This article raises an important and interesting problem, but would benefit from a lot more nuance. It seems to claim there is only one ubiquitous way people te

This article raises an important and interesting problem, but would benefit from a lot more nuance. It seems to claim there is only one ubiquitous way people teach, learn and do mathematics, but that is not the case. In my view, using abstract notions for describing is in no way incompatible to motivating them with concrete, visual notions, and that is what good teachers do and good students seek. This is done imperfectly by many teachers, but there is nothing new in stating that not everyone teaches perfectly. It also really depends on the particular skills and desires of the student. I'm a more abstraction-oriented person, and as such when studying physics I often wished the teachers would rely more on abstract mathematics because in my view it made the phenomena clearer; I have no doubt that many students feel otherwise.