Culture, Worldview and Transformative Philosophy of Mathematics Education in Nepal

424 Pages·2016·4.57 MB·English

Science and Mathematics Education Centre

Culture, Worldview and Transformative Philosophy of Mathematics
Education in Nepal: A Cultural-Philosophical Inquiry

Bal Chandra Luitel

This Thesis is presented for the Degree of
Doctor of Philosophy
of
Curtin University of Technology

July 2009
Declaration
This thesis contains no material which has been accepted for the award of any other
degree or diploma in any university. To the best of my knowledge belief this thesis
contains no material previously published by any other person or institution except
where due acknowledgement has been made.
 

(Trans: Telling truth is recommended, but more than
that, tell those things which are in the broader interests of
all. For me (i.e., Narada), that which is beneficial to the
large community, is truth. - Mahabharata)

To all known and unknown teachers, gurus, avatars, Buddhas, yogis, sages, philosophers
and unnamed higher spirits (not in a particular order) who bestow knowledge and
wisdoms on me in this life time.


To my parents (father Hari Prasad Luitel and mother Late Pabitra Luitel) whose
ideals of value-based living have been guiding my life along a valuable educational
journey.


To my brother Late Ram Chandra Luitel whose honesty, dedication and educative role

inspired me to be a good teacher.

To my wife, Sabita, whose care, warmth and continuous love and support has made my

‘seeking life’ exciting and rewarding.

To my sons, Bijaya and Binaya, who have important roles to play in their future lives.
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ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my supervisor Associate Professor
Peter Taylor whose collegial academic mentoring led me to such a multifaceted
inquiry that enabled me to be a creative seeker of new knowledge rather than a
reproducer of pre-existing knowledge. Peter’s comments and questions strengthened
further my deeply-seated desire to chart unconventional pathways for making this
research more real, lively and natural.
My sincere thanks go to my co-supervisor Dr. Lily Settelmaier whose critical
comments and questions on issues related to various contemporary issues arising
from Eastern Wisdom Traditions, especially nondualism, integralism and .
A special gratitude to my parents who made me able to see the world in a unique way
that every creature should be treated with care, compassion and sympathy. Although
I could not share this outcome of your education during your physical presence, I
owe you so much Mother and feel that you are always with me!
Many thanks to my parents-in-law, brothers, sisters, sisters-in-law, brothers-in-law,
and other well wishers from my extended family for their continuous moral support
in my studies.
I am also thankful to my wife, Sabita for her enduring support and care, and to my
sons, Bijaya and Binaya, for creating an interactive, lively and homely environment.
My sincere thanks go to Curtin University of Technology for providing the
Endeavour International Postgraduate Research Scholarship (EIPRS) without which
this research might have not been possible. A special thanks to all SMEC staff for
their prompt academic and administrative support whenever sought.
I am also indebted to my students and colleagues in Nepal for sending me relevant
documents and information.
Thanks to all known and unknown well-wishers, friends and colleagues who
contributed to my research directly and indirectly!
.
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ABSTRACT
This thesis portrays my multifaceted and emergent inquiry into the protracted
problem of culturally decontextualised mathematics education faced by students of
Nepal, a culturally diverse country of south Asia with more than 90 language groups.
I generated initial research questions on the basis of my history as a student of
primary, secondary and university levels of education in Nepal, my Master’s research
project, and my professional experiences as a teacher educator working in a
university of Nepal between 2004 and 2006. Through an autobiographical excavation
of my experiences of culturally decontextualised mathematics education, I came up
with several emergent research questions, leading to six key themes of this inquiry:
(i) hegemony of the unidimensional nature of mathematics as a body of pure
knowledge, (ii) unhelpful dualisms in mathematics education, (iii) disempowering
reductionisms in curricular and pedagogical aspects, (iv) narrowly conceived ‘logics’
that do not account for meaningful lifeworld-oriented thinking in mathematics
teaching and learning, (v) uncritical attitudes towards the image of curriculum as a
thing or object, and (vi) narrowly conceived notions of globalisation,
foundationalism and mathematical language that give rise to a decontextualised
mathematics teacher education program.
With these research themes at my disposal my aim in this research was twofold.
Primarily, I intended to explore, explain and interpret problems, issues and dilemmas
arising from and embedded in the research questions. Such an epistemic activity of
articulation was followed by envisioning, an act of imagining futures together with
reflexivity, perspectival language and inclusive vision logics.
In order to carry out both epistemic activities – articulating and envisioning – I
employed a multi-paradigmatic research design space, taking on board mainly the
paradigms of criticalism, postmodernism, interpretivism and integralism. The critical
paradigm offered a critical outlook needed to identify the research problem, to reflect
upon my experiences as a mathematics teacher and teacher educator, and to make my
lifetime’s subjectivities transparent to readers, whereas the paradigm of
postmodernism enabled me to construct multiple genres for cultivating different
aspects of my experiences of culturally decontextualised mathematics education. The
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paradigm of interpretivism enabled me to employ emergence as the hallmark of my
inquiry, and the paradigm of integralism acted as an inclusive meta-theory of the
multi-paradigmatic design space for portraying my vision of an inclusive
mathematics education in Nepal.
Within this multi-paradigmatic design space, I chose autoethnography and small p
philosophical inquiry as my methodological referents. Autoethnography helped
generate the research text of my cultural-professional contexts, whereas small p
philosophical inquiry enabled me to generate new knowledge via a host of innovative
epistemologies that have the goal of deepening understanding of normal educational
practices by examining them critically, identifying underpinning assumptions, and
reconstructing them through scholarly interpretations and envisioning. Visions
cultivated through this research include: (i) an inclusive and multidimensional image
of the nature of mathematics as an im/pure knowledge system, (ii) the metaphors of
thirdspace and dissolution for conceiving an inclusive mathematics education, (iii) a
multilogical perspective for morphing the hegemony of reductionism-inspired
mathematics education, (iv) an inclusive image of mathematics curriculum as
montage that provides a basis for incorporating different knowledge systems in
mathematics education, and (v) perspectives of glocalisation, healthy scepticism and
multilevel contextualisation for constructing an inclusive mathematics teacher
education program.

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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ................................................................................................................ IV
ABSTRACT .................................................................................................................................... V
TABLE OF CONTENTS................................................................................................................... VII
SECTION ZERO: SITUATING MYSELF: RESEARCH AGENDAS AND DESIGN .........................................1
CHAPTER ‐1: ALL THIS BEGAN FROM THERE —ARTICULATING MY RESEARCH PROBLEM...................................... 2
Encountering Foreign Mathematics ............................................................................................. 2
Transition to Meaningless Mathematics ...................................................................................... 5
My Master’s Research Project: A Stepping Stone......................................................................... 6
Post‐Master’s Professional Experience: Déjà vu and Emergent Issues ......................................... 9
Reaching Out to the Field: Interacting with My Research Agendas............................................ 13
Chapter Summary ....................................................................................................................... 23
CHAPTER 0: PLANNING THE JOURNEY: MEDIATING THE UN/MEDIATED........................................................... 24
Introduction ................................................................................................................................ 24
Multi‐Paradigmatic Design Space............................................................................................... 24
Research Methodology ............................................................................................................... 35
Imagining as Epistemic Technique.............................................................................................. 40
Theories as Referents.................................................................................................................. 46
Evidence as Cultural Construction .............................................................................................. 47
Multiple Research Logics ............................................................................................................ 48
Multiple Research Genres ........................................................................................................... 50
Quality Standards ....................................................................................................................... 53
Ethical Obligations...................................................................................................................... 56
Formation of Sections and the Structure of My Thesis ............................................................... 59
Section Summary ........................................................................................................................ 62
SECTION ONE: ENVISIONING A MULTIDIMENSIONAL NATURE OF MATHEMATICS FOR INCLUSION 
AND EMPOWERMENT..................................................................................................................63
Orientation.................................................................................................................................. 63
EPISODE I (OR CHAPTER 1): THE NATURE OF MATHEMATICS AS A BODY OF PURE KNOWLEDGE IS NOT INCLUSIVE . 67
Act 1: Experiencing a Fractured Worldview I .............................................................................. 67
Act 2: Experiencing a Fractured Worldview II ............................................................................. 71
Act 3: Experiencing a Fractured Worldview III ............................................................................ 74
Act 4: Prologue ........................................................................................................................... 77
Act 5: Ideology of Singularity ...................................................................................................... 79
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Act 6: Epistemology of Objectivism ............................................................................................ 82
Act 7: Language of Universality .................................................................................................. 85
Act 8: Logic of Certainty.............................................................................................................. 87
EPISODE II (OR CHAPTER 2): NOR IS THE NATURE OF MATHEMATICS AS IMPURE KNOWLEDGE INCLUSIVE............. 91
Act 1: Experiencing a Fractured Worldview IV............................................................................ 91
Act 2: Experiencing a Fractured Worldview V............................................................................. 95
Act 3: Prologue ........................................................................................................................... 97
Act 4: Potentially a Disempowering Notion of Culture ............................................................... 99
Act 5: Yet another Metonymic Hegemony................................................................................ 102
Act 6: Unhelpful Dualisms......................................................................................................... 104
EPISODE III (CHAPTER 3): MATHEMATICS AS AN IM/PURE KNOWLEDGE SYSTEM:  AN EMPOWERING VISION FOR 
INCLUSIVE MATHEMATICS EDUCATION ................................................................................................... 108
Act 1: Prologue ......................................................................................................................... 108
Act 2: Exploring Different Forms of Dialectical Logic ................................................................ 109
Act 3: Transforming ‘Pure versus Impure Mathematics’ to Im/Pure Mathematics .................. 116
Act 3: Im/Pure Knowledge System and its Possible Implications.............................................. 120
Recapitulating the Present, Mapping the Futures .................................................................... 123
SECTION TWO: DISSOLVING DUALISMS: SEARCHING FOR INCLUSIVE ALTERNATIVES ..................125
Orientation................................................................................................................................ 125
CHAPTER 4: PRELUDE TO DUALISM: MEANINGS, SOURCES AND IMPACTS...................................................... 127
Capturing a Moment with Mr. Stiff .......................................................................................... 127
Prologue.................................................................................................................................... 128
Constructing Meanings of Dualism........................................................................................... 129
Identifying Unhelpful Dualisms................................................................................................. 133
CHAPTER 5: IMAGINING LIVES UNDER DUALISM: A ‘LINELAND’ METAPHOR .................................................. 138
Enter Mr. Stiff’s Sacred Diary Page!.......................................................................................... 138
Prologue.................................................................................................................................... 138
The Not‐Known Recipient ......................................................................................................... 139
A Peripheral Authority .............................................................................................................. 141
A Reproducer of Status‐Quo ..................................................................................................... 142
CHAPTER 6: RESOLVING AND DISSOLVING DUALISMS: THINKING IN‐BETWEEN AND BEYOND............................ 145
Stuff Them Insofar As You Can! ................................................................................................ 145
Prologue.................................................................................................................................... 147
The Thirdspace Metaphor......................................................................................................... 147
The Dissolution Metaphor ........................................................................................................ 151
Recapitulating the Present, Mapping the Futures .................................................................... 154
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SECTION THREE: SURGERY ON REDUCTIONISM: A JOURNEY FROM ‘T/HERE’ ..............................156
Orientation................................................................................................................................ 156
EPISODE I (OR CHAPTER 7): EXPLORING MEANINGS OF REDUCTIONISM FROM WITHIN AND OUTSIDE................. 159
Act 1: Precise Curriculum, Short‐Cut Method and Standard Evaluation................................... 159
Act 2: Prologue ......................................................................................................................... 163
Act 3: Encountering Reductionism as Ideology......................................................................... 164
Act 4: Touring with Reductionism as Methodology.................................................................. 168
Act 5: Experiencing Reductionism as Logic ............................................................................... 173
Act 6: Understanding Reductionism through History ............................................................... 178
Act 7: Conclusions ..................................................................................................................... 182
EPISODE II (OR CHAPTER 8): DELVING INTO KEY TYPES OF REDUCTIONISM .................................................... 183
Act 1: Finally, The Monotonous Class Is Over! ................................................................................i
Act 2: Prologue ......................................................................................................................... 186
Act 3: Systemic Reductionism ................................................................................................... 187
Act 4: Curricular Reductionism ................................................................................................. 191
Act 5: Pedagogic Reductionism................................................................................................. 195
Act 6: Evaluative Reductionism................................................................................................. 200
Recapitulating the Present, Mapping the Futures .................................................................... 206
SECTION FOUR: ‘OLD’ AND ‘NEW’ LOGICS: CONSTRUCTING AN INCLUSIVE AND TRANSFORMATIVE 
VISION OF MATHEMATICS PEDAGOGY.......................................................................................208
Orientation................................................................................................................................ 208
CHAPTER 9: RADICALISING MATHEMATICS EDUCATION, BUT WITH OLD LOGICS ............................................ 211
Farewell to Euclid and Pythagoras: Mathematics Is Not A Universal Knowledge System!....... 211
Prologue.................................................................................................................................... 215
Constructing Meanings of Old Logics ....................................................................................... 216
Constructing Unhelpful Features of Old Logics ......................................................................... 221
CHAPTER 10: JOURNEYING WITH NEW LOGICS: CREATING TRANSFORMATIVE AND INCLUSIVE PEDAGOGIES ......... 230
Pythagoras And Euclid Are Still Useful!..................................................................................... 230
Prologue.................................................................................................................................... 233
Metaphorical Logic ................................................................................................................... 234
Poetic Logic............................................................................................................................... 239
Dialectical Logic ........................................................................................................................ 245
Narrative Logic.......................................................................................................................... 250
Recapitulating the Present, Mapping the Futures .................................................................... 254
SECTION FIVE: A CURRICULUM VISION FOR INCLUSIVE MATHEMATICSM EDUCATION................256
Orientation................................................................................................................................ 256
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CHAPTER 11:  UNPACKING THE TRIVIA OF EXCLUSIVE ‘MODERNIST’ CURRICULUM PRACTICES ........................... 259
I Want Proof, Can You Give Me One? ....................................................................................... 259
Encountering the Equilibrium View of Reality........................................................................... 265
Pondering about Language and Thinking................................................................................. 267
Detouring to Knowledge and Knowing ..................................................................................... 272
Critiquing the Mono‐Cultural Perspective................................................................................. 274
CHAPTER 12: APPRAISING MY ROLE AS A CURRICULUM COMMITTEE MEMBER: MAKING SENSE OF SITUATEDNESS .. 277
Devil’s Advocate: I Have Questions And Critiques! ................................................................... 277
Complexity in Context ............................................................................................................... 281
Transformative Aspirations and Actions................................................................................... 285
Delving into Multiple Images of Curriculum ............................................................................. 287
Featuring Un/Sustainable Logics of Practice ............................................................................ 291
CHAPTER 13: CONSTRUCTING A TRANSFORMATIVE CURRICULUM VISION: PLURALISM, SYNERGY AND MONTAGE. 294
Context Matters, Can You Suggest Some Visions For Nepali Mathematics Curriculum?.......... 294
Inclusive Worldviews and Visions ............................................................................................. 297
Additional‐Inclusive Logics........................................................................................................ 305
Holonic‐Inclusive Language ...................................................................................................... 308
Multiple Curriculum Images and the Meta‐Image.................................................................... 309
Structure and Agency Dialectic ................................................................................................. 312
Recapitulating the Present, Mapping the Futures .................................................................... 315
SECTION SIX: ‘WHAT IS OURS AND WHAT IS NOT OURS?’ ‐‐ INCLUSIVE IMAGININGS OF 
CONTEXTUALISED MATHEMATICS TEACHER EDUCATION ...........................................................317
Orientation................................................................................................................................ 317
CHAPTER 14: FAREWELL TO UNHEALTHY GLOBALISATION: IMAGINING AN INCLUSIVE GLOBALISATION ............... 321
Being There: We Need A Globally Justifiable Teacher Education! ............................................ 321
Being Here: We Need Globalisation, But The Empowering One!.............................................. 324
Critiquing Disempowering Globalisation .................................................................................. 324
Comprador Intelligentsia OR Transformative Attitude? ........................................................... 330
Glocalisation: A Transformative Vision for an Inclusive Teacher Education ............................. 334
CHAPTER 15: DECONSTRUCTING FOUNDATIONALISM: PROPOSING A HEALTHY SCEPTICISM FOR INCLUSIVE 
MATHEMATICS TEACHER EDUCATION..................................................................................................... 338
Being There: Follow The Foundation Of Mathematics Education! ........................................... 338
Being Here: Let Us Question The Indubitable Foundation!....................................................... 341
Welcome Healthy Scepticism.................................................................................................... 342
Deconstructing Decontextualisation......................................................................................... 346
Altering Mimetic and Transmissionist Pedagogies................................................................... 348
CHAPTER 16: NO TO EXCLUSIONARY VIEWS: IMAGINING INCLUSIVE MATHEMATICS TEACHER EDUCATION .......... 352
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