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İlköğretim Matematik Öğretmen Adaylarının Matematiksel Problem Çözmede Kullandıkları Temsiller

Yıl 2012, Cilt: 11 Sayı: 3, 681 - 700, 01.12.2012

Öz

Bu çalışmada, ilköğretim matematik öğretmen adaylarının problem çözme süreçlerinde ne tür temsil kullandıkları ve bu temsillerle ilgili yaşadıkları sorunları araştırılmıştır. Toplam 48 aday ile yürütülen bu çalışma kapsamındaki veriler problem çözmede çoklu temsilleri kullanma testi ve klinik mülakat ile toplanmıştır. Elde edilen verilere göre, adayların problemlerin çözüm sürecinde özellikle konuşma dili temsilini diğer temsil türlerine göre (cebirsel, grafiksel ve sayısal) daha yoğun kullandıkları belirlenmiştir. Bununla birlikte, özellikle problemi anlama aşamasında önemli işleve sahip olduğunu düşündükleri temsillerin kullanımında adayların probleme uygun temsil oluşturamama ve temsiller arasında geçiş yapamama gibi sorunlar yaşadıkları tespit edilmiştir

Kaynakça

  • Ainsworth, S., Bibby, P., & Wood, D. (1997). Evaluating principles for multirepresentational learning environments. Paper presented at the 7th European Conference for Research on Learning and Instruction, Athens, Greece.
  • Altun, M. (2009). Liselerde Matematik Öğretimi (3.Baskı). Bursa: Alfa Basım Yayım Dağıtım.
  • Baki, A. (2006). Kuramdan Uygulamaya Matematik Eğitimi. Trabzon: Derya Kitabevi.
  • Bayık, F. (2010). 11. sınıf öğrencilerinin geometrik problemlerle ilgili oluşturdukları dış temsillerle iç temsiller arasındaki etkileşimler, Yayınlanmamış Yüksek Lisans Tezi, Gazi Üniversitesi, Ankara.
  • Billings, E. M. H., & Klanderman, D. (2000). Graphical representations of speed: Obstacles preservice K-8 teachers experience. School Science and Mathematics, 100 (8), 440-451.
  • Bogdan, R. C., & Biklen K. (1998). Qualitative research in education: An introduction to theory and methods. Third Edition. Needham Heights.
  • Cai, J., & Lester, F. K. (2005). Solution representations and pedagogical representations in Chinese and U. S. classrooms. Journal of Mathematical Behavior. 24, 221-237.
  • Cifarelli, V. V. (1998). The development of mental representations as a problem solving activity, Journal of Mathematical Behavior. 17 (2), 239-264.
  • Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal forResearch in Mathematics Education, 23(1), 2–33.
  • Cuoco, A. (2001). The roles of representation in school mathematics (2001 Yearbook). Reston: NCTM.
  • De Jong, T., Ainsworth, S., Dobson, M., van der Hulst, A., Levonen, J., & Reimann, P. (1998). Acquiring knowledge in science and math: The use of multiple representations in technology-based learning environments. In M. W. van Someren et al. (Eds.), Learning with multiple representations (pp. 9–40). Amsterdam: Pergamon.
  • Duval, R. (2002). The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education, 1(2), 1–16.
  • Elia, I., Gagatsis, A., & Demetriou, A. (2007). The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction, 17, 658–672.
  • Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17 (2), 137–165.
  • Goldin, G. A., & Janvier, C. (1998). Representations and the psychology of mathematics education. Journal of Mathematical Behavior, 17(1), 1–4.
  • Goldin, G. (1998). Observing mathematical problem solving through task based interviews. A. Teppo. (Ed.), Qualitative Research Methods in Mathematics Education (pp. 40–62).Reston, Virginia:National Council of Teachers of Mathematics.
  • Graeber, A. (1999). Forms of knowing mathematics: what preservice teachers should learn. Educational Studies in Mathematics, 38, 189–208.
  • Janvier, C. (1987). Representation system and mathematics. In C. Janvier (Ed.), Problems of Representations in the Learning and Teaching of Mathematics, (p. 19–27). New Jersey: Lawrence Erlbaum Associates.
  • Kaput, J. J. (1987). Representation systems and mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 19–26). New Jersey: Lawrence Erlbaum Associates.
  • Kaput, J. J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan.
  • Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler, R. W. Scholz, R. Strasser, & B. Winkelman (Eds.), Didactics in Mathematics as a Scientific Discipline (pp. 379–397). Netherlands: Kluwer Academic Publishers.
  • Kılıç, Ç., & Özdaş, A. (2010). İlköğretim 5. Sınıf Öğrencilerinin Kesirlerde Karşılaştırma ve Sıralama Yapmayı Gerektiren Problemlerin Çözümlerinde Kullandıkları Temsiller. Kastamonu Eğitim Dergisi, 18(2), 513-530.
  • Lesh, R. (1979). Mathematical learning disabilities: considerations for identification, diagnosis and remediaton. In R. Lesh, D. Mierkiewicz, & M. G. Kantowski (Eds.), Applied Mathematical Problem Solving. Ohio: ERIC/SMEAC.
  • Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33–40). New Jersey: Lawrence Erlbaum Associates.
  • Mayer, R.E. (1985). Mathematical Ability. In R. J. Stenberg (Ed.), Human abilities: An information processing approach (pp. 127-150). San Francisco: Freeman.
  • MEB. (2005). İlköğretim matematik dersi (6-8. sınıflar) öğretim programı. Ankara: Devlet Kitapları Müdürlüğü Basımevi.
  • Miles, M. B., & Huberman A. M. (1994). An Expanded Sourcebook Qualitative Data Analysis. (2nd Ed.). California: Sage Publications.
  • Montague, M. (2006). Math problem solving for middle school students with disabilities. Washington, DC: The Access Center: Improving Outcomes for all Students K-8. Retrieved on May 3, 2011, from http://www.k8accesscenter.org/
  • Mosley, B. (2005). Students’ early mathematical representation knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60, 37-69.
  • National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Niemi, D. (1996). Assessing conceptual understanding in mathematics: representations, problem solutions, justifications, and explications. The Journal of Educational Research, 89(6), 351-363.
  • Nistal, A., Van Dooren, W., Clarebout, G., Elen, J., & Veschaffel, L. (2009). Conceptualizing, investigating and simulating representational flexibility in mathematical problem solving and learning: A critical review. ZDM- The International Journal on Mathematics Education, 41, 627–636.
  • Patterson, N. D., & Norwood, S. N. (2004). A case study of teacher beliefs on students’ beliefs about multiple representations. International Journal of Science and Mathematics Education, 2: 5–23.
  • Polya, G. (1957). Nasıl Çözmeli? Çev. Feryal Halatçı, İstanbul: Sistem Yayıncılık.
  • Yıldırım, A. ve Şimşek, H. (2005). Sosyal Bilimlerde Nitel Araştırma Yöntemleri, Seçkin Yayıncılık, Ankara.

The Representations of Pre-service Elementary Mathematics Teachers Used in Solving Mathematical Problems

Yıl 2012, Cilt: 11 Sayı: 3, 681 - 700, 01.12.2012

Öz

In this study, what kind of representations pre-service elementary mathematics teachers use in problem solving processes, and their problems that they had related to these representations were researched. The data within the scope of this study was obtained from total of 48 pre-service teachers, and were collected from the using multiple representation in problem solving test and clinical interviews. According to data obtained, the pre-service teachers were determined that using in particular verbal representations intensively rather than other representations (algebraic, graphical and numeric) in the problems solving process. However, the pre-service teachers who thought the usage of representations had important function particularly in the understanding the problem stage were determined that having problems like inability to create a representation to a problem, or inability to make translation between the representations

Kaynakça

  • Ainsworth, S., Bibby, P., & Wood, D. (1997). Evaluating principles for multirepresentational learning environments. Paper presented at the 7th European Conference for Research on Learning and Instruction, Athens, Greece.
  • Altun, M. (2009). Liselerde Matematik Öğretimi (3.Baskı). Bursa: Alfa Basım Yayım Dağıtım.
  • Baki, A. (2006). Kuramdan Uygulamaya Matematik Eğitimi. Trabzon: Derya Kitabevi.
  • Bayık, F. (2010). 11. sınıf öğrencilerinin geometrik problemlerle ilgili oluşturdukları dış temsillerle iç temsiller arasındaki etkileşimler, Yayınlanmamış Yüksek Lisans Tezi, Gazi Üniversitesi, Ankara.
  • Billings, E. M. H., & Klanderman, D. (2000). Graphical representations of speed: Obstacles preservice K-8 teachers experience. School Science and Mathematics, 100 (8), 440-451.
  • Bogdan, R. C., & Biklen K. (1998). Qualitative research in education: An introduction to theory and methods. Third Edition. Needham Heights.
  • Cai, J., & Lester, F. K. (2005). Solution representations and pedagogical representations in Chinese and U. S. classrooms. Journal of Mathematical Behavior. 24, 221-237.
  • Cifarelli, V. V. (1998). The development of mental representations as a problem solving activity, Journal of Mathematical Behavior. 17 (2), 239-264.
  • Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal forResearch in Mathematics Education, 23(1), 2–33.
  • Cuoco, A. (2001). The roles of representation in school mathematics (2001 Yearbook). Reston: NCTM.
  • De Jong, T., Ainsworth, S., Dobson, M., van der Hulst, A., Levonen, J., & Reimann, P. (1998). Acquiring knowledge in science and math: The use of multiple representations in technology-based learning environments. In M. W. van Someren et al. (Eds.), Learning with multiple representations (pp. 9–40). Amsterdam: Pergamon.
  • Duval, R. (2002). The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education, 1(2), 1–16.
  • Elia, I., Gagatsis, A., & Demetriou, A. (2007). The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction, 17, 658–672.
  • Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17 (2), 137–165.
  • Goldin, G. A., & Janvier, C. (1998). Representations and the psychology of mathematics education. Journal of Mathematical Behavior, 17(1), 1–4.
  • Goldin, G. (1998). Observing mathematical problem solving through task based interviews. A. Teppo. (Ed.), Qualitative Research Methods in Mathematics Education (pp. 40–62).Reston, Virginia:National Council of Teachers of Mathematics.
  • Graeber, A. (1999). Forms of knowing mathematics: what preservice teachers should learn. Educational Studies in Mathematics, 38, 189–208.
  • Janvier, C. (1987). Representation system and mathematics. In C. Janvier (Ed.), Problems of Representations in the Learning and Teaching of Mathematics, (p. 19–27). New Jersey: Lawrence Erlbaum Associates.
  • Kaput, J. J. (1987). Representation systems and mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 19–26). New Jersey: Lawrence Erlbaum Associates.
  • Kaput, J. J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan.
  • Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler, R. W. Scholz, R. Strasser, & B. Winkelman (Eds.), Didactics in Mathematics as a Scientific Discipline (pp. 379–397). Netherlands: Kluwer Academic Publishers.
  • Kılıç, Ç., & Özdaş, A. (2010). İlköğretim 5. Sınıf Öğrencilerinin Kesirlerde Karşılaştırma ve Sıralama Yapmayı Gerektiren Problemlerin Çözümlerinde Kullandıkları Temsiller. Kastamonu Eğitim Dergisi, 18(2), 513-530.
  • Lesh, R. (1979). Mathematical learning disabilities: considerations for identification, diagnosis and remediaton. In R. Lesh, D. Mierkiewicz, & M. G. Kantowski (Eds.), Applied Mathematical Problem Solving. Ohio: ERIC/SMEAC.
  • Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33–40). New Jersey: Lawrence Erlbaum Associates.
  • Mayer, R.E. (1985). Mathematical Ability. In R. J. Stenberg (Ed.), Human abilities: An information processing approach (pp. 127-150). San Francisco: Freeman.
  • MEB. (2005). İlköğretim matematik dersi (6-8. sınıflar) öğretim programı. Ankara: Devlet Kitapları Müdürlüğü Basımevi.
  • Miles, M. B., & Huberman A. M. (1994). An Expanded Sourcebook Qualitative Data Analysis. (2nd Ed.). California: Sage Publications.
  • Montague, M. (2006). Math problem solving for middle school students with disabilities. Washington, DC: The Access Center: Improving Outcomes for all Students K-8. Retrieved on May 3, 2011, from http://www.k8accesscenter.org/
  • Mosley, B. (2005). Students’ early mathematical representation knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60, 37-69.
  • National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Niemi, D. (1996). Assessing conceptual understanding in mathematics: representations, problem solutions, justifications, and explications. The Journal of Educational Research, 89(6), 351-363.
  • Nistal, A., Van Dooren, W., Clarebout, G., Elen, J., & Veschaffel, L. (2009). Conceptualizing, investigating and simulating representational flexibility in mathematical problem solving and learning: A critical review. ZDM- The International Journal on Mathematics Education, 41, 627–636.
  • Patterson, N. D., & Norwood, S. N. (2004). A case study of teacher beliefs on students’ beliefs about multiple representations. International Journal of Science and Mathematics Education, 2: 5–23.
  • Polya, G. (1957). Nasıl Çözmeli? Çev. Feryal Halatçı, İstanbul: Sistem Yayıncılık.
  • Yıldırım, A. ve Şimşek, H. (2005). Sosyal Bilimlerde Nitel Araştırma Yöntemleri, Seçkin Yayıncılık, Ankara.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA33BF49PS
Bölüm Makale
Yazarlar

Ali Sabri İpek Bu kişi benim

Samet Okumuş

Yayımlanma Tarihi 1 Aralık 2012
Gönderilme Tarihi 1 Aralık 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 11 Sayı: 3

Kaynak Göster

APA İpek, A. S., & Okumuş, S. (2012). The Representations of Pre-service Elementary Mathematics Teachers Used in Solving Mathematical Problems. Gaziantep University Journal of Social Sciences, 11(3), 681-700.