Some Remarks on Understanding in Mathematics.

Abstract

ing and epistemological obstacle are found; it is argued that understanding as an act and the act of overcoming an obstacle can be regarded as complementary images of the same mental reality. Further, a categorization of acts of understanding is presented, inspired, on the one hand, by the philosophies of Locke and Dewey, and, on the other, by the UDSG model for learning mathematics [Hoyles, 1986, 1987]. Finally, a method for elaborating epistemological studies of mathematical concepts, inspired by the philosophical hermeneutics of Paul Ricoeur, is suggested. In the second part of the paper this method is tried on the example of the concept of limit of numerical sequence, which the author has studied elsewhere from the point of view of epistemological obstacles [Sierpinska, 1985,, 1987, 2].