Universidade Federal de Minas Gerais – UFMG

Key words: mathematical teaching – curricular guidelines – tacit knowledge – mathematical knowledge In this paper the authors analyze the current curricular goals in mathematics as proposed for school levels K-7 to K-12 (ages 11 at 16) in different countries. Based on Paul Ernest’s view of mathematical knowledge, the authors consider school-acquired mathematical knowledge as multidimensional, in the sense that it involves components from different domains: cognitive and social, beliefs and values. Furthermore, most of those components are of a mainly tacit nature. The authors present evidence to support that the goals identified in those curricula foster the learning of a mathematical knowledge that is mainly tacit in nature. On the other hand, they argue that the curricular guidelines for the teaching of mathematics lack the supports to handle the processes involved in the learning of any knowledge of that nature. Part of the current literature on the subject emphasizes that such knowledge can be learned although it cannot be taught in the traditional sense of the word teach, that is, by the teachers ’ publicly transmitting or stating their knowledge. The same literature, although not dealing specifically with the teaching of mathematics, suggests, for instance, that the act of teaching a knowledge that is mainly tacit is closely linked to the teacher's public actions in face of authentic questions. That is, when he is engaged in a situation which demands the use of his own tacit knowledge. The authors conclude by discussing some curricular implications for the teaching of mathematics, which result from those issues