Abstract
Recent research in the field of affect has highlighted the need to theoretically clarify constructs such as beliefs, emotions and attitudes, and to better investigate the relationships among them. As regards the definition of attitude, in a previous study we proposed a characterization of attitude towards mathematics grounded in students’ experiences, investigating how students express their own relationship with mathematics. The data collected suggest a three-dimensional model of attitude towards mathematics that includes students’ emotional disposition, their vision of mathematics, and their perceived competence. In this paper, we discuss the relationship between beliefs and emotions, investigating the interplay among the three dimensions in the proposed model of attitude, as emerging in the students’ essays.
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Notes
The classification proposed by McLeod and McLeod (2002) of the definitions present in the mathematics education literature is based on the kind of audience to which a definition is for: informal definitions, directed to a general audience; formal definitions, appropriate to a more sophisticated audience with respect to the previous one, but still relatively broad; extended definitions, directed to an audience of specialists in a particular field.
In the tripartite model, instead, the implicit assumption that attitude is linked to behavior is made explicit. In the studies aimed at recognizing a relationship between attitude and behavior (like the early studies in this field), we believe that this explicit reference to behavior in the assumed (and possibly implicit) definition of attitude increases the risk of circularity already described for research on beliefs (see Lester, 2002).
The collected essays constitute a convenience sample, i.e. not fixed on a statistical basis but obtained through collaboration with teachers who accepted to participate in our research.
Referring to McLeod’s (1992) categorization, the construct attitude is therefore seen to be composed by emotions (associated to mathematics) and beliefs (about self and about mathematics).
The essays were translated by a bilingual expert, who tried to keep the sense of jargon terms and expressions as closer as possible to the original one. In the excerpts, the first number refers to the class level, the letter refers to the school level (Primary/Middle/High), the last number indicates the progressive numbering of the essay within the category.
References
Ajzen, I. (1988). Attitudes, personality, and behavior. Chicago, IL: Dorsey Press.
Brown, S., & Cooney, T. (1991). Stalking the dualism between theory and practice. Zentralblatt für Didaktik der Mathematik, 91(4), 112–117.
Bruner, J. (1990). Acts of meaning. Cambridge: Harvard University Press.
Buxton, L. (1981). Do you panic about maths? London: Heinemann.
Chapman, O. (1997). Metaphors in the teaching of mathematical problem solving. Educational Studies in Mathematics, 32(3), 201–228.
Daskalogianni, K., & Simpson, A. (2000). Towards a definition of attitude: The relationship between the affective and the cognitive in pre-university students. In Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 217–224). Hiroshima, Japan.
De Bellis, V., & Goldin, G. (1999). Aspects of affect: Mathematical intimacy, mathematical integrity. In Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249–256). Haifa, Israel.
De Bellis, V., & Goldin, G. (2006). Affect and meta-affect in mathematical problem solving: A Representational Perspective. Educational Studies in Mathematics, 63(2), 131–147.
Di Martino, P., & Zan, R. (2001). The problematic relationship between beliefs and attitudes. In Proceedings of the MAVI-X European Workshop, pp. 17–24. Kristianstad, Sweden.
Di Martino, P., & Zan, R. (2002). An attempt to describe a ‘negative’ attitude toward mathematics. In Proceedings of the MAVI-XI European Workshop, pp. 22–29. Pisa, Italy.
Di Martino, P., & Zan, R. (2003). What does ‘positive’ attitude really mean? In Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 451–458). Honolulu, Hawai’i.
Di Martino, P., & Zan, R. (2010). ‘Me and maths’: Towards a definition of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13(1), 27–48.
Eagly, A. H. (1967). Involvement as a determinant of response to favorable and unfavourable information. Journal of Personality and Social Psychology, 7, 1–15.
Eagly, A. H., & Chaiken, S. (1998). Attitude structure and function. In D. T. Gilbert, S. T. Fiske, & G. Lindzey (Eds.), The Handbook of Social Psychology (4th ed., Vol. 1, pp. 269–322). New York: McGraw-Hill.
Eisenhart, M. A. (1988). The ethnographic research tradition and mathematics education research. Journal for Research in Mathematics Education, 19(2), 99–114.
Evans, J. (2000). Adults’ mathematical thinking and emotions: A study of numerate practices. London: Routledge Falmer.
Evans, J., Hannula, M., Zan, R., & Brown, L. (Eds.). (2006). Affect in mathematics education—Exploring theoretical frameworks. Educational Studies in Mathematics, Special Issue, 63(2).
Evans, J., & Zan, R. (2006). Sociocultural approaches to emotions in mathematics education: Initial comparisons. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 41–48). Prague, Czech Republic.
Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of belief. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39–57). Dordrecht: Kluwer Academic Publishers.
Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory. Strategies for qualitative research. Chicago: Aldine.
Green, T. (1971). The activities of teaching. New York: McGraw-Hill.
Grigutsch, S., & Törner, G. (1998). World views of mathematics held by university teachers of mathematics science. Preprint Series No. 420. University of Duisburg, Department of Mathematics.
Haladyna, T., Shaughnessy, J., & Shaughnessy, M. (1983). A causal analysis of attitude toward mathematics. Journal for Research in Mathematics Education, 14(1), 19–29.
Hart, L. (1989). Describing the affective domain: Saying what we mean. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving (pp. 37–45). New York: Springer.
Kulm, G. (1980). Research on mathematics attitude. In R. J. Shumway (Ed.), Research in mathematics education (pp. 356–387). Reston, VA: National Council of Teachers of Mathematics.
Leder, G. (1985). Measurement of attitude to mathematics. For the Learning of Mathematics, 34(5), 18–21.
Leder, G. (1992). Measuring attitudes to mathematics. In Proceedings of the 16th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 33–39). Durham, USA.
Leder, G., Pehkonen, E., & Törner, G. (Eds.). (2002). Beliefs: A hidden variable in mathematics education? Dordrecht: Kluwer Academic Publishers.
Lester, F. K., Jr. (2002). Implications of research on students’ beliefs for classroom practice. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 345–353). Dordrecht: Kluwer Academic Publishers.
Mandler, G. (1984). Mind and body: Psychology of emotion and stress. New York: Norton.
Mandler, G. (1989). Affect and learning: Reflections and prospects. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving. A new perspective (pp. 237–244). New York: Springer.
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York, NY: McMillan.
McLeod, D. B., & Adams, V. M. (Eds.). (1989). Affect and mathematical problem solving. A new perspective. New York: Springer.
McLeod, D. B., & McLeod, S. H. (2002). Synthesis—beliefs and mathematics education: Implications for learning, teaching, and research. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 115–123). Dordrecht: Kluwer Academic Publishers.
Munby, H. (1984). A qualitative approach to the study of a teacher’s beliefs. Journal of Research in Science Teaching, 21(1), 27–38.
Nicholls, J., Cobb, P., Wood, T., Yackel, E., & Patashnick, M. (1990). Assessing students’ theories of success in mathematics: Individual and classroom differences. Journal for Research in Mathematics Education, 21(2), 109–122.
Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2006). ‘Accepting Emotional Complexity’: A socio-constructivist perspective on the role of emotions in the mathematics classroom. Educational Studies in Mathematics, Special Issue, 63(2), 193–207.
Ortony, A., Clore, G. L., & Collins, A. (1988). The cognitive structure of emotions. Cambridge: Cambridge University Press.
Pajares, F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332.
Pajares, F., & Miller, D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86(2), 193–203.
Pehkonen, E., & Törner, G. (1996). Mathematical beliefs and different aspects of their meaning. Zentralblatt für Didaktik der Mathematik, 28(4), 101–108.
Polanyi, M. (1958). Personal knowledge. Chicago: The University of Chicago Press.
Reyes, L. H. (1984). Affective variables and mathematics education. The Elementary School Journal, 84(5), 558–581.
Rokeach, M. (1968). Beliefs, attitudes, and values. San Francisco: Jossey-Bass.
Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics. Educational Studies in Mathematics, 35(1), 1–18.
Schlöglmann, W. (2002). Affect and mathematics learning. In Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 185–192). Norwich, UK.
Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press.
Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338–355.
Silver, E. A. (1982). Knowledge organization and mathematical problem solving. In F. Lester & J. Garofalo (Eds.), Mathematical problem solving: Issues in research (pp. 15–25). Philadelphia: Franklin Institute Press.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105–128.
Triandis, H. C. (1971). Attitudes and attitude change. New York: Wiley.
Weiner, B. (1986). An attributional theory of motivation and emotion. New York: Springer.
Neale, D. (1969). The role of attitudes in learning mathematics. The Arithmetic teacher, Dec. 1969, pp. 631–641.
Zan, R., Brown, L., Evans, J., & Hannula, M. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, Special Issue, 63(2), 113–121.
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Di Martino, P., Zan, R. Attitude towards mathematics: a bridge between beliefs and emotions. ZDM Mathematics Education 43, 471–482 (2011). https://doi.org/10.1007/s11858-011-0309-6
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DOI: https://doi.org/10.1007/s11858-011-0309-6