Top

Quality & Quantity

Published in:

01-11-2014

Misconceptions emerging in mathematics student teachers’ limit instruction and their reflections

Authors: Semiha Kula, Esra Bukova Güzel

Published in: Quality & Quantity | Issue 6/2014

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The purpose of this study is to investigate the misconceptions emerging in mathematics student teachers’ limit instruction and the reflections of these misconceptions on their teaching. In this study, which used the case study design, regarding the limit concept, four senior mathematics student teachers’ four-hour limit instruction was examined within the context of misconceptions as described in the literature. Mathematics student teachers’ lesson plans, video recordings of the participants’ lessons in which they taught the concept of limit and audio recordings of semi-structured interviews were used to gather data. Participants carried their instruction mostly by demonstrating that the function’s limit is different than the function’s value at \(x=a\). However, since mathematics student teachers did not have adequate knowledge of misconceptions regarding the limit concept, some misconceptions emerged in their teaching process. Three of the participants made illustrations by making use of the meaning attributed to limit in daily language, and this situation caused students to perceive the limit concept as the maximum value to be reached and as a boundary not to be exceeded.

previous article Self-reported cheating in web surveys on political knowledge

next article Exploring the connections among spiritual leadership, altruism, and trust in family businesses

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

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

Ball, D.L., Mcdiarmid, G.W.: The subject matter preparation of teachers. In: Houston, R. (ed.) Handbook of Research on Teacher Education. Macmillan, New York (1990)

Ball, D.L., Lubienski, S.T., Mewborn, D.S.: Research on teaching mathematics: the unsolved problem of teachers’ mathematical knowledge. In: Richardson, V. (ed.) Handbook of Research on Teaching, pp. 433–456. Macmillian, New York (2001)

Ball, D., Bass, H.: Interweaving content and pedagogy in teaching and learning to teach: knowing and using mathematics. In: Boaler, J. (ed.) Multiple Perspectives on Mathematics Teaching and Learning. Ablex, Westport (2000)

Bezuidenhout, J.: Limits and continuity: some conceptions of first-year students. Int. J. Math. Educ. Sci. Technol. 32(4), 487–500 (2001)CrossRef

Bukova Güzel, E.: An investigation of pre-service mathematics teachers’ pedagogical content knowledge, using solid objects. Sci. Res. Essays 5(14), 1872–1880 (2010)

Bukova, E.: Öğrencilerin limit kavramını algılamasında ve diğer kavramların ilişkilendirilmesinde karşılaştıkları güçlükleri ortadan kaldıracak yeni bir program geliştirme. Doktora Tezi, Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir (2006)

Carlsen, W.S.: Domains of teacher knowledge. In: Gess-Newsome, J., Lederman, N.G. (eds.) Examining Pedagogical Content Knowledge: The Construct and its Implications for Science Education, pp. 133–144. Kluwer Academic, Dordrecht (1999)

Carpenter, T.P., Fennema, E., Peterson, P.L., Carey, D.A.: Teachers’ pedagogical content knowledge of students’ problem solving in elementary arithmetic. J. Res. Math. Educ. 19, 385–401 (1988)CrossRef

Cinvestav, F.H., Chavez, H.L.: Limits, Continuity and Discontinuity of Functions from Two Points of View: That of the Teacher and That of the Student. In Bills, L. (Ed.) Proceedings of the British Society for Research into Learning Mathematics (1999)

Cornu, B.: Limits. In: Tall, D. (ed.) Advanced Mathematical Thinking, pp. 153–166. Kluwer, Boston (1991)

Davis, R., Vinner, S.: The notion of limit: some seemingly unavoidable misconception stages. J. Math. Behav. 5, 281–303 (1986)

Duru, A.: Öğretmen Adaylarının Limit Kavramına İlişkin Algıları. Kuram ve Uygulamada Eğitim Bilimleri 11(3), 1699–1717 (2011)

Frid, S.: Three approaches to undergraduate calculus instruction: their nature and potential impact on students’ language use and sources of conviction. In: Schoenfeld, A., Kaput, J., Dubinsky, E. (eds.) Research in Collegiate Mathematics Education I, pp. 69–100. American Mathematical Society, Providence (1994)

Grossman, P.L.: The Making of a Teacher: Teacher Knowledge and Teacher Education. Teachers College Press, New York (1990)

Grouws, D., Schultz, K.: Mathematics teacher education. In: Sikula, J. (ed.) Handbook of Research on Teacher Education, 2nd edn. Macmillan, New York (1996)

Halim, L., Meerah, S.M.: Science teachers’ pedagogical content knowledge and its influence on physics teaching. Res. Sci. Technol. Educ. 20(2), 215–227 (2002)CrossRef

Jaffar, S.M., Dindyal, J.: Language-related misconceptions in the study of limits. In: Clark, J., Kissane, B., Mousley, J., Spencer, T., Thornton, S. (eds.) Proceedings of the AAMT-MERGA Conference, pp. 390–397. Australian Association of Mathematics Teachers, Adelaide (2011)

Jordaan, T.: Misconceptions of the Limit Concept in a Mathematics Course for Engineering Students. Unpublished Master of Science Dissertation, University of South Africa, Pretoria (2005)

Juter, K.: Students’ attitudes to mathematics and performance in limits of functions. Math. Educ. Res. J. 17(2), 91–110 (2005)CrossRef

Karataş, İ., Guven, B., Çekmez, E.: A cross-age study of students’ understanding of limit and continuity concepts. Boletim de Educação Matemática 24(38), 245–264 (2011)

Kidron, I., Zehavi, N.: The role of animation in teaching the limit concept. Int. J. Comput. Algebra Math. Educ. 9, 205–227 (2002)

Kovarik, K.: Mathematics educators’ and teachers’ perceptions of pedagogical content knowledge. Doctoral Dissertation, Columbia University, Columbia (2008)

Kula, S.: Examining pre-service mathematics teachers’ subject matter and pedagogical content knowledge by using knowledge quartet: the case of limit. Master dissertation, Dokuz Eylül University, İzmir, Türkiye (2011)

Monaghan, J.: Problems with the language of limits. Learn. Math. 11(3), 20–24 (1991)

Nair, G.S.: College Students’ Concept Images of Asymptotes, Limits, and Continuity of Rational Functions. Doctoral dissertation, The Ohio State University, Columbus (2010)

Navarro, M., Carreras, P.: Constructing a concept image of convergence of sequences in the vanHiele framework. Res. Coll. Math. Educ. 6, 61–98 (2006)

Özkan, E.M., Ünal, H.: Misconception in calculus-I: Engineering students’ misconceptions in the process of finding domain of functions. Procedia Soc. Behav. Sci. 2009(1), 1792–1796 (2009)

Özmantar, M.F., Yeşildere, S.: Matematiksel Kavram Yanılgıları ve Çözüm Önerileri, (8. bölüm). Pegem Yayıncılık, Ankara (2008)

Rowland, T., Turner, F., Thwaites, A., Huckstep, P.: Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet. Sage, London (2009)

Salas, G.L., Hille, E.: Calculus: One and Several Variables, 6th edn. Wiley, New York (1990)

Şandır, H., Aztekin, S.: Pre-service teachers’ opinions and methods about finding students’ misconceptions. Mediterr. J. Res. Math. Educ. 12, 23–37 (2013)

Schmidt, W.H., Jorde, D., Cogan, L.S., Barrier, E., Gonzalo, I., Moser, U., Shimuzu, K., Sawada, T., Valverde, G.A., Mcknight, C., Prawat, R.S., Wiley, D.E., Raizen, S.A., Britton, E.D., Wolfe, R.G.: Characterising, Pedagogical Flow: An Investigation of Mathematics and Science Teaching in Six Countries. Kluwer, Dordrecht (1996)

Schoenfeld, A.H.: Toward a theory of teaching-in-context. Issues Educ. 4(1), 1–94 (1998)CrossRef

Schoenfeld, A.H.: Models of the teaching process. J. Math. Behav. 18(3), 243–261 (2000)CrossRef

Shulman, L.S.: Knowledge and teaching: foundations of the new reform. Harv. Educ. Rev. 57(1), 1–22 (1987)

Smith, D.C., Neale, D.C.: The construction of subject matter knowledge in primary science teaching. Teach. Teach. Educ. 5, 1–20 (1989)CrossRef

Szydlik, J.E.: Mathematical beliefs and conceptual understanding of the limit of a function. J. Res. Math. Educ. 31(3), 258–276 (2000)CrossRef

Tall, D.O., Schwarzenberger, R.L.: Conflicts in the learning of real numbers and limits. Math. Teach. 83, 44–49 (1978)

Wagner, L.: The best laid plans: preservice teachers’ use of lesson study as a model for attending to students’ mathematical thinking. Dissertation at the University of Wisconsin-Madison, Dissertation (2003)

Williams, J., Ryan, J.: National testing and the improvement of classroom teaching: Can they coexist? Br. Educ. Res. J. 26(1), 49–73 (2000)CrossRef

Williams, S.: Understanding of the limit concept in college calculus students. Doctoral Dissertation. The University of Wisconsin, Madison, WI. Dissertation Abstracts International 3174, 50–10 (1989)

Williams, S.R.: Predications of the limit concept: an application of repertory grids. J. Res. Math. Educ. 32(4), 343–367 (2001)CrossRef

You, Z.: Preservice Teachers’ Knowledge of Linear Functions Within Multiple Representation Modes. Doctoral Dissertation, Texas A &M University, College Station (2006)

Zembat, İ.Ö.: Kavram Yanılgısı Nedir? In: Özmantar, M.F., Bingölbali, E., ve Akkoç, H. (eds.) Matematiksel Kavram Yanılgıları ve Çözüm Önerileri, pp. 1–8. Pegem Akademi Yayınevi, Ankara (2008)

Title: Misconceptions emerging in mathematics student teachers’ limit instruction and their reflections
Authors: Semiha Kula
Esra Bukova Güzel
Publication date: 01-11-2014
Publisher: Springer Netherlands
Published in: Quality & Quantity / Issue 6/2014
Print ISSN: 0033-5177
Electronic ISSN: 1573-7845
DOI: https://doi.org/10.1007/s11135-013-9961-y

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 6/2014

Model-based approach for importance–performance analysis

Exploring the relationship between freedom from corruption and business governance in the Oceania region

Overly ambitious: contributions and current status of Q methodology

Mobbing in Turkish health institutions

Clustering eurozone cycles

Multivariate-based Granger causality between financial deepening and poverty: the case of Pakistan

Premium Partner