Throughout my teaching career narrowing gaps has featured prominently in the education discourse both within and beyond the schools I have worked in. Sometimes I am mystified as to why.
It stands to reason that if you divide a student population in any way it is highly probable that one group will have better results than the other. A few years ago I did a detailed analysis of the data of the school I was working at. The school decided to narrow the gap between boys and girls performance despite there being several more significant “gaps”. At that time there had been a more significant gap between left and right handed students for the last 3 years. Yet we weren’t intervening. There was an enormous gap between the performance of Vietnamese girls and every other group but we weren’t concerned with narrowing that gap (or indeed most of those gaps). I couldn’t get an adequate explanation as to why that might be. It appeared that some gaps were acceptable and some not. This was interesting to me so I gathered a whole bunch of data from the pupils by doing a huge survey. I discovered significant gaps all over the place. Surprisingly students that had an xbox 360 significantly outperformed those that had a playstation 3 and those that had no playstation. Also those with less than 2 siblings consistently significantly outperformed those with 2 or more. We did nothing to narrow either of those gaps.
Recently I read a piece suggesting that setting classes widens the gap between the most able (highest previously achieving?) and the least able (lowest previously achieving?). I was curious about this because I’ve taught maths in set and mixed ability classes. In my experience how pupils are grouped makes little difference in this regard. The gap widens regardless of how pupils are grouped, how the teacher teaches and almost any other factor to do with school and teaching that I can think of with a few exceptions.
This is because generally pupils that are good at Maths learn Maths more quickly than pupils that are not. Again there are exceptions but generally someone who understands or knows a lot of Maths will pick up new mathematical ideas more quickly than someone who doesn’t will pick up the same ideas.
The obvious exception is bad teaching. There is nothing like bad teaching for narrowing the gap. The quickest way to narrow the gap would be to either not teach able kids anything or teach them wrong. Obviously if the behaviour in lessons is so poor that listening and concentration are extremely difficulty then the gap will probably narrow as basic concrete maths often require less listening and concentration than complex abstractions.
Thus all other things being equal we can reasonably expect the better mathematician to learn maths more quickly and thus the gap to widen. We as a profession have long argued against the notion that pupils make linear progress or learn at the same rate. In my experience the differences in the rates at which pupils learn largely boil down to ability, motivation and behaviour.
It seems to me that this entire argument against setting hinges on the outcomes for “exceptions”. There are many reasons why pupils end up “lower previously achieving” which are not about their ability. EAL, poor behaviour, lack of motivation, problems at home, mental health, SEND and more can all result in pupils getting results that are not an accurate reflection of their ability. It is quite possible for schools to consider these factors when deciding which set a pupil should be in. It all depends on how pupils are set, how movement between sets is done and a variety of other things (It’s also worth noting that the longer an able students pisses about not learning for the less able they become in relation to their peer group. Mathematical ability is not set in stone.)
Thus the entire proposition that setting is a bad thing because it widens the gap between the most and least able is really an argument against setting done badly or an argument against the notion we can reasonably expect pupils that are good at Maths to learn Maths more quickly than those that aren’t.
I would argue that setting done badly is harmful to pupils that struggle with maths. That’s a separate argument to the one about widening gaps though. I would also argue that the only way to get pupils that struggle with maths learning maths more quickly than or even at the same rate as our best young mathematicians would require doing our brightest young mathematicians a massive disservice.