathematical came up in interviews she did with them.

12 March 2014 19:59 Rachael - I'm in the same boat as you.

I can't help thinking that the lessons that we can learn from Shanghai and China in general are in danger of being lost. What happens in the classroom in the UK is at least as good as anything that we saw in Shanghai but what happens around that, outside of the classroom is amazing!

I've found myself saying several times that, in Shanghai it's very hard to be a bad teacher. Shanghai teachers ride the wave of time, support and culture and do very well as a result.

Some of these things we can learn from and some, I think, are simply not transferable.

But focussing on 'teachers' rather than 'the education system' feels like it's missing the point.

12 March 2014 19:34 I was lucky enough to go to Shanghai in January. I saw much of what Charlie talks about here in Ningbo schools and it did challenge my preconceptions. I have emailed Elizabeth Truss to highlight the teaching load - imagine having time EVERY day to discuss, plan, and reflect with other subject specialists teaching the same content as you? How wonderful would that be!

I was educated in Pakistan and reading this article made me remind my own classroom, about 17 years ago. I still remember the days when I used to crack on my homework as soon as I arrived home after school. No phones or video games. Alot of practice of statistical and mathematical exercises every day during the week. I think it is mainly the practice which would make British perfect and fluent in mathematical operations - also a balance between being on the phones and studies ....