Abstract
The purpose of our study was to analyze teachers’ conceptions of creativity in mathematics teaching (CIMT). We differentiated between declarative conceptions that are expressed in teachers’ discourse about CIMT and conceptions-in-action that are expressed in teachers’ lessons. Elementary and middle school mathematics teachers (grades 4–8) were individually interviewed and then welcomed/allowed the first author of this paper to observe their lessons which in their view exemplified CIMT. In this paper we focus on two study participants, named Healy and Debby, in order to demonstrate that while teachers’ declarative conceptions seem to be very similar, their conceptions-in-action may differ dramatically. To explain this phenomenon we use a model of teachers’ conceptions of creativity devised earlier in this study (Lev-Zamir and Leikin, Res Math Educ 13:17–32, 2011). The distribution of teachers’ declarative conceptions, between those of a pedagogical and mathematical nature and those of a teacher-directed and student-directed nature, appears to be central when explaining the gap between declarative conceptions and conceptions-in-action. Additionally, we demonstrate that the model has not only descriptive but also explanatory and predictive power.
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Notes
Di-j, Hi-j denotes segments from interview excerpts: D for Debby; H for Healy; i, number of excerpt; j, number of the segment.
Note numbers of the quotes, intended for interim summaries and the paper summary.
References
Cooney, T. J. (1985). A beginning teacher’s view of problem solving. Journal for Research in Mathematics Education, 11(5), 324–336.
Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teachers: A model. Journal of Education for Teaching, 15(1), 13–33.
Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18(1), 59–74.
Kagan, D. M. (1992). Implications of research on teachers’ beliefs. Educational Psychologist, 27(1), 65–90.
Lampert, M. (2001). Teaching problems and the problem of teaching. New Haven: Yale University Press.
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Rotterdam: Sense Publishers.
Leikin, R. (2011). The education of mathematically gifted students: On some complexities and questions. Montana Mathematical Enthusiast Journal, 8, 167–188.
Leikin, R., & Dinur, S. (2007). Teachers’ flexibility in mathematical discussion. Journal of Mathematical Behaviour, 26(4), 328–347.
Leinhardt, G. (1993). On teaching. In R. Glaser (Ed.), Advances in instructional psychology (pp. 1–54). Hillsdale: Lawrence Erlbaum Associates.
Lev-Zamir, H., & Leikin, R. (2011). Creative mathematics teaching in the eye of the beholder: Focusing on teachers’ conceptions. Research in Mathematics Education, 13, 17–32.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26, 20–23.
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236–262.
Movshovitz-Hadar, N. (1988). School mathematics theorems: An endless source of surprise. For the Learning of Mathematics, 83(3), 34–40.
Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks: Sage.
Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practices. Journal for Research in Mathematics Education, 28(5), 550–576.
Sawyer, R. K. (2004). Creative teaching: Collaborative discussion as disciplined improvisation. Educational Researcher, 33(2), 12–20.
Scheffler, I. (1965). Conditions of knowledge. An introduction to epistemology and education. Chicago: The University of Chicago Press.
Sheffield, L. J. (2009). Developing mathematical creativity: Questions may be the answer. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 87–100). Rotterdam: Sense Publishers.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM—The International Journal on Mathematics Education, 29(3), 75–80.
Simon, M. A. (1997). Developing new models of mathematics teaching: An imperative for research on mathematics teacher development. In E. Fennema & B. Scott-Nelson (Eds.), Mathematics teachers in transition (pp. 55–86). Mahwah: Erlbaum.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17(1), 20–36.
Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105–127.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
Torrance, E. P. (1967). Scientific views of creativity and factors affecting its growth, creativity and learning. In J. Kagan (Ed.), Creativity and learning (pp. 73–91). Boston: Houghton Mifflin.
Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville: Scholastic Testing Service.
Vygotsky, L.S. (1930/1982). Imagination and its development in childhood. In V. V. Davydov (Ed.), General problems of psychology. The collected works of L. S. Vygotsky (vol. 2, pp. 438–454). Moscow, SSSR: Pedagogika (In Russian).
Vygotsky, L.S. (1930/1984). Imagination and creativity in adolescent. In D. B. Elkonin (Ed.), Child psychology. The collected works of L. S. Vygotsky (vol. 4, pp. 199–219). Moscow, SSSR: Pedagogika (In Russian).
Weber, R. P. (1990). Basic content analysis. Newbury Park: Sage Publications.
Wilkins, M.L.J. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs and practices. Journal of Mathematics Education, 11, 139–114.
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Lev-Zamir, H., Leikin, R. Saying versus doing: teachers’ conceptions of creativity in elementary mathematics teaching. ZDM Mathematics Education 45, 295–308 (2013). https://doi.org/10.1007/s11858-012-0464-4
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DOI: https://doi.org/10.1007/s11858-012-0464-4