Methodological considerations on investigating teachers’ beliefs of mathematics and its teaching

Erkki Pehkonen; Günter Törner

doi:10.7146/nomad.v9i1.147060

Authors

Erkki Pehkonen
Günter Törner

DOI:

https://doi.org/10.7146/nomad.v9i1.147060

Abstract

Our primary concerns are the methodological considerations on investigating teachers’ beliefs of mathematics teaching using a quantitative as well as qualitative approach. However, a discussion of this type cannot be completely detached from the textual determination that beliefs result from. Hereby, Dionne’s and Ernest’s characterizations of beliefs on mathematics served as a theoretical background; the dominant perspectives on mathematics can be described as toolbox aspect, system aspect and process aspect. Originally, our test subjects numbered a total of 13 experienced German mathematics teachers. However, we will limit the scope of the discussion to research on six representative persons. We used three data-gathering methods: questionnaires, videotaped interviews and graphical as well as numerical self-estimations, respectively. In our investigation a comparison of the self-estimations stands in the foreground. Since this information is mainly overlapping, partly redundant and likely contradictory, we have to question the data in order to describe the beliefs of the teachers. The research was conducted during the spring and summer of 1994.

References

Berger, P. (1995). Teachers' beliefs about computers and computer science. In G. Törner (Ed.), Current state of research on mathematical beliefs. Proceedings of the MAVI workshop (pp. 15-22). Duisburg: Schriftenreihe des Fachbereichs Mathematik, Gerhard-Mercator-University Gesamthochschule Duisburg.

Cohen, L. & Manion, L. (1994). Research methods in education. London & New York: Routledge.

Davis, R. B., Maher, C. A. & Noddings, N. (Eds.) (1990). Constructivist views on the teaching and learning of mathematics. JRME Monograph Number 4. Reston, VA: NCTM. https://doi.org/10.2307/749908

Denzin, N. K. (1970). The research act in sociology: A theoretical introduction to sociological method. London: The Butterworth Group.

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

Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: a model. Journal of Education for Teaching 15 (1), 13-33. https://doi.org/10.1080/0260747890150102

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

Furinghetti, F. (1996). A theoretical framework for teachers' conceptions. In E. Pehkonen (Ed.), Current state of research on mathematical beliefs III. Proceedings of the MAVI-3 workshop (pp. 19-25). Helsinki: University of Helsinki. Department of Teacher Education.

Green, T. F. (1971). The activities of teaching. Tokyo: McGraw-Hill Kogakusha.

Grigutsch, S., Raatz, U. & Törner, G. (1998). Einstellungen gegenüber Mathematik bei Mathematiklehrern. Journal für Mathematik-Didaktik 19 (1), 3-45.

https://doi.org/10.1007/BF03338859

Hill, R. (1986). A fififirst course in coding theory. Oxford: Clarendon Press.

Lerman, S. (1983). Problem-solving or knowledge-centered: the influence of philosophy on mathematics teaching. Int. J. Math. Educ. Sci. Technol. 14 (1), 59-66. https://doi.org/10.1080/0020739830140109

Lincoln, Y. S. & Guba, E. G. (1985). Naturalistic inquiry. Beverly Hills, CA: SAGE publications. https://doi.org/10.1016/0147-1767(85)90062-8

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

Noddings, N. (1990). Constructivism in mathematics education. In R. B. Davis et al. (Eds.), Constructivist views on the teaching and learning of mathematics. JRME Monograph Number 4 (pp. 7-18). Reston: NCTM. https://doi.org/10.2307/749909

Pehkonen, E. (1994). On teachers' beliefs and changing mathematics teaching. Journal für Mathematik-Didaktik 15 (3/4), 177-209. https://doi.org/10.1007/BF03338807

Pehkonen, E. (1995). Pupils' view of mathematics: Initial report for an international comparison project. Research Report 152. Helsinki: University of Helsinki, Department of Teacher Education.

Pehkonen, E. & Lepmann, L. (1995). Vergleich der Auffassungen von Lehrern über den Mathematikunterricht in Estland und Finnland. Research Report 139. Helsinki: University of Helsinki, Department of Teacher Education.

Pehkonen, E. & Törner, G. (1999). Teachers' professional development: what are the key change factors for mathematics teachers? European Journal of Teacher Education 22 (2/3), 261-277. https://doi.org/10.1080/0261976899020259

Robitaille, D. F. (1997). National contexts for mathematics and science education. An encyclopedia of the education systems participating in TIMSS. Vancouver: Pacific Educational Press.

Schmalz, R. (1993). Out of the mouth of mathematicians. A quotation book for philomaths. Washington, DC: The Mathematical Association. https://doi.org/10.1090/spec/008

Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context (draft version). Retrieved from http://www-gse.berkeley.edu/faculty/aschoenfeld/ TeachInContext/tic.html

Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics learning and teaching (pp. 334-370). New York: Macmillan.

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.

Törner, G. & Grigutsch, S. (1994). "Mathematische Weltbilder" bei Studienanfängern - eine Erhebung. Journal für Mathematik-Didaktik 15 (3/ 4), 211-251. https://doi.org/10.1007/BF03338808