The late 1970s and
early 1980s witnessed a growing support for mixed-ability teaching, consistent
with the more general public concern for educational equality that was
pervasive at the time. But in the 1990s, concerns with educational equity
have been eclipsed by discourses of ‘academic success’, particularly for
the most ‘able’, which has meant that large numbers of schools have returned
to the practices of ability grouping (Office For Standards in Education,
OFSTED, 1993). Indeed ability-grouping is now widespread in the UK, not
only in secondary schools, but also in primary schools, with children as
young as 6 or 7 being taught mathematics and science (and occasionally
other subjects) in different classrooms, by different teachers, following
different curricula with different schemes of work. This phenomenon may
also be linked directly to a number of pressures from government. The 1988
Education Reform Act (ERA) required schools to adopt a national curriculum
and national assessment which was structured, differentiated and perceived
by many schools to be constraining. Research into the effects of the ERA
on schools has shown that a number of teachers regard this curriculum as
incompatible with mixed-ability teaching (Gewirtz, Ball, & Bowe, 1993).
The creation of an educational ‘marketplace’ (Whitty, Power & Halpin,
1998) has also meant that schools are concerned to create images that are
popular with local parents and ‘setting’ is known to be popular amongst
parents, particularly the middle-class parents that schools want to attract
(Ball, Bowe & Gewirtz, 1994). The White Paper 'Excellence in Schools'
(DFEE, 1997) revealed the new Labour Government’s commitment to setting:
Previous research in the UK has concentrated, almost exclusively, upon the inequities of the setting or streaming system for those students who are allocated to ‘low’ sets or streams. These are predominantly students who are also disadvantaged by the school system because of their ‘race’, class or gender (Abraham, 1989; Tomlinson, 1987; Ball, 1981; Lacey, 1970; Hargreaves, 1967). These research studies predominantly used qualitative, case-study accounts of the experiences of students in high and low streams to illustrate the ways in which curricular differentiation results in the polarisation of students into ‘pro’- and ‘anti’-school factions. Such studies, by virtue of their value-based concerns about inequality (Abraham, 1994), have paid relatively little attention to the effects of setting or streaming upon the students’ development of subject understandings (Hallam & Toutounji, 1997). Furthermore, they have tended to concentrate on ‘streaming’, in which students are allocated to the same teaching group for a number of subjects—what Sorensen (1970) termed a wide scope system, rather than on ‘setting’ which is carried out on a subject by subject basis (narrow scope).
Research in the USA has provided a wealth of empirical evidence concerning the relative achievement of students in academic, general and vocational tracks. Such studies have consistently found the net effects of tracking on achievement to be small (Slavin 1990), with evidence that tracking gives slight benefits to students in high tracks at the expense of significant losses to students in low tracks (Hoffer, 1992; Kerchkoff, 1986). However, such studies have given little insight into the way that tracking impacts upon students’ learning of mathematics, the processes by which it takes effect or the differential impact it has upon students. This is partly because quantitative methods have been used almost exclusively, with no classroom observation and no analysis of the mechanisms by which tracking influences learning. Many of the studies into tracking have also focused upon differences in group means, masking individual differences within groups (Gamoran and Berends, 1987; Oakes, 1985).
This paper will report upon interim data from a four-year longitudinal study that is monitoring the mathematical learning of students in six UK schools. This follows on from a study of two schools that offered ‘traditional’ and ‘progressive’ approaches to the teaching of mathematics (Boaler, 1997a, b, c). Although ability grouping was not an initial focus of that study, it emerged as a significant factor for the students, one that influenced their ideas, their responses to mathematics, and their eventual achievement. One of the schools in that study taught to mixed-ability groups, the other to setted groups, and a combination of lesson observations, questionnaires, interviews and assessments revealed that students in the setted school were significantly disadvantaged by their placement in setted groups. A year group of students was monitored in each school over a three year period (n ? 300) from the beginning of year 9 until the end of year 11 (ages 13-16). The disadvantages affected students from across the spectrum of setted groups and were not restricted to students in low groups. The results of that study, that related to setting, may be summarised as follows:
• Students from a range of groups were severely disaffected by the limits placed upon their attainment. Students reported that they gave up on mathematics when they discovered their teachers had been preparing them for examinations that gave access to only the lowest grades.
• Social class had influenced setting decisions, resulting in disproportionate numbers of working-class students being allocated to low sets (even after ‘ability’ was taken into account).
• significant numbers of students experienced difficulties working at the pace of the particular set in which they were placed. For some students the pace was too slow, resulting in disaffection, while for others it was too fast, resulting in anxiety. Both responses led to lower levels of achievement than would have been expected, given the students’ attainment on entry to the school.
All six schools teach
mathematics to mixed-ability groups when students are in year 7 (age 11).
One of the schools puts students into ‘setted’ ability groups for mathematics
at the beginning of year 8 (age 12), three others ‘set’ the students at
the beginning of year 9 (age 13), and the other two schools continue teaching
to mixed ability groups. The students in our study have just completed
the end of year 9, which has meant a change from mixed ability to setted
teaching for three of the cohorts. There are approximately 1000 students
in the study. Research methods have included approximately 120 hours of
lesson observations, during years 8 and 9, questionnaires given to students
in the six cohorts (n=943 for year 8, n=977 for year 9, with matched questionnaires
for both years from 843 students) and in-depth interviews with 72 year
9 students. This has included 4 students each from a high, middle and low
set in the setted schools and students from a comparable range of attainment
in the mixed ability schools. We have also collected data on attainment,
social class, gender and ethnicity. This paper will draw upon questionnaire
responses, lesson observations and 72, 30-minute interviews to illustrate
the ways in which ability grouping practices have impacted upon students’
learning of mathematics.
We chose to observe
set 1 lessons and interview set 1 students in this follow-up study to determine
whether the environment of set 1 lessons in other schools was similar and
whether students were disadvantaged in similar ways. Early evidence suggests
that this is the case. Every one of the 8 girls interviewed from set 1
groups in the current study wanted to move down into set 2 or lower. Six
out of eight of the set 1 boys were also extremely unhappy, but they did
not want to move into lower groups, presumably because they were more confident
(although no more able), than the girls, and because of the status that
they believed being in the top set conferred. Observations of set 1 lessons
make such reactions easy to understand. In a range of top-set classes the
teachers raced through examples on the board, speaking quickly, often interjecting
their speech with phrases such as ‘come on we haven’t got much time’ and
‘just do this quickly’. Set 1 lessons were also more procedural than others
— with teachers giving quick demonstrations of method without explanation,
and without giving the students the opportunity to find out about the meaning
of different methods or the situations in which they might be used. Some
of the teachers also reprimanded students who said that they didn’t understand,
adding comments such as ‘you should be able to, you’re in the top set’.
Before one lesson the teacher told one of us (JB) that about a third of
his class were not good enough for the top set and then proceeded to identify
the ones that "were not academic enough", with the students concerned watching
and listening. The following are descriptions of ‘top set’ lessons, from
students in the 4 setted schools:
He wants to be successful, better than set 2, so he goes really fast, but it’s over the top. (school R, boys, set 1)
He explains work like we’re maths teachers — really complex, I don’t understand it. (school R, boys, set 1)
I want to get a good mark, but I don’t want to be put in the top set again, it’s just too hard and I won’t learn anything. (school R, girl, set 1)
Practically all the time you are rushing through and not understanding. (school W, girls, set 1)
I want to go down because they do the same work but they do it at a slower pace, so you can understand it better, but we just have to get it into our head the first time and that’s it. (school W, girls, set 1)
Most of the difference is with the teachers, the way they treat you. They expect us to be like, just doing it straight away, like we’re robots. (school A, boy, set 1)
I used to enjoy maths, but I don’t now because I don’t understand it —what I’m doing. If I was put down I probably would enjoy it. I’m working at a pace that is just too fast for me. (school F, girl, set 1)
In the same paper,
Boaler also argued that the fast, procedural and competitive nature of
set 1 classes particularly disadvantages girls and that the nature of high
set classes contributes to the disparity in attainment of girls and boys
at the highest levels. Despite media claims that girls are now overtaking
boys in all subjects (Epstein, Maw, Elwood & Hey, 1998), boys still
outnumber the number of girls attaining A or A* grades in mathematics GCSE
by 5 to 4. As the vast majority of able girls are taught within set 1 classes
for mathematics in the UK (The Guardian, 1996) and the four schools in
this study are unlikely to be particularly unusual in the way that they
teach set 1 lessons, it seems likely that the under-achievement and non-representation
of girls at the highest levels is linked to the environments generated
within top set classrooms.
’Cause they don’t think they have to bother with us. I know that sounds really mean, but they don’t think they have to bother with us, ’cause we’re group 5, so if they have a teacher who knows nothing about maths, they’ll give them to us, say a PE teacher. They think they can send anyone down to us, they always do that, they think they can give us anybody. (school R, set 5, girls)
We come in and sir tells us to be quiet and gives us some questions then he does them on the board, we want to do it ourselves but he does it.
Even though we’re second from bottom group, I think it would be much better if we didn’t have the help with it.
JB: Why does he write the answers on the board?
I don’t know, he thinks we’re stupid.
He thinks we’re really low. (school A, set 6, boys)
It’s too easy, it’s far too easy.
JB: What happens if it’s too easy?
You just have to carry on and do it, and if you don’t he gives you detention.
Last year it was
harder, much harder. (school R, set 5, boys)
He just writes down answers from the board, we tell him that we can do it, but he just writes down answers anyway.
JB: And what are you meant to do?
Just write them down. That’s what we say to him, ’cause people get frustrated from just copying off the board. (school A, set 6, girls)
We do baby work off the board — stupid stuff that we already know, like 3 times something equals 9, it’s boring and easy. (school R, set 5 girls)
And we’re not going to learn from that, ’cause we’ve got to think for ourselves.
Once or twice someone has said something and he’s shouted at us, he’s said — well you’re the bottom group, you’ve got to learn it, but you’re not going to learn from copying off the board.’ (school A, set 6, girls)
JB: He says that to you?
I don’t know, I don’t think he’s got faith in us, or whatever, he doesn’t believe we can do it. (school A, set 6, boys)
JB: How can you move up?
There is nothing you can do, he has no idea how we’re doing, he hasn’t taken our book in once. (school R, set 5 girls)
I want to be brainy and go up and be good at maths, but I won’t go up if the work is too easy. (school R, set 5, boys)
The work is far too easy, but if we try and complain he says, "Be quiet", and then, "Detention", because we tried to explain it to him. Today he sent Mark out, ’cause he told him it was too easy, so he just sent him out. (school R, set 5, boys)
In interviews students talked at length about the restrictions imposed upon their pace of working since changing to setted groups, describing the ways in which they were required to work at the same speed as each other. Students reported that if they worked slower than others they would often miss out on work as teachers moved the class on before they were finished:
It’s different ’cause in sets you all have to stay at the same stage. (school W, set 3, boys)
But the process of ability grouping did not only appear to initiate restrictions on the pace and level of work available to students, it also impacted upon the teacher’s choice of pedagogy. Teachers in the four schools in our study that used ability grouping responded to the move to setted teaching by adopting a more prescriptive pedagogy and teachers who offered worksheets, investigations and practical activities to students in mixed-ability groups concentrated upon chalk-board teaching and textbook work when teaching groups with a narrower range of attainment. This is not surprising given that one of the main reasons mathematics teachers support setting is that it allows them to ‘class teach’ to their classes, but it has important implications for the learning of students. When students were asked in their questionnaires to describe their maths lessons, the forms of pedagogy favoured by teachers in the schools using ability grouping were clearly quite different from those in the schools using mixed ability teaching. Some of the students’ responses to this question were given the code ‘lack of involvement’ because students wrote such comments as ‘lessons go on and on’ or ‘maths lessons are all the same’. Twelve per cent of responses from students in setted groups reflected a lack of involvement, compared with 4% of responses from students in mixed-ability groups. An additional 12% of students from setted groups described their lessons as ‘working through books’, compared with 2% of students in mixed ability groups; whilst 8% of setted students said that the ‘teacher talks at the board’, compared with 1% of mixed ability students. Fifteen per cent of students in setted groups described their mathematics lessons as either "OK", "fun", "good" or "enjoyable", compared with 34% of mixed ability students.
In a separate open question students were asked how maths lessons could be improved. This also produced differences between the students, with 19% of students taught in sets saying that there should be more open work, more variety, more group work, maths games or opportunity to think, compared to 9% of mixed ability students. Eight per cent of setted students said that lessons should be slower or faster, compared to 4% of mixed ability students and 4% of setted students explicitly requested that they return to mixed ability teaching.
The influence of ability grouping upon teachers’ pedagogy also emerged from the students’ comments in interview. The following comments came from students across the spectrum of setted groups:
Rubbish — we just do work out of a book.
It was better in years 7 and 8. We did all fun work (school R, set 1, girls)
I would like work that is more different. Also when you can work through a chapter, but more fun.
Could do a chapter for 2 weeks, then something else for 2 weeks, an investigation or something —the kind of investigations we used to do. (School R, set 5, girls)
Last year it was better, ’cause of the work. It was harder. In year 8 we did wall charts, bar charts etc, but we don’t do anything like that. It’s just from the board.
I really liked it
in year 7, we would work from books and end of year games — really good.
This year it’s just work from the board. (School R, set 5, boys)
In year 8, Sir did a lot more investigations, now you just copy off the board so you don’t have to be that clever.
Before, we did investigations,
like Mystic Rose, it was different to bookwork, ’cause books is just really
short questions but those were ones Sir set for himself, or posters and
that, that didn’t give you the answers. (School A, set 4, boys)
In year 7 maths was good, it was alright. He got us thinking for ourselves and we did much more stuff like cutting out, sticking in, worksheets. Now, everyday is copying off the board or doing the next page, then the next page and it gets really boring. (School A, set 6, girl)
The requirement to work at an inappropriate pace is a source of real anxiety for many students, particularly girls:
Yeah ’cause like especially when everyone else understands it and you think ‘Oh my God I’m the only one in the class that doesn’t understand it’
If you don’t understand something, then it’s just like, you know, it really depresses you. (School F, set 3, girls)
The major advantage that is claimed for ability-grouping practices is that they allow teachers to pitch work at a more appropriate level for their students. However, while ability-grouping practices can reduce the range of attainment in a class, within even the narrowest setting system, there will be considerable variations in attainment. Some of this will be due to the inevitable unreliability of mechanisms of allocating students to particular sets, and even if the average attainment of students in a set is reasonably similar, this will mask considerable variation in different aspects of mathematics and in different topics, as the students were well aware. Indeed the students held strong beliefs that individuals have different strengths and weaknesses and that it is helpful to learn from each other and to learn to be supportive of each other:
Classes should be mixed, then everyone can learn from everyone, it’s not like the dumb ones don’t know anything, they do know it, but the atmosphere around them in lessons means they can’t work and they just think to themselves — well, what’s the point? (School W, set 3, boys)
Another consequence of setting that emerged in Boaler’s previous study, and which is beginning to emerge in the current study, is the consequence of set allocation for students’ entry to the GCSE. The report of the Committee of Inquiry into the Teaching of Mathematics in Schools (1982), generally known as the ‘Cockcroft report’, argued that it was unacceptable that the majority of students entered for the school leaving examination would gain less than 40% of the available marks. The report recommended that school-leaving examinations in mathematics should be differentiated, so that students would take only those papers appropriate for their attainment. For the mathematics GCSE, there are currently three ‘tiers’ of entry, with different syllabuses. Because schools find it difficult to operate with students in the same class following different syllabuses, most schools in the country (and all the four schools using ability-grouping in our study) enter all the students in a particular class for the same tier of the examination. The effect of this is that students in the lower sets will be entered for an examination in which the highest grade they can achieve is a grade ‘E’, whereas the only grade that is ever specified for recruitment or for further study is a grade ‘C’.
In Boaler’s previous study, the students did not become aware of this restriction until their final year of schooling, year 11, and this discovery caused considerable resentment and disaffection. In the current study, only a few students (exclusively in the top sets) are aware of the effects of tiering, but it is already a significant issue for those beginning to understand the implications of the tiering system:
As we have noted above, many of the disadvantages of setting that we have described are contingent rather than necessary features of ability-grouping, but we believe that they are widespread, pervasive, and difficult to avoid. The adoption of ability-grouping appears to signal to teachers that it is appropriate to use different pedagogical strategies from those that they use with mixed-ability classes. The best teachers are allocated to the ablest students, despite the evidence that high-quality teaching is more beneficial for lower-attaining students (Black & Wiliam, 1998, p42). Curriculum differentiation is polarised, with the top-sets being ascribed qualities as mathematicians, not as a result of their individual qualities, but simply by virtue of their location in a top set. In order to ensure that the entire curriculum is covered, presumably to suit the needs of the highest-attaining students within the top set, the pace of coverage is both increased and applied to the whole class as a unit, and teachers seem to make increased use of ‘transmission’ pedagogies. For some students, who are able to conceptualise the new material as it is covered, the experience may be satisfactory, but for the remainder, the effect is to proceduralise the curriculum until it becomes a huge task of memorisation. The curriculum polarisation results in a situation in which upward movement between sets is technically possible, but is unlikely to be successful, because a student moving up will not have covered the same material as the class she is joining. Finally, because of the perversities of the examination arrangements for mathematics GCSE, the set in which a student is taught determines the tier for which a student is entered, and thereby, the maximum grade the student can achieve, and, for most students, this decision will have been made three years before the examination is taken.
Of course, we are not advocating that schools should dispense with ability-grouping immediately—that would clearly be disastrous—but we do believe that the features of the practices adopted by the schools who have maintained mixed-ability teaching with older students provide important suggestions as to how schools can reduce their dependence on between-class ability grouping as the primary strategy for dealing with the diversity of attitudes, capabilities and attainments of students in mathematics. We would also suggest that government ministers should be promoting research and inquiry into mixed ability teaching, and supporting those schools that use such forms of grouping succesfully, rather than discriminating against these schools and exerting pressure upon them to change (Boaler, 1997c).
Because all of the schools in ur study make some use of mixed-ability grouping in the earlier years, all the teachers in our sample have some experience of teaching mixed-ability classes, for which a variety of strategies are used. Some make substantial use of independent learning schemes which allow a teacher to give each student an individual programme of work. They also use within-class grouping, with students on different tables working on different materials and at different speeds. Most of the teachers in the sample also made some use of more open tasks, which can be tackled at a variety of levels. Although these more open tasks were used infrequently with setted classes, it was surprising how favourably these were regarded by the students. When the students who were taught in sets were asked for the best lesson they remembered that year, almost every student described a lesson where the whole class had worked on an investigation or a problem that could be tackled in different ways
Within-class grouping, a system which is used by some of the teachers in one of our ‘mixed ability’ schools, is much more flexible. It allows opportunities for whole classes to do the same work and allows students that are regarded as weaker on some areas to shine. One student, regarded by her teacher as the ‘weakest’ in her mixed ability mathematics class, described her best lesson thus:
Although there are substantial problems in interpreting the results of international comparisons (Brown, 1998, Wiliam, 1998), there is little doubt that, in a variety of respects, the performance of primary and secondary school students in the United Kingdom is modest by international standards (Beaton, Mullis, Martin, Gonzalez, Kelly & Smith, 1996; Mullis, Martin, Beaton, Gonzalez, Kelly & Smith, 1996). Kifer & Bursten’s (1992). Analysis of data from the Second International Mathematics Study (SIMS) suggests that the two factors that are most strongly associated with growth in student achievement in mathematics (indeed the only two factors that are consistently associated with successful national education systems) are opportunity to learn (ie the proportion of students who had been taught the material contained in the tests) and the degree of curricular homogeneity (ie the extent to which students are taught in mixed-ability, rather than setted, groups).
While Bennett, Desforges, Cockburn and Wilkinson (1984) found that teachers using within-class ability grouping tend to over-estimate the capabilities of weaker students, and set insufficiently challenging work to the most able, the evidence that we have found in the current study suggests very strongly that between-class ability grouping produces the opposite effect. Indeed, the strength of the curriculum polarisation, and the diminution of the opportunity to learn that we have found in the current study, if replicated across the country, could be the single most important cause of the unacceptably low levels of achievement in mathematics in Great Britain. The traditional British concern with ensuring that some of the ablest students reach the highest possible standards appears to have resulted in a situation in which the vast majority of students achieve well below their potential. As one student poignantly remarked:
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