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Mathematical challenges and the positive emotions they engender

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Abstract

Studies in mathematics education have shown interactions between a variety of emotions and the quality of learning. Research has found that positive emotions are among the main factors that engender a sense of well-being. In the current study, we focused on emotions that may be aroused while coping with mathematical challenges, and sought to evaluate their intensity and frequency in that context. The research was conducted among a unique group: competitors of the Israel International Math Competition for Girls (IIMCG), a competition involving problem solving in mathematical thinking, which targets female high school students. The participants were 403 of the competitors (304 Israeli, 99 American) who had reached the second round of the competition. The research instrument was a Math Emotions Measuring Instrument, which assesses positive and negative emotions expressed while coping with mathematical challenges. Results emphasized the numerical prominence of positive as opposed to negative emotions that were reported by participants. The ratio of positive to negative emotions (i.e., the positivity ratio) was high – 4.2:1. In addition, a statistically significant cultural difference was found between the participants from Israel and those from the USA in terms of the intensity of 10 out of 28 emotions experienced. Our findings shed new light on the connection between mathematics and emotions and prove the importance of generating strategies to enhance a positive climate in teaching and learning mathematics.

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References

  • Attard, C., Ingram, N., Forgasz, H., Leder, G., & Grootenboer, P. (2016). Mathematics education and the affective domain. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia 2012–2015 (pp. 73–96). Dordrecht: Springer.

    Google Scholar 

  • Bagozzi, R. P., Wong, N., & Yi, Y. (1999). The role of culture and gender in the relationship between positive and negative affect. Cognition and Emotion, 13(6), 641–672.

    Google Scholar 

  • Barbeau, E., & Taylor, P. (Eds.). (2009). Challenges beyond the classroom: the 16th ICMI study. New York: Springer.

    Google Scholar 

  • Biller, J. (1996). Reduction of mathematics anxiety. Paper presented at the Annual National Conference on Liberal Arts and Education of Artists, http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/16/71/9f.pdf

  • Boiger, M., Ceulemans, E., De Leersnyder, J., Uchida, Y., Norasakkunkit, V., & Mesquita, B. (2018). Beyond essentialism: cultural differences in emotions revisited. Emotion, 18(8), 1142–1162.

    Google Scholar 

  • Brislin, R. W. (1970). Back-translation for cross-cultural research. Journal of Cross-Cultural Psychology, 1(3), 185–216.

    Google Scholar 

  • Brown, N. J., Sokal, A. D., & Friedman, H. L. (2013). The complex dynamics of wishful thinking: the critical positivity ratio. American Psychologist, 68(9), 801–813.

    Google Scholar 

  • Carmona-Halty, M., Salanova, M., Llorens, S., & Schaufeli, W. B. (2019). How psychological capital mediates between study-related positive emotions and academic performance. Journal of Happiness Studies, 20(2), 605–617.

    Google Scholar 

  • Chamberlin, S. A. (2010). A review of instruments created to assess affect in mathematics. Journal of Mathematics Education, 3(1), 167–182.

    Google Scholar 

  • Chamberlin, S. A. (2019). The construct of affect in mathematical modeling. In S. A. Chamberlin & B. Sriraman (Eds.), Affect in mathematical modeling: advances in mathematics education (pp. 15–28). Cham: Springer.

    Google Scholar 

  • Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts during mathematical problem solving. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: a new perspective (pp. 117–148). New York: Springer-Verlag.

    Google Scholar 

  • Cohn, A. M., & Fredrickson, B. L. (2006). Beyond the moment, beyond the self: shared ground between selective investment theory and the broaden-and-build theory of positive emotions. Psychological Inquiry, 17(1), 39–44.

    Google Scholar 

  • Cooke, A., Kavussanu, M., McIntyre, D., & Ring, C. (2013). The effects of individual and team competitions on performance, emotions, and effort. Journal of Sport & Exercise Psychology, 35, 132–143.

    Google Scholar 

  • Credé, M., Tynan, M. C., & Harms, P. D. (2017). Much ado about grit: a meta-analytic synthesis of the grit literature. Journal of Personality and Social Psychology, 113(3), 492–511.

    Google Scholar 

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

    Google Scholar 

  • Diener, E., Sandvik, E., & Pavot, W. (1991). Happiness is the frequency, not the intensity, of positive versus negative affect. In F. Strack (Ed.), Subjective well-being: an interdisciplinary perspective (pp. 119–139). Oxford: Pergamon Press.

    Google Scholar 

  • D’Mello, S. K., Lehman, B., Pekrun, R., & Graesser, A. C. (2014). Confusion can be beneficial for learning. Learning and Instruction, 29, 153–170.

    Google Scholar 

  • Duckworth, A. L., & Gross, J. J. (2014). Self-control and grit: related but separable determinants of success. Current Directions in Psychological Science, 23(5), 319–325.

    Google Scholar 

  • Duckworth, A. L., Peterson, C., Matthews, M. D., & Kelly, D. R. (2007). Grit: perseverance and passion for long-term goals. Journal of Personality and Social Psychology, 92(6), 1087–1101.

    Google Scholar 

  • Durksen, T. L., Way, J., Bobis, J., Anderson, J., Skilling, K., & Martin, A. J. (2017). Motivation and engagement in mathematics: a qualitative framework for teacher-student interactions. Mathematics Education Research Journal, 29(2), 163–181.

    Google Scholar 

  • Eid, M., & Diener, E. (2001). Norms for experiencing emotions in different cultures: inter-and intranational differences. Journal of Personality and Social Psychology, 81(5), 869–885.

    Google Scholar 

  • Ekman, P. (1992). An argument for basic emotions. Cognition and Emotion, 6(3–4), 169–200.

    Google Scholar 

  • Feldman Barrett, L., & Russell, J. A. (1998). Independence and bipolarity in the structure of current affect. Journal of Personality and Social Psychology, 74(4), 967–984.

    Google Scholar 

  • Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: the broaden-and-build theory of positive emotions. American Psychologist, 56(3), 218–226.

    Google Scholar 

  • Fredrickson, B. L. (2013). Updated thinking on positivity ratios. American Psychologist, 68, 814–822.

    Google Scholar 

  • Fredrickson, B. L., & Branigan, C. (2005). Positive emotions broaden the scope of attention and thought-action repertoires. Cognition and Emotion, 19, 313–332.

    Google Scholar 

  • Frenzel, A. C., Becker-Kurz, B., Pekrun, R., Goetz, T., & Lüdtke, O. (2018). Emotion transmission in the classroom revisited: a reciprocal effects model of teacher and student enjoyment. Journal of Educational Psychology, 110(5), 609–628.

    Google Scholar 

  • Frenzel, A. C., Pekrun, R., & Goetz, T. (2007). Girls and mathematics—a “hopeless” issue? A control-value approach to gender differences in emotions towards mathematics. European Journal of Psychology of Education, 22(4), 497–514.

    Google Scholar 

  • Forgas, J. P. (2000). Feeling and thinking: summary and integration. In J. P. Forgas (Ed.), Feeling and thinking: the role of affect in social cognition (pp. 387–406). Cambridge: Cambridge University press.

    Google Scholar 

  • Fried, L., Mansfield, C., & Dobozy, E. (2015). Teacher emotion research: introducing a conceptual model to guide future research. Issues in Educational Research, 25(4), 415–441.

    Google Scholar 

  • Goetz, T., Frenzel, A. C., Hall, N. C., & Pekrun, R. (2008). Antecedents of academic emotions: testing the internal/external frame of reference model for academic enjoyment. Contemporary Educational Psychology, 33, 9–33.

    Google Scholar 

  • Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: a hidden variable in mathematics education? (pp. 59–72). Dordrecht: Kluwer.

    Google Scholar 

  • Goldin, G. A., Hannula, M. S., Heyd-Metzuyanim, E., Jansen, A., Kaasila, R., Lutovac, S., et al. (2016). Attitudes, beliefs, motivation and identity in mathematics education: an overview of the field and future directions. Cham: Springer.

    Google Scholar 

  • Greensfeld, H., & Deutsch, Z. (2016). The centrality of positive emotions in the field of mathematics. Athens Journal of Education, 3(4), 345–364.

  • Grootenboer, P., & Hemmings, B. (2007). Mathematics performance and the role played by affective and background factors. Mathematics Education Research Journal, 19(3), 3–20.

    Google Scholar 

  • Grootenboer, P., & Marshman, M. (2016). Mathematics, affect and learning: middle school students’ beliefs and attitudes about mathematics education. Singapore: Springer.

    Google Scholar 

  • Han, S., Liou-Mark, J., Yu, K. T., & Zeng, S. (2015). Self-efficacy and attitudes towards mathematics of undergraduates: a US and Taiwan comparison. Journal of Mathematics Education, 8(1), 1–15.

    Google Scholar 

  • Hannula, M. S. (2006). Motivation in mathematics: goals reflected in emotions. Educational Studies in Mathematics, 63, 165–178.

    Google Scholar 

  • Hannula, M. S. (2012). Exploring new dimensions of mathematics-related affect: embodied and social theories. Research in Mathematics Education, 14(2), 137–161.

    Google Scholar 

  • Hannula, M. S. (2019). Young learners’ mathematics-related affect: a commentary on concepts, methods, and developmental trends. Educational Studies in Mathematics, 100(3), 309–316.

    Google Scholar 

  • Hannula, M. S. (2020). Affect in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed.). Cham: Springer (in press).

    Google Scholar 

  • Hannula, M. S., Pantziara, M., & Di Martino, P. (2018). Affect and mathematical thinking: exploring developments, trends, and future directions. In T. Dreyfus, M. Artigue, D. Potari, S. Prediger, & K. Ruthven (Eds.), Developing research in mathematics education: twenty years of communication, cooperation and collaboration in Europe (pp. 128–141). London: Routledge.

    Google Scholar 

  • Ingram, N., Holmes, M., Linsell, C., Livy, S., McCormick, M., & Sullivan, P. (2020). Exploring an innovative approach to teaching mathematics through the use of challenging tasks: a New Zealand perspective. Mathematics Education Research Journal. (in press).https://doi.org/10.1007/s13394-019-00266-1

  • Jorgensen, R., & Larkin, K. (2017). Analysing the relationships between students and mathematics: a tale of two paradigms. Mathematics Education Research Journal, 29(1), 113–130.

    Google Scholar 

  • Kahneman, D. (1999). Objective happiness. In D. Kahneman, E. Diener, & N. Schwarz (Eds.), Well-being: the foundations of hedonic psychology (pp. 3–25). New York: Russell Sage Foundation.

    Google Scholar 

  • Lazarus, R. S. (1991). Emotion and adaptation. Oxford: Oxford University Press.

    Google Scholar 

  • Lazarus, R. S. (2000). How emotions influence performance in competitive sports. The Sport Psychologist, 14, 229–252.

    Google Scholar 

  • Leder, G., & Grootenboer, P. (2005). Affect and mathematics education. Mathematics Education Research Journal, 17(2), 1–8.

    Google Scholar 

  • Leikin, R., & Pitta-Pantazim, D. (2013). Creativity and mathematics education: the state of the art. ZDM, 45(4), 159–166.

    Google Scholar 

  • Lichtenfeld, S., Pekrun, R., Stupnisky, R. H., Reiss, K., & Murayama, K. (2012). Measuring students’ emotions in the early years: the achievement emotions questionnaire-elementary school (AEQ-ES). Learning and Individual Differences, 22(2), 190–201.

    Google Scholar 

  • Ma, X. (1999). A meta-analysis of the relationship between anxiety and toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30, 502–540.

    Google Scholar 

  • Mandler, G. (1989). Affect and learning: causes and consequences of emotional interactions. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: a new perspective (pp. 3–19). New York: Springer-Verlag.

    Google Scholar 

  • Martinent, G., Campo, M., & Ferrand, C. (2012). A descriptive study of emotional process during competition: nature, frequency, direction, duration and co-occurrence of discrete emotions. Psychology of Sport and Exercise, 13, 142–151.

    Google Scholar 

  • Matsumoto, D., Yoo, S. H., & Fontaine, J. (2008). Mapping expressive differences around the world the relationship between emotional display rules and individualism versus collectivism. Journal of Cross-Cultural Psychology, 39(1), 55–74.

    Google Scholar 

  • McDonough, A., & Sullivan, P. (2014). Seeking insights into young children’s beliefs about mathematics and learning. Educational Studies in Mathematics, 87(3), 279–296.

    Google Scholar 

  • McLeod, D. B. (1992). Research on affect in mathematics education: a reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan.

    Google Scholar 

  • Mesquita, B., De Leersnyder, J., & Boiger, M. (2016). The cultural psychology of emotion. In L. Feldmann Barrett, M. Lewis, & J. M. Haviland-Jones (Eds.), Handbook of emotions (4th ed., pp. 393–411). New York: The Guilford Press.

    Google Scholar 

  • Mesquita, B., & Ellsworth, P. (2001). The role of culture in appraisal. In K. R. Scherer, A. Schorr, & T. Johnstone (Eds.), Appraisal processes in emotion: theory, methods, research (pp. 233–248). New York: Oxford University Press.

    Google Scholar 

  • Mesquita, B., & Frijda, N. H. (1992). Cultural variations in emotions: a review. Psychological Bulletin, 112, 179–204.

    Google Scholar 

  • Middleton, J., Jansen, A., & Goldin, G. A. (2017). The complexities of mathematical engagement: motivation, affect, and social interactions. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 667–699). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Moen, F., Vitsøe, J., Rasdal, V., Myhre, K., Sandbakk, Ø., & Moen, F. (2017). The role of emotions for 4 athletes in nordic combined in ski jumping competitions in world cup. The Sport Journal, 20. Retrieved from http://thesportjournal.org/article/the-role-of-emotions-for-4-athletes-in-nordic-combined-in-ski-jjumping-competitions-in-world-cup/

  • Muñoz-Merino, P. J., Molina, M. F., Muñoz-Organero, M., & Kloos, C. D. (2014). Motivation and emotions in competition systems for education: an empirical study. IEEE Transactions on Education, 57(3), 182–187.

    Google Scholar 

  • Niederle, M., & Vesterlun, L. (2011). Gender and competition. Annual Review of Economics, 3, 601–630.

    Google Scholar 

  • Pavlov, D., Kelevedjiev, E., & Tabov, J. (2008). Risk-taking behavior in math competitions. Mathematics Competitions, 21(2), 45–60.

    Google Scholar 

  • Peixoto, F., Sanches, C., Mata, L., & Monteiro, V. (2017). How do you feel about math?: relationships between competence and value appraisals, achievement emotions and academic achievement. European Journal of Psychology of Education, 32(3), 385–405.

    Google Scholar 

  • Pekrun, R. (2019). The murky distinction between curiosity and interest: state of the art and future prospects. Educational Psychology Review, 31(4), 905–914.

    Google Scholar 

  • Pekrun, R., Goetz, T., Titz, W., & Perry, R. (2002). Academic emotions in students’ self-regulated learning and achievement: a program of qualitative and quantitative research. Educational Psychologist, 37(2), 91–105.

    Google Scholar 

  • Pekrun, R., & Linnenbrink-Garcia, L. (2014). Introduction to emotions in education. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 1–10). New York: Taylor & Francis.

    Google Scholar 

  • Pekrun, R., & Stephens, E. J. (2012). Academic emotions. In K. R. Harris, S. Graham, T. Urdan, J. M. Royer, & M. Zeidner (Eds.), APA educational psychology handbook (Vol. 2, pp. 3–31). Washington, DC: American Psychological Association.

    Google Scholar 

  • Plenty, S., & Heubeck, B. G. (2013). A multidimensional analysis of changes in mathematics motivation and engagement during high school. Educational Psychology, 33(1), 14–30.

    Google Scholar 

  • Russo, J., & Hopkins, S. (2017). Student reflections on learning with challenging tasks: ‘I think the worksheets were just for practice, and the challenges were for maths’. Mathematics Education Research Journal, 29(3), 283–311.

    Google Scholar 

  • Ryan, R., & Deci, E. (2000). Intrinsic and extrinsic motivations: classic definitions and new directions. Contemporary Educational Psychology, 25(1), 54–67.

    Google Scholar 

  • Scherer, K. R. (1997). The role of culture in emotion-antecedent appraisal. Journal of Personality and Social Psychology, 73, 902–922.

    Google Scholar 

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

    Google Scholar 

  • Schukajlow, S., Rakoczy, K., & Pekrun, R. (2017). Emotions and motivation in mathematics education: theoretical considerations and empirical contributions. ZDM, 49(3), 307–322.

    Google Scholar 

  • Schweinle, A., Meyer, D. K., & Turner, J. C. (2006). Striking the right balance: students’ motivation and affect in elementary mathematics. The Journal of Educational Research, 99(5), 271–294.

    Google Scholar 

  • Shuman, V., & Scherer, K. R. (2014). Concepts and structures of emotions. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 13–35). New York: Taylor & Francis.

    Google Scholar 

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

    Google Scholar 

  • Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Reston: National Council of Teacher of Mathematics.

    Google Scholar 

  • Spielberger, C. D. (1972). Anxiety: current trends in theory and research (Vol 1). New York: Academic Press.

    Google Scholar 

  • Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18(2), 123–140.

    Google Scholar 

  • Taylor, P. (2009). WFNMC 25 years on: some experiences. Mathematics Competitions, 22(1), 10–18.

    Google Scholar 

  • Tirri, K., & Campbell, J. (2002). Actualizing mathematical giftedness in adulthood. Educating Able Children, 6(1), 14–20.

    Google Scholar 

  • Triandis, H. (1997). Cross-cultural perspectives on personality. In R. Hogan, J. Johnson, & S. R. Briggs (Eds.), Handbook of personality psychology (pp. 439–464). San Diego: Academic Press.

    Google Scholar 

  • Tugade, M., & Fredrickson, B. L. (2007). Regulation of positive emotions: emotion regulation strategies that promote resilience. Journal of Happiness Studies, 8(3), 311–333.

    Google Scholar 

  • Watson, D., Clark, L. A., & Tellegen, A. (1988). Development and validation of brief measures of positive and negative affect: the PANAS scale. Journal of Personality and Social Psychology, 54, 1063–1070.

    Google Scholar 

  • Weiner, B. (1985). An attributional theory of achievement motivation and emotion. Psychological Review, 92(4), 548–573.

    Google Scholar 

  • Wikipedia (n.d). List of math competitions. Retrieved from http://en.wikipedia.org/wiki/List_of_mathematics_competitions

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Acknowledgments

We thank all the competitors of the Israel International Math Competition for Girls (IIMCG) who participated in our study.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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  1. Michlalah Jerusalem College, 36 Barukh Duvdevani Street, Bayit Vegan, P.O.B 16078, 9116002, Jerusalem, Israel

    Hava Greensfeld & Ziva Deutsch

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  1. Hava Greensfeld
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Correspondence to Hava Greensfeld.

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Greensfeld, H., Deutsch, Z. Mathematical challenges and the positive emotions they engender. Math Ed Res J 34, 15–36 (2022). https://doi.org/10.1007/s13394-020-00330-1

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