02366164

a

Oliveira, P. The mathematics class as a strong epistemological space. (A aula de matem\'atica como espa\c c{}o epistemol\'ogico forte.) Ponte, J.P. et al., Actividades de investiga\c c{}\~a{}o na aprendizagem da matem\'atica e na forma\c c{}\~a{}o dos professores. Sociedade Portuguesa de Ci\^e{}ncias da Educa\c c{}\~a{}o, Porto (ISBN 972-8614-03-9). 25-40 (2002). 2002 Sociedade Portuguesa de Ci\^e{}ncias da Educa\c c{}\~a{}o, Porto PT This theoretical paper argues for the possibility that students may generate relevant mathematical knowledge when they carry out investigation activities. The author posits several kinds of inferential thinking in mathematics, induction, deduction, abduction, and transformative thinking and suggests that the mathematics class may be seen as a "strong epistemological space", that is a personal, relational, and communicational space where knowledge is produced. The author indicates seven conditions to problematize the mathematics classroom as a strong epistemological space: (i) identify epistemic valences (positive e negative), associated to conditions that favour or inhibit the a production of knowledge; (ii) appreciate new knowledge and its esthetical dimension; (iii) establish criteria of validation of knowledge ; (iv) identify epistemological obstacles; (v) identify the value and the limits of such knowledge; (vi) establish the relationship between who knows and what knows; (vii) characterize the new mathematics knowledge (episteme). The author concludes stressing the role of the teacher in integrating knowledge and the generation of knowledge, that is the productive and reproductive dimensions of knowledge.