Chapter 1: Mathematics: A Critical Rationality?

“Mathematics” is an open concept with many possible meanings. In Philosophical Investigations, Ludwig Wittgenstein (1953/1958) talks about the variety of language games, and “mathematics” may operate in a huge number of such games. While mathematics as a research field includes a vast domain of unsolved issues and conceptions in development, mathematics as a school subject refers to a rather well-defined body of knowledge parcelled out in bits and pieces to be taught and learned according to preformed criteria. Mathematics could, however, also refer to domains of knowledge and understanding that are not institutionalized through research priorities or curricular structures. Thus, we can locate mathematics in many work practices.¹ It is part of technology and design. It is part of procedures for decision making. It is present in tables, diagrams, graphs, and we can experience a lot of mathematics just leafing through the daily newspaper.