Q1:

I ¯m still not clear why the developing child being thrown into conflict/failure by the lack of equilibration guarantees that what it comes up with next is better than what it tried before. It is likely that, based on its other experience, it will know that some alternatives are likely to be more effective than others, but I do not see how this translates into a guarantee of improvement.

A1:

I am not claiming that "the developing child being thrown into conflict/failure by the lack of equilibration guarantees that what it comes up with next is better than what it tried before."  I am claiming that Piagetian theory makes that claim--as far as concerns the development of logical structures.  Thus, I repeat, " I claim that for Piaget it [the double equilibration, equilibration of schemes with one another and the equilibration of schemes with an external world] comes about through some sort of phenocopy mechanism--the mechanism of generation of the new structure is such as to ensure that it copes better with the external world than do the earlier structures from which it derives.  I hold that this is  built into Piaget's theory of equilibration."

In reponse to your phrase "the developing child being thrown into conflict/failure by the lack of equilibration," I will add that the idea that it is the conflict that initates the development is problematic.  The equilibration among schemes must have already begun for the person to feel a conflict--which point is central to the paper I cited.  In this perspective, the initiation of each development is seen in terms of a new coordination among schemes that itself begins prior to any sense of conflict.