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5.Sınıf Öğrencilerinin Kesirlerle Toplama ve Çıkarma İşlemine Yönelik Kurdukları Problemlerin Analizi

Yıl 2020, Cilt: 21 Sayı: 1, 19 - 37, 20.07.2020
https://doi.org/10.12984/egeefd.556447

Öz

Bu çalışmanın amacı, 5. sınıf öğrencilerinin kesirlerle toplama ve çıkarma işlemine yönelik kurdukları problemleri incelemektir. Araştırmada nitel araştırma yöntemlerinden bütüncül tek durum deseni kullanılmıştır. Araştırma 2017-2018 eğitim-öğretim yılında, Kırıkkale il merkezindeki iki farklı devlet okulunda öğrenim gören 40 beşinci sınıf öğrencisi ile yürütülmüştür. Katılımcıların belirlenmesinde tipik durum örnekleme tekniği kullanılmıştır. Çalışmanın verileri, altı açık uçlu sorudan oluşan problem kurma soru seti kullanılarak toplanmış ve veriler içerik analizi ve betimsel analiz yöntemi kullanılarak analiz edilmiştir. İlk olarak, öğrencilerin yazdıkları ifadeler problem, problem değil ve boş kategorileri olarak sınıflandırılmıştır. İkinci olarak, problem olarak kodlanan ifadeler, matematiksel açıdan doğru olup olmadıklarına göre analiz edilmiştir. Çalışmadan elde edilen bulgulara göre, öğrencilerin yazdıkları ifadelerin % 81.25’i problem kategorisinde, % 16.25’i problem değil ve % 2.5’i boş kategorisinde yer almıştır. Çalışmanın amacı doğrultusunda problem olarak değerlendirilen ifadelerdeki hatalar incelenmiştir. Buna göre, parça-bütün ilişkisini kuramama, kesir sayılarına doğal sayı anlamı yükleme, problemde ifade eksikliği ve veri eksikliği olarak isimlendirilen dört farklı hata türü tespit edilmiştir.

Kaynakça

  • Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.), Proceedings of the International Conference on Mathematical Education into the 21st Century: Social Challenges, Issues and Approaches (vol. II, pp. 1-8). Cairo, Egypt: Third World Forum.
  • Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education, 25(1), 56-69.
  • Akay, H., Soybaş, D. ve Argün, Z. (2006) Problem kurma deneyimleri ve matematik öğretiminde açık-uçlu soruların kullanımı. Kastamonu Eğitim Dergisi, 14(1), 129-146.
  • Aktaş, G. S., & Ünlü, M. (2017). Understanding of eight grade students about transformation geometry: Perspectives on students’ mistakes. Journal of Education and Training Studies, 5(5), 103-119. doi:10.11114/jets.v5i5.2254
  • Altun, M. (2009). Eğitim fakülteleri ve ilköğretim matematik öğretmenleri için matematik öğretimi. Bursa: Erkam Matbaacılık.
  • Armstrong, B. E., & Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning. In J. Sowder & B. P. Schappelle (Ed), Providing a foundation for teaching mathematics in the middle grades (pp. 85-119). Albany, NY: State University of New York Press.
  • Ashlock, R. B. (2010). Errors patterns in computation: Using error patterns to help each student learn. (10th ed.). Boston, MA: Allyn & Bacon.
  • Australian Education Council & Curriculum Corporation (Australia). (1991). A national statement on mathematics for Australian schools. Victoria, Australia: Curriculum Press.
  • Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. doi:10.1016/j.jecp.2012.06.004
  • Barlow, A. T., & Cates, J. M. (2006). The impact of problem posing on elementary teachers' beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64-73. doi:10.1111/j.1949-8594.2006.tb18136.x
  • Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247-253. doi:10.1016/j.cedpsych.2012.07.001
  • Cai, J. (2003). Singaporean students mathematical thinking in problem solving and problem posing: an exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737. doi:10.1080/00207390310001595401
  • Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521-1540. doi:10.1007/s10763-016-9758-2
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zdm, 37(3), 149-158. doi:10.1007/s11858-005-0004-6
  • Cramer, K. A., & Whitney, S. (2010). Learning rational number concepts and skills in elementary classrooms: Translating research to the elementary classroom. In D. V. Lambdin, & F. K. Lester (Eds.), Teaching and learning mathematics: Translating research to the elementary classroom (pp. 15-22). Reston, VA: NCTM.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal Mathematics Teacher Education, 11, 395-415. doi:10.1007/s10857-008-9081-0
  • Çetinkaya, A. ve Soybaş, D. (2018). İlköğretim 8. sınıf öğrencilerinin problem kurma becerilerinin incelenmesi. Kuramsal Eğitim Bilim Dergisi, 11(1), 169-200. doi:10.30831/akukeg.333757
  • English, D. L. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106. doi:10.2307/749719
  • Ev Çimen, E. ve Tat, T. (2018) Sekizinci sınıf öğrencilerinin bölme işleminde kalanın yorumlanması konusunda problem kurma becerilerinin incelenmesi. Eğitim ve Öğretim Araştırmaları Dergisi, 7(4), 1-11.
  • Gökkurt, B., Örnek, T., Hayat, F. ve Soylu, Y. (2015). Öğrencilerin problem çözme ve problem kurma becerilerinin değerlendirilmesi. Bartın Üniversitesi Eğitim Fakültesi Dergisi, 4(2), 751-774. doi:10.14686/buefad.v4i2.5000145637
  • Hiebert, J., Carpenter, T., Fennema, E., Fuson, K. C., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
  • Işık, C., Işık, A. ve Kar, T. (2011). Matematik öğretmeni adaylarının sözel ve görsel temsillere yönelik kurdukları problemlerin analizi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(II), 39-49.
  • Işık, C. ve Kar, T. (2012). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online, 11(4), 1021-1035. doi:10.17051/io.2014.13224
  • Kar, T. ve Işık, C. (2014). Ortaokul yedinci sınıf öğrencilerinin kesirlerle çıkarma işlemine kurdukları problemlerin analizi. İlköğretim Online, 13(4), 1223-1239.
  • Kılıç, Ç. (2013). Sınıf öğretmeni adaylarının farklı problem kurma durumlarında sergilemiş oldukları performansın belirlenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 13(2), 1195-1211.
  • Kilpatrick, J. (1987). Problem formulating: Where do good problems come from. In A. H. Schoenfeld (Ed.) Cognitive science and mathematics education (pp. 123-147). Hillsdalc, NJ: Erlbaum.
  • Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. In J. H. Woo, H. C. Lew, K.H. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 129-136). Seoul, The Republic of Korea: PME.
  • Lin, K. M., & Leng, L. W. (2008, July). Using problem-posing as an assessment tool. In Proceedings of the 10th Asia-Pacific Conference on Giftedness. Retrieved from http://hkage.org.hk/en/events/080714_10th_APCG.htm
  • Lin, P. J. (2004). Supporting Teachers on Designing Problem-Posing Tasks as a Tool of Assessment to Understand Students' Mathematical Learning. International Group for the Psychology of Mathematics Education.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teacher's understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates, Incorporated.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441. doi:10.2307/749431
  • Mack, N. K. (1998). Building a foundation for understanding the multiplication of fractions. Teaching Children Mathematics, 5(1), 34-39.
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. Revised and expanded from “Case study research in education.”. San Francisco: Jossey-Bass Publishers.
  • Miles, M., & Huberman, M. (1994). An expanded sourcebook qualitative data analysis (2nd ed.). California: Sage Publications.
  • Milli Eğitim Bakanlığı [MEB]. (2015). İlkokul matematik dersi (1, 2, 3 ve 4. sınıflar) öğretim programı. Ankara, Türkiye: MEB.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Ortaokul matematik dersi öğretim programı 5 - 8. sınıflar. Ankara, Türkiye: MEB.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Ngah, N., Ismail, Z., Tasir, Z., Said, M., & Haruzuan, M. N. (2016). Students’ ability in free, semi-structured and structured problem posing situations. Advanced Science Letters, 22(12), 4205-4208. doi:10.1166/asl.2016.8106
  • Özgen, K., Aydın, M., Geçici, M. E. ve Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(2), 323-351. doi:10.16949/turkbilmat.322660
  • Özgen, K., Geçici, M. E., Aydın, M., & Bayram, B. (2019). An Investigation of Eighth Grade Students' Skills in Problem-Posing. International Journal for Mathematics Teaching & Learning, 20(1), 106-130.
  • Patton, M. Q. (2005). Qualitative Research. New York: John Wiley & Sons, Ltd.
  • Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological science, 23(7), 691-697. doi:10.1177/0956797612440101
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  • Silver, E. A. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157-162. doi:10.1007/s10649-013-9477-3
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539. doi:10.2307/749846
  • Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. doi:10.1016/j.learninstruc.2004.06.015
  • Stoyanova, E. (2003). Extending students' understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32-40.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in Mathematics Education (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia.
  • Şengül Akdemir, T. ve Türnüklü, E. (2017). Ortaokul 6. Sınıf öğrencilerinin açılar ile ilgili problem kurma süreçlerinin incelenmesi. International Journal of New Trends in Arts, Sports & Science Education (IJTASE), 6(2), 17-39.
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Analysis of the Problems 5th Grade Students Posed related to Addition and Subtraction in Fractions

Yıl 2020, Cilt: 21 Sayı: 1, 19 - 37, 20.07.2020
https://doi.org/10.12984/egeefd.556447

Öz

The aim of this case study is to examine the problems that 5th grade students posed related to addition and subtraction in fractions. Holistic single case design which is one of the qualitative research methods was used in this study. It was conducted with 40 fifth grade students enrolled in two different public schools in 2017-2018 academic year. The data were collected through a questionnaire consisting of 6 open-ended questions and analyzed by using content analysis and descriptive analysis methods. Firstly, the expressions of students were classified as problem, not problem and empty. Secondly, the expressions which were coded as problem were analyzed in terms of whether they were mathematically correct or not. According to the findings of the study, 81.25 % of the students' expressions were coded as problem, 16.25 % were coded as not problem and 2.5 % were denoted as empty. In accordance with the aim of the study, the expressions which were stated as problem were analyzed to determine the errors in the problems. Accordingly, four different errors were identified which were named as unable to establish part-whole relationship, attributing natural number meaning to the fractions, lack of expression in the problem, and lack of givens.

Kaynakça

  • Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.), Proceedings of the International Conference on Mathematical Education into the 21st Century: Social Challenges, Issues and Approaches (vol. II, pp. 1-8). Cairo, Egypt: Third World Forum.
  • Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education, 25(1), 56-69.
  • Akay, H., Soybaş, D. ve Argün, Z. (2006) Problem kurma deneyimleri ve matematik öğretiminde açık-uçlu soruların kullanımı. Kastamonu Eğitim Dergisi, 14(1), 129-146.
  • Aktaş, G. S., & Ünlü, M. (2017). Understanding of eight grade students about transformation geometry: Perspectives on students’ mistakes. Journal of Education and Training Studies, 5(5), 103-119. doi:10.11114/jets.v5i5.2254
  • Altun, M. (2009). Eğitim fakülteleri ve ilköğretim matematik öğretmenleri için matematik öğretimi. Bursa: Erkam Matbaacılık.
  • Armstrong, B. E., & Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning. In J. Sowder & B. P. Schappelle (Ed), Providing a foundation for teaching mathematics in the middle grades (pp. 85-119). Albany, NY: State University of New York Press.
  • Ashlock, R. B. (2010). Errors patterns in computation: Using error patterns to help each student learn. (10th ed.). Boston, MA: Allyn & Bacon.
  • Australian Education Council & Curriculum Corporation (Australia). (1991). A national statement on mathematics for Australian schools. Victoria, Australia: Curriculum Press.
  • Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. doi:10.1016/j.jecp.2012.06.004
  • Barlow, A. T., & Cates, J. M. (2006). The impact of problem posing on elementary teachers' beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64-73. doi:10.1111/j.1949-8594.2006.tb18136.x
  • Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247-253. doi:10.1016/j.cedpsych.2012.07.001
  • Cai, J. (2003). Singaporean students mathematical thinking in problem solving and problem posing: an exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737. doi:10.1080/00207390310001595401
  • Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521-1540. doi:10.1007/s10763-016-9758-2
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zdm, 37(3), 149-158. doi:10.1007/s11858-005-0004-6
  • Cramer, K. A., & Whitney, S. (2010). Learning rational number concepts and skills in elementary classrooms: Translating research to the elementary classroom. In D. V. Lambdin, & F. K. Lester (Eds.), Teaching and learning mathematics: Translating research to the elementary classroom (pp. 15-22). Reston, VA: NCTM.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal Mathematics Teacher Education, 11, 395-415. doi:10.1007/s10857-008-9081-0
  • Çetinkaya, A. ve Soybaş, D. (2018). İlköğretim 8. sınıf öğrencilerinin problem kurma becerilerinin incelenmesi. Kuramsal Eğitim Bilim Dergisi, 11(1), 169-200. doi:10.30831/akukeg.333757
  • English, D. L. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106. doi:10.2307/749719
  • Ev Çimen, E. ve Tat, T. (2018) Sekizinci sınıf öğrencilerinin bölme işleminde kalanın yorumlanması konusunda problem kurma becerilerinin incelenmesi. Eğitim ve Öğretim Araştırmaları Dergisi, 7(4), 1-11.
  • Gökkurt, B., Örnek, T., Hayat, F. ve Soylu, Y. (2015). Öğrencilerin problem çözme ve problem kurma becerilerinin değerlendirilmesi. Bartın Üniversitesi Eğitim Fakültesi Dergisi, 4(2), 751-774. doi:10.14686/buefad.v4i2.5000145637
  • Hiebert, J., Carpenter, T., Fennema, E., Fuson, K. C., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
  • Işık, C., Işık, A. ve Kar, T. (2011). Matematik öğretmeni adaylarının sözel ve görsel temsillere yönelik kurdukları problemlerin analizi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(II), 39-49.
  • Işık, C. ve Kar, T. (2012). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online, 11(4), 1021-1035. doi:10.17051/io.2014.13224
  • Kar, T. ve Işık, C. (2014). Ortaokul yedinci sınıf öğrencilerinin kesirlerle çıkarma işlemine kurdukları problemlerin analizi. İlköğretim Online, 13(4), 1223-1239.
  • Kılıç, Ç. (2013). Sınıf öğretmeni adaylarının farklı problem kurma durumlarında sergilemiş oldukları performansın belirlenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 13(2), 1195-1211.
  • Kilpatrick, J. (1987). Problem formulating: Where do good problems come from. In A. H. Schoenfeld (Ed.) Cognitive science and mathematics education (pp. 123-147). Hillsdalc, NJ: Erlbaum.
  • Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. In J. H. Woo, H. C. Lew, K.H. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 129-136). Seoul, The Republic of Korea: PME.
  • Lin, K. M., & Leng, L. W. (2008, July). Using problem-posing as an assessment tool. In Proceedings of the 10th Asia-Pacific Conference on Giftedness. Retrieved from http://hkage.org.hk/en/events/080714_10th_APCG.htm
  • Lin, P. J. (2004). Supporting Teachers on Designing Problem-Posing Tasks as a Tool of Assessment to Understand Students' Mathematical Learning. International Group for the Psychology of Mathematics Education.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teacher's understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates, Incorporated.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441. doi:10.2307/749431
  • Mack, N. K. (1998). Building a foundation for understanding the multiplication of fractions. Teaching Children Mathematics, 5(1), 34-39.
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. Revised and expanded from “Case study research in education.”. San Francisco: Jossey-Bass Publishers.
  • Miles, M., & Huberman, M. (1994). An expanded sourcebook qualitative data analysis (2nd ed.). California: Sage Publications.
  • Milli Eğitim Bakanlığı [MEB]. (2015). İlkokul matematik dersi (1, 2, 3 ve 4. sınıflar) öğretim programı. Ankara, Türkiye: MEB.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Ortaokul matematik dersi öğretim programı 5 - 8. sınıflar. Ankara, Türkiye: MEB.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Ngah, N., Ismail, Z., Tasir, Z., Said, M., & Haruzuan, M. N. (2016). Students’ ability in free, semi-structured and structured problem posing situations. Advanced Science Letters, 22(12), 4205-4208. doi:10.1166/asl.2016.8106
  • Özgen, K., Aydın, M., Geçici, M. E. ve Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(2), 323-351. doi:10.16949/turkbilmat.322660
  • Özgen, K., Geçici, M. E., Aydın, M., & Bayram, B. (2019). An Investigation of Eighth Grade Students' Skills in Problem-Posing. International Journal for Mathematics Teaching & Learning, 20(1), 106-130.
  • Patton, M. Q. (2005). Qualitative Research. New York: John Wiley & Sons, Ltd.
  • Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological science, 23(7), 691-697. doi:10.1177/0956797612440101
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  • Silver, E. A. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157-162. doi:10.1007/s10649-013-9477-3
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539. doi:10.2307/749846
  • Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. doi:10.1016/j.learninstruc.2004.06.015
  • Stoyanova, E. (2003). Extending students' understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32-40.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in Mathematics Education (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia.
  • Şengül Akdemir, T. ve Türnüklü, E. (2017). Ortaokul 6. Sınıf öğrencilerinin açılar ile ilgili problem kurma süreçlerinin incelenmesi. International Journal of New Trends in Arts, Sports & Science Education (IJTASE), 6(2), 17-39.
  • Tan-Şişman, G., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293-1319. doi:10.1007/s10763-015-9642-5
  • Tertemiz, N. I. ve Sulak, S. E. (2013). İlköğretim beşinci sınıf öğrencilerinin problem kurma becerilerinin incelenmesi. İlköğretim Online, 12(3), 713-729.
  • Tichá, M., & Hošpesová, A. (2009, January). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In meeting of CERME (Vol. 6).
  • Törner, G., Schoenfeld, A. H., & Reiss, K. M. (2007). Problem solving around the world: Summing up the state of the art. ZDM, 39(5-6), 353-353. doi:10.1007/s11858-007-0053-0
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). New York: Longman.
  • Van Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117-132. doi:10.1007/s10649-012-9456-0
  • Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: An analysis of high school students' mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201-221. doi:10.1007/s10649-012-9419-5
  • Yıldırım, A. ve Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Applied Social Research Methods Series, (Volume 5). Thousand Oaks, CA: Sage Publications, Inc.
  • Yükseköğretim Kurulu [YÖK]. (2016). Yükseköğretim kurulu bilimsel araştırma ve yayın etiği yönergesi. https://www.yok.gov.tr/Documents/Mevzuat/yuksekogretim_kurumlari_bilimsel_arastirma_ve_yayin_etigi_yonergesi.pdf adresinden elde edildi.
Toplam 59 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Alan Eğitimleri
Bölüm Makaleler
Yazarlar

Ayşe Özer 0000-0002-9979-9232

Arzu Karacaköylü

Reyhan Tekin Sitrava Bu kişi benim

Yayımlanma Tarihi 20 Temmuz 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 21 Sayı: 1

Kaynak Göster

APA Özer, A., Karacaköylü, A., & Tekin Sitrava, R. (2020). 5.Sınıf Öğrencilerinin Kesirlerle Toplama ve Çıkarma İşlemine Yönelik Kurdukları Problemlerin Analizi. Ege Eğitim Dergisi, 21(1), 19-37. https://doi.org/10.12984/egeefd.556447