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Öğretmenlerin Fonksiyonlar Konusunda Kullandıkları Örnek Türleri

Year 2017, Volume: 12 Issue: 23, 367 - 384, 28.06.2017

Abstract

Fonksiyon kavramı matematik dersinin önemli konularından biri olmasına rağmen yapılan birçok araştırma, bu konunun öğrenilmesinde öğrencilerin zorluk yaşadıklarını göstermektedir. Bu zorlukların temelini öğrencilerin önemli bir çoğunluğunun fonksiyonlar konusunu öğrenirken fonksiyonun tanımını değil, fonksiyonu açıklamak için kullanılan örnekler, temsiller ve cebirsel kurallar arasından kendi düşünce yapılarıyla uyuşan prototipleri zihinlerine kodlamaları oluşturmaktadır.  Bu nedenle öğretmenlerin fonksiyon konusunda sundukları örnekler öğrencilerin fonksiyonlar konusunu anlamalarında oldukça önemli bir yere sahiptir. Bu çalışmada, iki matematik öğretmenin fonksiyonlar konusunda kullandığı örnek türlerinin belirlenmesi amaçlanmıştır. Çalışma kapsamında yapılandırılmamış gözlemlerden yararlanılmıştır. Verilerin analizinde Bills vd. (2006)’ nin, örnekleri sınıflandırmak için kullanmış oldukları teorik çatıdan yararlanılmıştır.  Elde edilen bulgularda öğretmenlerin derslerinde jenerik örneklerden ve örnek olmayan örneklerden sıklıkla yararlandıkları, buna karşın derslerinde karşıt örnekleri hiç vermedikleri tespit edilmiştir. 

References

  • Bayazıt İ. & Aksoy Y. (2010). Öğretmenlerin fonksiyon kavramı ve öğretimine ilişkin pedagojik görüşleri. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 9(3), 697 -723.
  • Bayazit, I. & Gray, E. (2004). Understanding inverse functions: The relationship between teaching practice and student learning. In M. J. Honies & A. B. Fuglestad (Eds.), Proceedings of 28th Conference of the International Group for the Psychology of Mathematics Education (Vol 2, pp. 103-110), Norway: Bergen.
  • Bills, L., Mason, J., Watson, A., & Zaslavsky, O. (2006). Exemplification: The use of examples in teaching and learning mathematics. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol 1, pp. 125-154). Prague: PME.
  • Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247-285.
  • Carlson, M. P. (1998). A cross-sectional investigation of the development of the functions concept. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education. III. CBMS issues in mathematics education (pp. 114-162). Providence, RI: American Mathematical Society.
  • DeMarois, P. & Tall, D.O. (1996). Facets and layers of the function concept. Proceedings of 20th Conference of the International Groupfor the Psychology of Mathematics Education (Vol. 2, pp.297-304). Valencia.
  • Dubinsky, Ed. & Harel, G. (1992). The concept of function: Aspects of epistemology and pedagogy. United States of America: Mathematical Association of America. Evangelidou, A., Spyrou, P., Elia, I., & Gagatsis, A. (2004). University student’s conceptions of function. Proceedings of The 28 th Conference of The International Group for The Psychology of Mathematics Education, (Vol 2, pp. 351-358).
  • Gökbulut, Y. (2010). Sınıf öğretmeni adaylarının geometrik cisimler konusundaki pedagojik alan bilgileri. (Yayımlanmamış doktora tezi). Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.
  • Gökbulut, Y. & Ubuz, B. (2013). Sınıf öğretmeni adaylarının prizma bilgileri: tanım ve örnekler oluşturma. İlköğretim Online, 12(2), 401-412.
  • Gökkurt, B. (2014). Ortaokul matematik öğretmenlerinin geometrik cisimler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi, Yayımlanmamış doktora tezi, Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum.
  • Güler, M., Bülbül, B., Güven, B., Bülbül, S., Alkan, S., & Baki, A. (2015, Mayıs). Lise öğrencilerinin sahip oldukları kavram imgeleri ve prototiplerin fonksiyon konusu bağlamında incelenmesi. 2. Türk Bilgisayar ve Matematik Eğitimi Sempozyumunda sunulan sözlü bildiri. Adıyaman: Adıyaman Üniversitesi. Lakoff, G. (1987). Women, fire, and dangerous things. Chicago: University of Chicago Press.
  • Libarkin, J. C., & Kurdziel, J. P. (2002). Research methodologies in science education: The qualitative-quantitative debate. Journal of Geoscience Education, 50(1), 78-86.
  • Mason, J. & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15,(3) 227-289.
  • Merriam, Sharan B. (1998). Qualitative research and case study applications in education. revised and expanded from case study research in education. San Francisco: Jossey-Bass Publishers.
  • Michener, E. (1978). Understanding mathematics. Cognitive Science, 2, 361-383.
  • Mittal, V. O. & Paris, C. L. (1993). Categorizing example types in instructional texts: The need to consider context (No. ISI-RR-93-332). University of Southern California Marina Del Rey information Sciences Inst.
  • Muir, T. (2007). Setting a good example: Teachers' choice of examples and their contribution to effective teaching of numeracy. In J. Watson & K. Beswick (Eds.), Mathematics. Essential research, essential practice. Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, Hobart, (pp. 513-522). Adelaide, SA: MERGA.
  • Özdemir Erdoğan E., Erdoğan A., & Yanık B. H. (2012). İlköğretim matematik öğretmenliği programı birinci sınıf öğrencilerinin fonksiyonlar konusundaki hazırbulunuşlukları. Gaziantep University Journal of Social Sciences, 11(4), 1121-1149.
  • Özyürek, M (1984). Kavram öğrenme ve öğretme. Ankara Üniversitesi Eğitim Bilimleri Dergisi, 16(2), 347-366.
  • Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, 69(2), 149-163.
  • Senemoğlu, N. (1997). Gelişim öğrenme ve öğretim kuramdan uygulamaya. Ankara: Spot Matbaacılık.
  • Tall, D. O. & Bakar, M. (1992). Students’ mental prototypes for functions and graphs. International Journal of Math, Education, Science, and Technology, 23(1), 39–50.
  • Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive on examples: the case of triangles Educational Studies in Mathematics. 69, 81–95.
  • Ural A. (2006). Fonksiyon öğreniminde kavramsal zorluklar. Ege Eğitim Dergisi, 7(2), 75-94.
  • Watson, A. & Mason, J. (2002a). Extending example spaces as a learning/teaching strategy in mathematics. In PME Conference (Vol. 4, pp. 4-377).
  • Watson, A., & Mason, J. (2002b). Student-generated examples in the learning of mathematics. Canadian Journal of Science, Mathematics and Technology Education, 2(2), 237-249.
  • Watson, A. & Mason, J. (2005). Mathematics as a constructiveactivity: Learners generating examples. Mahwah, NJ: Erlbaum.
  • Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305.
  • 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.
  • Zaslavsky, O. (2010). The explanatory power of examples in mathematics: Challenges for teaching. In Instructional explanations in the disciplines (pp. 107-128). Springer US.
  • Zazkis, R. & Chernoff, E. (2006). Cognitive conflict and its resolution via pivotal/bridging example. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 465-472). Prague: PME.
  • Zodik, I. & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom. Educational Studies in Mathematics, 69(2), 165-182.

The Types of Examples Teachers Use in Teaching Function Concept

Year 2017, Volume: 12 Issue: 23, 367 - 384, 28.06.2017

Abstract

Although the concept of function is one of the important subject of mathematics courses, many studies show that learners have difficulty in this subject. The basis of these difficulties is that most students encode the prototypes of examples, representations and algebraic rules used for explaining function concept, which match with their own thinking, instead of the definition of function at learning the functions. Therefore, the examples which teachers present in the functions have an important roles in students’ learning on this subject. In this study, it is aimed to determine the types of examples which two teachers use in the functions. In the scope of the study, it is made use of unstructured observations and informal interviews. The theoretical framework which Bills et al (2006) use in classification of examples, is utilized in analyzing the data. In the findings, it is found that the teachers use generic examples and non-examples in their lessons, despite that they don’t use counter examples

References

  • Bayazıt İ. & Aksoy Y. (2010). Öğretmenlerin fonksiyon kavramı ve öğretimine ilişkin pedagojik görüşleri. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 9(3), 697 -723.
  • Bayazit, I. & Gray, E. (2004). Understanding inverse functions: The relationship between teaching practice and student learning. In M. J. Honies & A. B. Fuglestad (Eds.), Proceedings of 28th Conference of the International Group for the Psychology of Mathematics Education (Vol 2, pp. 103-110), Norway: Bergen.
  • Bills, L., Mason, J., Watson, A., & Zaslavsky, O. (2006). Exemplification: The use of examples in teaching and learning mathematics. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol 1, pp. 125-154). Prague: PME.
  • Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247-285.
  • Carlson, M. P. (1998). A cross-sectional investigation of the development of the functions concept. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education. III. CBMS issues in mathematics education (pp. 114-162). Providence, RI: American Mathematical Society.
  • DeMarois, P. & Tall, D.O. (1996). Facets and layers of the function concept. Proceedings of 20th Conference of the International Groupfor the Psychology of Mathematics Education (Vol. 2, pp.297-304). Valencia.
  • Dubinsky, Ed. & Harel, G. (1992). The concept of function: Aspects of epistemology and pedagogy. United States of America: Mathematical Association of America. Evangelidou, A., Spyrou, P., Elia, I., & Gagatsis, A. (2004). University student’s conceptions of function. Proceedings of The 28 th Conference of The International Group for The Psychology of Mathematics Education, (Vol 2, pp. 351-358).
  • Gökbulut, Y. (2010). Sınıf öğretmeni adaylarının geometrik cisimler konusundaki pedagojik alan bilgileri. (Yayımlanmamış doktora tezi). Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.
  • Gökbulut, Y. & Ubuz, B. (2013). Sınıf öğretmeni adaylarının prizma bilgileri: tanım ve örnekler oluşturma. İlköğretim Online, 12(2), 401-412.
  • Gökkurt, B. (2014). Ortaokul matematik öğretmenlerinin geometrik cisimler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi, Yayımlanmamış doktora tezi, Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum.
  • Güler, M., Bülbül, B., Güven, B., Bülbül, S., Alkan, S., & Baki, A. (2015, Mayıs). Lise öğrencilerinin sahip oldukları kavram imgeleri ve prototiplerin fonksiyon konusu bağlamında incelenmesi. 2. Türk Bilgisayar ve Matematik Eğitimi Sempozyumunda sunulan sözlü bildiri. Adıyaman: Adıyaman Üniversitesi. Lakoff, G. (1987). Women, fire, and dangerous things. Chicago: University of Chicago Press.
  • Libarkin, J. C., & Kurdziel, J. P. (2002). Research methodologies in science education: The qualitative-quantitative debate. Journal of Geoscience Education, 50(1), 78-86.
  • Mason, J. & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15,(3) 227-289.
  • Merriam, Sharan B. (1998). Qualitative research and case study applications in education. revised and expanded from case study research in education. San Francisco: Jossey-Bass Publishers.
  • Michener, E. (1978). Understanding mathematics. Cognitive Science, 2, 361-383.
  • Mittal, V. O. & Paris, C. L. (1993). Categorizing example types in instructional texts: The need to consider context (No. ISI-RR-93-332). University of Southern California Marina Del Rey information Sciences Inst.
  • Muir, T. (2007). Setting a good example: Teachers' choice of examples and their contribution to effective teaching of numeracy. In J. Watson & K. Beswick (Eds.), Mathematics. Essential research, essential practice. Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, Hobart, (pp. 513-522). Adelaide, SA: MERGA.
  • Özdemir Erdoğan E., Erdoğan A., & Yanık B. H. (2012). İlköğretim matematik öğretmenliği programı birinci sınıf öğrencilerinin fonksiyonlar konusundaki hazırbulunuşlukları. Gaziantep University Journal of Social Sciences, 11(4), 1121-1149.
  • Özyürek, M (1984). Kavram öğrenme ve öğretme. Ankara Üniversitesi Eğitim Bilimleri Dergisi, 16(2), 347-366.
  • Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, 69(2), 149-163.
  • Senemoğlu, N. (1997). Gelişim öğrenme ve öğretim kuramdan uygulamaya. Ankara: Spot Matbaacılık.
  • Tall, D. O. & Bakar, M. (1992). Students’ mental prototypes for functions and graphs. International Journal of Math, Education, Science, and Technology, 23(1), 39–50.
  • Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive on examples: the case of triangles Educational Studies in Mathematics. 69, 81–95.
  • Ural A. (2006). Fonksiyon öğreniminde kavramsal zorluklar. Ege Eğitim Dergisi, 7(2), 75-94.
  • Watson, A. & Mason, J. (2002a). Extending example spaces as a learning/teaching strategy in mathematics. In PME Conference (Vol. 4, pp. 4-377).
  • Watson, A., & Mason, J. (2002b). Student-generated examples in the learning of mathematics. Canadian Journal of Science, Mathematics and Technology Education, 2(2), 237-249.
  • Watson, A. & Mason, J. (2005). Mathematics as a constructiveactivity: Learners generating examples. Mahwah, NJ: Erlbaum.
  • Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305.
  • 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.
  • Zaslavsky, O. (2010). The explanatory power of examples in mathematics: Challenges for teaching. In Instructional explanations in the disciplines (pp. 107-128). Springer US.
  • Zazkis, R. & Chernoff, E. (2006). Cognitive conflict and its resolution via pivotal/bridging example. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 465-472). Prague: PME.
  • Zodik, I. & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom. Educational Studies in Mathematics, 69(2), 165-182.
There are 32 citations in total.

Details

Journal Section Research Article
Authors

Sevilay Alkan

Bülent Güven This is me

Şerife Yılmaz This is me

Publication Date June 28, 2017
Submission Date April 6, 2017
Published in Issue Year 2017 Volume: 12 Issue: 23

Cite

APA Alkan, S., Güven, B., & Yılmaz, Ş. (2017). The Types of Examples Teachers Use in Teaching Function Concept. Bayburt Eğitim Fakültesi Dergisi, 12(23), 367-384.