24 SES 09 A, Participatory Approaches in Mathematics Education
The premise and rationale of research on teachers’ beliefs is that beliefs about the contents of instruction and its teaching and learning significantly influence practice. This is apparent from the core of the beliefs concept as used in the literature, a core that refers to (1) subjectively true, (2) value-laden mental constructs that are the (3) relatively stable results of substantial prior experiences and that have (4) significant impact by guiding action and filtering information and experiences (Skott, 2013).
However, the concepts and methods of belief research are contentious, and the premise of belief impact has been challenged as much as confirmed in empirical studies of teachers’ beliefs (Fives & Buehl, 2012). In mathematics education the lack of congruity between beliefs and practice is sometimes blamed on the conceptual and methodological problems of the field (e.g. Speer, 2008), while others modify the substance of the premise and adopt a more dynamic perspective on the relationship between beliefs and practice than one of direct causality. In this theoretical essay I analyse reactions of the latter type and raise two research questions. The first is what the responses are in such studies to the empirical challenges to the field’s raison d’être, i.e. to the expectation of belief impact. More precisely I ask how the modifications to the expectation of immediate belief impact in research on teachers’ beliefs may be categorised.
In spite of significant differences between such categories of responses, most studies on teachers’ beliefs seem to share fundamental aspects of their theoretical framework. The last two of the four characteristics of the core of the beliefs concept (cf. above) suggest that beliefs attributed to teachers are expected to function as what Sfard calls objectifications. In her terminology, an objectification is a two-stage process that transforms human engagement in discursive practices into apparently self-sustained mental entities. The first stage is a reification, in which “sentences about processes and actions [are replaced by] propositions about states and objects” (Sfard, 2008, p. 44). The second stage is an alienation in which an independent existence is attributed to the reified objects and any connection to the processes that initially gave rise to them is lost. The interpretation of beliefs as objectifications links the larger part of belief research to acquisitionism, not least to constructivism, i.e. to a perspective on knowing and learning that views “knowledge as a kind of material, […] human mind as a container, and […] the learner as becoming an owner of the material stored in the container.” (Sfard, 2008, p. 49).
However, acquisitionism has been challenged by more participatory approaches that focus on (some understanding of) person-in-practice (Lerman, 2006). These latter approaches view action and meaning making as aspects of participation in social practices, rather than as enactments of reified mental entities. Following this line of thinking, I discuss a participatory conceptual framework in the making called Patterns of Participation (PoP) that draws on social practice theory (e.g. Wenger, 1998), symbolic interactionism (Blumer, 1969; Mead, 1934), and recent accounts of identity (e.g. Hodgen & Askew, 2007; Ma & Singer-Gabella, 2011). PoP views teachers’ participation in and renegotiation of past and present practices as an alternative to the elusive notion of beliefs as an entry to understanding their acts and meaning making. The second question I ask is what the potentials are of this more participatory stance for solving the conceptual and methodological problems of belief research and for understanding the role of the teacher in emerging classroom practices.
Blumer, H. (1969). Symbolic interactionism. Perspective and method. Berkeley: University of Los Angeles Press. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175–190. Fives, H., & Buehl, M. M. (2012). Spring cleaning for the messy construct of teachers' beliefs: What are they? Which have been examined? What can they tell us? In K. R. Harris, S. Graham & T. Urdan (Eds.), APA Educational Psychology Handbook (Vol. 2. Individual differences and cultural and contextual factors, pp. 471-499). Washington DC: APA. Hodgen, J., & Askew, M. (2007). Emotion, identity and teacher learning: becoming a primary mathematics teacher. Oxford Review of Education, 33(4), 369–287. Hoyles, C. (1992). Mathematics teachers and mathematics teaching: a meta-case study. For the Learning of Mathematics, 12(3), 32–44. Lerman, S. (2002). Situating research on mathematics teachers' beliefs and on change. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: a hidden variable in mathematics education (pp. 233–243). Dordrecht, NL: Kluwer. Lerman, S. (2006). Cultural psychology, anthropology and sociology: the developing ʻstrongʼ social turn. In J. Maasz & W. Schlöglmann (Eds.), New mathematics education research and practice (pp. 171–188). Rotterdam/Taipei: Sense. Ma, J. Y., & Singer-Gabella, M. (2011). Learning to teach in the figured world of reform mathematics: negotiating new models of identity. Journal of Teacher Education, 62(1), 8–22. Mead, G. H. (1934). Mind, self, and society from the standpoint of a social behaviorist. Chicago: University of Chicago. Schoenfeld, A. (2011). How we think. A theory of goal-oriented decision making and its educational applications New York: Routledge. Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourses, and mathematizing. Cambridge, UK: Cambridge University Press. Skott, J. (2001). The emerging practices of a novice teacher: the roles of his school mathematics images. Journal of Mathematics Teacher Education, 4(1), 3–28. Skott, J. (2013). Understanding the role of the teacher in emerging classroom practices: searching for patterns of participation. ZDM - The International Journal on Mathematics Education, 45(4), 547-559. doi: 10.1007/s11858-013-0500-z Speer, N. M. (2008). Connecting beliefs and practices: a fine-grained analysis of a college mathematics teacher's collections of beliefs and their relationship to his instructional practices. Cognition and Instruction, 26, 218–267. doi: 10.1080/07370000801980944 Wenger, E. (1998). Communities of practice. Learning, meaning, and identity. Cambridge, UK: Cambridge University Press.
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