Weaker Pupils or The Wrong Maths?
I have noticed a lot of people talking about ‘weaker pupils’ on Twitter. There are suggestions, for example, that certain representations of equations cannot be accessed by 'weaker pupils' or that concrete or pictorial modalities for exploring a mathematical idea are only suitable for ‘weaker pupils’.
My problem with this is that I don’t believe there is such a thing as a ‘weaker pupil’. There are just kids learning maths and, except for those children with the most severe learning difficulties, all pupils can learn the whole of school level maths.
So, where does this perception come from? In my experience (and this is certainly the case in lots of Twitter discussions too), when teachers talk about ‘weaker pupils’ what they are really referring to is a pupil who cannot grip the mathematical idea that they are trying to present to them. The thing is, this is not a sign of a ‘weaker pupil’, this is a sign that the teacher is presenting mathematical ideas that the pupil is not yet ready to grip.
Imagine the whole of human knowledge. Imagine it filling a space. At any given moment in time, every single one of us knows all that we know. There is no other possible scenario, it is always the case.
Let’s imagine the domain of one’s own knowledge as a circle in the whole of human knowledge.
As one grows older and learns more, the circle widens, with new knowledge and truth being integrated into one’s current schema.
For new knowledge to be assimilated, it must make sense from the perspective of what one already knows. That is to say, the new knowledge can only be just beyond the limits of the circle.
We only learn things that are just beyond our current understanding – this is necessarily the case, since knowledge well beyond one’s current view of the universe, one’s logic framework and one’s own living history and truth, is rejected as incomprehensible or just plain wrong.
When I hear teachers talking about ‘weaker pupils’, they are usually referring to a situation where a pupil is being presented with a mathematical idea way beyond what they are able to assimilate.
I have observed hundreds of lessons where pupils are being asked to, for example, understand how a formula works, and within just a few moments of discussion it is revealed that those same pupils haven’t even got to grips yet with, say, basic arithmetic or have a very loose grip of number sense. This happens all the time. Schools that have schemes of work based on a pupil’s age, rather than where that pupil is actually at mathematically, continually serve up the wrong maths.
The new idea is well beyond the limits of their current knowledge, leaving the pupil incapable of making sense of it.
So, of course the pupil can’t get to grips with the idea. These pupils are then labelled as weak.
As John B Carroll showed many times, all pupils can learn well if they are given the right amount of time and are starting from where they are already secure.
I would urge teachers to pause a moment before labelling a pupil ‘weak’ to consider the possibility that they are trying to teach a pupil the wrong maths.