Coming back to this thread after a morning of teaching children to do - among other things - maths.
I find the polarisation of this debate difficult.
1a. Kumon teaches children to know basic number facts fast. This is not a bad thing BUT it is a tiny subset of maths as a subject. Children who have, or develop alongside this recall through other teaching, a good concept of number will find such number facts useful and may be able to apply them in other contexts. This is a good thing but it requires additional teaching to the 'core' Kumon curriculum.
1b. There are other, cheaper and more enjoyable ways of learning basic number facts fast, but there is nothing intrinsically wrong with using Kumon to do it, as long as the child has other opportunities to develop a proper understanding of number, preferably in advance.
2a. Kumon is one example of an out of school activity which parents enter their children for, which has some academic content and thus may improve a child's in school performance in one small area of their academic life.
2b. There are many other examples of out of school activities which have some academic content and which parents organise for or do with their children, and which may improve a child's in-school performance This be something formal like another form of tutoring, or a different type of organised activity such as drama or music. There are also innumerable 'informal' activities - baking together, reading together, playing board games or card games, doing practical maths together, having a kitchen table covered with science experiments - which may equally boost a child's in-school performance.
3a. Kumon, with its very focused and structured approach, may help a child to acquire the ability to concentrate for short periods, and they may gain self-esteem from the measured progress such a system has built in.
3b. There are many other ways in which a child can acquire or practise the ability to concentrate and focus (reading with an adult, attending a dance or drama lesson, storytime at the local library, playing board games with the family, building a Lego model, drwing or painting or jigsaws etc etc). Equally there are many other ways in which a child's self-esteem may be reinforced - my DD's self-confidence, for example, comes primarily through dance.
I know no mathematicians (of whom, as it happens, I know an unusual number) who have ever attended anything like Kumon, and equally the academic and professional scientists and engineers I know spent more of their childhoods taking things apart, growing moulds on the kitchen table and making things go 'bang' than learning number facts by rote... However, as long as a child ALREADY has a strong concept of number through practical activities, receives a rounded maths education elsewhere and understands that arithmetic is not the whole of maths and that not all maths has a single right answer, then Kumon is unlikely to do any harm. Whether the benefit matches the cost - and the 'opportunity cost' of the time which could be spent receiving a more rounded and personalised type of education - and whether the same benefits could be delivered in a different form which might be better for the child, is a balance for each family to make..