General Understanding Regarding to the Fraction and Rational Number Concepts

Year 2022, Volume: 6 Issue: 1, 46 - 67, 30.06.2022

Berna Yıldızhan , Erhan Ertekin

https://doi.org/10.54535/rep.1115808

Abstract

The aim of the current research is to examine the studies carried out to determine the understanding of the concepts of fraction and rational number of students, teachers and prospective teachers and to reveal the general understanding by synthesizing the findings of these studies. For this purpose, meta-synthesis research method, in which qualitative studies are again interpreted and synthesized with a qualitative understanding, was used in the study. Within the scope of the study, a total of 14 studies conducted in Turkey within the framework of the qualitative research paradigm were examined in order to reveal the understanding regarding to the concepts of fraction and rational number. Content analysis was used in the analysis of the obtained data. As a result of the research; It has been determined that students, teachers and prospective teachers have various understandings regarding to the concepts of fraction and rational number. One of the remarkable results is that the prospective teachers have an understanding that the numerator and denominator of the fraction are real numbers, while the teachers have an understanding that the numerator and denominator can be integer, natural number or positive integer. Also, it was found that students associate the rational number with negativity while associating the fraction with positivity.

Keywords

Fraction, Rational Number, Understanding, Comprehension, Meta-Synthesis

References

• Aksu, Z. (2013). The development of pre-service primary school teachers' pedagogical content knowledge in fractions [Unpublished doctoral dissertation]. Atatürk University, Erzurum.
• Aktaş, D. G. (2019). The concept definition of students and teachers about fraction and rational number [Unpublished doctoral dissertation]. Gazi University, Ankara.
• Argün, Z., Arıkan, A., Bulut, S., & Halıcıoğlu, S. (2014). Temel matematik kavramların künyesi [Identity of basic mathematical concepts]. Ankara: Gazi Kitabevi.
• Bennett, A., Burton, L., Nelson, T., & Ediger, J. (2016). Mathematics for elementary teachers: A conceptual approach (10th. Edition). NY: The McGraw-Hill Companies.
• Büyüköztürk, S., Cakmak, E. K., Akgun, O. E., Karadeniz, S., & Demirel, F. (2017). Bilimsel araştırma yöntemleri [Scientific research methods] (23. Baskı). Ankara: Pegem Akademi.
• Carraher, D. W. (1993). Lines of thought: A ratio and operator model of rational number. Educational Studies in Mathematics, 25, 281-305. https://doi.org/10.1007/BF01273903
• Cramer, K., & Post, T. (1995). Facilitating children’s development of rational number knowledge. D. Owens, M. Reed, and G. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of PME-NA (s. 377-382). Columbus, OH: PME.
• Çelik, B. (2006). Temel matematik [Basic math]. Ankara: Nobel Yayın.
• Çetin, H. (2020). Investigation of the definitions of pre-service elementary mathematics teachers on fraction concept. Eurasian Journal of Teacher Education, 1(3), 172-185. https://dergipark.org.tr/en/pub/ejte/issue/59069/795482
• Çevikbaş, M., & Argün, Z. (2017). Future mathematics teachers' knowledge of rational and irrational number concepts. Journal of Uludağ University Faculty of Education, 30(2), 551-581. https://doi.org/10.19171/uefad.368968
• Doğan, A. (2018). Primary school teachers' knowledges toward fractional meanings and models used in fractions teaching [Unpublished doctoral dissertation]. Gazi University, Ankara.
• Ercire, Y. E., Narlı, S., & Aksoy, E. (2016). Learning difficulties about the relationship between irrational number set with rational or real number sets. Turkish Journal of Computer and Mathematics Education, 7(2), 417-439. http://dx.doi.org/10.16949/turcomat.47225
• Erdem, E. (2016). Prospective middle school mathematics teachers’(PMTs) content knowledge about concepts ‘fraction’ and ‘rational number’. Journal of Education and Training Studies, 4(6), 80-92. http://dx.doi.org/10.11114/jets.v4i6.1431
• Gümüş, S. (2018). Nitel araştırmaların sistematik derlemesi: Meta-sentez [Systematic review of qualitative research: Meta-synthesis]. K. Beycioğlu, N. Özer ve Y. Kondakçı (Ed.) içinde, Eğitim yönetiminde araştırma [Research in educational administration] (s. 533-551). Ankara: Pegem Akademi.
• Günaydın, R. (2018). Investigation in the APOS theoretical framework of the process of creating fraction concept in the 5th grade students' [Unpublished master's thesis]. Eskişehir Osmangazi University, Eskişehir.
• Gürel, Z. Ç., & Okur, M. (2016). 6th and 7th grade secondary school students’ misconceptions about fractions. Erzincan University Journal of Education Faculty, 18(2), 922-952. https://doi.org/10.17556/jef.30116
• Jones, J. C. (2012). Visualizing elementary and middle school mathematics methods. USA: John Wiley & Sons.
• Kieren, T. (1976). On the mathematical, cognitive and instructional foundations of rational numbers. R. Lesh (Ed.), Number and measurement: Papers from a research workshop (s. 101-144). Athens, Georgia: The Georgia Center for the Study or Learning and Teaching Mathematics.
• Lamon, S. J. (1999).Teaching fractions and ratios for understanding. New Jersey: Lawrence Erlbaum Associates.
• Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework. F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (s. 629-668). Charlotte, NC: Information Age Publishing.
• Macit, E. (2020). An investigation of the relationship between 6th grade students' images, misconceptions and academic achievement about fraction [Unpublished doctoral dissertation]. Inonu University, Malatya.
• Macit, E., & Nacar, S. (2019). Concept images for rational number and fraction of the students at the elementary mathematics education department. Inonu University Journal of the Graduate School of Education, 6(11), 50-62. https://doi.org/10.29129/inujgse.547277
• Milli Eğitim Bakanlığı [MEB] (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7, 8. Sınıflar) [Mathematics curriculum (primary and secondary school grades 1, 2, 3, 4, 5, 6, 7 and 8)]. Ankara: Talim Terbiye Kurulu Başkanlığı.
• Musser, G. L., Peterson, B. E., & Burger, W. F. (2014). Mathematics for elementary teachers: A contemporary approach (10th edition). USA: John Wiley & Sons.
• Niven, I. (1961). Numbers: Rational and irrational. Washington D.C.: Mathematical Association of America.
• Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. London: Sage publications.
• Pluye, P., Gagnon, M. P., Griffiths, F., & Johnson-Lafleur, J. (2009). A scoring system for appraising mixed methods research, and concomitantly appraising qualitative, quantitative and mixed methods primary studies in mixed studies reviews. International Journal of Nursing Studies, 46(4), 529-546. https://doi.org/10.1016/j.ijnurstu.2009.01.009
• Şen, C. (2021). Assessment of a middle-school mathematics teacher’s knowledge for teaching the 5th-grade subject of fractions. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(1), 96-138. https://doi.org/10.16949/turkbilmat.742136
• Temel, H., & Eroğlu, A. O. (2014). A study on 8th grade students’ explanations of concepts of number. Kastamonu Education Journal, 22(3), 1263-1278. https://dergipark.org.tr/en/pub/kefdergi/issue/22601/241491
• Thomas, J., & Harden, A. (2008). Methods for the thematic synthesis of qualitative research in systematic reviews. BMC Medical Research Methodology, 8(1), 1-10. https://doi.org/10.1186/1471-2288-8-45
• Yetim, S., & Alkan, R. (2010). Common mistakes and misconceptions of 7th grade students about the rational numbers and placement of the rational numbers on the number line. Manas Journal of Natural Sciences, 2(11), 87–109.
• Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative Research Methods in Social Sciences] (11. Baskı). Ankara: Seçkin Yayıncılık.