One of the most important and deepest disagreements between research mathematicians and mathematics educators concerns research in mathematics education. I know research mathematicians on the extremist fringe on this
issue who believe that “research in mathematics education” is an oxymoron. To them “research” is a word justified
only when applied to theorem-proof mathematical research or to the scientific-method paradigm of the physical sciences. Thus, essentially nothing written about education or about any of the social sciences would qualify as research.
This perspective is at least consistent, if not very helpful. Work in education or the social sciences will almost never
lead to ironclad, provable results.