Ontology, Agency, and Aesthetics in Mathematics Education Research: Methodological Reflections

Transcription

1 Ontology, Agency, and Aesthetics in Mathematics Education Research: Methodological Reflections Mathematics Education and Contemporary Theory II Manchester Metropolitan University July 18, 2013 Conversation Strand 3 Facilitator: Jerry Rosiek Handouts

2 looking out for cars and mortality trying to find some sort of geometry avoiding mistakes keep an eye on every step i take everything is building and it appears that you're all architects and engineers that's how it looks that's how it looks from here here's some questions that the writer sent can an observer be a participant? have i seen too much? does it count if it doesn't touch? if the view is all i can ascertain pure understanding is out of range if i make that call why can't i make that change? i'm an ex-spectator can't you see? i'm an ex-spectator never let my never let my vision get in the way of me Fugazi, Lyrics to Ex-Spectator the possibility of explanation carries the supposition of an explainable (even if not fully) universe and an explaining (even if imperfectly) subject every explanation must secure and assure a certain kind of being-in-the-world, which might as well be called our politics. --Gayatri Spivak, Explanation and Culture: Marginalia, 1979 Pragmatism, thus, presents itself as an extension of historical empiricism, but with this fundamental difference, that it does not insist upon antecedent phenomena but upon consequent phenomena; not upon the precedents but upon the possibilities of action. John Dewey, The Development of American Pragmatism,

3 AGENDA Premises of this Conversation o Qualitative Methodology Conversation A recent impasse The ontological turn o o Material Feminism analogy to quantum mechanics, ontoepistemology Pragmatist semiotics embodied semiotics, ontology of the future Indigenous methodology ontology of place, ceremony as praxis Arts based research research as performative, knowledge as aesthetic relation Contemporary Theory in Mathematics Education Later arrival to poststructuralist theory Facing a similar impasse Examples: Stinson, de Freitas, Gutierrez, Ramirez and Tiemann, many others Making Connections What can mathematics education scholarship usefully appropriate from the ontological turn in qualitative methodology literature? What can mathematics education scholarship uniquely contribute to the contemporary methodological conversation? Activities o Break-out conversation 1: The Object of Mathematics Research What is the presumed/produced objects of mathematics educational research? What research practices produce these objects as the focus of our relational activity? o Break-out conversation 2: The Subject of Mathematics Research What is the presumed/produced subject of mathematics education research? What research practices produce these subject relations? o (If we have time) Break-out conversation 3: Envisioning New Research Agendas How have you already begun ontologically generative practices of mathematics education research What new questions and research projects that use ontologically generative methodological practices can we imagine using? Closure o Observations, Comments, Appreciations, and Resentments. o Next Steps: A special edition of a methodology journal? 2

4 DIAGRAMS FIGURE 1: Construction of the Object and Subject of Research Subject shaped by adopting the habit of receiving representations Construction of the Subject Presumes a certain kind of knowing subject that can receive the representation Act of Representation or Performance Frames what counts as real or significant about an experience Shapes our reception and responses. Construction of the Object Subject repeats representation, by drawing on available semiotic resources Representation and performances recirculated in community We are changed by the object, adjust our representations/ performances. World responds, resists, and exceeds our expectations. FIGURE 2: Two Different Conceptions of Semiotics Structuralist and Post-Structuralist Semiotics are based in a Saussurean Dyadic Conception of the Sign Pragmatist Materialist Semiotics are based on a Peircean Triadic Conception of the Sign SIGNIFIER SIGNIFIER OBJECT SIGNIFIED INTERPRETANT Premises 1: Language is made a synecdoche for all semiosis (all meaning) 2. The relation between linguistic signifiers and the things they signify is arbitrary. 3 Premises 1: All signs must have a materially embodied interpreter. 2. There are three qualitatively distinct kinds of ontological relations between signifiers and their objects. Iconic: based on felt qualities (e.g. photograph) Indexical: based on causal relation (e.g. a weather vane) Symbolic: based on convention and logic (e.g. language)

5 Break-out conversation 1: The Object of Mathematics Research What is the presumed/produced objects of mathematics educational research? o You might consider the difference between the ontology of mathematical relations learning about mathematical relations (ontology of the mind) the social effects of mathematical learning (e.g. ascribed status of math achievement or lack thereof, identities related to mathematics, etc.) the habits of cultural relation hidden in mathematics curriculum (how some forms of certainty and inference are privileged over others in our collective decision making). the phenomenal or aesthetic qualities of encountering mathematical ideas the agency of mathematics knowledge to change us (in its symbolic or social forms) What research practices produce these objects as the focus of our relational activity? o Consider how our research contributes to the production or transformation of: Particular conceptions/practices of learning mathematics The social meaning/status of mathematics achievement The cultural significance of mathematical knowledge Appreciation of the phenomenal or aesthetic qualities of mathematical ideas or the experience of learning mathematics Our recognition of the agency of mathematical knowledge to change us. Identify someone to report out about your small group conversation 4

6 Break-out conversation 2: The Subject of Mathematics Research What is the presumed/produced subject of mathematics education research? o You might consider the following What are the characteristics of the presumed knowing subject in traditional conceptions of mathematical knowledge? What are the presumed characteristics of the mathematics learner? Are they the same? (Are mathematicians and K-12 math students thought of as similar knowers?) What are some alternatives to that traditional conception of a mathematical knower? (Individual, social, collective, abstract, instrumental, etc.) How does learning mathematics affect our wider habits of being? What is the most common conception of the mathematics education research knower? What research practices produce these subject relations? o Consider How our research contributes to the production or transformation of the knowing or learning subject of mathematical knowledge? How can aesthetic modes of representation be used in a transformative mathematics education research agenda? How can performative/ceremonial modes of representation be used in a transformative mathematics education research agenda? How can our research enhance/shape/resist the agency of mathematics knowledge to change us (in its symbolic or social forms). Identify someone to report out about your small group conversation 5

7 If we have time Break-out conversation 3: Envisioning New Research Agendas How have you already begun ontologically generative practices of mathematics education research? What new questions and research projects that use ontologically generative methodological practices can we imagine using? What literature will be most useful in advancing these projects? What publication/performance venues would support this work? Next Steps? o Collaborations o Special editions of a methodology or math education journal o Panels at conferences on new developments in mathematics education research methodology Identify someone to report out about your small group conversation 6

8 Session Proposal A few years ago the more reflexive branches of qualitative research scholarship seemed to have arrived at a sort of impasse. By reflexive we mean those traditions of research that direct some part of their analysis at the social and cultural location of the author as a means of qualifying their claims and inferences. By impasse we mean conversations had settled into predictable scripts of objection and response that provide diminishing illumination. On one side there were those who rejected the totalizing authority of positivism and post-positivism in favor of appeals to the more limited authority of lived experience as a ground for knowledge. We can include in this broad category developments such as standpoint theory, action research, testimonio, and autoethnography. On the other side were scholars who rejected the totalizing authority of positivism and post-positivism by calling into question the very process of representation itself. We can include in this category approaches to educational scholarship influenced by poststructuralist theory, postmodern cultural movements, and the ideal of reflexivity. The almost incommensurable differences between these two analytic stances gave rise to mutual commentary and critique that had become well-worn and repetitive. Qualitative methodology literature was in what might be called a rut. Fortunately, frustration with this impasse has inspired what is being called the ontological or onto-ethical turn in qualitative research methodology (Lather, 2006; Jackson & Mazzei, 2012; Rosiek, 2013.) This turn involves more than the mere acknowledgement that every epistemic position involves ontological implications, a well-established premise in the research methodology literature. Instead, it frames the object- and subjectconstituting effects of social inquiry, not as excesses that destabilize the goal of description, but as a new defining purpose of social inquiry in a post-reflexive era. In other words, it seeks a research practice that is ontologically generative and a corresponding practice of normative critique that can help refine the modes of being produced by our inquiry practices. Note that this is not a call for researchers to examine how curriculum generates student identities or coalesces real objects of study. It is instead an examination of the way performances of research itself generates ontological subject- and object-effects. Such methodological considerations have been most vigorously pursued by scholars influenced by Karen Barad s material feminism (Jackson & Mazzei, 2012; MacClure, 2011; de Freitas, 2013), indigenous philosophy (Kovach, 2010; Smith, 1999; Tuck, 2010), contemporary pragmatist philosophy (Koopman, 2011; Rosiek, 2013), and/or arts-based researchers (Chang & Rosiek, 2003; Barone, 2001; Saldana, 2011). Over the last decade, increasing numbers of mathematics education scholars have begun applying reflexive modes of inquiry to math education policy and practice (e.g. Gutierrez, 2010; Lerman 2000; Pais and Valero, 2011; Skovsmose, 2004; Stinson 2010; Valero, 2004). Although the field has been a bit late to the application of poststructuralist theory, it has caught up with the curve relatively quickly, moving quickly to the aforementioned point of frustration that is inspiring the ontological turn in social theory generally (e.g. de Freitas & Sinclair, 2013; Stinson & Bullock, 2012). This conversation will take a step back from the analysis of mathematics policy and practice and focus instead on the implications of the ontological turn in contemporary theory to mathematics education research methodology. Our conversation will invite conjecture about what a deliberatively ontologically generative methodological practice would look like in mathematics education research. We will briefly discuss the relevance of Karen Barad s notion of diffraction and Charles Sanders Peirce s pragmatist semiotics to mathematics education, both of which offer the means for thinking about affect, felt qualities, and ethics as an integral part of knowledge generation. Then we will discuss at length the use of arts-based, narrative, performative, and ceremony-based research practices in mathematics education research. We believe the uniquely abstract (though not immaterial) nature of mathematics subject matter provides unique opportunities to explore the ontologically generative nature of educational research. It is our hope that this conversation will seed more cross-talk between those interested in the ontological turn in qualitative research methodology and those interested in the application of contemporary theory to mathematics education research. Jerry Rosiek, University of Oregon 7

9 Barone, T. (2001). Touching eternity. New York: Teachers College Press. Chang, P., & Rosiek J. (2003). Anti-colonial antinomies: A case of cultural conflict in the high school biology curriculum. Curriculum Inquiry, 33(3), de Freitas, E. (2010). Making mathematics public: Aesthetics as the distribution of the sensible Educational Insights, 13(1). [Available: de Freitas, L & Sinclair, N. (2013). New materialist ontologies in mathematics education: The body in/of mathematics. Mathematics Studies in Education, DOI: /s z. Gutierrez, R. (2010). Introduction to JRME equity special issue: The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 41(0), Jackson, A. Y. and Mazzei, L. A. (2012). Thinking with theory in qualitative research: Viewing data across multiple perspectives. New York, NY: Routledge. Koopman, C. (2011). Genealogical pragmatism: How history matters for Foucault and Dewey. Journal of the philosophy of history, 5(3), Kovach, M. (2009). Indigenous Methodologies: Characteristics, Conversations, and Contexts. Toronto: University of Toronto Press. Lather, P. (2006) Getting lost: Feminist efforts toward a double(d) science. Albany, NY: SUNY Press). Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp ). Westport, CT: Ablex. MacLure, M. (2011); Qualitative inquiry: Where are the ruins? Qualitative Inquiry, 17 (10) Pais, A., & Valero, P. (2011). Beyond disavowing the politics of equity and quality in mathematics education. In B. Atweh, M. Graven, W. Secada & P. Valero (Eds.), Mapping equity and quality in mathematics education (pp ). New York: Springer. Rosiek, J. (2013). Pragmatism and Post-Qualitative Futures. International Journal of Qualitative Research. Saldaña, J. (2011). Ethnotheatre: Research from Page to Stage. Left Coast Press. Smith, L. T. (1999). Decolonizing Methodologies. London: Zed Books. Stinson, D. (2010). Negotiating the White Male Math Myth : African American male students and success in school mathematics. Journal for Research in Mathematics Education, 41(0), Stinson, D. & Bullock, E. (2013). Transitioning into contemporary theory: Critical postmodern theory in mathematics education research. In Van Zoest, L.R., Lo, J. J. & Kratky, J. L. (Eds.). Proceedings of the 34 th annual meeting of the North American chapter of the international group for the psychology of mathematics education. Kalamzoo, MI: Western Michigan University Press. Tuck, E. (2010). Breaking up with Deleuze: Desire and Valuing the Irreconcilable. International Journal of Qualitative Studies in Education 23(5), pp Valero, P. (2004). Socio-political perspectives on mathematics education. In P. Valero & R. Zevenbergen, (Eds.), Researching the socio-political dimensions of mathematics education: Issues of power in theory and methodology. Dordrecht, the Netherlands: Kluwer Academic Publishers. Contact Info: Jerry Rosiek Department of Education Studies College of Education University of Oregon Eugene, Oregon USA jrosiek@uoregon.edu (USA) 8