PROSPECTIVE TEACHERS’ UNDERSTANDING OF EQUATION, FUNCTION and POLYNOMIAL CONCEPTS

Yıl 2010, Cilt: 18 Sayı: 1, 67 - 88, 01.01.2010

Yüksel Dede İbrahim Bayazit Danyal Soybaş

Öz

The main purpose of this study is to explore prospective teachers’ understanding of function, equation and polinomials concepts and the relationships between these notions. The research sample includes 117 students from Gazi and Cumhuriyet Universities. Qualitative and quantitative methods were employed in this study. The notions of conceptual knowledge and concept images were used to establish a theoretical framework for the study. Research findings indicate that prospective teachers had sufficient knowledge related to function, equation and polinomials concepts, yet they demonstrated a lack of understanding concerning the relationships between these notions.

Anahtar Kelimeler

Function, equation, polinomials, conceptual knowledge, concept images.

ÖĞRETMEN ADAYLARININ DENKLEM, FONKSİYON VE POLİNOM KAVRAMLARINI ANLAMALARI

Öz

Bu çalışmada öğretmen adaylarının fonksiyon, denklem ve polinom kavramları ve bu kavramlar arasındaki ilişkilere ait bilgi düzeyleri incelenmiştir. Araştırmanın çalışma grubu, Gazi ve Cumhuriyet Üniversitesinden toplam yüz onyedi 117 matematik öğretmeni adayından oluşmaktadır. Veri toplama ve analiz aşamalarında nitel ve nicel araştırma yöntemlerinin araçları bütünleşik olarak kullanılmıştır. Çalışmaya teorik temel teşkil etmek üzere, literatürdeki kavramsal bilgi ve kavram imajları gibi farklı kavramlardan yararlanılmıştır. Çalışmadan elde edilen bulgular, öğretmen adaylarının fonksiyon, denklem ve polinom kavramlarından her birine ilişkin yeterli düzeyde bilgiye sahip olmakla birlikte bu kavramlar arasındaki içeriksel ilişkileri anlamada oldukça yetersiz kaldıklarını göstermektedir.

Anahtar Kelimeler

fonksiyon, denklem, polinom, kavramsal bilgi, kavram imajları

Kaynakça

• 1. Askew, M., Brown, M., Rhodes, V., William, D. & Johnson, D. (1996), ‘Effective Teachers of Numeracy’, London: King’s College.
• 2. Ball, D. L. (1991), ‘Research on Teaching Mathematics: Making Subject-Matter Knowledge Part of the Equation’, in J. Brophy (Ed.), Advances in Research on Teaching, Greenwich, CT: JAI Press, 2, pp. 1-48.
• 3. Bayazit (2006), ‘The Relationship between Teaching and Learning Through the Context of Functions’, Unpublished PhD Thesis, University of Warwick, United Kingdom.
• 4. Breidenbach, D., Dubinsky, Ed., Hawks, J., & Nichols, D. (1992), ‘Development of the Process Conception of Function’, Educational Studies in Mathematics, 23(3), pp. 247- 285.
• 5. Bromme, R. (1995), ‘What Exactly Is Pedagogic Content Knowledge? Critical Remarks Regarding a Fruitful Research Program’, in S. Hopmann & K. Riquarts (Eds.), Didactic and/or Curriculum, IPN Schriftenreihe, Kiel: IPN, 147, pp. 205-216.
• 6. Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Thousand Oaks, CA: Sage Publications.
• 7. DeMarois, P & Tall, D. (1996). Facets and Layers of the Function Concept. Proceedings of PME 20, Valencia, vol. 2, 297-304.
• 8. Dubinsky, Ed. & Harel, G. (1992), ‘The Nature of the Process Conception of Function’, in G. Harel & Ed. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy, United States of America: Mathematical Association of America, pp. 85- 107.
• 9. Eisenberg, T. (1991), ‘Function and Associated Learning Difficulties’, in D.O.Tall (Ed.), Advanced Mathematical Thinking, Dordrecht: Kluwer Academic Publishers, pp. 140- 152.
• 10. Even, R. & Tirosh, D. (2001), ‘Teacher Knowledge and Understanding of Students’ Mathematical Learning’, in L. English (Ed.), Handbook of international research in mathematics education, USA: Laurence Erlbaum, pp. 219-240.
• 11. Even, R. (1988, July). Pre-service teachers conceptions of the relationships between functions and equations. Paper presented at the Proceedings of the International Group for the Psychology of Mathematics Education XI (PME XII), Hungary.
• 12. Even, R. (1990), ‘Subject Matter Knowledge for Teaching and the Case of Functions’, Educational Studies in Mathematics, 21(6), pp. 521-544.
• 13. Even, R. (1992), ‘The Inverse Function: Prospective Teachers’ Use of Undoing’. International Journal of Mathematical Education in Science and Technology, 23(4), pp. 557-562.
• 14. 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), pp. 94-116.
• 15. Ginsburg, H. (1981), ‘The Clinical Interview in Psychological Research on Mathematical Thinking: Aims, Rationales, Techniques’, For the Learning of Mathematics, 1(3), pp. 57- 64.
• 16. Hadjidemetriou, C. & Williams, J. (2001), ‘Children’s Graphical Conceptions: Assessment of Learning for Teaching’, in M. Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, Netherlands: Program Committee, 3, pp. 89-96.
• 17. Heibert, J., Lafevre, P. (1986), ‘Conceptual and Procedural Knowledge: The Case of Mathematics’, New Jersey: Lawrence Erlbaum Assocıates Inc.
• 18. Hitt, F. (1998), ‘Difficulties in Articulation of Different Representations Linked to the Concept of Function’, Journal of Mathematical Behavior, 17(1), pp. 123-134.
• 19. Leinhardt, G. (2001), ‘Instructional Explanations: A Commonplace for Teaching and Location of Contrast’, in V. Richardson (Ed.), Handbook of Research on Teaching (4th ed.), Washington, DC: American Educational Research Association, pp. 333-357.
• 20. Marks, R. (1990), ‘Pedagogical Content Knowledge: From a Mathematical Case to a Modified Conception’, Journal of Teacher Education, 41(3), pp. 3-11.
• 21. Merriam, S. B. (1988), ‘Case Study Research in Education: Qualitative Approach’, London: Jossey-Bass Publishers.
• 22. Miles, M. B., & Huberman, A. M. (1994), ‘Qualitative Data Analysis: An Expanded Sourcebook’, London: Sage Publications
• 23. Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (2005a). İlköğretim Matematik Dersi 6-8. Sınıflar Öğretim Programı, Ankara.
• 24. Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (2005b). Orta Öğretim Matematik (9,10,11 ve 12. Sınıflar) Dersi Öğretim Programı, Ankara.
• 25. Norman, A. (1992), ‘Teachers’ Mathematical Knowledge of the Concept of Function’, in G. Harel & Ed. Dubinsky (Eds.), The Concept of Function Aspects of Epistemology and Pedagogy, United States of America: Mathematical Association of America, pp. 215-232.
• 26. Piaget, J. (1972), ‘Psychology and Epistemology: Towards a Theory of Knowledge’, Singapore: Pte Ltd.
• 27. Sfard, A. (1992), ‘Operational Origins of Mathematical Objects and the Quandary of Reification-The Case of Function’, in Harel & Ed. Dubinsky (Eds.), The Concept of Function Aspects of Epistemology and Pedagogy, United States of America: Mathematical Association of America, pp. 59-85.
• 28. Sherin, M. G., Sherin, B. L. & Madanes, R. (2000), ‘Exploring Diverse Account of Teacher Knowledge’, Journal of Mathematical Behaviour’, 18(3), pp. 357- 375.
• 29. Shulman, L. (1986), ‘Those Who Understand: Knowledge Growth in Teaching’, Educational Researcher, 15, pp. 4-14.
• 30. Skemp, R. R. (1987), ‘The Psychology of Learning Mathematics’, Great Britian: Richard Clay Ltd.
• 31. Stake, R. E. (1995), ‘The Art of Case Study Research’, London: Sage Publication Inc.
• 32. Tall, D. & Vinner, S. (1981), ‘Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity’, Educational Studies in Mathematics, 12, pp. 151-169.
• 33. Thompson, P. W. (1994), ‘Students, Functions, and the Undergraduate Curriculum’, in Ed. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in Collegiate Mathematics Education, I, CBMS Issues in Mathematics Education, 4, pp. 21-44.
• 34. Tirosh, D., Even, R., & Robinson, N. (1998), ‘Simplifying Algebraic Expressions: Teacher Awareness and Teaching Approaches’, Educational Studies in Mathematics, 35, pp. 51-64.
• 35. Vinner, S. (1983), ‘Concept Definition, Concept Image and the Notion of Function’, International Journal of Mathematical Education in Science and Technology, 14(3), pp. 293-305.
• 36. Vinner, S. (1992), ‘The Function Concept as a Prototype for Problems in Mathematics Learning’, in G. Harel & Ed. Dubinsky (Eds.), The Concept of Function Aspects of Epistemology and Pedagogy, United States of America: Mathematical Association of America, pp. 195-213.
• 37. Watkins, C. & Mortimore, P. (1999), ‘Pedagogy: What Do We Know?’, in P. Mortimore (Ed.), Understanding Pedagogy and its Impact on Learning, London: Paul Chapman Publishing Ltd, pp. 1-20.
• 38. Wilson, M. R. (1994). One preservice secondary teacher’s understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 25(4), 346- 370.
• 39. Wilson, S. M., Shulman, L. S. & Richert, A. E. (1987), ‘150 Different Ways” of Knowing: Representations of Knowledge in Teaching’, in J. Calderhead (Ed.), Exploring Teachers’ Thinking, London: Cassel Education Ltd, pp. 104-124.
• 40. Yin, R. K. (2003), ‘Case Study Research: Design and Methods’, United Kingdom: Sage Publications Ltd.
• 41. YÖK Raporu. (2007). Eğitim Fakültelerinde Uygulanacak Yeni Programlar Hakkında Açıklama. http://www.yok.gov.tr/egitim/ogretmen/aciklama.doc adresinden 1 Nisan 2007 tarihinde alınmıştır.