Construcciones SERLIST y SERFUNC de series infinitas

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.