Formulating a Modified Genetic Decomposition for the Concept of ‘Limit of a Sequence’

Abstract

In this paper we focused on university mathematics students’ mental constructions on the concept limit of a sequence. The aim was to explore the nature of the mental constructions and to contribute to Action–Process–Object–Schema (APOS) theory in terms of instructional strategy for teaching limit of sequences. The belief that understanding students’ mental constructions in learning mathematics leads to improved instructional strategy guided this study. Maple software was applied in the learning of limit of sequences to foster students’ understanding of the topic. Thirty university students took part in this study. The data was collected through the test questions and interviews. The results revealed that in most cases, the preliminary genetic decomposition could be used to appropriately describe students’ constructions of their responses. Furthermore, many students operated at an action/process/object level with the exception of a few students who were not able to operate at these levels. It was also revealed that few students carried out procedures effectively without the conceptual understanding of the concept limit of a sequence. It is recommended that the preliminary genetic decomposition be extended to include aspects necessary for conceptual understanding of the limit of sequences in modified genetic decomposition, such as prerequisites, concepts which include rules of inequalities and properties of the modulus function. These concepts are required for the understanding of proving or disproving the given limits of a sequence.