A comparative study on students' beliefs concerning their autonomy in doing mathematics
DOI:
https://doi.org/10.7146/nomad.v8i4.146841Abstract
This paper treats an investigation on beliefs about autonomy held by 260 Finnish and 246 Italian seventh-grade students. The data were collected by means of a questionnaire consisting of 32 closed questions dealing with different aspects of mathematics teaching and learning, and three open questions on students' good and bad experiences in mathematics instruction and their wishes for good instruction. We have confined ourselves to the eight questions of the questionnaire identified as pertaining to the students' beliefs about autonomy in doing mathematics.
The data was collected through the questionnaire allowed to outline the patterns of beliefs in each country and compare patterns with each other. We have identified a core of common patterns in the two countries which are mainly related to the issue of classroom interaction and to the students' need of their teacher's help. The biggest differences between the two countries were found in the items concerning the use of trial-and-error strategies and the possibility that the students solve mathematical problems on their own.
References
Abelson, R. 1979. Differences between belief systems and knowledge systems. Cognitive Science 3, 355-366. https://doi.org/10.1016/S0364-0213(79)80013-0
Berger, P. 1998. Exploring mathematical beliefs - the naturalistic approach. In M. Ahtee & E. Pehkonen (eds.), Research Methods in Mathematics and Science Education, 25-40. University of Helsinki. Department of Teacher Education. Research Report 185.
Borasi, R. & Siegel, M. 1994. Reading, writing, and mathematics: rethinking the "basics" and their relationship. In D. F. Robitaille, D. H. Wheeler & C. Kieran (eds.), Selected lectures from ICME 7, 35-48. Université de Laval.
Cohen, L. & Manion, L. 1994. Research methods in education. Routledge (4th ed.): London.
Confrey, J. 1990. What constructivism implies for teaching. In R. B. Davis, C. A Maher. & N. Noddings (eds.), Constructivist Views on the Teaching and Learning of Mathematics, 107-122. Journal for Research in Mathematics Education, Monograph no 4. Reston (VA): NCTM. https://doi.org/10.2307/749916
Cooney, T. J. 1993. On the notion of authority applied to teacher education, In J. R. Becker & B. J. Pence (eds.), Proceedings of the fifteenth PME-NA Conference, Vol. 1, 40-46. San José (CA): San José State University.
Demattè, A. & Furinghetti, F. 1999. An exploratory study on students' beliefs about mathematics as a socio-cultural process. In G. Philippou (ed.), MAVIS Proceedings, 38- 47. University of Cyprus.
Edwards, J.-A. & Jones, K. 1999. Students' views of learning mathematics in collaborative small groups. In O. Zaslavski (ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education. Vol. 2, 281-288. University of Haifa.
Furinghetti, F. 1994. Ghosts in the classroom: beliefs, prejudices and fears. In L. Bazzini (ed.), Proceedings of the fifth Conference SCTP, 81-91. Pavia: University of Pavia.
Furinghetti, F. & Pehkonen, E. 1999. A virtual panel evaluating characterizations of beliefs. In E. Pehkonen & G. Törner (eds.), Pre-Proceedings of Oberwolfach meeting (November 1999) 'Mathematical beliefs and their impact on teaching and learning of mathematics', 24-30. Schriftenreihe des Fachbereichs Mathematik. Gerhard-Mercator-Universität Duisburg Gesamthochschule. Preprint Nr. 457.
Kifer, E. & Robitaille, D.F. 1989. Attitudes, Preferences and Opinions. In D. F. Robitaille & R. A. Garden (eds.), The IEA study of mathematics II: Contexts and outcomes of school mathematics, 178-208. International studies in educational achievement. Oxford: Pergamon Press.
Lampert, M. 1990. When the problem is not the question and the solution is not the answer: mathematical knowing and teaching. American educational research journal 27(1), 29-63. https://doi.org/10.3102/00028312027001029
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, 575-596. New York: Macmillan.
NCTM 1989. Curriculum and evaluation standards for school mathematics, Reston (VA): NCTM.
Nespor, J. 1987. The role of beliefs in the practice of teaching. Journal of Curriculum Studies 19, 317-328. https://doi.org/10.1080/0022027870190403
Pajares, M. F. 1992. Teachers' beliefs and educational research: cleaning up a messy construct. Review of educational research 62, 307-332. https://doi.org/10.3102/00346543062003307
Pehkonen, E. 1992. Problem field in mathematics teaching. Part 3: View of Finnish seventh- graders about mathematics teaching, University of Helsinki. Department of Teachers Education. Research Report 108.
Pehkonen, E. 1995. Pupils' View of Mathematics: Initial report for an international comparison project. University of Helsinki. Department of Teacher Education. Research Report 152.
Pehkonen, E. & Lepmann, L. 1993. On Teachers' Conceptions about the Role of Answers in Solving Mathematical Problems in Estonia and Finland. In J.R. Becker & B. J. Pence (eds.), Proceedings of the fifteenth PME-NA conference. Volume 2, 203-209. San Jose State University, San Jose (Ca.).
Pehkonen, E. & Safuanov, I. 1996. Pupils' views of mathematics teaching in Finland and Tatarstan. Nordic Studies in Mathematics Education 4(4), 31-59.
Pehkonen, E. & Törner, G. 1996. Mathematical beliefs and different aspects of their meaning. International Reviews on Mathematical Education [= ZDM] 28(4), 101-108.
Pehkonen, E. & Törner, G. (eds.) 1999, Pre-Proceedings of Oberwolfach meeting 'Mathematical beliefs and their impact on teaching and learning of mathematics'. Schriftenreihe des Fachbereichs Mathematik. Gerhard-Mercator-Universität Duisburg Gesamthochschule. Preprint Nr. 457.
Schoenfeld, A. H. 1983. Beyond the purely cognitive: beliefs systems, social cognitions, and metacognitions as driving forces in intellectual performance. Cognitive science 7, 329-363. https://doi.org/10.1016/S0364-0213(83)80003-2
Schoenfeld, A. 1992. Learning to think mathematically: problem solving, metacognition and sense making in mathematics. In A. D. Grouws (ed.), Handbook of Research on Mathematics Learning and Teaching, 334-370. New York: Macmillan.
Siegel, S. & Castellan, J. 1988. Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill.
Silver, E. & Cai, J. 1996. An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education 27(5), 521-539. https://doi.org/10.5951/jresematheduc.27.5.0521
Thompson, A.G. 1992. Teachers' beliefs and conceptions: A synthesis of the research. In A. D. Grouws (ed.), Handbook of Research on Mathematics Learning and Teaching, 127-146. New York: Macmillan.
Törner, G. & Pehkonen, E. 1996. Literature on mathematical beliefs. Schriftenreihe des Fachbereichs Mathematik, Universität Duisburg. Preprint Nr. 341.
Yackel, E. & Cobb, P. 1996. Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education 27(4), 458-477. https://doi.org/10.5951/jresematheduc.27.4.0458
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