THE TOPIC-SPECIFIC STRATEGIES ON THE LIMIT CONCEPT IN MATHEMATICS STUDENT TEACHERS LESSONS

THE TOPIC-SPECIFIC STRATEGIES ON THE LIMIT CONCEPT IN MATHEMATICS STUDENT TEACHERS LESSONS

The purpose of this study is to investigate the topic-specific strategies used by the mathematics student teachers in their lessons on the limit concept. The participants were four secondary mathematics student teachers in the final year of mathematics teacher education program. The data were obtained from the participants lesson plans, video recordings of their lessons in which they taught the concept of limit, and from semi-structured interviews. Limit-specific strategies used by participants on their teach- ing examined under limit-specific representations and limit-specific activities. Limit- specific representations were categorized as (a) figural, (b) number line, (c) tabular, (d) graphical, (e) algebraic, and (f) verbal. Limit-specific activities were categorized as (a) game, (b) real life examples, (c) animation, (d) scenario supported by visuals, (e) ana- logy, (f) Escher s paintings, (g) other disciplines, (h) discussing the limit of the polyno- mial functions, and (i) reinforcing the properties of limit. The most used limit-specific representations by participants were verbal and algebraic representations. The partici- pants related to the limit concept with the real life generally on their first lesson and they stated in the interview the reason why they preferred this strategy was to provide better understanding of students on limit concept.

___

  • AKKOÇ, H. (2006). Bilgisayar Destekli Matematik Öğretimi: Grafik Analiz Yaklaşımı: İlköğretim İkinci Kademe ve Liseler İçin. Toroslu Kitaplığı: İstanbul.
  • BALL, D. L. (1990). “The Mathematical Understanding that Prospective Teachers Bring to Teacher Education”, Elementary School Journal, 90, 449-466.
  • BEZUIDENHOUT J (2001). “Limits and Continuity: Some Conceptions of First Year Students”, International Journal of Mathematical Education in Science and Technology, 32(4): 487-500. CARLSEN, W.S. (1991). “Effects of New Biology Teachers’ Subject-Matter Knowledge on Curricular Planning”, Science Education. 75, 631-647.
  • CHANG, Y. (2005). The Pedagogical Content Knowledge of Teacher Educator: A Case Study in A Democratic Teacher Preparation Program. Doctoral Dissertation. College of Education of Ohio University.
  • COX, S. (2008). A Conceptual Analysis of Technological Pedagogical Content Knowledge. Doctoral Dissertation, Brigham Young University. CORNU, B. (1991). Limits. In Tall, D. (Ed.) Advanced Mathematical Thinking. Boston: Kluwer, 153-166.
  • DANI, D. E. (2004). The Impact of Content and Pedagogy Courses on Science Teachers’ Pedagogical Content Knowledge. Doctoral dissertation, University of Cincinnati.
  • DAVIS, R. ve VINNER, S. (1986). “The Notion of Limit: Some Seemingly Unavoidable Misconception Stages”, Journal of Mathematical Behavior, 5, 281-303.
  • DeWINDT-KING, A.M., GOLDIN, G. A. (2003). “Children’s visual imagery: Aspects of cognitive representation in solving problems with fractions”, Mediterranean Journal for Research in Mathematics Education, 2 (1), 1-42.
  • DOMINGOS, A. (2009). “Learning Advanced Mathematical Concepts: The Concept of Limit”, Proceedings of CERME 6, January 28th-February 1st 2009, Lyon France. Millî Eğitim Sayı 206 Bahar/2015 183 Matematik Öğretmeni Adaylarının Derslerinde Kullandıkları Limit Kavramına Özgü ... ELIA, I., GAGATSIS, A., PANAOURA, A., ZACHARIADES, T. ve ZOULINAKI, F. (2009). “Geometric and Algebraic Approaches in the Concept of “Limit” and the Impact of the “Didactic Contract””. International Journal of Science and Mathematics Education, 7, 765-790.
  • FERNÁNDEZ-BALBOA, J.-M. ve STIEHL, J. (1995). “The Generic Nature of Pedagogical Content Knowledge among College Professors”, Teaching and Teacher Education, 11, 293–306. GOTTHEINER, D. M., SIEGEL, M. A. (2012). “Experienced Middle School Science Teachers’ Assessment Literacy: Investigating Knowledge of Students’ Conceptions in Genetics and Ways to Shape Instruction“, Journal of Science Teacher Education, 23(5), 531-557.
  • GROSSMAN, P. L. (1990). The Making of a Teacher: Teacher Knowledge and Teacher Education. New York: Teachers College Press.
  • HLAELA MOHLOUOA, N. M. (2011). Exploring PCK in the Process of Teaching Radioactivity: Strategies Employed by Lesotho Physics Teachers. Master thesis, University of the Witwatersrand, Johannesburg.
  • HOFE, R. V. (1997). Problems with the limit concept on a case study of a calculus lesson within computer-based learning environment. _____http://www.fmd.uniosnabrueck.de/ebooks/gdm/PapersPdf1997/vomHofe.pdf.> (15.06.2003).
  • JORDAAN, T. (2005). Misconceptions of the Limit Concept in a Mathematics Course for Engineering Students. Unpublished Master of Science Dissertation, University of South Africa.
  • JUTER, K. (2006). Limits of Functions, University Students’ Concept Development. Doctoral thesis, Lulea University of Technology, Department of Mathematics.
  • MAGNUSSON, S., KRAJCIK, J. ve BORKO, H. (1999). Nature, Sources, and Development of Pedagogical Content Knowledge for Science Teaching. In J. Gess-Newsome & N. Lederman (Eds.), Examining Pedagogical Content Knowledge (95-132). Dordrecht, the Netherlands: Kluwer Academic Publishers.
  • MARKS, R. (1990). “Pedagogical Content Knowledge: From A Mathematical Case to A Modified Conception”, Journal of Teacher Education, 41(3), 3-11.
  • MEB, (2006). Ortaöğretim Matematik Dersi Öğretim Programı. Ankara: MEB Basımevi.
  • MONET, J. A. (2006). Examining Topic-Specific PCK as a Conceptual Framework for In- Service Teacher Professional Development in Earth Science. Doctoral Dissertation, Rutgers The State University of New Jersey, New Brunswick.
  • MUDAU, A. V. (2014). “Lucid Perspectives on the Art of Physical Science Teaching from the South African Context“, Mediterranean Journal of Social Sciences. 5(10), 358-362.
  • NUSANTARI, E. (2014). “Genetics Misconception on High School Textbook, the Impact and Importance on Presenting the Order of Concept through Reorganization of Genetics”, Journal of Education and Practice, 5(36), (20-28).
  • ÖZALTUN, A., HIDIROĞLU, Ç. N., KULA, S. ve GÜZEL, E. B. (2014). “Matematik Öğretmeni Adaylarının Modelleme Sürecinde Kullandıkları Gösterim Şekilleri”, Turkish Journal of Computer and Mathematics Education, 4(2), 66-88.
  • ÖZMANTAR, M.F. ve YEŞILDERE, S. (2008). Matematiksel Kavram Yanılgıları ve Çözüm Önerileri, (8. Bölüm). Ankara: Pegem Yayıncılık.
  • SANCHEZ, R. A. (1996). Teacher’s and Students’ Mathematical Thinking In A Calculus Classroom: The Concept Of Limit, UMI Microform 9700247, Doctoral Dissertation, Florida State University, College of Education, USA. 184 Millî Eğitim Sayı 206 Bahar/2015 Semiha Kula / Esra Bukova Güzel SCHOENFELD, A. H. (1998). “Toward A Theory of Teaching-In-Context”, Issues in Education. 4(1), 1–94.
  • SHULMAN, L. (1986). “Those Who Understand: Knowledge Growth in Teaching”, Educational Researcher. 15, 4-14.
  • SHULMAN, L.S. (1987). “Knowledge and Teaching: Foundations of the New Reform”, Harvard Educational Review. 57(1), 1-22.
  • 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. O., SCHWARZENBERGER, R. L. (1978). “Conflicts in the Learning of Real Numbers and Limits”, Mathematics Teaching. 83, 44-49.
  • TAMIR, P. (1988). “Subject Matter and Related Pedagogical Knowledge in Teacher Education”, Teaching and Teacher Education, 4(2), 99–110.
  • WILLIAMS, S. (1989). Understanding Of The Limit Concept In College Calculus Students. Doctoral Dissertation, The University of Wisconsin, Madison. WILLIAMS, S. R. (2001). “Predications of The Limit Concept: An Application of Repertory Grids”, Journal for Research in Mathematics Education, 32(4), 343-367.
  • WILSON, S. M., SHULMAN, L. S., and RICHERT, A. E. (1987). “150 Different Ways” of Knowing: Representations of Knowledge in Teaching. In J. Calderhead (Eds.), Exploring Teachers’ Thinking (104-124). London: Cassel Education Ltd. YOU, Z. (2006). Preservice Teachers’ Knowledge of Linear Functions within Multiple Representations Modes, Doctoral Dissertation, Texas A&M University.