Paper short abstract:

Mathematics schooling as an Activity System should be related to three other Activity Systems, namely mathematics as a discipline, mathematics in action, and non-academic mathematical practices, and not exclusively the first, with direct implications for celebration of cultural diversity, and for diversity of forms of mathematical education.

Paper long abstract:

To situate arguments about mathematics education, a framework is proposed in terms of four Activity Systems (more accurately, families of Activity Systems) of mathematics, namely: mathematics-as-a-discipline, mathematics in action, non-academic mathematical practices, and mathematics-as-school subject.

The dominant view is that mathematics-as-school-subject can be unproblematically derived from mathematics-as-a-discipline. Planning mathematics education is a matter of setting out content within a developmental structure, influenced by theories of developmental psychology. This (typically unexamined) assumption has been problematized in a line of analysis beginning with Bernstein's work, and by persistent critiques that school mathematics fails to connect with children's lived experience, including the social and cultural diversity of that experience (the program of ethnomathematics being an important contributor to this critique). A further critique stems from the concept of "mathematics in action" elaborated by Skovsmose and others, which refers to the mathematical formatting of more and more aspects of our lives, often beyond our control or even influence. These considerations lead to the stance that mathematics education should pay more attention to the nature and limitations of mathematical modeling of physical and social phenomena, in order to prepare people for democratic citizenship with a disposition towards critique and agency (reflection and action, in Freire's dialectic).

The argument, then, is that the Activity System of mathematical schooling should be framed in terms of all three other Activity Systems described. Such an enhancement obviously implies celebration of diversity in forms of life and culturally situated mathematical practices, and diversity in the modes of mathematical education.