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Networking Theories to Understand Beliefs and Their Crucial Role in Mathematics Education

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From beliefs to dynamic affect systems in mathematics education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Many publications present research on teacher beliefs, whether concretized for pre-service or in- service teachers. Most of them have in common that they highlight the crucial role that beliefs play in the classroom. In this chapter, we explore more deeply what those crucial aspects are, what they consist of, and how they interact with other variables. Different theoretical lenses will be brought together to underline different perspectives and to gain explanatory power going beyond the single approaches. For the case of practising teachers, we will discuss some thoughts on the classical contributions by Shulman (Educ Res 15(2):4–14, 1986) and Schoenfeld (Issues Educ 4(1):1–94, 1998). On the one hand, we extend the knowledge categorization provided by Shulman to the fields of beliefs and goals. On the other hand, we elaborate on Schoenfeld’s theory of Teaching-In-Context. For the case of pre-service teachers, we combine the classification of mathematical beliefs based on the work of Ernest with ideas of conceptual change originally conceived in the context of knowledge (cf. Ernest, J Educ Teach 15:13–33, 1989; Vosniadou and Verschaffel, Learn Instr 14(5):445–451, 2004).

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Notes

  1. 1.

    Our ideas are based on Roesken and Rolka (2011).

  2. 2.

    These ideas are based on Liljedahl et al. (2007a, b) and Rolka et al. (2006).

  3. 3.

    Funded by the Robert-Bosch Foundation.

References

  • Appleton, K. (1997). Analysis and description of students’ learning during science classes using a constructivist-based model. Journal of Research in Science Teaching, 34(3), 303–318.

    Article  Google Scholar 

  • Artigue, M., Bartolini-Bussi, M., Dreyfus, T., Gray, E., Prediger, S., et al. (2006). Different theoretical perspectives and approaches in research in mathematics education. In M. Bosch et al. (Eds.), Proceedings of the 4th CERME, Sant Feliu de Guixols (pp. 1239–1244). Spain: Fundemi IQS – Universitat.

    Google Scholar 

  • Arzarello, F., Bosch, M., Lenfant, A., & Prediger, S. (2007). Different theoretical perspectives in research. In D. Pitta-Pantazi et al. (Eds.), Proceedings of the 5th CERME 5, Larnaca (pp. 1618–1627). Cyprus: ERME.

    Google Scholar 

  • Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation, Michigan State University, East Lansing. http://www-personal.umich.edu/~dball/books/index.html. Accessed 24 Jan 2014.

  • Bauersfeld, H. (1980). Hidden dimensions in the so-called reality of a mathematics classroom. Educational Studies in Mathematics, 11, 23–41.

    Article  Google Scholar 

  • Baumert, J., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.

    Article  Google Scholar 

  • Bikner-Ahsbahs, A., & Prediger, S. (2006). Diversity of theories in mathematics education: How can we deal with it? ZDM – The International Journal on Mathematics Education, 38(1), 52–57.

    Google Scholar 

  • Calderhead, J., & Robson, M. (1991). Images of teaching: The student teachers’ early conception of classroom practice. Teaching & Teacher Education, 7(1), 1–8.

    Article  Google Scholar 

  • Carter, G., & Norwood, K. S. (1997). The relationship between teacher and student beliefs about mathematics. School Science and Mathematics, 97(2), 62–67.

    Article  Google Scholar 

  • Chapman, O. (2002). Belief structures and inservice high school mathematics teacher growth. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 177–194). Dordrecht: Kluwer.

    Google Scholar 

  • Dahl, B. (2006). Various theoretical frameworks in concept construction and how to move forward as a field: A commentary to Pegg and Tall. ZDM – The International Journal on Mathematics Education, 38(1), 63–69.

    Google Scholar 

  • Di Martino, P., & Zan, R. (2001). Attitude toward mathematics: some theoretical issues. In Proceedings of 25th annual conference for the psychology of mathematics education (Vol. 3, pp. 351–358). Utrecht: PME.

    Google Scholar 

  • Dionne, J. J. (1984). The perception of mathematics among elementary school teachers. In J. M. Moser (Ed.), Proceedings of the 6th annual meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 223–228). Madison: University of Wisconsin, PME-NA.

    Google Scholar 

  • Ernest, P. (1989). The knowledge, beliefs, and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15, 13–33.

    Article  Google Scholar 

  • Ernest, P. (1991). The philosophy of mathematics education. Hampshire: Falmer.

    Google Scholar 

  • Ernest, P. (1994). The philosophy of mathematics and the didactics of mathematics. In R. Biehler, R. W. Scholz, R. Strasser, & B. Winkelmann (Eds.), Didactics of mathematics as scientific discipline (pp. 335–349). Dordrecht: Kluwer.

    Google Scholar 

  • Feiman-Nemser, S., & Featherstone, H. (1992). The student, the teacher, and the moon. In S. Feiman-Nemser & H. Featherstone (Eds.), Exploring teaching: Reinventing an introductory course. New York: Teacher College Press.

    Google Scholar 

  • Feiman-Nemser, S., McDiarmid, G., Melnick, S., & Parker, M. (1987). Changing beginning teachers’ conceptions: A description of an introductory teacher education course. Paper presented at American Educational Research Association, Washington, DC.

    Google Scholar 

  • Fosnot, C. (1989). Enquiring teachers, enquiring learners: A constructivist approach for teaching. New York: Teachers College Press.

    Google Scholar 

  • Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39–57). Dordrecht: Kluwer.

    Google Scholar 

  • Green, T. (1971). The activities of teaching. New York: McGraw-Hill.

    Google Scholar 

  • Grigutsch, S. (1996). Mathematische Weltbilder von Schülern. Struktur, Entwicklung, Einflußfaktoren (unveröffentlichte Dissertation).

    Google Scholar 

  • Grigutsch, S., Raatz, U., & Törner, G. (1998). Mathematische Weltbilder bei Mathematiklehrern. Journal für Mathematikdidaktik, 19, 3–45.

    Article  Google Scholar 

  • Hersh, R. (1991). Mathematics has a front and a back. New directions in the philosophy of mathematics. Synthese, 88(2), 127–133.

    Article  Google Scholar 

  • Hersh, R. (1997). What is mathematics, really? New York: Oxford University Press.

    Google Scholar 

  • Hofer, B. K. (2000). Dimensionality and disciplinary differences in personal epistemology. Contemporary Educational Psychology, 25, 378–405.

    Article  Google Scholar 

  • Hofer, B. K. (2004). Epistemological understanding as a metacognitive process: Thinking aloud during online searching. Educational Psychologist, 39(1), 43–55.

    Article  Google Scholar 

  • Hofer, B. K., & Pintrich, P. R. (1997). The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning. Review of Educational Research, 67, 88–140.

    Article  Google Scholar 

  • Kitchener, K. S. (1983). Cognition, metacognition, and epistemic cognition. Human Development, 26, 222–232.

    Article  Google Scholar 

  • Kuhn, T. S. (1970). The structure of scientific revolutions (2nd enlarged ed.). Chicago: University of Chicago Press.

    Google Scholar 

  • Kuntze, S. (2011). Pedagogical content beliefs: Global, content domain-related and situation-specific components. Educational Studies in Mathematics, 79(2), 273–292.

    Article  Google Scholar 

  • Leder, G. C., Pehkonen, E., & Törner, G. (2002). Beliefs: A hidden variable in mathematics education? Dordrecht: Kluwer.

    Google Scholar 

  • Lerman, S. (1983). Problem-solving or knowledge centered: The influence of philosophy on mathematics teaching. International Journal of Mathematical Education in Science and Technology, 14(1), 59–66.

    Article  Google Scholar 

  • Lerman, S. (2006). Theories of mathematics education: Is plurality a problem? ZDM – The International Journal on Mathematics Education, 38(1), 8–13.

    Google Scholar 

  • Liljedahl, P. (2006). Pentominoes and AHA!’s. In R. Zazkis & S. Campbell (Eds.), Number theory in mathematics education: Perspectives and prospects. Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Liljedahl, P., Rolka, K., & Rösken, B. (2007a). Affecting affect: the reeducation of preservice teachers’ beliefs about mathematics and mathematics teaching and learning. In W. G. Martin, M. E. Strutchens & P. C. Elliott (Eds.), The learning of mathematics. Sixty-ninth yearbook of the National Council of Teachers of Mathematics (pp. 319–330). Reston: NCTM.

    Google Scholar 

  • Liljedahl, P., Rolka, K., & Rösken, B. (2007b, February 22–26). Belief change as conceptual change. In Proceedings of CERME 5: Fifth conference of the European society for research in mathematics education, Larnaca, Cyprus.

    Google Scholar 

  • Lortie, D. (1975). Schoolteacher: A sociological study. Chicago: University of Chicago Press.

    Google Scholar 

  • McLeod, D. (1992). Research on the affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan.

    Google Scholar 

  • Millsaps, G. (2000). Secondary mathematics teachers’ mathematics autobiographies: Definitions of mathematics and beliefs about mathematics instructional practice. Focus on Learning Problems in Mathematics, 22(1), 45–67.

    Google Scholar 

  • Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2001). Problem solving in the mathematics classroom: a socio-constructivist account of the role of students’ emotions. In Proceedings of 25th annual conference for the psychology of mathematics education (Vol. 4, pp. 25–32). Utrecht: PME.

    Google Scholar 

  • Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332.

    Article  Google Scholar 

  • Perry, W. G. (1968). Patterns of development in thought and values of students in a liberal arts college: A validation of a scheme (Final Report Project No. 5–0825, Contract No. SAE-8873). Cambridge, MA: Bureau of Study Counsel, Harvard University.

    Google Scholar 

  • 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.

    Google Scholar 

  • Pintrich, P. R., Marx, R. W., & Boyle, R. A. (1993). Beyond conceptual change: The role of motivational beliefs and classroom contextual factors in the process of conceptual change. Review of Educational Research, 63, 167–199.

    Article  Google Scholar 

  • Posner, G., Strike, K., Hewson, P., & Gertzog, W. (1982). Accommodation of a scientific conception: Towards a theory of conceptual change. Science Education, 66, 211–227.

    Article  Google Scholar 

  • Rolka, K., Rösken, B., & Liljedahl, P. (2006). Challenging the mathematical beliefs of preservice elementary school teachers. In Proceedings of the 30th international conference for psychology of mathematics education. Prague: Czech Republic.

    Google Scholar 

  • Rösken, B., & Rolka, K. (2011). Goals and beliefs – Two sides of the same coin. In K. Kislenko (Ed.), Proceedings of MAVI 16, The 16th conference on mathematical views (pp. 1–9), Tallinn, Estonia, June 26–29, 2010.

    Google Scholar 

  • Rösken, B., & Törner, G. (2007, April 9–13). Beliefs of university teachers of mathematics – Revisited as epistemological world views. Paper presented at the 2007 annual meeting of the American Educational Research Association, Chicago, USA.

    Google Scholar 

  • Rösken, B., & Törner, G. (2010, April 29–May 4). Aspects of accomplished mathematics teaching reflected as characteristics of a signature pedagogy. Paper presented to the 2010 annual meeting of the American Educational Research Association (AERA), Denver, USA.

    Google Scholar 

  • Rösken, B., Höchsmann, K., & Törner, G. (2008, March 5–8). Pedagogies in action: The role of mathematics teachers’ professional routines. Paper presented to the symposium held on the occasion of the 100th anniversary of ICMI, Rome.

    Google Scholar 

  • Rösken, B., Pepin, B., & Törner, G. (2011). Editorial. Beliefs and beyond: Affecting the teaching and learning of mathematics. ZDM – The International Journal on Mathematics Education, 43(4), 451–455.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic.

    Google Scholar 

  • Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1–94.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Schoenfeld, A. H. (2010). How we think. A theory of goal-oriented decision making and its educational applications. New York: Routledge.

    Google Scholar 

  • Schommer, M. (1990). The effects of beliefs about the nature of knowledge on comprehension. Journal of Educational Psychology, 82, 498–504.

    Article  Google Scholar 

  • Schommer-Aikins, M. (2004). Explaining the epistemological belief system: Introducing the embedded systemic model and coordinated research approach. Educational Psychologist, 39(1), 19–29.

    Article  Google Scholar 

  • Schraw, G., & Olafson, L. (2002). Teachers’ epistemological world views and educational practices. Issues in Education, 8(2), 99–148.

    Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Shulman, L. S. (2005a). Signature pedagogies in the professions. Daedalus, Summer Issue, 52–59.

    Google Scholar 

  • Shulman, L. S. (2005b, February 6–8). The signature pedagogies of the profession of law, medicine, engineering, and the clergy: Potential lessons for the education of teachers. Manuscript delivered at the Math Science Partnerships (MSP) Workshop ‘Teacher Education for Effective Teaching and Learning’ hosted by the National Research Council’s Center for Education, Irvine, CA.

    Google Scholar 

  • Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and mathematics education. In A. J. Bishop et al. (Eds.), International handbook of mathematics education (pp. 827–876). Dordrecht: Kluwer.

    Google Scholar 

  • Skott, J. (2001). The emerging practices of novice teachers: The roles of his school mathematics images. Journal of Mathematics Teacher Education, 4(1), 3–28.

    Article  Google Scholar 

  • Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1, 157–189.

    Article  Google Scholar 

  • Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.

    Google Scholar 

  • Törner, G. (2002). Mathematical beliefs – A search for a common ground: some theoretical considerations on structuring beliefs, some research questions, and some phenomenological observations. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 73–94). Dordrecht: Kluwer.

    Google Scholar 

  • Törner, G., & Grigutsch, S. (1994). Mathematische Weltbilder bei Studienanfängern – eine Erhebung. Journal für Mathematikdidaktik, 15(3/4), 211–252.

    Article  Google Scholar 

  • Törner, G., Rolka, K., Rösken, B., & Sriraman, B. (2010). Understanding a teacher’s actions in the classroom by applying Schoenfeld’s theory Teaching-in-Context: Reflecting on goals and beliefs. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 401–417). Berlin/Heidelberg/New York: Springer.

    Chapter  Google Scholar 

  • Uusimaki, L., & Nason, R. (2004). Causes underlying pre-service teachers’ negative beliefs and anxieties about mathematics. In Proceedings of 28th annual conference for the psychology of mathematics education (Vol. 4, pp. 369–376). Bergen: PME.

    Google Scholar 

  • Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Learning and Instruction, 14(5), 445–451.

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics, Ruhr-Universität Bochum, Bochum, Germany

    Katrin Rolka

  2. Professional School of Education, Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany

    Bettina Roesken-Winter

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  1. Katrin Rolka
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  2. Bettina Roesken-Winter
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Correspondence to Katrin Rolka .

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Editors and Affiliations

  1. Sør-Trøndelag University College, Trondheim, Norway

    Birgit Pepin

  2. Professional School of Education Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany

    Bettina Roesken-Winter

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Rolka, K., Roesken-Winter, B. (2015). Networking Theories to Understand Beliefs and Their Crucial Role in Mathematics Education. In: Pepin, B., Roesken-Winter, B. (eds) From beliefs to dynamic affect systems in mathematics education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-06808-4_4

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