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Research with multiple epistemic metaphors: Searching for wisdom in science and mathematics education research

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Title: Research with multiple epistemic metaphors: Searching for wisdom in science and mathematics education research


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
2
(No Transcript)
3
This presentation includes
  • My ongoing doctoral research
  • Illustrate use of alternative logics
  • Metaphor
  • Dialectical logic
  • Poetic logic
  • Narrative logic
  • Vision logic
  • Non/dual logic
  • Conclusion

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
My doctoral research
  • Research Paradigms Post-modern and Integral
  • Methodology Arts-based auto/ethnography

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
Alternative logics
7
Metaphor
  • 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 languaging
  • Benefit A tool for exploring multiple meanings
    and perspectives

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).
  • 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
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
Dialectical logic
  • Triad/process Thesis, Antithesis and Synthesis
  • Opposites (A and A) co-exist within the same
    phenomenon
  • Conflict and contradiction is normal
  • Change is an internal process  based on internal
    contradictions /friction
  • Change is the unity of opposites  
  • Dialectical thinking is about looking for dynamic
    alternatives and widening ones horizon
  • Promotes the notion of interdependence of
    opposites
  • (Wong, 2006)

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
Poetic logic
  • helps express layered meanings
  • ???? ???????? ??? ?????? ?????? ??? !
  • a poet is able to reach the unreachable!
  • has the power to de-familiarize ones 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
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
Narrative logic
  • Narrative logic promotes
  • knowing as storying -- narrative truth
  • diachronic (emergent) representational style
  • fragmented knowledge
  • performance of possibilities
  • personal voice and sustainability (reflectivity
    and reflexivity)
  • crystallization moving from plane geometry to
    light theory in my textual creation
  • (Ellis Bochner, 2000 Richardson St.
    Pierre, 2005)

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
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-subje
    ct 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
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
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
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
conclusion just for now
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?
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.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_aurobin
    do/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.
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