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Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar

Year 2015, Volume: 6 Issue: 2, 179 - 208, 08.09.2015
https://doi.org/10.16949/turcomat.00708

Abstract

Çalışmanın amacı, teknoloji destekli matematiksel modelleme sürecinde ortaya çıkan üst bilişsel yapıları açıklamaktır. Üst bilişsel yapıların modelleme sürecinde nasıl şekillendiği planlama, izleme, değerlendirme ve tahmin boyutlarında ele alınarak incelenmiştir. Durum çalışması niteliğindeki çalışma, ortaöğre­tim matematik öğretmenliğinde öğrenim gören üç birinci sınıf öğrencisinin oluşturduğu bir çalışma grubuyla yürütülmüştür. Veriler, çalışma grubunun modelleme problemini çözerken alınan video kayıtlarından, problemin çözümü ile ilgili yazılı yanıtlarından, GeoGebra çözüm dosyalarından ve problemlerin çözüm sürecinde araş­tırmacılar tarafından alınan gözlem notlarından derlenmiştir. Verilerin analizinde tematik kodlamalar yapılarak kategoriler oluşturulmuş ve üst bilişsel yapılar belirlenmiştir. Analiz sonucunda modelleme sürecindeki üst bilişsel yapılar planlama, izleme, değerlendirme ve tahmin boyutları için on sekiz kategori altında toplanmıştır. Üst bilişsel eylemler, teknoloji destekli modelleme sürecinde bilişsel eylemleri düzenlediği gibi birbirlerini de desteklemiştir. Çalışmanın matematiksel modelleme sürecindeki üst bilişsel eylemlere farklı ve derin bir bakış getireceği düşünülmektedir.

Anahtar Kelimeler:  Matematiksel modelleme, üst bilişsel yapılar, GeoGebra, matematik öğretmen adayları, teknoloji destekli modelleme süreci

References

  • Allen, B. R. (1991). A study of metacognitive skill as influenced by expressive writing in college introductory algebra classes (Doctoral dissertation). Louisiana State University Louisiana, the USA.
  • Ang, K. C. (2010). Teaching and learning mathematical modelling with technology, nanyang technological university. Retrieved from http://atcm.mathandtech.org/ep2010/invited/3052010_18134.pdf
  • Baki, A. (2002). Öğrenen ve öğretenler için bilgisayar destekli matematik. İstanbul: BİTAV-Ceren Yayın Dağıtım,
  • Berry, J., & Houston, K. (1995). Mathematical Modelling. Bristol: J. W. Arrowsmith Ltd.
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work - experiences from an in-service course for upper secondary teachers. Zentralblatt für Didaktik der Mathematik. 38(2), 163-177.
  • Blomhøj, M. (2008). Different perspectives on mathematical modelling in educational research - Categorising the TSG21 papers. ICME 11 international Congress on Mathematics Education, 1-13.
  • Blomhøj, M. (2009). Different perspectives in research on the teaching and learning mathematical modeling. Categorising the TSG21 papers. In Blomhøj M. & S. Carreira (Eds.), Mathematical applications and modeling in the teaching and learning of mathematics (pp.1-17). Roskilde: Roskilde University.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86-95.
  • Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modelling behaviour. Journal für Mathematikdidaktik, 31(1), 99-118.
  • Brown, A. L. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, Motivation, and Understanding (pp. 65-116). London: LEA Lawrence Erlbaum Associates, Hillsdale, New Jersey.
  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research (3rd ed.). Thousand Oaks: Sage.
  • Crouch R., & Haines C. (2004). Mathematical modelling: transitions between the real world and the mathematical model. International Journal Mathematics Education Science Technology, 35, 197-206.
  • Desoete, A. (2001). Off-line metacognition in children with mathematics learning disabilities (Doctoral dissertation). Universiteit Gent, Belgium.
  • Desoete, A., Roeyers, H., & Buysse, A.(2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disability, 34(5), 435–449.
  • English, L. D. (2006). Mathematical modelling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323.
  • Ezzy, D. (2002). Qualitative analysis: Practice and innovation. Crows Nest, Australia: Allen & Unwin.
  • Flavell, J. H. (1979). Metacognition and cognitive monitoring. American Psychologist, 34(10) 906-911.
  • Fraenkel, J. R., & Wallen, N. F. (2010). How to design and evaluate research in education. New York: McGraw-Hill Companies.
  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 143-162.
  • Gama, C. A. (2004). Integrating metacognition instruction in interactive learning environments (Doctoral dissertation). University of Sussex, England.
  • Hacker, D. J. (1998). Metacognition: Definitions and empirical foundations. In D. J. Hacker, J. Dunlosky & A. C. Graesser (Eds.), Metacognition in educational theory and practice (pp. 1-23). Mahwah, NJ: Erlbaum.
  • Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matem¬atiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıkla¬ma (Yüksek lisans tezi). Dokuz Eylül Üniversitesi, İzmir.
  • Hıdıroğlu, Ç. N. ve Bukova-Güzel, E. (2013). Teknoloji destekli ortamda matematiksel modellemede modelin doğrulanmasindaki yaklaşimlarin ve düşünme süreçlerinin kavramsallaştirilmasi. Kuram ve Uygulamada Eğitim Bilimleri Dergisi (KUYEB), 13(4), 2487-2508.
  • Kaiser, G., & Sriraman, B. (2006). A Global Survey of International Perspectives on Modelling in Mathematics Education. Zentralblatt für Didaktik der Mathematik, 38(3), 302-310.
  • Kaiser, G. (2005). Introduction to the working group “Applications and Modelling”. In: Bosch, M. (Ed.), Proceeding of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4), pp. 1611-1622.
  • Lesh, R., Lester, F. K., & Hjalmarson, M. (2003). A models and modeling perspective on metacognitive functioning in everyday situations where mathematical constructs need to be developed. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models & modeling perspectives on mathematics problem solving, learning & teaching, (pp. 383-404). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Lingefjärd, T. (2000). Mathematical modeling by prospective teachers using technology (Doctoral dissertation, University of Georgia). Retrieved November 28, 2010 from http://ma-serv.did.gu.se/matematik/thomas.htm
  • Lingefjärd, T., & Holmquist, M. (2005). To assess students’ attitudes, skills and competencies in mathematical modeling. Teaching Mathematics and its Applications, 24(2-3), 123-133.
  • Lucangeli, D., & Cornoldi, C. (1997). Mathematics and metacognition: What is the nature of the relationship?. Mathematical Cognition, 3(2), 121-139.
  • Maaß, K. (2006) What are modelling competencies?. Zentralblatt für Didaktik der Mathematik, 38(2), 113-142.
  • Magiera, M. T., & Zawojewski, J. (2011). Characterizations of social-based and self-based contexts associated with students’ awareness, evaluation, and regulation of their thinking during small-group mathematical modeling. Journal for Research in Mathematics Education, 42(5), 486-520.
  • Mevarech, Z. R., & Kramarski, B. (2003). The effects of worked-out examples vs. meta-cognitive training on students’ mathematical reasoning. British Journal of Educational Psychology, 73, 449–471.
  • National Council of Teachers of Mathematics (1998). Principles and standards for school mathematics: Discussion draft. Reston, VA: Author.
  • National Council of Teachers of Mathematics (2000). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM Publications.
  • Niss, M. (1994). Mathematics in society. In R. Biehler, W. Scholz, R. Sträßer & B. Winkelmann, B. (Eds.), Didactics of mathematics as a scientific discipline (pp. 367-378). Dordrecht: Kluwer Academic Publishers.
  • Niss, M. (2004). Mathematical competencies and the learning of mathematics: The Danish KOM2 project. In A. Gagatsis & S. Papastavridis (Eds.), Proceedings of the 3rd Mediterranean conference on mathematical education (pp. 115-124). Athens, Greece: Hellenic Mathematical Society and Cyprus Mathematical Society.
  • Panaoura, A., Philippou, G., & Christou, C. (2003). Young pupils’ metacognitive ability in mathematics. Paper presented at CERME 3: Third Conference of the European Society for Research in Mathematics Education. Retrieved December 12, 2012 from http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG3/TG3_Panaoura_cerme3.pdf
  • Panaoura, A., & Philippou, G. (2005). The mental models of similar mathematical problems: A strategy for enhancing pupils´ self-representation and self-evaluation. In J. Novotna (Ed.), Proceedings of the International Symposium Elementary Mathematics Teaching (pp. 252-260), Prague.
  • Polya, G. (1957). How to solve it- A new aspect of mathematical method. New York: Doubleday & Company, Inc.
  • Pugalee, D. (2001). Writing, mathematics, and metacognition: Looking for connections through students' work in mathematical problem solving. School Science and Mathematics, 101(5), 236-246.
  • Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In Schoenfeld, A.H. (Ed.), Cognitive Science and Mathematics Education (pp. 189-215). Lawrence Erlbaum Associates.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning (pp. 334– 370). Macmillan: New York.
  • Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In Alan H. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 53-69). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Schraw, G., & Graham, T. (1997). Helping gifted students develop metacognitive awareness. Poeper Rev., 20, 4-8.
  • Schraw, G. (1998). Promoting general metacognitive awareness, Instructional Science, 26, 113-125.
  • Skolverket, S. (1997). Kommentar till grundskolans kursplan och betygskriterier i matematik [Commentary on the Comprehensive School Curriculum and Marking Criteria in Mathematics]. Stockholm: Liber Utbildningsförlaget.
  • Tanner, H., & Jones, S.(1999). Scaffolding metacognition: Reflective discourse and the development of mathematical thinking. Paper presented at the British Educational Research Association Conference, University of Sussex, Brighton. Retrieved November 12, 2012 from http://www.bera.ac.uk
  • Tanner, H. & Jones, S. (2002). ‘Assessing children’s mathematical thinking in practical modelling situations’. Teaching Mathematics and its Applications, 21, 4, 145–159.
  • Türk Dil Kurumu. [TDK]. (2013). Güncel Türkçe Sözlük. 13.01.2013 tarihinde http://www.tdk.gov.tr/index.php?option=com_gts&arama=gts&guid=TDK.GTS.51e292ec8a5eb4.94808124 adresinden alınmıştır.
  • Vos, H. (2001). Metacognition in Higher Education (Doctoral Thesis). University of Twente, Enschede, the Netherlands.
  • Wilburne. J. M (1997). The effect of teaching metacognition strategies to preservice elementary school teachers on their mathematical problem-solving achievement and attitude (Doctoral Thesis). Philadelphia: Temple University.
  • Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştirma yöntemleri (9. basım). Ankara: Seçkin Yayınevi.

Metacognitive Structures Occuring in Mathematical Modelling Within A Technology Enhanced Environment

Year 2015, Volume: 6 Issue: 2, 179 - 208, 08.09.2015
https://doi.org/10.16949/turcomat.00708

Abstract

The aim of this study is to explain metacognitive structures occurring in mathematical modelling within a technology aided environment. How metacognitive structures in modelling process are shaped within the dimensions of planning, monitoring, evaluation and prediction was examined. The study which is a case study, was conducted with a collaborative group of three freshman students who are studying in Secondary Mathematics teacher education programme. Data was collected from video recordings which were taken while collaborative group was solving the modelling problem, written answers of students on solution, GeoGebra solution files and observation notes which were taken by the researchers during problem solving process. During data analysis process, categories were formed by applying thematic coding and metacognitive structures were specified.  As a result of data analysis, metacognitive structures in modelling process for planning, monitoring, evaluation and prediction steps are grouped under eighteen categories. Metacognitive activities organised cognitive activities in technology aided modelling process and support other metacognitive activities. It is believed that this study will bring a different and detailed view into metacognitive activities in mathematical modelling process.

Keywords:  Mathematical modelling, metacognition, GeoGebra, mathematics student teachers, technology aided modelling process

References

  • Allen, B. R. (1991). A study of metacognitive skill as influenced by expressive writing in college introductory algebra classes (Doctoral dissertation). Louisiana State University Louisiana, the USA.
  • Ang, K. C. (2010). Teaching and learning mathematical modelling with technology, nanyang technological university. Retrieved from http://atcm.mathandtech.org/ep2010/invited/3052010_18134.pdf
  • Baki, A. (2002). Öğrenen ve öğretenler için bilgisayar destekli matematik. İstanbul: BİTAV-Ceren Yayın Dağıtım,
  • Berry, J., & Houston, K. (1995). Mathematical Modelling. Bristol: J. W. Arrowsmith Ltd.
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work - experiences from an in-service course for upper secondary teachers. Zentralblatt für Didaktik der Mathematik. 38(2), 163-177.
  • Blomhøj, M. (2008). Different perspectives on mathematical modelling in educational research - Categorising the TSG21 papers. ICME 11 international Congress on Mathematics Education, 1-13.
  • Blomhøj, M. (2009). Different perspectives in research on the teaching and learning mathematical modeling. Categorising the TSG21 papers. In Blomhøj M. & S. Carreira (Eds.), Mathematical applications and modeling in the teaching and learning of mathematics (pp.1-17). Roskilde: Roskilde University.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86-95.
  • Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modelling behaviour. Journal für Mathematikdidaktik, 31(1), 99-118.
  • Brown, A. L. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, Motivation, and Understanding (pp. 65-116). London: LEA Lawrence Erlbaum Associates, Hillsdale, New Jersey.
  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research (3rd ed.). Thousand Oaks: Sage.
  • Crouch R., & Haines C. (2004). Mathematical modelling: transitions between the real world and the mathematical model. International Journal Mathematics Education Science Technology, 35, 197-206.
  • Desoete, A. (2001). Off-line metacognition in children with mathematics learning disabilities (Doctoral dissertation). Universiteit Gent, Belgium.
  • Desoete, A., Roeyers, H., & Buysse, A.(2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disability, 34(5), 435–449.
  • English, L. D. (2006). Mathematical modelling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323.
  • Ezzy, D. (2002). Qualitative analysis: Practice and innovation. Crows Nest, Australia: Allen & Unwin.
  • Flavell, J. H. (1979). Metacognition and cognitive monitoring. American Psychologist, 34(10) 906-911.
  • Fraenkel, J. R., & Wallen, N. F. (2010). How to design and evaluate research in education. New York: McGraw-Hill Companies.
  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 143-162.
  • Gama, C. A. (2004). Integrating metacognition instruction in interactive learning environments (Doctoral dissertation). University of Sussex, England.
  • Hacker, D. J. (1998). Metacognition: Definitions and empirical foundations. In D. J. Hacker, J. Dunlosky & A. C. Graesser (Eds.), Metacognition in educational theory and practice (pp. 1-23). Mahwah, NJ: Erlbaum.
  • Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matem¬atiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıkla¬ma (Yüksek lisans tezi). Dokuz Eylül Üniversitesi, İzmir.
  • Hıdıroğlu, Ç. N. ve Bukova-Güzel, E. (2013). Teknoloji destekli ortamda matematiksel modellemede modelin doğrulanmasindaki yaklaşimlarin ve düşünme süreçlerinin kavramsallaştirilmasi. Kuram ve Uygulamada Eğitim Bilimleri Dergisi (KUYEB), 13(4), 2487-2508.
  • Kaiser, G., & Sriraman, B. (2006). A Global Survey of International Perspectives on Modelling in Mathematics Education. Zentralblatt für Didaktik der Mathematik, 38(3), 302-310.
  • Kaiser, G. (2005). Introduction to the working group “Applications and Modelling”. In: Bosch, M. (Ed.), Proceeding of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4), pp. 1611-1622.
  • Lesh, R., Lester, F. K., & Hjalmarson, M. (2003). A models and modeling perspective on metacognitive functioning in everyday situations where mathematical constructs need to be developed. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models & modeling perspectives on mathematics problem solving, learning & teaching, (pp. 383-404). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Lingefjärd, T. (2000). Mathematical modeling by prospective teachers using technology (Doctoral dissertation, University of Georgia). Retrieved November 28, 2010 from http://ma-serv.did.gu.se/matematik/thomas.htm
  • Lingefjärd, T., & Holmquist, M. (2005). To assess students’ attitudes, skills and competencies in mathematical modeling. Teaching Mathematics and its Applications, 24(2-3), 123-133.
  • Lucangeli, D., & Cornoldi, C. (1997). Mathematics and metacognition: What is the nature of the relationship?. Mathematical Cognition, 3(2), 121-139.
  • Maaß, K. (2006) What are modelling competencies?. Zentralblatt für Didaktik der Mathematik, 38(2), 113-142.
  • Magiera, M. T., & Zawojewski, J. (2011). Characterizations of social-based and self-based contexts associated with students’ awareness, evaluation, and regulation of their thinking during small-group mathematical modeling. Journal for Research in Mathematics Education, 42(5), 486-520.
  • Mevarech, Z. R., & Kramarski, B. (2003). The effects of worked-out examples vs. meta-cognitive training on students’ mathematical reasoning. British Journal of Educational Psychology, 73, 449–471.
  • National Council of Teachers of Mathematics (1998). Principles and standards for school mathematics: Discussion draft. Reston, VA: Author.
  • National Council of Teachers of Mathematics (2000). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM Publications.
  • Niss, M. (1994). Mathematics in society. In R. Biehler, W. Scholz, R. Sträßer & B. Winkelmann, B. (Eds.), Didactics of mathematics as a scientific discipline (pp. 367-378). Dordrecht: Kluwer Academic Publishers.
  • Niss, M. (2004). Mathematical competencies and the learning of mathematics: The Danish KOM2 project. In A. Gagatsis & S. Papastavridis (Eds.), Proceedings of the 3rd Mediterranean conference on mathematical education (pp. 115-124). Athens, Greece: Hellenic Mathematical Society and Cyprus Mathematical Society.
  • Panaoura, A., Philippou, G., & Christou, C. (2003). Young pupils’ metacognitive ability in mathematics. Paper presented at CERME 3: Third Conference of the European Society for Research in Mathematics Education. Retrieved December 12, 2012 from http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG3/TG3_Panaoura_cerme3.pdf
  • Panaoura, A., & Philippou, G. (2005). The mental models of similar mathematical problems: A strategy for enhancing pupils´ self-representation and self-evaluation. In J. Novotna (Ed.), Proceedings of the International Symposium Elementary Mathematics Teaching (pp. 252-260), Prague.
  • Polya, G. (1957). How to solve it- A new aspect of mathematical method. New York: Doubleday & Company, Inc.
  • Pugalee, D. (2001). Writing, mathematics, and metacognition: Looking for connections through students' work in mathematical problem solving. School Science and Mathematics, 101(5), 236-246.
  • Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In Schoenfeld, A.H. (Ed.), Cognitive Science and Mathematics Education (pp. 189-215). Lawrence Erlbaum Associates.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning (pp. 334– 370). Macmillan: New York.
  • Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In Alan H. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 53-69). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Schraw, G., & Graham, T. (1997). Helping gifted students develop metacognitive awareness. Poeper Rev., 20, 4-8.
  • Schraw, G. (1998). Promoting general metacognitive awareness, Instructional Science, 26, 113-125.
  • Skolverket, S. (1997). Kommentar till grundskolans kursplan och betygskriterier i matematik [Commentary on the Comprehensive School Curriculum and Marking Criteria in Mathematics]. Stockholm: Liber Utbildningsförlaget.
  • Tanner, H., & Jones, S.(1999). Scaffolding metacognition: Reflective discourse and the development of mathematical thinking. Paper presented at the British Educational Research Association Conference, University of Sussex, Brighton. Retrieved November 12, 2012 from http://www.bera.ac.uk
  • Tanner, H. & Jones, S. (2002). ‘Assessing children’s mathematical thinking in practical modelling situations’. Teaching Mathematics and its Applications, 21, 4, 145–159.
  • Türk Dil Kurumu. [TDK]. (2013). Güncel Türkçe Sözlük. 13.01.2013 tarihinde http://www.tdk.gov.tr/index.php?option=com_gts&arama=gts&guid=TDK.GTS.51e292ec8a5eb4.94808124 adresinden alınmıştır.
  • Vos, H. (2001). Metacognition in Higher Education (Doctoral Thesis). University of Twente, Enschede, the Netherlands.
  • Wilburne. J. M (1997). The effect of teaching metacognition strategies to preservice elementary school teachers on their mathematical problem-solving achievement and attitude (Doctoral Thesis). Philadelphia: Temple University.
  • Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştirma yöntemleri (9. basım). Ankara: Seçkin Yayınevi.
There are 52 citations in total.

Details

Primary Language Turkish
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Çağlar Hıdıroğlu

Esra Bukova Güzel

Publication Date September 8, 2015
Published in Issue Year 2015 Volume: 6 Issue: 2

Cite

APA Hıdıroğlu, Ç., & Bukova Güzel, E. (2015). Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6(2), 179-208. https://doi.org/10.16949/turcomat.00708
AMA Hıdıroğlu Ç, Bukova Güzel E. Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar. Turkish Journal of Computer and Mathematics Education (TURCOMAT). September 2015;6(2):179-208. doi:10.16949/turcomat.00708
Chicago Hıdıroğlu, Çağlar, and Esra Bukova Güzel. “Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 6, no. 2 (September 2015): 179-208. https://doi.org/10.16949/turcomat.00708.
EndNote Hıdıroğlu Ç, Bukova Güzel E (September 1, 2015) Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 6 2 179–208.
IEEE Ç. Hıdıroğlu and E. Bukova Güzel, “Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 6, no. 2, pp. 179–208, 2015, doi: 10.16949/turcomat.00708.
ISNAD Hıdıroğlu, Çağlar - Bukova Güzel, Esra. “Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 6/2 (September 2015), 179-208. https://doi.org/10.16949/turcomat.00708.
JAMA Hıdıroğlu Ç, Bukova Güzel E. Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2015;6:179–208.
MLA Hıdıroğlu, Çağlar and Esra Bukova Güzel. “Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 6, no. 2, 2015, pp. 179-08, doi:10.16949/turcomat.00708.
Vancouver Hıdıroğlu Ç, Bukova Güzel E. Teknoloji Destekli Ortamda Matematiksel Modellemede Ortaya Çıkan Üst Bilişsel Yapılar. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2015;6(2):179-208.