Concerning the structure of the learner's mind, psychologist Piaget claimed that

There exists, as a function of the development of intelligence as a whole, a spontaneous and gradual construction of elementary logico-mathematical structures and that these 'natural' ('natural' the way that one speaks of the 'natural' numbers) structures are much closer to those being used in 'modern' mathematics than to those being used in traditional mathematics. (p. 79 in Piaget 1973).

Piaget appears to postulate an affinity between, on the one hand, the structures of the mind and, on the other, the structures of modern mathematics (mainly following Bourbaki). The essay in question is

Piaget, J. "Comments on Mathematical Education," in A. G. Howson, ed., Developments in Mathematical Education: Proceedings of the Second International Conference on Mathematical Education, 79--87, Cambridge: Cambridge University Press, 1973.

Piaget's postulated affinity has apparently been challenged by some scholars in the context of the New Math controversy. Is there a source that provides a detailed analysis of such a postulation?

(Note that I am not looking for general sources on the New Math/Modern Math controversy, but rather for an analysis of this particular identification).