id: 02361448
dt: a
an: 2005d.01420
au: Dörfler, Willi
ti: Mathematical reasoning and observing transformations of diagrams.
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, 7-19
(2004).
py: 2004
pu: Linköping: Svensk Förening för MatematikDidaktisk Forskning
la: EN
cc: C30 E40 D50
ut:
ci:
li:
ab: The crucial role of diagrams in mathematical reasoning is the focus of the
plenary presentation. Recognising that diagrams of many different kinds
are ubiquitous in mathematics, and that reasoning often deal directly
with the transformations of diagrams, building on their structural
properties and often rule-governed transformations,rather than with
abstract ideas involved in mathematical concepts, the character and
relevance for mathematics education of Peirce’s notion of
diagrammatic reasoning is outlined. This points to the importance of
perspective aspects of mathematical thinking. Diagrammatic reasoning is
used to solve tasks, to be distinguished from a representational use of
diagrams. By offering examples from elementary arithmetic, and from
linear and abstract algebra, the author highlights the power and
usefulness of different kinds of diagrammatic reasoning.
rv: