The main page on redesign of mathematics education (RoME) is the book website: Elegance with Substance (EWS).
The distinction between convention and redesign is:
The subject of RoME can be divided w.r.t. primary, secondary, tertiary education, training of teachers, and whole curriculum. Perhaps these might develop into subcommunities.
For example, the pronunciation of numbers is mainly relevant for primary education, and the development of calculus would be for secondary education, and matricola (freshmen) for non-math majors.
However, there is substantial overlap for conceptual development. For example:
There is a tendency for higher up results to percolate down into primary education, in both choice of language en discussion of fundamental principles. See A child wants nice and no mean numbers (CWNN) for this effect.
Thus at this stage it might be premature to specialise.
There is a distinction between content of ME and the organisation of education (research), with definition of the programme, design of exams, training of teachers, creation of textbooks, and so on. Much of the discussion on content is fairly useless when there is no common ground for such a discussion. Each author might suggest a view, but such a view remains a personal view only when there is no discussion space where others can join in with also some decision. Thus, each nation has the need of an institute called "Mathematics Education Name of the Country" (MENC). For Holland, a suggestion is a "Simon Stevin Institute" (SSI), reflecting not quite abstract mathematics but practical engineering. To create such institutes, there might be an important role for economists who look at the "mathematics industry" from the angle of institutions and governance. The role of research mathematics (RM) would be limited, since RM is directed at the development of new (abstract) mathematics, while mathematics education research (MER) is an empirical science.
Contributions to MER have the limited scope that they are yet only suggestions to consider, and that there are the restrictions of both empirical testing and the creation of such MENC for an effective discussion environment. This for example concerns these books:
(1) Mathematics education has evolved over 5000 years and contains many crooked features that are didactically questionable. Math Ed better be re-designed or re-engineered, starting from sound principles of didactics and from what empirically works for students. (2) Contributions to this community concern texts for the empirical science of didactics of mathematics, and they don't concern texts "by mathematicians for mathematicians". (3) A key text is: "Elegance with Substance" (2009, 2015), https://zenodo.org/record/291974. (4) In texts, the preferred abbreviation of "redesign of mathematics education" is RoME.Read more
This community starts by uploading my own texts on this subject. Check out the general research idea in Elegance with Substance. You do not have to agree on particular proposals, since any particular proposal must be discussed by teachers and researchers and be submitted to randomised controlled tests. It are the students who tell us, and show in tests, what works for them. The current objective is to start identifying useful hypotheses for such testing. Contributions to this community are first evaluated by me and perhaps eventually there might be some editorial board.