There is a lot we know from a pedagogical perspective about how children learn. As technology improves we will know more from a neurological perspective. We have reached the stage where the knowledge of how learners learn could be a major contributor to building a maths curriculum that is effective for more pupils, from the highest to the lowest achievers.
There may be a parallel here with cycling and our impressive successes at the Olympic Games. A coach has to know more than how a bike works and how it can be ridden in races. He has to know the strengths and weaknesses of the athlete before he finalises the programme of training, the one that extracts the maximum performance. Sadly this basic principle is not applied to the maths curriculum and what it contains.
I lecture to teachers around the UK and I usually ask them: "At what age are enough children giving up on maths in class for you to notice?" The modal answer is "seven years old".
There are reasons for this. Much of what we see in humans can be viewed as a normal distribution, with upper and lower extremes - for example, from Mo Farah's running ability to mine.
Not every child can work as quickly as the quirky culture of maths requires, have enough working memory capacity to succeed at mental arithmetic, or rote learn a set of facts.
Maths is about understanding. Somehow this key concept is denied by those who seek an answer that comes from somewhere way down low on the normal distribution of curriculum design.
Dr Steve Chinn, Bath.