Towards a Participatory Approach to 'Beliefs' in Mathematics Education

Author(s):

Jeppe Skott(presenting / submitting)

Conference:

ECER 2014

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 09 A, Participatory Approaches in Mathematics Education

Paper Session

Time:

2014-09-04

11:00-12:30

Room:

B113 Sala de Aulas

Chair:

Birgit Pepin

Contribution

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.

Method

This paper is a theoretical essay based on a comprehensive reading of the literature on teachers’ beliefs in mathematics education and beyond. Consequently the question of method is mainly a question of the analytical approach adopted. As indicated before, the distinction between acquisition and participation as metaphors for human functioning is important for the analyses. In particular I use differences between acquisitionist and participatory frameworks concerning how the individual, the social, and the relationship between the individual and the social are conceptualised as an analytical perspective to address the two research questions. With regard to the first question, i.e. how responses to the empirical challenges to the congruity thesis may be categorised, this perspective proves helpful when distinguishing between the ways in which studies relate to the expected stability and impact of beliefs, i.e. to the last two aspects of the core of the beliefs concept (cf. above). Focusing on these two aspects, the analysis has resulted in four possible contextual and dynamic categories of interpretations of the role of teachers’ beliefs for practice (cf. the section below on conclusions). I refer to specific studies of teachers’ beliefs to elaborate on the meaning of and distinctions between the categories. However, the analysis does not primarily intend to ‘locate’ studies in particular categories, but to use the studies as starting points for specifying the character of the categories themselves. The distinction between different ways of conceptualising the individual, the social, and the relationship between the individual and the social is also helpful when distinguishing the acquisitionist perspective from a more participatory stance such as PoP. To address the second research question, I analyse two qualitative studies that have used PoP as their conceptual framework to understand the role of the teacher in emerging classroom practices. Both studies adopt relatively open approaches inspired by grounded theory to address the question of how the teachers’ contributions to classroom interaction relate to their engagement in other past and present practices. In the present paper I analyse if and how these PoP interpretations shed additional or different light on the question of the teacher’s role for classroom practice than the modified approaches to belief research mentioned above. Also, I compare the methodological and conceptual challenges of PoP with those of belief research.

Expected Outcomes

The analysis suggests four different categories of modifications to the premise that content related beliefs determine practice. These are the ones of belief enactment, activation, situatedness, and emergence. Belief enactment refers to the position that mathematics related beliefs are both stable and influential, but that local contingencies may modify their significance in a particular situation (Schoenfeld, 2011). Belief activation considers such beliefs stable, but suggests that classroom interaction may require the teacher to base instruction on other beliefs than those related to mathematics and that consequently mathematics related beliefs may lose their significance (Skott, 2001). A situated perspective suggests that beliefs are not contextually stable, but that the ones that teachers have in the classroom do influence practice (Hoyles, 1992; Lerman, 2002). Finally, an emergent view also sees beliefs as in some sense situated, but suggests that the relationship between beliefs and classroom practices is reflexive rather than causal, and that the latter are results of continuous renegotiation among all participants in the classroom community (Cobb & Yackel, 1996). These categories differ in significant ways, but they all represent relatively dynamic interpretations of the belief-practice quandary. Possibly with the exception of the emergent perspective, they also interpret beliefs as individual reifications that significantly influence practice, although the beliefs in question are not necessarily related to mathematics (activation) and not necessarily stable across contexts (situatedness). This indicates that the acquisitionist underpinnings of mainstream belief research continue to orient the field, also when more dynamic interpretations are developed. In contrast, PoP minimizes its reliance on objectifications, and it contributes with a differently dynamic interpretation of instruction that links current practices to other past and present ones. Also, I suggest that although PoP has methodological problems of its own, the framework does address the conceptual and methodological challenges of belief research.

References

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.

Author Information

Jeppe Skott (presenting / submitting)

Linnaeus University, S, & Aarhus University, DK, Denmark

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