Story problems created by elementary mathematics teacher candidates in real-life situations: An algebra learning area example

Year 2022, Volume: 3 Issue: 2, 111 - 123, 30.12.2022

Deniz Kaya , Bahar Dinçer

Abstract

This research aims to examine the story problems of elementary mathematics teacher candidates in the field of algebra, which are suitable for real-life situations. For this purpose, it was tried to determine the pre-service teachers' preferred grade level, sub-learning area, and outcomes while creating a real-life story problem for the field of algebra learning. In addition, the relationship between story problems and outcomes, the reasons for choosing the grade level and sub-learning area, and the issues they paid attention to while creating the story problems are among the questions sought to be answered in the research. The research was designed according to the case study model. The study group the research consists of 35 elementary mathematics teacher candidates studying at the undergraduate level. 57% of the participants are female, and 43% male teacher candidates. In the study group selection, a non-random convenient sampling method was preferred. The algebra study instruction developed by the researchers was used as a data collection tool. In addition to the outcome(s) in the field of algebra learning, there are some questions that the participants should answer in the study guide. Descriptive and content analysis were used in the analysis of the data. According to the findings, most pre-service teachers were at the eighth-grade level, and inequalities created story problems suitable for a real-life situation related to the sub-learning domain. Pre-service teachers gave place to technology association in story problems. The pre-service teachers stated that they aimed to attract the students' attention and make them love mathematics while creating story problems. While creating the story problems, the most attention was paid to using actual data and originality. It has been suggested to increase pre-service teachers' awareness about the algebra learning field and encourage them to pose problems by the nature of their daily life situations.

Keywords

Algebra learning, Real-life, Story problem

References

• Akkan, Y., Öztürk, M., Akkan, P., & Küçük-Demir, B. (2019). Ortaokul matematik öğretmenlerinin aritmetik ve cebir problemleri hakkındaki inanışları [Opinions and beliefs of middle school mathematics teachers about arithmetic and algebra problems] Erzincan University Journal of Education Faculty, 21(1), 156-176. https://doi.org/10.17556/erziefd.431583
• Akkan, Y., Akkan, P., & Güven, B. (2017). Aritmetik ve cebir kavramları ile ilgili farkındalık [Awareness of arithmetic and algebra concepts]. Journal of Bayburt Education Faculty, 12(24), 527-558.
• Akkaya, R., & Durmuş, S. (2006). İlköğretim 6-8. sınıf öğrencilerinin cebir öğrenme alanındaki kavram yanılgıları [Misconceptions of elementary school students in grades 6-8 on learning algebra]. Hacettepe University Journal of Education, 31, 1-12.
• Bayazit, İ., & Kırnap-Dönmez, S. M. (2017). Prospective teachers’ proficiencies at problem posing in the context of proportional reasoning. Turkish Journal of Computer and Mathematics Education, 8(1), 130-160. https://doi.org/10.16949/turkbilmat.303759
• Baykul, Y. (2020). Matematik öğretimi [Mathematics teaching] (4th ed.). Pegem Academy. https://doi.org/10.14527/9786053-646754
• Baykul, Y. (2016). İlkokulda matematik öğretimi [Teaching mathematics in primary school] (13th ed.). Pegem Academy.
• Brown, S. I., & Walter, M. I. (Eds.). (1993). Problem posing in mathematics education. Lawrence Erlbaum Associates.
• Büyüköztürk, S., Çakmak, E. K., Akgün, O. E., Karadeniz, S., & Demirel, F. (2018). Bilimsel araştırma yöntemleri [Scientific research methods in education] (25th ed.). Pegem Academy. https://doi.org/10.14527/9789944919289
• Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211-230. https://doi.org/10.1007/s10649-006-7834-1
• Chmiliar, I. (2010). Multiple-case designs. In A. J. Mills, G. Eurepas & E. Wiebe (Eds.), Encyclopedia of case study research (pp. 582-583). Sage Publication.
• Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt füur Didaktik der Mathematik, 37(3), 149-158. https://doi.org/10.1007/s11858-005-0004-6
• Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395-415.
• Creswell, J. W. (2018). Nitel araştırma yöntemleri. Beş yaklaşıma göre nitel araştırma ve araştırma deseni [Qualitative research methods. Qualitative research and research design according to five approaches] (M. Bütün & S. B. Demir, Trans.) (4th ed.). Siyasal Bookstore.
• Çoban, K., & Yenilmez, K. (2020). Sekizinci sınıf öğrencilerinin eşitsizlikler konusunda karşılaştıkları güçlüklerin incelenmesi [Investigation of the difficulties encountered by eighth grade students on inequalities]. Journal of Education in Eskişehir Osmangazi University Turkic World Apply and Research Center, 5(1), 40-56.
• Dede, Y., & Yaman, S. (2005). Matematik öğretmen adaylarının matematiksel problem kurma ve problem çözme becerilerinin belirlenmesi [Identification of mathematical problem posing and problem solving skills for prospective mathematics teachers]. Eurasian Journal of Educational Research, 18, 41-56.
• Dede, Y. (2004). Öğrencilerin cebirsel sözel problemleri denklem olarak yazarken kullandıkları çözüm stratejilerinin belirlenmesi [Identifying students’ solution strategies in writing algebraic word problem as equations]. Educational Sciences and Practice, 3(6), 175-192.
• English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183-217. https://doi.org/10.1023/A:1002963618035
• Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219. https://doi.org/10.1007/s10857-007-9070-8
• Güner, P., & Erbay, H. N. (2021). Metacognitive skills and problem-solving. International Journal of Research in Education and Science, 7(3), 715-734. https://doi.org/10.46328/ijres.1594
• Güner, P. (2021). Problem-posing skills and thinking styles of preservice teachers. HAYEF: Journal of Education, 18(2), 254-277. https://doi.org/10.5152/hayef.2021.21003
• Gürbüz, S., & Şahin, F. (2016). Sosyal bilimlerde araştırma yöntemleri: Felsefe-yöntem-analiz [Research methods in social sciences: Philosophy-method-analysis] (3th ed.). Seçkin Publishing.
• Işık, C., & Kar, T. (2012). Sınıf öğretmeni adaylarının problem kurma becerileri [Pre-service elementary teachers’ problem posing skills]. Journal of Mehmet Akif Ersoy University Faculty of Education, 23, 190-214.
• Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63-85. https://doi.org/10.1007/BF02300500
• Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5-17). Lawrence Erlbaum Associates.
• Kar, T., Çiltaş, A., & Işık, A. (2011). Cebirdeki kavramlara yönelik öğrenme güçlükleri üzerine bir çalışma [A study on the learning difficulties for algebra concepts]. Kastamonu Education Journal, 19(3), 939-952.
• Katz, V. J., & Barton, B. (2007). Stages in the history of algebra with implications for teaching. Educational Studies in Math, 66(2), 185-201. https://doi.org/10.1007/s10649-006-9023-7
• Kaya, D. (2018). Yedinci sınıf öğrencilerinin cebirsel sözel problemleri çözme becerilerinin incelenmesi [Examination of seventh grade students’ ability to solve algebraic verbal problems]. Balıkesir University The Journal of Social Sciences Institute, 21(39), 159-181. https://doi.org/10.31795/baunsobed.437730
• Kieran, C. (2014). Algebra teaching and learning. In S. Lerman (Ed.), Encyclopaedia of mathematics education (pp. 27-32). Springer Publishing.
• Kinzel, M. T. (2000). Characterizing ways of thinking that underlie college students interpretation and use of algebraic notation (Unpublished doctoral dissertation). The Pennsylvania State University.
• Korkmaz, E., & Gür, H. (2006). Öğretmen adaylarının problem kurma becerilerinin belirlenmesi. [Determining of prospective teachers’ problem posing skills]. Balıkesir University Journal of Science Institute, 8(1), 64-74.
• Lee, J. E. (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. Journal of Mathematics Teacher Education, 15(6), 429-452. https://doi.org/10.1007/s10857-012-9220-5
• Lew, H. C. (2004). Developing algebraic thinking in early grades: Case study of Korean elementary school mathematics. The Mathematics Educator, 8(1), 88-106.
• Merriam, S. B. (2013). Nitel araştırma: Desen ve uygulama için bir rehber [Qualitative research: A guide to design and implementation] (S. Turan, Trans.). Nobel Publishing.
• 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: Ministry of National Education.
• National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: Author.
• National Research Council (NRC) (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. J. W. Pellegrino & M. L. Hilton (Eds.). The National Academies Press.
• Özgeldi, M., & Osmanoğlu, A. (2017). Connecting mathematics to real-life: An investigation on how prospective secondary mathematics teachers build real-life connections. Turkish Journal of Computer and Mathematics Education, 8(3), 438-458. https://doi.org/10.16949/turkbilmat.298081
• Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi [Investigation of problem-posing skills of eighth grade students in terms of some variables]. Turkish Journal of Computer and Mathematics Education, 8(2), 323-351. https://doi.org/10.16949/turkbilmat.322660
• Polya, G. (1981). Mathematical discovery: On understanding, learning, and teaching problem-solving. John Wiley & Sons.
• Posamentier, A., & Krulik, S. (2016). Effective techniques to motivate mathematics instruction. Routledge.
• Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt für Didaktik der Mathematik, 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
• Stacey, K., & MacGregor, M. (1999). Learning the algebraic method of solving problems. The Journal of Mathematical Behavior, 18(2), 149-167. https://doi.org/10.1016/S0732-3123(99)00026-7
• Stickles, P. R. (2011). An analysis of secondary and middle school teachers’ mathematical problem posing. Investigations in Mathematics Learning, 3(2), 1-34. https://doi.org/10.1080/24727466.2011.11790301
• Sutherland, R., & Rojano, T. (1993). A spreadsheet approach to solving algebra problems. The Journal of Mathematical Behavior, 12(4), 353-383.
• Tekin-Sitrava, R., & Işık, A. (2018). Sınıf öğretmeni adaylarının serbest problem kurma becerilerinin incelenmesi [An investigation into prospective primary school teachers’ free problem posing skills]. Gazi University Journal of Gazi Educational Faculty, 38(3), 919-947.
• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Pearson Publishing.
• Williams, K. M. (2003). Writing about the problem solving process to improve problem solving performance. The Mathematics Teacher, 96(3), 185-187.
• Yazgan, Y., & Arslan, Ç. (2017). Matematiksel sıradışı problem çözme stratejileri ve örnekleri [Mathematical unusual problem solving strategies and examples]. Pegem Academy.
• Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences] (11th ed.). Seçkin Publishing.