Thermodynamics of learning

Last week I attended a conference on Emergent Learning and Threshold Concepts, here at the University of Waikato. It was a very interesting couple of days. As far as academic conferences go, it was unusual in that it was really cross-disciplinary. We had engineers mixing with physiotherapists, and management consultants with dancers. It certainly was interesting to hear about how other disciplines approach educating their students. A challenge faced by everyone presenting, me included, was to make the presentations accessible to someone with no expertise in the area whatsoever. It was a job that was surprisingly well done.

I'm not going to mention here what I talked about (you can find it on the ELTC website if you are that interested). Rather, I'll talk about what my colleague Jonathan Scott presented. He's been looking at Threshold Concepts and Learning for a while now and had some observations to make which he cased in terms of thermodynamics. Jonathan had to keep it pretty maths-easy for those in the audience that weren't mathematically inclined (probably most of them) and I think he did a good job. Here's a potted summary of things.

When we learn something 'thresholdy', things get more ordered in our brain. Pieces of information fit together better. We can see how concepts work, rather than just being pieces of knowledge. Things come into order. In thermodynamics, order is associated with a quantity called entropy. Specifically, something well ordered has low entropy; something with little order has high entropy. Ice has less entropy than water (since its molecules have an ordered structure), but water has less entropy than steam (since even in water there is some degree of ordering among the molecules).  We give entropy the symbol 'S'.  (Actually, I've never stopped to think why it's 'S' for entropy  – Does anyone know?)

Another key quantity in thermodynamics is heat. Heat is a form of energy. Practically, however, it's not always the best quantity to work with. That's because if we do experiments at constant pressure, which is what the laboratory usually has, gases and liquids expand when they heat up. That means a more useful quantity to work with is enthalpy. It's like heat energy, but it takes into account the fact that things can expand and contract, so the amount of stuff in say a 1 litre volume changes. When ice melts into water, for example, there is a change in enthalpy of the system. We need to put energy into the ice to melt it, which means that the enthalpy of the water is higher than that of the ice. We often give enthalpy the symbol 'H'.

We can combine the effects of a change in enthalpy and a change in entropy in something called the Gibbs' Free Energy.  We give it the symbol 'G'.  Specifically, it's the enthalpy minus the produce of temperature (T) and entropy – in maths terms G = H – TS.  Now, here's the neat bit. To make a system change its state (e.g. ice into water) the change in Gibbs' free energy needs to be negative. For ice turning to water, we note that the change in entropy is positive (more disorder). The change in enthalpy is also positive. To get the change in G to be negative, we need the temperature T to be large enough. At atmospheric pressure, if T > 0 degrees C, it will happen. If not, it won't.

What has that got to do with learning. Well, here's Jonathan's analogy. To learn a threshold concept, we need to have a move to more order. But a large, negative change in entropy means -TS is strongly positive and so if this is to happen we need to make the change in H (energy) strongly negative. In other words we need to 'take the heat out' of the system. If the system is 'the student', then this equates to getting the student to do lots of work. (Remember the first law of thermodynamics: Heat and work are equivalent). If a system does lots of work (on something else), it loses heat. A good example is gas from a pressurized bottle doing work as it moves to atmospheric pressure and expands  – the nozzle of the bottle will get cold. The bigger the ordering that is required in one's thoughts, the bigger the amount of work that the student needs to do.  The process is assisted by a lowering of the temperature – a 'cool' environment (as opposed to a hot one with too much going on)  helps the student learn.

Perhaps all this is taking a physics analogy a bit too far. If we think of the message as being "to get thoughts to order together is actually quite difficult" then it's got merit – that is really what the Threshold Concept environment is about.

Finally, it's been noted that Threshold Concepts, are indeed, a threshold concept. Therefore if you struggle to see what I'm commenting on, you need to do some more work 😉