From the Embodied to the Axiomatic World of
Mathematics: Students’ Perceptions on the Concept
‘Limit’

Petros Samartzis; Evgenios Avgerino; Panagiotis Gridos

doi:https://doi.org/10.14445/22315373/IJMTT-V68I5P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 5 | Year 2022 | Article Id. IJMTT-V68I5P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I5P508

From the Embodied to the Axiomatic World of Mathematics: Students’ Perceptions on the Concept ‘Limit’

Petros Samartzis, Evgenios Avgerino, Panagiotis Gridos

Received	Revised	Accepted	Published
19 Mar 2022	15 May 2022	26 May 2022	07 Jun 2022

Citation :

Petros Samartzis, Evgenios Avgerino, Panagiotis Gridos, "From the Embodied to the Axiomatic World of Mathematics: Students’ Perceptions on the Concept ‘Limit’," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 5, pp. 44-50, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I5P508

Abstract

This study aims to explore whether and if so, at what extent the students of the Mathematics department have developed the axiomatic/typical understanding of the concept of ‘limit’, after having firstly explored and examined students' current perceptions upon this concept. The sample of the study consisted of 37 students. The sample students were given a questionnaire constructed according to the theory of D. Tall about the three worlds of Mathematics (Embodied, Proceptual, and Axiomatic). The data were analyzed using a mixed approach; including a content analysis method and the use of two statistical programs (SPSS and CHIC). Findings of the study revealed students' perceptions regarding the concept ‘limit’ seem deviant from the typical concept of ‘limit’ that axiomatic world presents and accepts. As such they strongly suggest that the teaching of the concept limit shall follow a more holistic approach emphasizing the transition from the institutional comprehension of the ‘limit’ to its typical apprehension and reverse. Towards, this direction the use of a plethora of mathematical tools is deemed the way forward.

Keywords

Concept limit, University students, Three worlds of Mathematics, Teaching, Cognitive difficulties, Calculus.

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