Limitless: Why All Pupils Can Learn Well

Yesterday, I spoke at the ResearchEd National Conference about a very simple idea that has occupied much of my thinking and writing for several years: all pupils can learn well. I have previously described the collection of ideas underpinning this assertion as my Limitless model of education, although the name perhaps requires a little explanation.

To say that human cognitive potential is, for all practical educational purposes, limitless is not to claim that everyone will become a concert pianist, a theoretical physicist or a mathematician. Nor does it mean that everyone learns at the same rate, finds the same things interesting or will eventually reach the same level of expertise in every domain. Human beings plainly differ from one another in countless ways.

The more important claim is that we do not know where the intellectual limits of an individual child lie and, more importantly, that the whole of ordinary school-level learning sits so far within the extraordinary cognitive capacity of the human brain that organising schooling around supposed differences in intellectual potential makes very little sense. With the exception of the very small number of children with severe learning difficulties, there is no good reason to assume that some pupils are capable of learning the ideas we choose to teach in school while others are not.

This distinction is important because education systems routinely convert differences in present attainment into assumptions about future possibility. A pupil who knows less today is easily described as being less able, and from there it is a surprisingly short journey to constructing an education for that pupil in which less is expected tomorrow. The description becomes a prediction and the prediction, through the choices we make about curriculum and teaching, has every chance of becoming self-fulfilling.

The Limitless model begins somewhere quite different: with the extraordinary intellectual inheritance into which every human being is born.

The intellectual advantage of being human

Individually, human beings are not especially impressive creatures. We are born unusually helpless and remain dependent upon others for an extraordinarily long time. Very little of what we regard as ordinary human competence emerges spontaneously. Yet collectively, our species has achieved things that would be incomprehensible if each individual were required to work them out independently.

The explanation lies in cumulative culture. Human beings inherit the thinking of those who came before them. Each generation is therefore able to begin its intellectual life not at the beginning of human knowledge, but somewhere near its current frontier.

Newton and Leibniz are commonly said to have invented calculus, but neither invented it in any meaningful sense from nothing. Their achievements represented critical points in a process of thought extending backwards through centuries of mathematics. Newton had access to intellectual tools that would have been unavailable to a mathematician living a thousand years earlier, just as Einstein had access to centuries of thinking that Newton did not. Einstein was able to go further not because the human brain had undergone some dramatic evolutionary transformation in the intervening period, but because the starting point had moved.

The history of glass offers a more prosaic illustration. Imagine an intelligent person standing on a beach with no inherited knowledge of chemistry or manufacturing. There is sand everywhere, but it is difficult to imagine the thought spontaneously occurring that, with the addition of calcium carbonate and sodium carbonate followed by heating to an extreme temperature, this unremarkable material could be transformed into something solid and transparent. No single human being needed to make that conceptual leap. Glass emerged from a long history of experimentation, observation, communication and refinement.

Education allows children to exploit this peculiar human advantage. A pupil does not need to rediscover number, gravity, photosynthesis, harmony, democracy or the written word. Through teachers, books and the institutions of education, the child gains access to intellectual work accumulated over thousands of years. A good education therefore does something rather like time travel: it allows a person with a finite lifespan to benefit from vastly more thinking than could ever be accomplished within one life.

Teaching is the mechanism by which this inheritance is transferred. It prevents each new generation from being intellectually marooned at the beginning of history.

This is why the question of who receives a serious education has always been consequential. For much of human history, sustained education was the privilege of a small minority, frequently supported by individual tuition. As schooling became increasingly available to poorer children, particularly from the sixteenth century onwards and then at much greater scale during the nineteenth century, arguments emerged about whether those children were capable of benefiting from it. During the debates surrounding the expansion of education for the poor in the nineteenth century, opponents sometimes went considerably further than arguing that education was unnecessary, suggesting that excessive intellectual demands might actively damage children whose proper destination was manual labour.

The language has changed considerably since then, but the underlying question has never entirely disappeared: how much are different children capable of learning?

The conveyor belt

Modern schooling provides an apparently persuasive answer because pupils leave school with enormous differences in attainment. Some are accomplished mathematicians, fluent readers and sophisticated writers; others struggle with elementary arithmetic or to comprehend relatively simple texts. It is tempting to regard this distribution as revealing something fundamental about the intellectual capacities with which those children began.

There is, however, a serious problem with that inference. The system within which those differences emerged was never designed to discover how much each child could learn.

Most Western education systems organise curriculum substantially by age and time. A curriculum is divided into years, terms and lessons, and pupils encounter each part according to a predetermined schedule. The curriculum continues to move whether or not the individual pupil has securely understood what came before. Decades ago, I coined the phrase “the conveyor-belt model of schooling” to describe this phenomenon.

There is something deeply peculiar about this arrangement when considered from the perspective of learning rather than administration. Knowledge is highly dependent upon prior knowledge. Mathematics makes this particularly visible, although the principle applies across domains. A pupil cannot meaningfully engage with many algebraic ideas without a secure understanding of number and arithmetic; later ideas depend upon structures established earlier. Learning resembles an edifice in which new structures rest upon existing ones.

Chronological age tells us remarkably little about whether those foundations are secure. A child's twelfth birthday does not produce a neurological event that suddenly makes a particular piece of mathematics comprehensible. Yet the concept of age-related expectation encourages us to behave as though curriculum has a natural relationship with age rather than with prior understanding.

Once a pupil falls behind the conveyor belt, the problem compounds. New material arrives whose prerequisites are insecure, making the new material harder to understand. That material itself then becomes prerequisite knowledge for what follows. What began as a relatively small gap can therefore become a substantial one without requiring any difference in underlying learning potential.

The system then performs an interesting manoeuvre. Having exposed pupils to a curriculum that proceeds largely independently of whether they have learned its previous contents, we measure the resulting differences and interpret them as evidence of different ability. The system has helped to manufacture the spread and then treats that spread as evidence that the children possessed different potential all along.

This matters particularly for disadvantaged pupils because some families can purchase an escape from the conveyor belt. Private tuition is successful in part because the tutor is able to do something very simple: establish what the pupil understands, identify what is missing and respond accordingly. If necessary, the tutor goes backwards. If an explanation has not worked, another is attempted. If more practice is required, more practice is provided. Time becomes responsive to learning rather than learning being required to conform to time.

A pupil without access to those resources is much more dependent upon the classroom getting this right. An education system that takes insufficient account of current understanding therefore risks magnifying precisely the inequalities it claims to overcome.

Racing ants through custard

The conveyor belt also creates problems for the way we research education. If the underlying conditions for learning are poor, measuring the relative effectiveness of interventions within those conditions can tell us less than we imagine.

I have previously used the analogy of two ants racing through custard. We might intervene to help one ant move more quickly and conduct an impeccably designed experiment demonstrating that our intervention produces a statistically significant advantage. That finding may be perfectly correct. It does not follow that we have discovered the best way for ants to race. The more important intervention would be to remove the custard.

Much educational research compares interventions while leaving the basic architecture of schooling untouched. Pupils continue to encounter curriculum regardless of readiness; attainment continues to be heavily compensatory-referenced; short-term performance is used as a proxy for learning; and the resulting differences are translated into effect sizes. We then encounter claims that an intervention produces a certain number of "months of progress".

The precision of this language disguises a conceptual difficulty. What would four months of progress in mathematics actually mean? There is no coherent body of mathematics corresponding to four months. The measure generally tells us that one group performed differently from another on an assessment and that this difference has subsequently been translated into a temporal metaphor. It does not necessarily tell us what mathematical ideas pupils now understand, how those ideas are connected, whether that knowledge is durable or whether it can be deployed intelligently in unfamiliar situations.

None of this means that experimental research or effect sizes are worthless. It means that their claims must be interpreted within the conditions in which they were produced. An intervention that makes the custard slightly easier to traverse may be useful while we remain committed to racing in custard. It should not prevent us asking whether the race could be organised differently.

From presentation to learning

A limitless model requires a different starting question. Instead of asking what material a pupil of a particular age should be presented with next, we need to ask what the pupil currently understands, what they are ready to understand next and what conditions are required for them to learn it.

This demands a much more sophisticated conception of curriculum. Curriculum cannot simply be a sequence of content scheduled for presentation. It must represent a coherent account of a domain: its ideas, structures, relationships and dependencies. Teachers need sufficient command of that domain to understand how today's idea relates to yesterday's and how both will eventually support tomorrow's.

I describe the teaching that follows from this as forensic teaching. The word is intended to capture the precision involved. Teachers make continual judgements about what pupils know, where misconceptions lie, which examples will illuminate a structure, which representation will connect a new idea to an existing one, when to practise, when to explain and when to step backwards. Teaching, in this conception, is fundamentally different from presentation.

Forensic teaching cannot, however, guarantee learning by itself because learning takes place within the pupil. Attention, thought, practice and perseverance cannot be outsourced to the teacher. A pupil may have access to extraordinary teaching and still fail to make use of it.

The second component of the Limitless model is therefore pupil grit. The term has accumulated considerable baggage, not least because it can be used to shift responsibility for educational failure from institutions onto children. That is not its purpose here. Asking a pupil to persevere with bad teaching is no more defensible than providing excellent teaching while pretending the pupil need make no effort.

Learning is frequently difficult. It demands concentration and often involves frustration, repetition and temporary failure. Part of becoming educated is learning that such difficulty is neither evidence of incapacity nor a reason to stop. Csikszentmihalyi's work on flow is particularly interesting in this respect because the deeply satisfying state he describes tends to arise not from passive reception but when challenge and existing capability are finely balanced. Difficulty is not an unfortunate side effect of worthwhile learning. Properly calibrated, it is part of what makes intellectual accomplishment rewarding.

The interaction between forensic teaching and pupil grit is therefore central. The teacher has a responsibility to make learning possible; the pupil has a responsibility to undertake the learning. Neither proposition is particularly radical when stated plainly, although modern educational debate has sometimes contrived to make each sound controversial.

Learning is not one thing

There is a further complication. Even if we accept that all pupils can learn well, it does not follow that the same teaching behaviours are appropriate throughout the process. A great deal of disagreement about pedagogy arises because "learning" is treated as though it describes a single cognitive state.

Consider the perennial arguments about practice. One body of evidence might suggest that pupils benefit from a small number of carefully varied examples, while another emphasises extensive repeated practice. A third advocates mixed practice and a fourth deliberate practice targeted at specific weaknesses. These positions can easily be presented as contradictory, but much of the contradiction disappears when we recognise that they concern different points in the development of expertise.

The pupil encountering an idea for the first time has different needs from the pupil who understands it but remains inaccurate. Both differ from the fluent pupil learning to select and combine ideas in unfamiliar circumstances. The journey from novice to expert is extended, messy and reversible, but it is nevertheless possible to identify different qualities that emerge along the way.

In the Limitless model, I describe these as awareness, inflexibility, flexibility, automaticity, fluency, connectivity and maturity. They should not be understood as seven gates through which pupils march in order. They are better thought of as a vocabulary for describing changes in the character of knowledge as expertise develops.

At the point of awareness, the teacher's task is to make a genuinely novel idea intelligible. Human beings understand new things by relating them to things they already understand, which makes readiness fundamental. Story, metaphor and models allow the teacher to translate the unknown into the known, but they can only do so if the necessary conceptual vocabulary already exists. Where prerequisite knowledge is absent, the sensible response is to establish it before proceeding.

Initial understanding is then often deliberately inflexible. Through exposition and carefully chosen examples, the pupil learns what an idea means and how it can be used in a restricted range of circumstances. This is sometimes caricatured as rote learning, but the distinction is important. Rote learning is memorisation in the absence of meaning; inflexible knowledge has meaning but is deliberately constrained. Those constraints allow the novice to experience immediate success before being asked to appreciate the full complexity of an idea.

Knowledge subsequently becomes flexible as the pupil encounters examples and non-examples, variation and boundaries. The question changes from simply knowing what to do to understanding how, when and why an idea applies. Underlying principles and structures become increasingly visible.

Once that understanding is established, automaticity becomes desirable. Pupils replicate, rehearse and practise until familiar processes require substantially less conscious attention. This is an important achievement because limited attention can then be directed elsewhere. The danger is to mistake automaticity for the end of learning. Much everyday competence stops at this point because "good enough" performance is sufficient for most purposes. Education should demand more.

The transition from automaticity to fluency requires a different kind of practice. Purposeful practice focuses attention on accuracy and gives the pupil information about errors. Deliberate practice adds the intervention of an expert teacher who can identify why micro-errors persist and provide specific advice about how performance might improve. The distinction is subtle but consequential. Repetition makes performance familiar; properly structured practice makes it reliably excellent.

Fluent knowledge then makes connectivity increasingly achievable. Subjects are not lists of independent facts and techniques but interconnected webs of ideas. As pupils acquire more knowledge, old ideas can be viewed from new vantage points and relationships that were previously invisible become apparent. Transfer becomes possible because pupils possess not merely procedures but a repertoire from which they can select and combine methods according to circumstance.

This is one reason I have long argued for forward-facing teaching. The methods and explanations pupils encounter early should, as far as possible, remain truthful as their understanding develops. Good early teaching lays intellectual threads that can be picked up years later, producing those wonderful moments when a pupil suddenly understands why something encountered long ago mattered.

Finally, there is maturity, and maturity principally requires time. Knowledge becomes increasingly integrated as pupils spend years within a discipline, encounter its ideas repeatedly and begin to participate in its characteristic ways of thinking. Mathematics becomes something pupils do rather than merely something they know. The same is true of history, science, literature, music and other domains. At its richest, education inducts pupils into what Robert Maynard Hutchins called the Great Conversation: humanity's continuing attempt to understand, describe, challenge and improve what has been thought before.

The movement through these maturation phases is neither straightforward nor permanent. Learning can regress. Apparently secure knowledge can prove fragile when encountered in a different context. New ideas can expose old misconceptions. Expertise develops through continual movement backwards and forwards as knowledge is reconstructed and strengthened. The stages are therefore not a staircase but a way of examining a complex process from different vantage points.

What limitless really means

Seen in this way, several of education's apparently intractable debates begin to look rather different. Explicit instruction and independent problem solving need not be opposing philosophies if they describe appropriate activities at different stages of becoming expert. Repeated practice and carefully varied examples are not mutually exclusive if they serve different purposes. Even arguments about pupil grouping become less interesting once grouping is separated from assumptions about fixed potential. The useful question is not whether pupils should always be taught in mixed or attainment-based groups, but what arrangement best enables teachers to respond to what particular pupils currently know and need to learn next.

The word currently is doing a great deal of work there. Present attainment is real and consequential. A pupil who does not understand fractions cannot simply be treated as though they do. Meeting pupils where they are requires us to take those differences extremely seriously. What it does not require is treating those differences as evidence of where pupils will eventually end up.

This is perhaps the most important distinction in the Limitless model. Attainment describes a present state; it does not reveal a future limit. Confusing the two is one of the most damaging mistakes an education system can make.

Once we consider a pupil as not being able to learn well, present difficulty easily becomes imagined incapacity. Expectations change, curriculum changes and opportunities change. The pupil who knows less is given less to know, thereby increasing the probability that they will continue to know less. A description of attainment becomes an educational destiny.

A limitless education refuses to make that error. When a pupil has not learned something, the appropriate response is to investigate. Perhaps prerequisite knowledge is missing; perhaps an explanation failed; perhaps a representation created a misconception; perhaps insufficient time was available; perhaps practice was poorly designed; perhaps the pupil did not attend or exert sufficient effort. Each possibility presents a problem upon which teacher and pupil can act.

This is also why the model does not require the implausible assertion that all children are identical. They plainly are not. Pupils arrive at school with different experiences, knowledge, interests and dispositions. They learn at different rates and require different amounts of practice. They will eventually discover domains in which they are willing to invest extraordinary effort and others in which they are content with ordinary competence. A limitless model has no difficulty accommodating any of this.

What it rejects is the much stronger assertion that from these differences we can infer the boundaries of a child's future intellectual life.

We cannot know how far a pupil might eventually travel, but we can know what they understand now. We can identify the boundary of that understanding and teach in a way that helps them cross it. Having done so, we can locate the new boundary and begin again. Curriculum, teaching, assessment and time can all be organised around this process rather than around predictions of eventual capacity.

This leads to a rather different conception of educational ambition. The purpose of school is not to sort children efficiently according to the destinations we imagine appropriate for them. Nor is it simply to expose every child to the same sequence of presentations and then record the differences that emerge. It is to give each pupil access to humanity's accumulated intellectual inheritance and to develop in them the capacity and disposition to make use of it.

Human beings have spent thousands of years learning how to educate one another. We know far more about the journey from novice to expert than contemporary educational discourse sometimes suggests. We know that prior knowledge matters, that new ideas must connect meaningfully with existing understanding, that novices benefit from expert explanation, that practice changes in character as expertise develops, that feedback can refine performance, that knowledge becomes powerful through connection and that maturation takes time. None of this makes teaching easy, but it does mean we need not treat learning as an unknowable mystery.

The challenge is to build schools around that knowledge.

For me, that is ultimately what limitless means. It is not a claim that every pupil will become equally expert in everything. It is a refusal to pretend that we know in advance where any particular pupil's intellectual limits lie. Our responsibility is therefore not to predict those limits and construct an education around them, but to create the conditions in which pupils repeatedly move beyond what they can presently do.

We meet the child where they are, but we refuse to leave them there.