A few months ago I posted a blog about ability grouping in the mathematics classroom. I am re-posting the blog here because the beginning of the school year is the perfect opportunity to set up routines and strategies that will promote mathematical learning and ensure the diversities of your new class group are addressed. I strongly recommend flexible grouping in mathematics and I hope this post causes you to think about how you will be grouping your students in 2016.
During the primary years students either experience mathematics lessons within mixed ability classrooms or are ability grouped across or between grade levels. In mixed ability classes and to a lesser degree in ability grouped classrooms teachers often have to cater for a range of students whose previous attainment varies considerably. The gap between low and high achievers is said to increase as students progress through school, with as much difference in performance within year levels as there is between Years 5 and 9 students overall (State of Victoria Department of Education and Training, 2004). This concurs with findings by The Middle Years Numeracy Research Project (Siemon, Virgona, & Corneille, 2001) that cites teachers in the middle years can and should expect a range of up to seven school years in numeracy-related performance. Australian TIMSS and PISA reports show our middle years students, when compared to students in other countries, are not keeping up with some aspects of mathematics (Lokan, Greenwood, & Cresswell, 2001). Among the strategies teachers implement in order to cater to the diverse needs of the classroom is the use of ability grouping and the incorporation of differentiated tasks.
Although there are arguments both in favour and against the use of ability grouping, it is not uncommon for primary and secondary schools in Australia and internationally to use such grouping in mathematics classrooms. The following is an exploration of both arguments. Clarke (2003) maintains teachers need to think carefully about reasons for choosing to place students into groups according to perceived ability. Teachers need to consider the potential impact upon students’ self-esteem, and the ‘self-fulfilling prophecy’ (Brophy 1963, as cited in Clarke, 2003), in which students perform to the level expected of them by their teacher. He concludes that ability grouping is used in mathematics for teacher convenience more than for student benefit. This is a sentiment echoed by Boaler, Wiliam and Brown (2000), who also believe ability grouping is one of the main sources of disaffection.
Ability grouping, such as that which is common in Australian secondary schools, became the focus of a study conducted in the United Kingdom (Boaler, et al., 2000). The grouping of students into ability ‘sets’ emerged as a significant factor that influenced students’ ideas, their responses to mathematics, and their eventual achievement. The study found that students in the school that used ability grouping were significantly disadvantaged by their placement and this disadvantage was not restricted to students in the lower ability groups. Approximately one-third of students in the highest ability groups felt disadvantaged because of high expectations, fast-paced lessons and pressure to succeed. Students from a range of groups were ‘severely disaffected’ by the limits placed upon their attainment. Students reported that they gave up on mathematics once they discovered their teachers had been preparing them for examinations that gave access to only the lowest grades. Large numbers of students, in the study by Boaler et al., experienced difficulties working at the pace of their particular class. For some the pace was too slow, resulting in disengagement, although for others it was too fast, resulting in anxiety. Both responses led to lower levels of achievement.
In addition to the findings above, there is research that claims ability grouping causes behavioural problems for some within the mathematics classroom. Teachers in a study conducted by Ventakatakrishnan and Wiliam (2003) found behavioural problems more common in mixed ability groups than in their fast-track, higher ability group. These behavioural problems were compounded by the weak literacy skills of some individuals in these groups in addition to peer self-management skills. Interestingly, placing students in ‘tracked’ groups had an effect on students’ perceptions of themselves as learners of mathematics. Those who were fast-tracked perceived themselves as ‘doing well’ while those in mixed ability groups perceived themselves as ‘low’ in mathematical ability. The teachers involved in the study also noted they had problems motivating the higher attaining students within the mixed-ability groups – students who had ‘just’ missed out on being placed in the fast tracked group. Ventakatakrishnan and Wiliam also note that mixed-ability grouping decreases the opportunities for higher-achieving students to interact constructively with peers although ability groups have the same effect on lower achieving students. The study found that advantages of grouping by ability are limited and restricted to higher achieving students while causing disadvantage to those who are the lowest attainers.
Although there are advantages and disadvantages in grouping students according to ability, it is also reasonable to expect that a result of such grouping is differences in teacher expectations and instructional techniques. There is a tendency for instruction in lower ability groups to be of a different quality to that of higher ability groups (Ireson & Hallam, 1999). There appears to be a concern that instruction in low ability groups is conceptually simplified with a higher degree of structured, written work, as in the traditional method of teaching mathematics. Higher ability classes appear to include more analytic, critical thinking tasks with pupils allowed greater independence and choice along with opportunities for discussion, reflecting a more contemporary style of mathematics lesson. Based on stereotypes and past experiences, some teachers hold low expectations for low ability groups, further decreasing students’ own expectations and self-esteem, and leading to decreased levels of engagement with mathematics (Ireson & Hallam, 1999).
At the primary level classroom, research suggests students in mixed ability classrooms display more positive attitudes towards school in general (Ashton, 2008; Ofsted, 2008). However, the more common practice of ability grouping in the secondary mathematics classroom is a complex issue. Although it appears to perpetuate the inequities associated with mathematics and the notion of mathematics being an elitist subject, it is often an attempt to address the needs of all students as well as the needs of mathematics teachers.
So what is the answer? Again, my advice is to group flexibly. There are circumstances that require children to be grouped by ability, and other circumstances where it is more appropriate and beneficial for students to work in mixed groupings, where students can learn from each other. Another reason to have flexibility is that often children may excel in one area of mathematics, but may be challenged in other areas. Those who appear to struggle, may not necessarily struggle with all concepts. The key is knowing your students and their needs across all aspects of the mathematics curriculum, and ensuring that assessment of students’ ability informs teaching and the way students are grouped. And finally, have high expectations of all students!
Ashton, R. (2008). Improving the transfer to secondary school: How every child’s voice can matter. Support for Learning, 23(4), 176-182.
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), 631-649.
Clarke, D. (2003, 4-5 December). Challenging and engaging students in worthwhile mathematics in the middle years. Paper presented at the Mathematics Association of Victoria Annual Conference: Making Mathematicians, Melbourne.
Ireson, J., & Hallam, S. (1999). Raising standards: Is ability grouping the answer? Oxford Review of Education, 25(3), 343-358.
Lokan, J., Greenwood, L., & Cresswell, J. (2001). 15-up and counting, reading, writing, reasoning. How literate are Australia’s students? The PISA 2000 survey of students’ reading, mathematical and scientific literacy skills. Melbourne: ACER.
Ofsted. (2008). Mathematics: Understanding the score. London: Ofsted.
Siemon, D., Virgona, J., & Corneille, K. (2001). Final report of the middle years numeracy research project. Melbourne, Victoria: RMIT University and the Department of Education and Training (Victoria).
State of Victoria Department of Education and Training. (2004). Middle years of schooling overview of Victorian Research 1998-2004 Retrieved July 7, 2005, from http://www.sofweb.vic.edu.au/mys/docs/research/
Venkatakrishnan, H., & Wiliam, D. (2003). Tracking and mixed-ability grouping in secondary school mathematics classrooms: A case study. British Educational Research Journal, 29(2), 189-204.