BibTex RIS Cite

PROBLEM ÇÖZME SÜREÇLERİNDE ÖĞRENCİLERİN MODELLEME SEVİYELERİNİN BELİRLENMESİ

Year 2017, Volume: 18 Issue: 3, 608 - 632, 01.08.2017

Abstract

Bu çalışmanın amacı problem çözme etkinliklerinde öğrencilerin modelleme seviyelerini Llinares ve Roig’nin 2008 modelleme sürecindeki gelişme seviyeleri karakterizasyonu tablosuna göre belirlemektir. Yapılan çalışmada nitel araştırma yöntemlerinden durum çalışması kullanılmıştır. Araştırmanın katılımcıları toplam 24 ortaokul öğrencisinden oluşmaktadır. Veri toplama aracı olarak Llinares ve Roig’nin 2008 çalışmasındaki model kurmayı gerektiren 3 problem kullanılmıştır. Ayrıca, öğrencilerin problem durumlarını modelleme yolları hakkında daha fazla bilgi edinmek için, bazı öğrencilerle görüşmeler de yapılmıştır. Araştırmanın bulguları incelendiğinde, çözümlerin çok azının modelleme kullanılarak Seviye 3 düzeyinde yapıldığı görülmüştür. Öğrencilerin bazılarının soruyu anlayamadıkları için anlamsız aritmetik işlemler yürüterek problemin modelleme sürecinde zorluk yaşadığı ve Seviye 0’da kaldığı görülürken, diğer bazı öğrencilerin ise problemi anlayıp yorumlamasına rağmen herhangi bir matematiksel model geliştiremedikleri için Seviye 1 veya Seviye 2’de kalmıştır. Dolayısıyla, öğrencilerin modelleme yoluyla problem çözme sürecinde başarılı olması için modelleme becerilerini geliştirmeye yönelik etkinliklere ilköğretim öğretim programlarından başlanarak yer verilmesi ve öğretmenlere de bu bakış açısının kazandırılması için öğretmen yetiştirme programlarında matematiksel modellemeyi öğretmeye yönelik derslerin konulması önerilmektedir.

References

  • Artz, A. F. ve Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and instruction, 9(2), 137-175.
  • Aydın Güç, F. ve Baki, A. (2016). The Classification of Development and Assessment Approaches for Mathematical Modelling Competencies. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 7(3), 621-645. DOI: 10.16949/turkbilmat.277876
  • Becker, J. P. ve Miwa, T. (1987). Proceedings of the U.S.-Japan seminar on mathematical problem solving (Honolulu, Hawaii, July 14-18, 1986) (COLLECTED WORKS -Conference Proceedings No. INT-8514988): Southern Illinois Univ., Carbondale.
  • Berry, J. ve Nyman, M. (1998). Introducing mathematical modelling skills to students and the use of posters in assessment. Primus, 8(2), 103-115.
  • Blomhİj, M. (2004). Mathematical modelling-a theory for practice. İçinde B. Clark et al. (Eds.), Perspectives on learning and teaching mathematics (ss. 145-159). Göteborg University.
  • Blum, W. ve Kaiser, G. (1997). Vergleichendeempirische Untersuchungenzumathematischen Anwendungsfähigkeiten von englischen und deutschen Lernenden. Unpublished application to Deutsche Forschungsgesellschaft.
  • Blum, W. ve Niss, M. (1991). Applied mathematical problem solving, modelling, application, and links to other subjects-state, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68.
  • Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd Ed.). Los Angeles: SAGE Publications.
  • De Corte, E., Greer, B., ve Verschaffel, L. (1996). Mathematics teaching and learning. İçinde D. Berliner ve R. Calfee (Eds.), Handbook of educational psychology (ss. 491-549). New York: MacMillan.
  • Doerr, H. M. (2006). Examining the tasks of teaching when using students’ mathematical thinking. Educational Studies in Mathematics, 62(1), 3-24.
  • Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi. Doktora Tezi, Hacettepe Üniversitesi, Sosyal Bilimler Enstitüsü, Ankara, 265182.
  • English, L. D. (2003). Reconciling theory, research, and practice: A models and modelling perspective. Educational Studies in Mathematics, 54(2-3), 225-248.
  • English, L. D. (2011). Complex modelling in the primary/middle school years. İçinde G. Stillman ve J. Brown (Eds.), ICTMA Book of Abstracts (ss. 1-10). Melbourne, Victoria: Australian Catholic University.
  • English, L. D. ve Lesh, R. (2003). Ends-in-view Problems. İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (ss. 297-316). Mahwah, New Jersey: Lawrence Erlbaum Associates.
  • English, L. D. ve Watters, J. J. (2004). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 59-80.
  • Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., ve Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri [Educational Sciences: Theory and Practice], 14(4), 1-21.
  • Ferri, R. B. ve Blum, W. (2013). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. Proceedings of CERME 8, February 6-10.
  • Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modeling and Application, 1(5), 3-16.
  • Gravemeijer, K. ve Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111-129.
  • Greeno, J. (1991). Number sense as a situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170-218.
  • Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293-307.
  • Heymann, H. W. (2003). Why teach mathematics? A focus on general education. Dordrecht: Kluwer.
  • Julie, C. (2002). Making relevance in mathematics teacher education. İçinde I. Vakalis, D. Hughes Hallett, D. Quinney ve C. Kourouniotis (Compilers). Proceedings of 2nd International Conference on the Teaching of Mathematics. New York: Wiley.
  • Kaiser, G. ve Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM-The International Journal on Mathematics Education, 38(3), 302-310.
  • Lakatos, I. (1976). Proofs and refutations: the logic of mathematical discovery. Cambridge: Cambridge University Press.
  • Lesh, R. ve Doerr, H. M. (2000). Symbolizing, communicating, and mathematizing: Key components of models and modelling. İçinde P. Cobb, E. Yackel ve K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools and instructional design. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R. ve Doerr, H. M. (2003a). Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning and teaching. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R. ve Doerr, H. M. (2003b). In what ways does a models and modelling perspective move beyond constructivism? İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning and teaching (ss. 383-403). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R. ve Harel, G. (2003). Problem solving, modeling and local conceptual development. Mathematical Thinking and Learning, 5(2-3), 157-189.
  • Lesh, R. ve Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2), 109-129.
  • Lesh, R. ve Zawojewski, J. S. (2007). Problem solving and modeling. İçinde F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (ss. 763-804). Reston, VA: NCTM.
  • Lesh, R., Lester F. K., ve Hjalmarson, M. (2003). A models and modeling perspective on metacognitive functioning in everyday situations where problem solvers develop mathematical constructs. İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning and teaching (ss. 383–403). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Llinares, S. ve Roig, A. I. (2008). Secondary school students’ construction and use of mathematical models in solving word problems. International Journal of Science and Mathematics Education, 6(3), 505-532.
  • Milli Eğitim Bakanlığı (MEB). (2013). Ortaöğretim matematik dersi (9, 10, 11, ve 12. sınıflar) öğretim programı, Ankara: MEB.
  • National Commission on Mathematics and Science Teaching. (NCMST). (2000). Before it’s too late. A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21st century.
  • National Council of Teachers of Mathematics. (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Research Council. (NRC). (1998). High school mathematics at work: Essays and examples for the education of all students. DC: National Academy Pres., Washington.
  • Niss, M., Blum, W. ve Galbraith, P. L. (2007). Introduction. İçinde W. Blum, P. Galbraith, H. Henn ve M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (ss. 3-32). New York: Springer.
  • Ören Vural, D., Çetinkaya, B., Erbaş, A. K., Alacacı, C., ve Çakıroğlu, E. (2013). Lise matematik öğretmenlerinin modelleme ve modellemenin matematik öğretiminde kullanılmasına yönelik düşünceleri: Bir hizmet içi eğitim programının etkisi. 1.Türk Bilgisayar ve Matematik Eğitimi Sempozyumu. 20-22 Haziran 2013, Trabzon.
  • Organization for Economic Co-operation and Development. (OECD). (2013). PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. Paris: OECD Publishing.
  • Polya, G. (2008). How to solve it: A new aspect of mathematical method. Princeton University Press.
  • Restivo, S. (1993). Math worlds, philosophical and social studies of mathematics and mathematics education. Albany: State of University of NY.
  • Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. İçinde Grouws D. A. (Ed.), Handbook of research on mathematics teaching and learning (ss. 334-370). Macmillan, New York.
  • Schroeder, T. L. ve Lester, F. K. (1989). Understanding mathematics via problem solving. İçinde P. Trafton (Ed.), New directions for elementary school mathematics (ss. 31-42). Reston, VA: National Council of Teachers of Mathematics.
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36.
  • Silver, E. A. (1992). Referential mappings and the solutions of division story problems involving remainders. Focus on Learning Problems in Mathematics, 12(3), 29-39.
  • Stacey, K. (2015). The real world and the mathematical world. İçinde K. Stacey ve R. Turner (Eds.), Assessing mathematical literacy: The PISA experience (ss. 57-84). New York, NY: Springer.
  • Strauss, A. ve Corbin, J. (1994). Grounded theory methodology: An overview. İçinde N. K. Denzin ve Y. Lincoln (Eds.), Handbook of qualitative research (ss. 273-285). Thousand Oaks: Sage.
  • Verschaffel, L., De Corte, E., ve Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modeling of school word problems. Learning and Instruction, 7(4), 339-359.
  • Verschaffel, L., Greer, B., ve De Corte, E. (2002). Everyday knowledge and mathematical modelling of school word problems. İçinde K. Gravemejeir, R. Lehrer, B. Oers ve L. Verschaffel (Eds.), Symbolizing, modelling and tool uses in mathematics education (ss. 257-276). Dordrecht: Kluwer Academic Publishers.
  • Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Applied Social Research Series, Vol. 5, Sage Publications.
  • Zawojewski, J. S., Lesh, R., ve English, L. (2003). A models and modelling perspective on the role of small group learning activities. İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (ss. 337- 358). Mahwah, NJ: Lawrence Erlbaum Associates.

PROBLEM ÇÖZME SÜREÇLERİNDE ÖĞRENCİLERİN MODELLEME SEVİYELERİNİN BELİRLENMESİ

Year 2017, Volume: 18 Issue: 3, 608 - 632, 01.08.2017

Abstract

References

  • Artz, A. F. ve Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and instruction, 9(2), 137-175.
  • Aydın Güç, F. ve Baki, A. (2016). The Classification of Development and Assessment Approaches for Mathematical Modelling Competencies. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 7(3), 621-645. DOI: 10.16949/turkbilmat.277876
  • Becker, J. P. ve Miwa, T. (1987). Proceedings of the U.S.-Japan seminar on mathematical problem solving (Honolulu, Hawaii, July 14-18, 1986) (COLLECTED WORKS -Conference Proceedings No. INT-8514988): Southern Illinois Univ., Carbondale.
  • Berry, J. ve Nyman, M. (1998). Introducing mathematical modelling skills to students and the use of posters in assessment. Primus, 8(2), 103-115.
  • Blomhİj, M. (2004). Mathematical modelling-a theory for practice. İçinde B. Clark et al. (Eds.), Perspectives on learning and teaching mathematics (ss. 145-159). Göteborg University.
  • Blum, W. ve Kaiser, G. (1997). Vergleichendeempirische Untersuchungenzumathematischen Anwendungsfähigkeiten von englischen und deutschen Lernenden. Unpublished application to Deutsche Forschungsgesellschaft.
  • Blum, W. ve Niss, M. (1991). Applied mathematical problem solving, modelling, application, and links to other subjects-state, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68.
  • Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd Ed.). Los Angeles: SAGE Publications.
  • De Corte, E., Greer, B., ve Verschaffel, L. (1996). Mathematics teaching and learning. İçinde D. Berliner ve R. Calfee (Eds.), Handbook of educational psychology (ss. 491-549). New York: MacMillan.
  • Doerr, H. M. (2006). Examining the tasks of teaching when using students’ mathematical thinking. Educational Studies in Mathematics, 62(1), 3-24.
  • Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi. Doktora Tezi, Hacettepe Üniversitesi, Sosyal Bilimler Enstitüsü, Ankara, 265182.
  • English, L. D. (2003). Reconciling theory, research, and practice: A models and modelling perspective. Educational Studies in Mathematics, 54(2-3), 225-248.
  • English, L. D. (2011). Complex modelling in the primary/middle school years. İçinde G. Stillman ve J. Brown (Eds.), ICTMA Book of Abstracts (ss. 1-10). Melbourne, Victoria: Australian Catholic University.
  • English, L. D. ve Lesh, R. (2003). Ends-in-view Problems. İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (ss. 297-316). Mahwah, New Jersey: Lawrence Erlbaum Associates.
  • English, L. D. ve Watters, J. J. (2004). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 59-80.
  • Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., ve Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri [Educational Sciences: Theory and Practice], 14(4), 1-21.
  • Ferri, R. B. ve Blum, W. (2013). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. Proceedings of CERME 8, February 6-10.
  • Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modeling and Application, 1(5), 3-16.
  • Gravemeijer, K. ve Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111-129.
  • Greeno, J. (1991). Number sense as a situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170-218.
  • Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293-307.
  • Heymann, H. W. (2003). Why teach mathematics? A focus on general education. Dordrecht: Kluwer.
  • Julie, C. (2002). Making relevance in mathematics teacher education. İçinde I. Vakalis, D. Hughes Hallett, D. Quinney ve C. Kourouniotis (Compilers). Proceedings of 2nd International Conference on the Teaching of Mathematics. New York: Wiley.
  • Kaiser, G. ve Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM-The International Journal on Mathematics Education, 38(3), 302-310.
  • Lakatos, I. (1976). Proofs and refutations: the logic of mathematical discovery. Cambridge: Cambridge University Press.
  • Lesh, R. ve Doerr, H. M. (2000). Symbolizing, communicating, and mathematizing: Key components of models and modelling. İçinde P. Cobb, E. Yackel ve K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools and instructional design. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R. ve Doerr, H. M. (2003a). Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning and teaching. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R. ve Doerr, H. M. (2003b). In what ways does a models and modelling perspective move beyond constructivism? İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning and teaching (ss. 383-403). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Lesh, R. ve Harel, G. (2003). Problem solving, modeling and local conceptual development. Mathematical Thinking and Learning, 5(2-3), 157-189.
  • Lesh, R. ve Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2), 109-129.
  • Lesh, R. ve Zawojewski, J. S. (2007). Problem solving and modeling. İçinde F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (ss. 763-804). Reston, VA: NCTM.
  • Lesh, R., Lester F. K., ve Hjalmarson, M. (2003). A models and modeling perspective on metacognitive functioning in everyday situations where problem solvers develop mathematical constructs. İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning and teaching (ss. 383–403). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  • Llinares, S. ve Roig, A. I. (2008). Secondary school students’ construction and use of mathematical models in solving word problems. International Journal of Science and Mathematics Education, 6(3), 505-532.
  • Milli Eğitim Bakanlığı (MEB). (2013). Ortaöğretim matematik dersi (9, 10, 11, ve 12. sınıflar) öğretim programı, Ankara: MEB.
  • National Commission on Mathematics and Science Teaching. (NCMST). (2000). Before it’s too late. A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21st century.
  • National Council of Teachers of Mathematics. (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Research Council. (NRC). (1998). High school mathematics at work: Essays and examples for the education of all students. DC: National Academy Pres., Washington.
  • Niss, M., Blum, W. ve Galbraith, P. L. (2007). Introduction. İçinde W. Blum, P. Galbraith, H. Henn ve M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (ss. 3-32). New York: Springer.
  • Ören Vural, D., Çetinkaya, B., Erbaş, A. K., Alacacı, C., ve Çakıroğlu, E. (2013). Lise matematik öğretmenlerinin modelleme ve modellemenin matematik öğretiminde kullanılmasına yönelik düşünceleri: Bir hizmet içi eğitim programının etkisi. 1.Türk Bilgisayar ve Matematik Eğitimi Sempozyumu. 20-22 Haziran 2013, Trabzon.
  • Organization for Economic Co-operation and Development. (OECD). (2013). PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. Paris: OECD Publishing.
  • Polya, G. (2008). How to solve it: A new aspect of mathematical method. Princeton University Press.
  • Restivo, S. (1993). Math worlds, philosophical and social studies of mathematics and mathematics education. Albany: State of University of NY.
  • Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. İçinde Grouws D. A. (Ed.), Handbook of research on mathematics teaching and learning (ss. 334-370). Macmillan, New York.
  • Schroeder, T. L. ve Lester, F. K. (1989). Understanding mathematics via problem solving. İçinde P. Trafton (Ed.), New directions for elementary school mathematics (ss. 31-42). Reston, VA: National Council of Teachers of Mathematics.
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36.
  • Silver, E. A. (1992). Referential mappings and the solutions of division story problems involving remainders. Focus on Learning Problems in Mathematics, 12(3), 29-39.
  • Stacey, K. (2015). The real world and the mathematical world. İçinde K. Stacey ve R. Turner (Eds.), Assessing mathematical literacy: The PISA experience (ss. 57-84). New York, NY: Springer.
  • Strauss, A. ve Corbin, J. (1994). Grounded theory methodology: An overview. İçinde N. K. Denzin ve Y. Lincoln (Eds.), Handbook of qualitative research (ss. 273-285). Thousand Oaks: Sage.
  • Verschaffel, L., De Corte, E., ve Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modeling of school word problems. Learning and Instruction, 7(4), 339-359.
  • Verschaffel, L., Greer, B., ve De Corte, E. (2002). Everyday knowledge and mathematical modelling of school word problems. İçinde K. Gravemejeir, R. Lehrer, B. Oers ve L. Verschaffel (Eds.), Symbolizing, modelling and tool uses in mathematics education (ss. 257-276). Dordrecht: Kluwer Academic Publishers.
  • Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Applied Social Research Series, Vol. 5, Sage Publications.
  • Zawojewski, J. S., Lesh, R., ve English, L. (2003). A models and modelling perspective on the role of small group learning activities. İçinde R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (ss. 337- 358). Mahwah, NJ: Lawrence Erlbaum Associates.
There are 52 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Murat Genç

İlhan Karataş This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 18 Issue: 3

Cite

APA Genç, M., & Karataş, İ. (2017). PROBLEM ÇÖZME SÜREÇLERİNDE ÖĞRENCİLERİN MODELLEME SEVİYELERİNİN BELİRLENMESİ. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(3), 608-632.

2562219122   19121   19116   19117     19118       19119       19120     19124