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