id: 06585962
dt: j
an: 2016d.00747
au: Caglayan, Günhan
ti: Math majors’ visual proofs in a dynamic environment: the case of limit of
a function and the $ε$-$δ$ approach.
so: Int. J. Math. Educ. Sci. Technol. 46, No. 6, 797-823 (2015).
py: 2015
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: I25 U75 E55
ut: undergraduate mathematics education; dynamic geometry software;
visualization; representation; limits of functions; epsilon-delta
formalism
ci:
li: doi:10.1080/0020739X.2015.1015465
ab: Summary: Despite few limitations, GeoGebra as a dynamic geometry software
stood as a powerful instrument in helping university math majors
understand, explore, and gain experiences in visualizing the limits of
functions and the $ε$-$δ$ formalism. During the process of
visualizing a theorem, the order mattered in the sequence of
constituents. Students made use of such rich constituents as
finger-hand gestures and cursor gestures in an attempt to keep a record
of visual demonstration in progress, while being aware of the
interrelationships among these constituents and the transformational
aspect of the visually proving process. Covariational reasoning along
with interval mapping structures proved to be the key constituents in
the visualizing and sense-making of a limit theorem using the
delta-epsilon formalism. Pedagogical approaches and teaching strategies
based on experimental mathematics ‒ mindtool ‒ consituential visual
proofs trio would permit students to study, construct, and meaningfully
connect the new knowledge to the previously mastered concepts and
skills in a manner that would make sense for them.
rv: