Analysis of the relationship between mathematics teacher candidates’ reflective thinking levels and their philosophical views on the nature of mathematics

Year 2022, Volume: 10 Issue: 3, 453 - 465, 30.09.2022

Derya Özlem Yazlık , Solmaz Damla Gedik Altun , Deniz Kaya

https://doi.org/10.17478/jegys.1151891

Abstract

The main aim of the present study with relational screening model was to analyze the relationship between reflective thinking skills and philosophical views regarding the nature of mathematics (NoM) in secondary school mathematics teacher candidates. In addition, it was aimed to determine whether the reflective thinking levels of the candidates displayed a significant difference according to absolutist, mixed, and semi-experimentalist groups. The study group consisted of 196 secondary school mathematics teacher candidates studying in the mathematics teaching program in the spring semester of the 2021-2022 academic year. As data collection tools, The Scale for Determining Philosophical Views Regarding the NoM and The Scale for Determining the Level of Reflective Thinking were used. In the analysis of the data, in addition to descriptive statistics, Pearson Product-Moment Correlation Coefficient and multiple linear regression analysis were employed. In the study, it was determined that both reflective thinking levels and the philosophical views regarding the NoM were found to be high in mathematics teacher candidates. Besides, it was determined that there was a positive and moderate relationship between the reflective thinking level subdimensions and and the philosphocial views on the NoM in the teacher candidates, and that the variables of the reflective thinking level subdimensions explained 44% of the variance in the philosophical views on the NoM. Moreover, it was concluded that there was a statistically significant difference between the semi-experimentalist group and the mixed and absolutist groups in favor of the semi-experimentalist group in terms of critical reflection, reflection and understanding skills, and between the absolutist group and the mixed and semi-experimentalist groups in favor of the absolutist group in terms of habitual actions subdimension.

Keywords

Nature of Mathematics, Reflective Thinking, Teacher Candidate

References

• Aghadiuno, M. C. K. (1992). Mathematics: history, philosophy and applications to science. International Journal of Mathematical Education in Science and Technology, 23(5), 683-690. https://doi.org/10.1080/0020739920230506
• Agustan, S., Juniati, D., & Siswono, T. Y. E. (2017). Reflective thinking in solving an algebra problem: A case study of field independent-prospective teacher. Journal of Physics: Conference Series, 893(1), 1-6. https://doi.org/10.1088/1742-6596/893/1/012002
• Aktamış, H. (2012). How prospective mathematics teachers view the nature of science. Procedia-Social and Behavioral Sciences, 31, 690-694.
• Aldahmash, A. H., Alshalhoub, S. A., & Mohammed, M. A. (2021). Mathematics teachers’ reflective thinking: Level of understanding and implementation in their professional practices. PLoS ONE 16(10), 1-17. https://doi.org/10.1371/journal.pone.0258149
• Arslan, M. M. (2017). Candidates' awareness of teaching practice in their reflective diaries. Bartın University Journal of the Faculty of Education, 6(3), 1017-1026. https://doi.org/10.14686/buefad.311276
• Atılkan-Tunçer, A., & Sapancı, A. (2021). The relationship between reflective thinking tendencies of secondary school mathematics teachers and the levels of creating constructivist learning environment. Asian Journal of Instruction, 9(2), 75-96.
• Aydın, S., & Çelik, D. (2017). Adaptation of the scale of beliefs about the nature of mathematics to Turkish culture. Theory and Practice in Education, 13(4), 715-733.
• Baki, A. (2014). Matematik tarihi ve felsefesi [History and philosophy of mathematics]. Ankara: Pegem Academy.
• Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi [Mathematics from theory to practice]. Ankara: Harf Education Publishing.
• Baş, F., Işık, A. Çakmak, Z., Okur, M., & Bekdemir, M. (2015). Primary education mathematics teacher candidates' thoughts on the nature of mathematics: A structural equation model analysis. Kastamonu Journal of Education, 23(1), 123-140.
• Başol, G., & Evin-Gencel, İ. (2013). Reflective thinking scale: A validity and reliability study. Educational Sciences: Theory & Practice, 13(2), 941-946.
• Baydar, S. C., & Bulut, S. (2002). Importance of teachers' beliefs about nature of mathematics and teaching of mathematics in mathematics education. Hacettepe University Journal of Education, 23, 62-66.
• Bozan, S. (2021). Determining students’ reflective thinking levels and examining their reflections on science concepts. African Educational Research Journal, 9(2), 544-550. https://doi.org/10.30918/AERJ.92.21.070
• Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2014). Bilimsel araştırma yöntemleri [Scientific research methods] (17th ed.). Ankara: Pegem Publishing.
• Büyüköztürk, Ş. (2019). Sosyal bilimler için veri analizi el kitabı [Manual of data analysis for social sciences] (24th ed.). Ankara: Pegem Academy Publishing.
• Cengiz, C., & Karataş, F. Ö. (2016). Reflective thinking and teaching. Journal of National Education, 45(211), 5-27.
• Chrysostomoua, M., & Philippou, G. N. (2010). Teachers’ epistemological beliefs and efficacy beliefs about Mathematics. Procedia Social and Behavioral Sciences, 9, 1509-1515.
• Çokluk, Ö., Şekercioğlu, G., & Büyüköztürk, Ş. (2014). Sosyal bilimler için çok değişkenli istatistik: SPSS ve LISREL uygulamaları [Multivariate statistics for social sciences: SPSS and LISREL applications] (3th ed.). Ankara: Pegem Academy Publishing.
• Dede, Y., & Uysal, F. (2012). Examining Turkish pre-service elementary teachers’ beliefs about the nature and the teaching of mathematics. International Journal of Humanities and Social Science, 2(12), 125-135.
• Deng, Z. (1995). Estimating the reliability of the teacher questionnaire used in the Teacher Education and Learning to Teach (TELT). National Center for Research on Teacher Learning Technical Series, 95(1), 1-37.
• Deryakulu, D. (2002). The relationship of locus of control and epistemological beliefs and instructional material comprehension monitoring types and levels. Hacettepe University Faculty of Education Journal, 22, 55-61.
• Dewey, J. (1933). How we think: A Restatement of the relation of reflective thinking to the educative process. Boston: Heath & Co Publishers.
• Duban, N., & Yanpar-Yelken, T. (2010). Pre-service teachers' reflective thinking tendencies and views on reflective teacher characteristics. Journal of the Cukurova University Institute of Social Sciences, 19(2), 343-360.
• Durmaz, M. (2016). Philosophical views of primary school mathematics teacher candidates on the nature of mathematics. 3rd International Eurasian Educational Research Congress (p. 1327-1328). Muğla: Sıtkı Koçman University.
• Duru, A., & Göl, R. (2016). Beliefs of prospective teachers about mathematics, mathematics teaching and mathematics learning. Adıyaman University Journal of Educational Sciences, 6(2), 255-282.
• Erdoğan, F., & Şengül, S. (2014). The investigation of pre-service elementary mathematics teachers’ reflective thinking levels. Asian Journal of Instruction, 2(1), 18-30.
• Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13-33.
• Ersözlü, Z. N. (2018). The effects of reflective thinking activities on the academic successes and attitudes of fifth grade primary social studies students. (Unpublished doctoral dissertation), Fırat University, Elazığ.
• Fırat-Durdukoca, Ş., & Demir, M. (2012). Reflective thinking levels of primary school teachers according to some variables and the relevance of teacher qualities in their mind to the qualities of reflective teacher. Mustafa Kemal University Journal of Social Sciences Institute, 9(20), 357-374.
• Gess-Newsome, J. (2015). A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK Summit. In A. Berry, P. Friedrichsen, & J. Loughran (Eds.), Re-examining pedagogical content knowledge in science education (pp. 28-42). New York, NY Routledge.
• Gözel, E., & Toptaş, V. (2017). The relationship between mathematical teaching efficacy beliefs and reflective thinking skills of pre-service primary school teachers. Cumhuriyet International Journal of Education, 6(4), 412-425.
• Handal, B. (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator,13(2), 47-57.
• Işıksal, M., Kurt, G., Doğan, O., & Çakıroğlu, E. (2007). Epistemological conceptions of pre-service elementary mathematics teachers: effects of university and grade level. Elementary Education Online, 6(2), 313-321.
• Karasar, N. (2022). Bilimsel araştırma yöntemi [Scientific research method] (37th ed.). Ankara: Nobel Publishing.
• Kember, D., Leung, D., Jones, A., Loke, A., McKay, J., Sinclair, K., et al. (2000). Development of a questionnaire to measure the level of reflective thinking. Assessment and Evaluation in Higher Education, 25(4), 381-395. https://doi.org/10.1080/713611442
• Keskinkılıç-Yumuşak, G. (2015). Reflective thinking tendencies of preservice teachers and their attitudes towards the teaching profession. Bartın University Journal of Faculty of Education, 4(2), 466-481.
• Kızılkaya, G. (2009). The effect of web-based learning environments supported by reflective thinking activities on problem-solving. (Unpublished doctoral dissertation), Hacettepe University, Ankara.
• Korumaz, M., & Özkılıç, R. (2015). Examining the directions for reflection as a foreign language. Marmara University Atatürk Faculty of Education Journal of Educational Sciences, 42(42), 299-316.
• Kuryel, B. (2009). Bir kültür olarak matematik [Mathematics as a culture]. Social History, 34-41. Retrieved from https://silo.tips/download/bir-kltr-olarak-matematik
• Lee, H. J. (2005). Understanding and assessing preservice teachers’ reflective thinking. Teaching and Teacher Education, 21(6), 699-715. https://doi.org/10.1016/j.tate.2005.05.007
• Maksimovic, J. Ž., & Osmanovic, J. S. (2019). Teachers' self-concept and its benefits for science education. Journal of Baltic Science Education, 18(1), 105-116. https://doi.org/10.33225/jbse/19.18.105
• Maviş, F. Ö. (2014). Comparison of high school teachers’ reflective practice level and their students’ reflective thinking skills. (Unpublished master’s thesis), Gaziosmanpaşa University, Tokat.
• Mezirow, J. (1991). Transformative dimensions of adult learning. San Francisco: Jossey-Bass.
• Ministry of National Education (MoNE) (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics lesson curriculum (primary and middle school 3, 4, 5, 6, 7 and 8th grades)]. Ankara: MoNE.
• Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
• Nian, Z. (2020). To promote the development of teachers’ teaching beliefs from reflective teaching. Open Journal of Social Sciences, 8(11), 120-126. https://doi.org/10.4236/jss.2020.811012
• Prediger, S. (2007). Philosophy of mathematics in teacher training courses, François. In K. & Bendegem, J. P. (Eds.), Philosophical dimensions in mathematics education, (p. 43-59). New York: Springer Science Business Media.
• Rodgers, C. (2002). Defining reflection: another look at John Dewey and reflective thinking. Teachers College Record, 104(4), 842-866.
• Sanalan, V. A., Bekdemir, M., Okur, M., Kanbolat, O., Baş, F., & Sağırlı, M. Ö. (2013). Preservice teachers' philosophical thoughts about the nature of mathematics. Pamukkale University Journal of Education, 33(1), 155-168.
• Schon, D. A. (1987). Educating the reflective practitioner: Toward a new design for teaching and learning in the professions. San Francisco: Jossey-Bass.
• Soodmand A. H., & Farahani, M. (2018). Inhibitors to EFL teachers’ reflective teaching and EFL learners' reflective thinking and the role of teaching experience and academic degree in reflection perception. Reflective Practice, 19(1), 46–67. https://doi.org/10.1080/14623943.2017.1351353
• Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1(2), 157-189.
• Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher education and development study in Mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.
• Thahir, A., Komarudin, K., Hasanah, U. N., & Rahmahwaty, R. (2019). Murder learning and self efficacy models: impact on mathematical reflective thinking ability. Journal for the Education of Gifted Young Scientists, 7(4), 1123-1135.
• Thomas, P. J., & Kallarackal, T. J. (2020). Themes of critical incidents in student teachers’ reflective journal writings. International Journal of Multidisciplinary Educational Research, 9(4), 55-62.
• Toker, G. Z. (2016). A preservice mathematics teacher’s reflective practices on self-improvement regarding teaching and learning process in practice teaching. (Unpublished doctoral dissertation), Middle East Technical University, Ankara.
• Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. New York: Pearson Education, Inc.
• Viholainen, A., Asikainen, M., & Hirvonen, P. E. (2014). Mathematics student teachers’ epistemological beliefs about the nature of mathematics and the goals of mathematics teaching and learning in the beginning of their studies. Eurasia Journal of Mathematics, Science & Technology Education, 10(2), 159-171. https://doi.org/10.12973/eurasia.2014.1028a
• Yıldırım, S. (2012). Teacher support, motivation, learning strategy use, and achievement: A multilevel mediation model. The Journal of Experimental Education, 80(2), 150-172.