Volume 67 | Issue 9 | Year 2021 | Article Id. IJMTT-V67I9P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I9P518
The present research examine the perceptions of teachers and future teachers about creativity in teaching geometry but also how their cognitive and perceptual skills in geometry can influence the appearance of creativity in their teaching. Data were collected from 116 future teachers and two secondary school teachers with different years of practice. The analysis of the results showed that: a) Teachers' perceptions of creativity in the teaching of Mathematics converge and aim to make themselves and their students creative by choosing the appropriate teaching practices and b) the perceptions and the way that future teachers apprehend the geometrical figure seem to influence the way they will introduce mathematical creativity to the teaching of geometry.
[1] Bolden, D. S., Harries, A. V., & Newton, D. P., Pre-service primary teachers’ conceptions of creativity in mathematics, Educational Studies in Mathematics. 73(2) (2010) 143–157.
[2] Kattou, M., Kontoyianni, K., & Christou, C., Mathematical creativity through teachers’ perceptions, In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education. (Vol. 3) (2009) 297–304.
[3] Leikin, R., Subotnik, R., Pitta-Pantazi, D., Singer, F. M., & Pelczer, I., International survey on teachers’ perspectives on creativity in mathematics education, ZDM - The International Journal on Mathematics Education. (45) (2013) 309-324.
[4] Haylock, D. W., A framework for assessing mathematical creativity in school children, Education Studies in Mathematics. 18(1) (1987) 59–74.
[5] Leikin, R., Exploring mathematical creativity using multiple solution tasks, In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students, Netherlands: Sense Publisher. (2009) 129–145.
[6] Mann, E., Creativity: The essence of mathematics. Journal for the Education of the Gifted. 30(2) (2006) 236-260.
[7] Silver, E. A., Fostering creativity through instruction rich in mathematical problem solving and problem posing, ZDM. (3) (1997) 75–80.
[8] Ervynck, G., Mathematical creativity, In D. Tall (Ed.), Advanced mathematical thinking, Dordrecht, Netherlands: Kluwer. (1991) 42–53.
[9] Guilford, J. P., The nature of human intelligence, McGraw-Hill: New York. (1967).
[10] Runco, M. A., Creativity as an educational objective for disadvantaged students (RBDM 9306). Storrs: University of Connecticut. The National Research Center on the Gifted and Talented. (1993).
[11] Torrance, E.P., Creativity: Just wanting to know. Pretoria, South Africa: Benedic books. (1997).
[12] Kwon, O. N., Park, J. S., & Park, J. H., Cultivating divergent thinking in mathematics through an open-ended approach, Asia Pacific Education Review. (7) (2006) 51–61.
[13] Silver, E. A., On Mathematical Problem Posing. For the Learning of Mathematics. 14(1) (1994) 19–28.
[14] Stoyanova, E., & Ellerton, N. F., A framework for research into students’ problem posing in school mathematics, In P. C. Clarkson (Ed.), Technology in mathematics education, Mathematics Education Research Group of Australasia: Melbourne. (1996) 518–525.
[15] Jay, E. S., & Perkins, D. N., Problem finding: the search for mechanism, In M. A. Runco (Ed.), The creativity research handbook Cresskill, NJ: Hampton. (1997) 257–293.
[16] Singer, F. M., Ellerton, N., & Cai, J., Problem-posing research in mathematics education: new questions and directions, ESM. 83(1) (2013) 1–7.
[17] R.Vlachou, E.Avgerinos and P.Gridos, The Open-ended Problem as a key tool for the development of students’ mathematical ability and attitude, Mediterranean Journal for Research in Mathematics Education. 17 (2020) 53-63.
[18] Sullivan, P., Warren, E., & White, P., Students’ responses to content specific open-ended mathematical tasks, Mathematics Education Research Journal. 12(1) (2000) 2–17.
[19] Beghetto, R. A., & Kaufman, J. C., Teaching for creativity with disciplined improvisation, In R. K. Sawyer (Ed.), Structure and improvisation in creative teaching, Cambridge: Cambridge University Press. (2011) 94 – 109.
[20] Duval, R., The first crucial point in geometry learning: Visualization, Mediterranean Journal for Research in Mathematics Education. 13(1-2) (2014) 1-28.
[21] Herbst, P., Establishing a custom of proving in American school geometry: evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(3) (2002) 283-312.
[22] Gridos, P., Gagatsis, A., Elia, I. & Deliyianni, E., Mathematical creativity and geometry: The influence of geometrical figure apprehension on the production of multiple solutions, Proceedings of the 11th Conference of the European Society for Research in Mathematics Education: Working Group 4, Utrecht, Netherlands. (2019)
[23] Mesquita, A. L., On conceptual obstacles linked with external representation in geometry, Journal of mathematical behavior, 17(2) (1998) 183-195.
[24] Soury-Lavergne, S., & Maschietto, M., Articulation of spatial and geometrical knowledge in problem solving with technology at primary school, ZDM Mathematics Education. 47(3) (2015) 435–449.
[25] Van den Heuvel-Panhuizen, M. & Buys, K. (Eds.), Young children learn measurement and geometry, Rotterdam, the Netherlands: Sense Publishers. (2008).
[26] Duval, R., Geometrical Pictures: Kinds of Representation and Specific Processings. In R. Sutherland & J. Mason (Εds.), Exploiting Mental Imagery with Computers in Mathematics Education, Germany: Springer. (1995) 142 – 157.
[27] Duval, R., Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations, London: Springer. (2017)
[28] Elia, I., Gagatsis, Α., Deliyianni, Ε., Monoyiou, Α., & Michael, S., A structural model of primary school students’ operative apprehension of geometrical figures, Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (PME), Thessaloniki, Greece. (2009)
[29] Michael, S., Gagatsis, A., Elia, I., Deliyianni, E., & Monoyiou, A., Operative apprehension of geometrical figures of primary and secondary school students, In A. Gagatsis & S. Grozdev (Eds.), Proceedings of the 6th Mediterranean Conference on Mathematics Education, Plovdiv, Bulgaria: University of Plovdiv, CMS. (2009) 67 – 78.
[30] Deliyianni, E., Elia, I., Gagatsis, A., Monoyiou, A., & Panaoura, A., A theoretical model of students’ geometrical figure understanding, Proceedings of the 6th Conference of the European Society for Research in Mathematics Education (CERME 6), Lyon, France. (2010).
[31] P.Gridos, E.Avgerinos, J.Mamona-Downs and R.Vlachou, Geometrical figure apprehension, construction of auxiliary lines, and multiple solutions in problem solving: aspects of mathematical creativity in school geometry, International Journal of Science and Mathematics Education. 19(4) (2021).
[32] Lev-Zamir, H., & Leikin, R., Saying vs. doing: Teachers’ conceptions of creativity in elementary mathematics teaching, ZDM - The International Journal on Mathematics Education. 45(4) (2013) 295-308.
[33] Levenson, E., Tasks that may occasion mathematical creativity: teachers choices, Journal of Mathematics Teacher Education. 16(4) (2013) 269 – 291.
Evgenios Avgerinos, Gridos Panagiotis, Vlachou Roza, Mamona-Downs Joanna, "Mathematical Creativity as a Core Tool in Restoring Euclidean Geometry: Perception and Creative/Cognitive Mathematical Skills Of Teachers And Future Teachers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 9, pp. 151-160, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I9P518