Education Needs a GPS

For most of history, one of the principal constraints on education was access to information. Knowledge was expensive to produce, distribute and preserve. If you wanted to learn something, you needed access to the appropriate books, teachers, institutions or other people who already possessed that knowledge. Geography, money and institutional access all influenced what someone could realistically learn.

The internet fundamentally changed those economics. Information that previously required access to a university library can now be retrieved in seconds, often at negligible marginal cost. A student can find textbooks, lectures, worked examples, past papers and explanations covering almost any subject. More recently, advances in artificial intelligence have made it possible to interact with much of that information conversationally, asking questions and receiving explanations adapted to the immediate context.

Yet improvements in access have not produced equivalent improvements in educational outcomes. Students still struggle to understand concepts, retain information, identify their weaknesses and prepare effectively for examinations.

This is not particularly surprising when we consider education as a system rather than simply a mechanism for distributing information.

Improving the availability of a resource does not necessarily improve the output of a system when that resource is no longer its primary bottleneck.

Consider a manufacturing process. If a factory is constrained by the supply of raw materials, increasing that supply can improve production. However, once the factory has more materials than it can process, the bottleneck moves elsewhere. Perhaps the machinery cannot process materials quickly enough, or perhaps the logistics system cannot coordinate their movement between production stages. Continuing to increase the supply of raw materials produces diminishing returns because the constraint has shifted.

I think something similar has happened in education.

We have spent decades making educational content increasingly accessible, yet much of the infrastructure surrounding learning still assumes that the student is responsible for independently organising and navigating that content. We have increased the supply of information without making comparable improvements to the systems that determine how it should be used.

Of course, this does not mean that access to quality education is now universal, nor that content quality and teaching have ceased to matter. These remain genuine constraints, particularly where students lack adequate resources or support. But for a student who already has access to a reasonable library of educational material, simply providing another explanation or another set of notes may do relatively little to address what is actually limiting their progress.

The problem is increasingly one of coordination.

A student needs to determine what they already understand, what they have forgotten, which concepts they are missing, how those concepts relate to the wider curriculum, and where their time would be most productively allocated. They must make these decisions while possessing incomplete information about their own understanding.

This introduces an interesting problem: students are expected to manage a learning process whose internal state they cannot reliably observe.

The Difference Between Information and Navigation

A useful way to understand this distinction is through the development of navigation technology.

Maps existed long before GPS. A sufficiently detailed road map could contain practically all the geographical information necessary to complete a journey. It described the roads, their connections and the possible routes between locations.

But possessing a map is not the same as having a navigation system.

To navigate using a conventional map, the driver must establish their current position, identify their destination, calculate a route and continuously reconcile their surroundings with the information on the map. If they take a wrong turn, they need to recognise the deviation and calculate an alternative route.

GPS navigation did not fundamentally improve transportation by inventing new roads. Its contribution was to integrate several previously separate operations into a single system: mapping, position estimation, route planning, feedback and recalculation.

The driver still operates the vehicle, but no longer needs to devote as much attention to managing the route.

Education has undergone something resembling the digitisation of maps without fully developing the equivalent navigation infrastructure.

We have moved textbooks onto screens, made lectures searchable and created enormous libraries of educational material. But students are still frequently expected to navigate the curriculum manually, reconstructing the relationships between topics and deciding which activities are most likely to improve their understanding.

A curriculum itself is essentially a map. It describes what students are expected to learn, but it does not necessarily describe the individual student's position within that structure.

Two students studying the same topic may have completely different underlying knowledge states. One might understand the prerequisites but struggle with applying them. Another might be attempting to learn the topic without understanding a foundational concept introduced several years earlier.

Presenting both students with the same additional content does not necessarily resolve either problem.

What matters is identifying the particular constraint preventing each student from progressing.

This is where a navigation system becomes useful. Instead of treating the curriculum as a collection of independent topics, we can represent it as a network of concepts, skills and dependencies. We can then use evidence from a student's learning activities to estimate their current understanding and determine which interventions are likely to be most useful.

The distinction is between having access to the map and having a system capable of interpreting your position within it.

Learning as a Feedback System

One of the more interesting properties of learning is that understanding cannot be directly observed.

A student might report that they understand a concept, but that does not necessarily mean they can apply it. They might answer a question correctly through guessing, pattern recognition or memorising a particular procedure. Conversely, a student might understand the underlying principle but make an arithmetic mistake during an examination question.

This means that any system attempting to guide learning has to work with imperfect observations.

We can think of a student's understanding as a collection of internal states associated with different concepts and skills. These states are not directly measurable, but we can estimate them using evidence such as answers to questions, explanations, recurring errors and performance over time.

As more evidence becomes available, the estimates can be updated.

This creates the basis for a feedback loop: the student performs a learning activity, the system observes the result, updates its estimate of their understanding and uses that information to inform the next activity.

The process repeats as the student progresses.

Importantly, this is different from merely recording whether a student has completed a lesson. Completion tells us that an activity occurred; it does not necessarily tell us what was learned.

Even a percentage score is only a limited measurement. A student achieving 70% on an assessment might have several small gaps distributed across the material, or one substantial conceptual misunderstanding affecting a particular class of questions. These situations might produce identical scores while requiring very different interventions.

A useful learning system therefore needs to reason about the structure beneath the result.

For instance, if a student repeatedly struggles with algebraic manipulation, the immediate response might be to give them more algebra questions. But if the underlying issue is an earlier misunderstanding of negative numbers, additional algebra practice may be an inefficient use of time.

The visible failure is not always the underlying bottleneck.

This is why representing relationships between concepts matters. Learning is not simply a linear sequence of lessons. Knowledge has dependencies, and weaknesses in foundational concepts can propagate into several apparently unrelated areas of a curriculum.

A system that can identify these relationships has the potential to intervene closer to the source of a problem, rather than repeatedly treating its symptoms.

Of course, these estimates will never be perfect. A student's performance is influenced by attention, fatigue, question difficulty, prior exposure and numerous other factors. Any model of their understanding must therefore remain provisional and updateable rather than treating its own measurements as ground truth.

But imperfect feedback is still useful, provided the system accounts for uncertainty and responds to new evidence.

The Hidden Cost of Managing Learning

There is another constraint worth considering, and it concerns how students allocate their attention.

Learning requires cognitive effort. Understanding unfamiliar material, retrieving information from memory, solving problems and connecting ideas all demand attention. That effort is not something we should attempt to eliminate; it is an important part of how learning happens.

However, not all the effort involved in education contributes directly to learning.

Students also spend time deciding what to revise, locating suitable resources, comparing their progress against the curriculum, identifying weaknesses and planning future study sessions. These activities can be necessary, but they represent a second layer of work surrounding the learning process itself.

We might describe this as the coordination overhead of learning.

In computing, a system can spend an increasing proportion of its resources coordinating work rather than performing the work itself. Scheduling, communication and state management all introduce overhead. Some overhead is unavoidable, but reducing unnecessary overhead can improve the effective capacity of the system without increasing its underlying resources.

Students face a comparable allocation problem.

Attention and time are finite. Every minute spent deciding which resource to use is a minute that cannot simultaneously be spent engaging with the material. More importantly, the uncertainty surrounding those decisions can persist throughout a study session.

A student might spend an hour revising while remaining unsure whether they are studying the right topic, whether they are neglecting a more important weakness or whether the material even corresponds to their examination specification.

That uncertainty introduces friction into the learning process.

It is important to distinguish between productive difficulty and unnecessary friction. Struggling to understand a difficult mathematical proof may be precisely the kind of effort that produces learning. Struggling to determine which chapter contains the prerequisite knowledge needed to understand that proof is a different problem entirely.

The objective should not be to minimise all cognitive effort, but to allocate more of it towards activities that actually develop understanding.

This also explains why an effective educational system should not simply give students answers whenever they encounter difficulty. Doing so may reduce immediate friction while undermining the learning process itself.

The relevant question is whether a particular form of assistance removes an unnecessary obstacle or bypasses the intellectual work that the student needs to perform.

A navigation system should help the student reach the appropriate learning activity. It should not perform the learning on their behalf.

Building the Navigation Layer

This is the problem we are attempting to address with KnowledgeSet.

Rather than approaching education exclusively as a content distribution problem, we are interested in building infrastructure that can represent the curriculum, estimate a student's understanding and coordinate their progression through it.

At the centre of this approach is the distinction between the curriculum itself and the student's relationship to that curriculum.

The curriculum provides the underlying structure: the concepts, skills, topics, specifications and dependencies that define what needs to be learned. The student's interactions provide evidence about their current understanding of that structure.

Connecting the two allows us to approach learning as a continuously updated process rather than a static sequence of lessons.

If a student demonstrates a weakness, the system should be able to investigate the concepts associated with that weakness, identify plausible prerequisites and select an appropriate activity. If the student subsequently demonstrates understanding, that new evidence should influence future recommendations.

Similarly, if a student has already mastered a concept, the system should not repeatedly allocate substantial study time to it simply because it appears next in a predetermined sequence.

The aim is to make the allocation of learning activities responsive to the student's actual needs.

This is not a claim that educational progress can be reduced to a perfectly measurable optimisation problem. Students are not machines, and learning involves motivation, curiosity, social interaction and forms of understanding that are difficult to quantify. Teachers also contribute forms of judgement, encouragement and contextual understanding that are not straightforward to reproduce computationally.

But none of those limitations invalidate the usefulness of better information and coordination.

A navigation system does not need a perfect model of the world to be useful. It needs a sufficiently reliable model, mechanisms for detecting when its assumptions are wrong and the ability to adjust accordingly.

The same principle applies here.

If we can reduce the uncertainty surrounding what a student knows, what they need to learn and which activity would be useful next, we can make the educational process more coherent without removing the student's agency.

That last point matters. The student should still be able to explore, deviate from recommendations, ask questions and pursue their own interests. Navigation is useful precisely because it supports movement towards a destination; it should not dictate which destinations are worth pursuing.

Ultimately, I do not think the next major improvement in digital education will come from simply producing more educational material. We already have an extraordinary amount of it, and advances in generative AI will continue to make content production cheaper.

The more interesting opportunity is to improve the infrastructure connecting that material to the people trying to learn from it.

We have become remarkably good at making knowledge available. We now need to become better at making that knowledge navigable.