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EXAMINING OF SECONDARY SCHOOL STUDENTS’ ABILITIES TO DRAWING THE FUNCTION GRAPHICS

Year 2009, Volume: 17 Issue: 3, 919 - 932, 01.09.2009

Abstract

Functions are very important subjects in mathematics. Some students have difficulties to learn functions. In this study, it was examined secondary school students’ abilities to draw graphics of functions. The case study methodology was used in the study. It was prepared a test consisted of 5 open-ended questions about linear, parabolic, logaritmic, trigonometric, and exponential functions’grafiphics. This test was carried out 100 secondary school students from different four schools. Findings showed that the majority of students attended study were successful to draw the linear functions’graphics while some students drew parabolic function’graphic like the linear functions’graphics. As a result, it was said that teachers should attach importance to drawing graphics of the functions in mathematics teaching.

References

  • 1. Akkoç, H. (2006). Fonksiyon kavramının çoklu temsillerinin çağrıştırdığı kavram görüntüleri. Hacettepe Üni. Eğitim Fakültesi Dergisi, 30, 1–10. http:// www.egitimdergisi. hacettepe.edu.tr/200630HAT%C4%B0CE%20AKKO%C3%87.pdf
  • 2. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.
  • 3. Bleich, L., Ledford, S., Orrill, C.H. ve Polly, D. (2006). An analysis of the use of graphical representation in participants’solutions. The Mathematical Educator, 16(1), 22–34.
  • 4. Dubinsky, E. ve Harel, G. (1992). The nature of function. In G.Harel & E. Dubinsky (Eds.). The concept of function: Aspects of epistemology and pedagogy. (MAA Notes no. 25). Washington, DC: Mathematical Assosiation of America.
  • 5. Duval, R. (2002). The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education 1(2), 103-131. http://www.math.uncc.edu/~sae/dg3/duval.pdf.
  • 6. Elia, I., Panaoura, A., Eracleous, A. ve Gagatsis, A. (2007). Relatıons between secondary pupıls’conceptıons about functıons and problem solvıng ın dıfferent representatıons, Int. J.of Science and Mathematics Education, 5, 533–556.
  • 7. Elia, I. ve Spyrou, P. (2006). How students conceive function: a triarchic conceptualsemiotic model of the understanding of a complex concept. The Montana Mathematics Ensthusiant, ISSN 1551–3440, 3(2), 256–272.
  • 8. Hitt, F. (1998). Difficulties in the artification of the different representations linked to the concept of function, Journal of Mathematical Behavior, 17(1), 123–134.
  • 9. Markovits, Z., Eylon, B. ve Bruckheimer, M. (1986). Functions today and yesterday. For the Learning of Mathematics, 6(2), 18-24.
  • 10. MEB, (2005). Matematik Dersi Öğretim Programı ve Kılavuzu (9–12. sınıflar), Ankara.
  • 11. Merriam, S.B. (1998). Qualitative reseach and case study applications in educaton, Jossey-Bass Publishers, San Fransisco.
  • 12. Michelsen, C. (2006). Functions: a modelling tool in mathematics and science. ZDM The International Journal on Mathematics Education, 38 (3), 269–280.
  • 13. Monk, S. (2003). Representation in scholl mathematics: learning to graph and graphing to learn. In J. Kilpatrick (Eds.), A research companion to principles and standards for school mathematics. Reston, VA: National Council for Teachers of Mathematics
  • 14. NCTM (2000). Principles and standarts for school mathematics. Reston: National Council of Teachers of Mathematics. http://standards.nctm.org/document/chapter7 /index.htm
  • 15. Presmeg, N. ve Nenduradu, R. (2005). An investigation of a preservice teachers’ use of representations in solving algebraic problems involving exponential relationships, In Chick, H.L. & Vincent, J.L. Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 4, 105–112.
  • 16. Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification - the case of function. In G. Harel, & E. Dubinsky, (Eds) The Concept of Function: Aspects of Epistemology and Pedagogy, MAA, 59–84.
  • 17. Sierpinska, A. (1992). On understanding the notion of function. in: Harel. G.& Dubinsky, E. (eds.), MAA Notes and Reports Series, 25–58.
  • 18. Tall, D. (1997). Functions and calculus. in A.J. Bishop et al. (eds.), International Handbook of Mathematics Education, 289-325. Dordrecht: Kluwer.
  • 19. Taşar, M.F., İngeç, Ş.K. ve Güneş, P.Ü. (2006). Grafik çizme ve anlama becerisinin saptanması. http://w3.gazi.edu.tr/~mftasar/publications/Grafik.pdf VII. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, 6-8 Eylül 2006, Ankara.
  • 20. Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 195Y214). United States: Mathematical Association of America.
  • 21. Zachariades, T., Christou, C. ve Papageorgiou, E. (2001). The difficulties and reasoning of undergraduate mathematics students in the identification of functions. Proceedings in the 10th ICME Conference, Crete, Greece.

ORTAÖĞRETİM ÖĞRENCİLERİNİN FONKSİYON GRAFİKLERİNİ ÇİZEBİLME BECERİLERİNİN İNCELENMESİ

Year 2009, Volume: 17 Issue: 3, 919 - 932, 01.09.2009

Abstract

Fonksiyonlar, matematikte önemli bir konudur. Bazı öğrencilerin bu konuyu öğrenmede sorunları vardır. Bu çalışmada, ortaöğretim onuncu sınıf öğrencilerinin çeşitli fonksiyon grafiklerini çizebilme becerileri araştırılmıştır. Çalışmada özel durum çalışması yöntemi kullanılmıştır. Lineer, parabolik, logaritmik, trigonometrik ve üstel fonksiyonların grafiklerini çizmeyi araştıran 5 açık uçlu sorudan oluşan bir test hazırlanmıştır. Bu test dört farklı okuldan 100 lise öğrencisine uygulanmıştır. Bulgular çalışmaya katılan öğrencilerinin çoğunun doğrusal fonksiyon grafiklerini çizmede başarılı olduğunu, buna karşın bazı öğrencilerin parabolik fonksiyon grafiklerini doğrusal fonksiyon grafiği gibi çizdiklerini göstermiştir. Sonuç olarak, öğretmenlerin matematik öğretiminde grafik çizimlerine daha fazla önem vermesi gerektiği söylenebilir.

References

  • 1. Akkoç, H. (2006). Fonksiyon kavramının çoklu temsillerinin çağrıştırdığı kavram görüntüleri. Hacettepe Üni. Eğitim Fakültesi Dergisi, 30, 1–10. http:// www.egitimdergisi. hacettepe.edu.tr/200630HAT%C4%B0CE%20AKKO%C3%87.pdf
  • 2. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.
  • 3. Bleich, L., Ledford, S., Orrill, C.H. ve Polly, D. (2006). An analysis of the use of graphical representation in participants’solutions. The Mathematical Educator, 16(1), 22–34.
  • 4. Dubinsky, E. ve Harel, G. (1992). The nature of function. In G.Harel & E. Dubinsky (Eds.). The concept of function: Aspects of epistemology and pedagogy. (MAA Notes no. 25). Washington, DC: Mathematical Assosiation of America.
  • 5. Duval, R. (2002). The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education 1(2), 103-131. http://www.math.uncc.edu/~sae/dg3/duval.pdf.
  • 6. Elia, I., Panaoura, A., Eracleous, A. ve Gagatsis, A. (2007). Relatıons between secondary pupıls’conceptıons about functıons and problem solvıng ın dıfferent representatıons, Int. J.of Science and Mathematics Education, 5, 533–556.
  • 7. Elia, I. ve Spyrou, P. (2006). How students conceive function: a triarchic conceptualsemiotic model of the understanding of a complex concept. The Montana Mathematics Ensthusiant, ISSN 1551–3440, 3(2), 256–272.
  • 8. Hitt, F. (1998). Difficulties in the artification of the different representations linked to the concept of function, Journal of Mathematical Behavior, 17(1), 123–134.
  • 9. Markovits, Z., Eylon, B. ve Bruckheimer, M. (1986). Functions today and yesterday. For the Learning of Mathematics, 6(2), 18-24.
  • 10. MEB, (2005). Matematik Dersi Öğretim Programı ve Kılavuzu (9–12. sınıflar), Ankara.
  • 11. Merriam, S.B. (1998). Qualitative reseach and case study applications in educaton, Jossey-Bass Publishers, San Fransisco.
  • 12. Michelsen, C. (2006). Functions: a modelling tool in mathematics and science. ZDM The International Journal on Mathematics Education, 38 (3), 269–280.
  • 13. Monk, S. (2003). Representation in scholl mathematics: learning to graph and graphing to learn. In J. Kilpatrick (Eds.), A research companion to principles and standards for school mathematics. Reston, VA: National Council for Teachers of Mathematics
  • 14. NCTM (2000). Principles and standarts for school mathematics. Reston: National Council of Teachers of Mathematics. http://standards.nctm.org/document/chapter7 /index.htm
  • 15. Presmeg, N. ve Nenduradu, R. (2005). An investigation of a preservice teachers’ use of representations in solving algebraic problems involving exponential relationships, In Chick, H.L. & Vincent, J.L. Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 4, 105–112.
  • 16. Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification - the case of function. In G. Harel, & E. Dubinsky, (Eds) The Concept of Function: Aspects of Epistemology and Pedagogy, MAA, 59–84.
  • 17. Sierpinska, A. (1992). On understanding the notion of function. in: Harel. G.& Dubinsky, E. (eds.), MAA Notes and Reports Series, 25–58.
  • 18. Tall, D. (1997). Functions and calculus. in A.J. Bishop et al. (eds.), International Handbook of Mathematics Education, 289-325. Dordrecht: Kluwer.
  • 19. Taşar, M.F., İngeç, Ş.K. ve Güneş, P.Ü. (2006). Grafik çizme ve anlama becerisinin saptanması. http://w3.gazi.edu.tr/~mftasar/publications/Grafik.pdf VII. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, 6-8 Eylül 2006, Ankara.
  • 20. Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 195Y214). United States: Mathematical Association of America.
  • 21. Zachariades, T., Christou, C. ve Papageorgiou, E. (2001). The difficulties and reasoning of undergraduate mathematics students in the identification of functions. Proceedings in the 10th ICME Conference, Crete, Greece.
There are 21 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Birol Tekin This is me

Alper Cihan Konyalıoğlu This is me

Ahmet Işık This is me

Publication Date September 1, 2009
Published in Issue Year 2009 Volume: 17 Issue: 3

Cite

APA Tekin, B., Konyalıoğlu, A. C., & Işık, A. (2009). ORTAÖĞRETİM ÖĞRENCİLERİNİN FONKSİYON GRAFİKLERİNİ ÇİZEBİLME BECERİLERİNİN İNCELENMESİ. Kastamonu Education Journal, 17(3), 919-932.

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