There are of course a number of contrary voices. Here is Ivan Illich;
and Lave and Wenger (1991) make similar points about the acquisition of vocational skills. Even a review within the mainstream of educational research recommends that children in the UK should start school later (see here) as indeed they do in most other European countries.A second major illusion on which the school system rests is that most learning is the result of teaching. Teaching, it is true, may contribute to certain kinds of learning under certain circumstances. But most people acquire most of their knowledge outside school, and in school only insofar as school, in a few rich countries, has become their place of confinement during an increasing part of their lives. [Illich I (1973) De-schooling Society London; Penguin p.20]
But the Benezet experiment reported in the article link above was more specific. Children may go to school, but they should not learn arithmetic until 6th grade (12 years old; read the article for Benezet's reasons, noting that his work dates from the early 1930s). That does seem somewhat extreme, and there does not seem to have been any systematic exploration of what the best age is to start mathematics, but nowadays the policy would not doubt draw on the insights of developmental psychology.
The underlying principle is one of readiness, both for the subject and for--in a wider context--participating in the institution of a school itself. Without readiness, enormous effort may be expended to no benefit or even harm.
And that is the conclusion I am coming to about the much-vaunted practice of reflection in professional practice; it's no good plugging it until a practitioner is ready for it, and she will not be ready until she has attained a degree of pretty well unconscious competence or even proficiency in the routine practice of the discipline. The implication for professional education may actually be the desirability of discouraging reflection to begin with. That might even have the paradoxical effect of making people ever more enthusiastic about reaching the stage of being ready to do it...
(Thanks, Ruth, for your earlier comment which goaded me towards these thoughts...)
And for another comment, see also here: http://www.isegoria.net/2010/03/the-case-for-teaching-less-math-in-schools/
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