Summary
of Proposed Research Program
(Bal
Chandra LUITEL, 12369243)
Title
Culture, Worldview
and Transformative Philosophy of Mathematics Teacher Education in
Abstract
Through
this research my aim is to review critically the existing philosophies of
mathematics teacher education in
Objectives
During this inquiry
I propose to accomplish the following tasks.
Inquiry Agenda/Questions
My
inquiry intends to answer the following questions.
Background
While undertaking
my Masters degree research (Luitel, 2003), ‘Narrative Explorations of Nepali
Mathematics Curriculum Landscape: An Epic Journey’, I came to understand that
mathematics in Nepali schools and teacher education colleges is taught and
studied as a foreign subject without giving due consideration to local
contexts, worldviews and cultures. Using my experience as a student, a
mathematics teacher and a teacher educator, I employed autoethnography as a
method of inquiry, together with a number of referents such as radical and
critical constructivism, metaphor, ethnomathematics and a geometry theory
model, to further excavate the decontextualised nature of mathematics education
in
I
then continued working as a teacher educator in a newly established university
in
I
have considered the preparation of this candidacy proposal as setting the stage
of my inquiry, a to-and-fro performative act (Denzin, 2003) between my
narratives and others’ ideas (literature). During this process I have reflected
on closely related research studies (Che,
2005; Hoover, 1996; Lin, 1994) that
have contested and questioned - mildly and strongly - the Western Mathematical
Worldview (WMW) (Taylor, in press). I found Che (2005) starting to use
her own narratives and then moving to the field, showing a dialectical
relationship between self and other and interrogating the nature of Cameroonian
Worldviews and WMW — a similar agenda to mine. I have further crystallised how
an ethnomathematical perspective has potential to be a referent for
interrogating the alternative philosophy of mathematics teacher education, much
as D'Ambrosio (2006a; , 2006b) envisages by opening ‘new foci, new
methodologies, and new views of what science is and how it evolves’ (2006a,
p.9) and positioning his ‘Program Ethnomathematics’ beyond proto-mathematical
thinking. I share the vision of D’Ambrosio that mathematics teacher education
is in need of searching for alternative philosophies situated in local
cosmological grounds.
As in other transitional societies,
While arguing for my inquiry ‘space’ within
which to create an agenda for a cultural-philosophical inquiry into mathematics
teacher education, my attention has been drawn by the notion of a ‘signature
pedagogy’ (Wood, 2006) proposed by a leading North American educator, Lee
Schulman. His idea of a universalised signature pedagogy, to me, is another
neo-academic-rationalist-positivist movement guided by a neo-colonial
philosophy of teacher education. If I had accepted his idea of a signature
pedagogy, I would have been conforming to the ongoing and uncritical
transportation from Western universities to Nepali teacher education
institutes. However, agreeing with the notion of personal knowledge (Polanyi,
1969) and extending it to ‘cultural dwelling’, the important ‘poesis’
(Henderson & Kessen, 2004) for me is to inquire into an alternative
philosophy of mathematics teacher education that helps improve my practice of
being in a non-Western and spiritually exotic land of multiple cultures.
Klein’s (2004,
2001) focus on agency rather than on the meaning constructed by the temporal
and spatial self makes good sense to me. While there is a tendency to regard a
particular philosophy as a golden path, Klein’s idea of empowering
actors/agents in terms of their agency can be also linked with my agenda. How
about improving the agency of teacher education programs in transitional
societies? How about refocusing their worldview to extend the philosophy of
mathematics teacher education beyond its dominant and restrictive WMW
framework? In a similar vein, Klein (2004) rejects the ‘notion of a unified,
fixed identity (p.37)’ that acts as if the singular identity indicates a need
for an empowered and decentred identity of mathematics teachers. To me,
however, the empowerment of mathematics teachers does not simply complete the
‘Klein Project’ until and unless there is an empowerment of mathematics teacher
education programs through their contextual philosophical restructuring.
While I am
arguing from the perspective of decentring mathematics teacher education
philosophy, there is a call for expanding existing research practices of
mathematics education as they were not prepared for the South (Valero &
Vithal in Bishop, 2002). This call also applies to me as I need to explore
issues that are relevant for my context giving much impetus to my practice and
context (Bishop, 2002; McKinley, 2005). Reading Valero, Vithal and McKinley’s
arguments for recognition of indigenous knowledge and language, I have seen a
pressing need to inquire into the agenda of developing a non-Western,
grounded-in-my-context philosophy of mathematics teacher education that can
help ‘renovate my identity’ (Bhabha, 1994) and the identities of other
educators working in similar discursive and cultural contexts.
Arriving at this juncture, I felt the need to perform on the
stage of mathematics, education and philosophical perspectives. Although mathematics
education draws from sociology, psychology and other areas of the social and
human sciences, different philosophies of mathematics have been influential in
restraining and facilitating the dominant WMW philosophy of mathematics
education (Ernest, 2000, 2006). Western dualism has become a source of
controversy in conceptualising mathematical objects and the nature of
mathematics (Hersh, 1994). As the philosophy of mathematics school of formalism
and logicism are no longer free from controversy, the foundational project
remains elusive (Hersh, 1994). The mild challenge of social constructivism to
Western dualistic ontology has resulted in the possibility of generating
alternative philosophical traditions in mathematics education. Even within this
paradigm, there is still a possibility of searching for an alternative
‘cultural’ (cf. social) philosophy of mathematics teacher education.
To my understanding, what has been overlooked in the history of
Western mathematics is the nature of mathematical knowledge as perceived by
some highly influential mathematicians. Thus far, the main focus has been given
to only linear, dualistic and disconnected knowledge. Loy (1997) mentioned that
Henri Poincare and Karl Gauss claimed to have discovered mathematical knowledge
unseparated from their experience. However, the dualistic nature of the
dominant WMW has continued to (mis)represent such a claim, emphasising
hierarchical, unconnected and cold-reason-based knowledge (
Furthermore, Western dualistic epistemology
and its realist ontological counterpart have been challenged within the Western
intellectual enterprise—a movement towards philosophical pluralism in
education. To me, complexity theory (Byrne, 1998) and radical constructivism
(Glasersfeld, 1991, 1995) have strongly questioned the dualistic-realist
episteme while seeking for an holistic and ecological perspective of knowledge
and knowing. While reading Capra (1983, 1991, 2002) and watching the movie
Mindwalk (B. A. Capra, 1990), I came to understand that modern physics needs to
go beyond its mechanistic and inorganic cosmology in order to interpret the
mystic realities of the world. Capra has further elaborated his perspectives as
ecological holism, a symbiotic perspective of different knowledge traditions.
Amidst these contemporary challenges, a new philosophy of mathematics teacher
education that takes non-Western, ecological, holistic, non/dual and spiritual
dimensions into account is essential.
Embracing mathematics as contingent,
corrigible, fallible and an ever-developing knowledge system (Ernest, 2006)
gives me a perspective on mathematics education that can take into account
local knowledge systems. To me, these sets of ideas can open up further avenues
of philosophising mathematics teacher education, especially when considering
the image of mathematics as discourse/activity unseparated from power, agency
and context. The issue of power can be clarified by answering the question: Whose interests are being served by existing
mathematics education programs? The question requires me to search for
answers from the Habermasian notion of emancipation (
Significance
With
the aim of carrying out an interpretive and somewhat ‘in/ward’ focusing
inquiry, I am in a crisis of writing the significance as demanded by the
Candidacy Guide (Rennie & Gribble, 1999). I have adapted the ‘Candidacy idea’
to my specific research context and have organised it under four headings --
but not mutually exclusive -- in order to signify the importance of my inquiry
for myself, Nepali teacher educators, the field of mathematics education and
other researchers.
My ‘inquiry self’ and
‘professional self’
As
I will use reconceptualising self as one of the metaphors of this research, I
will have ample opportunity to develop myself as a transformative and culture
sensitive teacher educator. Whilst using the Vedic notion of tat tvam asi: meaning ‘you are that’
(Loy, 1997) in my act of data collection, generation and reflection, I will be
aware of my role as a transformative teacher educator. The major significance
of this type of inquiry is:
to make sense of what we were doing both as
living our stories in the ongoing experiential text and as telling our stories
in words we reflected on life and explained ourselves to others. (Clandinin,
1993, p.1)
The
process of telling and retelling the story of my praxis contributes to my
professional growth in three ways. First, the dialectical relationship between
person and profession gives me an opportunity to uncover my tacit assumptions
that could be hindering my professional development. Second, it is very
important to know my lived contradictions that could be impeding my praxis as a
teacher educator. Third, the reflexive relationship between generating and
living selves helps me to envision my professional future (Connelly &
Clandinin, 2000).
My inquiry and other Nepali
teacher educators
My
inquiry will help Nepali teacher educators in three ways. First, as my research
will look into the Nepali philosophy in mathematics teacher education, other
teacher educators can start to envision similar agenda for their field of
inquiry. Second, while
Contribution to the field of
Mathematics Education
I believe that the myth of ‘a knowledge body’ is
somewhat coercive and hegemonic because of its ‘out there’ and foundational
nature. Thus I will not subscribe to the idea that I will contribute to a body
of knowledge; rather I will contribute a discursive context for extending the
domain of culture sensitive philosophy of mathematics teacher education.
However, I do not believe that my philosophy will be the philosophy; instead I intend it to be a philosophy, developed in a particular cross-section of space,
time and self.
It has been more than 20 years since the
mathematics education community started talking about ethnomathematics. The
notion of ethnomathematics is still being conceptualised as the site of looking
into some proto-mathematical activities of ethnic/occupational groups, although
there is a call for a liberating attempt to ethnomathematical thinking from the
Modern Mathematical Worldview (D’
Ambrosio, 2006a; 2006b). I am hoping that my inquiry will be able to excavate
further the cultural nature of mathematics, but certainly to/for Nepali
contexts.
My
inquiry and other researchers
I believe that both collected and thereby
generated (data)texts ‘are always open to diverse interpretations’ (Kincheloe,
2003, p.198) in my research. However, other researchers can be benefited by a)
learning the process of my inquiry that demonstrates my reflexive growth over
the period of the inquiry; b) knowing my interpretive standpoints that will
employ various referents such as radical constructivism, non/dualism,
dialectical thinking, post/criticalism and integral philosophy; and c) the
diachronic and metaphoric representational approach that allows every
researcher to be open and emergent about their representational approach.
Methodology
Employing
interpretive and auto/ethnographic methodologies (Jones, 2005), my inquiry is
situated in the sixth, seventh and eighth moments of qualitative research
(Denzin & Lincoln, 2005). The sixth moment will allow me to use the
‘ethnographic alternative’, thereby opting for auto/ethnography and beyond. In
so doing, I will be able to link between self and contexts making visible the
invisible. This continuous performativity makes me aware of my layered
understanding of contexts and texts, thereby opening up unanticipated and
emergent understandings. The seventh
moment, the methodologically contested moment, facilitates me opening up alternative
frameworks for research in mathematics and science education. Frameworks such
as post/criticalism, non/dualism and integral philosophy will help in
generating inward understandings of the epistemological dimensions of the
so-called outward field of inquiry—mathematics and science education.
The
eighth moment is in the process of being created with the upsurge of culture
studies, culture sensitive methodologies and culturally embedded knowledge
(Denzin & Lincoln, 2005). My understanding of the eighth moment is of an
emerging era of decolonising methodologies and decolonisation of the field of
inquiry. Perhaps, my approach to developing an alternative and culture
sensitive philosophy of mathematics teacher education can help decolonise (to
some extent) the field of mathematics education and teacher education. However,
I will not be subscribing to the notion of a fractured future, instead I
subscribe to an ecologically holistic notion of inquiry based on integral
philosophy that demystifies the disconnected, fragmented and linear unconnected
nature of knowledge; it rather focuses on the notion of knowledge as integrated
holons thereby helping to realise
complemented consciousness (Settelmaier, 2003).
Specifically Wilber’s three quadrants —
Upper Left, Lower Left and Lower Right — will help me to develop an
holistic understanding of Nepali mathematics teacher education
philosophies.
Data collection, generation
and interpretation
In
my inquiry, there will be two types of data: collected and generated. My
conversations, or postmodern interviews (Ellis & Berger, 2003; Holstein
& Gubrium, 2003; Kvale, 1996), with mathematics teacher educators (maximum
12), pre-service teachers (maximum 10), mathematics teachers (maximum 15) and
parents (maximum 15) will constitute a major source of collected data. I will
be treating interviewing as a social encounter in which knowledge is
constructed (Holstein & Gubrium, 2003, p.68) and ensuring that:
The interviewing process becomes less a
conduit of information from informants to researchers that represents how
things are, and more a sea swell of meaning making in which researchers connect
their own experiences to those of others and provide stories that open up
conversations about how we live and cope. (Ellis & Berger, 2003, p.161)
Similarly,
my observations of rural and metro school mathematics classes (about 10) and
artefacts of mathematics teacher education in
Data
generation will be carried out before, during and after the collection of the
field data. With the notion of writing-as-inquiry (
In
qualitative inquiry interpretation is a performative act (Denzin, 2003). It
actually begins when the researcher starts to make sense of the world that s/he
aims to inquire into. Unlike in positivist research, my ‘data interpretation’
starts together with my act of data collection and generation, or even before,
during the writing of this proposal. Thus I have categorised the act of
interpretation in two ways: preliminary interpretation and conscious
interpretation (Polanyi, 1969; Polanyi & Prosch, 1975). My notion of
conscious interpretation can be linked with the conventional notion of ‘data
analysis and interpretation’. To me, conscious interpretation starts by making
sense of the world/data on the basis of frameworks, referents and underlying
theories.
Although
there is a blurred landscape between collection, generation and interpretation
of data, I have visualised the ‘process landscapes’ in terms of many viable
episodes for depicting the metaphorical nature of qualitative, emergent and
diachronic inquiry. Therefore, I consider the following three-stage set of
episodes not to be ‘the golden one’; instead, many emergent alternatives may be
employed in my inquiry.
Episode One
Episode Two
·
Conversations
with mathematics teacher educators focusing on the issue of contextualism.
·
Conversations
with secondary school teachers focusing on the issue of the usefulness of their
university training to their mathematics teaching.
·
Conversations
with trainee teachers about their perceptions of existing teacher education
programmes focusing on the issue of contextualism in mathematics
education.
·
Conversations
with parents about their vision of school mathematics.
·
Observations
of metro and rural school mathematics classes.
·
Collection
of (reform-associated) historical documents on mathematics teacher education in
·
Visiting
nodal places which are associated with my (hi)story as a student, teacher and
teacher educator.
·
Reinventing
my memory as a student, mathematics teacher and teacher educator through
talking, observing and sense-making of the places associated with my (hi)story.
·
Daily/weekly
journals based on my experience of the field.
Episode Three
Rigour Criteria
As
this research is situated in the postmodern era and beyond, it cannot be judged
according to the archaic modernist notions of rigor, namely, reliability and
validity. In the last twenty years efforts have been made to develop
alternative rigour criteria (e.g., Guba & Lincoln, 1989) to address the
issue of the emerging paradigms of constructivism, criticalism, poststructuralism
and many others. Denzin and Lincoln (2000; 2005) continue to project the issue
of the triple crisis - crisis of representation, crisis of legitimacy and
crisis of praxis. The triple crisis emerged substantially with the poststructuralist
notion that language does not represent reality but creates reality. To me the
aesthetics of the rigour of an inquiry lies in a creative approach to
addressing, but always leaving unresolved, the triple crisis. I will be
addressing the issue of the triple crisis together with other referent-specific
quality criteria.
First,
I need to be attentive to the crisis of representation. I do not claim
that I can represent all of those with whom I work, talk and converse. I shall
be representing others through my own conceptual lens, as it is impossible to
separate between the seen and the seer (Loy, 1997) in an act of inquiry which
also places self(-reflexivity) under scrutiny. I shall represent the multiple
selves through multiple genres and voices approaching an integral, but
contingent, understating of the world of my inquiry. Furthermore, the
dialectical relationship between presentation and representation – expressed as
re/presentation – can help me to address this crisis as a) the act of
re/presentation is associated with the self/other dialectic, and b) the means
of re/presentation are always co/constructed by auto/method (Roth, 2005).
Addressing
the crisis of legitimacy can be linked with the ’who’ of research
(Smith, 1999). While there is an upsurge of culture studies approaches in
social research, I claim that it is legitimate for me, a cultural insider, to
carry out research that is grounded culturally and professionally in my
context. I will employ a number of approaches to address this crisis: a)
ensuring cultural verisimilitude of my texts, b) demonstrating enriched
understanding of my professional context, c) developing critical reflexivity on
my process of inquiry, and d) attending to the poesis (aesthetic making) of my
inquiry.
The
crisis of praxis is associated with the intended impact of my inquiry on
the concerned participants as well as my actions as a researcher. The crisis
can be addressed through a) evoking readers to develop their pedagogical
thoughtfulness (van Manen, 1990) and wakefulness (Clandinin & Connelly,
2000) by means of my texts, b) my future professional actions arising from my
critical reflexivity, and c) how I strive to generate personal practical
knowledge, that is, phronesis for wisdom. As my focus is also on my multiple
‘selves’, demonstration of self-reflexivity can help to resolve this crisis to
some extent.
Ethical Issues
Cohen,
Manion, and Morrison (2000) mention that it is the obligation of researchers to
ensure the respect and safety of those who are affected by or involved in their
inquiry. In social and human research, participants should be treated with
dignity because they are the valuable co-constructors of knowledge (Guba &
Lincoln, 1989). Specifically, in qualitative research, those who participate in
the inquiry are not regarded as subjects but as participants who can contribute
to the development of enriched understandings of the studied phenomenon.
Therefore, it is important for me to be sensitive to and respectful of the
participants’ ideas and opinions.
While
collecting the data, I will obtain the consent of the school principals and
teachers to observe their classes. In so doing a written agreement between the
teacher/principal and I will be made and any participating teacher can withdraw
if s/he wants. In the process of observation, I will be committed not to
influence the situation so that the participating teachers feel secure to carry
out their activities as naturally as possible. Although it is hard to separate
power from discursive context, I will always be abiding by an ethic of care (
The
conversations with different stakeholders will also be contractual, indicating
the condition of ‘anytime withdrawal’ if they do not like to participate in my
inquiry. Rather than me asking questions all the time, the context will be
created in such a way that they can ask questions about my research and
challenge my focus of inquiry. Knowing the fact that conversations may enter
into a vulnerable state for both the participants and me, I will be aware of
the issue of self-disclosure (Ellis & Berger, 2003). The conversation can
go beyond the technical and practical level (
In
the process of generating the data, I will ensure anonymity using pseudonyms
and composite characters that allows me not to represent the exact person with whom
I have worked during the process of data collection. Because the issue of
narrative writing is an integral part of the representation of this inquiry, I
will be respectful of my context, culture and people. Furthermore, I will
consider the desired degree of exposure (i.e., vulnerability) of myself for my
own safety and care.
Facilities and resources
For
the fieldwork I will use my personal tape recorder, notebooks and computer.
Fieldwork expenses, except for the airfare, will be covered by the Curtin
University International Postgraduate Research Scholarship (IPRS). After
completing my fieldwork, I will use the resources provided by SMEC.
Data Storage
The
collected data will be stored initially as a paper format and indexed for my
convenience. Specifically the method of indexing (paper-based and
electronically) of data will be known to me only. It will only be presented if
my supervisor wants to see and verify it. The data will be stored in a secure
location, that is, university-provided computer, for a period of five years
after completion of the research and then will be destroyed.
Timeline
|
Year/Month |
Activities |
|
|
2006 |
A S O |
Candidacy
preparation and early data generation |
|
N D |
Field work, data
collection and data generation |
|
|
2007 |
J F |
|
|
M A M J J A S O N D |
Data
processing/transformation — data generation through writing, literature review |
|
|
2008 |
J F M A M J J A S O N D |
Continue
literature review and data generation through writing and literature review,
chapter organisation |
|
2009 |
J F M A M |
Chapter
organisation, incorporating any changes |
|
J J |
Final submission |
|
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