GEOMETRIC HABITS OF MIND OF MATHEMATICS TEACHERS IN THE CONTEXT OF THEIR GEOMETRY BACKGROUNDS

Authors: Özlem Turan, Çi̇ğdem Arslan, Menekşe Seden Tapan Broutin & Ridvan Ezentaş

ABSTRACT

This study aims to determine the geometric habits of mind of high school mathematics teachers and to examine these habits in the context of teachers’ geometry backgrounds. The study implements the qualitative research method and the case study design included in it. The participants of the study are 15 mathematics teachers. Eight open-ended questions revealing geometric habits of mind and an interview form about geometry background were used as data collection tools. The data were analyzed using descriptive and content analysis methods. It was observed that the teachers who had common results regarding the use of geometric habits of mind also showed similarities in their geometry backgrounds. Between the teachers who could use geometric habits of mind in their solutions and those who could not, the results were in favor of the ones who could them.

Keywords: Geometry education, geometric habits of mind, geometry background, high school, a mathematics teacher.

REFERENCES

  • Akay, S., & Kurtuluş, A. (2017). The analysis of geometric thinking levels and hemispheric dominance of preservice teachers in terms of some variables. Mehmet Akif Ersoy University Faculty of Education Journal 1(41), 38-61.
  • Akkan, Y., Akkan, P., Öztürk, M., & Demir, Ü. (2018). A qualitative study with mathematics teachers on visual theorems. Journal of Instructional Technologies and Teacher Education, 7(2), 56-74.
  • Altun, M. (2018). Teaching mathematics in secondary schools. (13th ed.). Aktüel.
  • Anthony, G., & Walshaw, M. (2009). Characteristics of effective teaching of mathematics: A view from the west. Journal of Mathematics Education, 2(2), 147-164.
  • Aslan-Tutak, F. (2011, February). Preservice elementary teachers’ geometry content knowledge in methods course. Paper presented at the Seventh Congress of the European Society for Research in Mathematics Education, Rzeszów, Poland.
  • Başer, N., & Cantürk Günhan, B. (2010). The profile of the contemporary mathematics teacher in the high scholl education. Gazi University Journal of Gazi Educational Faculty (GUJGEF), 30(2).
  • Bayrakdar Çiftçi, Z., Akgün, L., & Deniz, D. (2013). Teachers’ opinions and solution suggestions regarding encountered issues on the ninth grade mathematics curriculum. Anadolu Journal of Educational Sciences International, 3(1).
  • Bülbül, B. Ö. (2016). The evaluation of the learning environment designed for ımprove the geometric habits of mind of mathematic pre-service teachers [Doctoral Dissertation, Karadeniz Technical University].
  • Bülbül, B. Ö. (2021a). Examining the relationship between geometric habits of mind and achievements in geometry of preservice mathematics teachers. Adnan Menderes University Faculty of Education Journal, 12(1), 15-28.
  • Bülbül, B. Ö. (2021b). The effects of an online learning environment prepared by considering the problem solving steps and strategies on geometric habits of mind and geometry achievement. Uludağ University Faculty of Education Journal, 34(3), 1015-1050.
  • Bülbül, B. Ö., & Güven, B. (2019). Examining the relationship between geometric habits of mind and the mathematics achievement: The case of mathematics preservice teachers. Turkish Journal of Computer and Mathematics Education, 10(3), 711-731.
  • Cansız Aktaş, M., & Aktaş, D. Y. (2012). Students’ understanding of quadrilaterals: The sample of parallelogram. Journal of Research in Education and Teaching, 1(2), 319-329.
  • Creswell, J. W. (2013). Qualitative inquiry & research design (M. Bütün, and S. B. Demir, Trans. Eds.). Siyasal.
  • Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375-402.
  • Çakmak, D., & Güler, H. K. (2014). Determining the geometric thinking levels of pre-service elementary mathematics teachers. Journal of Turkish Educational Sciences, 12(1), 1-16.
  • Çiftci, O., & Tatar, E. (2015). Teachers’ opinions about the updated secondary mathematics curriculum. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6(2), 285-298.
  • Driscoll, M., DiMatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10. Heinemann.
  • Ergün (2010). 7th grade students’ perception, definition and classification of the polygons [Master’s Thesis, Dokuz Eylül University].
  • Erşen, Z. B. (2018). The design, implementation and evaluation of the teaching environment for improve the geometric habits of mind of tenth grade students [Doctoral Dissertation, Uludağ University].
  • Fan, L., Qi, C., Liu, X., Wang, Y., & Lin, M. (2017). Does a transformation approach improve students’ ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms. Educational Studies in Mathematics, 96(2), 229-248.
  • Goldenberg, E. P. (1996). “Habits of mind” as an organizer for the curriculum. Journal of Education, 178(1), 13-34.
  • Gordon, M. (2011). Mathematical habits of mind: Promoting students’ thoughtful considerations. Journal of Curriculum Studies, 43(4), 457-469.
  • Güler, H. K. (2016). Determining, developing and evaluating the characteristics of an effective geometry lesson [Doctoral Dissertation, Uludağ University].
  • Gündüz, N., Bulut, A. S., & Dündar, S. (2017). Examining knowledge levels, problem solving levels, and attitudes of teacher candidates on geometrical objects. İnönü University Faculty of Education Journal, 18(2), 01-15.
  • Gürbüz, M. Ç., Ağsu, M. & Güler, H. K. (2018).Investigating geometric habits of mind by using paperfolding. Acta Didactica Napocensia, 11(3/4), 157-173.
  • Henderson, P. B. (2002). Materials development in support of mathematical thinking. ACM SIGCSE Bulletin, 35(2), 185-190.
  • Idris, N. (2007). The effect of Geometers’ Sketchpad on the performance in geometry of Malaysian students’ achievement and Van Hiele geometric thinking. Malaysian Journal of Mathematical Sciences, 1(2), 169-180.
  • Kaiser, G., & Vollstedt, M. (2007). Teachers’ views on effective mathematics teaching: Commentaries from a European perspective. ZDM, 39(4), 341-348.
  • Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, (pp. 2330-2339). Larnaca, Cyprus.
  • Lim, K., & Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the thirty-first annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, (pp. 1576-1583). Bepress.
  • Merriam, S. B. (2018). Qualitative research a guide to design and implementation (S. Turan, Trans. Ed.). Nobel.
  • Napitupulu, B. (2001). An exploration of students’ understanding and Van Hiele levels of thinking on geometric constructions [Master’s Thesis, Simon Fraser University].
  • Okur, T. (2006).The reasons of failure in geometry and ways of solution [Master’s Thesis, Sakarya University].
  • Oral, B., & İlhan, M. (2012). Analysis of geometric thinking levels of candidate mathematics teachers of primary and secondary schools in terms of various variables. Necatibey Faculty of Education, Electronic Journal of Science and Mathematics Education, 6(1), 201-219.
  • Özen, D. (2015). Development of geometric thinking of elementary school mathematics teachers: A lesson study [Doctoral Dissertation, Anadolu University].
  • Özen Ünal, D., & Köse, N. (2019). A lesson study to develop teachers’ geometric habits of mind. Croatian Journal of Education, 21(4), 1133-1179.
  • Özkeleş Çağlayan (2010). Lise 1. The potential of predictive of the academic achievement points of geometry using the 9th grade students’ geometry self-efficacy and geometry attitude [Master’s Thesis, Yıldız Technical University].
  • Özsoy, N., & Kemankaşlı, N. (2004). Misconceptions and main errors of secondary education in circle subject. The Turkish Online Journal of Educational Technology, 3(4), 140-147.
  • Patton, M. Q. (2018). Qualitative research & evaluation methods (M. Bütün, S. B. Demir, Trans. Ed.). Pegem Akademi.
  • Perry, B. (2007). Australian teachers’ views of effective mathematics teaching and learning. ZDM, 39(4), 271-286.
  • Polat, K., Oflaz, G., & Akgün, L. (2019). The relationship of visual proof skills with Van Hiele levels of geometric thinking and spatialability. Erciyes Journal of Education, 3(2), 105-122.
  • Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for research in mathematics education, 20(3), 309-321.
  • Sezer, N. (2019). Mathematical thinking processes and skills of secondary school students’ longitudinal investigation [Doctoral Dissertation, Uludağ University].
  • Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2000). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213-226.
  • Tolga, A., & Cantürk Günhan, B. (2019). Determination of secondary school mathematics teachers’ geometric habits of mind. Western Anatolia Journal of Educational Sciences, 10 (1), 37-56.
  • Turan, Ö., & Kurtuluş, A. (2021). Investigating the geometric habits of mind and the hemispheric dominance status of mathematics teachers. Acta Didactica Napocensia, 14(2), 14-29.
  • Uygan, C. (2016). Learning processes of middle school students in dynamic geometry software regarding achievement of geometric habits of mind [Doctoral Dissertation, Anadolu University].
  • Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching children mathematics, 5(6), 310-316.
  • Wang, T., & Cai, J. (2007). United States teachers’ views of effective mathematics teaching and learning. ZDM, 39(4), 315-327.
  • Whitehurst, G. J. (2002, March). Scientifically based research on teacher quality: Research on teacher preparation and professional development. Paper presented at the White House Conference on Preparing Tomorrow’s Teacher, USA.
  • Yavuzsoy Köse, N., & Tanışlı, D. (2014). Primary school teacher candidates’ geometric habits of mind. Educational Sciences: Theory and Practice, 14(3), 1203-1219.
  • Yazlık, D. Ö. (2019). Opinions of secondary school mathematics teachers on the use of information and communication technologies in mathematics teaching. Bolu Abant İzzet Baysal Üniversitesi Faculty of Education Journal, 19(4), 1682-1699.
  • Yıldırım, A., & Şimşek, H. (2018). Qualitative research methods in the social sciences (11th Ed.). Seçkin Yayıncılık.
  • Zeybek, A. (2019). Geometry thinking levels of the secondary school students and teachers’ views about geometry learning area [Master’s Thesis, Pamukkale University].