id: 06307573
dt: j
an: 2014d.00717
au: Ángeles Navarro, María; Pérez Carreras, Pedro
ti: An empirical study in convergence via iteration and its visualization.
so: Teach. Math. 15, No. 2, 85-112 (2012).
py: 2012
pu: ,
la: EN
cc: I34 C34 U74
ut: convergence of a sequence; visualization; geometric progression; use of
technology; dynamic representations; iteration
ci:
li:
ab: Summary: Our aim is to provide an educative experience for high school
students leading to a precise verbal description of the notion of
convergence of a sequence of numbers generated by an iterative process
triggered by the visualization of an unending geometric progression.
Iteration as a guiding idea is chosen because it is easy to grasp,
opens the door to further mathematical topics of the curriculum and
encourages the use of technology. The experience is structured as an
interview where a computer-generated tool, providing data generated by
iteration and their visual dynamic representations, is available as an
unavoidable aid to our goal of getting insight before formality. It all
ends up to a very simple observation: the step-by-step implementation
of a manual/visual routine together with reporting verbally what you
see and what you don’t see at every step is the clue to the
understanding of the Weierstrassian definition of convergence, showing
that its reputation of unintelligibility is hardly deserved. A detailed
discussion of the experience concludes the exposition.
rv: