Geoff Tennant - Promoting access to mathematics for all
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5/3/17: what can we learn about mathematics teaching from the Chinese?

A very warm welcome to the post graduate teacher training course here at **** University.  And a particularly warm welcome to the teaching profession.  You are coming into one of the oldest professions in the world, working with the nation's youth to acculturate them into society and prepare them for the challenges of the working world.  Through your mediation children will do things which they could never do by themselves and which their parents would find unimaginable.  You will help shape the future of youngsters for decades to come, crucially engaging them with a love of learning as they adapt to the changing world around them.

But there is another side to this, of course, so let me start again.  Welcome to one of the most demoralised, underpaid, overworked, undervalued and taken for granted professions in the world.  Nothing you do will every be good enough, as you supposedly go home at 3.30pm and disappear for enormously long holidays.  No level of achievement of your pupils will persuade others that educational standards are doing anything over than falling.  No matter how experienced you become or skilled you get, every politician, journalist, taxi driver and hair dresser will know how to do your job better than you.

I devised the speech above when I was working in initial teacher training but never got to give it quite in this form.  But this perception that educational standards are low and / or falling is an interesting one.  If you want to believe it, you can find the 'evidence' and ignore everything else.  Examination results going down?  Standards are clearly falling.  Examination results going up?  The examination is clearly being dumbed down so standards are falling.  Examination results staying the same?  Standards are stagnating therefore falling.

And aligned to this point is the belief that other countries are doing things much better than we are.  When I was in Jamaica back in 2012 I was asked to speak on educational reform, and I went into this point.  You can find the PowerPoint I used here, but in brief I found newspaper articles comparing the educational systems with Jamaica (bad) with Ireland, Singapore and Finland (good), England (bad) with Scotland and Hong Kong (good), USA (bad) with Japan (good), Singapore (bad) with Finland (good).  Invariably the author is from the country coming out badly in the comparison.  I'm pretty sure that, if one were to put enough time into the escapade, it would be possible to go right round a circle and come back to where we started.

So, in the news a number of times fairly recently have been stories based on the premise that the place to learn how to teach mathematics is China.  Now, I haven't been to China at all, let alone to visit mathematics classrooms.  But if I dd, what would I be able to see?  If you'll excuse me stating the obvious, the lesson would be going on in a language which, literally and metaphorically, is Chinese to me (sorry, sorry, very bad pun, sorry).  So either there would be large gaps in what I was observing, or I would be very dependent on a translator who would be bringing his/her own understanding as to what was going on.  I would also be very dependent on others for any sense as to the extent what I was observing would be 'normal' across the whole of the country, or whether I was watching carefully selected teachers teaching carefully selected children.

But, whilst I have not visited China, I have read a few books specifically about teaching in China and rather more about comparative issues, particularly, recently I have read:

Li, Y., & Huang, R. (Eds.). (2013). How Chinese teach mathematics and improve teaching. New York: Routledge.

One thing which comes out immediately in the book that China implemented reforms in 2001 heavily influenced by the American National Council for Teachers of Mathematics.  Which in itself is interesting, and in accordance with my point above, we look to China whilst China looks to the USA whilst the USA looks to.....

As I read the book, three questions particularly came to mind: what is it that I am reading that I can readily agree represents good practice in mathematics teaching?  What is it that is different?  And what is it that we are not being told?  Let me address these below.

What can I easily agree represents good practice?
Actually, almost everything.  So the importance of strong foundations is emphasised, also plenty of practice, clear links between different areas of mathematics (number and algebra being one of my own hobby horses), knowledge prioritised alongside understanding.  Variety of teaching methods including teacher exposition.  And good programmes for teacher professional development, particularly emphasising joint planning, observation of each other's lessons and debriefing afterwards.  It is noted also that Chinese teachers overall have good subject knowledge.

And I would agree that, speaking from a UK context, that we possibly don't give enough time for routine practice, ensuring eg. that timestables are learnt to the point where they are right at our finger tips, and that in some places the teacher could usefully give more of a lead up front.  But these are matters of degree, I suggest, not of high principle.

What is it that is different?
A few points came out in the book which do not readily fit into a UK context for good practice.  One is that the expectation is that little is done to accommodate learners going at different speeds or with different prior knowledge, the expectation is that all learners keep to the same speed, so little differentiation is going on.

Now, differentiation is an interesting area, like so many educational concepts, everything seems obvious right to the point where you start thinking about it.  Back in 2001 I had a letter published in the Times Educational Supplement which helpfully pointed out that two then current Government policies were in direct contradiction.  One - Curriculum Online - was set to improve standards by allowing all children to work at their own pace, so unrestricted differentiation.  The other - the National Numeracy Strategy - said exactly the opposite, that standards were to be improved by restricting the range of differentiation.

(Parenthetical thought: whilst I was pleased to have this letter published, I wasn't so happy that it went into the edition least likely to be read in the entire year, ie between Christmas and New Year, an edition which has subsequently been discontinued.  Ah well, we can but try...)

More generally, I would tend to the view that too much differentiation leads to low standards and patronising attitudes, with bright but lazy youngsters able to coast along without making any much progress and not being challenged.  Too little differentiation leads to bright youngsters being held back and those with problems in the subject falling further and further behind.  As with so many issues, it is part of the skill of the teacher to find a balance between these two positions.  So the Chinese view, whilst being at one end of the debate, is not actually a million miles from what I would regard as good practice, as before, it is a matter of degree.

Another point of difference is the emphasis on doing things even when not understanding, that understanding can follow doing, with the UK emphasis tending to be the opposite way round, once one understands one can then get on with doing.  This is an interesting one, I think.  I can think of an example from when I was in school (involving resistors in parallel and series and restivity, do ask for more details if interested) when I was able to questions correctly for some years before the underlying concept made any sense to me.  One may well consider that this makes sense, give it a go, don't hold back, get involved.

But alongside this there are many many routines in mathematics, division of fractions being my favourite example, which are much, much easier to remember if the underlying concept is understood.  So rather than, "Ours not to reason why, just invert and multiply", if we instead say that 12 / 3 means how many lots of 3 are there are in 12, so 4, therefore (1/2) / (1/4) means how many lots of 1/4 are there in 1/2, therefore 2, we now have a way of connecting the concept of division from whole numbers to fractions.

So, again, I suggest this is a matter of degree, not high principle.  We want to understand the underlying concepts, but we don't want to hold back from doing things just because not everything is making 100% sense at the time.

The last point I want to look at under this heading is the authority of the teacher, which is emphasised in China.  Now, I want to know exactly this means.  If it means that teachers are respected, they ask for quiet and they get it, they ask for homework to be done and it happens, then this is all good.  If it means that children cannot ask if they can't read what's written on the blackboard, if what the teacher says is automatically considered right even when it is not, if teachers feel that they cannot answer a child's question by saying, "I don't know, how about you trying to find out, I will too, and let's see what we come up with," because that means their authority is undermined, then this is a bad thing.  And please believe me when I say that I have good reason to believe that teachers having authority in various parts of the world does indeed include elements in the second list. 

What we don't know
Now, I may be able to find out at least some of the information below if I try, but there are a large number of things which are not clear.  So, as I was saying about what I would be able to observe if I went to China, it is not clear the extent to which the accounts of lessons in the book reflect teaching across the entire country, all teachers, all learners, or just a few.  Putting the point into UK-friendly language, there is the very real danger of reading about grammar schools believing that we're reading about comprehensives.  It is not clear where teaching fits as an option for graduates against other options, so the extent to which people with options are inclined to choose teaching.

But there's a more fundamental question here: what's important?  Let me give an example from when I was a PhD student.  One of things I did was gather information from OFSTED reports enabling me to correlate the average class size in London schools with their overall GCSE (ie exams sat at the age of 16) results.  To discover that, in general, the higher the average class size in a school, the higher the GCSE score.

On the face of it this may seem surprising, but let me give a possible explanation.  The key issue here, I suggest, is popularity of the school.  Schools which are popular are oversubscribed, therefore are full, therefore have high average class sizes.  Alongside popularity goes a strong work ethic which then means results are good.  Meanwhile, poorly regarded schools contain learners and teachers with low morale working towards low scores - but in small classes corresponding to undersubscription.

Now, class size is an important variable in learners' experience, I believe that very strongly.  But it is easily swamped as an issue, when doing statistical analyses, by other things.  Of course, if we disregard this, then we would presumably decide that the way to improve school achievement is by increasing class sizes!  Researching class size is extremely difficult for this reason, all kind of ethical issues also come into play as to what one can and can't do.

Professor Dylan Willam, perhaps best known for his work with Professor Paul Black on formative assessment, coined the term 'policy tourism', the tendency to look to see what is happening in other countries, see what we want to see, and make simplistic analyses as to what is important.  So, if we accept the premise that Chinese youngsters are doing better than those in other parts of the world, it may be that the preparedness to work hard, do the practice, obey the teacher, have highly qualified, highly motivated teachers who good professional development opportunities relating to high morale are the important things here rather than precisely how the youngsters are taught.  

So, in summary, is it good to look to see what is happening in China?  Yes.  Are they doing things which are worth thinking through?  Yes.  Do they have hugely different methods for teaching mathematics which, if exported to the UK, would transform mathematics learning?  No, I don't think they do.  It is too easy to assume that the answers are out there in some other country, I would tend to the view that we know what to do, it's just a matter of doing it.  Which is both the easiest and most difficult thing in the world.

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Jamaica trip 2012
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Tanzania 2013
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