Hopefully this does not get downvoted as insufficiently specific. And it's not general NEw Math controversy but more on Piaget. I suggest reading a few articles in general about issues with his assertions.
Here is a simple overview, but several more are available by Googling Piaget and criticism. Some of the comments may indirectly or directly relate to your questions on development of the mind.
See here:
https://www.psychologicalscience.org/observer/jean-piaget#.WVAHDGfrvIU
In particular:
"The second criticism of Piaget concerns the nature of the stages themselves. Stage theories of development have fallen out of favor in developmental research. Although stages are seen as useful heuristics for describing the trajectory of human behavior, several problems have pushed stage theories aside. One problem is that stages often fail to capture the complexities of intraindividual and interindividual variation in development. Furthermore, in the case of Piaget’s theory, intelligence is now viewed more as a modular system than as a unified system of general intelligence. In Piaget’s system, once an individual has mastered an overall intellectual operation, it should apply across all domains of the mind, as a “structured whole” (or “structure d’ensemble,” to use Piaget’s phrase). Contemporary developmental approaches to intelligence consider modules of the mind to be largely independent, and do not assume a structured whole."
I would suggest that consideration will show that it is common that learners or even yourself does not immediately apply an intellectual structure (say in EE) to a problem in a domain that seems different (say econ). Of course we do have the ability to do this at times. But it is an aspect of general intelligence and not infallible. This is one reason why word problems are trickier than non-word problems.