Acknowledgements: My mentor, Peter Taylor, for their comments and suggestions... 1 Kathmandu University, School of Education on 12/15/2008

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An Auto/ethnography (mainly self study— relationships between ‘small self’ and ‘big self’) Critical mathematics education as a guiding referent A narrative envisioning of culturally contextualised mathematics education An Auto/ethnography (mainly self study— relationships between ‘small self’ and ‘big self’) Critical mathematics education as a guiding referent A narrative envisioning of culturally contextualised mathematics education 4 Kathmandu University, School of Education on 12/15/2008

Initial concept: differences and similarities between Eastern and Western philosophies of mathematics education Envisaged methodology: Philosophical Inquiry Data Sources: Philosophical Texts, philosophers’ perceptions (if possible) But this wouldn’t address the problem of culturally decontextualised mathematics education?? Initial concept: differences and similarities between Eastern and Western philosophies of mathematics education Envisaged methodology: Philosophical Inquiry Data Sources: Philosophical Texts, philosophers’ perceptions (if possible) But this wouldn’t address the problem of culturally decontextualised mathematics education?? Philosophy √ × 5 Kathmandu University, School of Education on 12/15/2008

Preparing for the candidacy proposal: – Main goal: Envisioning a transformative philosophy of mathematics education in Nepal.... – Michael Polyani: tacit knowing, ‘dwelling in’, post-scientific knowing – Thomas Kuhn’s notion of paradigm. – Denzin and Lincoln’s Handbooks (2000, 2005): Narrative knowing – Eastern perspectives: Non/dualism, Self-Inquiry, Personal Spirituality, – My own history as a student, teacher and teacher educator – Auto/ethnography as methodology, emergent inquiry, writing as inquiry, my professional practice as data source, self study –... Preparing for the candidacy proposal: – Main goal: Envisioning a transformative philosophy of mathematics education in Nepal.... – Michael Polyani: tacit knowing, ‘dwelling in’, post-scientific knowing – Thomas Kuhn’s notion of paradigm. – Denzin and Lincoln’s Handbooks (2000, 2005): Narrative knowing – Eastern perspectives: Non/dualism, Self-Inquiry, Personal Spirituality, – My own history as a student, teacher and teacher educator – Auto/ethnography as methodology, emergent inquiry, writing as inquiry, my professional practice as data source, self study –... 6 Kathmandu University, School of Education on 12/15/2008

Doing (the) fieldwork – My professional life history as a field of my research – A short visit during the months of November, 2006 – Mainly collected views of teachers, teacher educators and parents on existing pedagogies of mathematics education in Nepal... Doing (the) fieldwork – My professional life history as a field of my research – A short visit during the months of November, 2006 – Mainly collected views of teachers, teacher educators and parents on existing pedagogies of mathematics education in Nepal... 7 Kathmandu University, School of Education on 12/15/2008

a)Constructing data- texts – Writing autobiographical stories, poems and vignettes on the basis of my experiences as a student, teacher and teacher educator... – Generating personal practical perspectives – Making sketches of possible interpretive perspectives a)Constructing data- texts – Writing autobiographical stories, poems and vignettes on the basis of my experiences as a student, teacher and teacher educator... – Generating personal practical perspectives – Making sketches of possible interpretive perspectives 8 Kathmandu University, School of Education on 12/15/2008

b)Exploring philosophical/cultural theoretical perspectives – Different forms of dialectical reasoning (synthetic, negative, Hegelian, Chinese, Vedic, Buddhist...) – Non-violence as an worldview – Aurobindonian, Wilberian Integralism – Upanishads : Advaita Vedanta — Adi Shankara, Shaddarshan (Mainly Sāṃkhya and Nyāya ) – Madhyamika Buddhism – Nagarjuna (Two-truth theory) – Eastern Poetics – History of Vedic Mathematics (Invention of calculus...) – Vedic Poetry, Sufi Poetry – Hindu and Buddhist vernacular traditions b)Exploring philosophical/cultural theoretical perspectives – Different forms of dialectical reasoning (synthetic, negative, Hegelian, Chinese, Vedic, Buddhist...) – Non-violence as an worldview – Aurobindonian, Wilberian Integralism – Upanishads : Advaita Vedanta — Adi Shankara, Shaddarshan (Mainly Sāṃkhya and Nyāya ) – Madhyamika Buddhism – Nagarjuna (Two-truth theory) – Eastern Poetics – History of Vedic Mathematics (Invention of calculus...) – Vedic Poetry, Sufi Poetry – Hindu and Buddhist vernacular traditions 9 Kathmandu University, School of Education on 12/15/2008

b)Exploring philosophical/ theoretical perspectives Criticalist traditions (situated within Post/modern : Jurgen Habermas, Joe Kincheloe, Peter McLaren, Paulo Friere...) Holism in Biological Sciences and Science and Mathematics Education Critical Spirituality, Futures Studies Complexity Science Non-Euclidean Mathematics Pragmatism (Dewey, Rorty,...) Ethnomathematics and Cultural Perspectives of Science and Mathematics Education Transformative Education Research Different Research Paradigms Arts-Based Research in Education... b)Exploring philosophical/ theoretical perspectives Criticalist traditions (situated within Post/modern : Jurgen Habermas, Joe Kincheloe, Peter McLaren, Paulo Friere...) Holism in Biological Sciences and Science and Mathematics Education Critical Spirituality, Futures Studies Complexity Science Non-Euclidean Mathematics Pragmatism (Dewey, Rorty,...) Ethnomathematics and Cultural Perspectives of Science and Mathematics Education Transformative Education Research Different Research Paradigms Arts-Based Research in Education Kathmandu University, School of Education on 12/15/2008

Chapter Construction Emerging research focus based on my professional experience and readings of different perspectives Construction of datatexts Interpretations and discussions of thematic issue (with reflexivity) Accounting for emergent questions Envisioning of alternatives Boxed texts throughout each chapter Problem Interpretations, conscious textual construction 11 Kathmandu University, School of Education on 12/15/2008

1.Prelude: Methodological Overview 2.Re-conceptualising the Nature of Mathematics for Inclusion and Empowerment: A Dialectical Imagination 3.Dissolving Dualisms: Combining Lived Reality and Fictive Imagination 4.A Performative Inquiry into Meanings and Features of Reductionism 5.Conventional and Additional Logics: Constructing an Inclusive and Transformative Vision of Mathematics Pedagogy 6.A Curriculum Vision for Inclusive Mathematics Education 7.‘What Is Ours and What Is Not Ours?’: Post-Colonial Envisioning of Mathematics Teacher Education. 8.Envisioning an Inclusive Model for Culturally Contextualised Mathematics Education 9.Conclusions 12 Kathmandu University, School of Education on 12/15/2008

Ways of thinking Ways of expressing 13 Kathmandu University, School of Education on 12/15/2008

dualism, narrow scientism, depersonalised writing, control, objectivism Meaning, personalised writing, communicative emphasis Critique of social injustice and hegemony, critical ontology... Difference, pluralism, multiple logics, multiple expressions, subjectivisms Synergy, envisioning, postformal logics, dialectical thinking, inclusive thinking 14 Kathmandu University, School of Education on 12/15/2008

Different ways of expressing (storying, performative writing, poetry, reflective writing, propositional writing...) and thinking (dialectical, metaphorical poetic, narrative, deductive and analytical...); emergent design; diachronic representation; envisioning Control Meaning Critique Pluralism 15 Kathmandu University, School of Education on 12/15/2008

Multiple Research Logics Multiple Research Logics Multiple Research Genres Multiple Research Genres Transformative Education Transformative Education Complexity Science Complexity Science Curriculum Curriculum Embodied knowing Embodied knowing Referents Referents Nature of Mathematics Nature of Mathematics Multiple Research Logics Multiple Research Logics Multiple Research Genres Multiple Research Genres Transformative Education Transformative Education Complexity Science Complexity Science Curriculum Curriculum Embodied knowing Embodied knowing Referents Referents Nature of Mathematics Nature of Mathematics Kathmandu University, School of Education on 12/15/2008

Complexity Science of Emergence Kathmandu University, School of Education on 12/15/2008

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Transformative learning involves experiencing a deep, structural shift in the basic premises of thought, feelings, and actions. It is a shift of consciousness that dramatically and permanently alters our way of being in the world. Such a shift involves our understanding of ourselves and our self-locations; our relationships with other humans and with the natural world; our understanding of relations of power in interlocking structures of class, race, and gender; our body-awareness; our visions of alternative approaches to living; our sense of possibilities for social justice and peace and personal joy. (O’Sullivan, Morrell, & O’Connor, 2002, p.xvii) Transformative learning involves experiencing a deep, structural shift in the basic premises of thought, feelings, and actions. It is a shift of consciousness that dramatically and permanently alters our way of being in the world. Such a shift involves our understanding of ourselves and our self-locations; our relationships with other humans and with the natural world; our understanding of relations of power in interlocking structures of class, race, and gender; our body-awareness; our visions of alternative approaches to living; our sense of possibilities for social justice and peace and personal joy. (O’Sullivan, Morrell, & O’Connor, 2002, p.xvii) How can I transform mathematics education? (reflective, critical and imaginative understanding) How can I transform mathematics education? (reflective, critical and imaginative understanding) HorizonHorizon HorizonHorizon HorizonHorizon HorizonHorizon 20 Kathmandu University, School of Education on 12/15/2008

Butterfly versus caterpillar metaphor Structural shift in thinking and actions Mindful envisioning Trans-formation versus in-formation Understanding the dialectical relationship between ‘small self ‘ (Auto) and ‘big self’ (Ethno) Butterfly versus caterpillar metaphor Structural shift in thinking and actions Mindful envisioning Trans-formation versus in-formation Understanding the dialectical relationship between ‘small self ‘ (Auto) and ‘big self’ (Ethno) 21 Kathmandu University, School of Education on 12/15/2008

Antithesis of the science of equilibrium Non-linear view of world (non- Euclidean view of surface) Non-deterministic modelling Exploration of system behaviour beyond equilibrium states Chaos theory Fuzziology (fuzzy logic ~ Alternative Logics) Poetic thinking/visions (Meteorology) 22 Kathmandu University, School of Education on 12/15/2008

Metaphorical approach (as- though language) versus definitional approach Multi-perspectival view of curriculum through metaphorical images Post/modern view of curriculum (design view versus practitioners’ views) 1 a, b, c, …x, 2 y, z, +, -, x Kathmandu University, School of Education on 12/15/2008

Theory 1(t1 ) Theory 2 (t2) Theory 3 (t3) Theory n+1 (tn+1) Theory n (tn) R,RnC,I,IO, PS R,R+C,I,IO, PS R = Reflexivity of the researcher RnC = Reflective and Critical vision of the researcher I =Imaginative vision of the researcher IO =Inter-Objective knowledge offered by theories PS = Progressive Subjectivity of the researcher t n ’s = Visible theories r = research f = relations of r = f (IS, IT; IS = Invisible Self, IT = Invisible Theory) r = f {(R,t1), (RnC, t1), (I, t1) (IO, t1), (PS,t1), (R, t2), (RnC, t2),...(R, tn), (RnC, tn)...} 24 Kathmandu University, School of Education on 12/15/2008

philosophy as a basis for everyday imagination philosophy for making sense of our professional practice and vice versa philosophy helping us to raise important questions philosophy and lifeworlds philosophy versus Philosophy: openness versus certainty, multiplicities versus singularity, dualistic view versus nondualistic view of practitioners’ philosophies philosophy as a basis for everyday imagination philosophy for making sense of our professional practice and vice versa philosophy helping us to raise important questions philosophy and lifeworlds philosophy versus Philosophy: openness versus certainty, multiplicities versus singularity, dualistic view versus nondualistic view of practitioners’ philosophies 25 Kathmandu University, School of Education on 12/15/2008

Mind in the body and body in the mind views Knowing via actions Knowing through bodily activities—professional practice Connectedness of body and mind Metaphors and physiological process Body as cosmic manifestation (Vedic and Buddhist traditions) Chakras and human body Panchamahabhut, human body and knowing 26 Kathmandu University, School of Education on 12/15/2008

In qualitative research traditions it has been introduced as a quality standard after the onset of the triple crises of representation, legitimacy and praxis (Guba & Lincoln, 2005; Van Manen, 1991). – Does the text sound true according to your experience? – Are educational issues raised by my texts relevant beyond the research context? 27 Kathmandu University, School of Education on 12/15/2008

According to Van Manen, pedagogical thoughtfulness is an act of becoming attentive of and reflective upon those situations which have direct or indirect bearings with education and pedagogy. – To what extent does my text arouse interest in exploring the reader’s pedagogical history? – Does my text provoke readers to reflect upon their pedagogical beliefs and values? 28 Kathmandu University, School of Education on 12/15/2008

The idea of critical reflexivity entails the notion of exposing self as well as being self-conscious of my own (unfolding) subjectivity, thereby being aware of the limitations of my chosen epistemology, methodology and theoretical referents (Denzin, 2003). – Have I exposed enough about myself? – Have I made my theoretical standpoints clear to the reader? – Have I demonstrated my conscious awareness of my own subjectivity? 29 Kathmandu University, School of Education on 12/15/2008

To apply the standard of holism, the researcher needs to take into account possible adversaries, multiplicities and sometime antagonisms inherent in the phenomenon under study. – To what extent does the researcher take into account alternative viewpoints (adversaries)? – To what extent does the researcher unify logic, emotion and imagination so as to generate holistic understanding of issues/phenomena under study? – To what extent is the researcher motivated towards generating wisdom? 30 Kathmandu University, School of Education on 12/15/2008

Luitel, B. C., & Taylor, P. C. (2006). Envisioning transition towards a critical mathematics education: A Nepali educator’s autoethnographic perspective. In J. Earnest & D. F. Treagust (Eds.), Educational Change and Reconstruction in Societies in Transition: International Perspectives (pp ). Rotterdam, The Netherlands: Sense Publishers. Luitel, B. C., & Taylor, P. C. (2007a). Defrosting and re-frosting the ideology of pure mathematics: An infusion of Eastern-Western perspectives on conceptualising a socially just mathematics education. Philosophy of Mathematics Education Journal, 21, Downloadable from: Luitel, B. C., & Taylor, P. C. (2007b). The shanai, the pseudosphere and other imaginings: Envisioning culturally contextualised mathematics education Cultural Studies of Science Education 2(3), Adams, J., Luitel, B. C., Afonso, E., & Taylor, P. C. (2008). FORUM: A cogenerative inquiry using postcolonial theory to envisage culturally inclusive science education. Cultural Studies of Science Education 3(3). 31 Kathmandu University, School of Education on 12/15/2008

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