Demathematising Mathematics: Experiences from the field Bal Chandra Luitel SMEC, Curtin University of Technology Acknowledgements: My supervisor Prof. Peter Taylor, Associate Supervisor Dr. Elisabeth Settelmaier and my research participants in Nepal.

Bal Chandra Luitel, SMEC Curtin University of Technology 2 Experiences from the field My evolving ontology epistemology and methodologyMy evolving ontology epistemology and methodology My evolving research foci My proposed chapter plan

Bal Chandra Luitel, SMEC Curtin University of Technology 3 Interview: General information Interview participants: teachers, postgraduate students, teacher educators and curriculum experts. Recorded interviews of about 30 hours. Interview as conversation, exchange and sharing (Ellis & Berger, 2003; Holstein & Gubrium, 2003; Kvale, 1996 )

Bal Chandra Luitel, SMEC Curtin University of Technology 4 Selected Emerging themes (i) Different perceptions about the nature of mathematics Role of mathematics in national development Restructuring of mathematics curricula in accordance with mathematics education for all Connection between mathematical knowledge and ‘labour’ Developing/producing mathematics teacher with the vision of inclusive education

Bal Chandra Luitel, SMEC Curtin University of Technology 5 Selected Emerging themes (ii) Cultural contextualisation of mathematics education Nature of mathematical learning Biographies of interviewees pertaining to their experiences as students and teachers of mathematics Integrating mathematics with other subject areas Social construction of mathematical knowledge Mathematics, local languages and medium of instruction Mathematics and the world of work

Bal Chandra Luitel, SMEC Curtin University of Technology 6 Selected Emerging themes (iii) Ideological baggage of ‘pure mathematics people’ Education faculty’s role: What, how, why and when of mathematics Politics within mathematics: Example of Leibniz and Newton, Example of patenting eastern knowledge by some American companies Making mathematics curriculum meaningful: Bottom-up approach, praxis-oriented designs Linking academic world of mathematics education with the world of school Mathematics education in non-formal setting

Bal Chandra Luitel, SMEC Curtin University of Technology 7 Some selected nodal moments (i) Communication is a problem sir! … is good with seniors but not open with students. …sir is changing gradually. Harsh for professional development Timeline, project and material write-ups We all are subalterns in her class. This is the American system. Computer application and ethnomathematics Do you also teach content or only pedagogical ‘soft’ courses? We need a frame, structure and product. You are like a dictator! Looking into my ‘selves’

Bal Chandra Luitel, SMEC Curtin University of Technology 8 Some selected nodal moments (ii) School is a source of hierarchy! We need to restructure the feudal legacy in (mathematics) education. Math is math… you cannot localise it. The data, student (dis)satisfaction and my worry Culture? We need to get rid of it. Dr. America and myself Mathematics and culture: I am getting puzzled I am not happy with the grade you gave me! Why are you so critical about Algebra and Analysis? Do I need to study Algebra and Analysis here?

Bal Chandra Luitel, SMEC Curtin University of Technology 9 Some Examples of mathematical activities: UNESCO Report Math in khole (gruel making process) Math in Chyang making Process Math in Chheki Khel Math in squash Kheti Math in making Makaiko Jhutto (bunch of Maize) Math in selling Milk Math in Measuring the food grains from field Math in Total households in the village/total numbers of persons in the village Maths in Doko (Wicker basket)

Bal Chandra Luitel, SMEC Curtin University of Technology 10 The Mathematical Axis The Mandala Model (Taylor, Luitel, Belbase & Pokhrel, 2006) Decontextualised, shallow, superficial, formal, pure, algorithmic ( DCM) Contextualised, deep, informal, embodied, verbal, practical, artefactual (CM)

Bal Chandra Luitel, SMEC Curtin University of Technology 11 The Mandala Model The pedagogical axis Constructionist, Meaningful, open inquiry, communicative, emancipatory CP IP Instructionist, Reproductive, individualistic, ritualistic, rationalistic, closed inquiry

Bal Chandra Luitel, SMEC Curtin University of Technology 12

Bal Chandra Luitel, SMEC Curtin University of Technology 13 My ontology, epistemology and methodology

Bal Chandra Luitel, SMEC Curtin University of Technology 14 My ontology, epistemology and methodology (i) Ontology: What is reality? The world out there or the world inside my mind? Or both in a dialectical relationship? Where is the self that aims to claim to know? –Non/dual view of the world (Loy, 1997; Radhakrishnan, 1923; Wilber, 1996) I/Self + External Realities External Realities

Bal Chandra Luitel, SMEC Curtin University of Technology 15 My evolving ontology, epistemology and methodology (ii) self  --culturally embedded self --  culture self  --self that interprets other ---  other (Co-self and co-other) autobiography   ethnography autoethnography (Afonso & Taylor, in press; Roth, 2005)

Bal Chandra Luitel, SMEC Curtin University of Technology 16 My evolving ontology, epistemology and methodology (iii) Quality criteria: –The triple crisis: Crisis of representation, legitimacy and praxis –Art-based criteria: playfulness, verisimilitude, multiple textualities –Pedagogical criteria: pedagogical thoughtfulness and wakefulness

Bal Chandra Luitel, SMEC Curtin University of Technology 17 My evolving ontology, epistemology and methodology (iv) Transformation of conversation, reflective and other field-based texts into performance texts - poetic, storied, phenomenal and so forth. Generation of ‘data texts’ and interpretive texts (Taylor & Luitel, 2006; Luitel, in press). Organising them into chapters on the basis of the growth of my inquiry.

Bal Chandra Luitel, SMEC Curtin University of Technology 18 Research foci (i) 1.Which philosophies have been governing the existing Mathematics Teacher Education programs in Nepal? 2.In what ways are the Western Mathematical Worldview and Nepali Worldview similar and different in terms of their epistemologies and ontologies? 3.In what ways can nondual traditions of the East (Vedanta and Buddhism) contribute to the development of an alternative philosophy of mathematics teacher education in Nepal?

Bal Chandra Luitel, SMEC Curtin University of Technology 19 Research foci (ii) 4.What are alternative ways of knowing mathematics in my cultural context? How can those ways be brought into mainstream teacher education? 5.How can mathematical knowledge for teacher education in Nepal be made holistic, ecologically balanced, discursive and socially responsible? 6.What can a transformative philosophy of mathematics teacher education be for Nepal?

Bal Chandra Luitel, SMEC Curtin University of Technology 20 My chapter plan (i) Proposed Chapter TitlePossible theoretical referents Research foci Data sources 1.Defrosting the epistemology of mathematics: Three stories in five months Non/dualism Philosophy of mathematics, Constructivism 1, 42004: Feb to July: experience of working as a researcher at KU 2. Living with Pavlov: Teacher Training versus Teacher Development Reflective practice, non/dualism, constructivism and integral perspective 1, 2, 5Mid-2004 to End of 2004: working with NCED, Launching One- year Teacher Ed.

Bal Chandra Luitel, SMEC Curtin University of Technology 21 My chapter plan (ii) Proposed Chapter TitlePossible theoretical referents Research foci Data sources 3. More content, better teacher: My dilemma of designing teacher education courses Philosophy of mathematics and education Non/dualism 1,3Mid-2004 Mid -2005: Teaching One year Teacher Ed. 4. Philosophy and mathematics: How do you combine? Natures of mathematics Non/dualism Magical realism 1,2,42005: Designing 2- Year Teacher Ed. Program

Bal Chandra Luitel, SMEC Curtin University of Technology 22 My chapter plan (iii) Proposed Chapter TitlePossible theoretical referents Research foci Data sources 5. Educatising mathematicians: my quest for developing a teacher education program Integral pedagogy Natures of mathematics Philosophy of mathematics 1,2,32005: Developing 2-Year Teacher Ed. Program 6. Paul Ernest, D’Ambrosio and Peter Taylor: Why do you choose these names? Social constructivism, ethnomathematics and critical mathematics education 5,62006: Teaching M Ed students

Bal Chandra Luitel, SMEC Curtin University of Technology 23 My chapter plan (iv) Proposed Chapter TitlePossible theoretical referents Research foci Data sources 7. Demathematizing Mathematics: Experiences from the field Non/dualism Critical mathematics education, integral philosophy 1,2,3,4,5Nov 2006 to Feb 2007: Fieldwork 8. Envisioning a transformative mathematics teacher education in Nepal Non/dualism Critical mathematics education, integral philosophy, THE MANDALA MODEL 2,5,6Nov 2006 to Feb 2007: Fieldwork

Bal Chandra Luitel, SMEC Curtin University of Technology 24 My chapter plan Proposed Chapter TitlePossible theoretical referents Research foci Data sources 9. My journey of ‘being’ and becoming a mathematics teacher educator Non/dualism Radical constructivism Transformative education Critical reflexivity 5, : My biography as a teacher educator 10. Charting the inquiry process: My learning and findings Non/dualism Critical reflexivity 3, My experience of conducting this inquiry, previous chapters

Bal Chandra Luitel, SMEC Curtin University of Technology 25 …Finally S/he says ‘Oh mathematics! I never liked its tricks. I always wished to know. My teacher wanted me to ‘rote’ and go. I didn’t know where. I was still there. My teacher was also still there. We all were there. No one was moving but mathematics with its self-referential hoax of pure logic.’ Not really