MIDDLE SCHOOL MATHEMATICS TEACHERS’ KNOWLEDGE OF MATHEMATICAL REASONING

Figen Bozkuş, Ülkü Ayvaz

Abstract


Acknowledging the importance of mathematical reasoning in mathematics teaching, the present study analyzes middle school mathematics teachers’ understanding of reasoning. In line with the purpose, the study was performed using a phenomenological design, which is one of the qualitative research methods. The study was carried out with a total of 16 middle school mathematics teachers serving in different state schools in the 2016-2017 school year. The study employed an interview form consisting of four open-ended questions to determine the teachers’ theoretical and practical understanding of mathematical reasoning. Drawing on qualitative data, this study employed content analysis method for data analysis. As a result, it is understood that the middle school mathematics teachers do not have a comprehensive and adequate knowledge and view about mathematical reasoning when it is considered how they define, exemplify and support mathematical reasoning. Because it is appeared that mathematical reasoning means only making explanations, justifications and producing different solutions for a problem according to them. It is important that the teachers should broaden their view about mathematical reasoning to support their students’ reasoning better.

 

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mathematical reasoning, mathematical thinking, middle school mathematics teachers

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Altıparmak, K. & Öziş, T. 2005. Matematiksel ispat ve matematiksel muhakemenin gelişimi üzerine bir inceleme. Ege Eğitim Dergisi, 6 (1).

Annells M. 2006. Triangulation of Qualitative Approaches: Hermeneutical Phenomenology and Grounded Theory. Journal of Advanced Nursing, 56(1), 55-61.

Ayele, M. A. 2017. Mathematics Teachers’ Perceptions on Enhancing Students’ Reasoning Skills in Mathematics. British Journal of Education, Society & Behaviorual Science, 19(2): 1-12.

Australian Curriculum Assessment and Reporting Authority (ACARA), 2012. Australian Curriculum: English. Version 3.0. Sydney: Australian Curriculum Assessment and Reporting Authority. Retrieved from http://www.australiancurriculum.edu.au/English/Curriculum/F-10

Brodie, K., 2009. Teaching mathematical reasoning in secondary school classrooms (Vol. 775). Springer Science & Business Media.

Carpenter, T. P., Franke, M. L., & Levi, L, 2003. Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann, 361 Hanover Street, Portsmouth, NH 03801-3912.

Carroll WM, 1998. Middle school students’ reasoning about geometric situations. Mathematics Teaching in the Middle School, 3(6):398-403.

Chin, C, 2007. Teacher questioning in science classrooms: Approaches that stimulate productive thinking. Journal of research in Science Teaching, 44(6), 815-843.

Doğan, A. & Çetin İ, 2009. Doğru ve ters orantı konusundaki 7. ve 9. Sınıf öğrencilerinin kavram yanılgıları. Uşak Üniversitesi Sosyal Bilimler Dergisi 2(2), 118-128.

Duatepe A., Akkuş-Çıkla O. & Kayhan M, 2005, “Orantısal Akıl Yürütme Gerektiren Sorularda Öğrencilerin Kullandıkları Çözüm Stratejilerinin Soru Türlerine Göre Değişiminin İncelenmesi”, Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28: 73-81.

Clarke, D. M., Clarke, D. J., & Sullivan, P, 2012. Reasoning in the Australian Curriculum: Understanding its meaning and using the relevant language. Australian Primary Mathematics Classroom, 17(3), 28.

Fernández, C., Llinares, S., & Valls, J, 2013. Primary school teacher's noticing of students' mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1/2), 441.

Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D, 2009. Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380-392.

Haylock, D, 1997. Recognizing mathematical creativity in schoolchildren. ZDM-International Reviews on Mathematical Education, 29(3), 68-74.

Herbert, S., Vale, C., Bragg, L. A., Loong, E., & Widjaja, W, 2015. A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26-37.

Holton, D., Stacey, K., & FitzSimons, G, 2012. Reasoning: A Dog's tale. Australian Mathematics Teacher, 68(3), 22.

Kilpatrick, J. Swafford, J. & Findell, B. (eds.), 2001. Adding it up: Helping children learn mathematics. Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education, National Research Council. Washington, DC: National Academy Press.

Küchemann, D., & Hoyles, C, 2006. Influences on students' mathematical reasoning and patterns in its development: insights from a longitudinal study with particular reference to geometry. International Journal of Science and Mathematics Education, 4(4), 581-608.

Leikin, R., & Lev, M, 2007. July). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 161-168). Seoul, South Korea: PME.

Liu, Y., & Manouchehri, A, 2013. Middle school children’s mathematical reasoning and proving schemes. Investigations in Mathematics Learning, 6(1), 18-40.

Loong, E. Y. K., Vale, C., Bragg, L. A. & Herbert, S, 2013. Primary School Teachers' Perceptions of Mathematical Reasoning. Mathematics Education Research Group of Australasia.

Mann, E. L, 2006. Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236-260.

Milli Eğitim Bakanlığı [MEB], 2013. Ortaokul matematik dersi öğretim programı. Ankara: Talim Terbiye Kurulu Başkanlığı

National Council of Teachers of Mathematics (Ed.), 2000. Principles and standards for school mathematics (Vol. 1). National Council of Teachers of.

Perry, M., Vander Stoep, S. W., & Yu, S. L, 1993. Asking questions in first-grade mathematics classes: Potential influences on mathematical thought. Journal of Educational Psychology, 85(1), 31.

Silver, E. A, 1997. Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM—The International Journal on Mathematical Education, 29 (3), 75–80.

Simon, M. A., & Blume, G. W, 1996. Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15(1), 3-31.

Sriraman, B, 2008. The characteristic of mathematical creativity. In B. Sriraman (Ed.), Creativity, giftedness, and talent development in mathematics [Monograph 4, The Montana Mathematics Enthusiast] (pp. 1-32). Missoula, MT: University of Montana.

Stylianides, G. J, 2005. Investigating students’ opportunities to develop proficiency in reasoning and proving: A curricular perspective. Unpublished doctoral dissertation, University of Michigan, Ann Arbor.

Stylianides, G. J., Stylianides, A. J., & Philippou, G. N, 2007. Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10(3), 145-166.

Stylianides, G, 2010. Engaging Secondary Students in Reasoning and Proving. Mathematics Teaching, 219, 39-44.

Sullivan, P., Clarke, D., Spandel, U., & Wallbridge, M, 1992. Using content-specific open questions as a basis of instruction: A classroom experiment. Victoria: Mathematics Teaching and Learning Centre, Australian Catholic University.

Torrance, E. P, 1988. The nature of creativity as manifest in its testing. The nature of creativity: Contemporary psychological perspectives, 43.

Umay, A, 2003. Matematiksel muhakeme yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24 (4)

Van de Walle, K., & Karp, K. S. Bay-Williams, 2013. Elementary and Middle School Mathematics: Teaching Developmentally.

Yıldırım, A. & Şimşek, H, 2006. Sosyal bilimlerde nitel arastirma yöntemleri. Seçkin yayıncılık.

Yenilmez, K. & Kavuncu, Ö. T, 2017. 7. Sınıf öğrencilerinin oran orantı konusunda karşılaştığı güçlüklerin incelenmesi. Eğitim ve Öğretim Araştırmaları Dergisi, 6(4), 139-146




DOI: http://dx.doi.org/10.46827/ejes.v0i0.1736

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