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Üstel Fonksiyonların Öğrenimine Yönelik Bir Varsayımsal Öğrenme Yolu

Year 2022, Issue: 54, 1461 - 1479, 28.12.2022

Ali Özgün Özer Esra Bukova Güzel

https://doi.org/10.53444/deubefd.1194064

Abstract

Bu çalışma üstel fonksiyonların kavramsal öğrenimine odaklanıldığı, öğretim sürecinde teknoloji destekli modelleme etkinlikleri kullanıldığı, etkinlikleri oluşturma ve uygulama sürecinin gerçekçi matematik eğitimi ve radikal yapılandırmacılık teorilerine dayandırıldığı bir araştırmadır. Çalışmanın amacı, bu etkinliklerin uygulamaları esnasında bir öğrencinin öğrenme yolunu ortaya çıkarmaktır. Çalışma bir öğrenci ile yürütülen ve bu öğrencinin öğrenme yolunun ortaya çıkarılmaya çalışıldığı bir öğretim deneyidir. Uygulama öncesinde üstel fonksiyonların öğrenimine yönelik varsayımlar belirlenmiştir. Bu varsayımlar doğrultusunda, gerçekçi matematik eğitimi perspektifi altında üstel fonksiyonların öğrenimine yönelik bir varsayımsal öğrenme yolu belirlenmiş ve bu öğrenme yoluna uygun bir etkinlik dizisi tasarlanmıştır. Etkinlik dizisi yaklaşık 2 saatlik 4 oturumda uygulanmış ve öğrencinin öğrenme yolu ortaya çıkarılmıştır. Öğrencinin öğrenme yolu ile varsayımsal öğrenme yolu birbirine paralellik göstermiştir. Dolayısıyla tasarlanan etkinlik dizisi ile öğrencinin varsayımsal öğrenme yolundaki bilişsel süreçlerden geçtiği ve başarılı bir şekilde hem kavramsal hem de işlemsel boyutta üstel fonksiyon kavramını öğrendiği gözlemlenmiştir. Bu doğrultuda daha fazla öğrenci veya grup çalışmaları ile bu etkinlik dizisi uygulanabilir ve öğrencilerin öğrenme yolunun varsayımsal öğrenme yoluna uygunluğu incelenebilir.

Keywords

Varsayımsal öğrenme yolu üstel fonksiyon öğretim deneyi

References

  • Bayazit, İ., & Aksoy, Y. (2013). Fonksiyon kavramı: epistemolojisi, algı türleri ve zihinsel gelişimi. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 29(1), 1-9.
  • Borba, M. (1993). Students’ understanding of transformations of functions using multi- represen- tational software, [Unpublished doctoral dissertation], Cornell University.
  • Borba, M. & Confrey, J. (1992). 'Transformations of functions using multi-representational softwa Visualization and discrete points', a paper presented at the Sixteenth Annual Meeting of Psychology of Mathematics Education-NA, Durham.
  • Carlson, M., Jacobs, S., Coe, E., Larsen, S. & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: a framework and a study. Journal for Research in Mathematics Education, 33(5), 352–378.
  • Clements D. H. & Sarama, J. (2004). Learning trajectories in mathematics education, Mathematical Thinking and Learning, 6:2, 81-89, DOI: 10.1207/ s15327833mtl0602.
  • Cobb, P., & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83-94.
  • Confrey, J. (1991). 'The concept of exponential functions: A student's perspective', in L. Steffe (ed.), Epistemological Foundations of Mathematical Experience, New York, pp. 124-159.
  • Confrey, J. (1992). Using computers to promote students’ inventions on the function concept. In S. Malcom, L. Roberts and K. Sheingold (eds.), This Year in School Science 1991: Technology for Teaching and Learning, Washington, DC, pp. 141-174.
  • Confrey, J. & Smith, E. (1991). A framework for functions: Prototypes, multiple representations, and transformations. In R. Underhill & C. Brown (eds.), Proceedings of the Thirteenth An- nual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 57-63). Blacksburg, VA: Virginia Polytechnic Institute & State University.
  • Confrey, J. & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26(2-3), 135-164.
  • Confrey, J. & Smith, E. (1995). Splitting, covariation, and their role in the development of expo- nential functions. Journal for research in mathematics education, 26(1), 66-86.
  • Confrey, J., Smith, E., Piliero, S. and Rizzuti, J. (1991). 'The use of contextual problems and multi- representational software to teach the concept of functions', Final Project Report to the National Science Foundation (MDR-8652160) and Apple Computer, Inc.
  • Doerr, H. M. (2006). Teachers' ways of listening and responding to students' emerging mathematical models. ZDM, 38(3), 255-268.
  • Ellis, A. B., Ozgur, Z., Kulow, T., Dogan, M. F., Williams, C., & Amidon, J. (2013). Correspondence and covariation: Quantities changing together. In M. Martinez, & A. Superfine (Eds.), Proceedings of the 34th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 119–126). Chicago, IL: University of Illinois at Chicago.
  • Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht: Reidel Publishing Company.
  • Hunting, R. P. (1997). Clinical Interview Methods in Mathematics Education Research and Practice. The Journal of Mathematical Behavior, 16(2), 145-165.
  • Koştur, M. & Yılmaz, A. (2017). Technology support for learning exponential and logarithmic functions. Ihlara Eğitim Araştırmaları Dergisi, 2(2), 50-68.
  • Rizzuti, J. (1991). High school students’ uses of multiple representations in the conceptualization of linear and exponential functions, [Unpublished doctoral dissertation], Cornell University.
  • Rizzuti, J. & Confrey, J. (1988). A construction of the concept of exponential functions. In M. Behr, C. LaCompagne and M. Wheeler (eds.), Proceedings of the Tenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Dekalb, pp. 259-268.
  • Simon, M. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26,114-145.
  • Smith, E. & Confrey, J. (1994). Multiplicative structures and the development of logarithms: What was lost by the invention of function. In G. Harel & J. Confrey (Eds.), The development ofmultiplica- tive reasoning in the learning of mathematics (pp. 333-364). Albany, NY: State University of New York Press.
  • Smith, E. and Confrey, J. (1992). 'Using a dynamic software tool to teach transformations of functions', in L. Lum (ed.), a paper presented at the Fifth Annual International Conference on Technology in Collegiate Mathematics, Reading.
  • Steffe, L. P. (1991). The Constructivist Teaching Experiment: Implication and Illustrations. E. von Glasersfeld (Ed.), Radical Constructivism in Mathematics Education (s. 177-194). Dordercht, Hollanda: Kluver.
  • Steffe, L. P. & Thompson, P. W. (2000). Teaching Experiment Methodology: Underlying Principles and Essential Elements. R. Lesh & A. E. Kelly (Ed.), Research Design in Mathematics and Science Education (s. 267-307). Hillsdale, NJ: Erlbaum.
  • Thompson, P. W. (2008). Conceptual analysis of Mathematical Ideas: Some Padework at the Foundation of Mathematics Education. Plenary Paper Delivered at the 32nd Annual Meeting of the International Group for the Psychology of Mathematics Education. O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. SÈpulveda (Ed.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education, (Cilt 1, s. 45-64). MorÈlia, Mexico: PME.
  • Treffers, A. (1987). Three Dimensions (A Model of Goal and Theory Description In Mathematics Instruction – The Wiskobas Project). Holland: Kluwer Academic Publishers Group.
  • Van den Heuvel-Panhuizen, M. (1996). Assessment and Realistic Mathematics Education, CD-ß Press Utrecht University, Utrecht, The Netherlands.
  • Von Glasersfeld, E. (1987). Learning as a constructive activity. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 3-17). Hillsdale, NJ: Lawrence Erlbaum Associates
  • Weber, K. (2002a). Students' understanding of exponential and logarithmic functions. Second International Conference on the Teaching of Mathematics (pp. 1-10). Crete, Greece: University of Crete.
  • Weber, K. (2002b). Developing students’ understanding of exponents and logarithms. In D. S. Mewborn, P. Sztayn, D. Y. White, H. G. Wiegel, R. L. Bryant & K. Nooney (Eds), Proceedings of the International Group for the Psychology of Mathematics Education, North American Chapter (Vol. 2, pp. 1019–1027). Athens, GA.

Year 2022, Issue: 54, 1461 - 1479, 28.12.2022

Ali Özgün Özer Esra Bukova Güzel

https://doi.org/10.53444/deubefd.1194064

Abstract

References

  • Bayazit, İ., & Aksoy, Y. (2013). Fonksiyon kavramı: epistemolojisi, algı türleri ve zihinsel gelişimi. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 29(1), 1-9.
  • Borba, M. (1993). Students’ understanding of transformations of functions using multi- represen- tational software, [Unpublished doctoral dissertation], Cornell University.
  • Borba, M. & Confrey, J. (1992). 'Transformations of functions using multi-representational softwa Visualization and discrete points', a paper presented at the Sixteenth Annual Meeting of Psychology of Mathematics Education-NA, Durham.
  • Carlson, M., Jacobs, S., Coe, E., Larsen, S. & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: a framework and a study. Journal for Research in Mathematics Education, 33(5), 352–378.
  • Clements D. H. & Sarama, J. (2004). Learning trajectories in mathematics education, Mathematical Thinking and Learning, 6:2, 81-89, DOI: 10.1207/ s15327833mtl0602.
  • Cobb, P., & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83-94.
  • Confrey, J. (1991). 'The concept of exponential functions: A student's perspective', in L. Steffe (ed.), Epistemological Foundations of Mathematical Experience, New York, pp. 124-159.
  • Confrey, J. (1992). Using computers to promote students’ inventions on the function concept. In S. Malcom, L. Roberts and K. Sheingold (eds.), This Year in School Science 1991: Technology for Teaching and Learning, Washington, DC, pp. 141-174.
  • Confrey, J. & Smith, E. (1991). A framework for functions: Prototypes, multiple representations, and transformations. In R. Underhill & C. Brown (eds.), Proceedings of the Thirteenth An- nual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 57-63). Blacksburg, VA: Virginia Polytechnic Institute & State University.
  • Confrey, J. & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26(2-3), 135-164.
  • Confrey, J. & Smith, E. (1995). Splitting, covariation, and their role in the development of expo- nential functions. Journal for research in mathematics education, 26(1), 66-86.
  • Confrey, J., Smith, E., Piliero, S. and Rizzuti, J. (1991). 'The use of contextual problems and multi- representational software to teach the concept of functions', Final Project Report to the National Science Foundation (MDR-8652160) and Apple Computer, Inc.
  • Doerr, H. M. (2006). Teachers' ways of listening and responding to students' emerging mathematical models. ZDM, 38(3), 255-268.
  • Ellis, A. B., Ozgur, Z., Kulow, T., Dogan, M. F., Williams, C., & Amidon, J. (2013). Correspondence and covariation: Quantities changing together. In M. Martinez, & A. Superfine (Eds.), Proceedings of the 34th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 119–126). Chicago, IL: University of Illinois at Chicago.
  • Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht: Reidel Publishing Company.
  • Hunting, R. P. (1997). Clinical Interview Methods in Mathematics Education Research and Practice. The Journal of Mathematical Behavior, 16(2), 145-165.
  • Koştur, M. & Yılmaz, A. (2017). Technology support for learning exponential and logarithmic functions. Ihlara Eğitim Araştırmaları Dergisi, 2(2), 50-68.
  • Rizzuti, J. (1991). High school students’ uses of multiple representations in the conceptualization of linear and exponential functions, [Unpublished doctoral dissertation], Cornell University.
  • Rizzuti, J. & Confrey, J. (1988). A construction of the concept of exponential functions. In M. Behr, C. LaCompagne and M. Wheeler (eds.), Proceedings of the Tenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Dekalb, pp. 259-268.
  • Simon, M. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26,114-145.
  • Smith, E. & Confrey, J. (1994). Multiplicative structures and the development of logarithms: What was lost by the invention of function. In G. Harel & J. Confrey (Eds.), The development ofmultiplica- tive reasoning in the learning of mathematics (pp. 333-364). Albany, NY: State University of New York Press.
  • Smith, E. and Confrey, J. (1992). 'Using a dynamic software tool to teach transformations of functions', in L. Lum (ed.), a paper presented at the Fifth Annual International Conference on Technology in Collegiate Mathematics, Reading.
  • Steffe, L. P. (1991). The Constructivist Teaching Experiment: Implication and Illustrations. E. von Glasersfeld (Ed.), Radical Constructivism in Mathematics Education (s. 177-194). Dordercht, Hollanda: Kluver.
  • Steffe, L. P. & Thompson, P. W. (2000). Teaching Experiment Methodology: Underlying Principles and Essential Elements. R. Lesh & A. E. Kelly (Ed.), Research Design in Mathematics and Science Education (s. 267-307). Hillsdale, NJ: Erlbaum.
  • Thompson, P. W. (2008). Conceptual analysis of Mathematical Ideas: Some Padework at the Foundation of Mathematics Education. Plenary Paper Delivered at the 32nd Annual Meeting of the International Group for the Psychology of Mathematics Education. O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. SÈpulveda (Ed.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education, (Cilt 1, s. 45-64). MorÈlia, Mexico: PME.
  • Treffers, A. (1987). Three Dimensions (A Model of Goal and Theory Description In Mathematics Instruction – The Wiskobas Project). Holland: Kluwer Academic Publishers Group.
  • Van den Heuvel-Panhuizen, M. (1996). Assessment and Realistic Mathematics Education, CD-ß Press Utrecht University, Utrecht, The Netherlands.
  • Von Glasersfeld, E. (1987). Learning as a constructive activity. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 3-17). Hillsdale, NJ: Lawrence Erlbaum Associates
  • Weber, K. (2002a). Students' understanding of exponential and logarithmic functions. Second International Conference on the Teaching of Mathematics (pp. 1-10). Crete, Greece: University of Crete.
  • Weber, K. (2002b). Developing students’ understanding of exponents and logarithms. In D. S. Mewborn, P. Sztayn, D. Y. White, H. G. Wiegel, R. L. Bryant & K. Nooney (Eds), Proceedings of the International Group for the Psychology of Mathematics Education, North American Chapter (Vol. 2, pp. 1019–1027). Athens, GA.
There are 30 citations in total.

Details

Primary Language Turkish
Subjects Studies on Education
Journal Section Articles
Authors

Ali Özgün Özer 0000-0002-4204-9115

Esra Bukova Güzel 0000-0001-7571-1374

Publication Date December 28, 2022
Published in Issue Year 2022 Issue: 54

Cite

APA Özer, A. Ö., & Bukova Güzel, E. (2022). Üstel Fonksiyonların Öğrenimine Yönelik Bir Varsayımsal Öğrenme Yolu. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi(54), 1461-1479. https://doi.org/10.53444/deubefd.1194064
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