An investigation of prospective elementary mathematics teachers understanding of the formal definition of the limit of a sequence

Abstract

The purpose of this study was to investigate the understanding of prospective elementary mathematics teachers of the formal definition of the limit of a sequence. The participants were 32 prospective mathematics teachers (8 male and 24 female) who were in their third year of study in a four-year mathematics teacher preparation programme Istanbul University-Cerrahpasa in Türkiye. The data were collected via a test that was developed by the authors. The findings of the study demonstrate that the prospective elementary mathematics teachers had difficulty in defining the concept of limit of a sequence and in determining the graphical representations of the variables and the inequalities in the formal definition. Moreover, they also had difficulty comprehending the relationship between the variables of 𝜀 and 𝑛0 , and hence, when a numerical value was assigned to one of these variables, they were not able to find an appropriate value for the other. It was concluded that the prospective mathematics teachers generally tended to memorize the formal definition of the limit of sequences but lacked conceptual understanding of its meaning. Therefore, they were not able to reason about the variables it contained.