Setting things straight on mixed ability in mathematics

Almost all UK secondary schools use setting in mathematics. However, this system of grouping, wherein students are classed according to their ability, is currently a topic of vigorous debate. Many people think that teaching mathematics in mixed ability sets is better. In general, I do not believe this. Let me explain. 

Recently I’ve detected a worrying increase in the numbers of institutions adopting mixed ability in mathematics as standard. It’s my experience that delivery of a successful mixed-ability system relies on the few teachers who have the required level of specific expertise, natural charisma and skilfulness. They are in a distinct minority. So highly specialised is mixed ability that, for most schools, its adoption in practice represents a significant step backwards. Even if mixed ability is pursued well by the school, most teachers will still struggle. However, if setting is properly structured – by naming sets appropriately instead of around a simplistic, top-bottom pecking order; by creating a balanced combination of streams and sets; by allowing a constant, fluid movement of students between sets – the perceived disadvantages of setting largely fall away.

Before appraising my own views as an educationist, however, consider some from the sharp end. In 2011, the experienced London inner-city maths teacher Kris Boulton began his career in a school which applied setting to mathematics. He found the experience wanting; from the divisive, low-expectation language of scolding teachers, to a corrosively implicit belief across school that the bottom set of students would be left floundering with no real hope of improvement.

Moving to mixed ability, at first apparently a godsend, revealed a darker side, the incandescently smart thrown together with “pupils who couldn’t add and subtract negative numbers accurately”. Believing he was repeatedly failing his students, Kris hated it.

It strikes me, as it might have done Kris, that those who shout loudest for mixed ability are unaware of how difficult most teachers find it. And when mixed ability fails, it swamps the disadvantages of setting; shortcomings that largely disperse when setting is structured well.

Between 2011 and 2013, during the development of Sparx v0.1, I sat in on hundreds of mathematics lessons at a mid-league secondary school. With this institution’s structure of two streams and four sets within each stream relatively well-designed, I was grateful for the opportunity; beyond a school’s immediate hierarchy of teaching staff and local-authority evaluators, relatively few individuals are afforded the privilege.

These were formative years in Sparx’s development. With proprietary educational products then largely unstable, we were determined to perfect a solution that would successfully aid children’s learning by way of radical research and data techniques; understanding what applies to the student and, equally importantly, to the teacher.

Nurturing the infant Sparx obliged a maternal attention to detail. Fine tuning was essential, in various learning environments. As I gravitated between different classes, my presence became progressively unnoticed, both by students and by teachers; much as the all-seeing eye of the reality TV show camera is duly forgotten and participants relax and act naturally. Now reduced to a shadow in the corner, I was able dispassionately to watch and understand much about the nature of learning, and how students respond to the shifting nuances of a real classroom.

I wanted particularly to unpack the issues most likely to be inhibiting learning. Among many, the biggest issue was the lack of student motivation and engagement; in the school’s vernacular, being ‘on task’. Often the keen few would give the teacher and/or an observer the impression that all were engaged. My observations told me otherwise. By closely studying their expressions and their body language, I could tell they had lost the thread. It was a feeling reinforced as soon as a question was put directly to a student instead of thrown open to the room.

Following a golden rule always to rigorously check the facts before drawing a conclusion, I designed a way to collect objective data. Based on a straightforward 0/1/u metric, I recorded minute-by-minute stats from dozens of lessons. I’d quickly scan the room, assessing students one by one. An individual fully engaged with the learning process scored 1. Those diverted by thoughts of extra-schoolroom activity were demoted to a 0. Any uncertain classifications we scored a u.

Marshalling similar data week after week, I nailed down an average student concentration rate of around 20-25%. But whenever the all-seeing eye became suddenly material to everyone in the room, this changed. The unannounced arrival of a head-teacher, for example, would herald a palpable transformation in the class atmosphere, young eyes and ears suddenly alert and receptive.

Now there are clearly numerous reasons for classroom detachment. But after much thought and study and many conversations with experts, I concluded that student momentum was among the most important. After starting out feeling motivated, many – and this still brings a lump to my throat – switch off if the learning material or content is not pitched perfectly at their ‘sweet spot’. Cognitive scientists call it the Goldilocks Effect: not too complex, not too easy, just mildly challenging within the constraints of the world they know.

Given the wide range of abilities within the classes examined, only the middle portion – four or five students out of 30, say – was receiving the level of content needed to maintain momentum. The better teachers, those able to blend authority, charm, personality and deep experience, usually overcame this. But keeping an entire class on-point was like swimming upstream: exhausting; impressive if it could be done; and, by most of the teachers, generally unachievable. And remember, this was in a school with eight sets.

With this observation in mind, in developing Sparx we wanted at least four levels of highly-differentiated lessons at every topic, which could be used to pitch teaching at eight setted classes. To my knowledge, no other ed-tech product has more than one level for each topic. Having seen the difficulties in an eight-setted school, I would certainly have no fewer than four.

The idea of a completely mixed-ability, one-set grouping – or, at least, one that lacks exceptional teachers who are amply versed in mixed ability – seems ludicrous. In a typical mixed-ability scenario, with low-achieving students placed in the same class as high fliers, a weaker individual will not attain the exalted position of one who finds a topic easy relative to others in the class; they’ll never be the first to put up their hand and answer a question correctly. With the below-par left listless and languishing at the bottom, the social inequalities are intensified, not the other way around.

In summary, I can see the many pros and cons of both setting and mixed ability classes. If setting is done well, the hindrances go away; most teachers will perform well at schools whose setting structure is fit for purpose. But for mixed ability, even where it is properly applied, most teachers still struggle. A few can make it work but, all told, mixed ability inevitably falls short.

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