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Abstract

Emotions are important part of non-routine problem solving. A positive disposition to mathematics has a reciprocal relationship with achievement, both enhancing the other over time. In the process of solitary problem solving, emotions have a significant role in self-regulation, focusing attention and biasing cognitive processes. In social context, additional functions of emotions become apparent, such as interpersonal relations and social coordination of collaborative action. An illustrative case study presents the role of emotions in the problem solving process of one 10-year old Finnish student when he is solving an open problem of geometrical solids. The importance of emotions should be acknowledged also in teaching. Tasks should provide optimal challenge and feeling of control. The teacher can model the appropriate enthusiasm and emotion regulation. Joking and talking with a peer are important coping strategies for students.

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Notes

  1. 1.

    All names are pseudonyms

  2. 2.

    Curly brackets {} indicate observations and interpretations based on the video.

  3. 3.

    Square brackets [] indicate overlapping talk.

References

  • Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin and Review, 14, 243–248.

    Article  Google Scholar 

  • Bandura, A., & Schunk, D. H. (1981). Cultivating competence, self-efficacy and intrinsic interest through proximal self-motivation. Journal of Personality and Social Psychology, 41(3), 586–598.

    Article  Google Scholar 

  • Buck, R. (1999). The biological affects: A typology. Psychological Review, 106(2), 301–336.

    Article  Google Scholar 

  • Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: an emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45–75.

    Article  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.

    Chapter  Google Scholar 

  • Csikszentmihalyi, M., & Csikszentmihalyi, I. (Eds.). (1992). Optimal experience: Psychological studies of flow in consciousness. Cambridge: Press Syndicate of the University of Cambridge.

    Google Scholar 

  • Damasio, A. R. (1999). The feeling of what happens. New York: Harcourt Brace and Company.

    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(2), 131–147.

    Article  Google Scholar 

  • De Corte, E., Depaepe, F., Op ’t Eynde, P. & Verschaffel. L. (2011). Students’ self-regulation of emotions in mathematics: an analysis of meta-emotional knowledge and skills. ZDM—The international Journal on Mathematics Education, 43(4), 483–496.

    Google Scholar 

  • Durlak, J. A., Weissberg, R. P., Dymnicki, A. B., Taylor, R. D., & Schellinger, K. B. (2011). The impact of enhancing students’ social and emotional learning: A meta-analysis of school-based universal interventions. Child Development, 82(1), 405–432.

    Article  Google Scholar 

  • Ekman, P., & Friesen, W. V. (1971). Constants across cultures in the face and emotion. Journal of personality and social sychology, 17(2), 124.

    Article  Google Scholar 

  • Ekman, P. (1972). Universals and cultural differences in facial expression of emotion. In J. K. Cole (Ed.), Nebraska symposium on motivation (pp. 207–283). Lincoln, USA: University of Nebraska Press.

    Google Scholar 

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

    Article  Google Scholar 

  • Ekman, P., Friesen, W. V., & Hager, J. C. (2002). Facial action coding system. Salt Lake City: A Human Face.

    Google Scholar 

  • Else-Quest, N. M., Hyde, J. S., & Hejmadi, A. (2008). Mother and child emotions during mathematics homework. Mathematical Thinking and Learning, 10, 5–35.

    Article  Google Scholar 

  • Evans, J., Morgan, C., & Tsatsaroni, A. (2006). Discursive positioning and emotion in school mathematics practices. Educational Studies in Mathematics, 63(2), 209–226.

    Article  Google Scholar 

  • Forgas, J. P. (2008). Affect and cognition. Perspectives on Psychological Science, 3(2), 94–101.

    Article  Google Scholar 

  • Freeman, K. E. (2004). The significance of motivational culture in schools serving african american adolescents: A goal theory approach. In P. R. Pintrich & M. L. Maehr (Eds.), Advannces in motivation and achievement (Vol. 13, pp. 65–95)., Motivating students, improving schools: The legacy of Carol Midgley The Netherlands: Elsevier Jai.

    Google Scholar 

  • Frenzel, A. C., Goetz, T., Lüdtke, O., Pekrun, R., & Sutton, R. E. (2009). Emotional Transmission in the Classroom: exploring the relationships between teacher and student enjoyment. Journal of Educational Psychology, 101(3), 705–716.

    Article  Google Scholar 

  • Fried, L. (2012). Teaching teachers about emotion regulation in the classroom. Australian Journal of Teacher Education, 36(3), 117–127.

    Google Scholar 

  • Friedel, J. M., Cortina, K. S., Turner, J. C., & Midgley, C. (2007). Achievement goals, efficacy beliefs and coping strategies in mathematics: The roles of perceived parent and teacher goal emphases. Contemporary Educational Psychology, 32, 434–458.

    Article  Google Scholar 

  • Goldin, G. A. (1988). Affective representation and mathematical problem solving. In M. J. Behr, C. B. Lacampagne, & M. M. Wheeler (Eds.), Proceedings of the 10th annual meeting of PME-NA (pp. 1–7). DeKalb: Northern Illinois University, Department of Mathematics.

    Google Scholar 

  • Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning, 2(3), 209–219.

    Article  Google Scholar 

  • Goldin, G. A., Epstein, Y. M., Schorr, R. Y. & Warner, L. B. (2011) . Beliefs and engagement structures: behind the affective dimension of the mathematical learning. ZDM—The international Journal on Mathematics Education, 43(4), 547–560.

    Google Scholar 

  • Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2, 271–299.

    Article  Google Scholar 

  • Hannula, M. S. (2003). Fictionalising experiences–—experiencing through fiction. For the Learning on Mathematics, 23(3), 33–39.

    Google Scholar 

  • Hannula, M. S. (2004). Affect in mathematical thinking and learning. Acta universitatis Turkuensis B 273. Finland: University of Turku.

    Google Scholar 

  • Hannula, M. S. (2005). Shared cognitive intimacy and self-defence: Two socio-emotional processes in problem solving. Nordic studies on Mathematics Education, 1, 25–41.

    Google Scholar 

  • Hannula, M. S. (2006). Motivation in Mathematics: Goals reflected in emotions. Educational Studies in Mathematics, 63(2), 165–178.

    Article  Google Scholar 

  • Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, 33–46.

    Article  Google Scholar 

  • Immordino-Yang, M. H., & Faeth, M. (2010). The role of emotion and skilled intuition in learning. In D. Sousa (Ed.), Mind, brain, and education: Neuroscience implications for the classroom (pp. 67–81). Washington, DC: American Psychological Association.

    Google Scholar 

  • Kim, C. M., & Hodges, C. B. (2012). Effects of an emotion control treatment on academic emotions, motivation and achievement in an online mathematics course. Instructional Science, 40, 173–192.

    Article  Google Scholar 

  • Lang, P. J. (1995). The emotion probe: Studies of motivation and attention. American Psychologist, 50(5), 372–385.

    Article  Google Scholar 

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

    Google Scholar 

  • Lee, J. (2009). Universals and specifics of math self-concept, math self-efficacy, and math anxiety across 41 PISA 2003 participating countries. Learning and Individual Differences, 19, 355–365.

    Article  Google Scholar 

  • Lehman, B., D’Mello, S., & Person, N. (2008). All alone with your emotions: An analysis of student emotions during effortful problem solving activities. Paper presented at the workshop on emotional and cognitive issues in ITS at the ninth international conference on intelligent tutoring systems. Accessed April 15, 2012 at http://141.225.218.248/web-cslwebroot/emotion/files/lehman-affectwkshp-its08.pdf.

  • Levenson, R. W., & Gottman, J. M. (1983). Marital interaction: Physiological linkage and affective exchange. Journal of Personality and Social Psychology, 45, 587–597.

    Article  Google Scholar 

  • Linnenbrink, E. A., & Pintrich, P. R. (2004). Role of affect in cognitive processing in academic contexts. In D. Y. Dai & R. J. Sternberg (Eds.), Motivation, emotion, and cognition; Integrative perspectives on intellectual functioning and development (pp. 57–88). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Ludmer, R., Dudai, Y., & Rubin, N. (2011). Uncovering camouflage: Amygdala activation predicts long-term memory of induced perceptual insight. Neuron, 69(5), 1002–1014.

    Article  Google Scholar 

  • Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30, 520–541.

    Article  Google Scholar 

  • Ma, X., & Kishor, N. (1997a). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analyses. Journal for Research in Mathematics Education, 28(1), 26–47.

    Article  Google Scholar 

  • Ma, X., & Kishor, N. (1997b). Attitude toward self, social factors, and achievement in mathematics: A meta-analytic review. Educational Psychology Review, 9, 89–120.

    Article  Google Scholar 

  • Ma, X., & Xu, J. (2004). Determining the Causal Ordering between Attitude toward Mathematics and Achievement in Mathematics. American Journal of Education, 110(May), 256–280.

    Article  Google Scholar 

  • Malmivuori, M. L. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63(2), 149–164.

    Article  Google Scholar 

  • Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. New York: Addison Wesley.

    Google Scholar 

  • McLeod, D. B. (1988). Affective issues in mathematical problem solving: Some theoretical considerations. Journal for Research in Mathematics Education, 19, 134–141.

    Article  Google Scholar 

  • McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A.Grouws, (Ed.), Handbook of Research on Mathematics Learning and Teaching (pp. 575–596). New York: MacMillan.

    Google Scholar 

  • Middleton, J. A., & Spanias, P. A. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for Research in Mathematics Education, 30, 65–88.

    Article  Google Scholar 

  • Midgley, C., Kaplan, A., Middleton, M., Maehr, M. L., Urdan, T., Anderman, L. H., et al. (1998). The development and validation of scales assessing students’ achievement goal orientations. Contemporary Educational Psychology, 23, 113–131.

    Article  Google Scholar 

  • Minato, S., & Kamada, T. (1996). Results on research studies on Causal predominance between achievement and attitude in junior high school mathematics of Japan. Journal for Research in Mathematics Education, 27, 96–99.

    Article  Google Scholar 

  • Murphy, P. K., & Alexander, P. A. (2000). A motivated exploration of motivation terminology. Contemporary Educational Psychology, 25, 3–53.

    Article  Google Scholar 

  • Näveri, L., Pehkonen, E., Hannula, M.S., Laine, A. & Heinilä, L. (2011). Finnish elementary teachers’ espoused beliefs on mathematical problem solving. In: B. Rösken & M. Casper (Eds.), Current State of Research on Mathematical Beliefs XVII. Proceedings of the MAVI-17 Conference (pp. 161–171). University of Bochum: Germany.

    Google Scholar 

  • Nett, U. E., Goetz, T., & Hall, N. C. (2011). Coping with boredom in school: An experience sampling perspective. Contemporary Educational Psychology, 36, 49–59.

    Article  Google Scholar 

  • Niemivirta, M. (2004). Habits of Mind and Academic Endeavors. The Correlates and Consequences of Achievement Goal Orientation. Department of Education, Research Report 196. Helsinki: Helsinki University Press. Doctoral thesis.

    Google Scholar 

  • Nohda, N. (2000). Teaching by open approach methods in Japanese mathematics classroom. In. T. Nakahara and M. Koyama (Eds.), Proceedings of 24th conference of the international group for the psychology of mathematics education (Vol. 1, pp. 39–53). Hiroshima, Japan: PME.

    Google Scholar 

  • OECD. (2003). The PISA 2003 assessment framework—mathematics, reading, science and problem solving knowledge and skills. Paris: OECD.

    Google Scholar 

  • Op ’t Eynde, P. & Hannula, M. S. (2006). The case study of Frank. Educational Studies in Mathematics 63, 123–129.

    Google Scholar 

  • Pekrun, R., & Stephens, E. J. (2010). Achievement emotions: A control value approach. Social and Personality Psychology Compass, 4(4), 238–255.

    Article  Google Scholar 

  • Pekrun, R., Goetz, T., Daniels, L. M., Stupnisky, R. H., & Perry, R. P. (2010). Boredom in achievement settings: Exploring control-value antecedents and performance outcomes of a neglected emotion. Journal of Educational Psychology, 102(3), 531–549.

    Article  Google Scholar 

  • Pintrich, P. R. (1994). Continuities and discontinuities: Future directions for research in educational psychology. Educational Psychologist, 29, 137–148.

    Article  Google Scholar 

  • Polya, G. (1957). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Power, M., & Dalgleish, T. (1997). Cognition and emotion; from order to disorder. UK: Psychology Press.

    Google Scholar 

  • Rubinsten, O., & Tannock, R. (2010). Mathematics anxiety in children with developmental dyscalculia. Behavioral and Brain Functions, 6 (46). http://www.behavioralandbrainfunctions.com/content/6/1/46.

  • Schlöglmann, W. (2003). Can neuroscience help us better understand affective reactions in mathematics learning? In M. A. Mariotti (Ed.), Proceedings of Third Conference of the European Society for Research in Mathematics Education, 28 February—3 March 20. Bellaria, Italia. Accessed April 10, 2012 at <http://ermeweb.free.fr/CERME3/Groups/TG2/TG2_schloeglmann_cerme3.pdf>.

  • Schoenfeld, A. H. (1985). Mathematical problem solving. San Diego: Academic Press.

    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). New York: MacMillan.

    Google Scholar 

  • Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2011). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educational Studies in Mathematics, 79(2), 215–237.

    Article  Google Scholar 

  • Shmakov, P. & Hannula, M. S. (2010). Humour as means to make mathematics enjoyable. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of CERME 6, January 28th-February 1st 2009 (pp. 144–153). Lyon France: INRP 2010 <downloaded 15.6.2010: www.inrp.fr/editions/cerme6>.

  • Vogel-Walcutt, J. J., Fiorella, L., Carper, T., & Schatz, S. (2012). The definition, assessment, and mitigation of state boredom within educational settings: A comprehensive review. Educational Psychology Review, 24, 89–111.

    Article  Google Scholar 

  • Williams, G. (2002). Associations between mathematically insightful collaborative behaviour and positive affect. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 402–409). Norwich, UK: PME.

    Google Scholar 

  • Williams, T., & Williams, K. (2010). Self-efficacy and performance in mathematics: Reciprocal determinism in 33 nations. Journal of Educational Psychology, 102(2), 453–466.

    Article  Google Scholar 

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Acknowledgments

This research has been funded by Academy of Finland (project #135556).

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Correspondence to Markku S. Hannula .

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Hannula, M.S. (2015). Emotions in Problem Solving. In: Cho, S. (eds) Selected Regular Lectures from the 12th International Congress on Mathematical Education. Springer, Cham. https://doi.org/10.1007/978-3-319-17187-6_16

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