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Exploring the relationship between teachers’ values and their choice of tasks: the case of occasioning mathematical creativity

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Abstract

When it comes to choosing tasks, values can have a significant impact. This study explores teachers’ values as they choose one task from among three that they believe will have the most potential to occasion mathematical creativity in the classroom. Participants’ analyses of each task, as well as their reasons for choosing one task as most preferred, were analyzed in terms of task features and cognitive demands, as well as their explicit reference to fluency, flexibility, and originality. Two values shared by most participants were having several solution paths and a task that would challenge students. Of particular interest are task features and cognitive demands that were associated with a task at the initial stage of analysis but were not mentioned as a reason for choosing that task as occasioning mathematical creativity. Dilemmas and challenges regarding the study of values are discussed.

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References

  • Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8(6), 499–536.

    Article  Google Scholar 

  • Atweh, B., & Seah, W. T. (2008). Theorizing values and their study in mathematics education. Paper presented at the Australian Association for Research in Education Conference, Fremantle, Australia.

  • Bishop, A., Seah, W., & Chin, C. (2003). Values in mathematics teaching—The hidden persuaders? In A. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (pp. 717–765). Kluwer.

    Chapter  Google Scholar 

  • Bishop, A. J. (2012). From culture to well-being: A partial story of values in mathematics education. ZDM-Mathematics Education, 44(1), 3–8.

    Article  Google Scholar 

  • Cai, J., & Garber, T. (2012). Teaching values and valued teaching in the mathematics classroom: Toward a research agenda. ZDM-Mathematics Education, 44(1), 91–97.

    Article  Google Scholar 

  • Chan, Y. C., & Wong, N. Y. (2019). Methodological issues in the investigation of values in mathematics. In P. Clarkson, W. Seah, & J. Pang (Eds.), Values and valuing in mathematics education (pp. 197–208). Springer.

    Chapter  Google Scholar 

  • Chin, C., & Lin, F.-L. (2001). Value-loaded activities in mathematics classroom. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education (PME 25) (vol. 2, pp. 249–256). Utrecht University.

  • DeBellis, V. A., & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63(2), 131–147.

    Article  Google Scholar 

  • Department of Education (2006). Mathematics curriculum for grades one through six. Retrieved from https://meyda.education.gov.il/files/Tochniyot_Limudim/Math/Yesodi/mavo1.pdf.

  • Estrella, S., Zakaryan, D., Olfos, R., & Espinoza, G. (2020). How teachers learn to maintain the cognitive demand of tasks through Lesson Study. Journal of Mathematics Teacher Education, 23(3), 293–310.

    Article  Google Scholar 

  • Frade, C., & Machado, M. C (2008). Culture and affect: Influences of the teachers’ values on students’ affect. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the 32nd conference of the international group for the psychology of mathematics education (vol. 3, pp. 33–40). Cinvestav-UMSNH.

  • Hannula, M. S. (2012). Looking at the third wave from the West: Framing values within a broader scope of affective traits. ZDM-Mathematics Education, 44(1), 83–90.

    Article  Google Scholar 

  • Haylock, D. (1997). Recognizing mathematical creativity in schoolchildren. ZDM-Mathematics Education, 27(2), 68–74.

    Article  Google Scholar 

  • Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18(1), 59-74

  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.

    Article  Google Scholar 

  • Kaufman, J. C., & Beghetto, R. A. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13(1), 1–12.

    Article  Google Scholar 

  • Kim, H., Cho, S., & Ahn, D. (2004). Development of mathematical creative problem solving ability test for identification of the gifted in math. Gifted Education International, 18(2), 164–174.

    Article  Google Scholar 

  • Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: What do teachers do and feel? Educational Studies in Mathematics, 105(3), 349–365.

    Article  Google Scholar 

  • Kluckhohn, C. (1951). Values and value-orientations in the theory of action: An exploration in definition and classification. In T. Parsons & E. Shils (Eds.), Toward a general theory of action (pp. 388–433). Harvard University Press.

    Google Scholar 

  • Krutetskii, V.A. (1976). The psychology of mathematical abilities in schoolchildren. (Translated by Teller, J.; edited by J. Kilpatrick and I. Wirszup). The University of Chicago Press.

  • Kwon, O. N., Park, J. H., & Park, J. S. (2006). Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review, 7(1), 51–61.

    Article  Google Scholar 

  • 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. 129–135). Sense Publishers.

    Chapter  Google Scholar 

  • Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31(1), 73–90.

    Article  Google Scholar 

  • Levenson, E. (2013). Tasks that may occasion mathematical creativity: Teachers’ choices. Journal of Mathematics Teacher Education, 16(4), 269–291.

    Article  Google Scholar 

  • Levenson, E. (2015). Exploring Ava’s developing sense for tasks that may occasion mathematical creativity. Journal of Mathematics Teacher Education, 18(1), 1–25.

    Article  Google Scholar 

  • Lim, C. S., & Kor, L. K. (2012). Excellent primary mathematics teachers’ espoused and enacted values of effective lessons. ZDM-Mathematics Education, 44(1), 59–69.

    Article  Google Scholar 

  • Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276.

    Article  Google Scholar 

  • MacNab, D. (2000). Raising standards in mathematics education: Values, vision, and TIMSS. Educational Studies in Mathematics, 42(1), 61–80.

    Article  Google Scholar 

  • Mann, E., Chamberlin, S. A., & Graefe, A. K. (2017). The prominence of affect in creativity: Expanding the conception of creativity in mathematical problem solving. In R. Leikin & B. Sriraman (Eds.), Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond (pp. 57–76). Springer.

    Chapter  Google Scholar 

  • Patton, M. Q. (2002). Qualitative research and evaluation methods. Sage Publications.

    Google Scholar 

  • Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). National Council of Teachers of Mathematics.

  • Pólya, G. (1945). How to solve it. Princeton University.

    Book  Google Scholar 

  • Raths, L. E., Harmin, M., & Simon, S. B. (1987). Selections from ‘values and teaching’. In J. P.F. Carbone (Ed.), Value theory and education (pp. 198–214). Robert E. Krieger.

  • Rokeach, M. (1973). The nature of human values. Free press.

    Google Scholar 

  • Runco, M. (1996). Personal creativity: Definition and developmental issues. New Directions for Child Development, 72, 3–30.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). Macmillan.

    Google Scholar 

  • Schoenfeld, A. H. (2014). What makes for powerful classrooms, and how can we support teachers in creating them? A story of research and practice, productively intertwined. Educational Researcher, 43(8), 404–412.

    Article  Google Scholar 

  • Schwartz, S. H., & Bilsky, W. (1987). Toward a universal psychological structure of human values. Journal of Personality and Social Psychology, 53(3), 550.

    Article  Google Scholar 

  • Seah, W. T. (2002). Exploring teacher clarification of values relating to mathematics education. In C. Vale, J. Roumeliotis, & J. Horwood (Eds.), Valuing mathematics in society (pp. 93–104). Mathematical Association of Victoria.

  • Seah, W. T. (2011). Effective mathematics learning in two Australian Primary classes: Exploring the underlying values. In B. Ubuz (Ed.), Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 129–136). PME.

  • Seah, W. T. (2018). Improving mathematics pedagogy through student/teacher valuing: Lessons from five continents. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), Invited Lectures from the 13th International Congress on Mathematical Education (pp. 561–580). Springer International Publishing.

    Chapter  Google Scholar 

  • 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). Sense Publishers.

    Google Scholar 

  • Shriki, A. (2010). Working like real mathematicians: Developing prospective teachers’ awareness of mathematical creativity through generating new concept. Educational Studies in Mathematics, 73, 159–179.

    Article  Google Scholar 

  • Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM-Mathematics Education, 3, 75–80.

    Article  Google Scholar 

  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12, 129–135.

    Article  Google Scholar 

  • Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM-Mathematics Education, 41, 13–27.

    Article  Google Scholar 

  • Steen, L. A. (1988). The science of patterns. Science, 240(4852), 611–616.

    Article  Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455–488.

    Article  Google Scholar 

  • Sullivan, P., Borcek, C., Walker, N., & Rennie, M. (2016). Exploring a structure for mathematics lessons that initiate learning by activating cognition on challenging tasks. The Journal of Mathematical Behavior, 41, 159–170.

    Article  Google Scholar 

  • Tabach, M., & Friedlander, A. (2013). School mathematics and creativity at the elementary and middle-grade levels: How are they related? ZDM-Mathematics Education, 45(2), 227–238.

    Article  Google Scholar 

  • The Center for Educational Technology (CET). (2006). Geometry for the fourth grade. CET.

  • Tsamir, P., Tirosh, D., Tabach, M., & Levenson, E. (2010). Multiple solution methods and multiple outcomes—Is it a task for kindergarten children? Educational Studies in Mathematics, 73(3), 217–231.

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Correspondence to Esther S. Levenson.

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Levenson, E.S. Exploring the relationship between teachers’ values and their choice of tasks: the case of occasioning mathematical creativity. Educ Stud Math 109, 469–489 (2022). https://doi.org/10.1007/s10649-021-10101-9

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