The ICDME-Tsukuba Conference: International Cooperation Development in Mathematics Education

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Tokyo, 11th – 12th Feb., 2022

UNDERSTANDING NARRATIVES: A PATHWAY TOWARDS RESOLVINGISSUES AND CHALLENGES IN INTERNATIONAL COOPERATION IN
MATHEMATICS EDUCATIONUi Hock CHEAH
Penang Math Platform, Malaysia

Masami ISODA
University of Tsukuba, Japan

This paper explores the issues and challenges in international cooperation in mathematics education
by examining its history and the ecosystem of its projects. Historically, bilateral international
cooperation has existed for many centuries but it was only in the last century that multilateralinternational cooperation has been established, with two main purposes, that of increasing
international communication and serving as a platform for international aid. The ecosystem ofinternational cooperation in mathematics education embodies a community where agents from various
institutions and organisations interact at international as well as local levels. The complexity in thisecosystem has given rise to many issues which is the result of globalisation as well the possible
different agendas of the agents and the institutions involved. The issues and challenges in international
cooperation, briefly categorised as outer and inner issues according to its relatedness to mathematics
education, are then briefly discussed. The complexity in the international cooperation ecosystemsuggests that in order to initiate a pathway to resolve the issues and challenges, it is necessary thatthe narratives and voices of the agents at all levels be heard with the aim of creating solutions thatare relevant, practical, just and sustainable to the community. The initial emergent framework towards
resolving these issues and challenges comprises dispositions in the narratives towards the various
aspects of knowledge and beliefs of the agents: Views of self towards authority, views of knowledge,views of knowledge production, and views of management.
Keywords: International cooperation; Mathematics education; Issues and challenges; Globalisation;
Narratives; Knowledge and beliefs
INTRODUCTION
INTERNATIONAL COOPERATION AS COMMUNICATION
The formation of the Internationale L'Enseignement Mathématique in 1908, regorganised later as theInternational Commission on Mathematical Instruction (ICMI) in 1952, has been acknowledged as awatershed moment that formalised the beginning of international cooperation in mathematics
education (Karp, 2013). Cross-border activities on mathematics education had long existed before
1908 where mathematicians and educators have engaged in the sharing of mathematics educational
materials and ideas but these activities were manily bilateral and carried ou on a personal and informal
basis (Karp, 2013). The formation of ICMI thus provided the thrust for formal multilateralcommunication among countries, beginning first with countries in Europe (Furinghetti, 2014). In
examining the effects of ICMI on international cooperation, Karp (2013) and Furinghetti (2014) noted
the emergence of two key purposes in international cooperation: Internationalisation andcommunication. As a result, international cooperation was enhanced through increased formal
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communication across borders. This initial motivation for increased formal international networks was
soon utilized as a gateway towards internationalising the mathematics curriculum. This would laterlead to the debate as to whether the mathematics curriculum should be internationalised or localised.
After World War II, more international organisations and meetings were established as platforms forinternational cooperation. The Royaumont Conference in 1959 was the most notable of these meetings.
Though only represented by 18 countries, it led to the popularisation of the new mathematics
movement across the globe (Singh & Ellerton, 2013). The formation of other internationalorgansations followed. The International Association for the Evaluation of Educational Achievement(IEA) was formed in 1967 arising from the first meeting of psychometricians in Hamburg in 1958, andthe Organisation for Economic Co-operation and Development (OECD) was formed in 1961. Both the
IEA and OECD have evolved and have led the world mathematics education community to participate
in two international cooperation assessments, the Trends in International Mathematics and Science
Studies (TIMSS) and the Programme for International Student Assessment (PISA). Interest in TIMSS
later led to more cross-border international cooperation initiatives notably the TIMSS video study(Stigler et al., 1999) which generated world-wide interest in cross-cultural studies and lesson study as
areas of research on new innovative approaches to improve the teaching and learning of mathematics.
What have been discussed in this section is but a sampling of the expansive cross-border initiatives ininternational cooperation that have taken place since the formation of ICMI. In essense, these projects
were facilitated by the affordances made availabe through increased cross-border communications
leading to more formal platforms for international cooperation.
INTERNATIONAL COOPERATION AS ASSISTANCE AND AID
In the period after World War II, there were several developments across the globe that led to theemergence of a different kind of international cooperation.
1. New aspirations to raise living standards emerged, leading to reconstruction, rapid
development and more affluence in many advanced countries. This period is often refferred toas the golden age of capitalism (United Nations, 2017).
2. Many new countries gained independence. However, many of these countries which wereformer colonies lacked administrative structure, infrastructure and know-how for development.
3. The establishment of multilateral international organisations, such as the United Nations (UN)and its associated organisations, for exampe, the United Nations Educational, Scientific andCultural Organisation (UNESCO) and the United Nations Development Programme (UNDP)
became multilateral advocacy platforms for assistance to be provided to less developed
economies.
These events were followed by augmented efforts and movements to improve education and to provide
assistance to less developed countries across the globe. After the setting up of UNESCO and UNDP,
many affluent nations soon established international aid agencies of their own. For example, theNorwegian Agency for Development Cooperation (Norad) was set up in 1968, and the Japan JapaneseOverseas Development Assistance (ODA) which began in 1954 was later reconsituted as the Japan
International Cooperation Agency (JICA) in 1974. These international agencies operated
independently of each other. It was the UN and its associated agencies that provided the leadershiptowards providing a unifying vision for the work of international cooperation. Advocacy towards using
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education as a tool to improve living standards continued to grow and eventually led to the World
Conference on Education for All (EFA) held in Jomtien, Thailand in 1990. The Jomtien EFA
declaration was founded on the premise that education is a fundamental human right for everyone(UNESCO, 2000). Ten years later, this vison was reaffirmed, formalised and adopted in the Dakar
Framework for Action at the World Education Forum in 2000 (UNESCO, 2000). The Dakar
Framework outlined several goals for the attainment of the EFA vision. Among them were theimprovement of early childhood education, improving access to education for marginalized groups,
improving adult literacy, achieving gender equality, and improving all aspects of the quality ofeducation. Further, the EFA declaration envisioned that quality and excellence in education can beachieved especially in literacy, numeracy and essential life skills (UNESCO, 2000). One implicationof the Dakar Framework for Action was the emergence of mathematics education as a key theme ininternational cooperation. It can be seen that the Dakar Framework for Action which led to the launchof the United Nations Millennium Development Goals, and later superseded by the Sustainable
Development Goals (SDG) (United Nations, 2015) was to provide an internationally recognised
platform for international cooperation. The backdrop for the establishment of this cooperation was a
globalised world which had created, perhaps unintended, increasing inequality among the world’s
economies, and the awareness among institutions that international cooperation could be used as aplatform to acquire economic benefits for all (Atweh et al., 2008). It is against this backdrop that moreinternational cooperation in mathematics education were established.
MATHEMATICS EDUCATION IN INTERNATIONAL COOPERATIONThe universal importance of mathematics is reflected by its inclusion in the school curriculum
worldwide. Children learn mathematics as early as in pre-school and grade 1 in elementary school.
Moreover, mathematical competencies are currently seen as necessary for the advancement ofcomputational sciences and big data analysis which are essential for the economic development of
future societies. Often referred to as the queen of the sciences, the utility of mathematics in various
fields especially those related to science and technology is indisputable. The goals of education,
however, go beyond just preparing citizens for economic development. Ultimately education must aim
for the creation of a well-being and sustainable society (United Nations, 2015; OECD, 2018). In reality,
while mathematics education has been successful in empowering and liberating society, it has
sometimes brought about undesired consequences that are detrimental to the environment andhumanity (Skovsmose, 2007, 2016). While mathematics has often been viewed as the least value-ladenof school subjects and thus the least susceptible of being misused as a means for propaganda, Bishop(1990) challenged this myth by purporting that the mathematics brought by the authorities for use in
the colonies was embedded with hidden elements of western culture, and was in fact a tool for theimposition of western culture. Moreover, as recent history has showed mathematics has been misused,
for example, in wars and to maximize profits in planned computational experiments (Skovmose, 2016).
Similar arguments have been raised in the field of international cooperation in mathematics education
which includes various concerns about its effectiveness and outcomes (Atweh & Keitel, 2007). The
most commonly highlighted concerns are those of equity and social fairness. To address these concernsof the diverse community who participate in international cooperation projects in a holistic manner,
there is a need for equitable and authentic solutions to be instituted.

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COMPLEXITY OF THE INTERNATIONAL COOPERATION ECOSYSTEM
The planning and implementation of international cooperation projects often require the need tomobilise a diversity of organisations and their agents at various levels. These organisations compriseinternational institutions that fund and coordinate cross-boundary projects which includes those linked
to the United Nations or other international agencies established by more developed and affluent
countries. At the national level, the services of various organisations such as the education ministries,
teacher colleges, curriculum development centres, state and regional educations offices, and local
authorities are often sought to provide expertise and to manage the implementation of the projects.
Frequently, local and foreign universities also participate by offering their knowledge and expertise.
At every level, the institutions and their agents contribute a myriad of purposes and agenda into thedesign, planning, implementation and assessment of the projects. Moreover, the agents’ personal ideas,
knowledge and agenda become included and embedded as part of the narratives in the ecosystem.
A complex ecosystem such as this, thus encompasses a variety of knowledge in its implementation,such as scholarly knowledge, knowledge of educational systems as well as knowledge of practice(Artigue, 2018), which do not always work in synchronicity with one another. This milieu that
constitutes the knowledge developed in this ecosystem is dynamic. Its dynamic nature is not
unexpected as the development of this knowledge involves agents coming from various institutions
with diverse specialisations and training. Further, as this knowledge passes through the different levelsof implementation, a variety of its meanings and interpretations may emerge and not always leading
to a convergence of ideas. From one level to the next, there is a transposition and modification of theknowledge and ideas (Chevellard, 2019). Even mathematical knowledge, which is supposedly
objective, undergoes this transposition of knowledge across levels, resulting in various forms andformats (Chevellard, 2019). As Tall (2013) observed, mathematics knowledge has transposed into
three forms by the time it has crossed various levels from university to school, namely the axiomatic,
theoretical and practical forms of mathematics. This milieu of institutions, agents and knowledge
contributes to the complexity often seen in international cooperation. The pictorial representation in
Figure 1 describes the project phases, the organisations and agents involved and the types ofknowledge that can be found in international cooperation.
Metaphorically, the work in international cooperation in mathematics education is akin to an
ecosystem where the agents serve as organisms that learn to accommodate and adapt to each other inorder for the complex ecosystem to thrive towards achieving its goals and objectives. The developmentof ideas and plans in this ecosystem occurs not through individual effort but rather through sociallyconstructed discourse in both formal and informal forms (Ernest, 1991). To better understand how
negotiated solutions emerge in this complex ecosystem it would be therefore be necessary to examine
and understand the narratives of the agents at various levels of the projects.

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Proposal and planning forInternational organisations
Governments/ Ministries

Scholarly
knowledge

International Cooperation
projects
Project design

Implementation

Impact study/
Evaluation

Project phases

International organisations
Governments/ Ministries
Local & foreign universities
Local NGOs and private organisations

International organisations
Governments/ Ministries
Universities, Teacher colleges
Local authority
Local NGOs, Schools

Organisations and agents

Knowledge ofeducational
systems

Knowledge ofpractice

Types ofknowledge

Figure 1. Project phases, organisations, agents and types of knowledge in international cooperation
discourse.
ISSUES AND CHALLENGES IN INTERNATIONAL COOPERATION IN MATHEMATICSEDUCATION
Issues and challenges relating to international cooperation in mathematics education were firsthighlighted and discussed at the 10th International Congress on Mathematical Education (ICME 10)(Atweh et al., 2008). Most of the challenges that were discussed drew attention on emergent generalissues in international cooperation and were not specifically related to mathematics education. Issues
relating to mathematics education, however, could be gleaned from other literature that dwelt on crossnational and cross-cultural issues in mathematical instruction (Atweh et al., 2007; Montecillo et al.,2018; Shimizu & Vithal, 2018a; Doig et al., 2019). Together, these literatures provide a wider
perspective and bigger picture that covers both international cooperation and mathematics education.
The concerns and challenges affecting international cooperation in mathematics education can be
categorised into two main realms. The first covers issues related to international cooperation in generalwhich are labelled in this paper as outer issues. Outer issues although indirectly related to mathematics,
are sometimes key to the solutions in international cooperation in mathematics education. The second
area is labelled as inner issues which, as the name suggests, indicates its direct relation to mathematics
education. Specifically, all the inner and outer issues and challenges in this paper will be discussed inrelation to the professional discourse among the agents. It is by means of professional discourse thatideas and plans are argued, reconciled, reconstructed and implemented. Arguments, ambiguities, andvariations in ideas and opinions emerge through professional discourse. It is also through professional
discourse that reconciliations, solutions and resolutions are found. The analysis and understanding of
the narratives of the agents in this discourse provide the essential elements towards providing solutions
to the issues and challenges in international cooperation.

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Outer Issues
Among some of the outer issues mentioned by Atweh et al. (2008) were financial aid reaching andachieving its targeted agenda, dominance of English over local languages, conflicting cultural norms
and values, and the locus of authority which is often dependent on whether the agents represent thedonor or recipient countries. Based on these issues and challenges raised and through our personal
experiences in relation to international cooperation, the following aspects of general professional
discourse were identified.
Locus of authority. The plans and implementation of projects are often influenced by the extent thevoice of authority dominate professional discourse in shaping ideas, plans and implementation. The
power to command authority is dependent on several abilities of the authority that are specificallyrelated to the ability to provide or impose reward, coercion, legitimacy, expertise, reference, andinformation (Raven, 1992). Besides the ability to command authority, decision making in discourse
is influenced by several other factors which relates to the personality of the other participants in the
discourse. Generally, decision making is influenced by the dynamics of the group whether its members
resist or conform to authority, or are empowered in the decision-making process. Personality traits
such as adherence to traditional values, conscientiousness and agreeableness tend to support higher
conformity to authority while it can be expected that moral reasoning and social intelligence tend to
predict resistance to the authority figure (Bègue et al., 2015).
Institutional agenda vs. personal agenda. Agents in international cooperation often play multiple
roles. Some of the participants act as agents of organisations they represent while others participate intheir own personal capacity. Their views may express the views of the institutions they represent yetat the same time represent their own personal beliefs or expertise. Even when the agents represent theirorganisations their views may not necessarily be inconformity with that of the organisations they
represent. In contrast, academic scholars contribute their expertise in particular areas which are
generally based their personal ideas and agenda. Moreover, the agenda of the different institutions at
various levels may not always be synchronous which may lead to challenges to be resolved.
Practical ideas vs. Planned/Political ideas. The planning of projects in international cooperation isoften initiated at the international level that necessitates adherence to specific performance indicatorsand standard operating procedures as laid out by the organisations. At times political agenda takes
precedence in the planning process. International cooperation projects are very much affected bychanges in the local politics. Changes in government, for example, often leads to changes ingovernance policies which may result in projects being discontinued. Moreover, the selection of agentsand also the project site is very much dependent on political expediency. But as the international
projects move into the implementation stage, the participation of more agents from other local
institutions are normally sought. In projects involving mathematics, local agents who are recruited areoften local teacher specialists in the subjects whose practical ideas may be at variance with initial plansthat were drawn up in the initial planning stage. It is also noted that values and norms relating tocultural practices often vary both across boundaries and across different levels of the projects.
Inner Issues
In the era of globalisation and post-modernism, views about mathematics education and its aims andpurposes keep evolving (Ernest, 2016; Skovsmose, 2016). Widely acknowledged as the queen of the6

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sciences, mathematical ability is generally accepted as a must have for the progress of the modern
world (D’Ambrosio, 2016). Yet in the globalised world mathematics has now come to accommodate
new roles in order to achieve a wider spectrum of aims and purposes. Mathematics education itself is
continuously influenced by the commodification of knowledge where schools and universities are
driven by performance and managements standards (Ernest, 2016). Given this scenario, it is apparent
that the design, planning and implementation of mathematics education projects in international
cooperation would be influenced by these new standards and perspectives. It is foreseeable that theagents’ views about mathematics education would be just as diverse. The concern is to understand how
these differing views about mathematics education are manifested and resolved in the implementationof international cooperation projects. We suggest five inner issues of mathematics education which
may currently exist in international cooperation.
Behaviourist - Constructivist approaches. The debate between behaviourist and constructivist
approaches was at its peak at the turn of the century. Constructivist approaches highlights designingand providing learning experiences for learners to construct mathematical ideas whereas behaviorist
approaches focus on sequencing mathematical competencies for learners to master mathematical skillsin the learning process. While the sequencing and attaining of mathematical competencies provide
logical steps towards acquiring and applying algorithms, this instrumental approach has sometimes led
to unresolved misconceptions. Moreover, an important emphasis in behavioral approaches was theextensive use of behavioural objectives to assess learning. The misuse of behavioural objectives
eventually resulted in the shift towards constructivist approaches which instead, emphasise theconstructions of mathematical ideas by the learners themselves. The ensuing debate had also led tochanges in the perception and characterisation of teachers’ functions, from authoritative to facilitativeroles. This transformation from behaviourist to constructivist approaches, however, is not happening
at the same pace across the global community of mathematics educators. Some are more progressive
than others who may tend to adhere to the more traditional behaviourial approaches. It would be notcontentious to presume that serious argument and disagreements would emerge when agents withdiffering views on the behaviourist-constructivist discuss, plan and decide on the suitability andappropriateness of the didactics of mathematics to be used.
General education theories - mathematics education theories. One peculiarity in the implementationof international cooperation projects is that it often brings together agents from various specialisations,some with general education background and others who specialise in mathematics education. The
difference between the emphases of general education theories and mathematics education theories
may be subtle but it often leads to discords in practice. The well-known mathematician Han
Fruedenthal espoused disagreements in using educational research theories in designing themathematics curriculum (Gravemeijer & Terwel, 2000). General education theories focus on generallearning psychology whereas mathematics educators focus on mathematical thinking and problem
solving. General educational theories such as mastery learning, experiential learning, multiple
intelligence and 21st Century learning skills aims to enrich the learning environment for learners but
does not emphasise the learning trajectory as envisaged by mathematics education theories wheremathematising and problem solving are the main focus. The teaching strategies resulting from thesedifferent theories are at times divergent in its approaches. In planning for 21st Century skills, forexample, the general education approach would emphasise managing the class to create a learning

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environment that focuses on creativity, collaboration, critical thinking, problem solving, andcommunication. To fit into this structure, the mathematics educators would need to adapt and fit themathematics content and processes into this paradigm. In the process, often the mathematical process
like conjecturing, justifying, proofs, modelling, symbolizing and schematizing are de-emphasized.
Pure mathematics - applied mathematics. In pure mathematics, mathematics is viewed as a systemwith its own set of axioms, rules and theories immersed in logical and deductive thinking. It has its
roots on Platonism with little emphasis on applications. This emphasis on pure mathematics was themain focus of the new mathematics movement in the 1960s. While this approach keeps the purity ofthe mathematics discipline, it was not able to make mathematics relevant to learners in the school
context (Kline, 1973). Emphasis on applications on the other hand takes the approach of mathematicalideas being developed through real life applications which would make it more interesting for school
children. The balance of emphasis between the pure and applied approaches would very much dependon the ability of the learners to grasp the level of abstraction. This concern continues to be a hotly
debated issue in the development of the mathematics curriculum in the global mathematics education
community (Shimizu & Vithal, 2018b).
Universal mathematics – ethnomathematics continuum. Ethnomathematics assumes that it ispossible for practices of mathematics that to emerge from the local culture. While mathematics is often
accepted as a universal value-free discipline, yet its practice among non-literate children and adults
provide evidence that people are able to conceptualize mathematical ideas through their own culture
outside of the school setting (D'ambrosio, 1985; Terezinha et al., 1993; Gerdes, 1994; Barton, 1996).
The formal universal mathematics curriculum is therefore not necessarily the only path which makes
learning mathematics more meaningful. Projects in international cooperation should be cognizant oflocal practices and recognize that that these practices can be incorporated into the design of themathematics education projects. One of the challenges in international cooperation is to decide how
ethnomathematical practices can be incorporated into the development of the formal mathematical
instruction.
Mathematics classroom culture. One of the vital aims of mathematics education is to help teachers
create a learning environment that would provide children with the opportunities to develop
mathematical ideas. As a norm, there are three aspects that contribute towards this end, by designing
instruction that help children engage in mathematical activities, enabling teachers engage learners inmathematical discourse, and helping learners acquire the ability to reason with mathematical tools andsymbols (Cobb et al., 2011). Towards this end there have been numerous efforts to develop guidelines
to help teachers develop a classroom culture that would be conducive for children to learn mathematics(National Council of Teachers of Mathematics, 2000; Lewis et al., 2009). Yet this process of building
a classroom culture is complex. The aspects of culture in a mathematics classroom would include thetypes and sequence of classroom activities, the nature of mathematics discourse, the classroom
environment and teacher-student and student-student interactions which are accepted as the norm inparticular cultures. Inevitably, in constructing a vision for a mathematics classroom culture there is aneed to consider the activities and practices of the learners and teachers outside classroom, perhaps
even to examine the greater culture of the community. The beliefs and practices of the greater cultureof the learners and teachers matter. Views of accepted classroom culture inevitably vary acrosscountries. For example, Doig and Groves (2011) found that there were cultural impediments in
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adopting the Japanese lesson study in Australia. While the sharing of teaching practices in community
is widely accepted in Japan, Australian teachers view classroom practice as a private responsibility,
thus creating a constraint to its implementation. One of the challenges in international cooperation isfor the agents to resolve the conflicting cultural values that may impede the adoption of new teachingpractices.
UNDERSTANDING THE REALITIES IN INTERNATIONAL COOPERATION
Role of Narratives in Discourse
Situations in international cooperation at times present positions of disequilibria in authority especiallywhere donor-recipient relationships exist. This state of disequilibrium in authority and empowerment
could well create circumstances that lead to bottlenecks of opinions in the implementation ofinternational cooperation projects. Mindful of these possibilities, a pertinent first step towards
resolving the issues in international cooperation would be to better understand the discourse in thecomplex ecosystem of international cooperation. In situations where there is an imbalance of power, abroad spectrum of views of the self towards the authority is likely to exist. This can range from taking
a position of silence as a receiver of knowledge to one who is able to constructively contribute ideas
and knowledge (Belenky et al., 1986). Given the existence of different dispositions towards authority,
it is therefore essential that the interactions and discourse amongst the various agents be examined inorder to uncover the voices that are hidden in the narratives. Understanding the narratives of the various
agents would form a vital step towards understanding these interactions. Narratives are accounts orinterpretations of events that are expressed to reflect particular theories or one’s point of view (Bruner,1991). Narratives abound in both formal as well as informal settings. Bruner (1991) proposed several
characteristics that can be commonly found in narratives. Narratives are diachronic in nature. As
opposed to synchronicity, the diachronic nature of narratives implies that understanding narratives
requires the need to take into account its history and that its meaning evolves through time. Its
contextual character also means that its meanings need to be interpreted within the context in which it
is told. Moreover, narratives carry the narrator’s intentional state, yet possess hermeneutic
composability (Bruner, 1991). Narratives can be based either on true events or they could be fiction,in which case it would have the characteristic of truth likeness. Narratives are told to convey theintentions of the narrator, sometimes explicitly or at other times in subtle ways so as to protect theinterest of the narrator. Viewpoints and thoughts can be subtly conveyed through narratives insituations when explicit statements are inappropriate especially when these statements could result innegative consequences. One useful way to detect a narrative in a discourse is through events where thenarrator conveys a narrative which indicates a breach in canonicity or which is against accepted norms
and opinions. In the area of international cooperation, in situations where agents may not wish to
explicitly express their views for fear of reprisal, examining narratives could provide a pathway
towards uncovering the hidden views of the agents.
Dispositions of Narratives Related to Knowledge and Beliefs
Everyday narratives cover a wide range of topics. In order to examine narratives as a pathway towards
resolving the issues in international cooperation, it would be pertinent to focus on specific dispositions
towards knowledge and beliefs that are found in these narratives. Knowledge and beliefs ofmathematics have been acknowledged to influence mathematics instruction, not only in ways that9

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mathematics is learnt and applied to solve problems but also how it is taught (Ernest, 1991; Ball et al.,2008; Schoen & LaVenia, 2019). Knowledge and beliefs of mathematics provide the structural
foundations of thought that allows one to learn and acquire new mathematical knowledge, and to domathematics. In the current era of globalisation, Ernest (2016) reasoned that several aspects ofmathematical knowledge and beliefs influence the way the teaching and learning of mathematics ispracticed. It is our view that the mathematical knowledge and beliefs of the agents would similarly
impact on the way projects in international cooperation in mathematics education are designed,
planned and implemented. In view of its importance, this paper will focus on the dispositions in the
narratives that relate to the various aspects of knowledge and beliefs of mathematics (See Table 1.).
Views of self towards authority. Perceptions of self and views of teaching and learning are influenced
by biographical, contextual and interactional factors (Cheah, 2001; Cocklin, 1991). The context where
the workplace and the home influence the way these perceptions are constructed. Situations where
there is an unequal balance of power and authority cultivate perceptions that view the self as inept inconstructing knowledge. Belenky et al. (1986) outlined various epistemological perspectives
developed by people living and working in varying conditions where there is an imbalance of authorityand power. On one end, in situations where the authority gap between the authority and thesubordinates is wide, the encultured perspective is that of silence and being receivers of knowledge.
The subordinate would cultivate a self-perspective as being less able to contribute towards theconstruction of knowledge. As the authority gap narrows and people become more empowered, theperception moves towards that of constructed knowing, being one who is able to contribute andconstruct knowledge. A disposition of silence or receiver of knowledge could imply taking a positionof a follower during discourse. In the case of international cooperation, some possible causes for
adopting this disposition are: 1) cultural view of respect for superiors, 2) ineptness in communicatingin the language of discourse, 3) lack of knowledge in mathematics content or mathematical didactics,
and 4) personal benefit. The reason of personal benefit succinctly differs from the other three reasons
as it hints more of one’s personal volition rather than an imposition by environmental factors.
Views of knowledge. The modernist and postmodernist views of knowledge are two views commonlyused to describe personal philosophies of thought that emerged during the transition of society
following the industrial revolution (Ernest, 1991; 2016). The modernist views knowledge as objective,
depersonalised, value-neutral and easily transferable between persons; and prioritise the products oflearning. This belief translates into a behaviourist didactical approach. Teaching and learning
mathematics from the modernist view is therefore skewed towards fixed and predetermined procedures
where the infallible knowledge of mathematics is transmitted from the teacher to the learner. This is
in contrast to postmodernist view of knowledge as one that prioritises processes and the humandimensions of learning. The postmodernist view of knowledge posits that it is the learners whoconstruct mathematical ideas in the learning process.

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Table 1
Disposition of Narratives Towards Aspects of Knowledge and Beliefs
Aspects of Knowledge andDisposition
Beliefs
Views of self towards authority Receiver of knowledge

Views of knowledge

Constructed knowing- Able to create knowledge based on the context using subjective andobjective strategies
Modernist view of knowledge- Knowledge is objective, depersonalized, value-neutral and easilytransferable between persons; prioritize the products of learning
Postmodernist view of knowledge- Prioritize the process and human dimensions of learning

Views of knowledge
production(Gibbons et al. 1994)

Mode 1 – Source of knowledge is in academic disciplines

Views of management

Aligning beliefs and knowledge to accomodate elements of Performancebased management

Mode 2 – Source of knowledge is in the community of practitioners

Aligning elements of Perfomane-based management to accomodate beliefs
and knowledge

Views of source and production of knowledge. Gibbons et al. (1994) proposed that there are two typesof knowledge in regards to its source and production. Mode 1 knowledge refers to the production ofknowledge that is anchored in knowledge that is created by the community of researchers andacademics within the confines of academia in a specific discipline. The production of knowledge in
Mode 2, in contrast, theorises that the production of knowledge occurs in the real world wherepractitioners become active contributors in the production of knowledge. A belief in Mode 1
production of knowledge would emphasise a belief that knowledge about mathematics is created byresearchers in academia whereas a belief in Mode 2 production of knowledge leads to a belief thatpractitioners play an important role in the creation of knowledge in mathematics education.
Practitioners would be able to meaningfully add on and to expand knowledge especially in the practicalarea of the applied knowledge. Currently, there is a trend towards involving teachers actively in
education projects. This involvement of teachers as practitioners in education is purposively intended
to provide practical ideas to complement educational theories from academia. In this regard, having a
Mode 2 disposition towards the production of knowledge would serve as an enabler for the agents as
opposed to Mode 1 knowledge which would tend to inhibit the practitioner’s willingness to contributetowards discourse.
Views about management. Management practice too has evolved and is currently trending towards a
performance-based approach (Ernest, 2016). In performance-based management (PBM), the successand effectiveness of the project is evaluated and managed by setting key performance indicators andevaluating whether these targets have been attained. Performance-based management may or may not
be aligned to management practices that prioritise educational goals. Agents in international
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cooperation will thus be persuaded to adopt and adapt practices and plans so that they become aligned
to performance-based management indicators, forcing them to re-examine their values and beliefs
about the teaching and learning of mathematics. In response to the implementations of performancebased management, the dispositions of the agents towards management could include: 1) rejecting
performance-based management which would lead to positions of conflicts, 2) accepting performancebased management by either prioritizing PBM and adapting their beliefs and knowledge of educationto accommodate PBM, or prioritising their beliefs and knowledge of education and adapting theelements of PBM to accommodate their prior beliefs and knowledge.
Accessing and Analysing Narratives
There are some characteristics of narratives make accessing and analysing them challenging. It is
possible to access the narratives either as first-person narratives or as third-person narratives throughparticipatory observers. First-person narratives would require deep introspection to be carried out by
the agents and the ability to articulate them either verbally or in writing. This would be possible withsome of the agents at some levels in the international cooperation ecosystem. However, many agents
may not have the ability or volition to do this task. There is also the issue of reliability andtrustworthiness to consider. Accessing the narratives through participatory observers would be a better
choice. Ethnographic approaches could perhaps offer a more naturalistic setting to access thesenarratives. The diachronic and hermeneutic properties of narratives could entail a long period of datacollection, notwithstanding the possibility of a multitude of interpretation that needs verification.
These difficulties suggest that adopting a qualitative and interpretivist method to analyse narratives
could offer a more suitable approach than purely quantitative approaches. The interpretivist approach
adopts the assumptions that research is bounded by value, time and context, and that there are multiple
perspectives towards reality (Denzin & Lincoln, 1998). In the interpretivist approach, the researcher
and the participants mutually interact and are not expected to be detached as in positivist approaches.
Recommendations to ensure trustworthiness of the data analysis include prolonged engagement,
persistent observation and triangulation (Lincoln & Guba, 1985). Data collection methods could
include participant observations, ethnographic interviewing, search for artefacts and researcher
introspective reflections (Cheah, 2000). The standards and assumptions in the interpretivist approach
fit well with the context of international cooperation projects which are very often multicultural innature.
CONCLUSION
Trends in education in the twenty-first century are changing in response to changes in society that isundergoing transformation due to economical, technological and cultural shifts. Current trends point
to approaches that encourage and favor skills such as communication, collaboration, critical thinking
and creativity. Thus some dispositions may seem to be in the vogue while others may be seen as
traditional. The aim of examining the disposition in the narratives of the agents is not to endorse one
disposition over another as being superior. Rather, the aim of examining these narratives is to clarify
differences of opinions in discourse, taking into account the narratives of all the agents involved in theinternational cooperation projects. Examining the narratives allow us to determine the dispositions that
could be cause of these differences.

12Cheah & Isoda
The discussion in this paper offers a hopeful expectation that this discussion would lead to deeper
emprirical investigations into the narratives that exist in international cooperation in mathematics
education. Narratives provide a window into the thoughts of the agents in international cooperation.
This will provide a deeper understanding of the issues and challenges in international cooperation
leading to a resolution of these issues. Some immediate emergent questions about narratives relate toits cultural source: What narratives are specific to particular cultures and what narratives are common
across culttures? How does culture influence the ways the narratives are voiced? How can we create
environments that allow open dialogue so that agents can voice their narratives without fear of reprisal?
What are strategies that can be used to succesfully resolve differences in the narratives? Ultimately,
the aim for understanding these narratives is to strive for sustainability and improvements in the qualityof mathematics education globally.
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