Demathematising Mathematics: Experiences from the field

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

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• Experiences from the field

• My evolving ontology epistemology and methodology

• My evolving research foci • My proposed chapter plan


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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 )


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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


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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


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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


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Some selected nodal moments (i) • Communication is a problem sir! … is good with

seniors but not open with students.• …sir is changing gradually.• Harsh email 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’


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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?


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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)


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• 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)


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The Mandala Model• The pedagogical axis

Constructionist, Meaningful, open inquiry, communicative, emancipatory

CP

IP Instructionist, Reproductive,

individualistic, ritualistic, rationalistic, closed inquiry


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My ontology, epistemology and

methodology


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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


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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)


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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


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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.


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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?


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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?


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My chapter plan (i) Proposed Chapter Title Possible

theoretical referents

Research foci

Data sources

1. Defrosting the epistemology of mathematics: Three stories in five months

Non/dualism

Philosophy of mathematics, Constructivism

1, 4 2004: 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, 5 Mid-2004 to End of 2004: working with NCED, Launching One-year Teacher Ed. Program @KU


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My chapter plan (ii)

Proposed Chapter Title Possible 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

1,3 Mid-2004 Mid -2005: Teaching One year Teacher Ed. Program @KU

4. Philosophy and mathematics: How do you combine?

Natures of mathematics

Non/dualism

Magical realism

1,2,4 2005: Designing 2-Year Teacher Ed. Program


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My chapter plan (iii) Proposed Chapter Title Possible 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

1,2,3 2005: 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

5,6 2006: Teaching M Ed students


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My chapter plan (iv) Proposed Chapter Title Possible theoretical


Data sources

7. Demathematizing Mathematics: Experiences from the field

Non/dualism

Critical mathematics education, integral philosophy

1,2,3,4,5 Nov 2006 to Feb 2007: Fieldwork

8. Envisioning a transformative mathematics teacher education in Nepal

Non/dualism

Critical mathematics education, integral philosophy,

THE MANDALA MODEL

2,5,6 Nov 2006 to Feb 2007: Fieldwork


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My chapter plan Proposed Chapter Title Possible theoretical


Data sources

9. My journey of ‘being’ and becoming a mathematics teacher educator

Non/dualism

Radical constructivism

Transformative education

Critical reflexivity

5,6 --2008: My biography as a teacher educator

10. Charting the inquiry process: My learning and findings

Non/dualism

Critical reflexivity

3,6 --2008

My experience of conducting this inquiry, previous chapters


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…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

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Demathematising Mathematics: Experiences from the field