Geometric Habits of Mind: The Meaning of Quadrilaterals for Elementary School Student Teachers

Yıl 2022, Cilt: 9 Sayı: 1, 49 - 66, 28.03.2022

Atilla Özdemir Sıtkı Çekirdekci

https://doi.org/10.17278/ijesim.1033078

Cited By: 1

Öz

The primary purpose of this study is to determine the geometric habits of mind of classroom teacher candidates and the level of these habits. The study was conducted with 55 elementary education program students studying at an education faculty in the 2017-2018 spring term. The criterion used in the determination of the study group is that the teacher candidates should have knowledge about almost all the courses in the classroom education program and have taken courses I and II in mathematics teaching. Three worksheets were distributed to the teacher candidates as a data collection tool. Since the research is like a case study, the mathematical ideas developed by the teacher candidates about quadrilaterals and their written answers were summarized and interpreted according to the predetermined themes. When the findings obtained as a result of the research are examined in general, it can be said that teacher candidates are not sufficient in finding relationships between quadrilaterals, generalizing the relationships they find by using strategies, associating the feature valid for a quadrilateral with quadrilaterals that may have that feature, namely the whole, and making judgments.

Anahtar Kelimeler

geometric habits of mind, elementary school student teachers, rectangles, exclusion definition, inclusive definition.

Kaynakça

• Akkaş, E. N., & Türnüklü, E. (2014). Middle school mathematics teachers’ pedagogical content knowledge regarding student knowledge about quadrilaterals. Elementary Education Online, 14(2), 744-756, 2015. İlköğretim Online, 14(2), 744-756, 2015. [Online]: http://ilkogretim-online.org.tr http://dx.doi.org/10.17051/io.2015.12002
• Aktaş, D. Y., & Cansız Aktaş, M. (2012). Eighth Grade Students’ Understanding and Hierarchical Classification of Quadrilaterals. Elementary Education Online, 11(3), 714-728, 2012. İlköğretim Online, 11(3), 714-728, 2012. Retrieved from https://dergipark.org.tr/tr/pub/ilkonline/issue/8588/106722
• Akuysal, N. (2007). Seventh-grade students' misconceptions about geometrical concepts. [Unpublished master thesis]. Selçuk University.
• Ay, Y., & Başbay, A. (2017). Misconceptions about polygons and their possible reasons. Ege Eğitim Dergisi, 18 (1), 83-104. DOI: 10.12984/egeefd.328377
• Bass, H. (2008, January). Mathematical practices. Paper presented at a Project NExT session on helping students develop mathematical habits of mind, Joint Mathematics Meetings, San Diego, CA. Powerpoint was available at http://www2.edc.org/CME/showcase.html.
• Bütüner, S. Ö. (2017). Identifying mathematics teacher candidates geometry content knowledge: the example of angle-height-diagonal and quadrilateral. Amasya Education Journal, 6(2), 501-530.
• Bütüner, S. Ö. & Filiz, M. (2006). Examining prospective mathematics teachers' understanding of the classification of quadrilaterals. Journal of Subject Teaching Research, Volume 2, Issue 2, 43 - 56. Retrieved from https://dergipark.org.tr/tr/pub/aleg/issue/24315/257669
• Creswell, J. W. (2003). Research design: qualitative, quantitative, and mixed methods approaches. California: Sage Publications.
• Creswell, J. W. (2016). Qualitative research methods qualitative research and research design according to five approaches. M. Bütün & S. B. Demir (Edt.). Ankara: Siyasal.
• Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of minds: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375-402.
• Cuoco, A., Goldenberg, E. P. & Mark, J. (2010). Contemporary curriculum issues: organizing a curriculum around mathematical habits of mind. Mathematics Teacher, 103(9), 682-688.
• Driscoll, M., DiMatteo, R. W., Nikula, J. E. & Egan, M. (2007). Fostering geometric thinking: A guide for teachers grades 5-10. Portsmouth, NH: Heinemann.
• Driscoll, M., DiMatteo, R. W., Nikula, J., Egan, M., June, M. & Kelemanik, G. (2008). The fostering algebraic thinking toolkit: A guide for staff development. Portsmouth, NH: Heinemann.
• Duatepe Paksu, A. (2016). Van Hiele Levels of Geometric Thinking. E. Bingölbali, S. Arslan, ve İ. Ö. Zembat içinde, Theories in Mathematics Education (s. 265-274). Ankara: Pegem Akademi.
• Dursun, Ş., & Dede, Y. (2004). The factors affecting students’ success in mathematics: mathematics teachers’ perspectives. G.Ü. Gazi Eğitim Fakültesi Dergisi, 24 (2), 217-230.
• Erşen, Z. B. (2017). Investigation of the Relationship between 10th Science High School Students’ Geometric Habits of Mind and Attitudes towards Geometry. SDU International Journal of Educational Studies, 4 (2), 71-85.
• Erşen, Z., & Karakuş, F. (2013). Evaluation of Preservice Elementary Teachers’ Concept Images for Quadrilaterals. Turkish Journal of Computer and Mathematics Education, 4 (2), 124-146.
• Fer, S., (2014). Learning Teaching Theory and Approaches. (2. Baskı). Anı Yayıncılık, Ankara.
• Fujita, T., &Jones, K. (2006). Primary trainee teachers’ understanding of basic geometrical figures in Scotland. In J. Novotna, H. Morava, K. Magdelena and N. Stehlikova (Eds.), Proceedings of The 30th Conference of the International Group for the Psychology of Mathematics Education, 3, 14-21.
• Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.
• Horzum, T. (2018). The investigation of pre-service mathematics teachers’ knowledge about quadrilaterals through concept maps. Turkish Journal of Computer and Mathematics Education, 9 (1), 1 - 30.
• Houser, J. (2015). Nursing research: reading, using, and creating evidence. (3rd ed.). Burlington: Jones ve Bartlett Learning.
• Karasar, N. (2003). Scientific research method. (12. Baskı). Ankara: Nobel Yayıncılık.
• Kartal, B., & Çınar, C. (2017). Examining Pre-service Mathematics Teachers’ Geometry Knowledge of Polygons. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi (KEFAD) , 18 (2), 375-399.
• Koç, G., & Demirel, M. (2004). From behaviorism to constructivism: a new paradigm in education. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi (27), 174-180.
• Koç, Y., & Bozkurt, A. (2012). Investigating prospective mathematics teachers’ knowledge of the volume of cylinders. Energy Education Science and Technology Part B: Social and Educational Studies [Special Issue I], 4, 148-153.
• Korkmaz, S., Dündar, S., & Yaman, H. (2016). The mathematical habits of mind in problem solving. Türk Bilgisayar ve Matematik Eğitimi Dergisi , 7 (1), 35-61.
• Körükcü, E., & Şengül, S. (2017). The investigation of the improvement of seventh-grade school students' persistence skills in the enriched learning environment. The Journal of Academic Social Science Studies, 57, 163-198.
• Lim, K.H., & Selden, A. (2009). “Mathematical habits of mind." In Proceedings of the Thirty-First Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Edited by: Swars, S. L., Stinson, D. W. and Lemons-Smiths, S. 1576–1583. Atlanta: Georgia State University.
• Lincoln, Y.S., & Guba, E.G. (1985). Naturalistic inquiry. SAGE, Thousand Oaks, 289-331.
• Merriam, S. B. (2013). A guide to qualitative research design and practice. (Çev. Turan, S.). Ankara: Nobel Yayıncılık.
• Olkun, S., & Aydoğdu, T. (2003). What is the third international math and science survey (TIMSS)? What does it ask? Example geometry questions and activities. İlköğretim Online, 2(1), 28-35. [Online]: http://ilkogretim-online.org.tr/vol2say1/v02s01d.pdf adresinden alınmıştır.
• Romberg, T., & Carpenter, T. (1986). Research on teaching and learning mathematics: Two disciplines of scientific inquiry (s. 850–873). Ed: W.C. Wittrock., Handbook of Research on Teaching, MacMillan: New York.
• Özen, D. (2015). Development of geometric thinking of elementary school mathematics teachers: A lesson study. [Unpublished doctoral dissertation]. Anadolu University.
• Öztoprakçı, S., & Çakıroğlu, E. (2013). Quadrangles. İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır ve A. Delice içinde, Tanımları ve Tarihsel Gelişimleri ile Temel Matematiksel Kavramlar (s. 251-272). Ankara: Pegem Akademi.
• Shulman, L.S. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57, 1-22.
• Tolga, A., & Cantürk-Günhan, B. (2019). Determination of secondary school mathematics teachers’ geometric habits of mind. Western Anatolia Journal of Educational Sciences, (2019), 10 (1), 37-56.
• Türk Dil Kurumu, (2019, 15 September). Retrieved from https://www.sozluk.gov.tr/
• Türnüklü, E., Gündoğdu Alaylı, F., & Akkaş, E. N. (2013). Investigation of prospective primary mathematics teachers' perceptions and images for quadrilaterals. Educational Sciences: Theory and Practice 13(2):1225-1232
• Usiskin, Z., Griffin, J., Witonsky, D., & Willmore, E. (2008). The classification of quadrilaterals: A study in definition. Charlotte, NC: Information Age Publishing.
• Van de Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2016). Elementary and middle school mathematics teaching developmentally. (S. Durmuş, 7. Baskıdan Çev.). Nobel.
• Wiles, P. S. (2013). Folding corners of the habits of mind. Mathematics Teaching in the middle school Vol. 19, No. 4 (November 2013), pp. 208-213
• Whittemore, R., Chase, S. K., & Mandle, C. L. (2001). Validity in qualitative research. Qualitative Health Research, 11 (4), 522-537.
• Yavuzsoy Köse, N., & Tanışlı, D. (2014). Primary school teacher candidates’ geometric habits of mind. Educational Sciences: Theory & Practice, 14(3), 1220-1229.
• Yıldırım, C. (2000). Mathematical thinking. Remzi Kitabevi, İstanbul. Yıldırım, A. & Şimşek, H. (2013). Qualitative research methods in the social sciences. (9th edition). Ankara:SeçkinYayıncılık.
• Yin, R. K. (2011). Qualitative research from start to finish. New York: The Guilford Press.