Research Article
BibTex RIS Cite

Geleceğin Matematik Öğretmenlerinin Rasyonel ve İrrasyonel Sayı Kavramları Konusundaki Bilgileri

Year 2017, Volume: 30 Issue: 2, 551 - 581, 20.12.2017
https://doi.org/10.19171/uefad.368968

Abstract

Bu araştırmada matematik öğretmen adaylarının rasyonel ve irrasyonel sayı kavramlarına ilişkin bilgilerinin incelenmesi amaçlanmıştır. Nitel araştırma yöntemlerinin kullanıldığı bu çalışma, durum çalışması şeklinde tasarlanmıştır. Araştırmanın katılıcılarını 40 ortaöğretim matematik öğretmen adayı oluşturmaktadır. Araştırmacılar tarafından oluşturulan açık uçlu soru formu ve yarı yapılandırılmış görüşmeler aracılığıyla toplanan verilerin analizi sonucu katılımcıların birçoğunun rasyonel ve irrasyonel sayılar konusundaki kavram bilgilerinin eksik ya da hatalı olduğu belirlenmiştir. Katılımcıların bu konuda bazı kavram yanılgılarına sahip oldukları, rasyonel ve irrasyonel sayıları birbirinden ayırt etmede yeterince başarılı olamadıkları, bir sayının farklı temsillerinin eşitliğinin bilincinde olmadıkları ve rasyonel ve irrasyonel sayı kümelerinin kardinalitelerinin belirleme ve birbiri ile mukayese etme konusunda yetersiz kaldıkları belirlenmiştir.

References

  • Aktaş, M. C., Apaydın, Z., & Aktaş, D. Y. (2014). 9. Sınıf Öğrencilerinin Rasyonel Sayılar Kümesinin Yoğunluğunu Anlama Düzeyleri. Eğitim ve Bilim, 39(171).
  • Arcavi, A., Bruckheimer, M., & Ben-Zvi, R. (1987). History of mathematics for teachers: The case of irrational numbers. For the Learning of Mathematics, 7(2), 18-23.
  • Argün, Z., Arıkan, A., Bulut, S., & Halıcıoğlu, S. (2014). Temel matematik kavramlarının künyesi. Ankara: Gazi Kitabevi. Baki, A. & Bell, A. (1997). Ortaöğretim matematik öğretimi 1. Cilt, YÖK/Dünya Bankası Milli Eğitimi Geliştirme Projesi Hizmet Öncesi Öğretmen Eğitimi, Ankara.
  • Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8, 40-48.
  • Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for research in mathematics education, 132-144.
  • Baykul, Y. (2014). Ortaokulda matematik öğretimi (5-8 sınıflar) (2.Baskı). Ankara: Pegem Yayıncılık.
  • Behr, M. J., Lesh, R., & Post, T. R. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes. (pp.91-125). New York: Academic Press.
  • Behr, M. J., Harel, G., Post, T. R., & Lesh, R. (1992). Rational number, ratio, and proportion. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.296-333). New York: Macmillan.
  • Bezuk, N. S. & Bieck, M. (1993). Current research on rational numbers and common fractions: Summary and implications for teachers. In D.T. Owens (Ed.), Research ideas for the classroom-Middle grades mathematics (pp.118-136). New York: Macmillan.
  • Birgin, O., & Gürbüz, R. (2009). İlköğretim II. kademe öğrencilerinin rasyonel sayılar konusundaki işlemsel ve kavramsal bilgi düzeylerinin incelenmesi. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 22(2), 529-550.
  • Burroughs, E. A., & Yopp, D. (2010). Prospective teachers’ understanding of decimals with single repeating digits. Investigations in Mathematics Learning, 3(1), 23-42.
  • Courant, R., Robbins, H., & Stewart, I. (1996). What is Mathematics?: An elementary approach to ideas and methods. OUP Us.
  • Çiftçi, Z., Akgün, L., & Soylu, Y. (2015). Matematik öğretmeni adaylarının irrasyonel sayılarla ilgili anlayışları. Journal of Kırsehir Education Faculty, 16(1).
  • Desmet, L., Gregoire, J., & Mussolin, C. (2010). Developmental changes in the comparison of decimal fractions. Learning and Instruction, 20, 521-532.
  • Dubinsky, E., Arnon, I., & Weller, K. (2013). Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion. Canadian Journal of Science, Mathematics and Technology Education, 13(3), 232-258.
  • Durmuş, S. (2005). İlköğretim öğretmen adaylarının rasyonel sayıları anlama düzeylerinin belirlenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 5(2), 639-666
  • Fischbein, E., Jehiam, R., & Cohen, C. (1995). The concept of irrational number in high school student and prospective teachers. Educational Studies in Mathematics, 29, 29-44
  • Gelman, R. (2000). The epigenesis of mathematical thinking. Journal of Applied Developmental Psychology, 21, 27–37
  • Giannakoulias, E., Souyoul, A., & Zachariades, T. (2007). Students’ thinking about fundamental real numbers properties. In Proceedings of the fifth congress of the European society for research in mathematics education (pp.416-425).
  • Gürbüz, R., & Birgin, O. (2008). Farklı öğrenim seviyesindeki öğrencilerin rasyonel sayıların farklı gösterim şekilleriyle işlem yapma becerilerinin karşılaştırılması. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 23(23), 85-94.
  • Güven, B., Çekmez, E., & Karataş, I. (2011). Examining preservice elementary mathematics teachers' understandings about irrational numbers. PRIMUS, 21(5), 401-416.
  • Haser, Ç., & Ubuz, B. (2002). Kesirlerde kavramsal ve işlemsel performans. Eğitim ve Bilim, 27(126).
  • İpek, A. S., Işık, C., & Albayrak, M. (2005). Sınıf öğretmeni adaylarının kesir işlemleri konusundaki kavramsal performansları. Kazım Karabekir Eğitim Fakültesi Dergisi, 1, 537-547.
  • Kaminski, E. (2002). Promoting mathematical understanding: Number sense in action. Mathematics Education Research Journal, 14(2), 133-149.
  • Kieren, T. E. (1976). On the mathematical, cognitive, and ınstructional foundations of rational numbers. In R. A. Lesh (Ed.), Number and Measurement (pp.101-144). Columbus, Oh: Ohio State University, EEIC, SMEAC.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient field to recursive understanding. In T.P. Carperten, E. Fennema & T.A. Romberg (Eds.), Rational numbers: An integration of research (pp.49-84). Hillsdade, NJ: Erlbaum
  • Lamon, S. J. (2001). Presenting and representing: From fractions to rational numbers. In A. Cuoco (Ed.), The roles of representation in school mathematics (pp.41-52). Reston,VA: NCTM.
  • MacHale, D. (1980). The predictability of counterexamples. American Mathematical Monthly, 87(9),752
  • Mack, N. (1995). Confounding whole-number and fraction concept when building on informal knowledge. Journal for Research Mathematics Education, 26(5), 422-441.
  • Mason. J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15(3), 277–289.
  • MEB, (2013a). Ortaokul matematik dersi (5,6,7 ve 8.Sınıflar) öğretim programı. Ankara: Millî Eğitim Bakanlığı, Talim Terbiye Kurulu Başkanlığı.
  • MEB (2013b). Ortaöğretim matematik dersi (9,10,11 ve 12.Sınıflar) öğretim programı. Ankara: Millî Eğitim Bakanlığı, Talim Terbiye Kurulu Başkanlığı.
  • MEB (2015). İlkokul matematik dersi (1,2,3 ve 4.Sınıflar) öğretim programı. Ankara: Millî Eğitim Bakanlığı, Talim Terbiye Kurulu Başkanlığı.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation: Revised and expanded from qualitative research and case study applications in education. San Franscisco: Jossey-Bass.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. (2nd Edition). California: SAGE Publications.
  • Moseley, B. (2005). Students’ early mathematical representaion knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60, 37–69.
  • Moss, J. (2005). Pipes, tubes, and beakers: New approaches to teaching the rational-number system. How students learn: History, math, and science in the classroom, 309-349.
  • NCTM, (2000). National council of teachers of mathematics. Principles and standards for school mathematics. Reston, VA.: NCTM
  • Ni, Y., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.
  • O’Connor, M. C. (2001). Can any fraction turned into a decimal? A case study of a mathematical group discussion. Educational Studies in Mathematics, 46, 143-185.
  • Orfanos, S., & Kalavassis, F. (2002). THALIS-A representation system for utilization in teaching and learning fractions. In ICTM2 conference Crete.
  • Peled, I., & Hershkovitz, S. (1999). Difficulty in knowledge integration: Revisiting Zeno’s paradox with irrational numbers. International Journal of Mathematical Education in Science and Technology, 30(1), 39–46.
  • Pesen, C. (2008). Kesirlerin sayı doğrusu üzerindeki gösteriminde öğrencilerin öğrenme güçlükleri ve kavram yanılgıları. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15).
  • Reys, R. E., & Nohda, N. (Eds.) (1994). Computational alternatives for the twenty-first century: Cross-cultural perspectives from Japan and the United States. Reston, VA: National Council of Teachers of Mathematics.
  • Seyhan, G. & Gür, H., (2004). İlköğretim 7. ve 8. sınıf öğrencilerinin ondalık sayılar konusundaki hataları ve kavram yanılgıları. Matematikçiler Derneği. www.matder.org.tr
  • Shinno, Y. (2007). On the teaching situation of conceptual change: epistemological considerations of irrational numbers. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 185-192).
  • Sirotic, N., & Zazkis, R. (2007). Irrational numbers: The gap between formal and intuitive knowledge. Educational Studies in Mathematics, 65(1), 49-76.
  • Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.
  • Strauss, A., & Corbin, J. (1990). Basics of qualitative research (Vol. 15). Newbury Park, CA: Sage.
  • Şandır, H., Ubuz, B., & Argün, Z. (2007). 9. sınıf öğrencilerinin aritmatik işlemler, sıralama, denklem ve eşitsizlik çözümlerindeki hataları. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 32(32).
  • Şiap, İ., & Duru, A. (2004). Kesirlerde geometriksel modelleri kullanabilme becerisi. Gazi Üniversitesi Kastamonu Eğitim Dergisi, 12(1), 89-96.
  • Temel, H., & Eroğlu, A. O. (2014). İlköğretim 8. sınıf öğrencilerinin sayı kavramlarını anlamlandırmaları üzerine bir çalışma. Kastamonu Eğitim Dergisi, 22(3), 1263.
  • Tirosh, D., Fischbein, E., Graeber, A., & Wilson, J. W. (1998). Prospective elementary teachers’ conceptions of rational numbers.http://jwilson.coe.uga.edu/Texts.Folder/Tirosh/Pros.El.Tchrs.html adresinden 16.07.2014 tarihinde alınmıştır. Tirosh, D., & Graeber, A. (1990). Evoking cognitive conflict to explore pre-service teachers’ thinking about division. Journal for Research in Mathematics Education, 21, 98-108.
  • Toluk, Z. (2002). İlkokul öğrencilerinin bölme işlemi ve rasyonel sayıları ilişkilendirme süreçleri. Boğaziçi Üniversitesi Eğitim Dergisi, 19(2), 81-101.
  • Toluk Uçar, Z. (2016). Ortaokul matematik öğretmeni adaylarının reel sayıları kavrayışlarında temsillerin rolü. Kastamonu Eğitim Dergisi, 24(3), 1149-1164.
  • Toluk, Z, & Olkun, S. (2003). İlköğretimde etkinlik temelli matematik öğretimi. Ankara: Anı Yayıncılık.
  • Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14(5), 453–467.
  • Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and instruction, 28(2), 181-209.
  • Voskoglou, M., & Kosyvas, G. D. (2012). Analyzing students difficulties in understanding real numbers. Journal of Research in Mathematics Education, 1(3), 301-336.
  • Weller, K., Arnon, I., & Dubinsky, E. (2009). Preservice teachers' understanding of the relation between a fraction or integer and its decimal expansion. Canadian Journal of Science, Mathematics, and Technology Education, 9(1), 5-28.
  • Yang, D. C., Li, M. N., & Lin, C. I. (2008). A study of the performance of 5th graders in number sense and its relationship to achievement in mathematics. International Journal of Science and Mathematics Education, 6(4), 789-807.
  • Yanik, H. B., Helding, B., & Flores, A. (2008). Teaching the concept of unit in measurement interpretation of rational numbers. Elementary Education Online, 7(3), 693-705.
  • Yıldırım, A., & Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri (8.Baskı) Ankara: Seçkin Yayınevi. Yin, R. K. (2009). Doing case study research, (4th ed). Thousand Oaks, CA: Sage.
  • Zazkis, R. (2005). Representing numbers: Prime and irrational. International Journal of Mathematical Education in Science and Technology, 36(2–3), 207–217.
  • Zazkis, R., & Sirotic, N. (2004). Making sense of irrational numbers: focusing on representation, in Proceedings of 28th International Conference for Psychology of Mathematics Education, Bergen, Norway, 4, 497–505.
  • Zazkis, R., & Sirotic, N. (2010). Representing and defining irrational numbers: Exposing the missing link. CBMS Issues in Mathematics Education, 16, 1-27.

Future Mathematics Teachers' Knowledge of Rational and Irrational Number Concepts

Year 2017, Volume: 30 Issue: 2, 551 - 581, 20.12.2017
https://doi.org/10.19171/uefad.368968

Abstract

The purpose of the study was to explore prospective mathematics teachers’

knowledge of rational and irrational numbers. The study in which qualitative

research methods were used were designed as a case study. 40 prospective teachers

of secondary mathematics education constituted the participants of the study. The

data was collected through the open-ended questionnaire developed by the

researchers and semi-structured interviews. Based on the analysis of the data

collected, it was figured out that most of the participants lacked concept knowledge

regarding rational and irrational numbers. It was also found out that the participants

had some misconceptions about that subject, and that they were not successful

enough to differentiate between rational and irrational numbers. Moreover, it was

determined that they were not aware of equivalent of different representations used

for a number, and that they remained incapable of identifying cardinalities of

rational and irrational number sets, and of comparing one another.

References

  • Aktaş, M. C., Apaydın, Z., & Aktaş, D. Y. (2014). 9. Sınıf Öğrencilerinin Rasyonel Sayılar Kümesinin Yoğunluğunu Anlama Düzeyleri. Eğitim ve Bilim, 39(171).
  • Arcavi, A., Bruckheimer, M., & Ben-Zvi, R. (1987). History of mathematics for teachers: The case of irrational numbers. For the Learning of Mathematics, 7(2), 18-23.
  • Argün, Z., Arıkan, A., Bulut, S., & Halıcıoğlu, S. (2014). Temel matematik kavramlarının künyesi. Ankara: Gazi Kitabevi. Baki, A. & Bell, A. (1997). Ortaöğretim matematik öğretimi 1. Cilt, YÖK/Dünya Bankası Milli Eğitimi Geliştirme Projesi Hizmet Öncesi Öğretmen Eğitimi, Ankara.
  • Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8, 40-48.
  • Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for research in mathematics education, 132-144.
  • Baykul, Y. (2014). Ortaokulda matematik öğretimi (5-8 sınıflar) (2.Baskı). Ankara: Pegem Yayıncılık.
  • Behr, M. J., Lesh, R., & Post, T. R. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes. (pp.91-125). New York: Academic Press.
  • Behr, M. J., Harel, G., Post, T. R., & Lesh, R. (1992). Rational number, ratio, and proportion. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.296-333). New York: Macmillan.
  • Bezuk, N. S. & Bieck, M. (1993). Current research on rational numbers and common fractions: Summary and implications for teachers. In D.T. Owens (Ed.), Research ideas for the classroom-Middle grades mathematics (pp.118-136). New York: Macmillan.
  • Birgin, O., & Gürbüz, R. (2009). İlköğretim II. kademe öğrencilerinin rasyonel sayılar konusundaki işlemsel ve kavramsal bilgi düzeylerinin incelenmesi. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 22(2), 529-550.
  • Burroughs, E. A., & Yopp, D. (2010). Prospective teachers’ understanding of decimals with single repeating digits. Investigations in Mathematics Learning, 3(1), 23-42.
  • Courant, R., Robbins, H., & Stewart, I. (1996). What is Mathematics?: An elementary approach to ideas and methods. OUP Us.
  • Çiftçi, Z., Akgün, L., & Soylu, Y. (2015). Matematik öğretmeni adaylarının irrasyonel sayılarla ilgili anlayışları. Journal of Kırsehir Education Faculty, 16(1).
  • Desmet, L., Gregoire, J., & Mussolin, C. (2010). Developmental changes in the comparison of decimal fractions. Learning and Instruction, 20, 521-532.
  • Dubinsky, E., Arnon, I., & Weller, K. (2013). Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion. Canadian Journal of Science, Mathematics and Technology Education, 13(3), 232-258.
  • Durmuş, S. (2005). İlköğretim öğretmen adaylarının rasyonel sayıları anlama düzeylerinin belirlenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 5(2), 639-666
  • Fischbein, E., Jehiam, R., & Cohen, C. (1995). The concept of irrational number in high school student and prospective teachers. Educational Studies in Mathematics, 29, 29-44
  • Gelman, R. (2000). The epigenesis of mathematical thinking. Journal of Applied Developmental Psychology, 21, 27–37
  • Giannakoulias, E., Souyoul, A., & Zachariades, T. (2007). Students’ thinking about fundamental real numbers properties. In Proceedings of the fifth congress of the European society for research in mathematics education (pp.416-425).
  • Gürbüz, R., & Birgin, O. (2008). Farklı öğrenim seviyesindeki öğrencilerin rasyonel sayıların farklı gösterim şekilleriyle işlem yapma becerilerinin karşılaştırılması. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 23(23), 85-94.
  • Güven, B., Çekmez, E., & Karataş, I. (2011). Examining preservice elementary mathematics teachers' understandings about irrational numbers. PRIMUS, 21(5), 401-416.
  • Haser, Ç., & Ubuz, B. (2002). Kesirlerde kavramsal ve işlemsel performans. Eğitim ve Bilim, 27(126).
  • İpek, A. S., Işık, C., & Albayrak, M. (2005). Sınıf öğretmeni adaylarının kesir işlemleri konusundaki kavramsal performansları. Kazım Karabekir Eğitim Fakültesi Dergisi, 1, 537-547.
  • Kaminski, E. (2002). Promoting mathematical understanding: Number sense in action. Mathematics Education Research Journal, 14(2), 133-149.
  • Kieren, T. E. (1976). On the mathematical, cognitive, and ınstructional foundations of rational numbers. In R. A. Lesh (Ed.), Number and Measurement (pp.101-144). Columbus, Oh: Ohio State University, EEIC, SMEAC.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient field to recursive understanding. In T.P. Carperten, E. Fennema & T.A. Romberg (Eds.), Rational numbers: An integration of research (pp.49-84). Hillsdade, NJ: Erlbaum
  • Lamon, S. J. (2001). Presenting and representing: From fractions to rational numbers. In A. Cuoco (Ed.), The roles of representation in school mathematics (pp.41-52). Reston,VA: NCTM.
  • MacHale, D. (1980). The predictability of counterexamples. American Mathematical Monthly, 87(9),752
  • Mack, N. (1995). Confounding whole-number and fraction concept when building on informal knowledge. Journal for Research Mathematics Education, 26(5), 422-441.
  • Mason. J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15(3), 277–289.
  • MEB, (2013a). Ortaokul matematik dersi (5,6,7 ve 8.Sınıflar) öğretim programı. Ankara: Millî Eğitim Bakanlığı, Talim Terbiye Kurulu Başkanlığı.
  • MEB (2013b). Ortaöğretim matematik dersi (9,10,11 ve 12.Sınıflar) öğretim programı. Ankara: Millî Eğitim Bakanlığı, Talim Terbiye Kurulu Başkanlığı.
  • MEB (2015). İlkokul matematik dersi (1,2,3 ve 4.Sınıflar) öğretim programı. Ankara: Millî Eğitim Bakanlığı, Talim Terbiye Kurulu Başkanlığı.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation: Revised and expanded from qualitative research and case study applications in education. San Franscisco: Jossey-Bass.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. (2nd Edition). California: SAGE Publications.
  • Moseley, B. (2005). Students’ early mathematical representaion knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60, 37–69.
  • Moss, J. (2005). Pipes, tubes, and beakers: New approaches to teaching the rational-number system. How students learn: History, math, and science in the classroom, 309-349.
  • NCTM, (2000). National council of teachers of mathematics. Principles and standards for school mathematics. Reston, VA.: NCTM
  • Ni, Y., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.
  • O’Connor, M. C. (2001). Can any fraction turned into a decimal? A case study of a mathematical group discussion. Educational Studies in Mathematics, 46, 143-185.
  • Orfanos, S., & Kalavassis, F. (2002). THALIS-A representation system for utilization in teaching and learning fractions. In ICTM2 conference Crete.
  • Peled, I., & Hershkovitz, S. (1999). Difficulty in knowledge integration: Revisiting Zeno’s paradox with irrational numbers. International Journal of Mathematical Education in Science and Technology, 30(1), 39–46.
  • Pesen, C. (2008). Kesirlerin sayı doğrusu üzerindeki gösteriminde öğrencilerin öğrenme güçlükleri ve kavram yanılgıları. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15).
  • Reys, R. E., & Nohda, N. (Eds.) (1994). Computational alternatives for the twenty-first century: Cross-cultural perspectives from Japan and the United States. Reston, VA: National Council of Teachers of Mathematics.
  • Seyhan, G. & Gür, H., (2004). İlköğretim 7. ve 8. sınıf öğrencilerinin ondalık sayılar konusundaki hataları ve kavram yanılgıları. Matematikçiler Derneği. www.matder.org.tr
  • Shinno, Y. (2007). On the teaching situation of conceptual change: epistemological considerations of irrational numbers. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 185-192).
  • Sirotic, N., & Zazkis, R. (2007). Irrational numbers: The gap between formal and intuitive knowledge. Educational Studies in Mathematics, 65(1), 49-76.
  • Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.
  • Strauss, A., & Corbin, J. (1990). Basics of qualitative research (Vol. 15). Newbury Park, CA: Sage.
  • Şandır, H., Ubuz, B., & Argün, Z. (2007). 9. sınıf öğrencilerinin aritmatik işlemler, sıralama, denklem ve eşitsizlik çözümlerindeki hataları. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 32(32).
  • Şiap, İ., & Duru, A. (2004). Kesirlerde geometriksel modelleri kullanabilme becerisi. Gazi Üniversitesi Kastamonu Eğitim Dergisi, 12(1), 89-96.
  • Temel, H., & Eroğlu, A. O. (2014). İlköğretim 8. sınıf öğrencilerinin sayı kavramlarını anlamlandırmaları üzerine bir çalışma. Kastamonu Eğitim Dergisi, 22(3), 1263.
  • Tirosh, D., Fischbein, E., Graeber, A., & Wilson, J. W. (1998). Prospective elementary teachers’ conceptions of rational numbers.http://jwilson.coe.uga.edu/Texts.Folder/Tirosh/Pros.El.Tchrs.html adresinden 16.07.2014 tarihinde alınmıştır. Tirosh, D., & Graeber, A. (1990). Evoking cognitive conflict to explore pre-service teachers’ thinking about division. Journal for Research in Mathematics Education, 21, 98-108.
  • Toluk, Z. (2002). İlkokul öğrencilerinin bölme işlemi ve rasyonel sayıları ilişkilendirme süreçleri. Boğaziçi Üniversitesi Eğitim Dergisi, 19(2), 81-101.
  • Toluk Uçar, Z. (2016). Ortaokul matematik öğretmeni adaylarının reel sayıları kavrayışlarında temsillerin rolü. Kastamonu Eğitim Dergisi, 24(3), 1149-1164.
  • Toluk, Z, & Olkun, S. (2003). İlköğretimde etkinlik temelli matematik öğretimi. Ankara: Anı Yayıncılık.
  • Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14(5), 453–467.
  • Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and instruction, 28(2), 181-209.
  • Voskoglou, M., & Kosyvas, G. D. (2012). Analyzing students difficulties in understanding real numbers. Journal of Research in Mathematics Education, 1(3), 301-336.
  • Weller, K., Arnon, I., & Dubinsky, E. (2009). Preservice teachers' understanding of the relation between a fraction or integer and its decimal expansion. Canadian Journal of Science, Mathematics, and Technology Education, 9(1), 5-28.
  • Yang, D. C., Li, M. N., & Lin, C. I. (2008). A study of the performance of 5th graders in number sense and its relationship to achievement in mathematics. International Journal of Science and Mathematics Education, 6(4), 789-807.
  • Yanik, H. B., Helding, B., & Flores, A. (2008). Teaching the concept of unit in measurement interpretation of rational numbers. Elementary Education Online, 7(3), 693-705.
  • Yıldırım, A., & Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri (8.Baskı) Ankara: Seçkin Yayınevi. Yin, R. K. (2009). Doing case study research, (4th ed). Thousand Oaks, CA: Sage.
  • Zazkis, R. (2005). Representing numbers: Prime and irrational. International Journal of Mathematical Education in Science and Technology, 36(2–3), 207–217.
  • Zazkis, R., & Sirotic, N. (2004). Making sense of irrational numbers: focusing on representation, in Proceedings of 28th International Conference for Psychology of Mathematics Education, Bergen, Norway, 4, 497–505.
  • Zazkis, R., & Sirotic, N. (2010). Representing and defining irrational numbers: Exposing the missing link. CBMS Issues in Mathematics Education, 16, 1-27.
There are 66 citations in total.

Details

Journal Section Articles
Authors

Mustafa Çevikbaş

Ziya Argün

Publication Date December 20, 2017
Submission Date December 19, 2017
Published in Issue Year 2017 Volume: 30 Issue: 2

Cite

APA Çevikbaş, M., & Argün, Z. (2017). Future Mathematics Teachers’ Knowledge of Rational and Irrational Number Concepts. Journal of Uludag University Faculty of Education, 30(2), 551-581. https://doi.org/10.19171/uefad.368968