id: 06055810
dt: j
an: 2012d.00480
au: Montiel, Mariana; Wilhelmi, Miguel R.; Vidakovic, Draga; Elstak, Iwan
ti: Dimensional analogy and different coordinate systems, an onto-semiotic
approach.
so: Mediterr. J. Res. Math. Educ. 10, No. 1-2, 131-168 (2011).
py: 2011
pu: ,
la: EN
cc: I60 C30 E20 D20
ut: multivariable calculus; dimensional analogy; coordinate systems;
onto-semiotic approach; semiotic functions; epistemic network;
multivariate calculus; mathematics and philosophy; epistemology;
knowledge; research; didactic transposition; transfer of knowledge;
abstract reasoning
ci:
li:
ab: Summary: Dimensional analogy as a technique and different coordinate
systems, apart from their intrinsic mathematical interest, are used in
many types of applications in the sciences, engineering and art. As
part of the process of the construction of an epistemic network for the
subject, the identification of objects, and their dualities, that
emerge from this mathematical activity was carried out. The
transformation of expressions to content through semiotic functions,
and the identification of chains of signifiers and meanings, can be
accomplished because of the rich layering and complexity of these
mathematical concepts. Questions related to the geometrical aspects of
multidimensionality and different coordinate systems, as well as to
algebraic methods of transformation were presented to multivariate
calculus students, with a questionnaire and formal protocol. Written
work and group interviews were analyzed. It was found that dimensional
analogy is used by students to create understanding, even when training
in specific techniques has not been formalized.
rv: