This article has been provided by EQ Australia and will appear in its forthcoming Autumn 2008 edition, 'Let's teach maths and science'.

Following our time as classroom teachers, we have had the opportunity to work with teachers across the early and middle years of schooling in every Australian state and territory, in professional development settings and in classrooms. Our observations, conversations with teachers and students, and our reading of the research literature have convinced us that a major impediment to the mathematical learning of students and their beliefs about themselves as mathematical thinkers is the widespread practice of ability grouping in mathematics.

In what follows, we use the term ‘setting’ to refer to assigning students to different classes according to mathematical capability. We also use the word ‘ability’, taking it to mean student capability and/or performance as perceived by the person(s) who formed the various classes across a year level.

1.  The research evidence is clear that generally any benefits which accrue from ability grouping are only to very high achievers, with a negative impact on average and low-attaining students.

Although some research draws a different conclusion from our own, the vast majority of studies we have read and, very importantly, the meta-analysis of research in this area is in harmony with the statement that most students are disadvantaged by classes grouped according to ability, with the only demonstrated benefit, often slight or non-significant in a statistical sense, being to high attaining students (Boaler et al, 2000; Lou et al, 1996; Slavin, 1990; Wiliam et al, 2004).

2.  International testing data shows that ability grouping has an overall negative effect on a country’s performance.

There are two factors which are consistently associated with successful national educational systems. The first is termed ‘opportunity to learn’ and refers to the proportion of students who have been taught the material contained in assessments. Needless to say, students in lower ability classes are unlikely to have experienced important parts of the curriculum offered to average and higher attaining students, and are immediately disadvantaged in terms of opportunity to learn. The second factor is the degree of ‘curricula homogeneity’ in the country, which is the extent to which students are taught in mixed-ability rather than setted classes. That is, generally speaking, the greater the use of ability grouping in a given country, the lower overall performance of that country on international assessments.

3.  Ability grouping can lead to the mistaken perception that individual differences are no longer an issue.

When teachers talk about the reasons why their schools use ability grouping, they will indicate that it enables them to teach more clearly to the needs of students, by narrowing the range of capabilities in the class. Parental pressure is raised often as another factor in decisions to move to ability grouping. In practice, there is a temptation by teachers of so-called like-ability classes to teach as though they believe that individual differences have been taken care of, teaching to the middle, rather than catering for individuals.

4.  Many schools assign their least-qualified teachers to the lower ability classes.

It has been well documented that there is a crisis in Australia in regard to having sufficient numbers of teachers of mathematics with sound content knowledge in the middle years of schooling. For a variety of reasons, the more experienced and often the more capable mathematics teachers are assigned to the higher ability classes. This, in part, might explain the research findings discussed in point 1. In the Australian context of a considerable shortage of qualified mathematics teachers, teachers with specialisations other than mathematics are often assigned one mathematics class. This is usually one of the ‘lower’ classes in the ability group situation. We would argue that this is another reason why lower ability grouped students are disadvantaged by this setting.

5.  Teachers of lower classes often have low expectations of what students can do.

It is hard for the teacher not to develop lower expectations of students perceived to be of lower ability than others. We would argue that there is a cyclic effect. Students in lower classes are perceived to be less able to handle challenging tasks, leading to the provision of less challenging work, given in smaller and smaller ‘chunks,’ often making tasks so step-by-step that little thinking is required of the students. Students start to pick up on these low expectations and take them to be a reflection of their capabilities. They then, in effect, give the teacher what is expected from such students – little enthusiasm, little effort – and often classroom management problems. Zevenbergen (2005) conducted 96 interviews with Australian students, and noted that students in higher ability classes reported positive experiences, were exposed to significant mathematical content and considered the discipline relevant. The converse was true of students in lower groups. This pattern was evident, regardless of school, year level, or gender. Interestingly, the wait-time research from many years ago showed that teachers allowed an average of one to two seconds (only) after posing a question to students before rephrasing or redirecting the question. This figure was even less for students perceived to be of lesser ability. Also, observing students working in mathematics classes set by ability, we often notice that when working on problems, average and particularly lower ability classes lack the ‘spark’ provided by students with greater levels of understanding and confidence, and often just don’t know where to start. Working together also provides the opportunity for low achievers to learn from more high-achieving students, and for more capable students to understand the difficulties experienced by their lower achieving peers.

6.  Students are often grouped according to narrow criteria, and it is assumed that these classes are appropriate for all kinds of tasks and all content areas.

When we ask teachers how they decided on allocation of particular students to particular classes, the answers are usually a combination of teacher recommendation, performance on common tests and, occasionally, conversations with the students and/or their parents. Although we acknowledge that the Number domain is the most important one in early and middle years, decisions seem to be often made solely on the basis of performance on Number tasks, and the grouping is then assumed to be just as relevant for all manner of tasks including Geometry, Measurement, Chance and Data, and for any form of within-class group work. Although our focus here is largely on assigning students to different classes according to ability, we have similar concerns about within-class ability grouping, except where this is genuinely short-term and flexible. We are quite comfortable with a teacher pulling a small group aside for an extension task or to help a group having difficulty getting into a particular task or understanding a particular concept or skill. Such short-term flexible grouping seems appropriate and is unlikely to lead to the negative outcomes discussed above. We observed an excellent junior primary teacher who, on one particular day, paired students according to reading capabilities for a mathematics task, reasoning that the task had high reading demands, and therefore pairing a strong reader with a less strong reader was a sensible strategy.

7.  Despite claims of flexibility, lower ability classes are very hard to leave.

For all the reasons outlined above, students in practice rarely move ‘up’. Often, a common test is used across the various sets and ,not surprisingly, students in the lower classes, who very quickly know where they are on the ‘pecking order’ and who haven’t covered substantial parts of the work, perform poorly, reinforcing the ‘appropriateness’ of their placement in a lower class. A sad fact is that students in the lower classes, as well as missing out on more advanced work in Number, often miss out on other mathematical domains which they might enjoy more and/or for which they may have capability because the lower classes are seen as needing to focus on the ‘basics’. Such a diet of Number practice can reinforce further the negative views these students have of mathematics and of themselves.

8.  There is a range of strategies which can help teachers to cater for mixed abilities.

While ability grouping may have reduced the ability range on the variables which have been used to determine classes, there is little doubt that every class is a mixed ability class. It is important to acknowledge that catering for the wide range of levels of confidence and competence in mathematical understanding is possibly the greatest challenge which teachers face. A number of writers have outlined strategies for dealing with the challenge of mixed abilities. Small group work is one of them, with strong research evidence supporting its use. Also, many teachers have seen the benefits of using open-ended tasks, where all students are tackling the same task, but the openness means that they can respond to the prompt according to what they bring to the task. A classic example of this is the prompt, ‘a number has been rounded off to 5.8: What might the number be?’ In recent times, Peter Sullivan has demonstrated the power of enabling prompts for students who have difficulty with the starting task, and extending prompts, which a teacher may use for students who find the task relatively straightforward. We do believe strongly that high-achieving students need to be challenged through such extending prompts, and that the current trend of accelerating high achievers where, for example, ‘Year 7 students are doing the Year 8 book’, does not provide appropriate challenge, but essentially ‘more of the same’.

9.  Ability grouping cannot be supported in the interests of social justice.

There is considerable evidence that students from lower socioeconomic status groups are over-represented in lower ability classes. If we believe that such students already carry a high level of educational disadvantage, adding further to this disadvantage by placing them in lower ability classes cannot be justified if we believe that all students have the right to a meaningful and challenging mathematical experience. We would also argue that we are contributing to a more just society if we encourage students to support their classmates when they are having difficulty with understanding. We all know that the act of explaining a concept or skill to another person can greatly enhance our own understanding of the idea, or perhaps reveal a difficulty about which we were not aware.

Embedding sound practice

There are many views in the Australian mathematics education community about ability grouping, only some of which correspond to our own. Our hope is that this article will cause many to reflect on personal and school decisions, read the research, and talk to colleagues and students about the issues. Our concerns in this article focus particularly on the middle years of schooling. We believe that it is appropriate to provide a range of differentiated courses for students in upper secondary, where students choose courses according to their capabilities, future study and career interests. By Year 10, students hopefully have the background and maturity to choose the amount and type of mathematics they wish to study, while not having been disadvantaged by organisational choices made in earlier years.

However schools choose to organise their students for mathematics, we agree with Di Siemon that teaching is greatly enhanced in catering for individual needs when the teacher has access to accurate information about what students know and can do, a sound knowledge of typical learning trajectories, an expanded repertoire of teaching approaches, sufficient time with students to develop trust and supportive relationships, and flexibility to spend time with the students who need it most. This is no small ask!

So many Australian adults look back on their experience of school mathematics with a feeling of inadequacy and resentment. Grouping practices may be a major contributor to this. We believe that ability grouping has a largely negative effect, cognitively and affectively, and its time may be up!

Acknowledgement

We acknowledge gratefully comments of Gilah Leder, Helen Forgasz and Anne Roche in the development of this article.

References

Boaler, J, Wiliam, D & Brown, M 2000, ‘Students’ experiences of ability grouping disaffection, polarisation and the construction of failure’, British Educational Research Journal, 26(5), 631–48.

Lou, Y, Abrami, PC, Spence, JC, Poulsen, C, Chambers, B  & d’Apollonia, S 1996, ‘Within class grouping: A meta-analysis’, Review of Educational Research, 66(4), 423–58.

Slavin, RE 1990, ‘Achievement effects of ability grouping in secondary schools: A best-evidence synthesis’, Review of Educational Research, 60(3), 471–99.

Wiliam, D & Bartholomew, H 2004, ‘It’s not which school but which set you’re in that matters: The influence of ability grouping practices on student progress in mathematics’,  British Educational Research Journal, 30(2), 279–93.

Zevenbergen, R 2005, ‘The construction of mathematical habitus: Implications of ability grouping in the middle years’, Journal of Curriculum Studies, 37(5), 607–19.

Doug Clarke is professor, Mathematics Education and director, Mathematics and Literacy Education Research Flagship at Australian Catholic University.

Barbara Clarke is associate professor in Mathematics Education and associate dean (Staff) in the Faculty of Education at Monash University.