Abstract
The analysis reported in this chapter focuses on a second-grade classroom in which the children typically displayed positive emotional acts as they attempted to solve personally challenging mathematics problems. We argue that, within the microculture established in a particular classroom, certain emotional acts but not others are appropriate in situations such as solving challenging mathematical tasks. The emotional acts that are warranted in particular situations can differ significantly from one classroom to another depending on the nature of the social norms that have been established. We illustrate how the negotiation of social norms that contrasted sharply with those established in most US mathematics classroom made possible the children’s generally positive responses to mathematical problem solving. In the final section of the chapter, we discuss the implications for the development of productive classroom learning environments in which debilitating emotions such as frustration while solving mathematical problems are not warranted.
In D. B. McLeod & V. A. Adams (Eds.) (1989), Affect and mathematical problem solving: A new perspective (pp. 117–148). New York: Springer.
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References
Armon-Jones, C. (1986a). The thesis of constructionism. In R. Harré (Ed.), The social construction of emotions (pp. 33–56). Oxford: Blackwell.
Armon-Jones, C. (1986b). The social functions of emotions. In R. Harré (Ed.), The social construction of emotions (pp. 57–82). Oxford: Blackwell.
Averill, J. (1986). The acquisition of emotions during adulthood. In R. Harré (Ed.), The social construction of emotions (pp. 98–118). Oxford: Blackwell.
Balacheff, N. (1986). Cognitive versus situational analysis of problem-solving behavior. For the Learning of Mathematics, 6(3), 10–12.
Bateson, G. (1973). Steps to an ecology of mind. London: Paladin.
Bauersfeld, H. (1988). Interaction, construction, and knowledge: Alternative perspectives for mathematics education. In T. Cooney & D. Grouws (Eds.), Effective mathematics teaching (pp. 27–46). Reston, VA: National Council of Teachers of Mathematics and Hillsdale, NJ: Lawrence Erlbaum Associates.
Beford, E. (1986). Emotions and statements about them. In R. Harré (Ed.), The social construction of emotions (pp. 15–31). Oxford: Blackwell.
Bishop, A. (1985). The social construction of meaning: A significant development for mathematics education? For the Learning of Mathematics, 5(1), 24–28.
Blumer, H. (1969). Symbolic interactionism. Englewood Cliffs, NJ: Prentice-Hall.
Brousseau, G. (1984). The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics (Occasional paper 54). In H.G. Steiner (Ed.), Theory of mathematics education (pp. 110–119). Bielefeld, Germany: IDM.
Bruner, J. (1986). Actual minds, possible worlds. Cambridge, MA: Harvard University Press.
Cobb, P. (1985). Two children’s anticipations, beliefs, and motivations. Educational Studies in Mathematics, 16, 111–126.
Cobb, P. (1986a). Clinical interviewing in the context of research programs. In G. Lappan & R. Even (Eds.), Proceedings of the Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Plenary speeches and symposium (pp. 90–110). East Lansing, MI: Michigan State University.
Cobb, P. (1986b). Concrete can be abstract: A case study. Educational Studies in Mathematics, 17, 37–48.
Cobb, P. (1986c) Contexts, goals, beliefs, and learning mathematics. For the Learning of Mathematics, 6(2), 2–9.
Cobb, P., & Merkel, G. (1989). Thinking strategies as an example of teaching arithmetic through problems solving. In P. Trafton (Ed.), New Directions for Elementry School Mathematics, 1989 yearbook of the National Council of Teachers of Mathematics (pp. 70–81). Reston, VA: National Council of Teachers of Mathematics.
Cobb, P., & Steffe, L.P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83–94.
Cobb, P., & von Glasersfeld, E. (1984). Piaget’s scheme and constructivism. Genetic Epistemology, 13(2), 9–15.
Cobb, P., Wood, T., & Yackel, E. (1991a). A constructivist approach to second grade mathematics. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education. Kluwer: Dordrecht.
Cobb, P., Wood, T., & Yackel, E. (1991b). Philosophy of science as a source of analogies for analyzing classroom life. Science Education, 75, 23–44.
Confrey, J. (1984, April). An emmination of the conceptions of mathematics of young women in high school. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.
Confrey, J. (1987, July). The current state of constructivist thought in mathematics education. Paper presented at the annual meeting of the International Group for the Psychology of Mathematics Education, Montreal, Canada.
Coulter, J. (1986). Affect and social context: Emotion definition as a social task. In R. Harré (Ed.), The social construction of emotion (pp. 120–134). Oxford: Blackwell.
Davydov, V.V. (1975). The psychological characteristics of the “prenumerical” period of mathematics instruction. In L.P. Steffe (Ed.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 7, pp. 109–205). Stanford, CA: School Mathematics Study Group.
Erickson, F. (1985). Qualitative methods in research on teaching. In M.C. Wittrock, (Ed.), Handbook of research on teaching (3rd ed., pp. 119–161). New York: Macmillan.
Goodlad, J.I. (1983). A place called school: Prospects for the future. New York: McGraw-Hill.
Hargreaves, D.H. (1975). Interpersonal relations and education. London: Routledge and Kegan Paul.
Harré, R. (1986). An outline of the social constructionist viewpoint. In R. Harré (Ed.), The social construction of emotions (pp. 2–14). Oxford: Blackwell.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Procedural and conceptual knowledge: The case of mathematics (pp. 1–27). Hillsdale, NJ: Lawrence Erlbaum Associates.
Hundeide, K. (1985). The tacit background of children’s judgments. In J.V. Wertsch (Ed.), Culture, communication, and cognition (pp. 306–322). Cambridge, England: Cambridge University Press.
Kamii, C. (1985). Young children reinvent arithmetic: Implications of Piaget’s theory. New York: Teachers College Press.
Labinowicz, E. (1985). Learning from children. Menlo Park, CA: Addison-Wesley.
Levina, R.E. (1981). L.S. Vygotsky’s ideas about the planning function of speech in children. In J.V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 279–299). Armonk, NY: Sharpe.
Lortie, D.C. (1975). Schoolteacher. Chicago: University of Chicago Press.
McLeod, D.B. (1985). Affective issues in research on teaching mathematical problem solving. In E.A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 267–280). Hillsdale, NJ: Lawrence Erlbaum Associates.
Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press.
Menchinskaya, N.A. (1969). Fifty years of Soviet instructional psychology. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 1, pp. 5–27). Stanford, CA: School Mathematics Study Group.
Nicholls, J.G. (1983). Conceptions of ability and achievement motivation: A theory and its implications for education. In S.G. Paris, G.M. Olson, & W.H. Stevenson (Eds.), Learning and motivation in the classroom (pp. 211–237). Hillsdale, NJ: Lawrence Erlbaum Associates.
Nicholls, J.G. (1984). Conceptions of ability and achievement motivation. In R.E. Ames & C. Ames (Eds.), Research on motivation in education: vol. 1, Student motivation (pp. 39–73). New York: Academic Press.
Nicholls, J.G. (1987). Motivation, values, and education. Paper presented at the annual meeting of the American Educational Research Association, Washington, DC.
Perret-Clermont, A.N. (1980). Social interaction and cognitive development in children. New York: Academic Press.
Piaget, J. (1970). Genetic epistemology. New York: Columbia University Press.
Piaget, J. (1980). Adaptation and intelligence: Organic selection and phenocopy. Chicago: University of Chicago Press.
Pritchard, M. (1976). On taking emotions seriously. Journal for the Theory of Social Behavior, 6(2), 1–27.
Rumelhart, D.E.. & Norman, D.A. (1981). Analogical processes in learning. In J.R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 335–359). Hillsdale, NJ: Lawrence Erlbaum Associates.
Sarbin, T.R. (1986). Emotion and act: Roles and rhetoric. In R. Harré (Ed.), The social construction of emotion (pp. 83–97). Oxford: Blackwell.
Schoenfeld, A.H. (1985). Mathematical problem solving. New York: Academic Press.
Sigel, I.G. (1981). Social experience in the development of representational thought: Distancing theory. In I.E. Sigel, D.M. Brodzinsky, & R.M. Golinkoff (Eds.), New directions in Piagetian theory and practice (pp. 203–217). Hillsdale, NJ: Lawrence Erlbaum Associates.
Silver, E.A. (1982). Knowledge organization and mathematical problem solving. In F.K. Lester and J. Garofalo (Eds.), Mathematical problem solving: Issues in research (pp. 15–25). Philadelphia: Franklin Institute Press.
Silver, E.A. (1985). Research on teaching mathematical problem solving: Some underrepresented themes and needed directions. In E.A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247–266). Hillsdale, NJ: Lawrence Erlbaum Associates.
Smith, J.E. (1978). Purpose and thought: The meaning of pragmatism. Chicago: University of Chicago Press.
Steffe, L.P. (1983). The teaching experiment methodology in a constructivist research program. In M. Zweng, T. Green, J. Kilpatrick, H. Pollack, & M. Suydam (Eds.), Proceedings of the Fourth International Congress on Mathematical Education. Boston: Birkhauser.
Steffe, L.P., Cobb, P., & von Glasersfeld, E. (1988). Young children’s construction of arithmetical meanings and strategies. New York: Springer-Verlag.
Steffe, L.P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory, and application. New York: Praeger Scientific.
Thompson, P. (1985). Experience, problem solving, and learning mathematics: Considerations in developing mathematics curricula. In E.A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 189–236). Hillsdale, NJ: Lawrence Erlbaum Associates.
Voigt, J. (1985). Patterns and routines in classroom interaction. Recherches en Didactique des Mathématiques, 6, 69–118.
von Glasersfeld, E. (1983). Learning as a constructive activity. In N. Herscovics & J.C. Bergeron (Eds.), Proceedings of the Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol.1, pp. 41–69). Montreal: University of Montreal.
von Glasersfeld, E. (1984). An introduction to radical constructivism. In P. Watzlawick (Ed.), The invented reality (pp. 17–40). New York: Norton.
Weiner, B. (1979). A theory of motivation for some classroom experiences. Journal of Educational Psychology, 71, 3–25.
Wood, T., Cobb, P., & Yackel, E. (1988, April). The influence of change in teacher’s beliefs about mathematics instruction on reading instruction. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.
Wood, T., & Yackel, E. (1988, July). Teacher’s role in the development of collaborative dialogue within small group interactions. Paper presented at the Sixth International Congress on Mathematical Education, Budapest, Hungary.
Acknowledgments
The research reported in this paper was supported by the National Science Foundation under Grant No. MDR-8740400. All opinions and recommendations expressed are, of course, solely those of the authors and do not necessarily reflect the position of the Foundation.
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Cobb, P., Yackel, E., Wood†, T. (2010). Young Children’s Emotional Acts While Engaged in Mathematical Problem Solving. In: Sfard, A., Gravemeijer, K., Yackel, E. (eds) A Journey in Mathematics Education Research. Mathematics Education Library, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9729-3_5
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