id: 06683671
dt: j
an:
au: Fonseca, Daila Silva Seabra de Moura; Franchi, Regina Helena de Oliveira
Lino
ti: Exploring the convergence of sequences in the embodied world using
GeoGebra.
so: Teach. Math. Appl. 35, No. 2, 88-101 (2016).
py: 2016
pu: Oxford University Press, Oxford; Institute of Mathematics and its
Applications (IMA), Southend-on-sea, Essex
la: EN
cc: I30 U70
ut:
ci:
li: https://academic.oup.com/teamat/article/35/2/88/2223635/Exploring-the-convergence-of-sequences-in-the#main
ab: Summary: This study addresses the embodied approach of convergence of
numerical sequences using the GeoGebra software. We discuss activities
that were applied in regular calculus classes, as a part of a research
which used a qualitative methodology and aimed to identify
contributions of the development of activities based on the embodiment
of concepts, with the use of software, to the understanding of the
convergence of numerical sequences and to the transition of
mathematical thinking from elementary to advanced. Such activities had
an exploratory nature and were constructed based on the theoretical
frameworks of Advanced Mathematical Thinking and the Three Worlds of
Mathematics. For the data collection were used the recordings of the
computer screens, audio recordings of the discussion between students,
student records in the responses of the activities and field notes of
the researchers. The data were analyzed considering relations between
the embodiment of the concept of convergence and proceptualization
processes and axiomatization and also considering the transition from
elementary mathematical thinking to advanced. The results indicate that
the activities enabled the formation of the mental image that the
convergence of sequences occurs when the sequence terms are approaching
a certain value, and thus propitiated the embodiment of the concept of
convergence and established cognitive roots for formal definition of
convergence by the limit and further theoretical development. They also
indicate that relations between different representations were
established, which contributed to abstraction of the concept of
convergence of sequences and thus for the transition between elementary
and advanced mathematical thinking.
rv: