id: 05345906
dt: a
an: 2008e.00123
au: Otte, Michael
ti: Meaning and mathematics.
so: Kilpatrick, Jeremy et al., Meaning in mathematics education. Springer, New
York, NY (ISBN 0-387-24039-X). 231-260 (2005).
py: 2005
pu: New York, NY: Springer
la: EN
cc: D20 C30
ut: meaning; theory of mathematics education; Pierce’ theory of learning
ci:
li:
ab: From the book’s introduction: This philosophical discussion of
mathematical meaning considers the relevance of Pierce’s theory of
meaning and takes up the discussion of knowledge in terms of “modes
of knowing”. Thus the active part of coming to know becomes
essential. The author disputes the dualism, so carefully elaborated by
Descartes, which has been the basis of many interpretations of meaning:
that is, a mental entity, a conception belonging to an internal world,
has a meaning if it refers to something from the external world. A
conception of knowing becomes more complex when knowledge and meaning
cannot be thought of in terms of representations and references, but in
terms of activity. A dialectic between the subject (the knower) and the
object (what one could know about) is the basis for a “double”
constructivism where both subject and object will be constructed and
reconstructed in a process of coming to know. The author discusses the
relationship between the particular and the general, using as an
example the relationship between a particular and a general triangle.
He claims that mathematical objects do not exist independently of the
totality of their possible representations, but at the same time they
are not to be confused with any particular representation. Furthermore,
he emphasises that a mathematical problem is an objective structure
that nevertheless has no meaning apart from its possible
representations. In this way, he elaborates on the dynamic relationship
between the knowing subject and what knowledge can be about, arguing
that one pole in this relationship cannot be described independently of
the other. The author brings all these considerations together through
an analysis of Pierce’s theory of meaning.
rv: