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Dissolving Dualisms?Combining Lived Reality
and Fictive Imagination
Bal Chandra Luitel
Presented at 31/ March/2008
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My doctoral research
Title: Culture, Worldview and Transformative Philosophyof Mathematics Teacher Education in Nepal: ACultural-Philosophical Inquiry
Inquiry Agendas
In what ways are the Western Modern Worldviewand 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 thedevelopment of an alternative philosophy of
mathematics teacher education in Nepal? How can mathematical knowledge for teacher
education in Nepal be made holistic, ecologicallybalanced and discursive?
What can a transformative philosophy of
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My doctoral research
ResearchParadigms:
Critical, Post-modern Integral
Methodology:Arts-based
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Research questions addressed bythis chapter
Which philosophies have beengoverning the existing
Mathematics Teacher Educationprograms in Nepal?
In what ways can non-dual traditions of theEast (Vedanta and Buddhism) contribute tothe development of an alternativephilosophy of mathematics teachereducation in Nepal?
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Chapter outline
Capturing a Moment with Mr. Stiff Prelude to Dualism: Meanings,
Sources and Impacts
Enter Mr. Stiffs Sacred Diary Page Imagining Lives Under Dualism: A
Lineland Metaphor Stuff Them Insofar As You Can
Resolving and Dissolving Dualisms:Thinking in-between and Beyond
A Way Forward
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What is Dualism?
Literally speaking,dualism is thetendency to classifyconcepts,
statements andevents according toduals, as belongingto only one of twoall-encompassing,mutually-exclusivecategories withessentially fixed
1 a,b, c ,x, 2y, z Versu
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Poetically and metaphorically
a day without nighta life without plightimposed categories
replacing life
imprisoning living byrestrictions
ideas restrainingopenness andcreativity
despising presentmoments
dualism asexclusion, fracturing and
linearity
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Sources of dualism
Platos form versusForm
Cartesian Dualism Western Modern
Worldview (aparadigmatic view ofthe world promotedby scientism thatespouses nave
realism as itsontology andpositivism as itsepistemology)
the longstandingsocial hierarchybased on caste,gender, region and
ethnicitycontributing tounhelpful dualisms,such as superiorverses inferior, maleversus female, adultversus young, andmanager versusmanaged (Pradhan,Shrestha, & Mission,
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unhelpful dualisms
Content versusPedagogy :foundationlist legacythat content (subjectmatter) is deemed to be
superior to pedagogy Pure mathematics
versus impuremathematics: arisingfrom the onedimensional view of the
nature ofmathematicsas a body of pureknowledge, therebylabelling the impureforms of mathematics
No
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Teaching versuslearning: (i) arisingfrom behaviouristand cognitivist
traditions; and (ii)being generated viathe literalinterpretation of ourcultural traditionsthat teaching andlearning entail
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a lineland metaphor
The humble square, acharacter of aVictorian-time novel,Flatland (Abbott &Hoffman, 1952), finds
in the king oflineland who doesntreally know how tooperate within theflatlandbecause of its
two-dimensionality,which is drastically
The term linelandcan be a metaphor forthe prevailing one-dimensionality that is
embraced by adualistic worldview. Asthe image of linelandcomes to my mind, Ivisualize humans (and
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Lives under three dualisms
Students as not-known recipients:doing mathematicsas following thedictation of the
teacher(contentversus pedagogy),
justification of puremathematics in theschool curriculum
via
Teachers as PeripheralAuthority: thedominant image ofcurriculum as subjectmattermaking
teachers run througha line(land) of subjectmatter without givingdue emphasis tostudent participation
win-lose approach asthe dominant way ofenacting themathematicscurriculum, meaningthat if teachers get
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Two years ago, Kamala raised a question
Sir, Why should we study algebraicfactorisation?
The teacher plays the same old tape
It is useful for your future life
Last year, Kamala raised a similarquestion
Sir, where can I use the geometric proof inmy life?
The teacher opened his old notebook andread loudly
It wont help you now but will certainly helpyou in the future
This year Kamala raises yet anotherquestion
How can I use coordinate geometry in mylife?
The teacher replays his infamous answer
I dont know that but it surely helps in your
After six years, Kamala will raise thesame old question
Professor, what is the usefulness ofmathematics in my present life?
The professor opens his lecture notesand writes on the tatteredchalkboard
I dont know about its use in yourpresent life
But it is surely useful for your futurelife
***
Ms. Kamala, why should I studymathematics?
A talkative student asks bluntlyBecause it is useful for your future
life!
Ms Kamala re-produces the sameanswer
that has grown up with her!
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Teacher educators asreproducers of status-quo: promotingcurriculum as subjectmatter by ignoring the
agentive dimensionssuch as curriculum ascurrere and culturalreconstruction,subscribing to the viewthat mathematics hadnothing to do withqualitative, cultural,social, political and
Embracing a fixed notionof identity as a teachereducator, therebyresisting the urge forcritical reflection upon
his/her disempoweringvalues and assumptions.
Why do I need tolearn because I am
a teacher? banking concept ofeducation
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Resolving and DissolvingDualisms: envisioning in-between
The third spacemetaphor:The thirdspace of enunciation,popularly known as
hybrid space (Bhabha,1994), appears to bean empowering criticalcultural construct foraddressing dualisms
arising mainly fromthe Western ModernWorldview that isembedded in schoolmathematics curricula
The dissolutionmetaphor:
Vedic perspective ofdissolution
Notion of dissolutionfrom Chemistry
Dissolution from theviewpoints ofPostmodernism andIntegralism
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day with a good dream
like swimming in a clean stream
like flying in a clear skylike climbing a big tree
like becoming totally free
rom sorrows and pains
like marching toward mountains
like meeting someone who inspires
like watching doves making a nest
A day with a good dream
ossibly helps keep going
ossibly gives some clues
ossibly offers some directions
ossibly opens some new perspectives
A day with a good dream
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The third space metaphor
third space asdialecticalmovements
third space as
aspiration third space as
interdependentmode of thinking
Third space asoperating withinand beyond thenotion of unity
Where is subjectmatter that is freefrom pedagogy (ormethod or
methodology orepistemology) andvice versa?
Where is purity that
is free from impurityand vice versa?
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(a) I am a teachereducator(b) I am not a
teachereducator
(c) I am a teachereducator andnot a teachereducator
(d) I am neither a
teacher
The moment I am free to shareThe day I am released to wanderThe week I am allowed to speakThe month I am open to my heartThe year I embark on searchingThe decade I hear you telling
I will be no more a teacher
who pretends to be a knowerof all secrecies of what I teachof all mysteries of what I beholdof my life which I dont know a clue yetThen who will I be?
Perhaps a person who just tries tobe?
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The dissolution metaphor
Vedic tradition:dissolutionbecoming
inevitable for theCosmic Creatorwhen the existingframework turns
out to be incapable
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Scientificdisciplinaryperspective:dissolvingas finding
a solutionanddissolving
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Postmodernism:dissolving oldquestions of
education;Integralism:dissolution offractures and
demarcationssustaineddialogues between
http://www.allposters.com/-sp/Dissolution-of-Hell-
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Thinking aboutmathematics educationin contextualisedterms, that is, theexisting cultural, socialand lingual diversity ofNepal.
Shifting the focus ofthe mathematics
Rather than exclusivelyusing the mind
(buddhi, intellect,logic) RamanaMaharshis call foropening ones ownheart (hridaya: thecentre of body-mind,
empathy andmindfulness) is usefulfor me to come out ofthe limited identity
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andWhen will they enter in maths class?The petals of marigoldThe banquet of rhododendronThe collection of pippal (fig) tree leafsThe fractal of Bodhi treeWhen will they enter in maths class?When will they enter in maths class?The map of my village settlements
The matrix of my mothers work scheduleThe method of my fathers problem solvingThepattern of land distribution in myvillageWhen will they enter in maths class?When will they enter in maths class?
The algebra of my family genealogyThe geometry of wicker basketsThe arithmetic of local harvestsThe statistics of my village budgetWhen will they enter in maths class?
ctivity makes sense ofpassivity
Passivity gives rise toactivityWhere is passivity withoutactivity?How can I see activity
without passivity?day constitutes dawn
and darkdark can be a source of
spark
Where is puritythat does not arise fromimpurity?Where is impuritythat doesnt show us