Author :
Abstract
Pek çok matematik kavramı gibi fonksiyon kavramı öğretiminde de farklı gösterim şekillerinin kullanımı oldukça önemlidir. Bu kavramın öğretiminde farklı gösterim şekillerinin kullanılması ve gösterim şekilleri arasında geçişlerin yapılması öğrencilerin bu kavramı öğrenmesinde yardımcı olmaktadır. Bu nedenle matematik öğretmenlerinin gösterim şekilleri bilgilerinin geliştirilmesi gerekmektedir. Bu araştırmanın amacı matematik öğretmenlerinin fonksiyon kavramına yönelik gösterim şekilleri bilgilerinin gelişiminin incelenmesidir. Nitel araştırma yaklaşımının benimsendiği çalışmada veriler gönüllü altı matematik öğretmeninin fonksiyon kavramı öğretimlerinin gözlenmesi ile toplanmıştır. Verilerin analiz edilmesi sonucunda, araştırma süresince matematik öğretmenlerinin gösterim şekilleri bilgilerinin geliştiği belirlenmiştir. Araştırmada, öğretmenlere verilen eğitimin gösterim şekilleri bilgilerinin gelişimine katkı sağlandığı sonucuna ulaşılmıştır. Matematik öğretmenlerinin mesleki gelişimi konusunda öneriler sunulmuştur.
Keywords
Abstract
Using different representations is important for teaching function concept like many other concepts in mathematics. For teaching this concept, using different forms of representations and transferring between them help students learn this concept. Therefore, mathematics teachers’ knowledge of representations need to be improved. The aim of this study is to examine the development of mathematics teachers’ knowledge of representations towards function concept. Data of the study that qualitative research approach has been adopted collected via observations of six volunteer mathematics teachers’ lessons. By the analysis of the data, it is determined that mathematics teachers’ knowledge of representations has developed during the research. It is concluded that the training provided for teachers contributed their development of knowledge of representations. Suggestions were presented about mathematics teachers’ professional development.
Keywords
- Akkoç, H. (2005). Fonksiyon Kavramının Anlaşılması: Çoğul Temsiller ve Tanımsal Özellikler. Eğitim Araştırmaları Dergisi, 20, 14 - 24.
- Akkoç, H. (2006). Concept Images Evoked By Multiple Representations of Functions, Hacettepe University Journal of Education, 30, 1-10.
- Akkoç, H., Özmantar, F., Bingölbali, E., Yavuz, İ., Baştürk, Ş., & Demir, S. (2011). Matematik Öğretmen Adaylarına Teknolojiye Yönelik Pedagojik Alan Bilgisi Kazandırma Amaçlı Bir Program Geliştirme. Tübitak Projesi, 107K531, 2008- 2011.
- Altun, M. (1998). Matematik Öğretimi. Açıköğretim Fakültesi Yayınları, No:591.
- Bakar, M. & Tall, D. (1992). Students Mental Prototypes for Functions and Graphs. International Journal of Mathematics Education in Science and Technology. 23(1), 39-50.
- Baki, A. (2006). Kuramdan Uygulamaya Matematik Eğitimi. Derya Kitabevi: Trabzon.
- Başer, N., Narlı S., & Cantürk Günhan B,(2005). Öğretmenlerin Lisansüstü Eğitim Almalarında Yaşanan Sorunlar ve Çözüm Önerileri, Dokuz Eylül Üniversitesi Eğitim Fakültesi Dergisi. 17, 129-135.
- Bayazit, İ.& Aksoy, Y. (2010). Öğretmenlerin Fonksiyon Kavramı ve Öğretimine İlişkin Pedagojik Görüşleri. Gaziantep Üniversitesi Sosyal Bilimler Dergisi. 9(3): 697 723.
- Confrey, F. & Smith, E. (1991). A Framework for Functions: Prototypes, Multiple Representations and Transformations. In R.G. Underhill (Ed.), Proceedings of The 13th Annual Meeting of The North American Chapter of The International Group For The Psychology of Mathematics Education, 57-63, Blacksburg: Virginia Polytechnic Institute and State University.
- Cunningham, R. F. (2005). Algebra Teachers’ Utilization of Problems Requiring Transfer Between Algebraic, Numeric and Graphic Representations. School Science & Mathematics, 105(2), 73-82.
- Denzin, N.K., & Lincoln, Y.S. (2005). The SAGE Handbook of QualitativeResearch, Third Edition. Thousand Oaks, CA: Sage Publications.
- Dubinsky, E. (1991). Reflective Abstraction in Advanced Mathematical Thinking. In D. O. Tall (Ed.), Advanced Mathematical Thinking (pp. 95-126). Dordrecht: Kluwer.
- Eisenberg, T. (1991). Function and Associated Learning Difficulties. In D. O. Tall (Ed.). Advanced Mathematical Thinking. (pp. 140-152). Dordrecht: Kluwer Academic Publishers.
- Even, R. D. (1989). Prospective Secondary Mathematics Teachers’ Knowledge and Understanding of Mathematical Functions. Unpublished Doctorial Dissertation. Michigan State University.
- Friedlander, A. & Tabach, M. (2001). Promoting Multiple Representations in Algebra. In A.A. Cuoco & F.R. Curcio (Eds.), The Roles of Representation in School Mathematics (2001 yearbook) (pp. 173-185). Reston, VA: National Council of Teachers of Mathematics.
- Gagatsis, A. & Shiakalli, M. (2004) Ability to Translate from One Representation of the Concept of Function to Another and Mathematical Problem Solving, Educational Psychology: An International Journal of Experimental Educational Psychology, 24: 5, 645-657, DOI: 10.1080/0144341042000262953
- Goldenberg, E. P. (1995). Multiple Representations: A Vehicle for Understanding Understanding. In D. N. Perkins, J. L. Schwartz, M. M. West, & M. S. Wiske (Eds.), Software Goes to School: Teaching for Understanding with New Technologies (pp. 155-171). New York: Oxford University Press.
- Gray, E. & Tall, D. (1994). Duality, Ambiguity, and Flexibility: A Proceptual View of Simple Arithmetic. Journal for Research in Mathematics Education. 26(2), 115141.
- Hacıömeroğlu, G. (2006). Prospective Secondary Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge of The Concept of Function. Unpublished Doctoral Dissertation. Florida State University, USA.
- Higgins, J. & Parsons, R. (2009). A Successful Professional Development Model in Mathematics: A System- Wide New Zealand Case. Journal of Teacher Education. 60(3), 231- 242.
- Howald, C. L. (1998). Secondary Teachers’ Knowledge of Functions: Subject Matter Knowledge, Pedagogical Content Knowledge, and Classroom Practice. Unpublished Doctorial Dissertation. The University of Iowa.
- Hyde, P. R. (2003). Assessing Mathematical Thinking and Understanding in the Third Grade. [Print] North Central Regional Educational Laboratory. http://ww.ncrel.org/mands/docs/6-2.htm (erişim tarihi: 22 Ocak 2011).
- Kabael, T.U. (2010). Fonksiyon Kavramı: Tarihi Gelişimi, Öğrenilme Süreci, Öğrenci Yanılgıları ve Öğretim Stratejileri. Tübav Bilim Dergisi. 3(1), 128-136.
- Karahasan, B. (2010). Preservice Secondary Mathematics Teachers’ Pedagogical Content Knowledge of Composite and Inverse Functions. Unpublished Doctoral Dissertation. Middle East Technical University, Turkey.
- 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.
- Kovarik, K. (2008). Mathematics Educators' and Teachers' Perceptions of Pedagogical Content Knowledge. Doctoral Dissertation. Columbia University, Graduate School of Arts and Sciences.
- Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, Graphs and Graphing: Tasks, Learning, and Teaching. Review of Educational Research. 60, 1-64.
- Loucks-Horsley, S., Love, N., Stiles, K., Mundry, S., & Hewson, P. (2003). Designing Professional Development for Teachers of Science and Mathematics. Thousand Oaks, CA: Corwin Press.
- Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, Sources and Development of Pedagogical Content Knowledge for Science Teaching. In J. GessNewsome and N.G. Lederman (Eds.), Examining Pedagogical Content Knowledge. (95–132). Dordrecht, The Netherlands: Kluwer Academic Publishers.
- National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston: NCTM.
- National Council of Teachers of Mathematics (2000). Principles And Standarts For School Mathematics. Reston, VA: NCTM.
- Patton, M. Q. (2002). Qualitative Research & Evaluation Methods: (3rd ed.). Thousand Oaks, CA: Sage Publications.
- Piez, C. M. & Voxman, M. H. (1997). Multiple Representations—Using Different Perspectives to Form a Clearer Picture. The Mathematics Teacher. 90(2), 164-166.
- Ponte, J. P. (1992). The History of the Concept of Function and Some Educational Implications.
- Selden, A. & Selden, J. (1992). Research Perspective on Conceptions of Functions: Summary and Overview In G. Harel and E. Dubinsky (Eds). The Concept of Function: Aspects of Epistemology and Pedagogy, 1-16, Washington. DC: Mathematical Association Of America.
- Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin. Educational Studies in Mathematics, 22, 1-36.
- Sierpinska, A. (1992). On Understanding the Notion of Functions. In Harel G. & Dubinsky E.(Eds.), MAA Notes and Reports Series. 25-58.
- Sowder, J. T. (2007). The Mathematical Education and Development of Teachers. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp: 157-223). Charlotte, NC: Information Age Publishing.
- Steele, M.D., Hillan, A.F., & Smith, M.S. (2013). Developing Mathematical Knowledge for Teaching in a Methods Course: The Case of Function. Journal of Mathematics Teacher Education. 16 (6), 451-482.
- Tall, D. (1992). The Transition to Advanced Mathematical Thinking: Functions, Limits, Infinity, and Proof, in Grouws D.A. (ed.) Handbook of Research on MathematicsTeaching and Learning, Macmillan, New York, 495– 511.
- Tall, D. O. & Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Special Reference to Limits and Continuity. Educational Studies in Mathematics. 12, 151–169.
- Tataroğlu-Taşdan, B. & Çelik, A. (2014). Matematik Öğretmenlerine Yönelik Bir Mesleki Gelişim Programı Prototipi. NWSA-Education Sciences, 1C0621, 9(3), 323-340.
- Thompson, P. W. (1994). Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus. Educational Studies in Mathematics, 26, 229-274.
- Ubuz, B. (1996). Evaluating the impact of computers on the learning and teaching of calculus. Unpublished Doctoral Dissertation, University of Nottingham, UK.
- Ural, A. (2006). Fonksiyon Öğreniminde Kavramsal Zorluklar. Ege Eğitim Dergisi. 7(2), 75–94.
- Ural, A. (2012). Fonksiyon Kavramı: Tanımsal Bilginin Kavramın Çoklu Temsillerine Transfer Edilebilmesi ve Bazı Kavram Yanılgıları. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi. Sayı 31 (Ocak 2012/I), ss. 91-103.
- Vinner, S. (1983). Concept Definition, Concept Image and the Notion of Function. International Journal of Mathematical Education in Science and Technology. 14, 293–305.
- Vinner, S. & Dreyfus, T. (1989). Images and Definitions of the Concept of Function. Journal for Research in Mathematics Education. 20, 356-366.
- Yerushalmy, M. & Schwartz, J. L. (1993). Seizing the Opportunity to make Algebra Mathematically and Pedagogically Interesting. In Romberg, T. A., Fennema, E., & Carpenter, T. P. (Eds.), Integrating Research on the Graphical Representation of Functions (pp. 41-68). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Yılmaz, M. (2007). Sınıf Öğretmeni Yetiştirmede Teknoloji Eğitimi, Gazi Eğitim Fakültesi Dergisi. Cilt 27, Sayı 1, 155-167.
- Yıldırım, A. & Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (6.Baskı). Ankara: Seçkin Yayıncılık.
