Beliefs on Teaching/Learning Process and Classroom Practices of Mathematics Teachers – Consistency and (or) Contradictions

Author(s):

Jelena Radisic(presenting / submitting)Aleksander Baucal

Conference:

ECER 2011

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 04, Comparative Aspects in the Mathematics Classroom

Paper Session

Time:

2011-09-14

08:30-10:00

Room:

JK 28/130,G, 37

Chair:

Peter Kelly

Contribution

Research on classroom practices of teachers is divided into different traditions. Some authors emphasize on teachers’ philosophy, knowledge, beliefs, conceptions and attitudes believing that the mind of the teacher is the one shaping her/his practice (Munby et al. 2001; Bolhuis & Voeten, 2004; Fives & Buehl 2008) while others put stress on detailed analysis and interpretation of teachers’ practice in the classroom without taking into consideration what these practices mean for the teachers themselves, what they intent to achieve and why choosing specific ways in doing so (Adelsteinsdottir, 2004). In this research study, aim was to put these two traditions into a dialogue and to study interaction between teachers’ beliefs and their classroom practices. We presume that the relationship between teachers’ beliefs and classroom practices is not a simple and unidirectional one but can rather vary. In some cases they may be consistent to each other; sometimes practices can go beyond boundaries set up by beliefs, while sometimes practice can even contradict previously “established” beliefs. As mathematics is one of fundamental disciplines learned and taught in schools at all levels, its subject matter as well as how it is presented to students represent an important research theme. Throughout years different aspects of it have been explored in numerous numbers of studies (Stiegler & Hiebert, 1999; Stipek et al., 2001; Hugener et al., 2004; Clarke et al., 2006). Considering specifics of mathematics as a discipline and the content that is being taught this paper will focus on four types of teachers registered in previous steps of this study. Those are: “laissez faire”, “traditional”, “traditional stressing atmosphere“and “modern“type teacher and the interaction between their registered beliefs on teaching/learning and their classroom practices. All considered teachers teach mathematics at upper secondary level in Belgrade, capital of Serbia. For the purpose of analysis we have examined two videotaped classes of each of chosen type’s representative. Shown segment of research is part of a larger study that included 96 upper secondary teachers of both mathematics and Serbian language and literature.

Method

Quantitative methods were employed to discern different types of teachers considering their beliefs on teaching/learning using following instruments: Teachers’ beliefs scale, Teachers’ Sense of Efficacy Scale and Teachers’ practices list. Two dimensions were obtained from the first: “modern” and “traditional” teacher (reliability 0.866 and 0.820). On Teachers’ Sense of Efficacy Scale two dimensions were derived, in domain of student motivation and in domain of classroom discipline (reliabilities 0.836 and 0.747). Teachers’ practice list derived three sets of practices aiming students’ participation, structuring activities in class and creating positive atmosphere (reliability from 0.743 to 0.812). Employing hierarchical cluster analysis four types of teachers were derived based on above mentioned dimensions (1) ’’laissez faire’’ (eclectic approach to teaching, absence of structuring and creating atmosphere practices with experience of low capacity in maintaining discipline); (2) ’’traditional’’ (absence of participating and creating atmosphere practices, more traditional approach to teaching); (3) ’’traditional stressing atmosphere’’ (structures activities in class, stresses atmosphere, experience of high capacity in maintaining discipline) and (4) ’’modern’’ (creates atmosphere, stresses students’ participation, more modern approach to teaching). Qualitative methods, videotaping classes and interview were made with each of selected type representative to deepen understanding about interaction between teachers’ beliefs and practices.

Expected Outcomes

41% of mathematics teachers were found in “traditional” and 2% of them in “modern” cluster, 15% in “laissez-faire” group and again 41% in “traditional stressing atmosphere” category. First findings suggest consistency in some areas between teachers registered beliefs about the nature of learning and teaching and their actual classroom practices. Those teachers who held more traditional beliefs about teaching also gave their students relatively less autonomy and maintained a context in which they were more in charge of the class structure with clear instructions how certain procedure should be followed. Their interactions where mostly with the whole class, while student – student interactions were almost non-existing, as a contrary to the modern type teacher classroom setting. Video stimulated interviews with the teachers also allowed for a deeper understanding of their registered conceptions and contradictions between the practices and notions held (for example in a case when a task is being given to a student to be carried out in front of black board). All teachers during the interview emphasized on motivating their students “and getting them interested” at the beginning of the class. Yet in some cases it was difficult to gather how that is being done throughout the class.

References

Adelsteinsdottir, K. (2004). Teachers' behavior and practices in the classroom, Scandinavian Journal of Educational Research, 48, 1, 95 — 113 Bolhuis, S. & Voeten, M. J. M. (2004). Teachers' conceptions of student learning and own learning, Teachers and Teaching, 10, 1, 77 — 98 (eds.) Clarke, D., J., Emanuelsson, E., Jablonka & I., Mok (2006). Making Connections: Comparing Mathematics Classrooms Around the World, Rotterdam, Sense Publishers de Vries, Y. & Beijard, D. (1999). Teachers’ Conceptions of Education: A practical knowledge perspective on ‘Good’ Teaching, Interchange, Vol 30/4, 371-397 Eley, M. G. (2006). Teachers’ conceptions of teaching and the making of specific decisions in planning to teach, Higher Education, 51, 191–214 Fives, M. M. & Buehl, H. (2008). What do teachers believe? Developing a framework for examining beliefs about teachers’ knowledge and ability, Contemporary Educational Psychology, 33, 134–176 Hugener, I.; Pauli, C.; Reusser, K.; Lipowsky, F; Rakoczy, K and Klieme, E. (2009). Teaching patterns and learning quality in Swiss and German mathematics lessons, Learning and Instruction 19 pp. 66-78 Marton. F; Tsui, A.B.M.; Chik, P.P.M.; Ko, P.Y.; Lo, M.L. (2004). Classroom discourse and the space of learning, Routledge Mehan, H. (1979). ”What time is it, Denise?”: Asking known information questions in classroom discourse. Theory into Practice, 28(4), 285-294. Munby, H.; Russell, T. & Martin, A. K. (2001). Teachers’ Knowledge and How It Develops, in Richardson, V. (Ed.) Handbook of Research on Teaching, 4th Edition, American Educational Research Association Stiegler, J. & Hiebert, J (1999) The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the classroom. New York: The Free Press. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17, 213–226

Author Information

Jelena Radisic (presenting / submitting)

Faculty of Philosophy, University of Belgrade

Department of Psychology

Belgrade

Aleksander Baucal

Faculty of Philosophy, University of Belgrade, Serbia, Republic of

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