id: 02361449
dt: a
an: 2005d.01421
au: Nunes, Terezinha
ti: How mathematics teaching develops pupils’ reasoning systems.
so: Bergsten, Christer (ed.) et al., Mathematics and language. Proceedings of
MADIF4, the 4th Swedish mathematics education research seminar, Malmö,
Sweden, January 21‒22, 2004. Linköping: Svensk Förening för
MatematikDidaktisk Forskning (ISBN 91-973934-2-8). Skrifter vrån
Svensk Förening för MatematikDidaktisk Forskning (SMDF) 3, 20-34
(2004).
py: 2004
pu: Linköping: Svensk Förening för MatematikDidaktisk Forskning
la: EN
cc: C30 D20
ut:
ci:
li:
ab: Recent theoretical discussions have pinned constructivism and social
constructivism against each other. In this paper, the author argues
that Piagetian constructivism and Vygotsky’s social constructivism
are coherent and complementary. By reaching a synthesis of these two
theories, one will have a more encompassing approach to analysing how
pupils learn mathematics and how mathematics teaching develops their
minds. The author suggests that the theories are consistent because
they are based on the same metaphor of the mind and that they are
complementary because they explain different aspects of the development
of reasoning. Together they can help to understand the developments in
pupils’ reasoning system that result from changes in the thinker
(Piaget’s contribution) and in the thinker’s activity when using
different thinking tools (Vygotsky’s contribution). In order to
develop these ideas, the author first discusses the concept of thinking
systems. He then works with a simple example in mathematics education,
multiplicative reasoning. He first considers the origin of
multiplicative reasoning - i.e., the development of the thinker, and
then discusses how mathematics teaching can affect pupils’ reasoning
systems in this domain. To conclude the discussion, the author
considers a research agenda for mathematics education based on the
conception of thinking systems.
rv: