FONKSİYON ÖĞRENİMİNDE KAVRAMSAL ZORLUKLAR

Year 2006, Volume: 7 Issue: 2, 75 - 94, 01.08.2006

Alattin Ural

Abstract

Fonksiyon kavramı matematikte en önemli ve temel fikirlerden biridir Matematikteki çoğu kavramın tanımlanmasında ve kavramlar arası geçişin sağlanmasında birleştirici bir rol oynar Öğrenciler fonksiyon kavramı ile ilk olarak dokuzuncu sınıfta karşılaşırlar ve bu kavram onlara oldukça soyut ve anlaşılmaz gelir Fonksiyon kavramını yapısal boyutuyla kavramada birtakım zorluklar ve kavram yanılgıları yaşarlar Bu zorluklar ve kavram yanılgıları oldukça çeşitlidir Bunlar genellikle; fonksiyonun çeşitli gösterimleri bu gösterimler arası geçişler fonksiyonla ilgili notasyonlar sembolik yazılımlar ters fonksiyon bileşke fonksiyon ile ilgili kavramsal bilgilerdir Bunların aşılmasında öğretmenin fonksiyon kavramıyla ilgili hazırlayacağı öğretim materyallerinin içeriğin ve kullanacağı öğretim yönteminin önemi büyüktür Bu çalışmada; yaşanan bilişsel zorluklara kavram yanılgılarına ve fonksiyon kavramının hangi temelde öğretilmesi gerektiğine dair geniş bir literatür bilgisi verilmeye çalışılmıştır

Keywords

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Conceptual Obstacles Concerning the Learning of the Function

Abstract

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Keywords

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References

• Anastasia, E., Spyrou, P., Elia, I. ve Gagatsis, A. (2004). University Students’ Conceptions of Function. Proceedings of the 28th Conference of the Interntional Group for the Psychology of Mathematics Education, 2, (sf. 351-358).
• Altun, M. (1998). Matematik Öğretimi. Açıköğretim Fakültesi Yayınları, No:591.
• Biehler, R., Scholz, R. ve Winkelmann, B. (1993). Reflections on Mathematical Concepts As Points For Mathematical Thinking. Didactic of Mathematics as a Scientific Discipline, Dordrect, Boston, London, (sf. 61-72).
• Bowman, A.H. (1993). A Theoretical Framework for Research in Algebra: Modification of Janvier’s “Star” Model of Function Understanding. The Annual Meeting Of The American Educational Research Association, Atlanta, GA, April 12-16.
• Breslich, E. R. (1928): Developing functional thinking in secondary school mathematics. (ed. NCTM). The Third Yearbook (42–56). New York, NY: NCTM, Teachers College, Columbia University.
• Carlson, M. P. (1998). A cross-sectional investigation of the development of the function concept. Research in Collegiate Mathematics Education III, CBMS Issues in Mathematics Education.. 7, (sf. 114–163).
• Carlson, M. ve Oehrtman, M. (2005). Key Aspects of Knowing and Learning the Concept of Function. The Mathematical Association of America (Research Sampler).
• Carlson, M., Oehrtman, M. ve Engelke, N. (2005). Composition of Functions: What do Precalculus Level Students Understand? Proceedings of the 27th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Eugene, OR: All Academic.
• Cramer, K. (2001). Using Models To Build An Understanding Of Functions. Mathematics Teaching In The Middle School, 6(5), (sf. 310-318).
• Davidenko, S. (1997). Building The Concept Of Function From Students’ Everyday Activities. Mathematics Teacher, 90, (sf. 144-149).
• Davidson, P.M. (1987). Early Function Concepts: Their Development and Relation to Certain Mathematical and Logical Abilities. The Society for Research in Child Developmant, 58, (sf. 1542-1555).
• Dede, Y. (2005). Değişken Kavramı Üzerine. Kastamonu Eğitim Dergisi, 13(1), (sf. 139-148).
• Dennis, E.C. (2001). An investigation of the numerical experience associated with the global behavior of Polynomial Functions in the traditional Lecture Method and Cooperative Learning Method Classes. Yayınlanmamış Doktora Tezi. Graduate Faculty of the University of New Orleans.
• Dikici, R. (2003). Bağıntı ve Fonksiyon Konusundaki Öğrenme Güçlüklerinin Bazı Değişkenler Açısından İncelenmesi. Kastamonu Eğitim Dergisi, 11(2), (sf. 105-116).
• Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), (sf. 94–116).
• Hedrick, E.R. (1938). The Function Concept in Elementary Teaching and in Advanced Mathematics. The American Mathematical Monthly, 45(7), (sf. 448-455).
• Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In Wagner, S. ve Carolyn, K. (Eds.), Research issues in the learning and teaching of algebra. Reston, VA: National Council of Teachers of Mathematics.
• Hight, D. W. (1968). Functions: dependent variables to fickle pickers. Mathematics Teacher. 61(6), (sf. 575-579).
• Hitt, F. (1998). Diffuculties in the Articulation of Different Representations Linked to the Concept of Function. Journal of Mathematical Behavior, 17(1), (sf. 123-134).
• Işık, C., Albayrak, M. ve İpek, A.S. (2005). Matematik Öğretiminde Kendini Gerçekleştirme. Kastamonu Eğitim Dergisi, 13(1), (sf. 129-138).
• Janvier, C. (1998). The Notion of Chronicle as an Epistemological Obstacle to the Concept of Function. Journal of Mathematical Behavior, 17(1), (sf. 79-103).
• Kleiner, I. (1989). Evolution Of The Function Concept: A Brief Survey. The College Mathematics Journal, 20(4), (sf. 282-300).
• Malik, M.A. (1980). Historical and pedagogical aspects of the definition of function.
• International Journal of Mathematics Education in Science and Technology, 11, (sf. 489-492).
• Meel, D.E. (1999). Prospective Teachers’ Understandings: Function and Composite Function. Issues in the Undergraduate Mathematics Preparation of School Teachers:The Journal, 1, October.
• Monk, G.S. (1992). Students’ understanding of a function given by a physical model. (ed. G. Harel, E. Dubinsky). The concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America, Washington, D.C. (sf. 175-194).
• Monk, S., Nemirovsky, R. (1994). The case of Dan: Student construction of a functional situation through visual attributes. CBMS Issues in Mathematics Education: Research in Collegiate Mathematics Education. 4, (sf. 139–168).
• Moschkovich, J.N. (2004). Appropriating Mathematical Practise: A Case Study of Learning to Use and Explore Functions Through Interaction with a Tutor. Educational Studies in Mathematics, 55, (sf. 49-80).
• Olsen, J.R. (1995). The Effect Of The Use Of Number Lines Representations On Student Understanding Of Basic Function Concepts. The Annual Meeting Of The North American Chapter of the International Group for the Psychology Of Mathematics Education. (sf. 21-24). 17th PME-NA, Columbus, OH, October.
• Rho, K. (2000). A Case Study on the Changes of University Students’ Function Concept in a Virtual Environment. The Annual Meeting Of The American Educational Research Association. (sf. 24-28). New Orleans, LA, April.
• Sajka, M. (2003). A Secondary School Students’s Understandings Of The Concept Of Function-A Case Study. Educational Studies in Mathematics, 53, (sf. 229-254).
• Schaaf, W.A. (1930). Mathematics and World History. Mathematics Teacher. 23, (sf. 496- 503).
• 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 Mathematic, 22, (sf. 1-36).
• Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification -- The case of function. (ed. G. Harel, E. Dubinsky). The concept of function: Aspects of epistemology and pedagogy (MAA Notes, 25, 59-84), Washington.
• Sierpinska, A. (1992). On understanding the notion of function. (ed. E. Dubinsky, G. Harel). The Concept of Function: Aspects of Epistemology and Pedagogy, Mathematical Association of America (M.A.A.) Notes, 25, (sf. 25–58).
• Thompson, P. W. (1994). Students, functions, and the undergraduate mathematics curriculum. (ed. E. Dubinsky, A. H. Schoenfeld ve J. J. Kaput), Research in Collegiate Mathematics Education, 1 (Issues in Mathematics Education. 4, 21-44). Providence, RI: American Mathematical Society.
• Ural, A. (2007). İşbirlikli Öğrenmenin Matematikteki Akademik Başarıya, Kalıcılığa, Matematik Özyeterlilik Algısına ve Matematiğe Karşı Tutuma Etkisi. Yayınlanmamış Doktora Tezi, Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
• Vinner, S. ve Dreyfus, T. (1989). Images and definitions for the concept of function. Journalfor Research in Mathematics Education. 20(4), (sf. 356-366).
• Wilson, M. ve Lloyd, G. (1998). Supporting Innovation: The Impact of a Teacher’s
• Conceptions of Functions on His Implementation of a Reform. Journal for Research
• in Mathematics Education. 29(3), (sf. 248-274).