Dunning-Kruger Effect is that people who don’t know think they do and are confident. This operates in K-12 because almost no one in K-12 knows the Peano Axioms.
DK also operates in math ed in almost the same way. The Lance Rips et al papers on Peano Axioms have no impact on the math ed profession. A total bounce.
The math ed establishment is full of DK fads. These are barely tested according to some critics. Moreover, the results are inconsistent. They are also overwhelmed by the collapse of school systems under the assault of diversity in more and more cities.
Elementary math also needs to be fully exposited in the Peano Axiom framework. This is in the process of being done in the series of books associated with this website.
Keith Devlin’s pontifications against the Peano Axioms and teaching recursion are not helpful, but are not the real cause of the failure of PA and recursion to take hold either in K-12 directly or in math ed instruction in college. Although Devlin’s failure to recognize the work of Lance Rips et al is puzzling. It teaches exactly the opposite of what he says.
So we have a K-12 and college math ed establishment that is dead set against the Peano Axioms or using recursion or a logical exposition of elementary math.
DK explains this. They think they understand elementary math but don’t. The difficulty of working through the Dedekind book and David Joyce’s notes on it illustrate that it is a lot of work to understand the basics.
Understanding that natural numbers are about order and that addition and multiplication are methods for keeping one’s place in the count and counting is haphazard. Sometimes people recognize this, but at other times they float away from it. They can also state it and then reject it. That isn’t the best framework to teach from. The Peano Axiom framework is clear, the natural numbers are about a linear ordered chain and all its methods are about keeping track of one’s spot on such a chain.
The set theory idea of comparing sets as what counting means supports this concept of natural number operations as well. However, that was ridiculed by people like Richard Feynman who likely did not read the Dedekind book.