Arithmetic and algebraic problem-solving approaches of prospective teachers and teachers in service

Authors

Abstract

The aim of this study is to determine mathematical problem-solving approaches of elementary school pre-service mathematics teachers and elementary school mathematics teachers. This is a mixed method research and was carried out using exploratory sequential pattern. The sample of the study consists of 128 pre-service teachers (59 sophomores, 41 juniors and 28 seniors) registered to department of elementary mathematics teaching in a state university located in the Eastern Anatolian Region of Turkey and 22 secondary school mathematics teachers working in different cities of Eastern Anatolia Region at the same period. Clinical interviews were conducted with 12 pre-service teacher and 5 teachers. The data were obtained by Problem-solving Test [PST] and Semi-Structured Interview Form [SSIF]. The PST was prepared to examine the problem-solving processes of the teachers and pre-service teachers participating in the research. According to the findings of the research, it was observed that the participants preferred the algebraic approach while solving the problems and could not solve the problem with an arithmetical approach. It is also understood that they tend to use algorithms they know by heart while making algebraic solutions. These results show that the participants have some deficiencies in terms of bringing both arithmetic and algebraic solutions to the problems.

References

Akkan, Y. (2009). İlköğretim öğrencilerinin aritmetikten cebire geçiş süreçlerinin incelenmesi (Doctoral dissertation). Available from Yükseköğretim Kurulu Ulusal Tez Merkezi. (Thesis No. 259860)

Akkan Y., Baki A. & Çakıroğlu Ü. (2012). 5-8. sınıf öğrencilerinin aritmetikten cebire geçiş süreçlerinin problem çözme bağlamında incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 43(43), 1-13.

Altun, M., Memnun, D. S., & Yazgan, Y. (2007). Primary school teacher trainees’ skills and opinions on solving non-routine mathematical problems. Elementary Education Online, 6(1), 127-143.

Ball, D. L., Thames, M. D., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.

Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects-state, trends and issues-in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68.

Cai, J., & Nie, B. (2007). Problem-solving in Chinese mathematics education: Research and practice. ZDM, 39(5-6), 459-473.

Doruk, B. K., & Umay, A. (2011). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41(41), 124-135.

Driel, J. H., & Berry, A. (2010). The teacher education knowledge base: Pedagogical content knowledge. In B. McGraw, P. L. Peterson & E. Baker, (Eds.). International encyclopaedia of education (pp. 656-661). Oxford: Elsevier.

Grbich, C. (2012). Qualitative data analysis: An introduction. London: Sage.

Gürbüz, R., & Toprak, Z. (2014). Designation, implementation and evaluation of activities to ensure transition from arithmetic to algebra. Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education, 8(1), 178-203.

Kaya, D., Keşan, C., İzgiol, D., & Erkuş, Y. (2016). Yedinci sınıf öğrencilerinin cebirsel muhakeme becerilerine yönelik başarı düzeyi. Turkish Journal of Computer and Mathematics Education, 7(1), 142-163.

Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.). Handbook of research on mathematics teaching and learning, (pp. 390-419). New York: Macmillan.

Koedinger, K. R., Alibali, M. W., & Nathan, M. J. (2008). Trade‐offs between grounded and abstract representations: Evidence from algebra problem solving. Cognitive Science, 32(2), 366-397.

Linchevski, L., & Herscovics, N. (1996). Crossing the cognitive gap between arithmetic and algebra: operating on the unknown in the context of equations. Educational Studies in Mathematics, 30(1), 38–65.

MEB (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). Retrieved from http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329

Nathan, M. J., & Koedinger, K. R. (2000). An investigation of teachers' beliefs of students' algebra development. Cognition and Instruction, 18(2), 209-237.

National Governors Association Center for Best Practices, Council of Chief State School Officers (2010). Common core state standards for mathematics. Retrieved from URL: http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

Reed, S. K. (1999). Word problems: Research and curriculum reform. Mahwah, NJ: Lawrence Erlbaum Associates.

Schmidt, S., & Bednarz, N. (2002). Arithmetical and algebraic types of reasoning used by pre‐service teachers in a problem‐solving context. Canadian Journal of Math, Science & Technology Education, 2(1), 67-90.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Silk, J. S., Steinberg, L., & Morris, A. S. (2003). Adolescents' emotion regulation in daily life: Links to depressive symptoms and problem behavior. Child development, 74(6), 1869-1880.

Siswono, T. Y., Kohar, A. W., Rosyidi, A. H., & Hartono, S. (2017). Primary school teachers’ beliefs and knowledge about mathematical problem-solving and their performance on problem-solving task. World Trans. on Engng. and Technol. Educ., 15(2), 126-131.

Şener, Z. T., Ünal, H., & Bulut, A. S. (2017). Aritmetiksel ve cebirsel dinamikler: öğretmen adaylarının yaklaşımları. In F. Savaşan, F. Yardımcıoğlu, M.E. Altundemir & F. Beşel (Eds.), ICPESS (International Congress on Politic, Economic and Social Studies) (p. 335).

Turgut, S., Doğan, Ö. (2017). Erken cebir öğretim etkinliklerinin ilkokul dördüncü sınıf öğrencilerinin akademik başarılarına etkisi. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 6(1), 1-31.

Türnüklü, E. B., & Yeşildere, S. (2014). Problem, problem çözme ve eleştirel düşünme. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 25(3), 107-123.

Van Amerom, B. A. (2002). Reinvention of early algebra: Developmental research on the transition from arithmetic to algebra (Doctoral dissertation). Freudenthal Institute, Utrecht.

Van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of pre-service teachers’ content knowledge on their evaluation of students' strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319-351. doi: 10.2307/4149957

Yerushalmy, M. (2000). Problem-solving strategies and mathematical resources: A longitudinal view on problem-solving in a function based approach to algebra. Educational studies in mathematics, 43(2), 125-147.

Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.

Yıldızhan, B., & Şengül, S. (2017). 6. sınıf öğrencilerinin harflerin anlamına yönelik kavram yanılgılarının aritmetikten cebire geçiş süreci bağlamında incelenmesi ve öğrencilerin matematik tutum ve öz yeterlikleri ile karşılaştırılması. The Journal of International Lingual, Social and Educational Sciences, 3(2), 249-268.

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Published

2020-09-07