id: 05847579
dt: j
an: 2011a.00779
au: Rodríguez, Omar Hernández; Fernández, Jorge M. López
ti: A semiotic reflection on the didactics of the chain rule.
so: Mont. Math. Enthus. 7, No. 2-3, 321-332 (2010).
py: 2010
pu: Information Age Publishing (IAP), Charlotte, NC; Department of Mathematical
Sciences, The University of Montana, Missoula, MT
la: EN
cc: I44 I45 A30 C74 C75
ut: chain rule; composition of functions; differentiation; historical
heuristics; history of analysis; history of mathematics; Sausserian
semiotics
ci:
li:
ab: Summary: According to (Fried, 2008), there is an intrinsic tension in
trying to apply the history of mathematics to its didactics. Besides
the widespread feeling that the introduction of didactic elements taken
from the history of mathematics can detract the pedagogy of mathematics
from the attainment of important goals, (Fried, 2008, p.193) describes
a pair of specific pitfalls that can arise in implementing such
historical applications in mathematics education. The description in
(Fried, 2008), is presented in the parlance of Sausserian Semiotics and
identifies two semiotic “deformations" that arise when one fails to
observe that the pairing between signs and meanings in a given
synchronic “cross-section" associated with the development of
mathematics need not hold for another synchronic cross section at a
different time. In this exposition, an example related to an
application of the history of the chain rule to the didactics of
calculus is presented. Our example illustrates the semiotic
deformations alluded by (Fried, 2008), and points out a possible
explanation of how this may lead to unrealistic pedagogical
expectations for student performance. Finally, an argument is presented
for the creation of a framework for a historical heuristics for
mathematics education, possibly beyond the bounds of semiotics.
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