Research on Ability Grouping and Setting in Maths Classes

I’ve been trying to tie together some of the various bits of research I’ve come across for and against ability grouping in maths. Below is what I’ve got so far, but would love any other pointers, for or against.

The last 30 years’ research suggests setting marginally improves high-achievers, but to the detriment of everyone else.
Sources are: DfES (2004) Making Mathematics Count (London: TSO), Askew, M. and Wiliam, D. (1995) Recent Research in Mathematics Education 5-16 (London: HMSO), Sukhnandan, L. (1998) Streaming, setting and grouping by ability: a review of the literature (Slough: NFER), Education Endowment Foundation,

This may be for various reasons but some relevant findings are:

  1. Summer births are penalised (Much like ice-hockey players with December birthdays) (Ed Endowment link above)
  2. Approximately one-third of the students taught in the highest ability groups were disadvantaged by their placement in these groups because of high expectations, fast-paced lessons and pressure to succeed. This particularly affected the most able girls.
    Boaler, J., William, D., & Brown, M. “Students’ experiences of ability grouping —disaffection, polarisation and the construction of failure.” –
  3. Surprisingly, too, we all as teachers actually differentiate more poorly in set classes than when teaching mixed ability classes, teachers typically use methods and materials that allow students to progress at their own pace through suitably differentiated material. By contrast “setted lessons are often conducted as though students are not only similar, but identical – in terms of ability, preferred learning style and pace of working.” (Boaler and Wiliam)
  4. Setting is for life, though, not just for Christmas. Most children never change sets.
    Ollerton, M. (2001) “Inclusion, learning and teaching mathematics” in Gates ed. (2001b: 261-76)
  5. And nobody is very good at setting well. We are all more fallible and subjective than we like to admit.
    Watson, A. (2001) “Making judgements about pupils’ mathematics” in Gates ed. (2001b: 217-31)
  6. Ability grouping within a class has had tentatively positive results.
    Sukhnandan 1998: 17-8, 37-9. see above
  7. The conclusion from the research is that if it helps, it helps teachers more than children
    Director of IoE, Chris Husbands,
  8. The most successful maths countries set the least – PISA rankings

The Effects of School Are Overplayed

John Hattie’s book Visible Learning is a (dense) treasure trove of statistically backed educational research. He looks at 800 meta-analyses of school research and then analyses them for effect. The idea is essentially to try to come up with a way of measuring how much good various initiatives as compared to, say, a child’s natural development.

This snippet, with my highlight, is fascinating, I think. And it gives a sense of the way Hattie uses statistics and research to tease out the critical from the cosmetic.

The effects of schools too often are overplayed—particularly in developed countries. Take two students of similar ability; in many developed countries it matters not which school they attend. Many of the school effects are structural (e.g., architecture of school, timetabling differences) or working conditions (e.g., class size; tracking, or streaming, of classes; school finances). Of course these are important, but they do not define the differences in student achievement: they are among the least beneficial influences on student achievement. That has not stopped these structural and working conditions becoming the most discussed issues in education. Indeed, one of the fascinating discoveries throughout my research for this book is discovering that many of the most debated issues are the ones with the least effects. It is a powerful question to ask why such issues as class size, tracking, retention (that is, holding a student back a grade), school choice, summer schools, and school uniforms command such heated discussion and strong claims. Such cosmetic or “coat of paint” reforms are too common. So many structural claims involve the parents (more homework), lead to more rules (and therefore more rule breakers), have hints of cultural imperatives (quietness and conformity is desired), and often include appeals to common sense (reducing class size is obviously a good thing!). However, the most powerful effects of the school relate to features within schools, such as the climate of the classroom, peer influences, and the lack of disruptive students in the classroom—all of which allow students and teachers to make errors and develop reputations as learners, and which provide an invitation to learn.

To teach by theme or by subject

There’s a report here from Pearson about whether to teach by theme or by subject. It goes over the Rose Review, the Cambridge Primary Review, current research and some case studies of successful schools in the UK. Then it looks at successful models in Singapore, Finland, Canada, Korea and Australia.

The conclusions are

  1. A holistic approach:
    The best results are achieved when schools approach curriculum, pedagogy, assessment and behaviour holistically. None of these can make a significant difference in isolation.
  2. Strong subject knowledge: In-depth teacher subject knowledge is essential in designing and implementing curricula, whether subject- or theme-based, and is strongly linked with high achievement and other desirable outcomes.
  3. Strong pedagogical knowledge:
    Heads and teachers need to be skilled in curriculum design, to enable them to take an intelligent and flexible approach to curriculum planning and timetabling. They also need to engage deeply and critically with effective pedagogical techniques – the processes that translate knowledge into learning experiences – including learning strategies, thinking skills and formative assessment.
  4. A creative approach to getting the basics right:
    Outstanding schools focus relentlessly on core skills, knowledge and values. But they do so within a creative context. They are more effective at teaching the basics because they approach them creatively, not less.
  5. High expectations:
    Heads need to have high expectations of quality teaching in all subjects. Teachers need to have high expectations for every child, and to put in place good, timely interventions when those expectations aren’t being met.

This is the sort of research I find slightly depressing. I see the title and abstract – think woo hoo – and dive in. The case studies are all interesting, albeit a little shallowly described, but the conclusions…. aargh.

Aren’t they just common sense?

Stop giving mindless homework – a neutral, research-based view

Which would you prefer: Richard Feynman’s mum asking him “What did you ask at school today?” or “What homework have you got to do tonight? Can you get it done before supper.”

I am not pro-homework for its own sake. By and large I think much of it is a total waste of time and energy for all concerned. Worse than that, I think it damages what might be called the child’s “learning relationship” with their mum or dad. I am, though, keenly aware that parents (and teachers) can think many of the arguments are just cleverly-wrought excuses to try to get out of marking and assessing the children. (A little like a child trying to get out of having to homework). So I am always on the hunt for a neutral, research-based view.

I first read Alfie Kohn’s The Homework Myth a while back. It’s grounded in research but he’s a little overevangelical. If nothing else, I’d recommend it to teachers and parents to make them think about some easily made assumptions. (update:I’d recommend this shorter read in 10 minutes version first) Anyway, the two main points that stuck with me were that

  1. the burden of proof should be on those who claim homework helps and
  2. if homework is given it’s a good idea to co-design with the pupils.

Neither of which seem to cut the mustard with parents or teachers. Partly, I think, this is because when quoting Alfie Kohn it’s easy to feel a little “touched with fire” …

Anyway, more evidence at Time magazine or The Case Against Homework has pointed me in the direction of Harris Cooper.

  • The onslaught comes despite the fact that an exhaustive review by the nation’s top homework scholar, Duke University’s Harris Cooper, concluded that homework does not measurably improve academic achievement for kids in grade school. That’s right: all the sweat and tears do not make Johnny a better reader or mathematician.
  • Too much homework brings diminishing returns. Cooper’s analysis of dozens of studies found that kids who do some homework in middle and high school score somewhat better on standardized tests, but doing more than 60 to 90 min. a night in middle school and more than 2 hr. in high school is associated with, gulp, lower scores.
  • Teachers in many of the nations that outperform the U.S. on student achievement tests–such as Japan, Denmark and the Czech Republic–tend to assign less homework than American teachers, but instructors in low-scoring countries like Greece, Thailand and Iran tend to pile it on.

Cooper has written a book called The Battle Over Homework: Common ground for Administrators, Teachers, and Parents. Can’t wait for a neutral, research-based view.

The importance of estimation

Teaching children how to estimate properly is something I need to improve on.

As Jo Boaler points out in The Elephant in the Classroom:

“When an official report in the UK was commissioned to examine the mathematics needed in the workplace the reviewers found that estimation was the most useful activity. Yet when children who have experienced traditional maths classes are asked to estimate they are often completely flummoxed and try to work out exact answers then round them off to look like an estimate. This is because they have not developed a good feel for numbers, which would allow them to estimate instead of calculate, and also because they have learned, wrongly, that mathematics is all about precision, not about making estimates or guesses. Yet both are at the heart of mathematical problem solving.”

Bad fonts = Good learning

While certain fonts may be harder to read, researchers at Princeton and Indiana University have found that they may, in fact, improve your ability to remember facts. In a study of 200 students, they discovered that making things harder to read—whether that meant using fonts like Comic Sans and Bodoni MT or using bad photocopies—actually increased test scores, without any complaints from the students.

via Mind Hacks: Harder to Read Fonts May Improve Learning

It makes you wonder whether we should let children’s handwriting stay suboptimal for revision purposes …

Aliases, creeping, and wall cleaning: Understanding privacy in the age of Facebook

Based on a year long ethnographic study in Toronto, Canada, this paper looks at how – contrary to many mainstream accounts – younger users do indeed care about protecting and controlling their personal information. However, their concerns revolve around what I call social privacy, rather than the more conventional institutional privacy. This paper also examines the somewhat subversive practices which users engaged in to enhance their own social privacy, and in some cases, violate that of others.

Source: here