I don't really know much about the history of education, I only read the article I linked. From what I understand from that, it is not so much that constructivism has been debunked, but rather that in order to explain something properly, you need to understand it yourself deeply. Now, many teachers don't actually understand math on that level. So it will be difficult for them to teach it based on constructivism. That seems to me to be the main difficulty. Also, everybody understands things differently, so even if the teacher is capable, how do you scale that for an entire classroom?
> in order to explain something properly, you need to understand it yourself deeply. Now, many teachers don't actually understand math on that level. So it will be difficult for them to teach it based on constructivism.
Yes, this is a sad truth about teachers, many of them actually do not understand deeply the stuff they teach.
It seemed to me unlikely that e.g. a 10 years old kid could ask teacher a math question (related to what they are learning) that the math teacher couldn't answer. Like, any adult, especially one with a university education, should be able to answer any question from the first four grades of elementary school, right? Except... nope. I have friends that try to promote constructivist education at schools, and "what if the kids ask me something I will not be able to answer" is indeed a frequent objection made by actual teachers.
Like, okay, it is definitely possible to make an innocently sounding math question that is actually extremely hard to solve. My favorite example is: "can you cut a square into an odd number of triangles of equal area, but not necessarily the same shape?" (The answer is no, but the proof requires university-level math.) But in real life, this is extremely unlikely to happen; and if it happened to me, I would simply say "sorry, I do not know".
> everybody understands things differently
This is perfectly okay. You let the kids think about it individually first, then discuss their solutions with each other. If you get multiple explanations how things work, that's great -- having things described from multiple perspectives helps you understand it even better.
