1. 1 Research with multiple epistemic metaphors: Searching for wisdom in science and mathematics education research Bal Chandra Luitel Kathmandu University, Nepal Peter Charles Taylor Curtin University of Technology, Australia Presented at the Annual Conference of Australasian Science Education Research Association (11th - 14th July 2007): Fremantle, Western Australia

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3. 3 This presentation includes My ongoing doctoral researchMy ongoing doctoral researchMy ongoing doctoral researchMy ongoing doctoral research Illustrate use of alternative logicsIllustrate use of alternative logics –Metaphor Metaphor –Dialectical logic Dialectical logicDialectical logic –Poetic logic Poetic logicPoetic logic –Narrative logic Narrative logicNarrative logic –Vision logic Vision logicVision logic –Non/dual logic Non/dual logicNon/dual logic ConclusionConclusionConclusion

4. 4 My doctoral research Title: Culture, Worldview and Transformative Philosophy of Mathematics Teacher Education in Nepal: A Cultural-Philosophical Inquiry Inquiry Agendas In what ways are the Western Mathematical Worldview and Nepali Worldview similar and different in terms of their epistemologies and ontologies? In what ways can wisdom traditions of the East (e.g. Hinduism and Buddhism) contribute to the development of an alternative philosophy of mathematics teacher education in Nepal? How can mathematical knowledge for teacher education in Nepal be made holistic, ecologically balanced and discursive? What can a transformative philosophy of mathematics teacher education be for Nepal?

5. 5 My doctoral research Research Paradigms: Post-modern and Integral Methodology: Arts-based auto/ethnogra phy Owing to the nature of my inquiry, I cannot rely on only propositional, deductive and rational-analytical logics of positivism. Therefore, I need to cultivate alternative logics which help me to unpack various facets of the holistic (socio-cultural and spiritual) nature of mathematics education, thereby helping me to be a wise teacher educator.

6. 6 Metaphor Poetic logic Dialectics Non/dual logic Vision logic Narrative logic Alternative logics

7. 7 Metaphor According to Lakoff and Johnson (1980, p.5):According to Lakoff and Johnson (1980, p.5): metaphor is understanding and experiencing one kind of thing in terms of another Examples: Life as journey, learning as constructing, conversing as languagingExamples: Life as journey, learning as constructing, conversing as languaging Benefit: A tool for exploring multiple meanings and perspectivesBenefit: A tool for exploring multiple meanings and perspectives

8. 8 Metaphors Epistemic metaphors help me to embrace multiple ways of knowing/inquiry: knowing as storying, inquiry as currere, knowing as reconceptualising self, knowing as generating wisdom, inquiry as talking to heart, knowing as creating, knowing as being (Miller, Karsten, Denton, Orr, & Kates, 2005).Epistemic metaphors help me to embrace multiple ways of knowing/inquiry: knowing as storying, inquiry as currere, knowing as reconceptualising self, knowing as generating wisdom, inquiry as talking to heart, knowing as creating, knowing as being (Miller, Karsten, Denton, Orr, & Kates, 2005). I have used metaphor as a tool for exploring different images of mathematics that I have experienced as a student, teacher, teacher educator and researcher (Luitel & Taylor, in prep a).I have used metaphor as a tool for exploring different images of mathematics that I have experienced as a student, teacher, teacher educator and researcher (Luitel & Taylor, in prep a).

9. 9 Example “After leaving my brief career as a tutor in a teacher education college, I joined the University of Himalaya as a mathematics teacher trainer. While working with teachers of semi-rural schools, I continued to develop many (helpful) images of mathematics as storytelling, mathematics as cultural enactment and mathematics as languaging.” (Luitel & Taylor, in prep a)

10. 10 Dialectical logic Triad/process: Thesis, Antithesis and SynthesisTriad/process: Thesis, Antithesis and Synthesis Opposites (A and ~A) co-exist within the same phenomenonOpposites (A and ~A) co-exist within the same phenomenon Conflict and contradiction is normalConflict and contradiction is normal Change is an internal process based on internal contradictions /frictionChange is an internal process based on internal contradictions /friction Change is the unity of oppositesChange is the unity of opposites Dialectical thinking is about looking for dynamic alternatives and widening one’s horizonDialectical thinking is about looking for dynamic alternatives and widening one’s horizon Promotes the notion of interdependence of oppositesPromotes the notion of interdependence of opposites (Wong, 2006)

11. 11 Example “We wish to make clear that our intention is not to reject conventional images of mathematics. Rather we subscribe to the integral perspective of de/contextualisation which represents a dialectical relationship between alternative and conventional images of mathematics. At times it might be ok to teach ‘as though’ (i.e., metaphorically) mathematics is universalist in nature by, for example, focussing exclusively on manipulation of abstract symbolic expressions, whereas at other times and in other contexts it might be better for an alternative pedagogical focus.” (Luitel & Taylor, 2007, p.13)

12. 12 Poetic logic helps express layered meanings जहाँ पुग्दैनन रवी त्यहाँ पुग्छन कवी ! “a poet is able to reach the unreachable!” has the power to de-familiarize one’s experiences helps cultivate aesthetic aspects of inner self(s) and exterior realities can help magnify my understanding of issues under study (Cahnmann, 2003; Faulkner, 2007; Sri Aurobindo, 1972)

13. 13 Example He Never Quoted His Father He produced a lecture. He told us mathematics is difficult. He positioned himself up there. He looked at us down here. He symbolised us as subjects. He quoted Western mathematicians. He never quoted his parents. He …

14. 14 Narrative logic Narrative logic promotes: knowing as storying -- narrative truthknowing as storying -- narrative truth diachronic (emergent) representational stylediachronic (emergent) representational style fragmented knowledgefragmented knowledge performance of possibilitiesperformance of possibilities personal voice and sustainability (reflectivity and reflexivity)personal voice and sustainability (reflectivity and reflexivity) crystallization – ‘moving from plane geometry to light theory’– in my textual creationcrystallization – ‘moving from plane geometry to light theory’– in my textual creation (Ellis & Bochner, 2000; Richardson & St. Pierre, 2005)

15. 15 Example I “I crossed many minor and major borders while conducting this research. In the beginning, it was a shift from knowing as probing to knowing as storying and reflecting. Even after subscribing to such an epistemological standpoint, I tried initially to use a traditional epistemic structure for my research. However, as I moved towards the process of writing the research proposal and preliminary chapters, I realised that the traditional five-chapter structure does not help promote the notion of research as an emergent and evolving enterprise.” (Luitel, 2003, p.117)

16. 16 Example II “Working with senior professors, who seemed to regard designing a mathematics teacher education program as though a mixmaking of ‘pure mathematics’ courses and education courses, put me in a dilemma because of not being able to fully translate my vision of culturally contextualised mathematics education. I could see that the déjà vu of mathematics-is-a- foreign-subject was occurring all over again as my colleagues put renewed emphasis on the same heartless and soulless mathematics that I aimed to refurbish. What does it mean to transform mathematics education in Nepal? Does it mean to promote unquestioningly the image of mathematics as a foreign subject? Does this mean to neglect the diverse cultural-rural realities of Nepal by its mathematics education programs?” (Luitel & Taylor, in prep a)

17. 17 Vision logic Vision logic enables me to: –develop a perspectival view of the field of mathematics education –embrace and apply a futuristic approach to my textual creation –cultivate an holistic view of (mathematics) education –look for possibilities –cultivate critical, reflexive, reflective and imaginative thinking –operate through the principles of freedom, creativity and uniqueness. (Aurobindo, 1998; Chaudhuri, 1972; Wilber, 1996)

18. 18 Example “Primarily, we envision that teachers working within the context of culturally contextualised mathematics education endeavour to generate meanings of alternative natures of mathematics. Subscribing to the metaphor of teacher as awakened facilitator, they will recognise students’ cultural and individual differences, promote inclusive participation of students, create a caring and collaborative learning environment, thereby promoting meaningful mathematical acculturation by which students often cross the two-way borders of local and formal mathematics. Engaged in exploring connections between formal and informal mathematics, we would see Nepali students a) co-generating mathematics from their cultural contexts; b) linking their cultural experiences with formal mathematics; c) developing local classifications of mathematical ideas, based on their uses in local cultural contexts; and d) solving real world problems by using different forms of mathematics.” (Luitel & Taylor, in prep b)

19. 19 Logic of Non/dualism The logic of non/dualism helps me to: –explore an inclusive view of my identity –critique and transcend unhelpful dichotomies promoted by the modernist and dualist worldview –envision an integral (and de/contextualized) view of mathematics education through multiple and often contradictory natures of mathematics. Nagarjuna: Without relation to good there is no bad, in dependence on which we form the idea of good. Therefore good is unintelligible. There is no good unrelated to bad; yet we form our idea on bad in dependence on it. There is therefore no bad. (Cited in Loy, 1997)

20. 20 By the help of ‘Self’ I explain ‘Other’ Fusing Self and Other I generate a vision of Self-Other. Some people say: Self-Other is not ‘Self’ Because it has Other within it. Self-Other is not ‘Other’ Because it has Self within it. But I say: Self-Other is also Self Because it is inclusive of Other Self-Other is also Other Because it is inclusive of Self. I start with two: Self and Other. They become three: Self, Self-Other and Other. Indeed, they are many as facets of the Being which I aim to attain! Does this mean that I will be a wise teacher educator? conclusion… just for now

21. 21 List of references Cahnmann, M. (2003). The craft, practice, and possibility of poetry in educational research. Educational Researcher, 32(3), 29-36. Ellis, C., & Bochner, A. (2000). Autoethnography, personal narrative, reflexivity: Researcher as subject. In N. Denzin & Y. Lincoln (Eds.), The handbook of qualitative research (2nd ed., pp. 733-768). Thousand Oaks, CA: Sage. Faulkner, S. L. (2007). Concern with craft: Using Ars Poetica as criteria for reading research poetry. Qualitative Inquiry, 13(2), 218-234. Loy, D. (1997). Nonduality : A study in comparative philosophy. Atlantic Highlands, N.J.: Humanities Press. Luitel, B. C. (2003). Narrative explorations of Nepali mathematics curriculum landscapes: An epic journey Unpublished Master's Project, Curtin University of Technology, Perth: Downloadable from http://pctaylor.comhttp://pctaylor.com Luitel, B. C., & Taylor, P. (2007/in press). The shanai, the pseudosphere and other imaginings: Envisioning culturally contextualised mathematics education Cultural Studies of Science Education 2(2). Luitel, B. C., & Taylor, P. (in preparation (a)). Blending inside-out and outside-in: An holistic approach to sustainable mathematics education Luitel, B. C., & Taylor, P. (in preparation (b)). Defrosting the ideology of pure mathematics: Social justice and contextualisation imperatives in mathematics education. Philosophy of Mathematics Education. Miller, J. P., Karsten, S., Denton, D., Orr, D., & Kates, I. C. (Eds.). (2005). Holistic learning and spirituality in education : breaking new ground. Albany, NY: State University of New York Press. Richardson, L., & St Pierre, E. (2005). Writing: a method of inquiry. In N. Denzin & Y. Lincoln (Eds.), The Sage handbook of qualitative research (3rd ed., pp. 959-578). Thousand Oaks: Sage. Sri Aurobindo. (1972). Collected poems. Twin Lakes, WI: Lotus Press. Available Online http://www.poetseers.org/the_poetseers/sri_aurobindo/sritwo/ascent. http://www.poetseers.org/the_poetseers/sri_aurobindo/sritwo/ascent Sri Aurobindo. (1998). Supramental manifestation and other writings (2nd ed.). Twin Lakes, WI: Lotus Press Wilber, K. (1996). A brief history of everything (1st ed.). Boston: Shambhala. Wong, W.-c. (2006). Understanding dialectical thinking from a cultural-historical perspective. Philosophical Psychology, 19(2), 239-260.