Learning Ceilings

When ‘just knowing’ isn’t enough

At 11 o’clock this morning, I headed into a local café where I was due to meet with a prospective tutee. The meeting proved to be really enlightening for me as a tutor. The tutee, Barney (not his real name), described himself as generally pretty able – he never struggled in school and was able to pass exams without the need to revise, achieving 4 ‘A’s and a B at Higher [AS Level equivalent]. He overlooked the C he got for Advanced Higher [A Level equivalent] Maths, saying that he’d been more focussed on enjoying his last year of high school. No doubt, alarm bells should have started ringing, but to a young mind, it is easy to prefer the excuse of “I could have done better if I’d tried” and leave it at that. That mistake would take over a year to reveal itself. Barney cruised through his first semester of Mechanical Engineering, no doubt thinking that everything was back to normal – no revision required. The moment of truth came with the second semester’s results: two out of four modules failed; overall: first year failed.

The situation Barney found himself in is not uncommon. I don’t mean actually failing exams, but the manner in which he failed them. In fact, I’d bet that something similar affects most students at some point in their learning career. I would describe it as reaching a “comfortable learning” ceiling. Let me quickly point out that I don’t mean that the student has reached the extent of his abilities, the limit of his knowledge, filled his tank of learning. No. What I emphasise is the adjective comfortable. In my opinion, each student can absorb a certain amount of knowledge without expending a lot of extra energy by poring over books for hours and practising hundreds of problems – this is what I would describe as ‘comfortable’ learning. Reaching a ceiling will occur when learning in this way can no longer be sustained. I believe this phenomenon is natural and occurs at different stages of learning for everyone.

Understanding knowledge

A solid foundation is... fundamental!
A solid structure can only be achieved with solid foundations.

Is it a question of complacency? I don’t think so. I didn’t have to do much work at school either – this isn’t a point of bragging – it’s stating a fact. The result of it is that a student does not learn to learn. I think that the best way to describe this phenomenon is that the learning process is almost non-existent. A bright student simply ‘picks up’ knowledge in school and it immediately enters his knowledge base, from which he can draw facts come exam time. The difficulties arise when an exam question requires the student to not only draw on existing knowledge, but also combine different threads of learning to find the solution to a more complex problem. Suddenly, the existing knowledge reveals itself to be fragmented and insufficient at dealing with the complexity of the problem.


The solution is simple, but may require a lot of work. What the student needs is a thorough understanding of where his knowledge comes from, which will allow him to use it when approaching these complex problems. This means going right back to the basics and understanding the key concepts rather than just knowing a method for solving a given problem. I would describe this situation as follows: a number of disjointed methods for solving individual problems can be seen as a number of stand-alone pylons which will allow someone to climb in one particular point and reach their goal. If, however, they wish to reach a goal somewhere in-between two such pylons, they can only extend a rope, which will not be sufficient for reaching their goal safely. What is required is a safe base to be built from the ground up, connecting the pylons and allowing any point (or goal) to be reached with a solid foundation. This base is formed of connections joining the different elements of knowledge into a single entity – a thorough understanding of the topic – and can only be achieved by progressive learning of that same topic from its foundations to its edges, where it interacts with other adjacent topics.