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Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları

Year 2016, Volume: 15 Issue: 4, 0 - 0, 01.10.2016

Makbule Gözde Didiş , Ayhan Kürşat Erbaş , Bülent Çetinkaya

https://doi.org/10.17051/io.2016.75429
Cited By: 2

Abstract

Bu çalışmanın amacı, modelleme etkinlikleri bağlamında öğrenci çalışmalarını inceleyen ve öğrencilerin düşünme biçimlerindeki hatalarını tespit eden lise matematik öğretmen adaylarının, öğrencilerin bu hatalarına yönelik ne tür pedagojik yaklaşımlar sergilediklerini araştırmaktır. Çalışmanın verileri araştırmaya katılan 7 matematik öğretmen adayıyla gerçekleştirilen bire-bir görüşmelerle toplanmıştır. Çalışmanın bulguları öğretmen adaylarının öğrencilerin hatalarına yönelik müdahalelerinin beş yaklaşım altında toplanabileceğini göstermiştir: soru sorma (sorgulatma), doğruyu açıklama, doğru yolu hissettirme, hatayı söyleme/gösterme ve müdahale etmeme. Çalışmanın bulguları öğretmen adaylarının öğrenci hatalarına yaklaşımlarına yönelik pedagojik yeterliliklerinin zayıflığına da işaret etmektedir. Bu çerçevede, matematik öğretmen eğitimcilerine matematik eğitimi derslerinde öğretmen adaylarının öğrenci düşünme şekillerini incelemesi ve cevap vermesine yönelik çalışmalara yer vermesi önerilmektedir.

References

  • An, S., & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analyzing misconceptions in homework. International Journal of Science and Mathematics Education, 10(3), 717–753.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
  • Borromeo Ferri, R. (2013) Mathematical modeling—The teacher’s responsibility. In B. Dickman, & A. Sanfratello (Eds.), Proceedings of conference on mathematical modeling (pp. 26–32). New York, NY: Teachers College, Columbia University.
  • Borromeo Ferri, R., & Blum, W. (2011). Are integrated thinkers better able to intervene adaptively? A case study in a mathematical modeling environment. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 927–936). Rzesow, Poland: CERME.
  • Cabana, C., Cooper, J., Dietiker, L., Douglas, L., Gulick, D., Simon, S., & Thomas, E. (2000). College preparatory mathematics 5: Calculus. Sacramento, CA: CPM Educational Program.
  • Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating models and modeling perspective with existing research and practice. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 465-478). Mahwah, NJ: Lawrence Erlbaum.
  • Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.
  • Chick, H. L., & Baker, M. K. (2005). Investigating teachers’ responses to student misconceptions. In Chick, H. L., & Vincent, J. L. (Eds). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249–256). Melbourne, Australia: PME.
  • Doerr, H. M. (2006). Examining the tasks of teaching when using students' mathematical thinking. Educational Studies in Mathematics, 62(1), 3-24.
  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: the 14th ICMI study (pp. 69–78). New York, NY: Springer.
  • Doerr, H. M., & English, L. D. (2006). Middle grade teachers’ learning through students’ engagement with modeling tasks. Journal of Mathematics Teacher Education, 9(1), 5–32.
  • Galbraith, P. (2011). Models of modelling: Is there a first among equals?. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.), Mathematics: Traditions and [new] practices (Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia and the Australian Association of Mathematics Teachers) (Vol.1, pp. 279-287). Adelaide, Australia: AAMT and MERGA.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College Press.
  • Haines, C., & Crouch, R. (2007). Mathematical modeling and applications: ability and competence frameworks. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: the 14th ICMI study (pp. 417–424). New York, NY: Springer.
  • Intermath (n.d.). Bouncing ball. Retrieved from http://intermath.coe.uga.edu/topics /nmcncept/ra tios/r16.htm
  • Leiß, D., & Wiegand, B. (2005). A classification of teacher interventions in mathematics teaching. ZDM- Mathematics Education, 37(3), 240–245.
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh, & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Hillsdale, NJ: Lawrence Erlbaum.
  • Lingefjärd, T., & Meier, S. (2010). Teachers as managers of the modelling process. Mathematics Education Research Journal, 22(2), 92–107.
  • Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. The Journal of Mathematical Behavior, 18(1), 53–78.
  • National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Santagata, R., & Yeh, C. (2014). Learning to teach mathematics and to analyze teaching effectiveness: Evidence from a video-and practice-based approach. Journal of Mathematics Teacher Education, 17(6), 491–514.
  • Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
  • Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Son, J. W. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84(1), 49–70.
  • Son, J. W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 110(1), 31–46.
  • Swetz, F., & Hartzer, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. Reston, VA: NCTM
  • Talim ve Terbiye Kurulu [TTKB] (2011). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı ve kılavuzu. Ankara, Türkiye: Devlet Kitapları Müdürlüğü.
  • Talim ve Terbiye Kurulu [TTKB] (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı ve kılavuzu. Ankara, Türkiye: Devlet Kitapları Müdürlüğü.
  • Yıldırım, A. ve Şimşek, H. (2006). Sosyal bilimlerde nitel arastirma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Wilson, P. H., Lee, H. S., & Hollebrands, K. F. (2011). Understanding prospective mathematics teachers’ processes for making sense of students’ work with technology. Journal for Research in Mathematics Education, 42(1), 39–64.
  • Zawojewski, J. S., & Lesh, R. (2003). A models and modelling perspective on problem solving. In R. A. Lesh, & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 317–336). Mahwah, NJ: Lawrence Erlbaum.
  • Zawojewski, J. S., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspective on mathematics problem solving, learning, and teaching (pp. 337–358). Mahwah, NJ: Erlbaum.

Year 2016, Volume: 15 Issue: 4, 0 - 0, 01.10.2016

Makbule Gözde Didiş , Ayhan Kürşat Erbaş , Bülent Çetinkaya

https://doi.org/10.17051/io.2016.75429
Cited By: 2

Abstract

References

  • An, S., & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analyzing misconceptions in homework. International Journal of Science and Mathematics Education, 10(3), 717–753.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
  • Borromeo Ferri, R. (2013) Mathematical modeling—The teacher’s responsibility. In B. Dickman, & A. Sanfratello (Eds.), Proceedings of conference on mathematical modeling (pp. 26–32). New York, NY: Teachers College, Columbia University.
  • Borromeo Ferri, R., & Blum, W. (2011). Are integrated thinkers better able to intervene adaptively? A case study in a mathematical modeling environment. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 927–936). Rzesow, Poland: CERME.
  • Cabana, C., Cooper, J., Dietiker, L., Douglas, L., Gulick, D., Simon, S., & Thomas, E. (2000). College preparatory mathematics 5: Calculus. Sacramento, CA: CPM Educational Program.
  • Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating models and modeling perspective with existing research and practice. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 465-478). Mahwah, NJ: Lawrence Erlbaum.
  • Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.
  • Chick, H. L., & Baker, M. K. (2005). Investigating teachers’ responses to student misconceptions. In Chick, H. L., & Vincent, J. L. (Eds). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249–256). Melbourne, Australia: PME.
  • Doerr, H. M. (2006). Examining the tasks of teaching when using students' mathematical thinking. Educational Studies in Mathematics, 62(1), 3-24.
  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: the 14th ICMI study (pp. 69–78). New York, NY: Springer.
  • Doerr, H. M., & English, L. D. (2006). Middle grade teachers’ learning through students’ engagement with modeling tasks. Journal of Mathematics Teacher Education, 9(1), 5–32.
  • Galbraith, P. (2011). Models of modelling: Is there a first among equals?. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.), Mathematics: Traditions and [new] practices (Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia and the Australian Association of Mathematics Teachers) (Vol.1, pp. 279-287). Adelaide, Australia: AAMT and MERGA.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College Press.
  • Haines, C., & Crouch, R. (2007). Mathematical modeling and applications: ability and competence frameworks. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: the 14th ICMI study (pp. 417–424). New York, NY: Springer.
  • Intermath (n.d.). Bouncing ball. Retrieved from http://intermath.coe.uga.edu/topics /nmcncept/ra tios/r16.htm
  • Leiß, D., & Wiegand, B. (2005). A classification of teacher interventions in mathematics teaching. ZDM- Mathematics Education, 37(3), 240–245.
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh, & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Hillsdale, NJ: Lawrence Erlbaum.
  • Lingefjärd, T., & Meier, S. (2010). Teachers as managers of the modelling process. Mathematics Education Research Journal, 22(2), 92–107.
  • Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. The Journal of Mathematical Behavior, 18(1), 53–78.
  • National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Santagata, R., & Yeh, C. (2014). Learning to teach mathematics and to analyze teaching effectiveness: Evidence from a video-and practice-based approach. Journal of Mathematics Teacher Education, 17(6), 491–514.
  • Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
  • Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Son, J. W. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84(1), 49–70.
  • Son, J. W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 110(1), 31–46.
  • Swetz, F., & Hartzer, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. Reston, VA: NCTM
  • Talim ve Terbiye Kurulu [TTKB] (2011). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı ve kılavuzu. Ankara, Türkiye: Devlet Kitapları Müdürlüğü.
  • Talim ve Terbiye Kurulu [TTKB] (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı ve kılavuzu. Ankara, Türkiye: Devlet Kitapları Müdürlüğü.
  • Yıldırım, A. ve Şimşek, H. (2006). Sosyal bilimlerde nitel arastirma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Wilson, P. H., Lee, H. S., & Hollebrands, K. F. (2011). Understanding prospective mathematics teachers’ processes for making sense of students’ work with technology. Journal for Research in Mathematics Education, 42(1), 39–64.
  • Zawojewski, J. S., & Lesh, R. (2003). A models and modelling perspective on problem solving. In R. A. Lesh, & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 317–336). Mahwah, NJ: Lawrence Erlbaum.
  • Zawojewski, J. S., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspective on mathematics problem solving, learning, and teaching (pp. 337–358). Mahwah, NJ: Erlbaum.
There are 34 citations in total.

Details

Journal Section Articles
Authors

Makbule Gözde Didiş

Ayhan Kürşat Erbaş

Bülent Çetinkaya This is me

Publication Date October 1, 2016
Published in Issue Year 2016 Volume: 15 Issue: 4

Cite

APA Didiş, M. G., Erbaş, A. K., & Çetinkaya, B. (2016). Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları. İlköğretim Online, 15(4). https://doi.org/10.17051/io.2016.75429
AMA Didiş MG, Erbaş AK, Çetinkaya B. Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları. İOO. September 2016;15(4). doi:10.17051/io.2016.75429
Chicago Didiş, Makbule Gözde, Ayhan Kürşat Erbaş, and Bülent Çetinkaya. “Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları”. İlköğretim Online 15, no. 4 (September 2016). https://doi.org/10.17051/io.2016.75429.
EndNote Didiş MG, Erbaş AK, Çetinkaya B (September 1, 2016) Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları. İlköğretim Online 15 4
IEEE M. G. Didiş, A. K. Erbaş, and B. Çetinkaya, “Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları”, İOO, vol. 15, no. 4, 2016, doi: 10.17051/io.2016.75429.
ISNAD Didiş, Makbule Gözde et al. “Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları”. İlköğretim Online 15/4 (September 2016). https://doi.org/10.17051/io.2016.75429.
JAMA Didiş MG, Erbaş AK, Çetinkaya B. Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları. İOO. 2016;15. doi:10.17051/io.2016.75429.
MLA Didiş, Makbule Gözde et al. “Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları”. İlköğretim Online, vol. 15, no. 4, 2016, doi:10.17051/io.2016.75429.
Vancouver Didiş MG, Erbaş AK, Çetinkaya B. Matematik Öğretmen Adaylarının Öğrenci Hatalarına Yönelik Pedagojik Yaklaşımları. İOO. 2016;15(4).

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