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Young Children’s Emotional Acts While Engaged in Mathematical Problem Solving

  • Paul CobbEmail author
  • Erna Yackel
  • Terry Wood†
Chapter
Part of the Mathematics Education Library book series (MELI, volume 48)

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.

Keywords

Emotional acts Beliefs Social context Social norms Classroom social interaction Obligations and expectations 

Notes

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.

References

  1. Armon-Jones, C. (1986a). The thesis of constructionism. In R. Harré (Ed.), The social construction of emotions (pp. 33–56). Oxford: Blackwell.Google Scholar
  2. Armon-Jones, C. (1986b). The social functions of emotions. In R. Harré (Ed.), The social construction of emotions (pp. 57–82). Oxford: Blackwell.Google Scholar
  3. Averill, J. (1986). The acquisition of emotions during adulthood. In R. Harré (Ed.), The social construction of emotions (pp. 98–118). Oxford: Blackwell.Google Scholar
  4. Balacheff, N. (1986). Cognitive versus situational analysis of problem-solving behavior. For the Learning of Mathematics, 6(3), 10–12.Google Scholar
  5. Bateson, G. (1973). Steps to an ecology of mind. London: Paladin.Google Scholar
  6. 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.Google Scholar
  7. Beford, E. (1986). Emotions and statements about them. In R. Harré (Ed.), The social construction of emotions (pp. 15–31). Oxford: Blackwell.Google Scholar
  8. Bishop, A. (1985). The social construction of meaning: A significant development for mathematics education? For the Learning of Mathematics, 5(1), 24–28.Google Scholar
  9. Blumer, H. (1969). Symbolic interactionism. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  10. 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.Google Scholar
  11. Bruner, J. (1986). Actual minds, possible worlds. Cambridge, MA: Harvard University Press.Google Scholar
  12. Cobb, P. (1985). Two children’s anticipations, beliefs, and motivations. Educational Studies in Mathematics, 16, 111–126.CrossRefGoogle Scholar
  13. 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.Google Scholar
  14. Cobb, P. (1986b). Concrete can be abstract: A case study. Educational Studies in Mathematics, 17, 37–48.CrossRefGoogle Scholar
  15. Cobb, P. (1986c) Contexts, goals, beliefs, and learning mathematics. For the Learning of Mathematics, 6(2), 2–9.Google Scholar
  16. 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.Google Scholar
  17. Cobb, P., & Steffe, L.P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83–94.CrossRefGoogle Scholar
  18. Cobb, P., & von Glasersfeld, E. (1984). Piaget’s scheme and constructivism. Genetic Epistemology, 13(2), 9–15.Google Scholar
  19. 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.Google Scholar
  20. Cobb, P., Wood, T., & Yackel, E. (1991b). Philosophy of science as a source of analogies for analyzing classroom life. Science Education, 75, 23–44.CrossRefGoogle Scholar
  21. 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.Google Scholar
  22. 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.Google Scholar
  23. 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.Google Scholar
  24. 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.Google Scholar
  25. 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.Google Scholar
  26. Goodlad, J.I. (1983). A place called school: Prospects for the future. New York: McGraw-Hill.Google Scholar
  27. Hargreaves, D.H. (1975). Interpersonal relations and education. London: Routledge and Kegan Paul.Google Scholar
  28. Harré, R. (1986). An outline of the social constructionist viewpoint. In R. Harré (Ed.), The social construction of emotions (pp. 2–14). Oxford: Blackwell.Google Scholar
  29. 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.Google Scholar
  30. 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.Google Scholar
  31. Kamii, C. (1985). Young children reinvent arithmetic: Implications of Piaget’s theory. New York: Teachers College Press.Google Scholar
  32. Labinowicz, E. (1985). Learning from children. Menlo Park, CA: Addison-Wesley.Google Scholar
  33. 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.Google Scholar
  34. Lortie, D.C. (1975). Schoolteacher. Chicago: University of Chicago Press.Google Scholar
  35. 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.Google Scholar
  36. Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press.Google Scholar
  37. 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.Google Scholar
  38. 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.Google Scholar
  39. 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.Google Scholar
  40. Nicholls, J.G. (1987). Motivation, values, and education. Paper presented at the annual meeting of the American Educational Research Association, Washington, DC.Google Scholar
  41. Perret-Clermont, A.N. (1980). Social interaction and cognitive development in children. New York: Academic Press.Google Scholar
  42. Piaget, J. (1970). Genetic epistemology. New York: Columbia University Press.Google Scholar
  43. Piaget, J. (1980). Adaptation and intelligence: Organic selection and phenocopy. Chicago: University of Chicago Press.Google Scholar
  44. Pritchard, M. (1976). On taking emotions seriously. Journal for the Theory of Social Behavior, 6(2), 1–27.CrossRefGoogle Scholar
  45. 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.Google Scholar
  46. Sarbin, T.R. (1986). Emotion and act: Roles and rhetoric. In R. Harré (Ed.), The social construction of emotion (pp. 83–97). Oxford: Blackwell.Google Scholar
  47. Schoenfeld, A.H. (1985). Mathematical problem solving. New York: Academic Press.Google Scholar
  48. 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.Google Scholar
  49. 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.Google Scholar
  50. 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.Google Scholar
  51. Smith, J.E. (1978). Purpose and thought: The meaning of pragmatism. Chicago: University of Chicago Press.Google Scholar
  52. 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.Google Scholar
  53. Steffe, L.P., Cobb, P., & von Glasersfeld, E. (1988). Young children’s construction of arithmetical meanings and strategies. New York: Springer-Verlag.Google Scholar
  54. Steffe, L.P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory, and application. New York: Praeger Scientific.Google Scholar
  55. 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.Google Scholar
  56. Voigt, J. (1985). Patterns and routines in classroom interaction. Recherches en Didactique des Mathématiques, 6, 69–118.Google Scholar
  57. 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.Google Scholar
  58. von Glasersfeld, E. (1984). An introduction to radical constructivism. In P. Watzlawick (Ed.), The invented reality (pp. 17–40). New York: Norton.Google Scholar
  59. Weiner, B. (1979). A theory of motivation for some classroom experiences. Journal of Educational Psychology, 71, 3–25.CrossRefGoogle Scholar
  60. 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.Google Scholar
  61. 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.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.Purdue University CalumetHammondUSA

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