Original Research

University students’ mental construction when learning the Convergence of a Series concept

Conilius J. Chagwia, Aneshkumar Maharaj, Deonarain Brijlall
Pythagoras | Vol 41, No 1 | a567 | DOI: https://doi.org/10.4102/pythagoras.v41i1.567 | © 2020 Conilius J. Chagwiza, Aneshkumar Maharaj, Deonarain Brijlall | This work is licensed under CC Attribution 4.0
Submitted: 10 July 2020 | Published: 15 December 2020

About the author(s)

Conilius J. Chagwia, Department of Science and Mathematics, Faculty of Science Education, Bindura University, Bindura, Zimbabwe
Aneshkumar Maharaj, Department of Mathematics, Faculty of Education, University of KwaZulu-Natal, Durban, South Africa
Deonarain Brijlall, Department of Mathematics, Faculty of Education, Durban University of Technology, Durban, South Africa


This article uses action-process-object-schema theory to study the mental constructions about the limit of series during a Calculus 1 course at a university. The researchers also used the theory’s teaching methodology to teach the topic. A plethora of research on the limit concept is available and suggests that the concept is on record as being difficult for students to learn and comprehend. The study proposed a genetic decomposition on how undergraduate students might demonstrate their mental constructions in learning the limit of a series. Students were taken through the activities-classroom discussions-exercises cycle. Thirty students participated in answering questions based on the convergence of a series. The students’ written responses together with the interviews were analysed and based on the findings a revision of the preliminary genetic decomposition was done. We found that there were students who did not display the predicted mental construction indicated by the preliminary decomposition in the application of the definition for the convergence of a series, but displayed the predicted mental construction for the application of the series convergence tests. We also found that certain schema were necessary for the achievement of a complete understanding of the convergence of a series concept. The mental constructions within the missing schema were included in the modified genetic decomposition. This empirically enriched model is now expected to inform pedagogy on the convergence of a series concept.


action; process; object; schema; limit; series


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