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

Received | Revised | Accepted | Published |
---|---|---|---|

19 Mar 2022 | 15 May 2022 | 26 May 2022 | 07 Jun 2022 |

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.

[1] Β. Cornu, Limits, in D. Tall (Ed.), Advanced Mathematical Thinking Dordrecht: Kluwer Academic Publishers. (1991) 153-166.

[2] J. Bezuidenhout, Limits and Continuity: Some Conceptions of First-Year Students. International Journal of Mathematical Education in Science and Technology, 32(4) (2001) 487-500.

[3] J. Cottrill, E. Dubinsky, D. Nichols, K. Schwingendorf, K. Thomas, & D. Vidakovic, Understanding the Limit Concept: Beginning With A Coordinated Process Scheme. the Journal of Mathematical Behavior, 15(2) (1996) 167-192.

[4] M. Przenioslo, Images of the Limit of Function Formed in the Course of Mathematical Studies at the University. Educational Studies in Mathematics, 55(1) (2004) 103-132.

[5] I. Elia, A. Gagatsis, A. Panaoura, T. Zachariades, & F. Zoulinaki, Geometric and Algebraic Approaches in the Concept of Limit and the Impact of the "Didactic Contract". International Journal of Science and Mathematics Education, 7(4) (2009) 65-790.

[6] D. Tall, Introducing Three Worlds of Mathematics. for the Learning of Mathematics, 23(3) (2004) 29–33.

[7] D. Tall, the Transition to Formal Thinking in Mathematics. Mathematics Education Research Journal, 20(2) (2008) 5-24.

[8] Tall, D. (1995). Cognitive Development, Representations & Proof. in Justifying and Proving in School. London: Mathematics Institute of Education. (1995) 27-38.

[9] R. Gras, E. Suzuki., F. Guillet, & F. Spagnolo, Statistical Implicativen Analysis. Germany: Springer, (2008).

[10] S. R. Williams, Models of Limit Held By College Calculus Students. Journal for Research in Mathematics Education, (1991) 219-236.

[11] J. Mamona-Downs, Letting the Intuitive Bear on the Informal: A Didactical Approach for the Understanding of the Limit of A Sequence. Educational Studies in Mathematics, 48 (2002) 259–288.

[12] E. M. Gray, & D. O. Tall, Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic. Journal of Research in Mathematics Education, 26(2) (1994) 115–141.

[13] D. O. Tall, Understanding the Calculus, Mathematics Teaching, (1985) 49-53.

[14] D. O. Tall, Visual Organizers for Formal Mathematics. in R. Sutherland & J. Mason(Eds.), Exploiting Mental Imagery With Computers in Mathematics Education, (1995) 52–70. Berlin: Springer-Verlag.

[15] D. O. Tall, Real Functions and Graphs (for the Bbc Computer, Master, Compact, Nimbus Pc& Archimedes Computer), (1991). Cambridge: Cambridge University Press.

[16] A. Sierpińska, Humanities Students and Epistemological Obstacles Related to Limits. Educational Studies in Mathematics, 18(4) (1987) 371-397.

[17] M. Przenioslo, Images of the Limit of Function Formed in the Course of Mathematical Studies at the University. Educational Studies in Mathematics, 55(1) (2004) 103-132 .

[18] J. Monaghan, Problems With the Language of Limits. for the Learning of Mathematics , 11(3) (1991) 20-24 .

[19] E. Mastorides & T. Zachariades, Secondary Mathematics Teachers' Knowledge Concerning the Concept of Limit and Continuity. in M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education , (2004) 481-488 .

[20] I. Kidron & D. Tall, the Roles of Visualization and Symbolism in the Potential and Actual Infinity of the Limit Process. Educational Studies in Mathematics, 88(2) (2015) 183-199.

[21] B. Cornu, Limits. in D. Tall (Ed.), Advanced Mathematical Thinking. Dordrecht: Kluwer Academic Publishers, (1991) 153-166.

[22] K. H. Roh, Students’ Images and Their Understanding of Definitions of the Limit of A Sequence. Educational Studies in Mathematics, 69(3) (2008) 217-233 .

[23] A. Bodin, R. Coutourier & R. Gras, Chic: Classification Hiérarchique Implicative Et Cohésive-Version Sous Windows – Chic 1.2. Association Pour La Recherche En Didactique Des Mathématiques Rennes , (2000).

[24] S. R. Williams, Predications of the Limit Concept: an Application of Repertory Grids. Journal for Research in Mathematics Education, (2001) 341-367.

[25] D. Tall. & R. Schwarzenberger, Conflicts in the Learning of Real Numbers and Limits, Mathematics Teaching, 82 (1978) 44– 49.

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