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Year 2013, Volume: 28 Issue: 28-2, 564 - 576, 01.06.2013

Rezan Yılmaz Ziya Argün

Abstract

The purpose of this study was to investigate the visualization in mathematical generalization process and its importance. To do this, we searched which visualizations were used by the participants in appropriate situations, how they set forth these and what kind of visual images they had. We employed case study technique as a quantitative research method on five participants that were pre-service mathematics teachers. The results showed that the visualization was widely employed by the participants, but in different styles and different visual images were presented in the process. Visualizations had an important place on the relations between concepts, had observable effects on the development of the processes. In the light of the results, some suggestions were given about visualization and visual images to make clear this process for mathematics learning and future academic researches.

Keywords

generalization visualization visual image mathematics education.

References

  • Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.
  • Ben-Chaim, D., Lapan, G., & Houang, R.T. (1989). The role of visualisation in the middle school mathematics cirriculum. Focus on Learning Problems in Mathematics 11 (1), 49-60.
  • Bishop, A. J. (1989). Review of research on visualization in mathematics education. Focus On Learning Problems In Mathematics, 11 (1), 7-16.
  • Davydov, V. V. (1990). Types of generalisation in instruction: logical and phsycological problems in the structuring of school curricula. In: J. Kilpactrick (Ed.). Soviet studies in mathematics education, (2). Reston, VA: National Council of Teachers of Mathematics.
  • Eisenberg, T. (1994). On understanding the reluctance to visualize. Zentralblatt für Didactic der Mathematik, 26 (4), 109Ellis, A. B. (2007). A taxonomy for categorizing generalizations: generalizing actions and reflection generalizations. The Journal of The Learning Sciences, 16 (2), 221–262.
  • Garcia-Cruz, J. A., & Martinon, A. (1998). Levels of genaralizations in linear patterns. Proceeding of the 22 nd Conference of the International Group for the Psychology of Mathematics Education, 2, 329-336.
  • Guzman, M. (2002). The role of visualization in the teaching and learning of mathematical analysis. Paper presented at the Proceedings of the 2 nd International Conference on the Teaching of Mathematics, Greece.
  • Hershkowitz, R. (1989). Visualization in geometry: two side of the coin. Focus on learning Problems in Mathematics. 11 (1), 61-76.
  • Krutetski, V. A. (1976). The Psychology of Mathematical Abilities in School Children. Chicago: University of Chicago Press.
  • Mitchelmore, M. (2002). The role of abstraction and generalisation in the development of mathematical knowledge. Paper presented at the 2nd Proceeding of The East Asia Regional Conference on Mathematics Education, Singapore.
  • Piaget J. (1970). The Principles of Genetic Epistomology. London: Routledge & Keegen Paul Press.
  • Polya, G. (1954). Mathematics and Plausible Resoning: Induction and Analogy in Mathematics (2nd. Ed.). Princeton, NJ: Princeton University Press.
  • Presmeg, (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6 (3), 42-46.
  • Presmeg (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies In Mathematics, 23, 595-610.
  • Presmeg, (1997). Generalization using imagery in mathematics. In L.D. English (Ed.), Mathematical reasoning: Analogies, metaphors and images (pp. 299-312). Malwah, NJ: Erlbaum.
  • Schramm, (1971). Notes on Case Studies of Instructional Media Projects, Working paper for the Academy for Educational Development, Washington, DC.
  • Skemp (1986), The Pphyscology of Learning Mathematics (2nd. Ed.). Harmondsworth: Penguin Press
  • Sriraman, B. (2004). Reflective abstraction, uniframes and the formulation of generalizations. Journal of Mathematical Behavior, 23, 205-222.
  • Strauss, A. & Corbin, J. (1998). Basics of Qualitative Research. Thousand Oaks, London & New Delhi: Sage Puplication.
  • Stylianou, D.A., & Silver, E.A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expert-novice similarities and differences. Mathematical Thinking and Learning, 6(4), 3533
  • Villiers, M. (2007). A hexagon result and its generalization via proof. The Montana Mathematics Enthusiast, 4 (2), 188-1
  • Vinner, S. (1997). From intuition to inhibition – Mathematics, education and other endangered species. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of The International Group for the Physcology of Mathematics Education. (1), 63-78.
  • Wheatley, G. (1998). Imagery and mathematics learning. Focus on Learning Problems in Mathematics, 20 (2), 7-16. Yıldırım, A. ve Şimşek, H. (2006). Nitel Araştırma Yöntemleri, Ankara: Seçkin Yayıncılık.
  • Yılmaz, R., Argün Z., & Keskin, M. Ö. (2009). What is the role of visualization in generalization processes: The case of preservice secondary mathematics teachers. Humanity and Social Sciences Journal 4 (2) , 130-137.
  • Yin R. K. (2003). Case Study Research, Designs and Methods. (3rd Ed.). California: Sage Publications.
  • Zazkis, R., Dubinsky, E. & Dautermann, J. (1996). Coordınatıng visual and analytıc strategies a study of students' understandıng of the group D4, Journal for Research in Mathematics Education, 27 (4), 435-437.
  • Zimmermann, W. & Cunningham, S. (1991) Visualisation in Teaching and Learning Mathematics. Washington DC: Mathematical Association of America.

Matematiksel Genelleme Sürecinde Görselleştirme ve Önemi

Year 2013, Volume: 28 Issue: 28-2, 564 - 576, 01.06.2013

Rezan Yılmaz Ziya Argün

Abstract

Araştırmanın amacı, matematik yapma yöntemlerinden biri olan genelleme sürecinde görselleştirmeyi ve önemini incelemektir. Bunun için, katılımcıların genelleme yapabilecekleri uygun ortamlar içinde hangi görselleştirmeleri nasıl kullandıkları ve ne tür görsel imajlara sahip oldukları araştırılmıştır. Nitel yaklaşımlarından durum çalışması (case study) ile 5 öğretmen adayının katılımcı olduğu araştırmada bulgular, katılımcıların görselleştirmelere sıklıkla ve farklı şekillerde başvurulduğunu ve farklı görsel imajlara sahip olunduğunu göstermektedir. Kullandıkları görselleştirmeler kavramlar ve kavramlar arasındaki ilişkileri tamamlamada önemli bir yere sahip olmuş ve genelleme sürecinin gelişimine tespit edilebilen etkilerde bulunmuştur. Bulgular ışığında genelleme sürecini daha anlaşılır hale getirmek için görselleştirme ve görsel imajlarla ilgili matematik öğretimine yönelik ve ileride yapılacak bilimsel araştırmalara dair öneriler sunulmuştur.

Keywords

genelleme görselleştirme görsel imaj matematik eğitimi.

References

  • Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.
  • Ben-Chaim, D., Lapan, G., & Houang, R.T. (1989). The role of visualisation in the middle school mathematics cirriculum. Focus on Learning Problems in Mathematics 11 (1), 49-60.
  • Bishop, A. J. (1989). Review of research on visualization in mathematics education. Focus On Learning Problems In Mathematics, 11 (1), 7-16.
  • Davydov, V. V. (1990). Types of generalisation in instruction: logical and phsycological problems in the structuring of school curricula. In: J. Kilpactrick (Ed.). Soviet studies in mathematics education, (2). Reston, VA: National Council of Teachers of Mathematics.
  • Eisenberg, T. (1994). On understanding the reluctance to visualize. Zentralblatt für Didactic der Mathematik, 26 (4), 109Ellis, A. B. (2007). A taxonomy for categorizing generalizations: generalizing actions and reflection generalizations. The Journal of The Learning Sciences, 16 (2), 221–262.
  • Garcia-Cruz, J. A., & Martinon, A. (1998). Levels of genaralizations in linear patterns. Proceeding of the 22 nd Conference of the International Group for the Psychology of Mathematics Education, 2, 329-336.
  • Guzman, M. (2002). The role of visualization in the teaching and learning of mathematical analysis. Paper presented at the Proceedings of the 2 nd International Conference on the Teaching of Mathematics, Greece.
  • Hershkowitz, R. (1989). Visualization in geometry: two side of the coin. Focus on learning Problems in Mathematics. 11 (1), 61-76.
  • Krutetski, V. A. (1976). The Psychology of Mathematical Abilities in School Children. Chicago: University of Chicago Press.
  • Mitchelmore, M. (2002). The role of abstraction and generalisation in the development of mathematical knowledge. Paper presented at the 2nd Proceeding of The East Asia Regional Conference on Mathematics Education, Singapore.
  • Piaget J. (1970). The Principles of Genetic Epistomology. London: Routledge & Keegen Paul Press.
  • Polya, G. (1954). Mathematics and Plausible Resoning: Induction and Analogy in Mathematics (2nd. Ed.). Princeton, NJ: Princeton University Press.
  • Presmeg, (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6 (3), 42-46.
  • Presmeg (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies In Mathematics, 23, 595-610.
  • Presmeg, (1997). Generalization using imagery in mathematics. In L.D. English (Ed.), Mathematical reasoning: Analogies, metaphors and images (pp. 299-312). Malwah, NJ: Erlbaum.
  • Schramm, (1971). Notes on Case Studies of Instructional Media Projects, Working paper for the Academy for Educational Development, Washington, DC.
  • Skemp (1986), The Pphyscology of Learning Mathematics (2nd. Ed.). Harmondsworth: Penguin Press
  • Sriraman, B. (2004). Reflective abstraction, uniframes and the formulation of generalizations. Journal of Mathematical Behavior, 23, 205-222.
  • Strauss, A. & Corbin, J. (1998). Basics of Qualitative Research. Thousand Oaks, London & New Delhi: Sage Puplication.
  • Stylianou, D.A., & Silver, E.A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expert-novice similarities and differences. Mathematical Thinking and Learning, 6(4), 3533
  • Villiers, M. (2007). A hexagon result and its generalization via proof. The Montana Mathematics Enthusiast, 4 (2), 188-1
  • Vinner, S. (1997). From intuition to inhibition – Mathematics, education and other endangered species. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of The International Group for the Physcology of Mathematics Education. (1), 63-78.
  • Wheatley, G. (1998). Imagery and mathematics learning. Focus on Learning Problems in Mathematics, 20 (2), 7-16. Yıldırım, A. ve Şimşek, H. (2006). Nitel Araştırma Yöntemleri, Ankara: Seçkin Yayıncılık.
  • Yılmaz, R., Argün Z., & Keskin, M. Ö. (2009). What is the role of visualization in generalization processes: The case of preservice secondary mathematics teachers. Humanity and Social Sciences Journal 4 (2) , 130-137.
  • Yin R. K. (2003). Case Study Research, Designs and Methods. (3rd Ed.). California: Sage Publications.
  • Zazkis, R., Dubinsky, E. & Dautermann, J. (1996). Coordınatıng visual and analytıc strategies a study of students' understandıng of the group D4, Journal for Research in Mathematics Education, 27 (4), 435-437.
  • Zimmermann, W. & Cunningham, S. (1991) Visualisation in Teaching and Learning Mathematics. Washington DC: Mathematical Association of America.
There are 27 citations in total.

Details

Primary Language Turkish
Journal Section Makaleler
Authors

Rezan Yılmaz This is me

Ziya Argün This is me

Publication Date June 1, 2013
Published in Issue Year 2013 Volume: 28 Issue: 28-2

Cite

APA Yılmaz, R., & Argün, Z. (2013). Matematiksel Genelleme Sürecinde Görselleştirme ve Önemi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28(28-2), 564-576.