Öz
–This study is a follow-up of the research, in which the researcher investigated relationship between students’ understanding of functions in Cartesian and Polar Coordinate Systems. Teaching of polar transformation and polar functions was included in the context of transformation concept in the course of Analysis II in a mathematics education program of an education faculty. This teaching process was designed in line of literacy in which the previous study was included. It was showed in the literature that the students who was not given the concept of polar functions could not transfer the function concept to polar coordinates and they use polar coordinates by memorize. It was aimed to examine Analysis II students’ constructions of polar functions in this qualitative study. For data collection, open-ended test and clinical interview techniques were used. Data was analyzed by using the content analysis technique (Yıldırım ve Şimşek, 2003). It was concluded that polar function concept was constructed. Moreover, it was seen that students’ construction of polar functions and their understanding level of function concept were directly related
Anahtar Kelimeler
Kaynakça
- Asiala, M., Brown, A., DeVries, D.J, Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education, 2, 1-32.
- Bakar, M., & Tall, D. (1991). Students’ mental prototypes for functions and graphs. Proceedings of PME 15, Assisi, 1,104–111
- Breidenbach, D., Hawks, J., Nichols, D., & Dubinsky, E. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247–285.
- Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education, 547-589. London: Lawrence Erlbaum Associates, Publishers.
- Cobb, P. & Steffe, L.P. (1983) The Constructivist Researcher as Teacher and Model Builder. Journal for Research in Mathematics Education. 14(2), 83-94.
- Confrey, F. ve 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.
- Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D.Tall, (Ed.), Advanced Mathematical Thinking, (pp.82-94). London: Riedel.
- Dubinsky, E.& Harel, G. (1992). The nature of the process conception of function, In G. Harel and E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA notes 25, 85-106. Mathematical association of America, Washington.
- Ferrini-Mundy, J. & Graham, K. (1990). Functions and their representations. Mathematics Teacher, 83(3), 209-16.
- Ginsburg, H. P. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For Th e Learning of Mathematics, 1(3), 4-11.
- Janvier, C. (1987). Representation and understanding: the notion of functions as an example. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, 67-72, Hillsdale, N.J.: Lawrence Erlbaum Associates.
- Kelly, A. E. & Lesh, R. A. (2000) Handbook of Research Design in Mathematics and Science Education. Lawrence Erlbaum Associates, Publishers: London.
- Miles, M., & Huberman, M. (1994). .An expanded sourcebook qualitative data analysis (2nd ed.). California, CA: Sage Publications.
- Montiel,M., Vidakovic,D.ve Kabael,T. (2008). Relationship between students’ understanding of functions in cartesian and polar coordinate systems", Investigations in Mathematics Learning, 1(2), 52-70.
- Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics. 12, 151– 169
- Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26, 229-274.
- Sierpinska, A. (1992). On understanding the notion of function. In E. Dubinsky & G. Harel (Ed.), The Concept of Function: Aspects of Epistemology and Pedagogy, 25-58. United States: Mathematical Association of America.
- Vinner, S.,& Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356-366.
- Yerushalmy, M. (1997). Designing representations: reasoning about functions of two-variables. Journal for Research in Mathematics Education, 28, 431–466.
- Yıldırım, A., & Şimşek, H. (2003). Sosyal bilimlerde nitel araştırma yöntemleri (beşinci baskı). Ankara: Seçkin Yayıncılık.
Öz
Bu çalışma araştırmacının, üniversite öğrencilerinin fonksiyon kavramını kartezyen ve kutupsal koordinatlarda anlamaları arasındaki ilişkiyi inceleyen önceki çalışmasının devamı niteliğindedir. Bir eğitim fakültesi matematik öğretmenliği programı Analiz II dersi içeriğinde yer alan dönüşümler konusu bağlamında kutupsal dönüşüm ve kutupsal fonksiyonlar kavramlarının öğretimine yer verilmiştir. Bu öğretim süreci, kutupsal fonksiyon kavramına ilişkin araştırmacının da katkı sağladığı, alan yazında bulunan birkaç çalışmanın bulguları ışığında tasarlanmıştır. Bu çalışmalar yalnızca ilişkili matematiksel konularda kutupsal koordinatları kullanan ve kutupsal fonksiyon kavramına ilişkin öğretim yapılmamış olan öğrencilerin fonksiyon kavramını kutupsal koordinatlara taşıyamadıklarını, düşey doğru testi gibi Kartezyen koordinatlarda kullandıkları yöntemleri ezbere kutupsal koordinatlarda kullanmaya çalıştıklarını göstermiştir. Nitel olarak desenlenen bu çalışma ile Analiz II öğrencilerinin kutupsal fonksiyonları oluşturma durumlarının incelenmesi amaçlanmıştır. Çalışmanın verileri açık uçlu test ve klinik görüşme teknikleri ile elde edilmiş ve veriler içerik analizi tekniği ile analiz edilmiştir. Çalışmada Analiz II öğrencilerinin kutupsal fonksiyon kavramını oluşturdukları sonucuna ulaşılmıştır. Ayrıca öğrencilerin kutupsal fonksiyon kavramını oluşturmaları ile fonksiyonları anlama düzeyleri arasında direk bir ilişki olduğu görülmüştür.
Anahtar Kelimeler
kutupsal fonksiyonlar kutupsal koordinatlar fonksiyon kavramı.
Kaynakça
- Asiala, M., Brown, A., DeVries, D.J, Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education, 2, 1-32.
- Bakar, M., & Tall, D. (1991). Students’ mental prototypes for functions and graphs. Proceedings of PME 15, Assisi, 1,104–111
- Breidenbach, D., Hawks, J., Nichols, D., & Dubinsky, E. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247–285.
- Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education, 547-589. London: Lawrence Erlbaum Associates, Publishers.
- Cobb, P. & Steffe, L.P. (1983) The Constructivist Researcher as Teacher and Model Builder. Journal for Research in Mathematics Education. 14(2), 83-94.
- Confrey, F. ve 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.
- Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D.Tall, (Ed.), Advanced Mathematical Thinking, (pp.82-94). London: Riedel.
- Dubinsky, E.& Harel, G. (1992). The nature of the process conception of function, In G. Harel and E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA notes 25, 85-106. Mathematical association of America, Washington.
- Ferrini-Mundy, J. & Graham, K. (1990). Functions and their representations. Mathematics Teacher, 83(3), 209-16.
- Ginsburg, H. P. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For Th e Learning of Mathematics, 1(3), 4-11.
- Janvier, C. (1987). Representation and understanding: the notion of functions as an example. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, 67-72, Hillsdale, N.J.: Lawrence Erlbaum Associates.
- Kelly, A. E. & Lesh, R. A. (2000) Handbook of Research Design in Mathematics and Science Education. Lawrence Erlbaum Associates, Publishers: London.
- Miles, M., & Huberman, M. (1994). .An expanded sourcebook qualitative data analysis (2nd ed.). California, CA: Sage Publications.
- Montiel,M., Vidakovic,D.ve Kabael,T. (2008). Relationship between students’ understanding of functions in cartesian and polar coordinate systems", Investigations in Mathematics Learning, 1(2), 52-70.
- Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics. 12, 151– 169
- Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26, 229-274.
- Sierpinska, A. (1992). On understanding the notion of function. In E. Dubinsky & G. Harel (Ed.), The Concept of Function: Aspects of Epistemology and Pedagogy, 25-58. United States: Mathematical Association of America.
- Vinner, S.,& Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356-366.
- Yerushalmy, M. (1997). Designing representations: reasoning about functions of two-variables. Journal for Research in Mathematics Education, 28, 431–466.
- Yıldırım, A., & Şimşek, H. (2003). Sosyal bilimlerde nitel araştırma yöntemleri (beşinci baskı). Ankara: Seçkin Yayıncılık.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 24 Haziran 2015 |
| Gönderilme Tarihi | 24 Haziran 2015 |
| Yayımlandığı Sayı | Yıl 2015 |