id: 06647467
dt: j
an: 2016f.01151
au: Fernández-Plaza, José Antonio; Simpson, Adrian
ti: Three concepts or one? Students’ understanding of basic limit concepts.
so: Educ. Stud. Math. 93, No. 3, 315-332 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: I30 I20 C30
ut: limits; advanced mathematical thinking; definitions; card-sorting;
phenomenography
ci:
li: doi:10.1007/s10649-016-9707-6
ab: Summary: In many mathematics curricula, the notion of limit is introduced
three times: the limit of a sequence, the limit of a function at a
point and the limit of a function at infinity. Despite the use of very
similar symbols, few connections between these notions are made
explicitly and few papers in the large literature on student
understanding of limit connect them. This paper examines the nature of
connections made by students exposed to this fragmented curriculum. The
study adopted a phenomenographic approach and used card sorting and
comparison tasks to expose students to symbols representing these
different types of limit. The findings suggest that, while some
students treat limit cases as separate, some can draw connections, but
often do so in ways which are at odds with the formal mathematics. In
particular, while there are occasional, implicit uses of neighbourhood
notions, no student in the study appeared to possess a unifying
organisational framework for all three basic uses of limit.
rv: