id: 06639210
dt: j
an: 2016f.00933
au: Durand-Guerrier, Viviane
ti: Conceptualization of the continuum, an educational challenge for
undergraduate students.
so: Int. J. Res. Undergrad. Math. Educ. 2, No. 3, 338-361 (2016).
py: 2016
pu: Springer US, New York, NY
la: EN
cc: F55 E65 C35
ut: continuum; density-in-itself; discreteness; number line; didactical
situations
ci:
li: doi:10.1007/s40753-016-0033-2
ab: Summary: The continuum is one of the most difficult mathematical concepts
for undergraduate students. We hypothesize that among the difficulties
they face in relation with this notion, the graphical evidence provided
by the number line fosters the idea of a dichotomy between discreteness
and continuity, hiding the property of density-in-itself, i.e. the
intrinsic density with respect to order in a totally ordered set. In
this paper, we first provide evidences of the weakness of fresh
university studentsâ€™ knowledge about real numbers. Then, we briefly
present Dedekindâ€™s construction of real numbers, which relies on the
intuitive idea of the continuous line. Finally, we present a didactical
situation aimed at fostering the understanding of the relationships
between discreteness, density-in-itself and continuity for an ordered
set of numbers.
rv: