Här är en text som jag inte fick publicerat i Malmö Högskolas tidskrift EDUCARE, 2013 – där den referade texten av Dahl och Johansson kan hittas. Jag blev påmind om den genom en kommentar på FaceBook där texten legat ”gömd” sedan det begav sig. När jag nu läser tycker jag den är helt OK och förtjänar en plats, åtminstone på min och Dittes nya fina blogg.
Let me start by noting three characteristic features of the state of the discussion concerning mathematics and citizenship. Firstly, there is no doubt that all contributors care for the well-being of pupils and want make the world a better place. Part of the discussion looks almost like a competition for finding the most striking and convincing way of talking about what good mathematics education should bring about. With reference to ethnomathematics Dahl and Johansson mention “peace, equity and human dignity”; with reference to mathematical literacy, they talk about “a good foundation for personal development and active participation in the life of society”. As they try to transcend the tension between these two perspectives, they turn to the concept of a “socially responsible mathematics education”, as being “for the Other”, as bringing about “a more equal social order”, “a more sustainable world”.
Secondly, however, and problematically, it is not clear to what extent mathematics does, or even can contribute to these desirable ends. Dahl and Johansson tell us that mathematics education is a Western phenomenon, potentially excluding other cultures. We learn about power and that ”the real function” of mathematics education perhaps is one of “sorting students”. They quote my work here, together with a quite significant choir of other critical voices, such as those of Paul Dowling, Ole Skovsmose, Alexandre Pais and Louis Radford. In “Hating School, Loving Mathematics” (Lundin, 20112) I introduced the concept of the “standard critique” to talk about how mathematics education is often on the one hand conceived of as potentially leading to something very good for the individual and for society but on the other hand that its present state is pictured as doing quite the opposite, as being useless and boring and contributing to the reproduction of an unfair society.
Thirdly, the discussion tends to circle around texts and their claims, and make claims about these other texts and claims, rather than saying something about how it actually is. This is a tricky question, so let me make the phenomenon concrete with some examples. For instance, it is surely important for the questions discussed by Dahl and Johansson what kind of mathematical knowledge citizens actually need or want in their everyday life. But what we learn about is instead what is “expressed in the curriculum”, what is “considered necessary”, what the citizen is “supposed to need” (my emphases, here and below). Dahl and Johansson do not talk about “the role mathematics plays in producing certain kinds of citizens”, but the role it plays, “according to the curriculum”. We read that the definitions of mathematical literacy are based on “the assumption that mathematical knowledge has a functional value”. But we get no answer to the question if it in fact has a functional value. Dahl and Johansson point out that what they talk about is the mathematics that is “seen as crucial” and that their argument only makes sense “presupposing that school mathematics is useful in the world outside school”, but we get no answer to the question if it actually is useful, and so on. Dahl and Johansson is far from alone in putting themselves at distance from reality in this way. They produced an exceptionally clear example, but this approach is fairly common in mathematics education research.
What these three features of the discussion allow for is a seemingly never ending and quite ineffectual practice of compilation, discussion and making of claims concerning mathematics education, without ever running into what the great philosopher of science Karl Popper (1902-1994) would call falsification. It is a never ending debate, with little contact with what Popper would perhaps simply have called “reality”, and it is tempting to call this mode of discussion scholastic. Standing as governors of the modern church of school and science, we debate the proper way of conceiving of its sacraments.
I think that this connection to theology is potentially useful. Among other things it points to the presence of a number of presuppositions, common to everybody who takes part in the discussion. In the fifteenth century, everybody agreed that there was a God – and given that, they could quarrel about his properties and relationship to nature and humanity. The concept of atheism was not unthinkable, but it was unthinkable that a sane person would be an atheist, and even more important: it was unthinkable that a good, virtuous person would be an atheist. For better or worse, these presuppositions lost their grasp of the western world, and we entered, in the nineteenth century, our era of secular modernity.
It is my firmly held conviction, based on my work on the history of mathematics education and corroborated by the study of authors such as Ivan Illich, Stephen Gaukroger, Amos Funkenstein, Michael Allen Gillespie and Talal Asad, that the concepts of science, education and knowledge – and of course mathematics – belong to a set of ideas or concepts that have a similar place today, as those of God, providence and the immortality of the soul, had before the establishment of secularity. They are so fundamental to our world view that they cannot be put into question, without this reflecting back unfavorably on both the sanity and morality of the dissenter. As the French philosopher of science Bruno Latour succinctly put it in §4.1.8 of his Irreductions: “Belief in the existence of ’science’ has its reformers, but it does not have its skeptics”.
Mathematics education is far from an unequivocally malignant institution. Following the psychoanalytically inspired philosopher Robert Pfaller I see it as part of a compromise formation that took shape as a response to the dramatic transformation of western societies in the nineteenth century. It is thegood and bad result of the struggle between ideas of a rational meritocratic social order, and forces working for the preservation of traditional hierarchies. As part of the education system, mathematics education is relatively fair. It opens up for social mobility. On the other hand it functions as a powerful mechanism of exclusion. Mathematics education is thus a functional part of our not that bad society. As should be clear from the news, one can do far worse.
Importantly however, this god and bad function of mathematics education has nothing to do with any inevitable need, demand or use of “mathematical knowledge”. The language of education and science, of learning and knowing must, I think, be seen as the discursive counterpart to an institution of schooling that functions as ritual in modern society. Juggling with such words will never lead to anything. It is an ineffectual play for priests. If we want to change mathematics education, and thus society – something which is of course somewhat risky, since society could certainly be a lot worse than it presently is – we need to find another way of talking about it. Then, importantly, we need to make words matter, that is, not only compile and compare claims, but decide on what we hold to be true, and then take this truth as a point of departure for action.