Imagine a class where every student was on the same level, and followed the subjects in lock-step. Maybe they first understand polynomial single-variable differentiation, then they get exponentials, logarithms, chain rule, etc. If any student has a question, all other students also have that question. When the teacher answers, all students learn at the same time.

This is ability homogeneity, and it works wonders. It's the same reason why before a corporate meeting you make sure everyone's read the agenda, everyone is "on the same page".

Even with perfect homogeneity, sometimes students have different questions maybe due to scheduling or just variances in performance across the day. That's when the teacher needs to offer enough bandwidth to address all of their questions.

It SEEMS like class size is having an effect because there aren't that many students which share the same (narrow) ability band. Now if you're located in a dense urban centre, you could potentially have many students of very close abilities in one class.

Edit to add: I suppose cultural influences could be important. If the child is unused to being one in a crowd, it could hamper his psychological well-being and thus learning-rate. But that's a secondary impact, not a direct impact of class sizes on teaching quality.


Re: home environment. Agreed, this is absolutely a huge factor, on the same order of magnitude as natural intelligence.


Re: mathematical aptitude testing. This is a chicken and egg problem. If they're testing children on learned material then it's not an aptitude test. But if they give tests like Raven's Advanced Matrices (series of pictures for pattern-recognition) then some parents whose offspring have done rote memorization but lack raw pattern recognition power will protest. It's a hard call for the teachers to make: you can't please everyone. I guess the best solution for a parent whose offspring are untrained but talented would be to have the child take extra time to study for the aptitude test. But this is a vicious cycle and parents will just race one another to give their children the best training. I've seen some children grow up neurotic from all the stress put upon them by their parents (one of my friends is a classic example of this).

I hope a personal anecdote can ease some of your concerns about your children getting into the "right bracket". Many people I've worked with or studied with were very fortunate to be naturally intelligent, and not all of them were always in the "right environment". I'll give two examples (one is myself), but there are many more:

(1) My parents, while not poor, were NOT at all prepared for parenting. They did nothing to push me or prepare me, and even forgot to sign me up for primary school and the government had to remind them that it was illegal not to send your child to primary school. The consequence was that I lazed around all day as a young child, and did not get selected into the top-tier group for "gifted children" at 10 years old, and was in the second-tier group instead. None of that mattered at all once I got my hands on actual schooling material, and now I have one of those ridiculously rarefied academic records. (Deleted: initially I included details, but it did seem gauche to toot my own horn and it doesn't add to the story)

(2) Another one of my friends did Maths at Cambridge (my vote for one of the hardest undergrad courses in the English-speaking world to complete), but he grew up as a kid in a poor northern city with unemployed parents on benefits. His middle school was so bad that he was the only single student in his year to make it into Oxford/Cambridge.

Main point: children are more resilient than their parents give them credit for. If they have a combination of intelligence, ambition, and impulse-control (discipline), they will make it, as long as you don't actively screw them up. Being in a low bracket school for a while is pretty unlikely to harm their long-term prospects.


In contrast to many other liberals, I'm going out on a limb to say: the comfortable story about "everyone can be _good_ at maths if they try" is just a lie. Not everyone is equally good at maths, in fact the natural aptitude for this subject is very unequally distributed in the population. There's a greater gulf between John von Neumann and your average maths major, than the gulf between the average maths major and the average chap on the street.

There is such a thing as natural (especially mathematical) intelligence, and lying about it simply holds us back and makes us worse at teaching. Students who lack natural aptitude should be focusing on preparing for and nailing easy rote questions. They should also not take highly mathematical disciplines in university (or not go to university at all, if they lack other non-mathematical aptitudes as well).

However, I will admit that pre-University maths is so easy that the vast majority of the population, with hard work, should be able to pass the tests. Many of them won't truly "understand" it, but they can memorize the formulae and use them in the exam to pass.



Edited 2 time(s). Last edit at 05/04/2017 02:56AM by starbright.