Skolans matematik : En kritisk analys av den svenska skolmatematikens förhistoria, uppkomst och utveckling

I argue that common beliefs regarding mathematics originate in the practices of elementary mathematics instruction rather than in science. While learning how to solve mathematical problems in school, we come to believe that mathematics has a set of properties in itself, for instance that it is useful in everyday life, even though this is not necessarily so. I call this object of belief the mathematics of schooling (skolans matematik), while the system of practices by which the belief is produced is called mathematics education (skolmatematik). I introduce a terminology inspired by psychoanalytic theory to describe the peculiar properties of the mathematics of schooling and suggest that it can be understood as a sublime object of an ideology propagated by the system of education. To substantiate this claim I give an overview of the history of Swedish mathematics education, based on curricula, textbooks, discussions in teacher magazines, and other published material – covering in general terms the eighteenth to the twenty-first century. The historical narrative moves between social factors determining the practices of mathematics education, the changing ideas about mathematics expressed in these contexts, and the interplay between external social factors and internal “ideological” meaning. My conclusion is that while elementary arithmetics is, and should be, a part of common knowledge, the mathematics of schooling is something quite different. This object is thoroughly ideological and plays a central part in society mainly by making the social effects of mathematics education – keeping children away from production while sorting them – to appear as something else, namely as most often failed attempts to give children a necessary knowledge of mathematics