# Affect, Meta-Affect, and Mathematical Belief Structures

Chapter

## Abstract

Beliefs are defined here to be multiply-encoded, internal cognitive/affective configurations, to which the holder attributes truth value of some kind (e.g., empirical truth, validity, or applicability). This chapter offers some theoretical perspectives on mathematical beliefs drawn from analysis of the affective domain, especially the interplay between meta-affect and belief structures in sustaining each other in the individual.

## Keywords

Mathematical Problem Belief System Mathematical Ability Belief Structure Affective Domain
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## References

- Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research.
*Educational Psychologist*,*31*, 175–190.CrossRefGoogle Scholar - Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while engaged in 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 - Confrey, J. (2000). Leveraging constructivism to apply to systemic reform.
*Nordisk Matematik Didaktik*(Nordic Studies in Mathematics Education),*8*(3), 7–30.Google Scholar - Damasio, A. (1999).
*The feeling of what happens: Body and emotion in the making of consciousness*. New York: Harcourt Brace & Co.Google Scholar - DeBellis, Valerie A. (1996).
*Interactions betweenAffect and Cognition during Mathematical Problem Solving: A Two Year Case Study of Four Elementary School Children*. Rutgers University doctoral dissertation. Ann Arbor, MI: Univ. Microfilms 96-30716.Google Scholar - DeBellis, V. A. (1998). Mathematical intimacy: Local affect in powerful problem solvers. In S. Berenson et al. (Eds.),
*Proceedings of the 20th annual meeting of PME-NA*Vol. 2 (pp. 435–440). Columbus, OH: ERIC.Google Scholar - DeBellis, V. A., & Goldin, G. A. (1991). Interactions between cognition and affect in eight high school students’ individual problem solving. In R. G. Underhill (Ed.),
*Proceedings of the 13th annual meeting of PME-NA*Vol. 1 (pp. 29–35). Blacksburg, VA: Virginia Tech.Google Scholar - DeBellis, V. A., & Goldin, G. A. (1993), Analysis of interactions between affect and cognition in elementary school children during problem solving. In J. R. Becker & B. Pense (Eds.),
*Proceedings of the 15th annual meeting of PME-NA*Vol. 2 (pp. 56–62). Pacific Grove, CA: San Jose State Univ. Ctr. for Math. and Computer Sci. Educ.Google Scholar - DeBellis, V. A., & Goldin, G. A. (1997). The affective domain in mathematical problem solving. In E. Pehkonen (Ed.),
*Proceedings of the 21st annual conference of PME*Vol. 2 (pp. 209–216). Helsinki, Finland: University of Helsinki Dept. of Teacher Education.Google Scholar - DeBellis, V. A., & Goldin, G. A. (1999). Aspects of affect: Mathematical intimacy, mathematical integrity. In O. Zaslavsky (Ed.),
*Proceedings of the 23rd annual conference of PME*Vol. 2 (pp. 249–256). Haifa, Israel: Technion, Dept. of Education in Technology and Science.Google Scholar - Drodge, E. N., & Reid, D. A. (2000). Embodied cognition and the mathematical emotional orientation.
*Mathematical Thinking and Learning*,*2*(4), 249–267.CrossRefGoogle Scholar - Goldin, G. A. (1987). Cognitive representational systems for mathematical problem solving. In C. Janvier (Ed.),
*Problems of representation in the teaching and learning of mathematics*(pp. 125–145). Hillsdale, NJ: Erlbaum.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, IL: Northern Illinois Univ. Department of Mathematics.Google Scholar - Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics.
*Journal of Mathematical Behavior*,*17*(2), 137–165.Google Scholar - Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving.
*Mathematical Thinking and Learning*,*2*(3), 209–219.CrossRefGoogle Scholar - Gomez-Chacon, I. M. (2000).
*Matematica emotional*. Madrid: Narcea, S. A. de Ediciones.Google Scholar - Kohlberg, L., Levine, C., & Hewer, A. (1983).
*Moral stages: A current formulation and a response to critics*. Basel: Karger.Google Scholar - Leder, G. (1982). Mathematics achievement and fear of success.
*Journal for Research in Mathematics Education*,*13*, 124–135.Google Scholar - Leder, G. (1993). Reconciling affective and cognitive aspects of mathematics learning: Reality or a pious hope? In I. Hirabayashi et al. (Eds.),
*Proceedings of the 17th annual meeting of PME*Vol. 1 (pp. 46–65). Tsukuba, Japan: Univ. of Tsukuba.Google Scholar - Lester, F. K., Garofalo, J., & Lambdin Kroll, D. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior. In D. B. McLeod & V. M. Adams (Eds),
*Affect and mathematical problem solving: A new perspective*(pp. 75–88). New York: Springer-Verlag.Google Scholar - McLeod, D. B. (1988). Affective issues in mathematical problem solving: Some theoretical considerations.
*Journal for Research in Mathematics Education*,*19*, 134–141.Google Scholar - McLeod, D. B. (1989). Beliefs, attitudes, and emotions: New views of affect in mathematics education. In D. B. McLeod & V. M. Adams (Eds.),
*Affect and mathematical problem solving: A new perspective*(pp. 245–258).. New York: Springer-Verlag.Google Scholar - McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grouws (Ed.),
*Handbook of Research on Mathematics Teaching and Learning*(pp. 575–596). New York: Macmillan.Google Scholar - McLeod, D. B. (1994). Research on affect and mathematics learning in the JRME: 1970 to the present.
*Journal for Research in Mathematics Education*,*25*(6), 637–647.Google Scholar - McLeod, D. B. & Adams, V. M., Eds. (1989).
*Affect and mathematical problem solving: A new perspective*. New York: Springer-Verlag.Google Scholar - Picard, R. W. (1997).
*Affective computing*. Cambridge, MA: The MIT Press.Google Scholar - Rogers, T. B. (1983). Emotion, imagery, and verbal codes: A closer look at an increasingly complex interaction. In J. Yuille (Ed.),
*Imagery, memory, and cognition: Essays in honor of Allan Paivio*(pp. 285–305). Hillsdale, NJ: Erlbaum.Google Scholar - Schoenfeld, A. (1985).
*Mathematical problem solving*. Orlando, FL: Academic Press.Google Scholar - Vinner, S. (1997). From intuition to inhibition—mathematics, education, and other endangered species. In E. Pehkonen (Ed.),
*Proceedings of the 21st annual conference of PME*Vol. 1 (pp. 63–78). Lahti, Finland: University of Helsinki Dept. of Teacher Education.Google Scholar - Zajonc, R. B. (1980). Feeling and thinking: Preferences need no inferences.
*American Psychologist*,*35*, 151–175.Google Scholar

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