id: 06191756
dt: j
an: 2013d.00333
au: Otte, Michael Friedrich; Campos, Tânia M. M.; Abido, Alexandre S.
ti: Plato, Pascal, and the dynamics of personal knowledge.
so: Educ. Stud. Math. 82, No. 3, 397-415 (2013).
py: 2013
pu: Springer Netherlands, Dordrecht
la: EN
cc: E20 D20
ut: philosophy in mathematics education; complementarity; Plato; Pascal; Peirce
ci:
li: doi:10.1007/s10649-012-9435-5
ab: Summary: Abstract educational practices are to be based on proven
scientific knowledge, not least because the function science has to
perform in human culture consists of unifying practical skills and
general beliefs, the episteme and the techne [{\it S. Amsterdamski},
Between experience and metaphysics: philosophical problems of the
evolution of science. Dordrecht: Reidel (1975), pp. 43‒44]. Now,
modern societies first of all presuppose regular and standardized ways
of organizing both our concepts and our institutions. The explanatory
schemata resulting from this standardization tend to destroy
individualism and enchantment. But mathematics education is in fact the
only place in which to treat the human subject’s relationship with
mathematics. And that is what mathematics education is all about: make
the human subject grow intellectually and as a person by means of
mathematics. At first sight, mathematics, in its formal guise, seems
the opposite of philosophy, because philosophy constructs concepts
(meanings), whereas mathematics deals with extensions of concepts
(sets). We shall, however, turn this problem into an instrument, using
the complementarity of intensions and extensions of theoretical terms
as our main device for discussing the relationship between philosophy
and mathematics education. The complementarity of the “how” and the
“what” of our representations outlines, in fact, the terrain on
which epistemology and education are to meet.
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