Preservice mathematics teachers’ competencies in the process of transformation between representations for the concept of limit: A qualitative study

Authors

DOI:

https://doi.org/10.14527/pegegog.2020.032

Keywords:

External representations, Limit, Multiple representations

Abstract

In this study, external representations and the problems encountered related transformation process between representations towards limit concept were investigated. "Limit Representation Conversion Test" was administered to 41 preservice mathematics teachers studying at a state university in central Turkey during 2018–2019 academic years. In this study, which was designed with the case study model, which is one of the qualitative research models, the data were analyzed by content analysis. Unstructured interviews were made with preservice mathematics teachers whose explanations were insufficient or differed and the problems encountered were determined. It was observed that preservice mathematics teachers had most difficulties in the verbal representation type questions. It was revealed that preservice mathematics teachers who gave the wrong answers mostly had deficiencies in the concept and the process and could not fully understand the limit problems. It was determined that preservice mathematics teachers had difficulties in knowing the concept of limit point, determining the function and interpreting verbal data. It was seen that preservice mathematics teachers who proceeded towards the concept and process answered wrong due to mathematical operations errors and carelessness. When the wrong answers were examined, it was observed that errors were gathered under the themes "lack of content knowledge" and "lack of reading comprehension" for verbal type input; under the theme "carelessness" for graphical type input; under the theme "lack of content knowledge" for algebraic and numerical type input.

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References

Akbulut, K., & Işık, A. (2005). Limit kavramının anlaşılmasında etkileşimli öğretim stratejisinin etkinliğinin incelenmesi ve bu süreçte karşılaşılan kavram yanılgıları. Kastamonu Eğitim Dergisi, 13(2), 497-512.

Artigue, M. (2000). Teaching and learning calculus: What can be learned from education research and curricular changes in France?. Research in collegiate mathematics education 4(8), 1-15.

Bezuidenhout, J. (2001). Limits and continuty: Some conceptions of first-year students. International Journal of Mathematics Education in Science and Techonolgy, 32(4), 487-500.

Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education. London: Routledge Falmer

Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced mathematical thinking (pp.153-166). Dordrect: Kluwer Academic.

Cottrill, J., Dubinsky, E., Nichols, D., Schwinngendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: Beginning with a coordinated process schema. Journal of Mathematical Behavior, 15, 17-192.

Çil, O., Kuzu, O., & Şimşek, A.S. (2019). 2018 Ortaöğretim matematik programının revize edilmiş Bloom taksonomisine ve programın ögelerine göre incelenmesi. YYÜ Eğitim Fakültesi Dergisi, 16(1), 1402-1418.

Davis, R. B., & Vinner, S. (1986). The notion of limit; some seemingly an avoidable misconception stages, Journal of Mathematical Behavior, 5, 281-303.

Delice, A., & Sevimli, E. (2010a). Matematik öğretmeni adaylarının belirli integral konusunda kullanılan temsiller ile işlemsel ve kavramsal bilgi düzeyleri. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 9(3), 581-605.

Delice, A., & Sevimli, E. (2010b). Öğretmen adaylarının çoklu temsil kullanma becerilerinin problem çözme başarıları yönüyle incelenmesi: Belirli integral örneği. Kuram ve Uygulamada Eğitim Bilimleri, 10(1), 111-149.

Delice, A., & Sevimli, E. (2016). Matematik eğitiminde teoriler: Matematik eğitiminde çoklu temsiller. Ankara: Pegem Akademi Yayıncılık.

Dufour-Janvier, B., Bednarz, N., & Belanger M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp.109-122). Hillsdale, NJ: Erlbaum.

Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de didactique et de sciences cognitives. 5(1), 37-65.

Elia, I., & Spyrou, P. (2006). How students conceive function: A triarchic conceptual-semiotic model of the understanding of a complex concept. TMME, 3(2), 256-272.

Goldin, G. A. (1998). Representations, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17(2), 137-165.

Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. Theories of mathematical learning, 397-430.

Girard, N. R. (2002). Students’ representational approaches to solving calculus problem: Examining the role of graphing calculators. Unpublished doctorate dissertation, University of Pittsburg, USA.

Hale, P.L. (1996). Building conceptions and repairing misconceptions in student understanding of kinematic graphs-using student discourse in calculator based laboratories. Unpublished doctorate dissertation, Oregon State University, USA.

Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.65-100). Reston, VA.

Howell, D.C. (2013). Statistical methods for psychology. Wadsworth: Cengage Learning.

Kaya, Y. S. (2017). Öğretmen adaylarının matematiksel örnekleri algılayışları üzerine bir metafor analizi. Bartın Üniversitesi Eğitim Fakültesi Dergisi, 6(1), 48-67.

Keller, B. A., & Hirsch, C. R. (1998). Student preferences for representations of functions. International Journal of Mathematical Education in Science and Technology, 29(1), 1-17.

Kendal, M., & Stacey, K. (2003). Tracing learning of three representations with the differentiation competency framework. Mathematics Education Research Journal, 15(1), 22-41.

Kuzu, O. (2017). Matematik ve fen bilgisi öğretmen adaylarının integral konusundaki kazanımlarının incelenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(3), 948-970.

Lesh, R., & Doerr, H. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. Doerr (Eds.), Beyond constructivism (pp. 3-34). Hillsdale, NJ: Erlbaum.

Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. John Wiley & Sons.

National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

National Research Council (NRC) (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.

Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage.

Prain, V., & Waldrip, B. (2006). An exploratory study of teachers’ and students’ use of multi‐modal representations of concepts in primary science. International Journal of Science Education, 28(15), 1843-1866.

Polat, Z. S., & Şahiner, Y. (2010). Bağıntı ve fonksiyonlar konusunda yapılan yaygın hataların belirlenmesi ve giderilmesi üzerine boylamsal bir çalışma. Eğitim ve Bilim, 32(146), 89-95.

Radojevic, N. (2006). Exploring the use of effective learning strategies to increase students' reading comprehension and test taking skills. Unpublished master’s thesis, The Brock University, Canada.

Quesada, A., Einsporn, R. L., & Wiggins, M. (2008). The impact of the graphical approach on students' understanding of the formal definition of limit. International Journal for Technology in Mathematics Education, 15(3), 95-102.

Salkind, N. J. (2010). Encyclopedia of research design. London: SAGE Publications.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Handbook of research on mathematics teaching and learning, 334-370.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.

Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18, 371-397.

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.

Szymanski, E. M., & Linkowski, D. C. (1993). Human resource development: An examination of perceived training needs of certified rehabilitation counselors. Rehabilitation Counseling Bulletin, 37(2), 163- 176.

Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educatfmional Studies in Mathematics, 12, 151-169.

Williams, S. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22(3), 219-236.

Yaman, H. (2010a). Öğrencilerinin matematiksel örüntülerdeki ilişkileri algılayışları üzerine bir inceleme. Unpublished doctorate dissertation, Hacettepe Üniversitesi, Ankara.

Yaman, E. (2010b). Psikoşiddete (Mobbinge) maruz kalan öğretim elemanlarının örgüt kültürü ve iklimi algıları. Kuram ve Uygulamada Eğitim Bilimleri, 10(1), 567-578.

Zachariades, T., Christou, C., & Papageorgiou, E. (2002). The difficulties and reasoning of undergraduate mathematics students in the identification of functions. Proceedings in the 10th ICME Conference, Crete, Greece.

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Published

2021-02-01

How to Cite

Kuzu, O. (2021). Preservice mathematics teachers’ competencies in the process of transformation between representations for the concept of limit: A qualitative study. Pegem Journal of Education and Instruction, 10(4), 1037–1066. https://doi.org/10.14527/pegegog.2020.032