Microsoft Word - 386- Ontology to ontologies (Proof 2).docx


 Journal of Urban Mathematics Education
  December 2021, Vol. 14, No. 2, pp. 42–70 

©JUME. https://journals.tdl.org/jume  

 
 BRIAN TWEED is a Senior Lecturer in Te Kura o te Mātauranga/The Institute of Education 
at Massey University, Private Bag 11-222, Palmerston North, New Zealand; email: b.tweed@mas-
sey.ac.nz. His research interests focus on the intersections of the ethics, sociology, and philosophy 
of education. He has a special focus on interactions between legitimation regimes, societal/social 
conditions, and the nature of different pedagogies and how non-Māori teachers and researchers en-
gage with Māori knowledge and practices. 

Indigenous Struggle With Mathematics  
Education in the New Zealand Context: 

From Neo-Liberal Ontology to Indigenous, 
Urban Ontologies?  

 
Brian Tweed 

Te Kūnenga ki Pūrehuroa, Aotearoa/Massey University, New Zealand  
 
In this article, the learning of conventional curriculum mathematics in one Indige-
nous Māori school in Aotearoa/New Zealand is conceptualized as a site of ontolog-
ical struggle. The major finding of a research project which analyzed extensive eth-
nographic data gathered in partnership with this school identified an ontological 
disjunction between curriculum mathematics education and the ethos of the school. 
This disjunction can be related to the complex and emergent phenomenon in Aotea-
roa/New Zealand of Indigenous schools in neoliberal, capitalist urban conditions. 
Centering the ontological commitments of the Māori school challenges the ontolog-
ical hegemony of curriculum mathematics education and points to a consideration 
of the possibilities of forms of contemporary mathematical education based on In-
digenous ontologies. Embedded in the discussion is a consideration of the ethical 
position of non-Indigenous researchers working in Indigenous contexts. 
 
KEYWORDS: critical culturally sustaining/revitalizing pedagogy, Indigenous edu-
cational sovereignty, Indigenous Māori mathematics education, urban indigeneity 
research ethics 
 

 
 
 
 
 
 
 
 
 
 
 
 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

43 

he focus of this article is on the ontological work that the presence of mathemat-
ics education based on a mandated national curriculum does in an Indigenous 

Māori school. The discussion is necessarily intimately connected with the Aotea-
roa/New Zealand context, which will be briefly outlined in the next sections. Aotea-
roa (the long white cloud) is the original, Indigenous name for the land now governed 
by the New Zealand State. 

To be clear from the outset, this article is not about the nature of disciplinary 
mathematics knowledge, Indigenous mathematical practices (ethnomathematics), or 
pedagogical practices designed to improve Indigenous student achievement in the 
terms of the New Zealand national curriculum. To paraphrase Foucault (Dreyfus & 
Rabinow, 1983, p. 187), the focus is on what the “doing of curriculum mathematics 
education does” when located in an Indigenous, Māori school, itself embedded in a 
long-term emancipatory social movement complicated by living in neo-liberal urban 
conditions. This focus prompts an investigation into the ontological commitments of 
both the Māori school and the curriculum mathematics education as constructed 
through the social practices of both. 

 
Urbanization and Urban Māori 

 
New Zealand society is now a thoroughly neo-liberalized, capitalist society that 

has established a neo-liberal ontology as the basis of almost all social and economic 
life (Fisher, 2013; Harvey, 2005; Kelsey, 2015). National education systems have 
also been transformed as part of the establishment of a neoliberal, capitalist hegem-
ony (Ward, 2012). Urbanization is understood as intimately and inextricably con-
nected with capitalism and, in the early 21st century, its neo-liberal governance for-
mations (Rossi, 2017). In New Zealand, colonization can be viewed as both a settler-
colonization project and a capitalist project that has successfully created dependency 
on market transactions for survival as well as a predominantly urban-dwelling Indig-
enous population (Poata-Smith, 2015).  

Māori have to a large extent migrated to urban centers, a process that intensified 
after World War 2 (Peters & Andersen, 2013). Now, over 80% of Māori live in towns 
and cities, with one quarter of all Māori living in Auckland, New Zealand’s largest 
city, and one sixth living in Australia, with the greatest concentration in Sydney 
(Haami, 2018). Today, in terms of location at least, Māori can be described as an 
urban people (Kukutai, 2013). 

In this migration to urban living, the nature of Māori identity has become con-
tested (see Hokowhitu, 2013; Kukutai, 2007). Whilst genealogical connections to an-
cestral, pre-colonization communities and homelands remain central to being Māori, 
urban living has resulted in an emergent range of Māori identities and adapted social 
practices (Kukutai & Webber, 2017). Generations of Māori have grown up in urban 
centers and identify primarily with these locations as urban Māori, who are far from 

T 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

44 

a homogeneous group (Ryks et al., 2016). In some ways, urbanization has blurred the 
traditional cultural and spatial separation between Pākehā (European New Zealander) 
and Māori, but even so, Māori communities remain distinctive and centered on Māori 
values and practices. These practices have been adapted to urban conditions and 
maintain commitments to Māori ontologies, values, and epistemologies in novel and 
creative ways (Gagné, 2013; Metge, 1995). For example, Māori have created suc-
cessful Māori businesses and business models (Mika et al., 2019), founded health 
providers (Durie, 2011), influenced the criminal justice system (Tauri, 1998), and 
established early childhood centers, schools, and universities (G. H. Smith, 2000).   

Māori continue to resist neo-colonization and the toxic aspects of urbanization 
whilst taking advantage of the beneficial aspects by reorganizing the resources avail-
able to maintain Māori social practices, community integrity, and social structures 
(Keiha & Moon, 2008). In addition, Māori are developing sufficient strength politi-
cally and economically to renegotiate relationships with the state and the multicul-
tural nature of general society (Gagné, 2016). This also positions Māori to be able to 
engage on different ontological and epistemological terrain with the challenges that 
face humanity in the 21st century. In relation to this article, this includes forging new 
relations with all existing knowledge domains, regardless of cultural location, and, in 
particular, the discipline of mathematics. 

The perspective adopted here is that Māori schools are integral to this urban 
experience and are another example of how Māori have adapted to urban, neo-liberal 
conditions in ways that maintain Maori language and cultural reference points. The 
school that partnered in the research reported in this article was based on Māori lan-
guage and culture but also dealt with events and attributes related to the school being 
situated within urban conditions. For the purposes of this article, Māori schools are 
understood in this context: they are part of a wide-ranging, multidimensional, Indig-
enous response to urbanization and the neo-colonial, neo-liberal subtext as a funda-
mental part of a Māori emancipatory movement. 

 
Non-Indigenous Researchers and Indigenous Contexts 

 
Linda Tuhiwai Smith explains that there has been a history of researcher abuse 

of Indigenous populations, which rightly sounds a warning and creates caution about 
the engagement of non-Indigenous researchers in Indigenous contexts (L. T. Smith, 
2013). In Aotearoa/New Zealand, the broad research orientation known as Kaupapa 
Māori Theory has established itself at the center of research ethics and excellence 
with, by, and for Māori (Bevan-Brown, 1998; Pihama et al., 2015; G. H. Smith, 2009, 
2011, 2012; L. T. Smith, 2005, 2011).  

In this regard, two factors need to be considered. The first is the non-Indigenous 
ethnicity of the researcher. The second is the influence of non-Indigenous theory in 
the construction of analytical frameworks. 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

45 

Who Is This Researcher? 
 

The researcher was born and brought up in England and migrated to New Zea-
land in the late 1980s. Strictly speaking, because the author is not Māori, the research 
described here cannot be described as Kaupapa Māori. The researcher, however, has 
been closely associated with Māori schools and communities for over 20 years, has 
taught, as a fluent speaker of te reo Māori (the Māori language), in Māori schools and 
universities, and has created professional learning opportunities for Māori teachers 
in mathematics and science (Te Maro et al., 2008). Moreover, the researcher contin-
ues in and is committed to these relationships with Indigenous communities built up 
over many years (Tweed, 2019). By marriage, the researcher is also connected to the 
Iwi (tribe) Ngāti Porou. The long association and commitment to te ao Māori (the 
Māori world) by the researcher through work, family, and social life places this non-
Indigenous researcher appropriately for research in the Māori communities of which 
the researcher is already an accepted member. 

The researcher also has a longstanding relationship with the Māori school that 
partnered in this research. This relationship was established well before the research 
was conducted and continues in the present well after it has been completed. 
 
Non-Indigenous Theory and Engagement in Indigenous Research Contexts? 
 

Whilst acknowledging the power and relevance of theoretical frameworks 
grown from entirely within Māori/Indigenous cultural spaces and communities, it is 
suggested here that this does not mean that research employing non-Indigenous, Eu-
rocentric frameworks has nothing meaningful to contribute to Indigenous research. 
The use of theoretical frameworks created by European researchers/thinkers is not 
sufficient by itself to assert that the research is automatically Eurocentric in its en-
tirety. Eurocentrism also entails that European/North American (Western) interests 
and outcomes as well as conceptual understandings are centered. Research using the-
ory produced by European thinkers to critique this Eurocentrism counters oppressive 
systems that prevent the emergence of spaces in which Indigenous culture, language, 
and worldview are centralized. This signposts a direction towards an ethical position 
for non-Indigenous researchers working in Indigenous contexts. 

The exclusionary stance by some scholars that dogmatically rejects research by 
non-Indigenous researchers and/or using non-Indigenous theoretical frameworks is 
problematical and ultimately unproductive. Several prominent Māori scholars have 
commented on this issue.  

Te Kawehou Hoskins (2012) explains that Māori essentialism, which lies be-
hind such dogmatic exclusions, has been a necessary political stance over the last 40 
years in order to resist European-based cultural, material, and political dominance in 
New Zealand. She also contends that such a stance is unsustainable because it reifies 
both Māori and non-Māori identities and thereby cannot recognize the heterogeneity 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

46 

of both Māori and non-Māori (the researcher and the participants in this research, for 
example, do not match these reified identities). Instead, Hoskins argues for an open, 
relational stance that accepts the potential and risks for new knowledge generation of 
engaging ethically with the non-Indigenous other and non-Indigenous knowledge 
frameworks.   

In a similar vein, Stewart (2018) argues for the deliberate and critical working 
of the Indigenous-settler relationship. She refers to dualities between social reality 
and discourses that pervade Māori lives in all spheres of life, creating “hyphens” that 
she contends should be productive relationships rather than antagonistic and exclu-
sionary. Stewart comments that 

 
Critical Māori scholarship is better off working with hyphens rather than against them. 
This can also be expressed as seeing hyphens, such as the Māori-Pākeha [Europeans 
settler] hyphen, not as symbols of either-or exhausting battles, but of both-and enriching 
collaborations. (Stewart, 2018, p. 773) 
 
The research detailed in this article could be viewed in these terms as a critical 

and productive working of the Māori-Pākeha hyphen, which explores the tensions 
created by a duality established between the discourses of curriculum mathematics 
education and social realities of Māori. 

 For Te Ahukaramū Charles Royal, who has written extensively about Māori 
knowledge (mātauranga Māori) and epistemology, it is understood that 

 
…movement ‘towards a new Indigenous epistemology,’ at least in Aotearoa/New Zea-
land, will involve the development of a way of studying the nature of knowledge (and 
its attendant questions) that finds inspiration both in conventional Western epistemology 
and in mātauranga Māori. (Royal, 2009, p. 119) 
 
Royal contends that contemporary mātauranga Māori can benefit from and in-

form other knowledge domains and proposes a new Indigenous epistemology based 
on contemporary forms of Māori concepts and practices, which has the potential to 
engage with any other domain of knowledge from a Māori ontological position. Alt-
hough this is not an argument for the involvement of non-Indigenous researchers, it 
does carry with it an understanding that non-Indigenous people may be involved in a 
contextualized manner, that is, appropriate to the context of research. Here it is un-
derstood that in some contexts, non-Indigenous involvement is appropriate with suf-
ficient ethical and cultural understandings, whilst in other contexts it is entirely inap-
propriate regardless of the competencies of the researcher. Moreover, it is for Indig-
enous communities themselves to decide on the appropriacy of such involvement in 
any given context. 

In this regard, it should be noted that the research outlined in this article is not 
a purely Indigenous one; it involves the interaction between a Western knowledge 
system (curriculum mathematics education) and an Indigenous school in urban 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

47 

conditions. There is an entanglement here that sees history as simultaneously both 
Māori history and Pākehā (European settler) history, with multiple and varied inter-
actions, overlaps, and ambiguities. As Jones (2007) points out, there is also the pos-
sibility that multiple distinct and irreconcilable events occur simultaneously, result-
ing in an interminable tension” between them, which may be the case in this research.   

Penetito (2010) contends that Māori education is in fact circumscribed by gov-
ernment, majority culture concerns, policies, and agency. Māori schools are still 
charged with producing the same outcomes as any other school in addition to their 
efforts towards emancipation. In this context, both Indigenous and non-Indigenous 
theoretical frameworks have a place. Te Maro (2019), for example, uses both Fou-
cault and Marx to reveal how curriculum mathematics education confines time, 
space, and subjectivity to the instrumental domains of the economy. She argues that 
Indigenous frameworks must drive development of Indigenous communities from 
the inside, but Western theory can be powerful in the analysis, and therefore minimi-
zation of harm, of systems that impinge upon/oppress Māori from the outside. 

Thus, it is considered here that the use of non-Indigenous frameworks in Indig-
enous contexts is challenging but, with care, critical engagement, and cognizance of 
the history of the Māori/Pākehā relationship, potentially productive. This care and 
critical engagement with theory involves the researcher as bricoleur, carefully attend-
ing to how concepts from many disciplinary domains are reinterpreted and relocated 
in the research context to create robust and rigorous research methodologies (Kin-
cheloe, 2001, 2005). Done well, the use of non-Indigenous theory can support the 
purposes of Māori communities and maintain their centrality whilst generating useful 
knowledge of interest in other contexts. Kaupapa Māori research prioritizes the use-
fulness and ownership of the research but maintains an open stance about the methods 
used (Moewaka-Barnes, 2015). The Māori school involved in this research certainly 
owns this research and continues to use the findings to develop its own approaches 
to engaging with mathematics. 

Having argued for the conditional legitimacy of non-Indigenous researcher in-
volvement in Indigenous-oriented research (conditional upon context), more remains 
to be unpacked about the nature and ethics of this involvement. The “doing” of re-
search always comes under an ethical umbrella, the importance of which is amplified 
when non-Indigenous researchers engage in Indigenous-oriented research. Here, I 
will draw briefly on the work of Biesta (2015) and Yukich and Hoskins (2011), who 
are inspired by the philosophical work of Levinas’s concept of ethical responsibility 
for the other (see Levinas, 1961/1969, 1974/1998).  

Biesta (2015) critiques what he describes as the dominant discourse of learning 
on the grounds that it positions teachers and students (and people in general) in a 
particular relationship with the world. In this relationship, we are meant to grasp and 
know the world in its entirety and to continue learning until this is achieved. The 
world, which includes other people, is, in this view, a thing that is at our disposal, 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

48 

subject to and an object of our knowing. This relationship is a form of possession. 
Instead, Biesta argues for an education that allows us to be confronted by the world 
and for us to be taught by it. In this relationship, the world is not positioned as a thing 
to be known but as an entity with its own purposes and actions that in certain aspects 
must always remain unknowable to us. 

Yukich and Hoskins (2011) take up this Levinasian perspective in the context 
of Pākehā school principals who have developed competencies in engaging with 
Māori communities. The central theme here is that these principals developed prac-
tices of simultaneous knowing and not-knowing with respect to Māori. Over time, 
they developed understandings of language and practices and were able to participate 
competently in them. At the same time, this knowing automatically highlighted what 
they, as Pākehā, do not yet know and can never know. The position suggested here 
is an ethical one. Whilst learning from Māori and developing cultural competencies 
and responsivity as non-Māori is pursued, this must not be a pursuit of ownership, 
possession, and control. It must rather be a pursuit of self-knowledge precisely so 
that an ethical care for Māori, as the other, can exist, which reminds “…dominant 
groups such as Pākehā to resist the will to mastery, the desire to wholly know and 
‘see’ others… to protect the radical alterity and the cultural difference of others” 
(Yukich & Hoskins, 2011, p. 63). 

Taking up this same ethical position in Indigenous research, demands that non-
Indigenous researchers, even as we gain valuable insights and generate new 
knowledge and understanding, acknowledge the historical relationship that has ex-
isted between Western research and Indigenous communities, a relationship which 
L. T. Smith (2013) describes as a claim to ownership of Indigenous ways of knowing 
and being and a rejection of the people who created them. This entails the under-
standing that the knowledge generated by research is not knowledge of the other but 
knowledge for the other, spoken inevitably from a position of power but spoken in 
such a way that attempts to simultaneously challenge this power; it is spoken by the 
non-Indigenous researcher without expectation of reciprocity, without any expecta-
tion that it will be implemented. Resisting the will to know here means that the non-
Indigenous researcher offers their work not as a claim to truth but as a tentative pos-
sibility, a suggestion of possible meaning always prefaced by statements of fallibility 
and subjectivity. Indigenous people and communities may accept or reject such work 
on their own sovereign terms (which always remain partially unknowable to the non-
Indigenous researcher). Research becomes a mixed practice of tentative knowing, 
speaking, and deliberate ignorance. 

  
 
 
 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

49 

Research Methodology 
 

The overall aim of the research was to infer ontological commitments from 
social practices operating in mathematics classes and in the general operation of 
school life (the ethos). Since the researcher already had an established relationship 
with the partner school in the research, an ethnographic methodology was used. The 
researcher spent a period of 12 months collecting data from classroom video record-
ings, individual interviews, focus groups, and field notes.  

Analysis of data employed concepts taken from Legitimation Code Theory 
(LCT; Maton, 2014), recontextualized to suit the Indigenous context of the school. 
The main concept employed from LCT was that of specialization, which refers to the 
ways in which social practices specialize a person’s subjectivity. LCT informs the 
analysis by alerting us to the nature of social life as involving (amongst other things) 
a specialization of the relation to knowledge and a specialization of the relation be-
tween people. Thus, analysis of data involves asking the following question: what 
kind of epistemic relation (how knowledge is understood and is to be acquired) and 
what kind of social relation (how people live with each other) are legitimized in the 
social field?  

LCT further recognizes two forms of each relation. The epistemic relation is 
considered as ontic or discursive, indicating a direct relation to the object of study 
(ontic) or the study of an established discourse about it (discursive). The social rela-
tion is considered as subjective or interactive, indicating social practices based on 
belonging to a certain group (subjective) or based on ways of interacting (interactive).  

These concepts come together by viewing social fields as having characteristic 
configurations of how knowledge and knowers are structured, which in turn special-
ize subjectivity in particular ways (Maton, 2006). The specialization of subjectivity 
is considered to be equivalent to an ontological commitment to a certain kind of per-
son constructed through participation in the practices of that field. 

 
Findings and Discussion 

 
Throughout analysis of empirical data, these specialization concepts were re-

contextualized and sharpened for the Indigenous context of the school. The ontic ep-
istemic relation was reinterpreted to correspond to direct experience of students and 
teachers in real event (a participatory epistemology) as a preferred form of knowledge 
generation and learning for students. The discursive epistemic relation came to mean 
an engagement in a formalized knowledge discourse about an object of study rather 
than a direct engagement with that object of study. Similarly, for the social relation, 
a subjective social relation came to mean the possession of genealogical links to tribal 
ancestors (of any Iwi/tribe), and an interactive social relation became a focus on 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

50 

explicit, institutional/disciplinary specific rules of behavior/interaction between peo-
ple, regardless of genealogy.  

This led to the major finding of the research: the overall specialization of the 
whole school ethos was based on an ontic epistemic relation and a subjective social 
relation, but the specializations in mathematics classes were based on a discursive 
epistemic relation and an interactive social relation. In other words, the school ethos 
was about an engagement with the world as it currently exists from a position of 
Indigenous inclusion in ways (both formal and situational) dictated by the nature of 
this engagement. Curriculum mathematics education was about mastering the exist-
ing discourse of curriculum mathematics from the position of a generic learner. 

The following sections present some examples of empirical data, with interpre-
tations in italics relating them to specializations of the school ethos and three mathe-
matics classrooms.  

Quotations appear in English, but the original data was entirely in te reo Māori 
(Māori language). This presented the methodological problem of how to maximize 
the fidelity of the English translations. This was accomplished by an iterative process 
of collaborative translation and checking with participants (who are all bilingual 
speakers of Māori and English) until participants confirmed that the English version 
conveyed the intended meanings. 

 
The School Ethos 
 

The school is small, with around 120 students and six full-time teachers. It is 
located in the center of a medium-sized town and has the full range of students from 
age five to 18. Students come from a wide variety of socio-economic backgrounds, 
with all of them being Māori and being able to function in a cultural context in which 
Māori language and cultural practices are centralized.   

The school is a second home for students, teachers, and their families. It is com-
mon for teachers, students, and visitors to sleep overnight in the school. There is a 
supply of mattresses and bedding for that purpose. Teachers and students have a re-
sponsibility to look after the school as if it were their home. The caring of the grounds 
and buildings of the school is direct; responsibility for its upkeep rests with everyone 
who lives in the school. 

 

 

Interpretation: 

Although the school is small, it caters for a full range of students from all socio-economic 
groups in the town.  Being Māori and forming a community based on Māori cultural protocols 
and norms (tikanga) is a way in which the school responds to urban conditions and the wealth 
disparities that have been exacerbated under neo-liberal reforms over the last 40 years. This 
has a clear association with a subjective social relation. 

 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

51 

The school has a particular orientation towards students being kaitiaki (custo-
dians) of their lands and natural resources, being upholders of the Māori language, 
and being exemplary representatives of their Iwi (tribe). Quoting a kaumatua (an el-
der, Koro1), one teacher, Te Mana, made this statement:  

 
Koro says that we must learn all of the real (Māori) names of places and the histories of 
them in our Iwi (tribal) area. If we don’t, we will be just like the Pākehā (European New 
Zealander), who are only visitors to our lands and will soon be gone. 

 
The school operates on the basis of tikanga (culturally correct actions), which 

are not written down as a set of policy statements. Tikanga are culturally correct ac-
tions learned through participation in real cultural activities. Several comments from 
various teachers during family and staff meeting reiterate the prioritization of lan-
guage and tikanga. The prioritization is certainly related to both a need to protect the 
Māori language and tikanga Māori as well as a response to perceived oppression.  
Two such examples are given here: 

 
What’s important is that our own knowledge is fed to our children… we have been op-
pressed for long enough by those external systems that tell us what knowledge we should 
be teaching and how we should organize ourselves 
 
What’s important is not math, it is the Māori language... mathematics is not endangered; 
it can look after itself and will be there when we are ready for it... if we don’t speak 
Māori, it will die. 
 

                                                
1 All names are pseudonyms. 

Interpretation: 

The social relation includes a relation between people and the land. Being Māori and having 
an ancestral connection with the land on which you stand gives a more nuanced understand-
ing of what a subjective social relation means in this context.  

 

Interpretation: 

The strong desire to base all aspects of school life on Māori philosophy is clearly expressed 
here. Tikanga relates to an underlying Māori worldview (ontology) that recognizes language 
as a fundamental aspect of how Māori relate to the world and think of themselves in it. The 
frustration with external systems, including curriculum mathematics education, is also clearly 
expressed. The desire to relate to the world not through external knowledge systems but 
through an autonomous Indigenous ontology characterizes a strong ontic epistemic relation in 
this context. The recognition that mathematics will look after itself recognizes its discursive 
nature, but Māori language and Indigenous knowledge have a high degree of ontic urgency 
about them—the ontic imperative exists for them to survive. 

 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

52 

A general feature of the school is a prioritization of naturally occurring, expe-
riential learning. Priority is always given to real cultural events, such as pōwhiri (wel-
come ceremonies) and tangihanga (funerals). Often the whole school will travel large 
distances in order to attend such events. The school is a genuine cultural institution 
in its own right that engages in actual cultural life. It is already embedded in the wider 
cultural constellation of the Iwi and in this sense is much more than just a school.  
Celebration of times of the Māori calendar are real participations. For example, the 
celebration of Matariki in June or July (the beginning of the Indigenous new year in 
the southern hemisphere winter) is not a school learning experience but a genuine 
celebration of the changeover of a natural cycle in Aotearoa/New Zealand—it is a 
cultural connection with the land, a recognition of change and the continuing pres-
ence of ancestors. One teacher commented on it in this way: 

 
Participating in Matariki reestablishes a spiritual link with ancestors. In the early morn-
ing, it is still dark, its cold... the connection is easier to make... somehow Nanny is close, 
and I remember her and mihi [greet] to her for all that she has done for us... she is still 
doing it right now actually. 
 

 
The relationship with the New Zealand national curriculum is ambivalent.  One 

teacher commented as follows: 
 
The [national qualifications] are done as quickly as possible so that we can get on with 
what really counts... developing students as Māori people located in a Māori reality.  
 
Officially mandated knowledge is seen as an imposition in some respects, but 

this is completely consistent with the school’s basis on tikanga and real learning 
through real cultural participation; time spent on curriculum learning is time taken 
from the main purposes of the school. Students must have qualifications in order to 
gain access to university or other tertiary training or employment, but the real job of 
the school is to grow Māori speaking and thinking people. 

Interpretation: 

There is a strong sense of the immediacy and authenticity of this event. Teachers and students 
experience a closeness with ancestors at this time. This can be related to a strong ontic epis-
temic relation; teachers and students participate in this event and experience it in all aspects 
of their being—intellectually, emotionally, physically, and spiritually. The learning is both col-
lective and personal, but it is not reproducible in precisely the same way. This represents an-
other important difference from a curriculum mathematics discourse, which to a large extent is 
about fungibility; students are expected to pass through the levels of the curriculum and 
emerge at the end in possession of similar knowledge, skills, and dispositions. From a curricu-
lum mathematics viewpoint, students are effectively interchangeable, a situation which is con-
sistent with an economic demand for cohorts of students who have been equipped with neces-
sary knowledge and skills for employability. 

 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

53 

Assessing students against external measures based on the age of students, such 
as the levels in the New Zealand national curriculum, is rejected. The principal of the 
school expressed it in this way: 

 
It feels like a real intrusion, an intrusion of judgmental thinking into our family where 
the development of our tamariki-mokopuna (children and grandchildren) as people is the 
most important thing. 
 
Despite a strong tendency for integrated and thematic approaches throughout 

the school, mathematics remains as the most defined standalone learning area. All 
teachers have dedicated times when mathematics learning happens in isolation.  
There are also dedicated assessments of students. 

 

 
The principal also commented on a mismatch between family interests and the 

school ethos in relation to mathematics: 
 
Even when we report how well children are doing in terms of growing and learning in 
their Māori identities, like growth of manaakitanga (caring), tautoko (support), and 
mātauranga Māori (Māori knowledge), they still want to know where their child is in 
mathematics.  I think even if we reported about integrated mathematics, they would still 
want to know about basic facts and levels... and it’s all pressure from outside. It’s not 
our kaupapa (reason for being/purpose), it doesn’t belong to us. If the compliance thing 
wasn’t there, mathematics could be very different.   
 

 

Interpretation: 

This illustrates the mixed and somewhat confused discursive nature of societal attitudes to 
knowledge even in Māori communities. Urban conditions make the necessity to gain employ-
ment paramount, and competency in mathematics is seen as fundamental to this economic im-
perative. Both families, teachers, and students carry these discourses about the universality of 
mathematics and its importance to “everything” into the school. Resisting this pressure from 
outside takes a lot of energy. The desire for a different form of mathematics education is very 
apparent and represents a manifestation of the clash between ontic and discursive epistemic 
relations. 

 

Interpretation: 

This highlights the disjuncture between the ethos of the school and mathematics classes, 
which remain outside the integrating themes uniting the rest of learning in the school. This is 
a clash between the ontic epistemic relation of the school and the discursive epistemic relation 
of the mathematics classes. The rejection of assessment against the levels of the national cur-
riculum also emphasizes the ontic epistemic relation; for this school, students (and people in 
general) develop knowledge at their own pace through their own experiences over time and in 
real events. This cannot be hurried or planned ahead in a step-by-step hierarchical structure. 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

54 

The principal expresses a very strong feeling of frustration with the need to 
comply with external regulations, especially the national curriculum. The thinking is 
certainly present that the school should create its own curriculum. Coupled with a 
rejection of a curriculum that is designed in levels that are used to measure students’ 
learning, there is a desire to ground any new curriculum in the local Iwi context. One 
teacher put it like this: 

 
I went through an English-medium school, and the teachers knew exactly what we were 
going to do each lesson... but that destroyed my creativity... it was like I couldn’t have 
my own thoughts... that’s why I think it’s better for us to create our own curriculum, so 
that the people who are based here, who live here, decide what’s in it and how its orga-
nized... how it can be planned so that the students are alive in it. 
 

 
The school as an institution prioritizes the personal development of each unique 

child located in a Māori reality. The collection of unique and very different people 
who make up the school community is bound together by a common understanding 
of tikanga, Māori language, and Iwi identity. Tikanga provides a central common 
grounding that is the basis on which individual development is made. The following 
two comments, the first by the principal and the second by a senior teacher, express 
this aspect of the school: 

 
Tikanga is about meeting each person’s physical and spiritual needs... that’s really what 
Maslow’s hierarchy of needs is about as well... when a person’s needs are met, they have 
everything they need to become who they are, and they will be able to do anything they 
want. 
 
Rather than preparing our children for university and conventional careers, we should be 
preparing them to exist in the world as unique people defined in their own ways... it’s 
not about economics even, or about preparing students so that they can bring skills back 
for the Iwi, like becoming doctors or accountants... it’s about students being their own 
unique selves in the world. 

Interpretation: 

Again, the tension and the sense of constraint and oppression through external regulation is 
clearly expressed. Importantly, the deeper impact of this on Indigenous people’s thought pro-
cesses and identity is also expressed. The response to this is to create a curriculum based not 
only on Indigenous worldviews but also, specifically, driven by the lived experiences of Māori 
people in this locality. In other words, a curriculum based on an ontic epistemic relation and a 
subjective social relation is desired. 

 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

55 

 

 
Teachers and students responded in a variety of ways in mathematics lessons. 

The following sections focus on three mathematics classes and the teachers Te Ara, 
Te Mana, and Te Ao.  

 
Classroom 1, Teacher: Te Ara 
 

Te Ara organized very structured lessons that adhered very closely to official 
curriculum resources and engaged students in learning the standard procedures, strat-
egies, and algorithms required to solve problems. In many ways, Te Ara embodies a 
strong version of the standard curriculum mathematics discourse. 

Te Ara expresses a high level of anxiety about mathematics achievement data.  
Major concerns center on the lack of adequate achievement data and a lack of con-
sistency between different teachers. Te Ara comments: 

 
The school hasn’t given me any information about the children I am teaching. I have no 
knowledge or where the children in the class are at in mathematics. I think things would 
be so much easier for everyone if we all follow the same journey and use the same as-
sessments. We will all know then where we are in the curriculum and what we should 
be doing next. 
 
For Te Ara, curriculum mathematics knowledge is essential for survival in the 

modern world and is a fundamental aspect of the happiness of the child. If the school 
does not prioritize mathematics in favor of developing children in a holistic sense, 
problems will arise. This is associated with the ubiquitous nature of mathematics as 
an inherent part of everything, especially the well-being of children. 

 
Mathematics is important because it is all around us… and I have seen a lot of children 
who lack confidence and have felt they are dumb and have hidden and shied away from 
mathematics because they don’t want to other people to see that. Outside the gate, there 
are numbers all around us. Children have to be competent to deal with the numbers they 
will meet in their lives. There is nothing wrong with building the child’s wairua (spirit), 
but the reality is that mathematics is in everything… this building has to do with num-
bers… the school runs on mathematics really, I think. 
 

Interpretation: 

These quotes all circulate around an emerging conception of education in this Māori school 
based on being Māori and engaging in/with the contemporary world as unique beings. This in-
tegration of collectivity (being Māori, being Iwi) and individuality (flourishing as a unique be-
ing embedded in the world) is expressed in the more formal terms of this research as the overall 
legitimation of people based on a subjective social relation and an ontic epistemic relation.  



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

56 

For Te Ara, mathematics has its own protocols and culture that must be learned 
if students are to find a place in the economic system outside of a Māori context and, 
more importantly, be able to understand the world, which is inherently mathematical. 

 
The children at my last school were happy in mathematics because... in a psychological 
sense... they were strengthening their minds, and this strengthens their spirit… because 
they have overcome a challenge, and this is a good thing no matter what the challenge; 
to overcome it strengthens the spirit. 
 
Mathematics is construed as having fundamental connections to the material 

world and human life.  Mathematics is necessary for understanding and being able to 
participate in the modern world. Te Ara expands the importance of mathematics, 
which is the same as English-medium curriculum mathematics, from being about 
numbers to being about “the ability of people to speak and to understand the world.”  
It is a form of knowledge that underpins the nature of being human itself.   

Students in Te Ara’s class are for the most part happy because they can follow 
the procedures laid out for them to follow. Te Ara has a very definite set of behavioral 
rules. Students are strongly controlled to adopt a quiet, thoughtful approach and pay 
careful attention to correct procedures and language use. A common practice is for 
individual students to stand up in front the class and explain how they solved a prob-
lem using correct mathematical terms and symbols.  

Students occasionally experienced distress when they were unable to follow a 
procedure. When this happened, Te Ara momentarily relaxed the usual behavioral 
rules and defaulted to ways of speaking and interacting that were aligned with the 
school ethos; students’ well-being and personhood were prioritized. 

 

 

Interpretation: 

Te Ara represents a very formal approach to mathematics education. Legitimation is very much 
about mastery of the techniques, language, and symbolic representations of the curriculum ver-
sion of mathematics coupled with “proper” behavior and participation in public displays of 
mathematical performance. 
There is much tension between this approach and that of the school ethos expressed in a variety 
of ways, but all centered on Te Ara’s focus on the importance of mathematical competencies to 
life in a capitalist economic system and the urban context. In the perspective underpinning 
practices in this classroom, without mathematics, students are not only destined for poverty but 
also an inability to understand the world, which is conceived as inherently mathematical. This 
tension peaks and is resolved when students show distress, which allows the school ethos to re-
assert itself in Te Ara’s mathematics classroom.  
The dominant form of legitimation here is based strongly on a discursive epistemic relation (the 
engagement with mathematics mediated by the official discourse of curriculum mathematics ed-
ucation) and an interactive social relation (based on explicit formal rules of behavior/perfor-
mance). In this class, being Māori, being unique, only resurfaces in times of distress. 
 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

57 

Classroom 2, Teacher: Te Mana 
 
Te Mana prioritizes real world skills that are needed to operate in the wider 

world. This usually means handling money and everyday activities like cooking and 
fishing. 

The usual practices and lessons are thought of in terms of pedagogical tech-
nique and mathematics knowledge acquisition. Te Mana mentions adjusting practices 
sometimes if the students are unsettled but otherwise there is a consistent sharp focus 
on mathematics learning and ensuring that students “stick to the point.” 

Te Mana indicates a strong influence from English-medium mathematics edu-
cation. Lessons focus strongly on what the teacher needs to do for students to 
“achieve the highest levels.”  At the same time, there is an awareness of a potential 
injustice that lies within the universal status of mathematics. Te Mana had this to say 
on the matter: 

 
I haven’t thought about who wrote the curriculum and other resources in Māori.... no 
doubt they are just translations of the English versions... it seems like assimilation...  be-
ing pressured so that our ways of organizing things and thinking about things are just the 
same as Pākehā [European New Zealanders]... we don’t want that. 
 
The tension Te Mana feels here is strong; Te Mana would rather reject these 

imposed practices in favor of developing unique, Iwi (tribal)-specific mathematics 
practices and language. This is desirable, but it may contradict a need to be able to 
measure progress of students’ learning and the need to “know whether you are at the 
national average.” 

The strength of this contradiction, which Te Mana calls a “weird situation,” is 
summarized so: “we try and think mathematics and we don’t relate it to the actual 
way we are.”  Te Mana thinks that her own consciousness is changed when teaching 
mathematics in part because you “have to think like this (mathematically)” and “you 
can’t do what you want.”   

Te Mana is conflicted in several ways about mathematics and how it is learned.  
In terms of making progress through the levels of the curriculum, Te Mana professes 
impatience at not being able to “hurry up and finish tasks” but at the same time rec-
ognizes the need for patience and time to allow students to develop deeper under-
standings. For Te Mana, there is a strong tension between meeting targets and mean-
ingful learning. Te Mana predominantly uses standard curriculum problems but 
sometimes attempts integrated work, which she believes will “increase the creativ-
ity.”  However, Te Mana comments: 

 
When we do the integrated work, we sort of lose sight of the mathematics that we are 
supposed to be learning. It’s hard to tell what the children are learning sometimes, and 
they might go off and do all kinds of things... good things... but not mathematical. It 
doesn’t feel like mathematics anymore. 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

58 

 
Te Mana comments that the overall purpose of the school is to produce a kind 

of person primarily defined in terms of personal human attributes. Such a person is, 
 
...a type of Māori person: a gentle person, caring, open to all kinds of learning, with 
humility... so we should be producing a sort of person who in the first place will be 
following their gifts and enthusiasms and that makes them all different but at the same 
time they will all be the same in other personal qualities, like caring, hospitality, open-
ness, respecting others. 
 
Apart from a potential place in following their gifts and enthusiasms, Te Mana 

does not regard mathematics knowledge or any other kind of knowledge to be essen-
tial, but people should be open to all kinds of learning. 

Te Mana has a number of critical insights that appear to undermine a commit-
ment to the way mathematics is being done. For example, the performance of math-
ematics merely to show that you have mastered what is expected (i.e., “doing math-
ematics to show you have done mathematics”) is rejected. Te Mana also contends 
that there is a destruction of the unique cultural understandings in traditional activities 
when they are treated as mathematics exercises. Te Mana explains how students ex-
amined number patterns in tukutuku panels (traditional geometric designs that ex-
press cultural understandings). Here it was realized that the cultural purpose of doing 
tukutuku had been lost. Te Mana commented further: 

 
I’d like to get them to make a real tukutuku, an authentic one… I should ask Nanny P (a 
Māori elder)... not just do nice mathematics patterns as if they were tukutuku. 
 
In a similar way, Te Mana finds the notion of standardized assessment ex-

tremely problematic because of the idea that “a child should show predefined attain-
ments at a certain age when the curriculum doesn’t have any idea about the child and 
the world they live in. This is a real affront to the child.”  



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

59 

 
Classroom 3, Teacher: Te Ao 

 
Te Ao is a young teacher who has been teaching at the school for four years. 

Te Ao is the only teacher who has been exclusively educated in kohanga reo (Māori 
language preschool) and Māori schools; all other teachers were educated in English-
medium schools and made the switch to the Māori school after teacher training.   

Te Ao’s current view of mathematics focusses on informal knowledge useful 
in the world outside of the school. This includes providing tools that support, for 
example, dealing with finances and managing time. Te Ao prioritizes work that is 
relevant to things that will benefit students outside of the school. 

Te Ao expresses a belief in the universality of the basis of mathematics across 
languages and cultures.  Mathematics has a common basis for all people in the world.  
For Te Ao, this derives from universal needs that cause all people to develop practices 
such as navigating, cultivation and gathering of food, and creating shelter. 

Te Ao asserts that in modern times, mathematics has become similar all over 
the world because of national school systems. Te Ao suggests that before such sys-
tems, mathematical knowledge was more varied and dependent on context, language, 
and culture.   

Te Ao picks the parts of the curriculum that are most relevant for students. In-
formal types of mathematics are associated with traditional cultural activities, such 
as rāranga (flax weaving), providing food for visitors, building canoes, and navi-
gating by the stars. These activities are based largely on estimating measurements 
and the testing out of ideas through direct experimentation. This informality is 

Interpretation: 

The mathematics classroom of Te Mana represents an “intermediate” position. The approach 
is similar to that of Te Ara, but there are many points at which tension is felt in a variety of 
ways. Te Mana has a growing sense of unease with the curriculum version of mathematics edu-
cation, which is enacted and expresses a number of important insights. Te Mana recognizes 
how the curriculum prioritizes tasks, work completion, and progress through the levels of the 
curriculum and how this works against a natural acquisition of knowledge appropriate for 
each child. Te Mana conceptualizes curriculum mathematics education as a form of assimila-
tion or colonization, which is eloquently expressed in epistemological and ontological terms as 
“being pressured so that our ways of organizing things and thinking about things” are 
changed.  
Te Mana also notices how seeing things in mathematical ways can erase the original, authen-
tic Māori meanings of cultural artefacts and practices. This connects with the discourse of 
power that surrounds mathematics—somehow it is allowed to explain everything in the world 
in mathematical terms and make everything inherently mathematical. 
Although Te Mana’s mathematics classroom shows strong legitimation based on a discursive 
epistemic relation and interactive epistemic relation in a similar way to that of Te Ara, there is 
a simmering discontent that is a precursor to a shift in practice in which legitimation is more 
aligned with that of the school ethos.  



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

60 

contrasted with mathematics resources that are regarded as formal and in need of 
contextualizing.   

Te Ao locates being Māori when learning mathematics in the nature of peda-
gogy. According to Te Ao, “the way you approach mathematics, that is the most 
important thing.”  For Te Ao, there is no Māori thinking in the curriculum resources 
themselves; rather, it is in the way the teacher works and relates to students: 

 
I quite like having the curriculum documents around… it’s good to know the assessment 
levels, but for me, it is always better to try to gauge the student’s achievements directly 
by what they are doing, materially, in front of me right then and there by listening to 
them and seeing what they are doing when we are working together. 
 
The construal of mathematics is strongly influenced by Te Ao’s own nature and 

the knowledge of students in the class, many of whom are related: 
 
I am a new teacher, but I have a lot of experience from other areas, and I know the 
students well because I am related to many of them. I use the curriculum resources some-
times, parts of them anyway, but I mostly rely on my own knowledge and my experience 
and what is working with the students. 
 
For Te Ao, the benefits for students from learning mathematics are an ability to 

be successful in the world based on a strong sense of Māori identity derived from 
genealogy. In this view, it is essential that students, 

 
know who they are and have a strong sense of identity… it is important that they have 
all the necessary elements in place so that they are whole and know the structure of a 
person… their identity and origins.  If this is all in place, students will be settled inside... 
if identity is good, the journey in life will be good as well. 
 

For Te Ao, a major benefit of a Māori education is that students know their identity 
and their whakapapa (descent, genealogical origins). Te Ao interprets the social and 
spiritual well-being, the happiness of students, as a sign of the strong grounding of 
identity and extends this to be a sign that the foundational philosophical principles of 
the school are being enacted successfully. There is a location of success in the stu-
dent-teacher relationship with reciprocal notions of give and take; respect must be 
given to be received. In this way, explicit links are made to the philosophical princi-
ples of the school in the mathematics learning. This justifies a particular view of 
learning as being primarily about relationship, identity, positive participation, and 
reciprocity.   

The activities designed by Te Ao usually involve physical movement or real 
material objects and are often unique, having been designed specifically for the par-
ticular lesson and students involved. There is no routine structure in Te Ao’s lessons; 
instead, students engage in a series of activities that may or may not relate to each 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

61 

other in terms of mathematics learning. Mathematics learning is another context in 
which the identity of students can be realized; the development of identity is the 
theme that relates different mathematics activities and gives coherence to them over 
time.   

A genuine, strongly felt tension between Te Ao’s mathematics practices and 
those of other teachers is felt. There is a vulnerability to criticism from other teachers 
and parents, and Te Ao expresses a need to be careful because being “too far out of 
the box is dangerous.”  This may arise because such people cannot recognise that 
mathematics is happening in Te Ao’s lessons. In Te Ao’s view, 

 
…other teachers are trying to be the ideal mathematics teacher, use the curriculum re-
sources and get the students to do what is expected… this makes it all predictable, boring, 
and routine. I just go on my own thinking and what I can see is the most useful for my 
students. People might look at my lessons and see the students yelling, excited and mov-
ing around, standing on chairs maybe in some kind of game, and they think there’s no 
mathematics going on… but it’s there, mathematics is happening, but you just have to 
look carefully… it might not be what you are used to seeing. 
 
Because of this tension and perceived risk, Te Ao organizes a small part of each 

lesson in which bookwork or worksheets are done to show to others that “real math-
ematics is being done.” 

In all of the lessons in the data, students and Te Ao are highly collaborative, 
physically active, very vocal, and socially interactive. Te Ao does not maintain a 
separation from students and often participates in the activities as well. A sign of the 
success in Te Ao’s lessons is when students “come out of your class with a smile and 
are still keen on your lessons.”   

Te Ao does not attend strongly to how students are acquiring mathematics 
knowledge other than through participation in game-like activities. Learning is as-
sumed to happen spontaneously as a natural result of participation in activities.  
Learning should be in context and have a real purpose. This involves integrating 
many learning areas in one activity. 

Along with a focus on the practical and the integrated task, Te Ao elaborates 
the view that formal resources are not focused on the kind of math required in every-
day life. Te Ao relies instead on personal thinking and resources. 

In all the lessons in the data, there is no emphasis given to the learning of the 
newly invented Māori words for the mathematics curriculum. Te Ao assumes that 
the students’ language proficiencies are such that that they will learn any new termi-
nology required.  Te Ao asserts that “it’s up to each school to use their own words 
for mathematics; this is no big problem.” 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

62 

 
Student Perspectives 
 

Students tended to hold views that aligned with those of the teachers who taught 
them. For most students, mathematics was definitely about the mind and “sharpening 
the brain” so that mathematics activities, primarily “working out answers,” could be 
done quickly and efficiently. Quickness is associated with sharpness of mind. Stu-
dents attribute the importance of mathematics to having essential skills in order to 
“succeed in a career or get a good career.”  One student commented, 

 
If you want to have a good job, you need mathematics so that you will achieve in the 
world. Mathematics will make you sharp... like on a scale of one to ten, you will get a 
ten. In all activities you have to use mathematics. Like in rugby, you have to count the 
points, and in your career… you will need lots of subjects like English, Māori... and 
brainy people will do science and mathematics. 
 
When asked about who real mathematicians were and what they were like, 

there was a very strong assertion that mathematicians would be male, European or 
Asian. and probably “geeky loners” with poor social skills. It was apparent to stu-
dents that Māori people weren’t mathematicians. 

 
 
 
 
 

Interpretation: 

Te Ao’s mathematics classroom represents a regime closely aligned with the school ethos and 
is based on strong ontic epistemic and subjective social relations. Behavior and interaction 
between students and teacher are based on family-like relationships in which students and 
teachers interchange roles frequently and knowledge is generated largely through direct en-
gagement and experience of unique activities. Students behave in many different ways in ac-
tivities that require direct involvement and engagement (often physical). Mathematics learn-
ing is implicit to these activities, which has an overall purpose of supporting the identity de-
velopment of each student as an individual and as Māori. In this perspective, mathematics ed-
ucation is another context in which students may come to know themselves as unique and as 
Māori. The legitimation is based on a strong ontic epistemic relation and subjective social re-
lation in the ways understood in the school ethos—participatory epistemology and the person 
as a unique, Māori being. 
This case also highlights how tensions with curriculum mathematics education manifest with 
this form of legitimation. Te Ao feels forced to include curriculum resources and demand cer-
tain behaviors from students (the reintroduction of a legitimation based on discursive epis-
temic and interactive social relations) for political reasons—to show other teachers and par-
ents that this form of mathematics education is happening. 
 
 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

63 

Students tended to make somewhat circular arguments about the importance of 
mathematics, as these researcher-student interactions show: 

 
Mahia (student): You will need mathematics in your career. 
Researcher: To do what? 
Mahia: To do the mathematics that is needed. 
 
Ānaru (student): Mathematics will make your brain sharp 
Researcher: Sharp in what sort of ways? 
Ānaru: So that you can be good at games. 
Researcher: What sort of games? 
Ānaru: Oh... mathematics games... like cool math games 
 
Researcher: How will mathematics help you when you are older? 
Tuki (student): It will be very useful. 
Researcher: In what ways? 
Tuki: I’ll be able to help my own children with the math they have to learn at school. 
 
Commenting about mathematics work, one student offered the opinion that it 

wasn’t real math because there was “too much discussing and drawing pictures.”  
Another student associated learning lots of mathematics strategies for calculating cor-
rect answers with an ability to “decide which pathway in your life is the good one.” 

Students have a clear appreciation of mathematics as a challenge to the mind.  
Without a challenge, there “could be no learning,” and through challenge, “correct 
mathematics learning” could be achieved.  

In contrast to this view of mathematics, a senior student, who had decided not 
to continue with mathematics learning in the senior school, explained that learning 
cultural knowledge from elders who, perhaps, would soon be lost was more im-
portant: 

 
I can pick mathematics up any time when I need it and know that it won’t be a struggle... 
that’s why I am knocking it out [not doing it anymore]... so I can concentrate on te reo 
Māori [Māori language] and doing kapa haka [Māori performing arts] where I can ex-
press myself... and I am going to learn about my marae [tribal settlement and people] 
from my Koro and Kuia [elders]... they won’t be around for very much longer, and I 
want to learn from them. 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

64 

 
 

Conclusion 
 

The findings just presented and discussed paint a complex and nuanced picture 
of life in this Māori school. At a high level of generality, and in the formal terms of 
the analytical concepts of legitimation, the school as a whole bases its practices on 
an ontic epistemic relation and a subjective social relation. In curriculum mathemat-
ics classes, on the other hand, legitimation involves a discursive epistemic relation 
and an interactive social relation. The former centralizes being Māori and having a 
direct, participatory engagement with real events and the world in general. The latter 
centralizes being a mathematics student who has knowledge of the official mathe-
matics education discourse.  

There are strong indications in the data about the desire to create a mathematics 
curriculum, and a full school curriculum in general, that is consistent with the legiti-
mation prioritized in the school ethos. According to the analysis in this research, this 
is a mathematics curriculum based on an ontic epistemic relation and a subjective 
social relation (as understood in this Indigenous context). It is here that a return is 
made to the ethical stance described earlier with respect to non-Indigenous research-
ers working in Indigenous contexts. At this point, it is very tempting to launch into a 
discussion of what is entailed in the creation of such a curriculum and to list recom-
mendations. Despite the generation of new knowledge that has taken place in this 
project, no recommendations can be made. In the spirit of ethical care for the other, 
in the sense of Levinas, all that is possible is the unconditional offering of these find-
ings with the understanding that they are possibilities or even a fantasy. 

Interpretation: 

Students generally have an instrumentalized view of mathematics education as something nec-
essary for employment and necessary for participation in the education system itself. No stu-
dents made strong links between their experiences in mathematics and being Māori. Societal 
discourses about the importance and power of mathematics and who does mathematics (brainy 
people, non-Māori) were surprisingly strong given the fact that almost all students had been 
brought up from early childhood in Māori schools and preschool centers. At the same time, 
students believed that they could learn mathematics but had an ambivalent attitude towards it; 
it was necessary and important for employment and careers but could be picked up as and 
when needed.  
In terms of specialization, students present a variegated picture. There are elements that can 
be interpreted as aligning with the discursive epistemic and interactive social relations of cur-
riculum mathematics and somewhat contradictory elements that align with the school ethos. 
There may be some evidence that students are moving to a position that centralizes their own 
Indigenous identity, language, and culture, which then allows them to operate strongly in so-
cial fields that do not legitimate these. Curriculum mathematics certainly seemed to cause less 
angst for students than for their teachers. 
 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

65 

Recommendations, if any are to be made at all, are entirely an internal matter for 
Māori schools and communities themselves, as are the following concluding com-
ments. 

Firstly, it seems likely that schools that may wish to embark on an exploration 
of mathematics education in a new paradigm will have to meet the challenge posed 
by the strong connection between mathematics attainment and success in urban, cap-
italist conditions. Curriculum mathematics education plays a powerful role, if not a 
central role, in the creation of subjectivities aligned with neo-liberal social ontologies 
now deeply embedded in New Zealand society. The identity formatting effect of 
mathematics education and complicity in the production of neo-liberal subjectivities 
is well documented in the critical mathematics education literature (see, for example, 
Pais & Valero, 2012; Popkewitz, 2002; Skovsmose, 1994; Valero, 2018). Encour-
agement can be garnered, however, from the phenomenon of Māori resistance in ur-
ban conditions in general. As discussed earlier, Māori have already successfully 
maintained cultural integrity whilst adapting to and adapting urban/capitalist condi-
tions with respect to a number of domains of activity, which taken together might be 
thought of as a Māori economy. If this wider view is taken, the creation of an ontic- 
and subjective-based mathematics education might gradually be aligned with this 
Māori economy rather than the existing mainstream economy. This accepts that ed-
ucation in general and mathematics education in particular is always prefigured by 
the nation’s economy; it seems plausible then that as the Māori economy (itself based 
on its own ontological commitments) grows in strength, Māori mathematics educa-
tion may be pulled into its orbit. 

A second important and related challenge concerns the “gaze” of mathematics 
education, which Dowling (1998) has labelled the myth of reference. In this gaze, 
mathematics education redescribes the contents of non-mathematical domains of all 
kinds in its own terms, recasting the whole world, in effect, as inherently mathemat-
ical in nature. As Te Mana recognizes clearly, there is a very significant problem 
when curriculum mathematics education casts its powerful gaze upon Indigenous ar-
tefacts, practices, and the public and personal lives of Indigenous people; in an un-
critical engagement with curriculum mathematics education, and uncritical ac-
ceptance of its discursive epistemic relation, a cultural and historical revisionism, a 
form of symbolic violence, can result. This suggests that a form of perspective man-
agement might be employed in which the cultural origins and meanings (the ontolo-
gies and epistemologies) that underpin and create the artefacts and practices of Māori 
life are protected from being redefined by this mathematical gaze.  

To do this, a critical awareness and careful distinction can be made between the 
mathematical perspective, which sees things in a mathematical way, and the authen-
tic meanings inherent in Indigenous artefacts and practices. In other words, we can 
understand that a mathematical gaze is possible of any entity but that the mathemat-
ical understanding generated is not the entity itself. The entity retains its own 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

66 

ontological integrity, which may have nothing to do with mathematics. Being explicit 
about both perspectives and when switches are made between them is necessary in 
order to avoid the very common assertion that an Indigenous practice is “really” a 
mathematical one even when the participants themselves have no cognizance of any 
mathematics being enacted. 

There is a strong resonance here with the critique of culturally relevant and 
responsive pedagogical practices as asset-based pedagogies made by Django Paris 
and H. Samy Alim (Paris & Alim, 2014). These two authors build on the foundations 
laid by the earlier developments of culturally relevant and culturally responsive ped-
agogies (e.g., Ladson-Billings, 1995a, 1995b, 1997) to promote Culturally Sustaining 
Pedagogy (CSP) as a critical centering of the ways of being of Indigenous commu-
nities and communities of color. CSP should operate to automatically involve a dis-
ruption of dominant education systems that only legitimate “White, middle-class, 
monolingual, cisheteropatriarchal, able-bodied superiority” (Alim & Paris, 2017, p. 
13). Paris and Alim critique asset-based approaches, such as funds of knowledge, 
culturally relevant/responsive pedagogies, and third space, as too easily defaulting in 
practice, if not in theory, to an instrumental usage of Indigenous practices, language, 
and, indeed, Indigenous bodies for the purposes of achieving success defined in terms 
of a panoptic White gaze. Here, the connection with Dowling’s myth of reference and 
the mathematical gaze so keenly felt by Te Mana becomes clear; we can understand 
the recontextualizing gaze of curriculum mathematics education as part of the pan-
optic White gaze—Indigenous Māori artefacts and practices are repurposed as assets 
to bring students into the legitimation regimes of curriculum mathematics education. 
Paris and Alim provide vital insights by recognizing the tendency of asset pedagogies 
to work on static, “archaic,” and reified forms of Indigenous cultural practice, 
knowledge, and identities and neglect contemporary and emergent forms forged in 
urban, capitalist conditions such as those emerging in the Māori school of this study. 
In the New Zealand context, this manifests clearly as a persistent focus on traditional 
Māori contexts and practices, such as flax weaving, ocean navigation, carving, and 
hāngi (traditional earth ovens). Contemporary (urban) realities for Māori communi-
ties are rarely present, and if they are, they tend to be indistinguishable from “Whit-
estream” activities apart from being translated into the Māori language, involving 
brown bodies, and with only their mathematical aspects emphasized. 

Paris and Alim (2014) also describe the necessity of developing an inward gaze, 
which critically addresses both the liberatory aspects of contemporary Indigenous 
culture, language, and practices, and the restrictive. For the participants in this study, 
there was considerable critical reflection on their existing mathematics practices, the 
effects on identity, language, and Māori knowledge, as well as the benefits of coming 
to know mathematics. For the researcher, the inward gaze is a constant critical reflec-
tion on his own position, the impact of his words, and the limits of what he can say 
and know, which has led to his position of ethical knowing and not-knowing. 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

67 

In a further development of CSP, McCarty and Lee (2014) developed the con-
cept of Culturally Sustaining/Revitalizing Pedagogy (CSRP), specifically in Indige-
nous contexts where Indigenous sovereignty is a fundamental issue. McCarty and 
Lee’s work resonates strongly with the situation in the Māori school of this study. 
Indeed, the desire to create a curriculum centering on Māori ontology and epistemol-
ogy is an expression of Māori sovereignty, and the process that the Māori school is 
going through may be thought of as an example of critical CSRP. There is, it seems, 
a significant difference here in New Zealand. The current strengthening position of 
Māori in our small country is creating the possibility at least that rather than Indige-
nous educational sovereignty being thought of as accountability to Indigenous com-
munities in the same way as to the national government, that education itself may 
eventually come directly under this Indigenous sovereignty. Despite the homogeniz-
ing cosmopolitanism and “melting pot discourses” prevalent in capitalist, urban con-
ditions, Māori in general, and this Māori school in particular, are showing that a plu-
ralistic society in which communities co-exist with deep level ontological differences 
is possible and necessary. 
 

References 
 
Alim, H. S., & Paris, D. (2017). What is culturally sustaining pedagogy and why does it matter? In 

D. Paris & H. S. Alim (Eds.), Culturally sustaining pedagogies: Teaching and learning for 
justice in a changing world (pp. 1–21). Teachers College Press. 

Bevan-Brown, J. (1998). By Māori, for Māori, about Māori — Is that enough? In T. P. Hauora (Ed.), 
Te oru rangahau — Māori Research and Development Conference Proceedings 7–9 July, 
1998 (pp. 231–246). Massey University. 

Biesta, G. (2015). Freeing teaching from learning: Opening up existential possibilities in educational 
relationships. Studies in Philosophy and Education, 34(3), 229–243. 
https://doi.org/10.1007/s11217-014-9454-z 

Dowling, P. (1998). The sociology of mathematics education: Mathematical myths/pedagogic texts. 
RoutledgeFalmer. 

Dreyfus, H. L., & Rabinow, P. (1983). Michel Foucault: Beyond structuralism and hermeneutics 
The University of Chicago Press. 

Durie, M. (2011). Indigenizing mental health services: New Zealand experience. Transcultural Psy-
chiatry, 48(1–2), 24–36. https://doi.org/10.1177%2F1363461510383182 

Fisher, M. (2013). Capitalist realism: Is there no alternative? John Hunt Publishing. 
Gagné, N. (2013). Being Māori in the city: Indigenous everyday life in Auckland. University of To-

ronto Press. 
Gagné, N. (2016). The waxing and waning of the politics of authenticity: The situation of urban-

based Māori through the lens of municipal politics. City & Society, 28(1), 48–73. 
https://doi.org/10.1111/ciso.12073 

Haami, B. (2018). Urban Māori: The second great migration. Oratia Books. 
Harvey, D. (2005). A brief history of neoliberalism. Oxford University Press. 
Hokowhitu, B. (2013). Producing indigneity. In E. J. Peters & C. Andersen (Eds.), Indigenous in the 

city: Contemporary identities and cultural innovation (pp. 354–376). UBC Press. 
Hoskins, T. K. (2012). A fine risk: Ethics in Kaupapa Māori politics. New Zealand Journal of Edu-

cational Studies, 47(2), 85–99.  



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

68 

Jones, A. (2007, October 24). Ka whawhai tonu mātou: The interminable problem of knowing others 
[Inaugural professorial lecture]. University of Auckland. https://cdn.auckland.ac.nz/assets/ed-
ucation/about/schools/tepuna/docs/Inaugural_Lecture.pdf 

Keiha, P., & Moon, P. (2008). The emergence and evolution of urban Māori authorities: A response 
to Maori urbanisation. Te Kaharoa, 1(1).  https://doi.org/10.24135/tekaharoa.v1i1.132 

Kelsey, J. (2015). The fire economy: New Zealand's reckoning. Bridget Williams Books. 
Kincheloe, J. L. (2001). Describing the bricolage: Conceptualizing a new rigor in qualitative re-

search. Qualitative Inquiry, 7(6), 679–692. https://doi.org/10.1177%2F107780040100700601 
Kincheloe, J. L. (2005). On to the next level: Continuing the conceptualization of the bricolage. 

Qualitative Inquiry, 11(3), 323–350. https://doi.org/10.1177%2F1077800405275056 
Kukutai, T. (2007). White mothers, brown children: Ethnic identification of Maori-European chil-

dren in New Zealand. Journal of Marriage & Family, 69(5), 1150–1161. 
https://doi.org/10.1111/j.1741-3737.2007.00438.x 

Kukutai, T. (2013). The structure of urban Māori identities. In E. J. Peters & C. Andersen (Eds.), In-
digenous in the city: Contemporary identities and cultural innovation (pp. 311–333). UBC 
Press. 

Kukutai, T., & Webber, M. (2017). Ka pū te ruha, ka hao te rangatahi: Māori identities in the twenty-
first century. In A. Bell, V. Elizabeth, T. McIntosh, & M. Wynyard (Eds.), A land of milk and 
honey? Making sense of Aotearoa New Zealand (pp. 71–82). Auckland University Press. 

Ladson-Billings, G. (1995a). But that's just good teaching! The case for culturally relevant pedagogy. 
Theory Into Practice, 34(3), 159–165. https://doi.org/10.1080/00405849509543675 

Ladson-Billings, G. (1995b). Toward a theory of culturally relevant pedagogy. American Educa-
tional Research Journal, 32(3), 465–491. https://doi.org/10.3102%2F00028312032003465 

Ladson-Billings, G. (1997). It doesn't add up: African American students' mathematics achievement. 
Journal for Research in Mathematics Education, 28(6), 697–708. 
https://doi.org/10.2307/749638 

Levinas E. (1969). Totality and infinity: An essay on exteriority (A. Lingis, Trans.). Duquesne Uni-
versity Press. (Original work published 1961) 

Levinas, E. (1998). Otherwise than being, or, beyond essence (A. Lingis, Trans.). Duquesne Univer-
sity Press. (Original work published 1974) 

Maton, K. (2006). On knowledge structures and knower structures. In R. Moore, M. Arnot, J. Beck, 
& H. Daniels (Eds.), Knowledge, power and educational reform: Applying the sociology of 
Basil Bernstein (pp. 44–59). Routledge. 

Maton, K. (2014). Knowledge and knowers: Towards a realist sociology of education. Routledge. 
McCarty, T. L., & Lee, T. S. (2014). Critical culturally sustaining/revitalizing pedagogy and Indige-

nous sovereignty. Harvard Educational Review, 84(1), 101–124.  
Metge, J. (1995). New growth from old: The Whānau in the modern world. Victoria University Press. 
Mika, J. P., Fahey, N., & Bensemann, J. (2019). What counts as an indigenous enterprise? Evidence 

from Aotearoa New Zealand. Journal of Enterprising Communities: People and Places in the 
Global Economy, 13(3), 372–390. https://doi.org/10.1108/JEC-12-2018-0102 

Moewaka-Barnes, H. (2015). Kaupapa Māori: Explaining the ordinary. In L. Pihama, S. Tiakiwai, & 
K. Southey (Eds.), Kaupapa Rangahau: A reader (pp. 29–34). Te Kotahi Research Institute. 

Pais, A., & Valero, P. (2012). Researching research: Mathematics education in the political. Educa-
tional Studies in Mathematics, 80(1–2), 9–24. https://doi.org/10.1007/s10649-012-9399-5 

Paris, D., & Alim, H. S. (2014). What are we seeking to sustain through culturally sustaining peda-
gogy? A loving critique forward. Harvard Educational Review, 84(1), 85–100. 
https://doi.org/10.17763/haer.84.1.982l873k2ht16m77 

Penetito, W. (2010). What's Māori about Māori education? Victoria University Press. 
Peters, E. J., & Andersen, C. (Eds.). (2013). Indigenous in the city: Contemporary identities and cul-

tural innovation. UBC Press. 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

69 

Pihama, L., Tiakiwai, S., & Southey, K. (Eds.). (2015). Kaupapa rangahau: A reader. Te Kotahi Re-
search Institute. 

Poata-Smith, E. T. (2015). Marxism. In J. Hayward (Ed.), New Zealaand government and politics 
(pp. 84–95). Oxford University Press. 

Popkewitz, T. (2002). Whose heaven and whose redemption? The alchemy of the mathematics cur-
riculum. In P. Valero & O. Skovsmose (Eds.), Third International MES Conference: Adden-
dum (pp. 1–26). Copenhagen, Denmark: Centre for Research in Learning Mathematics. 

Rossi, U. (2017). Neoliberalism. In M. Jayne & K. Ward (Eds.), Urban theory: New critical perspec-
tives (pp. 205–217). Routledge. 

Royal, T. A. C. (2009). ‘Let the world speak’: Towards Indigenous epistemology. Mauriora-ki-te-
ao/Living Universe. 

Ryks, J., Pearson, A. L., & Waa, A. (2016). Mapping urban Māori: A population-based study of 
Māori heterogeneity. New Zealand Geographer, 72(1), 28–40. 
https://doi.org/10.1111/nzg.12113 

Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Springer. 
Smith, G. H. (2000). Māori education: Revolution and transformative action. Canadian Journal of 

Native Education, 24(1), 57–72.  
Smith, G. H. (2009). Mai i te māramatanga, ki te putanga mai o tahuritanga: From conscientisation to 

transformation. In J. Andrzejewski, M. P. Baltodano, & L. Symcox (Eds.), Social justice, 
peace, and environmental education: Transformative standards (pp. 19–28). Routledge. 

Smith, G. H. (2011, April 28). Transforming education: Māori struggle for higher education 
[Presentation]. Te Whare Wānanga o Awanuiārangi Indigenous University. 
http://www.manu-ao.ac.nz/massey/fms/manu-ao/documents/Graham%20Smith%20Power-
point.pdf 

Smith, G. H. (2012). Kaupapa Māori: The dangers of domestication. New Zealand Journal of Educa-
tional Studies, 47(2), 10–21.  

Smith, L. T. (2005). Building a research agenda for Indigenous epistemologies and education. An-
thropology & Education Quarterly, 36(1), 93–95. https://doi.org/10.1525/aeq.2005.36.1.093 

Smith, L. T. (2011). Story-ing the development of kaupapa Māori—A review of sorts. In Te 
Wāhanga, J. Hutchings, H. Potter, & K. Taupo (Eds.), Kei Tua o te Pae Hui Proceedings: The 
challenges of kaupapa Māori research in the 21st century (pp. 10–15). New Zealand Council 
for Educational Research. https://www.nzcer.org.nz/system/files/Hui_Proced-
ings__v3_Web_1_2.pdf 

Smith, L. T. (2012). Decolonizing methodologies: Research and Indigenous peoples (2nd ed). Zed 
Books. 

Stewart, G. (2018). From both sides of the indigenous-settler hyphen in Aotearoa New Zealand. Edu-
cational Philosophy and Theory, 50(8), 767–775. 
https://doi.org/10.1080/00131857.2016.1204904 

Tauri, J. (1998). Family group conferencing: A case-study of the indigenisation of New Zealand's 
justice system. Current Issues in Criminal Justice, 10(2), 168–182. 
https://doi.org/10.1080/10345329.1998.12036125 

Te Maro, P. (2019). Mai i ngā rā o mua: Dialectical and knowledge-power relations in the interac-
tions of kura and maths education [Unpublished PhD thesis]. Te Whare Wānanga o 
Awanuiārangi. 

Te Maro, P., Averill, R., Higgins, J., & Tweed, B. (2008). Fostering the growth of teacher networks 
within professional development: Kaiako wharekura working in pāngarau. In Te Poutama Tau 
Evaluation Report 2008: Research findings in pāngarau for Years 1–10, 34–46. NZ Maths. 
http://nzmaths.co.nz/te-poutama-tau-evaluation-report-2008-research-findings-p-ngarau-
years-1-10 



 
 
 
Tweed                                         Indigenous Struggle With Mathematics Education 
 

Journal of Urban Mathematics Education Vol. 14, No. 2 
 

70 

Tweed, B. (2019). Kua tae mai a Tokotoko – Me aha ahau? A Pākehā on the paepae? Kairaranga, 
20(1), 9–15.  

Valero, P. (2018). Human capitals: School mathematics and the making of the homus oeconomicus. 
Journal of Urban Mathematics Education, 11(1&2), 103–117. https://doi.org/10.21423/jume-
v11i1-2a363 

Ward, S. C. (2012). Neo-liberalism and the global restructuring of knowledge and education. 
Routledge. 

Yukich, R., & Hoskins, T. K. (2011). Responsibility and the other: Cross-cultural engagement in the 
narratives of three New Zealand school leaders. Journal of Systemic Therapies, 30(3), 57–72. 
https://doi.org/10.1521/jsyt.2011.30.3.57 

 
 
Copyright: © 2021 Tweed. This is an open access article distributed under the terms of a Creative 
Commons Attribution-NonCommercial-ShareAlike 4.0 International License, which permits unre-
stricted use, distribution, and reproduction in any medium, provided the original author and source 
are credited.