Reflective Thinking in The Problem-Solving Process: A Model Proposal

Abstract

Problem solving is one of the basic skills that individuals need in a lot of fields throughout their lives. Problem solving is among the process standards in mathematics education; mathematics education aims to develop students' problem-solving skills in teaching all content domains. Reflective thinking is an important skill that directly affects problem solving and ensures its successful outcome. This research aims to determine the reflective thinking skills used in problem-solving and to model this process. The research was conducted as a case study, and the participants were selected using criterion sampling. Twenty pre-service primary teachers with different mathematics achievements participated in the study. Data collection tools are worksheets, think-aloud protocol, and semi-structured interview forms. In order to determine the reflective thinking skills used in problem-solving, a non-routine problem was solved by pre-service teachers in the worksheets through the think-aloud protocol and interviews were conducted with pre-service teachers. The data were analyzed considering the components and indicators of reflective thinking. The research results showed that the components of reflective thinking were used in all the problem-solving stages. Based on this result, a model proposal was developed regarding the problem solving process in which reflective thinking is used, and the results were discussed in light of the relevant literature.

Keywords

• problem solving
• reflective thinking
• components of reflective thinking

Problem Çözme Sürecinde Yansıtıcı Düşünme: Bir Model Önerisi

Abstract

Problem çözme bireylerin hayatları boyunca birçok alanda ihtiyaç duydukları en temel becerilerdendir. Problem çözme aynı zamanda matematik eğitiminde temel süreç becerileri arasındadır; tüm konu alanlarının öğretiminde öğrencilerin problem çözme becerilerinin geliştirilmesi hedeflenir. Yansıtıcı düşünme ise problem çözme sürecine doğrudan etki eden önemli bir beceridir. Bu araştırma problem çözme sürecinde kullanılan yansıtıcı düşünme becerilerini belirlemeyi ve bu süreci modellemeyi amaçlamaktadır. Nitel araştırma desenlerinden durum çalışması şeklinde gerçekleştirilen araştırmanın katılımcıları ölçüt örnekleme ile seçilmiş, farklı matematik başarı düzeylerine sahip 20 sınıf öğretmeni adayı çalışmaya katılmıştır. Araştırmanın veri toplama araçları çalışma kağıtları, sesli düşünme protokolü ve yarı yapılandırılmış görüşme formudur. Öğretmen adaylarının problem çözme sürecinde kullandıkları yansıtıcı düşünme becerilerinin belirlenmesi amacıyla onlara rutin olmayan bir problem sunulmuş, problemi sesli süşünme protokolü ile çözmeleri istenmiştir. Ayrıca öğretmen adayları ile görüşmeler yapılmıştır. Veri analizi aşamasında, ses kayıtları bilgisayarda transkript edilmiş ve transkriptler yansıtıcı düşünmenin bileşenleri ve göstergeleri dikkate alınarak analiz edilmiştir. Araştırma sonuçları problem çözme aşamalarının tamamında yansıtıcı düşünme bileşenlerinin kullanıldığını göstermiştir. Araştırmada bu sonuca bağlı olarak yansıtıcı düşünmenin kullanıldığı problem çözme sürecine ilişkin bir model önerisi sunulmuş, sonuçlar ilgili literatür ışığında tartışılmıştır.

Keywords

• problem çözme
• yansıtıcı düşünme
• yansıtıcı düşünme bileşenleri

References

1. Altun, M. (2014). Eğitim fakülteleri ve sınıf öğretmenleri için matematik öğretimi (18.baskı). Bursa: Alfa basım yayım dağıtım.
2. Baş, G., & Kıvılcım, Z. S. (2013). Lise öğrencilerinin problem çözmeye yönelik yansıtıcı düşünme becerileri ile matematik ve geometri derslerindeki akademik başarıları arasındaki ilişki. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi (KEFAD), 14(3), 1-17.
3. Baykul, Y. (2011). İlköğretimde matematik öğretimi: 1-5. sınıflar (10. Baskı). Ankara: PegemA Yayıncılık.
4. Bernardo, A. B. (1999). Overcoming obstacles to understanding and solving word problems in mathematics. Educational Psychology, 19(2), 149-163.
5. Bingham, A. (2004). Çocuklarda problem çözme yeteneklerinin geliştirilmesi (Developing problem solving skills in children) (A. F. Oğuzkan, Çev.). İstanbul: Millî Eğitim Basımevi.
6. Buzdar, M., & Akhtar, A. (2013). Development of reflective thinking through distance teacher education programs at AIOU Pakistan. International Review of Research in Open and Distance Learning, 14(3), 43-58.
7. Charles, R. I. (1985). The role of problem solving. The Arithmetic Teacher, 32(6), 48-50.
8. Demirel, Ö. (2002). Kuramdan uygulamaya eğitimde program geliştirme. Ankara: PegemA yayıncılık.

9. Dervent, F. (2015). The effect of reflective thinking on the teaching practices of pre-service physical education teachers. Issues in Educational Research, 25(3), 260–275.
10. Dewey, J. (1910). How we think. Boston, MA: DC Heath & Co.
11. Dewey, J. (1933). Why have progressive schools? Current History, 38(4), 441-448.
12. Donnelly, R., & Fitzmaurice, M. (2005). Collaborative project-based learning and problem-based learning in higher education: A consideration of tutor and student role in learner-focused strategies. In G. O'Neill, S.
13. Moore & B. McMullin (Eds.), Emerging issues in the practice of University Learning and Teaching (pp. 87-98). AISHE/HEA.
14. Epstein, A. S. (2003). How planning and reflection develop young children's thinking skills. Young children, 58(5), 28-36.
15. Fraenkel, J. R., Wallen, N. E., & Hyun, H. (2003). How to design and evaluate research in education (8th ed.). Boston: McGraw-Hill.
16. Gelter, H. (2003). Why is reflective thinking uncommon. Reflective practice, 4(3), 337-344.
17. Gencel, I. E., & Saracaloğlu, A. S. (2018). The effect of layered curriculum on reflective thinking and on self-directed learning readiness of prospective teachers. International Journal of Progressive Education, 14(1), 8–20. https://doi.org/10.29329/ijpe.2018.129.2
18. Ghanizadeh, A. (2017). The interplay between reflective thinking, critical thinking, self-monitoring, and academic achievement in higher education. Higher Education, 74(1), 101–114. https://doi.org/10.1007/s10734-016-0031-y
19. Guba, E. G., & Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Communication and Technology Journal, 30(4), 233-252.
20. Haylock, D., & Cockburn, A. D. (2008). Understanding mathematics for young children: A guide for foundation stage and lower primary teachers. Sage.
21. Hong, Y. C., & Choi, I. (2011). Three dimensions of reflective thinking in solving design problems: A conceptual model. Educational Technology Research and Development, 59(5), 687-710.
22. Hsieh, P. H., & Chen, N. S. (2012). Effects of reflective thinking in the process of designing software on students’ learning performances. Turkish Online Journal of Educational Technology, 11(2), 88–99.
23. Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63-85.
24. Kember, D., Leung, D. Y., Jones, A., Loke, A. Y., McKay, J., Sinclair, K., ... & Yeung, E. (2000). Development of a questionnaire to measure the level of reflective thinking. Assessment & evaluation in higher education, 25(4), 381-395.
25. Kholid, M., Sa'dijah, C., Hidayanto, E., & Permadi, H. (2020). How are students’ reflective thinking for problem solving? Journal for the Education of Gifted Young Scientists, 8(3), 1135-1146.
26. Kızılkaya, G. & Aşkar, P. (2009). Problem çözmeye yönelik yansıtıcı düşünme becerisi ölçeğinin geliştirilmesi. Eğitim ve Bilim, 34(154), 82-92.
27. Kitchener, K. S., & Fischer, K. W. (1990). A skill approach to the development of reflective thinking. Contributions to Human Development, 21, 48–62. https://doi.org/10.1159/000418980
28. Lai, T. L., & Land, S. M. (2009). Supporting reflection in online learning environments. Educational Media And Technology Yearbook, 141-154.
29. Mason, A. J. (2009). Reflection on problem solving in introductory and advanced physics (Unpublished doctoral dissertation). University of Pittsburgh School of Arts and Sciences, USA.
30. Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. Pearson.
31. Mezirow, J. (1990). Fostering critical reflection in adulthood: A guide to transformative and emancipatory learning. San Francisco: Jossey-Bass Publishers.
32. Mezirow, J. (1991). Transformative dimensions of adult learning. San Francisco: Jossey-Bass.
33. Ministry of National Education [MNE], (2018). Mathematics curriculum (Primary and secondary school grades 1, 2, 3, 4, 5, 6, 7 and 8). Ankara.
34. National Council of Teachers of Mathematics [NCTM], (1980). Problem solving in school mathematics. Reston, VA: The Council.
35. National Council of Teachers of Mathematics [NCTM], (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
36. Olkun, S., & Toluk Uçar, Z. (2012). İlköğretimde etkinlik temelli matematik öğretimi (5. Baskı). Ankara: Eğiten kitap.
37. Özkubat, U., & Özmen, E. R. (2018). Öğrenme güçlüğü olan öğrencilerin matematik problemi çözme süreçlerinin incelenmesi: Sesli düşünme protokolü uygulaması. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 19(1), 155-180.
38. Öztürk, S. (2003). Developing a reflective reading model (Unpublished doctoral dissertation). Marmara Universitesi, Turkey.
39. Polya, G. (1945). How to solve it. Princeton University Press.
40. Rieger, A., Radcliffe, B. J., & Doepker, G. M. (2013). Practices for developing reflective thinking skills among teachers. Kappa Delta Pi Record, 49(4), 184–189. https://doi.org/10.1080/00228958.2013.845510
41. Rodgers, C. (2002). Defining reflection: Another look at John Dewey and reflective thinking. Teachers College Record, 104(4), 842-866.
42. Rosenzweig, C., Krawec, J., & Montague, M. (2011). Metacognitive strategy use of eighth-grade students with and without learning disabilities during mathematical problem solving: A think-aloud analysis. Journal of Learning Disabilities, 44(6), 508-520.
43. Rott, B., Specht, B., & Knipping, C. (2021). A descriptive phase model of problem-solving processes. ZDM–Mathematics Education, 53(4), 737-752.
44. Satjatam, P., Sarintip, R., & Teerachai, N. (2016). Developing reflective thinking instructional model for enhancing students desirable learning outcomes. Educational Research and Reviews, 11(6), 238–251. https://doi.org/10.5897/ERR2015.2380
45. Schoenfeld, A. H. (1982). Expert and novice mathematical problem solving. Final Project Report and Appendices BH.
46. Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (Reprint). Journal of Education, 196(2), 1-38.
47. Schön, D. A. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books.
48. Schön, D. (1987). Educating the reflective practitioner: Toward a new design for teaching and learning in the professions. Jossey Bass Publications.
49. Shermis, S. S. (1992). Critical thinking: Helping students learn reflectively. Bloomington: INFO Press.
50. Sivaci, S. Y. (2017). The relationship between reflective thinking tendencies and social problem solving abilities of pre-service teachers. Journal of Education and Training Studies, 5(11), 21. https://doi.org/10.11114/jets.v5i11.2273
51. Toraman, Ç., Orakci, S., & Aktan, O. (2020). Analysis of the relationships between mathematics achievement, reflective thinking of problem solving and metacognitive awareness. International Journal of Progressive Education, 16(2), 72-90.
52. Tripp, D. (2003). Action inquiry. Action research e-reports, (17). https://researchrepository.murdoch.edu.au/id/eprint/34606/1/action%20inquiry.pdf
53. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics. London: Pearson Education UK.
54. Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 57–77). MacMillan.
55. Yimer, A., & Ellerton, N. F. (2010). A five-phase model for mathematical problem solving: Identifying synergies in pre-service-teachers’ metacognitive and cognitive actions. ZDM - The International Journal on Mathematics Education, 42, 245–261.
56. Zehavi, N., & Mann, G. (2005). Instrumented techniques and reflective thinking in analytic geometry. The Montana Mathematics Enthusiast, 2(22), 1551–3440.