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It is a few years now since I left the classroom and my thoughts today are with the scores of teachers up and down the country currently revelling in or reeling from the results that their students receive.
In the moment that students open their envelopes, many of their teachers will be on hand to share in the joy of achievement -sometimes unexpected, sometimes well-deserved. They will also provide support to the poor souls whose world comes crashing down as their grades don't match their expectations; convincing them that they still have options and helping them through those first few moments of panic.
But when the dust settles, many teachers will find themselves in an uncomfortable position: potentially asked to justify the performance of individual students against target grades. As someone whose job is focused on exploring how statistical literacy can be taught more effectively I find this scenario a little troubling, as it is a clear indicator of a lack of comprehension of how statistics and probability are related to each other.
For any student, their predicted grade is essentially a probability based on a range of parameters assigned to the student, postcode, previous key stage performance, socio-economic background etc. Once established, a comparison is made against a model distribution of students who have historically performed similarly to generate a most likely grade for the student. It is important to be aware that this theoretical grade is not based on any surface factors that affect the student, -such as: what's their motivation? Do they like the subject? Did they study well? What did they eat for breakfast? Did a car alarm go off in the middle of the night before a key exam and wake them up?
The power of statistics is not in how these theoretical grades match up to individual students, but how an aggregate distribution of the theoretical grades of many students combine to overcome the individual inaccuracies of the prediction to create an outcome that is likely to closely match the model. When large numbers of students under-perform against the aggregate prediction for their individual grades, it is reasonable to ask questions about whether there is some underlying issue with teaching and learning, although even here care must be taken if looking at for example a bottom set class - which may only contain 15 or 20 students, and therefore not enough for aggregate features to become indicative, never mind that the model is much more skewed at the bottom.
Realistically, and only if the size of the dataset is large enough, the data should be explored in context. Questions asked about the performance of the cohort against theoretical grades may provoke an important professional dialogue. Questions asked about the performance of a class against theoretical grades may provide some useful pointers - but must be treated with a healthy dose of scepticism. Questions asked about the performance of an individual student against their theoretical grade should be treated as proof that the person asking the question needs to read more blogs about statistics (!).
It is this kind of statistical literacy that is fundamental to understanding information presented in the modern world - and as teachers of mathematics we are more qualified than most to deal with data thoughtfully and spread this measured approach to colleagues.