Mathematics Teacher Candidates’ Conceptual Knowledges of the Concept of Limit in Single-Variable Functions

Year 2020, Volume: 11 Issue: 4, 511 - 532, 26.10.2020

Birgül Yıldız Gonca İnceoğlu

https://doi.org/10.17569/tojqi.748187

Cited By: 1

Abstract

The aim of this study is to investigate teacher candidates’ conceptual understanding of the concept of limit in single-variable functions. The study sample consisted of 30 students who were studying Primary School Mathematics Teaching at the Department of Mathematics and Science Education at a state university in Turkey and were enrolled in the Analysis I course in their second year. This study used a basic qualitative research design, and data were collected through open-ended questions and clinical interviews with focus students. The results revealed that the teacher candidates gave memorized answers to conceptual knowledge questions. The results showed that the teacher candidates’ concept definitions were generally based on the right-left limit equation theorem and the dynamic form of the limit. However, the results of the clinical interviews indicated that teacher candidates avoided giving the formal definition of a limit.

Keywords

limit, single-variable functions, conceptual knowledge

Supporting Institution

Anadolu University

Project Number

41452

Matematik Öğretmen Adaylarının Tek Değişkenli Fonksiyonların Limit Kavramına Yönelik Kavramsal Bilgileri

Abstract

Bu araştırmanın amacı öğretmen adaylarının tek değişkenli fonksiyonların limit kavramına yönelik kavramsal anlamalarının incelenmesi üzerinedir. Araştırma, Türkiye’ de bir devlet üniversitesi Matematik ve Fen Bilimleri Eğitimi Bölümü İlköğretim Matematik Öğretmenliği Programı ikinci sınıf Analiz 1 dersini alan otuz öğretmen adayının katılımı ile gerçekleştirilmiştir. Araştırmanın modeli temel nitel araştırma olup veri toplama araçları açık uçlu sorular ve odak öğrencilerle yapılan klinik görüşmeyi içermektedir. Araştırmadan elde edilen veriler incelendiğinde öğretmen adaylarının kavramsal bilgi içeren sorulara ezbere dayalı yanıtlar verdikleri görülmüştür. Sonuçlar, öğretmen adaylarının kavram tanımlarını genellikle sağ-sol limit eşitliği teoremine ve limitin dinamik formuna dayandırdığını gösterdi. Bununla birlikte, klinik görüşmelerin sonuçları, öğretmen adaylarının limitin formal tanımını vermekten kaçındıklarını göstermiştir.

Keywords

Limit, tek değişkenli fonksiyonlar, kavramsal bilgi

Project Number

41452

References

• Artigue, M. (2000). Teaching and learning calculus: What can be learnt from education research and curricular changes in France? CBMS Issues in Mathematics Education, 8, 1-15.
• Baki, A. (1995). What prospective teachers need to know to teach conceptually in mathematics?, The world conference on teacher education, Çeşme, Turkey
• Baki, A., & Bell, A. (1997). Ortaöğretim Matematik Öğretimi [Secondary School Mathematics Teaching] (Vol 1). YÖK Öğretmen Eğitimi Dizisi
• Bezuidenhout, J. (2001). Limits and continuity: Some conceptions of first-year students. International Journal of Education, Science, and Technology, 32(4), 487 – 500.
• Cobb, P. (1986). Context, goals, beliefs, and learning mathematics, For the Learning of Mathematics FLM, 6. , pp.2-9.
• Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced mathematical thinking (pp. 153-166). Dordrecht/Boston/London: Kluwer Academic Publishers.
• Dubinsky, E., Elterman, F., & Gong, C. (1988). The student’s construction of quantification. For the Learning of Mathematics, 8(2), 44–51.
• Ervynck, G. (1981). Conceptual difficulties for first year university students in the acquisition of limit of a function. In Equipe de Recherche Pédagogique (Ed.), Proceedings of the Fifth Conference of the International Group for the Psychology of Mathematics Education (pp. 330–333). Grenoble, France: Laboratoire I.M.A.G.
• Fernández, E. (2004). The students’ take on the epsilon-delta definition of a limit. Primus, 14(1), 43–54. doi:10.1080/10511970408984076
• Ferrini-Mundy, J., & Graham, K. (1994). Research in calculus learning: Understanding of limits, derivatives, and integrals. In E. Dubinsky & J. J. Kaput (Eds.), Research issues in undergraduate mathematics learning: Preliminary analyses and results (pp. 31–45). Washington, DC: Mathematical Association of America. Hiebert, J., & Lefevre, P., (1986). Conceptual and procedural knowledge in mathematics: an introductory analysis, The case of mathematics, pp.1-28.
• Juter, K., & Grevholm, B. (2006). Limits and infinity: A study of university students' performance. To appear in C. Bergsten, B. Grevholm, H. Måsøval, & F. Rønning (Eds.), Relating practice and research in mathematics education. Fourth Nordic Conference on Mathematics Education, Trondheim, 2nd-6th of September 2005. Trondheim: Sør-Trøndelag University College.
• Kabael, T., Barak, B., & Özdaş, A. (2015) Öğrencilerin Limit Kavramına Yönelik Kavram İmajları ve Kavram Tanımları, Anadolu Journal of Educational Sciences International (AJESI), January 2015, 5(1),88-114.
• Mamona-Downs, J. (2001). Letting the intuitive bear on the formal: A didactical approach for the understanding of the limit of a sequence. Educational Studies in Mathematics, 48, 259-288.
• Monaghan, J. D. (1986). Adolescent’s Understanding of Limits and Infinity. Unpublished Ph.D. thesis, Warwick University, U.K.
• Monaghan, J. (1991). Problems with the language of limits. For the Learning of Mathematics, 11(3),20–24. Noss, R., & Baki, A. (1996). Liberating school mathematics from procedural view, Journal of Education Hacettepe University, pp.179-182.
• Porter, M. and Masingila, J. (2000). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics. (42). pp. 165-177.
• Przenioslo, M. (2004). Images of the limit of function formed in the course of mathematical studies at the university. Educational Studies in Mathematics, 55, 103-132.
• Roh, H. K. (2007). An activity for development of the understanding of the concept of Limit. In Woo, J. H., Lew, H. C., Park, K. S. & Seo, D. Y. (Eds.).Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 105-112. Seoul: PME.
• Schoenfeld, A.H., (1985). Mathematical Problem Solving. Academic Press, Orlando. Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18, 371-397.
• Skemp, R.R., (1987). The Psychology of Learning Mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates. Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function, Journal for Research in Mathematics Education, 31(3), 258–276.
• Tall, D. (1980). Mathematical intuition, with special reference to limiting processes. In R. Karplus (Ed.), Proceedings of the Fourth International Conference for the Psychology of Mathematics Education (pp. 170-176). Berkeley, CA: PME.
• Tall, D. O. & Vinner, S. (1981). Concept image and concept definition in Mathematics with particular reference to limit and continuity. Educational Studies in Mathematics, 12, 151-169.
• Todorov, T.D. (2001). Back to classics: teaching limits through infinitesimals, International Journal of Mathematical Education in Science and Technology, 32, 1, 120.
• Vinner, S. (1991). The Role of Definitions in the Teaching and Learning of Mathematics. In Tall, D. (Ed.), Advanced Mathematical Thinking (pp. 65-81). Boston: Kluwer.
• Williams, S. R. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22, 219-236.
• Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences] (6th ed). Ankara: Seçkin Yayınevi