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Üstün Yetenekli Öğrencilerin Karşılaştıkları Matematik Problemleri İle İlgili Bilişsel Öngörüleri

Year 2016, Volume: 29 Issue: 2, 445 - 467, 29.12.2016

Abstract

Üstün yetenekli öğrenciler; çoğunlukla, meraklı, zeki, motive olmuş ve başarıya odaklanmış olarak tarif edilmektedir. Bu gruptaki öğrencilerin neden daha başarılı oldukları sorusuna henüz tatmin edici bir cevap / cevaplar bulunamamıştır. Bu araştırmanın amacı, üstün yetenekli öğrencilerin karşılaştıkları matematik problemleri ile ilgili bilişsel öngörülerini derinlemesine ve detaylı olarak ortaya koymaktır. Onuncu sınıfa devam eden üç üstün yetenekli öğrenci ile 10 tane problem çözme oturumu gerçekleştirilmiştir. Elde edilen bulgulara göre, üstün yetenekli öğrencilerin; kendilerine yöneltilen bazı problemlerin benzerleri ile hangi ortamlarda, nasıl karşılaştıklarını ve çözüm yolunda attıkları adımları detaylı bir şekilde hatırladıkları görülmüştür. Araştırmada ilk defa karşılaştıkları bazı problemler için çözüm planı üretemedikleri, bazıları için ise üretebildikleri durumlar görülmüştür. Diğer taraftan plan üretebildikleri bu tür problemler için çoğunlukla birden fazla çözüm yolu önermeleri dikkat çekmiştir.

References

  • Auerbach, C. F. and Silverstein, L. B., 2003.Qualitative data: An introduction to coding and analysis. New York: New York University Press.
  • Bandura, A., 1997. Self-efficacy: The exercise of control. New York: Freeman.
  • Cleary, T. and Zimmerman, B. J., 2001.Self-regulation differences during athletic practice by experts, non-experts, and novices. Journal of Applied Sport Psychology, 13, 61–82.
  • Davis, G. A. and Rimm, S. B. (Eds.), 2004.Education of the gifted and talented, 3rd ed., Allyn and Bacon, Boston.
  • De Corte, E., Verschaffel, L. and Op’tEynde, P., 2000. Self-regulation: A characteristic and a goal of mathematics education. M. Boekaerts, P.R. Pintrich, and M. H. Zeidner, (Eds.), Handbook of self-regulation (pp.687-726). San Diego, CA: Academic Press.
  • Demircioğlu, H., 2008. Matematik öğretmen adaylarının üst bilişsel davranışlarının gelişimine yönelik tasarlanan eğitim durumlarının etkililiği. Yayınlanmamış Doktora Tezi, Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü. Ankara.
  • Denzin, N. K., and Lincoln, Y.S., 1998. The landscape of qualitative research: theories and issues. Thousand Oaks, CA: Sage Publications.
  • Dresel, M. and Haugwitz, M., 2006. The relationship between cognitive abilities and self regulated learning: evidence for interactions with academic self-concept and gender. High Ability Studies, 16(2), 201-218.
  • Feldhusen, J. F. and Kroll, M. D., 1991. Boredom or challenge for the academically talented in school. Gifted Education International, 7, 80-81.
  • Gagné, F., 2003.Transforming Gifts into Talents: The DMGT as a Developmental Theory. N. Colangelo and G. A. Davis (Eds.) Handbook of Gifted Education (pp. 60-74). Boston MA: Allyn and Bacon.
  • Gardner, M., 1997. Hah, buldum! (Çev. B. Bıçakçı) Ankara: Tübitak Yayınları
  • Gardiner, A., 1987. Mathematical puzzling. Oxford, England: Oxford University Press.
  • Geiger, V. and Galbraith, P., 1998. Developing a diagnostic framework for evaluating student approaches to applied mathematics problems, International Journal of Mathematics, Education, Science and Technology, 29, 533–559.
  • Glaser, B. and Strauss, A. L., 1967. The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine Publishing Company.
  • Greene, J.A., Moos D. C., Azevedo R. and Winters, F.I., 2008. Exploring differences between gifted and grade-level students’ use of self-regulatory learning processes with hypermedia.Computers & Education, 50, 1069–1083.
  • Kitsantas, A. and Zimmerman, B. J., 2002.Comparing self-regulatory processes among novice, non-expert, and expert volleyball players: A microanalytic study. Journal of Applied Sport Psychology, 14, 91-105.
  • Krantz, S. G., 1996. Techniques of problem solving. Providence, RI: American Mathematical Society.
  • Krutetskii, V. A., 1976. The psychology of mathematical abilities in school children. Chicago: University of Chicago Press.
  • Lester, F.K., 1994. Musings about mathematical problem solving research: 1970–1994, Journal for Research in Mathematics Education, 25, 660–675.
  • Malpass, J.R., 1999. Self regulation, goal orientation, self efficacy, worry and high stakes math achievement of mathematically gifted high school students. Roeper Review, 21(4), 281-289.
  • Mayer, R. E., 1985. Implications of cognitive psychology for instruction in mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving (pp. 123–145). Hillsdale, NJ: Lawrence Erlbaum.
  • Merriam, S. B., 1998. Qualitative research and case study applications in education. San Francisco, CA: Jossey-Bass.
  • Miller, R. C., 1990. Discovering mathematical talent. Reston, VA: Council for Exceptional Children, ERIC Clearinghouse on Disabilities and Gifted Education. ERIC Document Reproduction Service No: ED 321 487.
  • Mingus, T. and Grassl, R., 1999.What constitutes a nurturing environment for the growth of mathematically gifted students? School Sciences and Mathematics, 99(6), 286-293.
  • Montague, M., 1991.Gifted and learning disabled gifted students’ knowledge and use of mathematical problem-solving strategies. Journal for the Education of the Gifted, 14, 393-411.
  • Montague, M. and Applegate, B., 1993.Middle school students’ mathematical problem solving: An analysis of think-aloud protocols. Learning Disabilities Quarterly, 16, 19-32.
  • Neber, H. and Schommer-Aikins, M., 2002. Self-regulated science learning with highly gifted students: The role of cognitive, motivational, epistemological, and environmental variables. High Ability Studies, 13(1), 59-74.
  • Pajares, F., 1996.Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543–578.
  • Panaoura, A. and Philippou, G., 2003. The construct validity of an inventory for the measurement of young pupils’ metacognitive abilities in mathematics. N. A. Pateman, B. J. Doherty and J. Zilliox (Eds.), Proceedings 27th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 437-444). Honolulu, USA: PME.
  • Pape, S. J. and Wang, C., 2003. Middle school children’s strategic behavior: Classification and relation to academic achievement and mathematical problem solving. Instructional Science, 31, 419-449.
  • Pativisan, S. and Neiss, M., 2007. Mathematical problem solving processes of Thai gifted students. B. Sriraman (Guest Ed.), Mediterranean Journal for Research in Mathematics Education, 6(1-2), 47–68.
  • Patton, M. Q., 2002. Qualitative research and evaluation methods. Newbury Park: Sage Publication.
  • Pintrich, P.R., 1999. The role of motivation in promoting and sustaining self-regulated learning. International Journal of Educational Research, 31,459-470.
  • Pintrich, P. R., 2000. The role of goal orientation in self-regulated learning. M. Boekaerts, P. R. Pintrich, and M. Zeidner (Eds), Handbook of self- regulation (pp, 451-501). San Diego, CA: Academic Press.
  • Polya, G., 1945. How to solve it: A new aspect of mathematical method. Princeton : Princeton University Press.
  • Posamentier, A. and Krulik, S., 1998. Problem solving strategies for efficient and elegant Solutions. California: Corwin Pres. A Sage Publications.
  • Posamentier, A. and Salkind, C. T., 1988.Challenging problems in geometry. New York: Dover.
  • Risemberg, R. and Zimmerman, B. J., 1992.Self-regulated learning in gifted students. Roeper Review, 15(1), 98-101.
  • Ruban, L. and Reis, S.M., 2006.Patterns of self-regulatory strategy use among low-achieving and high-achieving university students. Roeper Review, 28(3), 148-156.
  • Schoenfeld, A. H., Burkhardt, H., Daro, P., Ridgway, J., Schwartz, J., and Wilcox, S., 1999. High school assessment. White Plains, NY: Dale Seymour Publications.
  • Schunk, D. H., 1998. Teaching elementary students to self-regulate practice of mathematical skills with modeling. In D. H. Schunk and B. J. Zimmerman (Eds.), Self-regulated learning: From teaching to self-reflective practice (pp. 137-159). New York: Guilford.
  • Schraw, O. and Moshman, D., 1995. Metacognitive theories. Educational Psychology Review, 7, 351-371.
  • Shore, B., 1986. Cognition and giftedness: New research directions. Gifted Child Quarterly, 30, 24–27
  • Stillman, G.A. and Galbraith, P.L., 1998. Applying mathematics with real world connections: Metacognitive characteristics of secondary students’, Educational Studies in Mathematics, 36, 157–195.
  • Strauss, A. L., 1987. Qualitative analysis for social scientists. Cambridge Cambridgeshire; New York: Cambridge University Press.
  • Sowell, E. J., 1993. Programs for mathematically gifted students: A review of empirical research. Gifted Child Quarterly,37, 124-132.
  • Strauss, A. and Corbin, J., 1998. Basics of qualitative research: Grounded theory procedures and techniques. London: Sage.
  • Yazgan-Sağ, G., 2012. Üstün yetenekli ortaöğretim öğrencilerinin matematiksel problem çözme durumlarındaki öz düzenleme davranışları. Yayınlanmamış Doktora Tezi, Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Yazgan-Sağ, G., 2014. Üstün yetenekli öğrencilerde özdüzenleme faaliyetleri. G. Sakız (Ed.), Özdüzenleme: Öğrenmeden öğretime özdüzenleme davranışlarının gelişimi, stratejiler ve öneriler (ss. 154-187). Ankara: Nobel Yayınevi,
  • Yazgan-Sağ, G ve Argün, Z., 2016. Üstün yetenekli öğrencilerin matematiksel problem çözme durumlarındaki motivasyonel öngörüleri. Kastamonu Eğitim Dergisi, 24(3), 811-828.
  • Yetkin, İ.E., 2006.The role of classroom context in student self-regulated learning: an exploratory case study in a sixth-grade mathematics classroom. Yayınlanmamış Doktora Tezi, Ohio State University.
  • Yıldırım, A. ve Şimşek, H., 2006. Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yin, R. K., 1994.Case study research: Designs and methods. Newbury Park, CA: Sage.
  • Wieczerkowski, W., Cropley, A. J. and Prado, T. M., 2000.Nurturing talents/gifts in mathematics. K. A. Heller, F. J. Monks, R. J. Sternberg, and R. F. Subotnik (Eds.), International handbook of giftedness and talent education (pp. 413- 425). Oxford, United Kingdom: Pergamon.
  • Zimmerman, B. J., 2000. Attaining of self-regulation: A social cognitive perspective. M. Boekaerts, P. Pintrich and M. Zeidner (Eds.), Self-regulation: Theory, research, and applications (pp. 13-39). Orlando, FL: Academic Press.
  • Zimmerman, B. J., 2001. Theories of self-regulated learning and academic achievement: An overview and analysis. B. J. Zimmerman and D. H. Schunk, (Eds.), Self- regulated learning and academic achievement: Theoretical perspectives (pp. 1-37). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Zimmerman, B.J., 2008. Investigating self-regulation and motivation: Historical background, methodological developments, and future prospects. American Educational Research Journal, 45(1), 166-183.
Year 2016, Volume: 29 Issue: 2, 445 - 467, 29.12.2016

Abstract

References

  • Auerbach, C. F. and Silverstein, L. B., 2003.Qualitative data: An introduction to coding and analysis. New York: New York University Press.
  • Bandura, A., 1997. Self-efficacy: The exercise of control. New York: Freeman.
  • Cleary, T. and Zimmerman, B. J., 2001.Self-regulation differences during athletic practice by experts, non-experts, and novices. Journal of Applied Sport Psychology, 13, 61–82.
  • Davis, G. A. and Rimm, S. B. (Eds.), 2004.Education of the gifted and talented, 3rd ed., Allyn and Bacon, Boston.
  • De Corte, E., Verschaffel, L. and Op’tEynde, P., 2000. Self-regulation: A characteristic and a goal of mathematics education. M. Boekaerts, P.R. Pintrich, and M. H. Zeidner, (Eds.), Handbook of self-regulation (pp.687-726). San Diego, CA: Academic Press.
  • Demircioğlu, H., 2008. Matematik öğretmen adaylarının üst bilişsel davranışlarının gelişimine yönelik tasarlanan eğitim durumlarının etkililiği. Yayınlanmamış Doktora Tezi, Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü. Ankara.
  • Denzin, N. K., and Lincoln, Y.S., 1998. The landscape of qualitative research: theories and issues. Thousand Oaks, CA: Sage Publications.
  • Dresel, M. and Haugwitz, M., 2006. The relationship between cognitive abilities and self regulated learning: evidence for interactions with academic self-concept and gender. High Ability Studies, 16(2), 201-218.
  • Feldhusen, J. F. and Kroll, M. D., 1991. Boredom or challenge for the academically talented in school. Gifted Education International, 7, 80-81.
  • Gagné, F., 2003.Transforming Gifts into Talents: The DMGT as a Developmental Theory. N. Colangelo and G. A. Davis (Eds.) Handbook of Gifted Education (pp. 60-74). Boston MA: Allyn and Bacon.
  • Gardner, M., 1997. Hah, buldum! (Çev. B. Bıçakçı) Ankara: Tübitak Yayınları
  • Gardiner, A., 1987. Mathematical puzzling. Oxford, England: Oxford University Press.
  • Geiger, V. and Galbraith, P., 1998. Developing a diagnostic framework for evaluating student approaches to applied mathematics problems, International Journal of Mathematics, Education, Science and Technology, 29, 533–559.
  • Glaser, B. and Strauss, A. L., 1967. The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine Publishing Company.
  • Greene, J.A., Moos D. C., Azevedo R. and Winters, F.I., 2008. Exploring differences between gifted and grade-level students’ use of self-regulatory learning processes with hypermedia.Computers & Education, 50, 1069–1083.
  • Kitsantas, A. and Zimmerman, B. J., 2002.Comparing self-regulatory processes among novice, non-expert, and expert volleyball players: A microanalytic study. Journal of Applied Sport Psychology, 14, 91-105.
  • Krantz, S. G., 1996. Techniques of problem solving. Providence, RI: American Mathematical Society.
  • Krutetskii, V. A., 1976. The psychology of mathematical abilities in school children. Chicago: University of Chicago Press.
  • Lester, F.K., 1994. Musings about mathematical problem solving research: 1970–1994, Journal for Research in Mathematics Education, 25, 660–675.
  • Malpass, J.R., 1999. Self regulation, goal orientation, self efficacy, worry and high stakes math achievement of mathematically gifted high school students. Roeper Review, 21(4), 281-289.
  • Mayer, R. E., 1985. Implications of cognitive psychology for instruction in mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving (pp. 123–145). Hillsdale, NJ: Lawrence Erlbaum.
  • Merriam, S. B., 1998. Qualitative research and case study applications in education. San Francisco, CA: Jossey-Bass.
  • Miller, R. C., 1990. Discovering mathematical talent. Reston, VA: Council for Exceptional Children, ERIC Clearinghouse on Disabilities and Gifted Education. ERIC Document Reproduction Service No: ED 321 487.
  • Mingus, T. and Grassl, R., 1999.What constitutes a nurturing environment for the growth of mathematically gifted students? School Sciences and Mathematics, 99(6), 286-293.
  • Montague, M., 1991.Gifted and learning disabled gifted students’ knowledge and use of mathematical problem-solving strategies. Journal for the Education of the Gifted, 14, 393-411.
  • Montague, M. and Applegate, B., 1993.Middle school students’ mathematical problem solving: An analysis of think-aloud protocols. Learning Disabilities Quarterly, 16, 19-32.
  • Neber, H. and Schommer-Aikins, M., 2002. Self-regulated science learning with highly gifted students: The role of cognitive, motivational, epistemological, and environmental variables. High Ability Studies, 13(1), 59-74.
  • Pajares, F., 1996.Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543–578.
  • Panaoura, A. and Philippou, G., 2003. The construct validity of an inventory for the measurement of young pupils’ metacognitive abilities in mathematics. N. A. Pateman, B. J. Doherty and J. Zilliox (Eds.), Proceedings 27th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 437-444). Honolulu, USA: PME.
  • Pape, S. J. and Wang, C., 2003. Middle school children’s strategic behavior: Classification and relation to academic achievement and mathematical problem solving. Instructional Science, 31, 419-449.
  • Pativisan, S. and Neiss, M., 2007. Mathematical problem solving processes of Thai gifted students. B. Sriraman (Guest Ed.), Mediterranean Journal for Research in Mathematics Education, 6(1-2), 47–68.
  • Patton, M. Q., 2002. Qualitative research and evaluation methods. Newbury Park: Sage Publication.
  • Pintrich, P.R., 1999. The role of motivation in promoting and sustaining self-regulated learning. International Journal of Educational Research, 31,459-470.
  • Pintrich, P. R., 2000. The role of goal orientation in self-regulated learning. M. Boekaerts, P. R. Pintrich, and M. Zeidner (Eds), Handbook of self- regulation (pp, 451-501). San Diego, CA: Academic Press.
  • Polya, G., 1945. How to solve it: A new aspect of mathematical method. Princeton : Princeton University Press.
  • Posamentier, A. and Krulik, S., 1998. Problem solving strategies for efficient and elegant Solutions. California: Corwin Pres. A Sage Publications.
  • Posamentier, A. and Salkind, C. T., 1988.Challenging problems in geometry. New York: Dover.
  • Risemberg, R. and Zimmerman, B. J., 1992.Self-regulated learning in gifted students. Roeper Review, 15(1), 98-101.
  • Ruban, L. and Reis, S.M., 2006.Patterns of self-regulatory strategy use among low-achieving and high-achieving university students. Roeper Review, 28(3), 148-156.
  • Schoenfeld, A. H., Burkhardt, H., Daro, P., Ridgway, J., Schwartz, J., and Wilcox, S., 1999. High school assessment. White Plains, NY: Dale Seymour Publications.
  • Schunk, D. H., 1998. Teaching elementary students to self-regulate practice of mathematical skills with modeling. In D. H. Schunk and B. J. Zimmerman (Eds.), Self-regulated learning: From teaching to self-reflective practice (pp. 137-159). New York: Guilford.
  • Schraw, O. and Moshman, D., 1995. Metacognitive theories. Educational Psychology Review, 7, 351-371.
  • Shore, B., 1986. Cognition and giftedness: New research directions. Gifted Child Quarterly, 30, 24–27
  • Stillman, G.A. and Galbraith, P.L., 1998. Applying mathematics with real world connections: Metacognitive characteristics of secondary students’, Educational Studies in Mathematics, 36, 157–195.
  • Strauss, A. L., 1987. Qualitative analysis for social scientists. Cambridge Cambridgeshire; New York: Cambridge University Press.
  • Sowell, E. J., 1993. Programs for mathematically gifted students: A review of empirical research. Gifted Child Quarterly,37, 124-132.
  • Strauss, A. and Corbin, J., 1998. Basics of qualitative research: Grounded theory procedures and techniques. London: Sage.
  • Yazgan-Sağ, G., 2012. Üstün yetenekli ortaöğretim öğrencilerinin matematiksel problem çözme durumlarındaki öz düzenleme davranışları. Yayınlanmamış Doktora Tezi, Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Yazgan-Sağ, G., 2014. Üstün yetenekli öğrencilerde özdüzenleme faaliyetleri. G. Sakız (Ed.), Özdüzenleme: Öğrenmeden öğretime özdüzenleme davranışlarının gelişimi, stratejiler ve öneriler (ss. 154-187). Ankara: Nobel Yayınevi,
  • Yazgan-Sağ, G ve Argün, Z., 2016. Üstün yetenekli öğrencilerin matematiksel problem çözme durumlarındaki motivasyonel öngörüleri. Kastamonu Eğitim Dergisi, 24(3), 811-828.
  • Yetkin, İ.E., 2006.The role of classroom context in student self-regulated learning: an exploratory case study in a sixth-grade mathematics classroom. Yayınlanmamış Doktora Tezi, Ohio State University.
  • Yıldırım, A. ve Şimşek, H., 2006. Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yin, R. K., 1994.Case study research: Designs and methods. Newbury Park, CA: Sage.
  • Wieczerkowski, W., Cropley, A. J. and Prado, T. M., 2000.Nurturing talents/gifts in mathematics. K. A. Heller, F. J. Monks, R. J. Sternberg, and R. F. Subotnik (Eds.), International handbook of giftedness and talent education (pp. 413- 425). Oxford, United Kingdom: Pergamon.
  • Zimmerman, B. J., 2000. Attaining of self-regulation: A social cognitive perspective. M. Boekaerts, P. Pintrich and M. Zeidner (Eds.), Self-regulation: Theory, research, and applications (pp. 13-39). Orlando, FL: Academic Press.
  • Zimmerman, B. J., 2001. Theories of self-regulated learning and academic achievement: An overview and analysis. B. J. Zimmerman and D. H. Schunk, (Eds.), Self- regulated learning and academic achievement: Theoretical perspectives (pp. 1-37). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Zimmerman, B.J., 2008. Investigating self-regulation and motivation: Historical background, methodological developments, and future prospects. American Educational Research Journal, 45(1), 166-183.
There are 57 citations in total.

Details

Journal Section Articles
Authors

Gönül Yazgan Sağ

Ziya Argün

Publication Date December 29, 2016
Submission Date December 29, 2016
Published in Issue Year 2016 Volume: 29 Issue: 2

Cite

APA Yazgan Sağ, G., & Argün, Z. (2016). Üstün Yetenekli Öğrencilerin Karşılaştıkları Matematik Problemleri İle İlgili Bilişsel Öngörüleri. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 29(2), 445-467.