Numbers don’t actually exist. There is no actual number three somewhere. It is not a thing. There is just ‘threeness’, a relationship between things that we learn to recognise; that this small cluster of cubes is similar to that small cluster of counters in a way we learn to call ‘three’. The cubes themselves are not three; we declare their threeness when they are associated together in a certain way. We learn what three means through repeated exposure to clusters exemplifying this relationship and thus come to learn what three and not-three look like. But there is no spatiotemporally locatable prototype ‘three’ against which all other instances of three can be verified.
Pupil progress is a bit like that. We tend to act as if ‘Progress’ is a real, tangible thing that really exists. Worse than that, we even believe that we can measure it. This is an illusion.
View original post 3,723 more words