Yesterday, at the excellent ResearchED 2016, I was fortunate enough to attend a talk by Michael Fordham. Part of his talk was a discussion on the possible redundancy of the word ‘understanding’ in education. His argument, which he acknowledged he was still not completely convinced by, was that when discussing ‘understanding’, people are really talking about knowing. This is interesting as often ‘understanding’ is used as a higher level signifier of learning than knowing.
I am interested in how the expertise reversal effect might shed some light on this argument. David Didau describes this as ‘instructional techniques that reduce working memory load may become counter-productive when applied to students who have developed a degree of expertise’. I accept that there is a qualitative difference in how a novice and an expert learns. A novice learns best by explicit instruction and explanations, worked examples, modelling, scaffolding, and practise. At some point in one’s experience of learning, one’s mental schemas reach a sophisticated enough level to be thought of as expert. It may well be that threshold concepts signify this transition. (1)
My contention is that the knowledge learned by a novice through the methods I have mentioned is necessary to move into expertise and pass exams, but insufficient for the confidence one associates with ‘understanding’, and the knowledge learned when expert mental schemas are in place then becomes sufficient for that confidence. I am proposing that there are two types of knowledge: compartmentalised knowledge learned by a novice, and integrated knowledge learned by an expert.
In the questions following Fordham’s talk, a teacher mentioned that she had only felt she had ‘understood’ her subject once she had taught it for a while, and this was despite obtaining an excellent degree in it. This resonates with me completely; I feel exactly the same. Indeed, I felt that it was only during the sessions on my PGCE that I really felt that I had started to ‘understand’ maths, and I have a First from a Russell Group university in the subject. I believe that this feeling will resonate with the majority of teachers.
Having given consideration to Fordham’s talk, I think that it was only when I was able to revisit my knowledge of maths from an expert’s standpoint, that my knowledge became integrated enough for the confidence I associate with ‘understanding’. School and university march one’s knowledge ever forward, in this respect, students can be considered novices throughout their whole formal education. For example, at GCSE, I learned enough knowledge to move into expertise in Quadratic Equations, at A-level, I learned enough knowledge to move into expertise for Equations of Motion, and at university similarly for Group Theory.
It is here that I bring pedagogy into my argument and there are two points I want to make. First, my experience of formal education is that I was taught up to the level of expertise and the ability to pass exams: the necessary knowledge. I believe this gave me, what I call compartmentalised knowledge. I think this is true of many people’s experience of education. I was not given a chance to have less guidance given to me, as advocated by the expertise reversal effect, which I believe had it been offered would have allowed me to gain integrated knowledge of the topics I was studying, this would have been sufficient knowledge. Second, there are pedagogical decisions made by teachers that can inhibit the development of integrated knowledge. For example, if I am learning Pythagoras’ theorem, and I am taught it in only an algebraic way, and the geometry of it is left out, then this will damage my chances of gaining an integrated knowledge of the topic.
To summarise, influenced by Fordham’s talk, I think that the point de captiton ‘understanding’ is unhelpful in Educational discourse. I propose that the expertise reversal effect and the qualitative differences in learning by novices and experts can determine that it useful to think of knowledge in a binary way: compartmentalised knowledge learned by novices, and integrated knowledge learned by experts. I think this distinction can illuminate pedagogical choices and practice in general.
(1) I have gleaned my knowledge of novices, experts, the expertise reversal effect and threshold concepts from David Didau; any misunderstandings are my fault, as is the case for Fordham’s talk.