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.

Can the weather tell you about people?

Unwittingly, I find myself writing about the weather again. It has been pointed out to me that this is simply an example of Britishness. The thing is, I’m not British (yet), but it appears that living in a country for more than half of my life and adapting to its customs has rubbed off on me somewhat.

Today has been quite remarkable. We’re only into the afternoon and already, I’ve almost lost track of the number of times the weather has changed. And I don’t just mean it was a little cloudy and then the sun came out. No. The changes have been pretty dramatic. When I got up, I was happy to register a blue sky, knowing I’d soon have to leave the house on foot. By the time I was finishing breakfast, it was grey and the first few drops started hitting the windows. I didn’t have any other choice but to put on a long coat and brave the weather. On the way into town, I could see patches of blue sky ahead of me, but the umbrella was definitely a necessity. Half an hour later, just as I reached my destination, the sun was out shining brightly in an almost perfectly clear sky. During the couple of hours I was indoors, another shower had passed over the city, but it was clear again as I left. In fact, walking south was particularly unpleasant as the already low autumn sun was being reflected off the wet pavement and directly blinding me. Before I’d finished preparing my lunch, another heavy downpour had begun, the sun coming out once more for dessert. Then another shower; and more blue sky. You get the picture.Singing in the rain

Let’s be honest though – talking about the weather itself can get a little boring. Its primary use is, after all, simply as a conversation starter when two Brits meet and attempt to establish some common ground. Or alternatively as a filler when a conversation dies down. The interesting stuff happens from observing the interactions between the weather (mostly unchangeable, but definitely not unchanging) and people (who have the possibility of adapting to it, but do they?). Take a day like today, for example. Unless you don’t know Edinburgh at all, it’s obviously fairly foolish to venture outside on an autumn’s day without something to protect you from the elements (wind or rain, depends what affects you more). Yet the number of people who do just that is quite incredible. I will pick on students now (without any guilt, as I was one myself not so long ago), a stream of whom walks down my street to the science and engineering campus of the university every day. During one of those downpours, while I was safely sheltered behind my window, I could see very few of them walking under an umbrella. The sight of a completely sodden hoodie was much more common. In such a situation, it’s quite easy to start drawing conclusions about the people one is observing: the sodden students were freshers, away from home for the first time and unable to look after themselves without their mothers telling them to put on a coat. Those with coats were either older, more sensible, more experienced or had actually rung mummy up before leaving the house.

For others, of course, the weather is an opportunity to display all kinds of fashion sense (or nonsense, in some cases). A pair of bright red wellies could perhaps not be considered particularly attractive, but they certainly draw the eye. Soaked jeans and trainers – less so. Thus whether a person takes the weather into consideration can also tell us something about their personality. Simply put, whether they can be bothered to adapt the way they dress. And if they do, whether it’s to look good, or just to stay dry. In Scotland, however, I have observed an additional dimension to ‘dressing for the weather’: more precisely, it’s actually that of not dressing. Imagine this: a cold January morning – no rain, just a chilly wind on a crisp day. I’m trying to decide whether to put on that fourth layer. In the end I do. Not long after leaving the house, I pass a guy who is wearing absolutely nothing on top of his T-shirt. I shiver. How can he possibly not be cold? Perhaps one day I’ll be let in on the true secret, but for now I’ll explain it to myself like this: a warm of bowl of Scots porridge is somehow keeping him warm. So that accounts for the need to look macho. But at least there aren’t any fashion pressures for guys. Or perhaps there are, but I am, and will remain, blissfully ignorant of them.

A foggy day…

Here it is, finally… the rain I’ve been waiting for all day. Don’t get me wrong, I would prefer it to be sunny, but I am trying to be realistic. This is October in Edinburgh and the last couple of days of September were glorious, so I was not surprised to find that the forecast was predicting change. What did frustrate me though was that the morning was overwhelmingly hazy and hence unpredictable.

It then became decidedly foggy, so that even the other side of the street lost its normally sharp outline. The hill usually visible from the windows hid behind a solid veil of light grey, reminding me of the intensely foggy experience I had in the ARoS museum in Århus a few days ago and which I will hopefully be writing about soon.

Now I’m not sure if it’s an effect of the fog, or simply the acclimatisation from one location to the next, but my senses seem to be suffering from a similar dumbing down, as though my mind was a little foggy too – lacking colour and out of focus, just like the view outside. And now the first few drops of rain have left their ellipsis streaks on the window… what next?