Experts and the elements of understandingPosted: January 31, 2016
This is one for the cognitive science nerds. A paper has just been released pre-publication by Ouhao Chen, Slava Kalyuga, John Sweller*. It attempts to unify the well-known ‘expertise reversal effect’ with the ‘element interactivity effect’. I’ll try to put this succinctly but I’ll surely miss some important nuances in the process.
Imagine we are solving a problem and that different parts of the problem rely upon each other. A typical example would be rearranging an equation: We can’t do the steps in isolation because the second step depends upon the first and so on. Similarly, construction of a paragraph will draw upon different elements that each depend upon the other. Contrast this with learning a list of labels. The example Chen et. al. use is learning the Periodic Table in chemistry. It would be a complicated task to complete but learning the symbol for fluorine is not dependent upon learning the symbol for iron so the element interactivity is low (no pun intended).
Van Gog and Sweller have previously used this idea to explain experiments which seem to show that retrieval practice works for low element interactivity learning but studying worked examples is better when interactivity is high. The new paper uses the same idea to reconcile the seemingly contradictory ‘generation’ and ‘worked example’ effects and draws on Chen’s experiments to bring this into focus: For novices, generation works better for low element interactivity and worked examples work better for high element interactivity and for more knowledgeable learners, generation was best all round.
Element interactivity is not straightforward to define. Chen et. al. themselves suggest that processes such as making inferences to construct mental representations, integrating them with prior knowledge, or blocking irrelevant information are hard to define in terms of interacting elements and it is worth pointing out that Van Gog and Sweller’s findings are contentious and a matter of some debate.
If we accept the notion of element interactivity – setting aside concerns that it might sometimes be hard to identify the elements – then it should change as we become more expert at a task. Once we have completed a certain kind of process often enough, that routine becomes like the subroutine of a computer. We can pull it out of long term memory as and when required. We don’t have to deal with all of the interacting elements in working memory and it consumes fewer working memory resources. Element interactivity effectively reduces with increased expertise. This could account for the expertise reversal effect where experts learn more by solving problems than by studying worked examples – the opposite of what we see for novices.
Those who follow the rhetoric of mathematics education reform will also be interested to find that Chen et. al. have a go at defining ‘understanding’:
“Element interactivity also can be used to define “understanding.” Information will be fully understood if all interactive elements can be processed in working memory simultaneously (Sweller et al. 2011). Nevertheless, the term understanding tends to not be used when dealing with low element interactive information. If someone deals with information low in element interactivity, such as “Cu” stands for “copper”, we would not refer to them understanding or failing to understand the relation. If we fail to recall this relation, we will attribute the failure to forgetting or having no prior knowledge rather than failing to understand. Therefore, understanding is only used for materials high in element interactivity.
The distinction between learning by understanding and learning by rote is also related to element interactivity. Learning by understanding increases the number of interactive elements that must be processed in working memory simultaneously. However, if a large number of interactive elements cannot be handled simultaneously, learning by rote reduces the number of interacting elements albeit at the expense of understanding. Of course, learning by understanding is the ultimate goal of instruction.”
Some of this is similar to ideas that I have tried to articulate before about ‘subjective understanding’ – we feel that we understand something when we can manipulate the elements in our working memory. I am a little bit uncomfortable with the second paragraph because I see no reason why we cannot both memorise something and also see how it fits into the bigger picture or ‘understand’ it. So I don’t see that memorisation is necessarily at the expense of understanding. I can memorise a multiplication fact such as 7 x 8 = 56 whilst also understanding why this is the case and how I could demonstrate it to be true should the need arise.
I think that all educators need a basic theory of expertise given that this is what we are aiming at for our students and the idea of element interactivity could add something here. I might also take this opportunity to shamelessly plug my new book (which you can buy here) which addresses the issue of expertise and the misconceptions that we have about it.
*Disclosure: Kalyuga and Sweller are my PhD supervisors