Is education a zero-sum game?

Opportunity makes a thief.

Francis Bacon

A zero-sum game is one in which there is a winner and a loser; if you haven’t won, you’ve lost. The term derives from game theory and economics and describes a situation in which one person’s gain utility (the ability to satisfy his or wants) is exactly balanced by another’s loss of utility.

In The Uses of Pessimism, Scruton points out that much wrong-heading thinking and behaviour derives from what he calls the ‘zero-sum fallacy’ where all gains are paid for by the losers.

Society therefore is a zero-sum game, in which costs and benefits balance out, and in which the winners’ winnings cause the losers’ losses. (p.81)

This kind of dichotomous thinking was the basis for Marx’s theories of economics, but is a bit unfashionable now. Most economists would agree that it’s a little bit more complicated than that. Most transactions are mutually beneficial to some degree; although one participant might do better than the other, profit making is not necessarily rapacious. Scruton argues this is a potent cognitive trap whereby idealistic, utopian thinkers fail to acknowledge reality; it’s not that their schemes are harebrained and unworkable, it’s that they’ve been thwarted by an enemy. He then goes on to argue that the move to replace grammar schools with comprehensive schools was rooted in a belief in this zero-sum fallacy:

But clearly a procedure that enables some pupils to succeed must cause others to fail: so the zero-sum fallacy maintains. Such a procedure generates a ‘two-tier’ education system, with the successful enjoying all the opportunities, and the failures left by the wayside to be ‘marked for life’. In other words, the success of some is paid for by the failure of others. And thus was born the movement for comprehensive education, together with the hostility to streaming and the downgrading of examinations, in order to prevent the state education system from producing and reproducing ‘inequalities’. (p.95)

Equality is easy to achieve, Scruton argues, all you have to do is put a lid of achievement and ensure no child gets ahead. This is the kind of silliness that results in a lot of the closing the gap narrative: if the gap between the most advantaged and least advantaged is too wide then a school is failing. This creates a perverse incentive; it’s easier to reduce some students’ performance than it is to increase others’, therefore the most effective way to narrow the gap is to limit the ‘winnings’ of those at the top end to ensure the losses incurred by Pupil Premium students are less severe.

Scruton’s point is this:

Zero-sum thinking, which sees the educational success of one child as paid for by the failure of another, forces education into a mould that is alien to it. The child who fails at Latin might succeed at music or metalwork; the one who fails to get to university might succeed as an army officer.

And to a degree he’s right – children have a diversity of ability and an education system which fails to acknowledge this diversity is one in which excellence will struggle to exist. But something seems not quite right with this picture. Here are some of the objections I have:

  1. It’s all very well for Scruton to equate metalwork with Latin, but that doesn’t really square with the perceptions of society; few middle-class parents are content for their children to fail academically but “find the skill, expertise or vocation that suits their abilities.” As long as our children ‘win’, what happens to ‘kids like these’ is by the by.
  2. If a grammar school has a limited number of places, one child’s success at the 11+ exam really does result another child with perhaps one less mark being unable to attend.
  3. Whilst grammar schools might have existed to offer to “children from poor families an opportunity to advance by talent and industry alone”, in practice, children from wealthier backgrounds are routinely coached and tutored to pass the 11+.  The less socially advantaged your family background, the less likely you are to get in.
  4. Comprehensive education does not have to lead, ipso facto, to dumbing down. Excellence is surely possible without a two-tier school system, isn’t it?

Obviously the 11+ is a very extreme form of differentiation, but as Scruton says, we’ve become equally hostile to the concept of streaming and setting too is increasingly under attack. I’m not certain about this, but instinct tells me that any attempt to differentiate be ability leads, inexorably, to students being treated differently – how could it not? It then becomes a self-fulfilling prophecy – those that are perceived as less able remain less able.

If we divide children into ‘more able’ and ‘less able’ then it follows that we will treat them differently. Alex Quigley posted this morning about teacher expectations and the pygmalion effect. Our beliefs about pupils have a tremendous impact on their progress and attainment. In 1968, Rosenthal and Jacobson ran a landmark experiment which demonstrated that if teachers were led to expect enhanced performance from children, then their performance was indeed enhanced. Pupils were given a disguised IQ test at the beginning of the study. Teachers were told that some of their students (about 20% of the school chosen at random) would likely be ‘spurters’ that year, doing better than expected in comparison to their classmates. At the end of the study, all pupils were retested and showed statistically significant gains favouring the experimental group.

Making these kinds of distinctions and then acting on them really does seem a zero-sum game and one that is subject to the Matthew Effect – the more able get more able, the less able get, comparatively, less able as a consequence of how they are treated in the classroom. Children don’t get access to same resources, opportunities and support. They’re treated differently. My favourite way of thinking about differentiation is that everyone should be expected to struggle, no matter their ability. This doesn’t mean everyone should be treated the same, but it does suggest we shouldn’t make school easy for anyone.

This is, of course, not to say that any form of differentiation is bad – expert teachers should be encouraged to act on their professional instincts and treat their students as they think befits their personalities. Challenge students to do things they’re not currently able to do and then, perhaps, differentiate by support. But differentiation by ability is, I think, pernicious.

I’ve written before about both my concerns with differentiation and also some of the critique of the growth mindset trope – these to me seem almost like competing, opposing forces in education – on the one hand, children should be treated differently depending on their ability and on the other, everyone can improve if they have the right set of beliefs. I’m not sure of the truth of these statements, but I do know that no one rises to low expectations.

I’d be grateful for any views offered below – my thoughts aren’t settled on this and I’m more than willing to listen to reasoned and thoughtful counter-arguments.

28 Responses to Is education a zero-sum game?

  1. al says:

    Good piece and for me a core issue in education. I am of the left and believe we live in a deeply unequal society. I am a primary school teacher who teaches in one of the most deprived areas of my country and I am committed to helping my children reach their potential.
    I agree with you that grouping by ability is dangerous because who defines ability and when do you start defining who and who is not able? However, what about differentiation based on dealing with overcoming specific education needs?

    If a year group of 45 kids has 13 kids who have varying degrees of difficulty with reading and/or writing, at a year group level, then why not combine all those children and group then acording to their needs? Give those 13 the additional supports they need in order that they can attempt to bridge the gap. To do this the teachers need to have identified specific isues they are attempting to address and then put in place a programme of work to do this. In addition once children have made sufficient progress the expectation should be they will move on. When this move does occur then then need to be supported through the transition.

    This is the model of differentiation that I support.

    • David Didau says:

      You’re right – if a child has a specific need then of course we should address it as far as possible. Of course, this isn’t always possible in the classroom, but we can strive to do so. A

  2. heatherfblog says:

    I Have decided there are two competing truths.

    1. Setting and differentiating tend to put a ceiling on achievement.
    2. Mixed ability teaching doesn’t work very well in many contexts and attempts at differentiation can put an intolerable strain on teachers to detriment of students.

    We need to acknowledge both are true and work out the best balance in each context.
    In my school perhaps the very strong pressure to get the weaker students grades we know to be a tough call means setting has less pernicious impact. If teachers have very developmentalist assumptions as seems to be strongly the culture in our primary schools then the ability grouping within classes is particularly harmful.

    • David Didau says:

      That’s an interesting dilemma you’ve identified – damned if we do and damned if we don’t. So the question becomes, which course does least harm in every context?

      Thanks Heather

  3. suecowley says:

    Differentiation makes more sense if you think of it as a support, perhaps? Also, a support that is not just about ability, because ‘difference’ is about much more than that (it might be knowledge of English, ability to concentrate, lots of different things). I think that teachers can and do support different needs in very subtle ways, for instance, picking a child to answer a question because you know that he or she needs to build confidence, or using a very slightly different tone of voice with one child and another. It is surely about knowledge of your students, and your reaction to that knowledge, rather than a set of expectations about ability. (Hope that makes some kind of sense.)

    • David Didau says:

      Hi Sue – I think I acknowledged this in the post: “This is not to say that any form of differentiation is bad – expert teachers should be encouraged to act of their professional instincts and treat their students as they think befits their personalities”. If this is what you mean, then yes, of course.

  4. Tom Burkard says:

    We are kidding ourselves if we think that all pupils perform best in mixed-ability classes. There is quite respectable research demonstrating that low-ability pupils perform better in mixed-ability classes, but Gamoran argues that when the same teachers teach the top and bottom sets using the same curriculum, this is not so.

    Common sense tells us that the one of the problems is that our staff rooms are similarly mixed-ability–no prizes for guessing who gets the bottom sets in most cases. Which is why Gove put so much emphasis on closing the gap. However, this still ignores a number of major problems, and not just the fact that the easiest way to close the gap is to suppress the achievement of the most able.

    In the first instance, we fail to distinguish between ability and achievement. I once had a pupil with very poor literacy skills and massive behaviour problems, but because he came from one of our most depressed council estates everyone assumed he had low ability. I introduced a non-verbal reasoning test for our intake, and we found that this boy had the highest score (out of 140) in his intake. I should add that his primary school came in dead last in England the first time league tables were published. In three years we got his literacy skills up to scratch, but his knowledge base was so impoverished that he was incapable of doing the work set for the higher sets. Effectively, his education was wasted. Until educators get over their absurd insistence that all humans are born with the same intellectual potential and start testing non-verbal reasoning ability, pupils like this boy will continue to fail.

    Another major factor is our obsession with higher-order skills. Even though it is finally beginning to trickle through that you cannot teach all-purpose ‘critical thinking skills’, we still believe that schools’ major task is to teach children to think. So long as this is the case, we will always have a problem with children who have either a low IQs or an impoverished knowledge base. Even though the former are entirely capable of learning declarative knowledge and can learn simple algorithms and techniques that allow them to solve some problems, the pre-mature emphasis on higher order skills will leave them demoralised and frustrated–especially when they are taught by a low-ability teacher! I should add that I firmly believe that all children should study an academic curriculum until age 16; shunting them off on vocational courses might be workable were it not for the fact that most vocational education is a complete waste of time. I doubt that Alison Wolf has had time to cleanse that vast Augean Stable.

    I won’t bang on about discipline–I can’t stand Wilshaw, but to give him credit he has shown what can be achieved in inner-city schools. Until we flip two fingers at the UN Convention for the Rights of the Child and their Platonic ideal of the child, real existing children will suffer because adults abnegate their responsibilities.

    Yet in the end, Scruton was right: bright kids lose out because we’re still playing the zero-sum game. Any society which fails to educate its most able children is doomed; somehow, we don’t seem to worry overmuch about this.

    • David Didau says:

      So, you’re argument boils down to, ‘bright kids can’t reach their potential in a mixed ability setting’? I’m not certain that’s true – feels more like ‘truthiness’.

  5. Rob Old says:

    As a PGCE student I am innundated with conflicting advice on the question of what differentiation actually means. To one teacher, it means providing different ladders to reach the same goal. To another, it means recognising the fact that the same activity will be boringly easy for one student and depressingly hard for another. This latter teacher is happy if I design a worksheet of questions of increasing difficulty that pushes everybody to the point of being challenged; but some teachers would label this as differentiation by outcome, which is a ‘cop-out’.

    There’s probably a context-specific aspect to this. As a physics trainee, I find this latter approach pragmatic. For a GCSE separate science group with a big spread of ability, the first questions on a worksheet are quick KS3 designed to check if the student has the basic skills the need to access the topic, whilst the last would stretch a-level students. Everyone has to think, and therefore everybody learns. The ideal situation is that the spread in outcomes is narrowed because I have the time to give those who struggle more help, whilst the attainment of those who are more able is only limited at the top by the A* GCSE grade- although I wouldn’t say I’m there yet!

    The former approach- of different ladders- by contrast, is probably more helpful in English, when some students might simply have no idea of how to start an essay on a given subject. I can imagine giving everyone an essay question, encouraging everyone to get on with it, then providing some sort of scaffolding framework to those who haven’t written anything after 5 mins.

    What I don’t see as being helpful is a crude binary distinction of ‘high- and low- ability learners’ being given colour-coded sheets, but maybe this is just my inexperience. I’m sure good teachers do exactly that, so it may just be that they’re better at pitching the different difficulties than me.

    • I wish I had been reading twitter blogs based on evidence when on my PGCE instead of hearing about what Ofsted wanted. Good work my friend 🙂 I teach science and also use questions of differing difficulty.

  6. chemistrypoet says:

    It seems to me that expectation is all important, because it does significantly effect the way people (adults and children) act towards one another. At the beginning of their time in education no-one has much of a clue as to what a child is capable of 20 years later. I believe that everyone has a limit to what they are capable of, but not that we can know what that really is during the time span of school based education. Consequently, expectations should be high, and teachers/the education system should expect all students to be capable of working hard. No-one should be written off.

    With respect to differentiation, I agree with Sue Cowley above. It should be seen as a way of supporting students, not a way of limiting what they do. Anything that in practice limits a student should be eyed with suspicion.

    Good post.

  7. I devised and have tested over the years my own theory: The more you do for another human, the less that human does for him or herself.

    Based on this, I decided to take the drastic step to not sit with and constantly help all of the IEPs in my class. Instead, I encouraged all to just ‘have a go’. The result has been a dramatic increase in writing quality and quantity amongst the lowest achievers (over and above what I have analysed over their previous years). I basically forced them, for the first time ever, to think for themselves. Believe me, it was concerning to others that I was not producing special, differentiated ‘scaffolds’ for them to fill in (so that they wouldn’t have to write as much). These children had also somehow assimilated the assumption that all adults were their personal help-meets. Still, I have stuck to my guns and it has paid off.

    These children have shocked me with their ability to cope and achieve in the stark face of their own previous underachievement although perhaps deep down I knew they could pull it off. It is indeed a testament to the incredible abilities that human beings have evolved over thousands of years; to be able to adapt and conquer in the face of adversity. It behoves us to let children naturally find their own way of coping, adapting and improving in order to succeed in life.

    I should also add that I asked for extra interventions to take place OUTSIDE the main English and Maths lessons because the idea of children being removed from English or Maths lessons in order to obtain basic skills interventions seemed completely illogical: they would be both improving and falling behind at the same time. So, I’m afraid those art lessons had to be put on hold!

    Interestingly, I have also applied my theory to other scenarios in life. Could it be that the more that mothers do for their teenage sons, the less these teenage boys do for themselves? If women were happy to take on the double workload of bringing up children whilst working, then perhaps men would then do less child rearing themselves? If teachers are willing to take on more and more of a parenting role, are parents less likely to do their job properly? If the state is willing to take on the role of looking after the elderly, are families less likely to want to do it themselves?

    On the face of it, it does seem to fly in the face of the whole premise of ‘society’. However, I would add that for a true society to exist, each member must be adding value of some kind in addition to taking from others (whether it be resources or services). The trouble is, people just don’t feel obliged to do their bit. In a way, we’re all grown-up victims of child-centred ideology. In the absence of conscience, shame and self-respect my theory seems to hold true for many scenarios.

    Further, I am also conscious of different child-rearing practices of indigenous communities around the world. Having decided long ago to abandon the assumption that the Western Way was the best, I approached the practices of other cultures with an open mind. It certainly seems that at a certain age (10 ish) boys in particular leave their mothers’ sides and are ‘taught’ to become men. Additionally, children are given responsibilities at a very young age. Is this exploitation? No. These children add value to the mini-society they live in and feel good about themselves as a result. It just makes sense. Plus they’re not spending their whole lives messing about and thinking the whole world revolves around them.

    Sometimes I wonder whether we Westerners are just doing absolutely everything wrong.

  8. Mark says:

    There is differentiation (those attempts made by a teacher in a classroom to stretch and challenge all their students ) and segregation (dividing students into different sets / schools according to gender, faith, ability to pay for a tutor etc.)
    I am clear that I am for the first (however hard it is in practice ) and opposedcto the second (however seductive it is in theory.)

  9. julietgreen says:

    A couple of thoughts.

    My suspicion is that a ‘creaming off’ system will always contribute negatively to what remains. That is to say the grammar and public schools have an impact on the quality of the rest because of expectations. I personally favour a fully comprehension system where everyone benefits from the kinds of privilege experienced by pupils currently in grammar schools and private education. I do, of course recognise that I’m generalising here and that individual cases vary. I am tired of hearing parents discuss the options for their children as they think about secondary school and whether or not to push for the grammar school or pay for private education as opposed to having to settle for a state school. There should be no settling.

    In this way – segregation bad.

    In terms of setting and streaming, I’ve always thought, in spite of the evidence, that setting was useful and streaming was not. That is to say pupils, like students of everything, are probably best suited to different courses. I’ve imagined it along the lines of how I would feel taking an evening course and being put in the advanced class. If I were just starting out, I’d rather be in the beginners’ class.

    But the evidence indicates that setting does not work and I would like to question why. I’m fairly sure that it is down to expectations. So what about setting without ceilings? I’ve taught the ‘lower’ and ‘higher’ ability maths groups over the years and I like to think I’ve had the same expectations for both. That is to say – no limit on what we’re able to learn – just the likelihood of a different starting point or a different time scale. Frequently we’ve outstripped our peers in certain areas, simply because we pushed further, given the time.

    Completely mixed ability groups for some subjects make no sense to me. It begs the question as to why we put pupils into classes and not just mix them all up. But maybe I kid myself.

  10. Interesting read David. I would agree with the idea that the concepts of differentiation and growth mindset seem opposed. Certainly the strategy of differentiation that is so prevalent in schools and teacher training courses is based on a premise of fixed ability mindset. These pupils will find this work too difficult (despite it being what they need to learn) therefore they need to do some easier work. Thus leading to the golem effect for both teachers and pupils.

    What do you think of the idea of presenting pupils with two or three tasks of varying challenge level? All tasks are matched to meeting the main learning objective of the lesson. Pupils then choose which task to complete at a level that challenges them but is achievable (or not as they may find). This thereby still allows for a culture of growth mindset for the pupil and the teacher as no individual or group is given a glass ceiling that a ‘traditional’ model of differentiation provides. This would only work if the most basic task was challenging enough for at least some of the pupils and the other tasks increased in complexity to a level that is challenging for all. Trial and refinement is needed on the part of the teacher to provide tasks at the right pitch and guidance and practice is needed for the pupils to choose the task that will ensure they are challenged.

    I’m certainly not yet convinced that this is somehow the definite answer to the problem of differentiation vs growth mindset, but it’s something I’m been experimenting with. It is something that Dame Alison Peacock has written about in her book ‘Learning Without Limits’.

  11. I think there is a paradox in the assertion that “expert teachers should be encouraged to act of [sic] their professional instincts and treat their students as they think befits their personalities” soon after identifying the Pygmalion Effect as an issue with differentiation. Your answer is that all pupils are consistently challenged – “everyone should struggle no matter their ability” – but ‘struggle’ is, ultimately, as invisible as ‘learning’ and ‘progress’.

    Is it possibly the case that ‘an expert teacher’ is not an adequate answer to this challenge? Maybe the problem is not ‘differentiation by ability’ per se but that differentiation needs a stronger evidence-base than teacher opinion (however expert that teacher is).

  12. Hello! I’m a bit late to this party but wanted to say how interesting this post was… and how insightful the comments are! Great read. Speaking here as a student who was ‘creamed’ off into a grammar school, and then selected for every ‘top-set’ going… I never understood what they were trying to achieve. I never understood why my teachers were considered so incapable of of deciding for themselves and communicating what they will teach, who their lessons are for, when the course will be and how their students can expect to be measured and improve? Why were my teachers silenced in this way? I never understood why my friends and I were considered so incapable of deciding for ourselves which of the available ‘sets’ would be best for us? Instead, someone else tried to figure out ways to see, measure and categories our ‘ability’ which, frankly, is a mixture of impossible, harmful and patronising. It’s all very subtle, of course. It’s a slow, steady dis-empowerment. No dramatic ‘whack’ that would leave us horrified. And it’s sustained, in part, because people like me are supposed to develop a sense of superiority over those who weren’t selected for the ‘best’ instruction.

    • As someone who was educated in a comprehensive, I understood ability-grouping very well. The English department used mixed-ability teaching in years 7 and 8. As such, I basically learnt nothing in those years as we slowly plodded through Charlie and the Chocolate factory.

      I don’t advocate a grammar system, but I do think setting (and ability-grouping in class) serves a very useful practical purpose. The intent is not to develop a sense of superiority in pupils (this is a side-effect that can/should be mitigated).

  13. teachwell says:

    Having once been told that I should give some children ‘easy challenges’ whatever that means – I have no doubt that mixed ability classes do not work for the middle and higher ability children. Their needs are regularly ignored by teachers who feel that the lower ability and SEN are more deserving and needing of their time.

    I taught very much like QT. The fact is that we can not have children in a class in a mainstream school who feel they are entitled to a 1:1 from adults (and the parents who think so too). So much of what goes on in primary school is short sighted and ultimately detrimental to the ability of children to develop further. SEN and LA are too dependent, MA and HA rarely get the time, attention, and no one is pushed and challenged to the extent they need. In fact the self esteem argument against grammar schools belies the fact that in mixed ability classes children know who is smarter than who (especially as we are required to tell them their levels!!) and in which subject, be that Art, PE, Maths.

    This does not even require one to say anything – they are able to see the beautiful drawing of a flower by the person next to them is a world away from the blot on their paper (which btw I would have been the latter!!). It is false to assume that all children can be equal in terms of achievement but they can be challenged to achieve as much as they can in each area. We need to accept this too – equality of opportunity does not mean equality of outcome.

  14. […] 18th April – Is differentiation a zero-sum game? […]

  15. w11wun says:

    to ask a really basic question, what is this differentiation of which you write? I mean how does it make lesson delivery look, or indeed what does a lesson look like when it is absent?

    for example – the class are to be thinking about imagery to affect the reader’s response – all the class get a copy of the witches’ spell from Macbeth, from the play. they all ewwww and urgh as we read through it together. they all pick some favourites and explain what effect these have on them. no differentiation.
    (until they get feedback. then some are asked to offer more examples, some are asked to further consider how the imagery affects how consumers of the play view the witches. some are asked to make sure they answer in full sentences. some are asked to think about describing the images with words other than “minging” or “gross”)

    for example – the class are to be thinking about imagery to affect the reader’s response – all the class get a copy of the witches’ spell from Macbeth, some get the original text, some get a modern rewriting, some read it along with me. some read it independently. they all ewwww and urgh as we then read through it together. they all pick some favourites and explain what effect these have on them. no differentiation? or ok differentiation? or differentiation by resource which is likely to communicate low expectations as they have been handed their particular version to consume? or is that irrelevant because they are all completing the same task and these different resources are the different ladders, so it isn’t differentiated actually?

    I am getting myself in to quite a tangle trying to decide what differentiation at the point of delivery actually is.

    and I think I am asking this because of my sector background. I teach in a multi-composite primary class. I teach 25 children from age 8 to 11. all day. in all their subjects. I do a lot of whole class teaching. I have to stay sane.

    does this buy me a special dispensation to differentiate?

    • David Didau says:

      I think the most useful & manageable form of differentiation is to provide scaffolding to allow all students to reach the desired level of achievement and then to withdraw it as fast as possible. Some children will be able to do with support quite quickly, others will need it for much longer. One of the most important differences between children is the speed at which they pick up new concepts or sills

  16. Caroline says:

    Very thought-provoking piece.

    Are growth mindset and differentiation really opposites? They seem to me to refer to different things – growth mindset refers to outcomes, whereas differentiation seems to me to refer (ideally at least, though not in some of the examples of poor practice given above) to inputs. it’s perfectly possible to have both in the same class – expecting all children to reach to the sky, and keep reaching, whilst giving some an aeroplane to get there, some a pair of stilts, some a balloon etc. As appropriate.

    Or to put it another way, as Teachwell implies, that growth mindset is about equality of opportunity not outcome. And differentiation is a means for that equality of opportunity to be manifested in practice. It is not about (or should not be about) equality of outcome, ie capping by perceived ability.

    To me, the point of a teacher is to recognise and inspire potential – it’s why students with a good teacher will do better than someone teaching themselves with a book, and it’s why e-learning fails to live up to its promise.

    Because nothing beats having another human being believing in you and spurring you on to achieve at a higher level than you ever thought possible.

Constructive feedback is always appreciated

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