Tuesday, February 12, 2013

The tyranny of the discontinuous mind

While on the subject of education, I once heard a debate on TV about whether a marks system or a grade system is better. I don't remember the arguments (this was before I started this blog, else I would have listened more carefully and noted some points) but the consensus was to favour a grade system. In this connection, Richard Dawkins talks of the tyranny of the discontinuous mind, the tendency of many people to see the world in binary terms.He discusses it in The Ancestor's Tale (my favourite Dawkins book) in the course of which he writes about marks vs grades:
Students do not really separate neatly into good, middling and poor.  There are not discrete and distinct classes of ability or diligence.  Examiners go to some trouble to assess students on a finely continuous numerical scale, awarding marks or points that are designed to be added to other such marks, or otherwise manipulated in mathematically continuous ways.  The score on such a continuous numerical scale conveys far more information than classification into one of three categories.  Nevertheless, only the discontinuous categories are published.  
In a very large sample of students, the distribution of ability and prowess would normally be a bell curve with few doing very well, few doing very badly and many in between.  It might not actually be a symmetrical bell ... but it would certainly be smoothly continuous, and it would become smoother as more and more students are added in.
If, against all my expectations, it should turn out that the more students you add in, the more the distribution of exam marks approximates to a discontinuous distribution with three peaks ... it would be a fascinating result.  The awarding of First, Second and Third Class degree might then actually be justifiable.
But there is certainly no evidence for this, and it would be very surprising given everything we know about human variation.  As things are, it is clearly unfair: there is far more difference between the top of one class and the bottom of the same class, than there is between the bottom of one class and the top of the next class. It would be fairer to publish the actual marks obtained, or a rank order based upon those marks.  But the discontinuous or qualitative mind insists on forcing people into one or other discrete category.

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