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ZDM

, 43:451 | Cite as

Beliefs and beyond: affect and the teaching and learning of mathematics

  • Bettina RoeskenEmail author
  • Birgit Pepin
  • Guenter Toerner
Original Article

Abstract

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.

Keywords

Mathematics Education Mathematics Teacher Mathematics Classroom Teacher Knowledge Epistemic Belief 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bauersfeld, H. (1980). Hidden dimensions in the so-called reality of a mathematics classroom. Educational Studies in Mathematics, 11, 23–41.CrossRefGoogle Scholar
  2. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., & Jordan, A. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.CrossRefGoogle Scholar
  3. Buehl, M. M., & Alexander, P. A. (2005). Motivation and performance differences in students’—domain-specific epistemological belief profiles. American Educational Research Journal, 42(4), 697–726.CrossRefGoogle Scholar
  4. Cogan, L. S., & Schmidt, W. H. (1999). An examination of instructional practices in six countries. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International Comparisons in mathematics education (pp. 68–85). London: Falmer.Google Scholar
  5. 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.CrossRefGoogle Scholar
  6. De Corte, E., Mason, L., Depaepe, F., & Verschaffel, L. (2011). Self-regulation of mathematical knowledge and skills. In B. J. Zimmerman & D. H. Schunk (Eds.), Handbook of self-regulation of learning and performance (pp. 155–172). New York: Routledge.Google Scholar
  7. De Corte, E., Op’t Eynde, P., & Verschaffel, L. (2002). Knowing what to believe: the relevance of students’ mathematical beliefs for mathematics education. In B. K. Hofer & P. R. Pintrich (Eds.), Personal epistemology: The psychology of beliefs about knowledge and knowing (pp. 297–320). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  8. 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.CrossRefGoogle Scholar
  9. Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In C. Keitel, P. Damerow, A. Bishop, & P. Gerdes (Eds.), Mathematics, Education and Society (pp. 99–101). Paris: UNESCO Science and Technology Education Document Series No. 35.Google Scholar
  10. Frank, M. L. (1988). Problem solving and mathematical beliefs. Arithmetic Teacher, 35(5), 32–34.Google Scholar
  11. Frank, M. L. (1990). What myths about mathematics are held and conveyed by teachers? Arithmetic Teacher, 37(5), 10–12.Google Scholar
  12. Frost, L. A., Hyde, J. S., & Fennema, E. (1994). Gender, mathematics performance, and mathematics related attitudes and affect: a meta-analytic synthesis. International Journal of Educational Research, 21, 373–385.CrossRefGoogle Scholar
  13. Garofalo, J. (1989). Beliefs and their influence on mathematical performance. The Mathematics Teacher, 82(7), 502–505.Google Scholar
  14. Goldin, G. A., Roesken, B., & Toerner, G. (2009). Beliefs: No longer a hidden variable in mathematics teaching and learning processes. In J. Maass & W. Schloeglmann (Eds.), Beliefs and Attitudes in Mathematics Education: New Research Results (pp. 1–18). Rotterdam: Sense.Google Scholar
  15. Green, T. F. (1971). The activities of teaching. New York: McGrawhill.Google Scholar
  16. Hannula, M., Evans, J., Philippou, G., Zan, R. (2004) Affect in mathematics education-exploring theoretical frameworks. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 107–36).Google Scholar
  17. Kloosterman, P. (1996). Students’ beliefs about knowing and learning mathematics: Implications for motivation. In M. Carr (Ed.), Motivation in mathematics (pp. 131–156). Cresskill: Hampton press.Google Scholar
  18. Lave, J., & Wenger, E. (1991). Situated learning: legitimate peripheral participation. Cambridge: CUP.Google Scholar
  19. Leder, G. C., Pehkonen, E., & Toerner, G. (2002). Beliefs: A hidden variable in mathematics Education? Dordrecht: Kluwer Academic Publishers.Google Scholar
  20. Lester, F. K. (1996). Implications of research on students’ beliefs for classroom practice. In G. C. Leder, E. Pehkohnen, & G. Toerner (Eds.), Beliefs: a hidden variable in mathematics education (pp. 345–353). Dordrecht: Kluwer Academic Publishers.Google Scholar
  21. Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics, a meta-analysis. Journal for Research in Mathematics Education, 28(1), 26–47.CrossRefGoogle Scholar
  22. McLeod, D. B. (1994). Research on affect and mathematics learning. Journal for Research in Mathematics Education, 25, 637–647.CrossRefGoogle Scholar
  23. Mtetwa, D., & Garofalo, J. (1989). Beliefs about mathematics: An overlooked aspect of student difficulties. Academic Therapy, 24(5), 611–618.Google Scholar
  24. Muis, K. R. (2004). Personal epistemology and mathematics: a critical review and synthesis of research. Review of Educational Research, 74(3), 317–377.CrossRefGoogle Scholar
  25. Op’t Eynde, P., & De Corte, E. (2003). Students’ mathematics-related belief systems: design and analysis of a questionnaire. Paper presented at the 2003 Annual Meeting of the American Educational Research Association, April 21–25, Chicago.Google Scholar
  26. Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs. A quest for conceptual clarity and a comprehensive categorization. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: a hidden variable in mathematics education? (pp. 13–37). Netherlands: Kluwer Academic Publishers.Google Scholar
  27. Pajares, M. F. (1992). Teachers’ beliefs and educational research: cleaning up a messy construct. Review of Educational Research, 62(3), 307–332.Google Scholar
  28. Pehkonen, E. (1994). On differences in pupils’ conceptions about mathematics teaching. The Mathematics Educator, 5(1), 3–10.Google Scholar
  29. Pehkonen, E., & Toerner, G. (1999). Teachers’ professional development: What are the key change factors for mathematics teachers? European Journal of Teacher Education, 22(2,3), 259–275.Google Scholar
  30. Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics (pp. 157–224). Charlotte: Information Age Publishing.Google Scholar
  31. Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of research on teacher education (Second edition ed., pp. 102–119). New York: Macmillan.Google Scholar
  32. Roesken, B. (2011). Hidden dimensions in the professional development of mathematics teachers—Inservice education for and with teachers. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  33. Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando (FL): Academic Press.Google Scholar
  34. Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 209(4), 338–355.CrossRefGoogle Scholar
  35. Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.Google Scholar
  36. Schoenfeld, A. H. (1994). Mathematical thinking and problem solving. New York: Lawrence Erlbaum Publisher.Google Scholar
  37. Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1–94.CrossRefGoogle Scholar
  38. Schoenfeld, A. H. (2007). Problem solving in the United States, 1970–2008: research and theory, practice and politics. ZDM, The International Journal on Mathematics Education, 39(5–6), 537–551.CrossRefGoogle Scholar
  39. Schommer, M. (1990). Effects of beliefs about the nature of knowledge on comprehension. Journal of Educational Psychology, 82(3), 498–504.CrossRefGoogle Scholar
  40. Schommer-Aikins, M. (2004). Explaining the epistemological belief system: Introducing the embedded systemic model and coordinated research approach. Educational Psychologist, 39(1), 19–29.CrossRefGoogle Scholar
  41. Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. In A. J. Bishop, et al. (Eds.), International handbook of mathematics education (Volume 4 (pp. 827–876). Dordrecht: Kluwer.Google Scholar
  42. Sowder, J. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics (pp. 157–224). Charlotte: Information Age Publishing.Google Scholar
  43. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: a synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics learning and teaching (pp. 127–146). New York: Macmillan Publishing.Google Scholar

Copyright information

© FIZ Karlsruhe 2011

Authors and Affiliations

  • Bettina Roesken
    • 1
    Email author
  • Birgit Pepin
    • 2
  • Guenter Toerner
    • 3
  1. 1.Faculty of MathematicsRuhr-Universitaet BochumBochumGermany
  2. 2.Sør-Trøndelag University CollegeTrondheimNorway
  3. 3.Faculty of MathematicsUniversitaet Duisburg-EssenDuisburgGermany

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