Resumen

MARTINEZ-PLANELL, Rafael; GONZALEZ, Ana Carmen; YUMET, Gladys Di Cristina  y  ACEVEDO, Vanessa. Construcciones SERLIST y SERFUNC de series infinitas. Educ. mat [online]. 2011, vol.23, n.3, pp. 183-207. ISSN 1665-5826.

This is a study of how college students construct the notion of an infinite series as a sequence of partial sums. Using Action-Process-Object-Schema theory (APOS) it is shown that students tend to construct two different cognitive objects, SERLIST and SERFUNC, which are described in the article. Essentially, in a SERLIST conception a series is perceived as an infinite sum while in a SERFUNC conception it is perceived as a sequence of partial sums. The SERLIST and SERFUNC notions generalize analogous notions that have been used in the case of infinite sequences. The qualitative study is based on semi-structured interviews to 14 undergraduate students. We found that 12 of the 14 interviewed students had great difficulty constructing a notion of infinite series as a sequence of partial sums. Our study suggests some activities that may help remedy this situation.

Palabras llave : calculus; infinite series; APOS; sequence of partial sums; sequences.