The part-time Masters course I’m following is called “International Perspectives on Mathematics Education”, and so a lot of our reading and discussions focus on the way maths is taught throughout the world. One of the course requirements is for all students to present on an aspect of maths education that interests them, drawing on their own experience, and to lead the group in discussion on that topic.
Last night was my turn, and I chose the topic “Grouping by Ability”. I started by outlining my own experiences as a learner – I was educated in Lincolnshire where there are still grammar schools, but my dad chose not to enter me for the 11+ and instead I went to the rural comprehensive school just up the road. The grammar schools tended to cream off the top, so it wasn’t a true comprehensive. Thinking back, in Year 10 and 11 we were in mixed ability groups for our option subjects and it was only English, Maths and Science where we were setted. The top Maths set ended up with a wide variety of grades anyway; only a small handful (four or five of us maybe?) were entered for the Higher paper at GCSE and the rest of Set 1 sat the Intermediate paper. In explaining all of this background to the rest of the students on the Masters course, I trotted out a little mantra of mine that I used to remind myself of regularly, whether teaching a “mixed ability” or “setted” group:
Every classroom is a mixed-ability classroom
The top set I found myself in as a learner was a mixed-ability classroom. My teacher had to work very hard to make sure there was an appropriate level of challenge for pupils like me who were very quick on the uptake and did lots of maths outside the classroom, while making sure there was appropriate support for people who took longer to come to grips with certain new concepts. She encouraged us to talk to each other and seek help within the classroom community rather than all lining up at her desk to ask her for help. These are the sort of strategies that teachers adopt through necessity when faced with learners working at a wide range of levels, but I think they are good teaching practices whatever the spread of achievement within a class. Of course my underlying philosophy of maths teaching is one where learners explore, conjecture and develop new understanding through collaboration with each other rather than one where the teacher imparts knowledge from the front, so this model of mixed-ability teaching doesn’t seem so alien to me as it might to others. The idea of having a set where everyone is “working at level 6” so the lesson is pitched at some pupil who is somewhere in the middle of whatever level 6 means, and those who are thinking above that level just have to slow down a bit, and those working below that level will have to follow on as best as they can – that seems like laziness to me. If we accept that we’re going to have to differentiate within whatever class we are faced with, why should the range over which we need to differentiate make that job any harder?
The most interesting part of my student-led seminar was the discussion which followed. Most of the cohort were educated overseas, and when I took them through my own experiences not just as a learner but also as a teacher in schools where setting was the norm, they were quite shocked. Unfortunately, the half-hour we had for me to present and for us to discuss wasn’t enough to get into the intricacies of other countries’ education systems, but I need to have a lot more conversation with my peers from overseas about how exams are structured and how lessons are taught to cater for a wide range of pupils. I have been so embedded in a system where grouping by ability is the norm that I find it very hard to imagine how it can be otherwise.
Were you educated in the UK? In a setted or mixed ability classroom? Or in an area with grammar schools? How did it affect your experiences of learning maths? Or perhaps you were educated somewhere where mixed ability teaching is the norm, and my experience is as alien to you as yours is to me – tell me about it in the comments!
Alison Kiddle's blog 
November 18, 2010 at 12:18 |
Disclaimer: I was only in NZ until 14/15 (left about a week before my 15th birthday), so this is formed from a child/learner’s POV not an informed adult one.
I think in NZ at least when I was growing up … we were less worried about ‘failing’ people (as in, giving them a mark of an F, which is acknowledged to be a fail). This is out of date, because the year I left they started doing much more coursework-based assessment and all sorts of things like that (and grading things pass / merit / distinction), but generally in the experience that I had, everyone had the same tests and grades were ABCD F – I found it really weird that in the UK you have grades E, F, G and U.
It may be laudable that you want to say ‘well, someone who answered 1 question out of 10 correctly should get a G, whereas someone who got them all wrong should get a U’ but I think it’s a distraction and is ultimately detrimental to the system (cf how I think it’s really odd that we have ‘differentiated’ exam papers Foundation/Int/Higher).
In my opinion (and I’m probably prejudiced because we all think that the way we grew up is the natural order of things) if you’re going to grade with letters, 5 is plenty. ABCD F – where ‘F’ is ‘Frankly, you failed’, ‘D’ is ‘you failed, but you’re not too far from a C, try a retake’ and A-C are passes. And I think if you’re only trying to capture grades ‘ABCD’ on a paper it’s much easier to write that exam paper.
And if a huge proportion of your kids are not getting Ds then there’s something wrong with the exam / the teaching / the curriculum / the system – adding in extra things to let them ‘achieve’ a grade G is NOT THE ANSWER.
I guess my thoughts are: assume for the moment that we are going to test kids in a reasonably traditional manner (because assessment is another can of worms). Then if everyone is taking the same test, then that makes it less problematic to teach everyone in the same class. Also it breaks down some barriers of labelling some kids as ‘the ones who can’t possibly get a B so they will sit the foundation paper’, and this is analagous to / connected with labelling the kids as ‘the ones who will get Cs and Ds so they are Set 3 kids’.
rant over 🙂
November 18, 2010 at 13:14 |
It would definitely be interesting to know more about some other countries’ education systems.
I was struck by a comment from a year 10 Chinese pupil: “I think the teaching is much better here than in China.” To put this in context, she was attending a school in special measures, and was in a year 10 set much like the one you were in: all the Intermediate candidates and a handful of Higher. She was at least two years ahead of the next best, so if you measure by attainment, it seemed unlikely that our teaching was better.
She told me when she arrived that she had started calculus but had been really struggling with it. I gave her an AS textbook, and she started again, with a minimal amount of help from me. I got the impression that in China, she had sat in her class (of 58) failing to understand and keep up; here, although she got precious little direct teaching, what she did get was fully differentiated.
November 18, 2010 at 14:53 |
If I remember correctly, we were streamed in years 9-11 for Maths and Science. Science was only loosely setted: the top half of the year did separate science GCSEs, while the bottom half did combined-science (worth 2 GCSE’s). But Maths was streamed into six or seven different sets, the top of which did GCSE a year early.
I don’t know if it helped me or not. I was in the top maths and science sets, and did well, but I didn’t do badly in the subjects that were not streamed. I know that the very bottom maths set was much smaller than the others and made up of students who were really struggling, so they probably benefitted from being in a small class.
But my experience is atypical: I was educated at a selective school, and so the spread of ability was concentrated at the top. A true mixed-ability class with A* students and U students would, I suspect, be very different.
Is there anywhere in the world that sets by ability but not age? That is, the students are all at about the same level, but of different years. There’s probably a good overlap in the abilities of year n and year n-1 students, and I can see no immediate reason why they couldn’t be taught in the same class.
November 18, 2010 at 22:04 |
Thank you, Alison, for reminding us of the ‘every classroom is a mixed-ability classroom’ mantra. Really important and, to my shame, one that I was often guilty of forgetting when I was teaching.
I wonder whether teacher expectation is a key factor in this debate …
November 19, 2010 at 19:43 |
Teacher expectation is very important I think. Often when I work with groups of children I don’t know, the ones who shine are not necessarily the ones their usual teacher would have picked out in advance as the ‘best’, but they have a chance to shine for me because I have no prior expectations. I think it’s very hard for teachers who were themselves educated in a setted or streamed environment to picture what good mixed-ability teaching might look like. As long as our education system is so exam-driven and as long as the exams belong to the current two-tier system with grades from A* to U, it’s difficult to see how change can happen, at least at GCSE level. But identifying some kids as being “bad at maths” in lower primary seems like a bad idea to me.
November 19, 2010 at 23:49 |
The success or failure of China’s mathematics education has been a debating topic for quite some time, without any clear conclusion so far.
One the one hand, Chinese school students resent the pressure from drills and exams. The more children-oriented teaching style and much, much more relaxed classroom atmosphere in western countries easily win their love. Emma’s student may be an example. The Chinese government also suspects its schools and the teaching possibly damage the development of students’ ability of creativity. The Chinese parents are also keen in sending their children to western schools (mostly private schools).
On the one hand, however, the academic world cannot ignore the solid basic knowledge and sound skills that students obtained from the Chinese (also other oriental countries, together called CHC: Confucius Heritage Culture) classrooms, even though their way of teaching is regarded old-fashioned, even anti-learning. Many of the graduates, who benefited from these knowledge or skills in employment or life, appreciate it even adore the system.
Is it good or bad? I can’s say for sure, although I learnt Mathematics in China and now trying to teach Maths in the English way. It seems to be crucial that through whose lens you look at it, children’s or adults’.