The addressed question from the interface between theory and teaching practice of constructivism is discussed at the background of whereabouts of the Common Core (CCSS-M) constructivist-based mathematics curriculum. It concerns the formulation of constructivist methodology of teaching, whose existence is called in doubts by US constructivist researchers who formed the basics of the approach of the constructivist philosophy into education. The presentation argues that the research tool, constructivist teaching experiment does define the constructivist teaching methodology and through mathematics teaching-research, it can be introduced into mathematics classroom at large. The conference presentation will address socially based reasons for the professed absence of constructivist teaching methodology, and it will address critically the method of 'scripted lessons' as the substitution for teaching methodology--the two theme absent from the proposal below due to lack of space.