The Analysis of Problem Posing Skills about Integers of Prospective Primary School Mathematics Teachers Who Have Experienced in Problem Posing

Abstract

This study aims to analyze the problem-posing skills of primary school mathematics teacher candidates with problem-posing experience and their views on problem posing. The case study, one of the qualitative studies, was used in the study. The study group is ten prospective elementary mathematics teachers who were selected using the purposive sampling method and are in their third year in the academic years 2020-2021 Teaching Mathematics in Primary Schools Major at a private university in Istanbul.The data collection process consists of two stages: 9 problem-posing drafts in total for performance evaluation prepared by examining the literature and obtaining an expert opinion and semi-structured interview forms with three questions. The participants were asked to pose problems on the subject of integers. The problems were evaluated and analyzed by the researchers and two mathematics teachers according to the problem-posing evaluation criteria developed by the researchers. As a result of the findings obtained in the performance determination phase of the study, it was determined that the participants posed more successful problems in the case of structured problem posing. It was determined that some of the problems were not problematic; they were prepared without paying attention to grammar rules, the sentences were not in a clear and logical framework that the middle school students could understand. The numbers were not used according to a certain logic pattern to make the problem solvable. Some problem situations were left unanswered. In the second stage of the study, the data obtained through semi-structured interviews with the primary school mathematics prospective teachers were analyzed using content analysis. In examining the research findings, the main issues are what the participants pay attention to in problem setting, whether they emphasize problem setting in the instructional process, whether problem setting is necessary for each student, and whether anxiety occurs in problem setting.

Keywords

• Mathematics education
• problem posing
• mathematics prospective teachers
• integers

References

1. Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In Proceedings of the International Conference on Mathematical Education into the 21st Century: Social challenges, Issues, and Approaches (Vol. 2, pp. 1-8).
2. Akay, H., & Boz, N. (2010). The effect of problem posing oriented analyses-II course on the attitudes toward mathematics and mathematics self-efficacy of elementary prospective mathematics teachers. Australian Journal of Teacher Education, 35(1), 59-75.
3. Akay, H., Soybaş, D., & Argün, Z. (2006). Problem kurma deneyimleri ve matematik öğretiminde açık-uçlu soruların kullanımı [Problem-posing experiences and using open-ended questions in teaching mathematics]. Gazi Üniversitesi Kastamonu Eğitim Dergisi, 14(1), 129-146.
4. Akyazı, N., & Kaplan, A. (2018). İlköğretim altıncı sınıf öğrencilerine drama yöntemiyle tam sayılarla toplama işleminin öğretim sürecinin incelenmesi. Bayburt Eğitim Fakültesi Dergisi, 13(25), 259-294.
5. Altun, M. (2001). Matematik öğretimi (İlköğretim ikinci kademede) [Teaching mathematics (Middle schools)] Alfa.
6. Altun, M. (2006). Matematik öğretiminde gelişmeler. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 19(2), 223-238.
7. Arıkan, E. E., & Ünal, H. (2013). The analysis of mathematical problem posing skill of elementary second grade students. Amasya Education Science, 2(2), 305-325.
8. Arıkan, E. E., & Unal, H. (2014). Development of the structured problem posing skills and using metaphoric perceptions. European Journal of Science and Mathematics Education, 2(3), 155-166.

9. Arıkan, E. E., ve Dede, Y. (2020). Elementary freshmen’s mathematical attitudes in teaching ıncorporating free problem posing activities. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, 10(2), 105-121.
10. Aydın-Güç, F. (2021). Matematik öğretmenlerinin geogebra ile çözülebilen problem kurma performansları. Başkent University Journal of Education, 8(2), 392-410.
11. Bağdat, A. G. O., & Yenilmez, K. (2014). Yedinci sınıf öğrencilerinin tam sayılarla işlemler konusundaki öğrenme güçlükleri.[Learning Difficulties of 7th Grade Students in operations with integers] Avrasya Eğitim Araştırmaları Kongresi Bildiri Özetleri Kitapçığı, 631-632.
12. Bahadır, E., ve Özdemir, A. Ş. (2013) Tam sayılar konusunun canlandırma tekniği ile öğretiminin öğrenci başarısına ve hatırlama düzeyine etkisi [The effect of teaching ıntegers subject with animation technique on student achievement and recall level]. International Journal of Social Science Research, 2(1), 114-136.
13. Bayazit, İ., & Dönmez, S. M. K. (2017). Öğretmen adaylarının problem kurma becerilerinin orantısal akıl yürütme gerektiren durumlar bağlamında incelenmesi [The analysis of prospective teachers' problem posing skills in the context of situations requiring proportional reasoning] Turkish Journal of Computer and Mathematics Education, 8(1), 130-160.
14. Bayraktar İ., (2020). Online eğitim sitesi [Online educational website] Erişim: 16 Aralık 2020. https://www.sanalokulumuz.com/tam-sayilar-problemler-7sinif-matematik/741
15. Berisha, V. (2015). The general characteristics of mathematics textbooks for lower secondary school in Kosovo. International Journal of Novel Research in Education and Learning, 2(2), 19-23.
16. Berkant, H. G., ve Yaren, R. (2020). Altıncı sınıf tam sayılar konusunda uygulanan gerçekçi matematik eğitiminin öğrencilerin matematik motivasyonlarına etkisi. Kahramanmaraş Sütçü İmam Üniversitesi Sosyal Bilimler Dergisi, 17(2), 543-571.
17. Bintaş, J. , & Yazgan, Y. (2005). İlköğretim dördüncü ve beşinci sınıf öğrencilerinin problem çözme stratejilerini kullanabilme düzeyleri: Bir öğretim deneyi [Primary school fourth and fifth grade students’ levels of using problem solving strategies: A teaching experiment]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28(28), 210-218.
18. Brown, S. I., & Walter, M. I. (2005). The art of problem posing. Psychology Press.
19. Cai, J. & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 1-8.
20. Can, H. N. (2019). Ortaokul matematik öğretmenlerinin kesirlerde işlemler konusu ıle ılgili pedagojik alan bilgilerinin öğrenci zorlukları ve kavram yanılgıları bileşeninde ıncelenmesi (ınvestigation of secondary school mathematics teachers' pedagogical content knowledge related to the subject of fractional operations in the component of student difficulties and misconceptions) [Doctoral dissertation]. Marmara Universitesi.
21. Cihangir, A. ve Çevik, Y. (2020). Tam sayıların modellenmesine ilişkin durum çalışması [Case Study of modelling ıntegers]. Necmettin Erbakan Üniversitesi Ereğli Eğitim Fakültesi Dergisi, 2(2), 136-151.
22. Creswell, J. W. (2014). Qualitative, quantitative and mixed methods approaches. Sage.
23. Çetinkaya, A., & Soybaş, D. (2018). İlköğretim 8. sınıf öğrencilerinin problem kurma becerilerinin incelenmesi. Journal of Theoretical Educational Science, 11(1), 169-200.
24. Çıldır, S. & Sezen, N. (2011). A study on the evaluation of problem-posing skills in terms of academic success. Procedia Social and Behavioral Sciences, 15, 2494-2499.
25. Çıldır, S., & Sezen, N. (2011). Skill levels of prospective physics teachers on problem posing. Hacettepe University Journal of Education Faculty, 40, 105-116.
26. Dede, Y., & Yaman, S. (2005). Matematik öğretmen adaylarının matematiksel problem kurma ve problem çözme becerilerinin belirlenmesi [Determination of mathematical problem posing and problem solving skills of pre-service mathematics teachers] Eurasian Journal of Educational Research (EJER), (18), 41-56.
27. Dereli, M. (2008). Tam sayılar konusunun karikatürle öğretiminin öğrencilerin matematik başarılarına etkisi [Yayınlanmamış yüksek lisans tezi]. Marmara Üniversitesi, İstanbul.
28. Doğan, M., & Işıtan, H. (2018). Gerçekçi matematik eğitiminin tam sayılar konusunda başarıya ve kalıcılığa etkililiği [Effectiveness of realistic mathematics education on success and permanence on ıntegers]. Medeniyet Eğitim Araştırmaları Dergisi, 1(4), 1-9.
29. Duatepe Paksu, A. (2010). Üslü ve köklü sayılar konularındaki öğrenme güçlükleri. İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm önerileri [Learning difficulties in exponential and radical numbers. Mathematical difficulties encountered in primary education and solution suggestions]. Pegem.
30. English, L. D. (2020). Teaching and learning through mathematical problem posing: commentary. International Journal of Educational Research, 102, 101451.
31. Ev-Çimen, E., & Yıldız, Ş. (2018). Ortaokul matematik ders kitaplarında yer verilen problem kurma etkinliklerinin incelenmesi [Examining the problem-posing activities in middle school mathematics textbooks]. Turkish Journal of Computer and Mathematics Education, 8(3), 378-407.
32. Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education. McGraw Hill.
33. Freire, P. (2018). Bir özgürlük pratiği olarak eğitim (pp. 396-398). Duke Üniversitesi Yayınları.
34. Fuadiah, N. F., Suryadi, D., & Turmudi, T. (2017). Analysis of didactical contracts on teaching mathematics: A design experiment on a lesson of negative ıntegers operations. Infinity Journal, 6(2), 157-168.
35. Galbraith, M. J. (1974). Negative numbers. International Journal of Mathematical Education in Science and Technology, 5(1), 83-90.
36. Gallardo, A. (2002). The extension of the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49(2), 171-192.
37. Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78-84.
38. Gür, H. & Korkmaz, E. (2003). İlköğretim 7. sınıf öğrencilerinin problem ortaya atma becerilerinin belirlenmesi [Determining the problem posing skills of primary school 7th grade students]. Matematikçiler Derneği Matematik Köşesi Makaleleri.
39. Güzel, R., & Biber, A. Ç. (2019). Eşitsizlikler konusunun öğretiminde problem kurma yaklaşımının akademik başarıya etkisi. Kastamonu Eğitim Dergisi, 27(1), 199-208.
40. Işık, A. Çiltaş, A., & Bekdemir, M. (2008). Matematik eğitiminin gerekliliği ve önemi [The necessity and importance of mathematics education]. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 17, 174-184.
41. Işık, C. ve Kar, T. (2015). Altıncı sınıf öğrencilerinin kesirlerle ilgili açık-uçlu sözel hikayeye yönelik kurdukları problemlerin incelenmesi [Examination of sixth grade students' problems related to open-ended verbal stories about fractions]. Turkish Journal of Computer and Mathematic Education (TURCOMAT), 6(2), 230-249.
42. Işık, C. ve Kar, T. (2012). Sınıf öğretmeni adaylarının problem kurma becerileri. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 1(23), 190-214.
43. Ministry of National Education (2005). İlköğretim matematik dersi 6-8. sınıflar öğretim programı ve kılavuzu [Teaching program and guide for primary school mathematics, 6-8th grades]. Talim ve Terbiye Kurulu Başkanlığı, MEB Yayınları.
44. İpek, A. S. , & Ünal, Z. A. (2009). Gerçekçi matematik eğitiminin ilköğretim 7. sınıf öğrencilerinin tam sayılarla çarpma konusundaki başarılarına etkisi [The effect of realistic mathematics education on the success of elementary school 7th grade students in multiplying with integers]. Eğitim ve Bilim Dergisi, 34(152).
45. İskenderoğlu, T. A., & Güneş, G. (2016). Pedagojik formasyon eğitimi alan matematik bölümü öğrencilerinin problem kurma becerilerinin incelenmesi [Examining the problem posing skills of the students of the mathematics department who receive pedagogical formation]. Sakarya University Journal of Education, 6(2), 46-65.
46. Kaba, Y., & Şengül, S. (2016). Developing the rubric for evaluating problem posing (REPP). International Online Journal of Educational Sciences, 8(1), 8-25.
47. Kanbur, B. (2017). İlköğretim matematik öğretmen adaylarının dinamik geometri yazılımı ile desteklenmiş ortamda problem kurma durumlarının ve görüşlerinin incelenmesi [Yayınlanmamış yüksek lisans tezi]. Gazi University.
48. Kılıç, Ç. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22(4), 677-686.
49. Kırnap-Dönmez, S. M. (2014). İlköğretim matematik öğretmen adaylarının problem kurma becerilerinin incelenmesi. Unpublished master’s thesis, Erciyes Üniversitesi Eğitim Bilimleri Enstitüsü, Kayseri.
50. Kilhamn, C. (2008). Making sense of negative numbers through metaphorical reasoning. GöteborgsUniversity. WW. mai. Liu. se/SMDF/madif6/Kilhamn.
51. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from. Cognitive science and mathematics education, 123-147.
52. Kiraz, K. Ş., & Işık, C. (2020). Tam sayıların öğretim sürecinin öğretmenlerin model kullanımları üzerinden analizi. Bayburt Eğitim Fakültesi Dergisi, 15(29), 81-108.
53. Koç Şanlı, K. (2018). Ortaokul matematik öğretmenlerinin tam sayıların öğretim sürecinde model kullanma becerileri ve model kullanımına yönelik görüşleri [Yüksek lisans tezi]. Erciyes Üniversitesi.
54. Kojima, K., Miwa, K., & Matsui, T. (2015). Experimental study of learning support through examples in mathematical problem posing. Research and Practice in Technology Enhanced Learning, 10(1), 1-18.
55. Kutluca, T. (2012) Matematiksel kavram yanılgıları ve çözüm önerileri [Mathematical misconceptions and suggestion]. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 18, 287-291.
56. Kwon, H., & Capraro, M. M. (2021). Nurturing problem posing in young children: using multiple representation within students’ real-world ınterest. International Electronic Journal of Mathematics Education, 16(3), em0648.
57. 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.
58. Linchevski, L., & Williams, J. (1999). Using intuition from everyday life in filling the gap in children's extension of their number concept to include the negative numbers. Educational Studies in Mathematics, 39(1), 131-147.
59. Ministry of National Education (MoNE) (2013). Ortaokul (5-8. sınıflar) matematik öğretim programı [Middle School (5th-8th grades) Mathematics Curriculum]. MEB Basımevi.
60. Miles, M. B., ve Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
61. Ministry of National Education (MoNE), (2008a). Yetiştirici sınıf öğretim programı yönerge ve uygulanma kılavuzu [Catch-up education program guidelines and application guide]. MEB Basımevi.
62. Ministry of National Education (MoNE), (2018a). Matematik dersi (1-8. sınıflar) öğretim programı [ Mathematics Curriculum (1st-8th grades)]. MEB Basımevi.
63. Nixon-Ponder, S. (2001). Using problem-posing dialogue in adult literacy education. Retrieved September 1, 2018, from http://literacy.kent.edu/Oasis/Pubs/0300-8.htm
64. National Council of Teachers of Mathematics (NCTM) (2000). Standards for school mathematics, Reston, VA. EE. UU.
65. Özdemir, A. S., & Şahal, M. (2018). The effect of teaching integers through the problem posing approach on students’ academic achievement and mathematics attitudes. Eurasian Journal of Educational Research, 18(78), 117-138.
66. Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi. Turkish Journal of Computer and Mathematics Education, 8(2), 323-351.
67. Patton, M. Q. (1987). How to use qualitative methods in evaluation (No. 4). Sage.
68. Seng, K. L. (2010). An error analysis of form 2 (Grade 7) students in simplifying algebraic expressions: A descriptive study. Electronic Journal of Research in Educational Psychology, 8(1), 139-162.
69. Silver, E. A. (1994). On mathematical problem posing. For the learning of mathematics, 14(1), 19-28.
70. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Adam, 29(3), 75-80.
71. Soylu, Y. ve Soylu, C. (2005). İlköğretim beşinci sınıf öğrencilerinin kesirler konusundaki öğrenme güçlükleri: kesirlerde sıralama, toplama, çıkarma, çarpma ve kesirlerle ilgili problemler [Fifth grade students' learning difficulties in fractions: ordering, adding, subtracting, multiplying in fractions and problems about fractions]. Erzincan Eğitim Fakültesi Dergisi, 7(2), 101-117
72. Stickles, PR (2011). Ortaokul ve ortaokul öğretmenlerinin matematiksel problem pozlarının analizi [The Analysis of middle school teachers’ mathematical problem poses] Matematik Öğrenmede Araştırmalar, 3(2), 1-34.
73. Stoyanova, E. (2003). Extending students' understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32-40.
74. Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. Technology in mathematics education, 518-525.
75. Wessman-Enzinger, N. M., & Tobias, J. M. (2020). The dimensions of prospective elementary and middle school teachers’ problem posing for integer addition and subtraction. Journal of Mathematics Teacher Education, 1-33.
76. Yıldız, Z., & Özdemir, A. Ş. (2015). Hizmet öncesi ortaokul matematik öğretmenlerinin problem oluşturma yeteneklerinin analizi. Uluslararası Online Eğitim Bilimleri Dergisi, 7(2).