id: 02368674
dt: j
an: 2006c.01716
au: Otte, Michael
ti: Mathematical epistemology from a Peircean semiotic point of view.
so: Educ. Stud. Math. 61, No. 1-2, 11-38 (2006).
py: 2006
pu: Springer Netherlands, Dordrecht
la: EN
cc: E20 E40 D20
ut: complementarity of mathematical terms; genetic epistemology; semiotics
(Peirce); phenomenology (Peirce); meaning; sign; mathematics and
philosophy; theory of mathematics education
ci:
li: doi:10.1007/s10649-006-0082-6
ab: Learning is better than knowing, generalization is more illuminating than
abstract generality or universality because we perceive and thus become
conscious of change or development only. Signs and representations
establish the dialectic of fixation on the one hand and transformation
on the other, which is so essential to learning and cognition.
Mathematical epistemology from a semiotic point of view therefore is
above all a genetical epistemology. All real mathematical activity is
concerned with representations of mathematical entities rather than
with things in themselves and with the processes of continuous
transformation of a given representation into others. This paper tries
to give an overview of the essential relationships between activity
theory, epistemology and mathematical education, using the semiotics of
Charles S. Peirce as a unifying reference. It is certainly beyond the
scope of such a paper to spell out all the questions involved in every
detail. Much of what is said in the four short sections to follow is
calling for further concretization and research. (orig.)
rv: