One of the enduring problems of English schools is their practice of setting by ability, which means that many thousands of students languish in low sets on diets of low-level, uninteresting work.
One of the enduring problems of English schools is their practice of setting by ability, which means that many thousands of students languish in low sets on diets of low-level, uninteresting work. Most of these are capable of achieving infinitely more, but their experience of being told that they are incapable turns them against learning and against school.
England is more committed to setting than most countries, and this practice continues despite numerous reports pointing to its ineffectiveness. I work in California now, but last year I spent a hot English summer interviewing young adults who had attended schools I had studied eight years ago in England, one of which used ability grouping. The young adults from this school reflected on the eight sets into which they had been sorted for maths. One young man told me that these had worked as a "psychological prison". Once students had been told that they were in a low set, they developed low self-esteem that stayed with them for years.
When I was a researcher at King's College London, my colleagues and I interviewed students in low and high maths sets. We were moved by the pleas of students in low sets who said they "just wanted to learn" but were not given the opportunity to do so. Some people believe the practice is right because it keeps the high achievers away from low achievers. The irony is that high achievers do not do any better in high sets than in mixed-ability groups, and for some students, being in a high set is a source of considerable anxiety.
Comparisons of test performance in different countries always show that countries that set students the least and latest have the highest performance. The reasons for this are obvious: once students are told that they are low-achieving and given low-level work, their learning diminishes. Yet we perform this strange, unfair labelling ritual all the time in English schools, and the Government would like to see the ritual begin when students are five or six years old.
Why is mixed-ability teaching so unpopular in England? I have recently completed a research study in California, in which I studied a mixed-ability maths approach in an urban multicultural school. Students achieved at higher levels than other students, they enjoyed maths more, and the ethnic cliques common in other schools did not form. Class visitors are amazed by the calm environment, with all students on-task, working hard and treating each other respectfully.
The approach was successful for high-attaining students in our four-year study, who achieved more in mixed-ability classes than high-attaining students in other schools who were put into high "tracks". Students told us that they learnt to respect students from different cultures and circumstances. Significantly, the equitable relations students formed came through a maths approach that also brought about extremely high achievement. By their senior year, 41 per cent of the students, many of whom were from ethnic minorities and low-income homes, were in calculus classes (similar to A-level maths in England), such was the love of maths they developed.
Longer accounts of the approach that the school used are available elsewhere, but one feature I want to highlight is the multi-dimensionality of the classrooms. Multi-dimensional classrooms are those in which teachers value many dimensions of mathematical work, not just the execution of procedures. Students work on open-ended problems that provide different access points and solution paths, and that allow for multiple representations. As students work on the problems, they are rewarded for such activities as asking good questions, rephrasing problems, explaining ideas, being logical, justifying methods, or bringing a different perspective to a problem.
Put simply, there are many more ways to be successful, so that many more students are successful. This mixed ability, multi-dimensional approach means that success was an option for all students. It gives them access to university and to higher-level jobs, and it allows many to plan mathematical careers. Such results are not usually achieved in urban schools in the US or England. I hope that English schools may benefit, too, from this approach, though I fear that UK politicians' blind commitment to setting will make this difficult.
The writer is professor of mathematics education at Stanford University, California
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