A Portrait of a Native Hawaiian Ethnomathematics Educator

Abstract

This paper introduces an analytical framework, complex mathematical personhood, to broaden understandings of how teacher identity is developed over time through an emancipatory lens. A single case study, or portrait, is shared of a Native Hawaiian middle school mathematics teacher who uses Indigenous and ethno-mathematical practices to inform his instruction. A bricolage of case study and portraiture methods was invoked as the methodological framework for this project. Key results demonstrate the importance of broadening mathematics teaching practices that center and reorient de/colonial practices in teacher pedagogical orientations.

1. Introduction

In his second term as President of the United States of America, Donald J. Trump and his regime have initiated the following: (1) the dismantling of the Department of Education (Baker, 2024), (2) the removal of words related to gender, including “sexual orientation and gender identity,” “diversity, equity, and inclusion,” “abortion,” “reproductive health,” and “gender equality” from every federal website (Simmons-Duffin & Stone, 2025), (3) the prohibition of “divisive symbols such as the rainbow flag or the Black Lives Matter flag” at U.S. embassies (Hauser & Vigdor, 2025), and (4) enacted the Alien Enemies Act of 1798, ‘an obscure law that has been used sparingly throughout U.S. history to detain or deport nationals of an enemy nation during wartime or an invasion’ (Treisman, 2025). While this list is certainly not all-encompassing, the actions above are examples of the explicit re-entrenchment of settler-colonial White supremacist male rage (Kimmel, 2013; Oluo, 2020; Phipps, 2021).

However, the logic being enacted above cannot solely be categorized as ‘Trumpism’. This would be far too simplistic a rendering. As Ta-Naheisi Coates (2017) notes, Trump and his explicit White nationalist message are not outliers but rather extensions of the White supremacist settler-colonial origins of the United States of America carried into the present. And yet, where there exists power and oppression, there is always resistance and counter-narrative. De/colonial studies continues to be an important emergent discipline and an ongoing response to the White nationalist and patriarchal pathologies that have undergirded this country. Its origins reside in movements borne of social struggle beginning in the early 1970s and continuing into current present-day discourse. These include but are not limited to ongoing emerging disciplinary fields including ‘Labor Studies, Women’s Studies, LGBT Studies, Disability Studies and Black, Chicana/o Latina/o, American-Indian and Asian-American studies—often referred to together as Ethnic Studies’ (Winkler-Morey, 2010, p. 53). And as can be evidenced by the attacks on public libraries, universities, and K12 education by the current administration, these disciplines have always been sites of contestation, discipline, and surveillance by Western colonial powers.

Ethnomathematics, as one extension of de/colonial studies, is rooted in these transdisciplinary practices. According to Ubiratan D’Ambrosio, ethnomathematics is defined as ‘the mathematics practiced among identifiable cultural groups, such as national-tribal societies, labor groups, children of a certain age bracket, professional classes, and so on’ (D’Ambrosio, 1985, p. 45). Borba clarifies that this definition can be broadly applied to European and/or Western epistemologies on how professional mathematics is constructed for a small swath of the global population as a particular way of engaging with the subject. Building on D’Ambrosio’s definition, Borba states that ‘ethnomathematics can be seen as a field of knowledge intrinsically linked to a cultural group and to its interest, being in this way tightly linked to its reality and being expressed by a language, usually different from the ones used by mathematics seen as science. This language is umbilically connected to its culture, to its ethnos’ (Borba, 1987, p. 38).

Furuto (2014) also notes that another characteristic of ethnomathematics practices is ‘finding relevance in real-world applications through physical, environmental, spiritual and cultural capacities’ (Jonsson, 1988; Gutstein & Peterson, 2006, p. 4).

Research has been conducted on how students respond to ethnomathematical connections. In The Tale of Two Noras (2008), Hogan (2008) presents a case study of a single Yup’ik middle school student, Nora, whose mathematical abilities were mediated very differently by two teachers across two years. In sixth grade, Nora thrived in a culturally relevant, student-centered classroom that incorporated Yup’ik knowledge through the Math in a Cultural Context (MCC) curriculum. Her teacher, a young Yup’ik woman, cultivated collaborative learning, inquiry, and student agency, leading Nora to be recognized as a confident leader and even a co-teacher. In contrast, in seventh grade under a Western-style, procedural, and teacher-centered approach aligned with No Child Left Behind reforms, Nora was seen as a struggling, quiet D+ student. The study illustrates how classroom practices, cultural relevance, and teacher perceptions profoundly shape student mathematical identity and learning, emphasizing the need for sustained culturally responsive teaching to support Indigenous students’ success.

In the growing field of ethnomathematics scholarship, Dr. Linda H. Furuto’s research at the Ethnomathematics Institute offers key insights into the significance and particular impact on community members who identify as Pacific Islanders, those that are ‘original peoples of Hawai‘i, Guam, Samoa and other Pacific Islands.’ (US Census Bureau, 2011, as cited by Furuto, 2014, p. 2). As Furuto explains, the Institute ‘brings together major stakeholders throughout the Pacific including the University of Hawai‘i System, Hawai‘i State Department of Education, Hawai‘i P-20 Partnerships for Education, Pacific American Foundation, Pacific Resources for Education and Learning, and Polynesian Voyaging Society, to support professional development for teachers’ (Furuto, 2014, p. 5).

Through a partnership with the Polynesian Voyaging Society, a 5-year study conducted by the Institute found that using traditional sailing techniques and first-hand experiences, in-service and pre-service teacher participants in Hawai’i gained mathematical insights into how culture and history can link, along with expanding concepts that can be extended into classrooms across the islands. Dr. Furuto emphasizes that all of this is ultimately in service of caring for the planet amid a changing climate and, in line with Indigenous cultural practices, ensuring that a sustainable future for the next several generations is fought for. She notes the impact of this work, in which ‘the Polynesian Voyaging Society’s prototype canoe Hōkūle‘a (“star of gladness”) has sailed over 150,000 nautical miles and inspired a revival of voyaging and Indigenous practices around the world (Finney et al., 1986; Furuto, 2014, p. 4). On the back of the Hōkūle‘a canoe, a phrase is written that travels everywhere the canoe does—kapu nā keiki [hold sacred the children in the Hawaiian language].

It is notable that both Furuto (2014) and Hogan’s (2008) work center on the experiences of Indigenous cultural practices. In other cultural contexts, Johnson et al. (2022) created an IOS mathematics app that connected 6th grade Emirati students to ethnomathematical practices. Using Bayesian networks to inform their analysis, the authors found that there was significant data that supported that the students who participated in this study (n = 160) ‘desired mathematics problems based on the Emirati culture’ (p. 12), including using an IOS math app developed by the researchers to explore the mathematics behind culturally significant items such as ‘henna, prayer beads, and bamboo baskets’ (2022, p. 15). Given the significant role Middle Eastern and Muslim mathematicians have impacted the field, the findings of the study demonstrated that there was significant interest by the Emirati students to continue linking their cultural practices to the mathematics modules developed by the researchers.

Despite the abundance of literature around the interplay of ethnomathematics in school settings and its impact on students and pre-service teachers broadly, the literature around veteran teachers’ use of ethnomathematics (those who have been in the field for more than 5 years) remains limited. As such, there continue to be calls for additional research on the intersections of teacher identity development over time for teachers of color (Nicol et al., 2024; Rosa et al., 2017). For example, the National Council of Teachers of Mathematics has repeatedly made calls for math educators to ‘provide more equitable opportunities to learn mathematics’. Anderson-Pence (2015) notes that there are cultural implications that require math educators ‘to expand their beliefs regarding mathematical competence and to incorporate culturally relevant pedagogy into…teaching practices’ (p. 59). Furuto (2014), citing NCTM’s call for a ‘culture of equity,’ emphasizes that creating meaningful and relevant ethnomathematical learning experiences requires the collective efforts of students, educators, families, and policymakers. Such collaboration is essential for expanding access to high-quality mathematics for Pacific Islander communities.

2. Research Questions

In light of the current research and calls for further inquiry, I wondered about the following questions:

(1)

What contradictions and tensions must C-VMTOC’s occupy and confront if they wish to bring de/colonial and/or ethno-mathematical practices into their teaching praxis?

(2)

How do the ‘contradictions and tensions’ referred to in RQ1 impact C-VMTOC’s own burgeoning critical consciousness and complex mathematical personhood (Rezvi, 2025)?

(3)

How do C-VMTOC’s work within (and simultaneously subvert) colonial systems of education?

The study offered here shares some insights on the importance of centering Indigenous teacher voices and sharing their experiences of what can and might exist in schools beyond its present paradigms.

Researcher Ni’yaat (Intention/نِيَّة)ٌ

In this piece, I present a portrait of Kahiau, a Native Hawaiian mathematics teacher whose work and professional self-identity is deeply shaped by the cultural, historical, and political context of Hawai‘i. Teaching at a Hawaiian private school dedicated to de/colonizing pedagogy for its predominantly Native Hawaiian student body, Kahiau exemplifies how ethnomathematics and de/colonizing approaches continue to shape his evolving and complex mathematical personhood.

Moreover, the portrait provides insight into how he negotiates and evolves his own understanding of what it means to be one of the few Native Hawaiian mathematics teachers teaching from a specific and intentional ethnomathematical perspective and epistemology—a role made even more significant given that Kahiau pointed out how Native Hawaiian educators often typically teach Hawaiian history, language or cultural subjects rather than mathematics. As Kahiau noted in our first interview together, “I was the only Brown teacher on the faculty. Everyone [else] was either White or Japanese…So, I guess I was effectively the only Brown STEM teacher, [and] all my native Hawaiian students looked towards me.” [Interview 1, 17 December 2023]

I use the term ‘portrait’ intentionally, as the analysis of the data used a bricolage of portraiture methodologies pioneered by Lawrence-Lightfoot (1983), Lawrence-Lightfoot and Davis (2002) along with case study (Merriam, 1998; Yin, 2009), to construct the findings of this piece. As Lawrence-Lightfoot notes,

…portraiture has become the bridge that has brought these two worlds together for me, allowing for both contrast and coexistence, counterpoint and harmony in my scholarship and writing, and allowing me to see clearly the art in the development of science and the science in the making of the art.

(2002, p. 3).

My intention is three-fold in utilizing portraiture as a methodology. The first is to highlight the myriad ways in which Kahiau intentionally weaves ideas of Indigenous teaching practices, culturally relevant pedagogy, and mathematics as both a scientific art and artistic science. The second is to underscore how portraiture embodies a particular feminist political standpoint and commitment, in which… ‘the portraits are shaped through dialog between the portraitist and the subject, each one participating in the drawing of the image (Lawrence-Lightfoot & Davis, 2002, p. 3)’. Third, and finally, to share the radical idea that mathematics education research that made this study possible requires particular ethical and spiritual commitments to ensure, above all, that any work co-constructed with teachers is performed with humility and respect.

Furthermore, as a culturally Muslim and South Asian researcher, I share my intentions here as part of my ongoing efforts to engage with de/colonial methodologies and practices that center Indigenous ways of knowing and are grounded in Global South and Black feminist orientations. The Islamic concept of ni’yaat guides my work and ethical commitments to this work. There is a particular hadith, which is a phrase or saying attributed to the Prophet Mohammed (pbuh), that I come back to often, which is—(the value of) an action depends on the intention behind it—[Sahih Muslim, Book 33, Hadith 222]. What is my intention behind this work? What are my responsibilities and commitments to not reproduce harm or tokenize the lived experiences of Indigenous teachers? In what ways can the production of knowledge reject extraction and coercion? In a similar vein, I ask the reader also to reflect on these questions. What does it mean to engage with data, informed by Indigenous knowledge, in our current socio-political landscape and context? As Gutiérrez observes, ‘the production of knowledge is an ongoing process that is not cumulative but relational’ (Gutiérrez, 2017, p. 7). It is my intention to display that relationality here and how that might be made legible in mathematics educational research.

My ni’yaat, as it were, is to demonstrate that those in the Global South1 are interconnected, and that though I am not an Indigenous Hawaiian person like Kahiau, my own personal histories have also been haunted by ongoing colonial violence and in that, there is a shared commitment and intention to not perpetuate that further2. Bhattacharya (2019), a de/colonial qualitative education scholar, argues that the term decolonial should include a slash, de/colonial, to acknowledge that all people today carry hybridized understandings of Indigeneity, culture, empire, and self. In alignment with this conception, Gutiérrez (2017) notes that it would be reductive to position Western knowledge systems as solely hegemonic and Indigenous knowledge systems as solely incapable of domination. Rather, she argues for an ‘epistemology of knowledges’ (Santos, 2007) that is necessary to engage in the work of what it means to know, do, create, teach, and think in mathematics spaces that center Indigenous knowledge and cultural practices.

Given the many ways mathematics is currently being used to advance the brutality of technologically driven settler-colonial violence and genocide, such as the use of AI to target Palestinian civilians in Gaza (Frenkel & Odenheimer, 2025), it is crucial, from a de/colonial perspective, to pursue research that envisions mathematics as a tool for relationality rather than harm. It is with this niyaat, I hope to bring this work into being. In the next few sections, I offer some contextualization of the colonization of Hawaii by centering the voices of Dr. Haunani Kay Trask and Dr. Rochelle Gutiérrez, two Native Hawaiian and Rarámuri scholar-activists who have heavily informed my understanding of Indigenous scholarship.

3. Theoretical Framework

3.1. MathematX

Gutiérrez’s (2017, 2019) work on mathematX was essential to the analysis of the data. She argues that (current) whitestream/Western/Eurocentric mathematics education is enacted as a site of dispossession, and that this particularly represents a form of violence towards Indigenous people.

In MathematX: Towards a Way of Being (2019), she notes that much of the landscape of public education for Indigenous people has been characterized as sites of mass dispossession. This can be evidenced in the theft of Indigenous land, outlawing the practice of Indigenous language, culture, and spiritual traditions, and human trafficking of Indigenous children into residential schools. A ‘first-of-its-kind federal study of Native American boarding schools that for over a century sought to assimilate Indigenous children into White society has identified more than 400 such schools that were supported by the U.S. government and more than 50 associated burial sites, a figure that could grow exponentially as research continues.’ The horrors visited upon Indigenous people through White supremacist settler-colonial violence is a haunting that extends into the present.

In her theoretical framework surfacing mathematX, Gutiérrez calls for a revisioning of mathematics that ‘respects and supports Indigenous worldviews among others. This form of mathematics seeks, acknowledges, and creates patterns and relationships that solve problems and offer joy’ (Gutiérrez, 2019, p. 2). She also clarifies what she does not mean by this kind of framework—e.g., that it would be reductive, problematic, and ahistorical to suggest that Indigenous and Eurocentric ways of knowings are in opposition to one another, when these two ways of knowings have co-evolved over time.

Finally, Gutiérrez notes that she is deliberate in her usage of the term ‘knowings’ to ‘highlight the fact that anything known is always an ongoing act—a way of being—that connects humans with our animal, plant, land, water, and other relatives in the physical and spiritual world’ (Gutiérrez, 2023, p. 4). She goes on to observe that ‘knowings are not things; they are a process of deep engagement. Knowings are not developed and permanent; they need to be renewed regularly. In doing so, they renew persons’ (Gutiérrez, 2023, p. 4).

Related to Gutiérrez’s de/colonial theoretical framework, I examine how Kahiau’s complex mathematical personhood emerges throughout our conversations. The CMP framework reveals how desire-based research and the principles of mathematX are reflected in his experiences as a Native Hawaiian mathematics teacher.

3.2. Decolonization/Colonization

It is also important to note that I invoke the concepts of decolonization/colonization not as simplistic binaries linguistically in opposition to one another but align with Kakali Bhattacharya’s (2019) deliberate choice of conceptualizing the term de/colonization. This term is centered on her own learnings from Tuhiwai Smith’s (2012) groundbreaking efforts in decolonizing methodologies in qualitative research spaces.

• Bhattacharya writes,

I have always conceptualized a decolonizing agenda to be forever entangled with colonialism. These terms are binary opposites, with one representing freedom and the other enslavement. However, by writing de/colonizing with a slash I disrupt the notion of a pure, discrete binary relationship between colonial oppression and the decolonial desires of resistance and freedom. I choose this disruption to emphasize that there are no pure (real or imagined), utopian spaces devoid of resistance to colonialism, because the resistance implies being in an oppositional relationship with colonialism. Those of us who resist colonization often live in hybridized spaces where we shuttle between encounters with colonial oppression, internalized forms of colonization, utopian dreams of decolonization, and mitigated resistance to colonial oppression in ways that are strategic to our survival. By introducing a slash in the word, I demonstrate the relationality, the movement, and the impermanence of both colonialism and its resistant counterpart. This move conveys a hybrid state of being, knowing, existing, resisting, and accommodating across, within, and against de/colonialism.

(p. 177)

• Bhattacharya’s recognition that de/colonization is entangled with past, present, and future, and that we all, in our complexity (and complicity), live within these hybridized spaces, parallels the multiplicity of knowings Gutiérrez describes in her conceptual framing of mathematX. This also aligns with my theorization of Complex Mathematical Personhood (CMP) as a lens for understanding how teacher identities are constructed and evolve over time. I view Bhattacharya’s call for care and intention when it comes to the term de/colonization as a reminder that all of us are Learning & (Un)Learning [CMP 4] and continuously engaged in the acts of Remembrance and Forgetting [CMP 1] in the ways in which we view and forge our own mathematical identities within the colonial borders of the United States of America.

3.3. Complex Mathematical Personhood

I constructed the concept of complex mathematical personhood [CMP] based on the poignant work of Avery Gordon. As a cultural theorist and sociologist, Gordon’s work focuses on radical thought and practice. She writes about ‘captivity, enslavement, war, and other forms of dispossession and how to eliminate them’ (Gordon, 2008) Her book, Ghostly Matters (Gordon, 2008), offers a profound and intricate analysis of the forcibly disappeared (desparecido) in Argentina and the ongoing impact of chattel slavery in the United States. Gordon notes that ‘to study social life one must confront the ghostly aspects of it’ (p. 7, 2008) and describes memories of injustice as a form of haunting that traverses across time and space. Within this construct, she offers her definition of complex personhood, which is summarized in part below.

• According to Gordon,

Complex personhood means that all people...remember and forget, are beset by contradiction, and recognize and misrecognize themselves and others. Complex personhood means that people suffer graciously and selfishly too, get stuck in the symptoms of their troubles, and also transform themselves. Complex personhood means that even those called “Other” are never never that. Complex personhood means that the stories people tell about themselves, about their troubles, about their social worlds, and about their society’s problems are entangled and weave between what is immediately available as a story and what their imaginations are reaching towards. Complex personhood means that even those who haunt our dominant institutions and their systems of value are haunted too by things they sometimes have names for and sometimes do not. At the very least, complex personhood is about conferring the respect on others that comes from presuming that life and people’s lives are simultaneously straightforward and full of enormously subtle meaning.

(2008, pp. 4–6)

• Inspired by Gordon’s conception of complex personhood and Gutiérrez’s surfacing of mathematX, I suggest that complex mathematical personhood [CMP] can be constructed as a theoretical framework as follows:

Teacher identity has been the topic de rigueur in recent years (Alsup, 2006; Battey & Franke, 2008; Clandinin et al., 1999; Drake et al., 2001; Enyedy et al., 2006; Gresalfi & Cobb, 2011). As Darragh notes, ‘if the 1980s and 1990s saw a “social turn” (Lerman, 2000; Gee, 2000) in mathematics education research, it seems the 2000s and beyond suggest an ‘identity turn’ within social perspectives of our discipline’ (2016, p. 22). Since the 2000s these ‘turns’ have become increasingly more informed by broader contexts, with the 2010s invoking both socio-political turns in math education (Gutiérrez, 2013) and calls for decolonization in mathematics education (Trinder & Larnell, 2015; Gutiérrez, 2017, 2019).

Indigenous scholars such as Eve Tuck have long called for a pivot from damage-centered research which is characterized as ‘research that operates, even benevolently, from a theory of change that establishes harm or injury in order to achieve reparation (p. 413)’. Tuck (2009) critiques damage-centered research, in which even well-intentioned scholars often reproduce the harmful notion that marginalized communities are inherently broken. As an alternative, she proposes a desire-based research framework—one that recognizes individuals and communities as complex, contradictory, and self-determining. Rather than focusing solely on pain or disenfranchisement, this approach seeks to honor the fullness of lived experience (p. 416).

Building on the literature in mathematics education research that focuses on critical perspectives, the work of understanding teacher identity has been broadened to incorporate theoretical, epistemological, and qualitative perspectives outside of the recent field of education (Sfard & Prusak, 2005; Darragh, 2016; Lerman, 2001).

Gale et al. (2013) define an analytical framework as… “a set of codes organized into categories…that can be used to manage and organize the data. The framework creates a new structure for the data rather than the full original accounts given by participants that is helpful to summarize/reduce the data in a way that can support answering the research questions. (p. 1)”. The analytical framework I am theorizing for the purposes of this paper is built on the conception of complex mathematical personhood.

I utilized the four components described in

Table 1. Complex Mathematical Personhood Theoretical Framework.

CMP 1|Remembrance and Forgetting: CMP 1 means that people remember and forget their mathematical experiences, they flow in and out of different identity locations in their personal and professional lives.

CMP 2|Harm and Joy: CMP 2 means that people might experience harm in mathematical spaces but can also potentially experience transformation, joy, and liberation. This is not binary. The way they suffer might reproduce further harm or other sites of possibility. This is not a binary either—it is possible that both might occur concurrently.

CMP 3|Socio-Historical and Socio-Cultural Navigations: CMP 3 means that people might experience mathematics classroom spaces as a cross-hatched weaving where the historical exclusionary practices of mathematics are enmeshed when viewed within the current manifestations of White supremacy, patriarchy, colonialism, transphobia, racism, misogyny, sexism, ableism and other forms of exploitation and oppression towards marginalized people.

CMP 4|Learning and (Un)Learning: CMP means that people might experience mathematics as a straightforward process and simultaneously a subtle reality where there is the possibility to (un)learn, transform, reject, liberate, and alchemize. The latter can be experienced unconsciously, without acute awareness until other actions bring that to the forefront.

as initial codes to reveal the phenomenon being studied. The components for complex mathematical personhood also informed the design and focus of the semi-structured interviews that were conducted for the study.

4. Definition of Critical Veteran Mathematics Teacher of Color

I define the figure of the critical veteran mathematics teacher of color (C-VMToC) as a full-time, US-based teacher, currently working in a K12 public or charter school setting, who self-identifies as racially and/or ethnically from the Global Majority, and who characterizes their personal orientation and professional practice as critical. Some examples of these critical orientations in professional practice include teaching from an ethnic studies or humanizing framework (D’Ambrosio et al., 2013; Yeh & Otis, 2019; Yeh et al., 2021; Gutiérrez, 2019; Su, 2020), culturally relevant and/or culturally sustaining pedagogy (Paris, 2017; Ladson-Billings, 2018; Hammond, 2014), social justice (Gutstein, 2006; Larnell et al., 2016; Appelbaum & Davila, 2007; Kokka, 2018, 2020), anti-racist (Ladson-Billings, 2021; Kokka & Chao, 2023); abolitionist (Love, 2019; Bullock & Meiners, 2019) and/or civics-oriented perspectives (Moses & Cobb, 2002).

Furthermore, I define the veteran status of a teacher as someone who has been in the field for 5 or more years as attrition is of particular concern especially for teachers of color. The literature on teacher attrition indicates the following: (1) teachers serving students from low-income families or students of color are more likely to leave the profession entirely or laterally shift between schools (Rosenholtz, 1985; Scafidi et al., 2007), (2) teachers of color are more likely to serve in schools from low-income families or students of color (Sutcher et al., 2016), and (3) the cost of teacher turnover impacts not only the school, but also the community the school serves (Ewing, 2018; Sutcher et al., 2016).

According to the 2020 US Census Bureau, the occupied lands of Hawaii are one of the most diverse, multi-racial states in the country. Unlike the mainland’s teaching workforce, Hawaii’s teaching workforce is 33.9% Asian-American, 31% White, and the remaining third equally distributed between Native Hawaiian or other Pacific Islander, Black or African American, and Multi-Racial/Other. And so, while Native Hawaiian people remain a majority in the state, the teaching workforce does not retain proportionality to this data. This reality was a recurring theme in Kahiau’s reflections, as he was often the only Native Hawaiian STEM teacher in his workplace—a fact that carried deep significance for both himself and the Native Hawaiian students he serves that was evident in our conversations together.

5. Positionality

I taught mathematics to middle and high-school aged children in three large urban locations: New York City, Mexico City, and Chicago for close to a decade from 2007 to 2015. As a first generation, genderqueer, neurodivergent, South Asian, culturally Muslim immigrant, it was rare to encounter teachers from the same cultural and social background as me. My students were capricious, frustrating, bright, chaotic and beautiful. During this time, I was theirs and they were mine and together we did our best to create a classroom space that infused mathematical joy and a sense of wonder in our work. Sometimes, I was invited to my students’ homes for dinner. Other times, I was invited to their funerals. These memories continue to haunt and animate me to this day.

In 2015, and what was to be my last year of teaching mathematics as a full-time critical veteran mathematics teacher of color, I found myself increasingly unraveling. I could not keep up with the pace that the latest ‘teacher-proof’ curriculum required me to set, nor could I justify teaching to tests designed to exploit and experiment on students of color. So, I left. I walked out. I did not return. I could no longer be complicit in a system that I felt was willfully malicious—an immortal poltergeist that neither I nor my students could ever fully vanquish. In this, I joined the ranks of those that Santoro and Morehouse (2011) name as ‘principled leavers’—teachers who ‘refuse to fight wars they deem unjust’ (p. 265) and thus, resign ‘from teaching on grounds that they are being asked to engage in practices that they believe are antithetical to good teaching and harmful to students’ (p. 267).

Entering my doctoral program in 2015 and sometime in the middle of my coursework, I had started to think about what I would name for those teachers of color who deliberately choose to stay, who insist on charting their own pathways and navigating the tensions of systems that are inherently unjust and harmful to students of color. Extending Santoro & Morehouse’s terminology around ‘principled leavers’, I began to wonder about those critical veteran mathematics teachers of color who might be considered ‘principled remainers’, teachers who embody self-reflection, critical and complex understandings of how race, gender, and class manifest in their mathematics classroom spaces, and continue to be committed to enhancing their teaching practice as a never-ending journey.

Through graduate coursework that nurtured my burgeoning critical consciousness (Freire, 1968/1970; Andrews & Castillo, 2016), I began to view teaching K12 mathematics in the United States as a site of political, social, and cultural contestation. This space demands specific forms of labor, especially from those marginalized by their gender, disability, race, class, citizenship, and/or other categories of difference. Simultaneously, I had also begun to wonder how privileges afforded by the same systems that subjugate teachers of color are navigated by these same individuals. Upon encountering Avery Gordon’s (2008) work on complex personhood, I wondered how I could extend her conceptualization to mathematics teacher identities. I also wondered to what extent these systems are leveraged in the service of a complex mathematical personhood identity. I also wanted to explore how time is experienced by teachers as a formatting space on their lived experiences and evolving teacher identities.

This study was borne from those questions and the acknowledgement of the daily contradictions and tensions these ‘principled remainers’ contend with. As a former high school mathematics teacher, my lived experiences are central to this study; as a nascent portraitist, I carried these experiences into every interaction with Kahiau. Memories of my own tensions and contradictions were evident in both the research design and how the semi-structured interviews were conducted. Furthermore, portraiture methodologies, which I relied heavily upon to inform the analysis and trajectory of this work, itself acknowledges the relevance of researcher’s lived experiences. Lawrence-Lightfoot and Davis (2002) highlight how ‘the element of self is at play in all parts of the implementation of the methodology—forging relationships, determining context, searching for coherence, defining expression, and balancing a unified representation. (p. 35)’. I focus on Kahiau’s experiences in this piece to share, with the deepest respect, how his Indigeneity, teacher identity, and mathematical knowledge construct Kahiau’s daily practices as a C-VMTOC with the acknowledgement that my experiences are also interwoven into the fabric of this work.

6. Methods

The question of ‘principled remainers’ stuck with me, and the subsequent study took shape from 2020–2022 to design, obtain IRB approval, and implement. While the original study design had larger aspirations of traveling and observing participants teaching mathematics, the aftermath of COVID and its impact on research, funding, and personal health issues required a reset of the design and methodology of the study.

Upon IRB approval, I set out to recruit participants through snowball sampling methods and ended up connecting with Kahiau via email. Although 3 interviews were originally planned, our conversations together proved to be so thought-provoking and rich that an additional interview was necessary to work through the semi-structured interview protocol constructed for this study. Despite the time differences in Hawai’i and Chicago, Kahiau generously offered his experiences in a total of four 1–1.5 h Zoom interviews duringthe 2023–2024 academic year. Each interview had a specific focus and design, where Kahiau and I discussed conceptions of identity, mathematical knowledge, cultural background, and critical consciousness and how this had evolved particularly for him throughout his teaching journey.

The data from which this portrait was written was collected beginning in the fall of 2023 with all data collection concluded by January 2024. Data analysis took place using NVivo 12 during the spring and summer of 2024. The focal point of this piece is Kahiau’s work at his current school, where he is a middle school mathematics teacher. The school serves Native Hawaiian students and has a long-term goal of implementing de/colonization practices within its institution.

Finally, throughout this piece, it is my intention to make it clear that Kahiau is not a research subject nor an object of study, but a human being, a teacher, an interpreter, and one I am in dialog with as part of the methodological commitments to this work. As a nascent feminist qualitative researcher leaning into portraiture, I am not a clinical and dispassionate holder of expertise or knowledge. If anything, I view my work alongside teachers as tide, as orbit, and as push and pull between living beings learning in relation to and with each other.

6.1. Portraiture and Case Study—An Overview

Portraiture is a type of ethnographic research that focuses on the critical feminist notion that, “authentic findings will only emerge from authentic relationships” (1981, as cited in Lawrence-Lightfoot & Davis, 2002, p. 138) and blends scientific processes and artistic elements. I use this methodology in concert with other qualitative methods to construct richly constructed within-case studies (Merriam, 1998; Yin, 2009) to write Kahiau’s portrait in the findings section of this article. The research design for the project itself takes the political and anti-positivist stance that teachers, and particularly teachers of color are grappling with the complexities of an increasingly challenging workplace environment, and that to conduct research within this space requires solidarity, empathy and careful analysis.

• As Lightfoot notes,

Surely analysis and solidarity could stand as two poles of scholarship. Much research has neglected the second, studying teachers, for example, as though they were fruit flies…It is in the quest of the empowerment that comes from looking beyond the isolation at the little difference there is between humans, and the supreme importance of that difference. It searches for the energizing shock of sympathy and of the human community.

(Oakley, pp. 375–376, as cited by Lightfoot, p. 10)

• I utilize a combination of portraiture and case study methods. Data included collecting teaching artifacts such as student letters that had an affective impact on the participant, copies of unit or lesson plans that were critically oriented in nature, semi-structured interview prompts, and readings and reactions to a poem all participants read. In Kahiau’s case, a picture of a handmade woven vase was emailed to me, and explained in detail about what the weaving represents for his teaching praxis. The data sources provided the ability to develop a thick description and construct analysis via NVivo that proved very generative in connecting larger emergent themes. For much of this study, I connected how the larger macro socio-political context that teachers face can be found in the particular daily milieu that construct VMToC’s experiences in their workplaces and mathematics classrooms. As Geertz (1973) observes, “small facts are the grist for the social theory mill” (p. 23).

Lawrence-Lightfoot and Davis (2002) describe a portraitist as one whose stance is built upon “acceptance and discernment, generosity and challenge...she sees the actors as knowledge bearers, as rich resources, as the best authorities of their own experience” (p. 141) and that in attempting to create a portrait of an actor (e.g., research participant), the portraitist seeks to capture goodness, which is “an approach to inquiry that resists the more typical social science preoccupation with documenting pathology and suggesting remedies” and instead is a shift in research stance that positions goodness as a “complex, holistic, dynamic concept that embraces imperfection and vulnerability; a concept whose expression is best documented through detailed, nuanced narratives placed in context.” (p. 142). This, in turn, allowed for the interviews to have a more holistic and interpersonal approach that built trust, reciprocity and goodness between the participants and myself as the researcher. I offer an example of the type of rapport and community that was built in our conversations together. It offers a brief glimpse into what’s possible when critical feminist research centers trust, reciprocity, and goodness; especially meaningful given that this was only our second virtual interview and Kahiau and I had never met in person before the study.

[Int. 1, 4 February 2024, Kahiau]

Sara: 44:09...But you know, I’m just really honored that our ancestors, however, they were with us, are here in this conversation today. Like the fact that you brought that up and were willing to share that with me… I’m humbled and I’m honored because this is literally the second time we’re talking and we’re just like sitting here crying…

[Sara wiping tears]

Kahiau 44:53...because we’re Indigenous people! That’s what Indigenous people do.

[also weeping on camera]

Lawrence-Lightfoot describes her portraiture methods as a means to “document and illuminate the complexity and detail of a unique experience or place” (Lawrence-Lightfoot, 2005, p. 13). Thus, for the purposes of this study, the single bounded unit or case is the VMToC [Kahiau], and the means to engage in cataloging his lived experiences is through portraiture.

6.2. Hawaiian Contextualization

In the context of Hawai’i, colonization and land dispossession began in the 18th century, starting in 1778 and culminating in the forced removal of Queen Liliʻuokalani by the United States military in 1893. According to Haunani-Trask, a Kānaka Maoli [Indigenous Hawaiian] scholar and activist, following the events of 1893, ‘an all-White puppet government called the Republic of Hawai’i was put in place in 1894. The ruling planter’s party, composed primarily of missionary descendants, governed Hawai’i as an oligarchy throughout the territorial era.” (1991, p. 22). Despite mass opposition by Kānaka Maoli the colony of Hawai’i became a state of the American government in 1959. One of the many aspects of colonization and ethnic cleansing practiced by White settler-colonizers in the 18th and 19th century was the deliberate bans imposed by the United States government on speaking native Hawaiian language. Haunani Kay-Trask notes in her piece, Lovely Hula Lands: Corporate Tourism and the Prostitution of Hawaiian Culture, that, “all schools, government operations and official transactions were thereafter [1900 onward] conducted in English, despite the fact that most people, including non-natives, still spoke Hawaiian at the turn of the century” (Trask, 1991, p. 23).

Within the first 100 years of colonization, almost 95% of Kānaka Maoli were killed, reducing a population from close to one million Indigenous inhabitants to less than one hundred thousand people. This was due to a variety of effects including the introduction of European diseases, land dispossession, food insecurity and starvation, and poverty.

The ongoing ravages of early 18th century colonization and land dispossession of Native Hawaiian land continues into the present. As recently as 2018, a report published by the state of Hawai’i, notes that of the five most common racial groups in Hawai’i, Native Hawaiians “have the highest poverty rates for individuals and families, with 6610 families (12.6% of families) and 45,420 individuals (15.5% of the population) living below the poverty level.” Furthermore, the same report finds that the educational attainment of people living in Hawai’i can be categorized by racial and ethnic disparities with White and East Asian peoples having a higher educational attainment rate than Native Hawaiian, Tongan, Samoan, Marshallese Island, or American Indian peoples (2018, State of Hawaii). I include these numbers not as a form of deficit framing (Tuck, 2009) but to highlight how colonization works systemically to violently maintain and reproduce itself. In the findings section of this piece, I describe how colonial legacies have shaped Kahiau’s personal and professional journey, leading to the ethnomathematical teachings he continues to develop as he enters his next decade of teaching.

7. Findings

Introducing Kahiau

The first word that comes to mind to describe Kahiau is Weaver. In our first interview, Kahiau, a Native Hawaiian man who shared anecdotes about his Chinese, Japanese, Irish, Samoan, and Filipinx ancestry with me, spun stories of reclaiming his Native Hawaiian language and culture, describing this as his first act of decolonizing his identity. For Kahiau, language, culture, land, and teaching are interwoven threads that add texture to his complex mathematical personhood identity.

In Global South traditions around the world including my own, the act of naming someone has deep spiritual meaning. I chose the pseudonym ‘Kahiau’ with intention and purpose. The name has etymological roots to the Hawaiian language and means ‘Very Generous’ or ‘Giving’, qualities Kahiau fully shared of himself freely though we had never met before or heard of one another. By our second interview together, Kahiau and I were sharing both tears and laughter as he shared insights on shark goddesses, leaving his short-lived mechanical engineering Navy career working at Pearl Harbor, and his understandings of weaving ethnic studies and mathematics into his classroom space serving keiki o ka ʻāina [Hawaiian for ‘child of the land’].

Kahiau’s teaching journey begins with sitting in a cubicle working in isolation over naval plans as a mechanical engineer, which he describes “as the most boring job ever…primarily because of all of the red tape of the United States government” [Int. 1, 17 December 2023]. After enrolling in Hawaiian language courses to better understand his Indigenous heritage and realizing that his mathematics background could help Native Hawaiian students connect with STEM, Kahiau decided to leave his nascent engineering career to teach at three different Native Hawaiian-serving institutions. For Kahiau, it meant grappling with his desire to weave mathematics and teaching outside of his initial career in mechanical engineering working at Pearl Harbor. Referring to his brief time there, Kahiau notes: “...I felt hypocritical to be there. So, this is not the route for me. I shouldn’t be doing this. When I took three, four years worth of math courses. I don’t want to waste that either. And that’s when I discovered ethno-math education.” [Int. 1 (pt 1), 17 December 2023].

As highlighted in his career trajectory in Figure 1, Kahiau taught in a public school for six years. There, he taught primarily in Hawaiian since the school was the only immersion school of its kind in the public system. In his seventh year, Kahiau chose to move to a charter school, motivated by an initial desire to pursue a doctoral degree. There, he collaborated with ethnomathematics researchers, already working at the school, to develop programs that supported learning rooted in La Hui [Hawaiian nationhood]. As Kahiau shared in our second interview, he decided to forgo pursuing a doctoral degree in his tenth year of teaching due to personal family reasons. Instead, Kahiau joined a private school that aligned with his evolving and complex mathematical personhood—one that embraced the ethnomathematical pedagogy he had spent his first decade developing. At the time these interviews took place, Kahiau expressed his long-term commitment to stay at his current school and remain a mathematics teacher there.

8. Kahiau’s Portrait

I’m fighting to decolonize. But I don’t recognize that I’m colonized myself

~[Kahiau, Int. 1 (pt 1), 17 December 2023]

As a nascent portraitist, I believe that the act of naming and defining carries deep weight and power; that this act is a form of building universes within universes. I also believe that part of creating and cultivating critical consciousness in mathematics spaces is a perpetual act of gleaning, of gardening, of seeding, and of pruning, and that we have to be ethically mindful of terms that are too often exploited and co-opted in academic spaces. Terms like intersectionality, de/colonization, and anti-racism have deep theoretical roots to Black and Indigenous liberatory and emancipatory projects that are seen as threats by White academic establishments. And it is exactly for that reason, these terms are often neutralized and incorporated into academic-industrial complexes. Kahiau’s portrait interrogates his tensions with the process of de/colonization in multi-layered and interconnected perspectives—as a husband, as a teacher, as a son mourning his father’s recent passing, as a gay man, as a staff member, and as a Native Hawaiian person reconnecting with his roots. I approach both his conceptualization of decolonization with carefulness and empathetic regard (Lawrence-Lightfoot & Davis, 2002, p. 147) since decolonization theory has become so exploited and overused in academic circles.

Kahiau comes from a mechanical engineering background and briefly worked for the United States Navy before transitioning into his teaching career. In this portrait, I describe and share Kahiau’s journey into reclaiming his Indigenous heritage, his reflections on decolonization, and the intersections with his mathematics pedagogical practice.

The findings are analyzed and presented as vignettes, with direct quotes from our interviews together. They are also organized by the relevant complex mathematical personhood introduced earlier in this article that was used as a component to analyze the data. As a nascent portraitist, my aim is to center Kahiau’s words and experiences as much as possible, while also offering deeper analysis of how complex mathematical personhood and Gutiérrez ’s concept of mathematX can illuminate the evolution of critically oriented mathematics teacher identities over time. I explore the deep interlinked bond between land and people that Kahiau and his school’s community continue to grapple with daily. I then offer how Kahiau evolved his critical knowledge and teaching practices. I pay respect to the closing of this portrait by offering ways in which Kahiau continues to grapple with what it means to decolonize as a dialectic act between self and world and his ongoing development of complex mathematical personhood, in his own words and the art he offered to share graciously in our final interview together.

9. Complex Mathematical Personhood: Socio-Historical and Socio-Cultural Navigations

In advocating for a mathematX framework, Gutiérrez (2019) explains that while Western mathematics often conceives of time as linear and unidirectional, many Indigenous cultures view time as nonlinear—understanding the past, present, and future as interconnected and continuously in motion. Below, Kahiau reflects on the impact and legacy of colonialism within his family history, particularly his disconnection from the Hawaiian language. He emphasizes how the interwoven forces of past, present, and future contributed to the intergenerational loss of not having access to his native language:

For me, I guess in Hawaii because of our colonized history there, every Hawaiian person will list you their entire list of mixed race. And I remember, at one point maybe in high school, it came down to who has the most ethnic backgrounds in your ancestry. And I’m actually surprisingly, I’m one of those smaller ones…[my parents] raised us very, what we call, loco style. That’s a term we use in Hawaii... My mom is Filipino-Japanese, my dad was Hawaiian, Chinese, everything else, Samoan, Irish…Also, all I know is that I’m the first in my family, in maybe three or four generations, to speak Hawaiian. My papa, my Filipino grandfather. I know he spoke Bisaya [a FilipinX language]…my mom said they remember as kids hearing it, but they were never spoken to in Bisayan. So it’s just this colonized era, you know the 20th century.

~[Int. 1 (pt 1), 17 December 2023]

• The history of the colonization of Hawaii and its ongoing present-day occupation by the United States government reflects and refracts into the dynamics of how Kahiau experiences his day-to-day teaching life. I offer his insights in this section to highlight the linkages between land, Indigeneity, and his ethnomathematics teaching philosophy here in response to the first and second research questions for this study.

Kahiau is proud to come from a multi-ethnic and multicultural background. However, in our first interview together, he noted that he was the first in his family in about three to four generations to (re)learn how to speak Hawaiian. He notes:

So, for me to identify came down to the food and just the little bits of superstition here and there. But I think that’s why when I finally took Hawaiian language courses and Hawaiian studies courses, I didn’t realize that there’s been in local culture so much Hawaiianness is embedded in there. It just evolved. I got mixed up in the diaspora of everybody else…I’m now identified because I practice my Hawaiian culture.

[Int. 1, 17 December 2023]

• For Kahiau, reclaiming language and practicing Hawaiian culture are central to his de/colonization praxis. This includes his evolving spiritual practices rooted in Native Hawaiian traditions such as hula, his commitment to ensuring that future kānaka maoli [Indigenous Hawaiian person] generations do not face the same barriers he encountered in pursuing STEM pathways, and his integration of cultural connections between people, language, and mathematics into his daily teaching.

Kahiau’s journey to his current role as a critical veteran mathematics teacher of color begins in a cubicle looking at Navy submarine blueprints as a mechanical engineer. In his limited tenure working as a mechanical engineer, Kahiau did not achieve the work satisfaction that he was seeking:

Well, I’m open to any job. I’m excited…I’m ready to explore whether there’s two major divisions that mechanical engineers are sent to. And there’s just a regular engineering division, HVAC—heating, ventilation. Basic mechanical stuff usually, because it’s Pearl Harbor. It’s a naval fleet. …the other one was nuclear engineering. So, they placed me in nuclear engineering, which is fine. But it was the most boring job ever. And it’s primarily because of all the red tape of the United States government. It was you just sat there the whole summer at a desk. But because I didn’t have top level clearance for a lot of the things in my department, I couldn’t do anything…I got paid a nice federal paycheck to just sit there…Maybe you’re busy in meetings, but that’s like the extent of your social life. It’s just meeting with other engineers talking about how we’re going to maintain the fleet.

[Int. 1 (pt 1), 17 December 2023]

• In particular, the beginning of this endeavor was deeply connected to his reconnection to the Hawaiian language. Kahiau clarifies that:

…anywhere in the UH system, it is required that students take a Hawaiian course and take Hawaiian studies, Hawaiian language. So, the majority of students, I would say like 80% plus take Hawaiian studies… And we get a very surface level in the high school system…And I realized, wow, I am a native Hawaiian living in Hawaii. And I don’t know my own language. So, I decided to take the course as an elective, obviously. And eventually I tried to make it a double major with engineering and Hawaiian. And I also participated in this program… where they have year-round weekend or one week, two week long activities for Native Hawaiian students [in] K12. And one of my scholarships I had was to volunteer. So, taking that program, understanding that I am a Hawaiian student who is studying for engineering, and I can help other students K 12, who love STEM, one of the STEM course routes was available and that’s when I realized I wanted to be an educator.

[Int. 1 (pt 1), 17 December 2023]

• Connecting language, literacy and mathematics was essential to Kahiau’s mathematical identity as well. However, this was further challenging because he was one of the few native Hawaiian people studying both STEM and Hawaiian language; a reality of both the mathematical field as a largely White institutional space but also the recognition that the field of education is itself also a White institutional space as well. Part of Kahiau’s master’s thesis work involved looking through Hawaiian textbooks that missionaries had translated from French from the 1800s. He describes discovering mathematics as a form of poetry in his native language, an experience that was both exhilarating and isolating, like stumbling upon a secret song with no one else to sing it with.

So, it was…it was hard for me, I had to just navigate it myself. Because I remember when I did my thesis, I looked through textbooks from the 1800s. Because there were Hawaiian textbooks that missionaries translated from French textbooks. So, reading through, they were so fascinating to me, because I had to know Hawaiian language and mathematics…there was a book explaining what a plane was…And the words they were using was like, wow, is there a beautiful Hawaiian word, I feel like looking it up, because I never knew a bunch of them. But [it was said so] beautifully and poetically, where it’s a surface that goes on forever and never without any wrinkles…. beautiful terminology, because Hawaiian is a poetic language. This is beautiful. But no one else can understand this except me. Like, it’s, I felt empowered because I had this little pearl.

~[Int. 1 (pt 1), 17 December 2023]

• After teaching in a few different schools during his initial teaching years, Kahiau was hired due to his background in ethnomathematics and his ability to braid Hawaiian culture and STEM at a school that predominantly serves native Hawaiian students. The school itself is engaging in a collective and collaborative act of de/colonizing the curriculum and intentionally creating spaces for faculty and staff to have conversations about how to do this work together, including reading Paulo Freire’s work. Kahiau observes the following:

We had to read excerpts of Paulo Freire. I love…a lot of what Dr. Freire says in his book …it really hit us hard... But once we realized, for me, it was I am the colonizer by continuing this path [referring to working at Pearl Harbor]…Okay, no, I can’t do this. I’m fighting to decolonize. But I don’t recognize that I am colonized myself (emphasis added). Oh, boy [K visibly emotional on camera]. That was the one that did it for me…I need to hold on to my math, I need to hold on to ELA because of math test scores. And then we were like, Wait a minute. Yeah, what are we doing? So it hit us hard. And now we’re just like, alright, let’s just flood the gates. Decolonize everything we’re doing. But for some teachers, it’s very difficult, because they have not hit that wall, or they’re too afraid to hit that wall of, wow, I’m colonized. Some of our White faculty, I think it is also hard…for them to realize too, where they are because of the education system, not because of who they are. It’s the system.

[Int. 1 (pt 1), 17 December 2023]

• Kahiau’s observation is revelatory in several ways in response to the second and third research questions, which concern the contradictions and tensions C-VMTOCs occupy and confront in their teaching praxis and the CMP framework: (1) it embodies the ‘epistemology of knowledges’ central to Gutiérrez’s MathematX conceptualization; (2) it highlights [CMP 4], the attribute of learning and (un)learning as mutually entangled phenomena; (3) it underscores that this work is ongoing and shaped dialectically by both individual and collective actions within the school community as described by the slash in Bhattacharya’s explanation of de/colonization; and (4) it invites reflection on how White faculty members may experience and engage with this process differently under systems of oppression as an extension of [CMP 3], socio-historical and socio-cultural navigations.

9.1. Complex Mathematical Personhood: Remembrance and Forgetting

Gutiérrez argues that “mathematics both as a school subject and as a practice in society has played a powerful role in dispossession, by valuing and sanctioning only certain kinds of ontologies and epistemologies that side with colonialism” (2019, p. 3). She asks the reader to heed the following complexity and notes that:

…presenting Western and Indigenous knowledges as “opposites” has been the strategy of colonizers who suggest Indigenous knowledges are in contrast to Western ones that have served as the foundation for progress in the modern world (Harding, 2008). So, while there is no such thing as a single Indigenous “way of knowing” or “worldview,” there are underlying epistemologies (ways of knowing) and ontologies (views of reality) that differ from modern Western/Northern/Eurocentric views and that contribute to Indigenous systems (Battiste et al., 2002; Cajete, 2000)

(p. 3)

• In the act of writing and bearing witness to Kahiau’s narration of his complex mathematical personhood and how it has evolved for him over time, I kept returning to Gutiérrez’s (2019) concept of mathematX. I wondered about all the ways in which Kahiau had experienced dispossession both as something that could be seen and observed physically and in what ways he had experienced the kind of dispossession Gutiérrez is describing from an epistemological orientation in mathematics spaces. I respond to the second research question below by offering an example of how Kahiau engages in the act of living mathematX epistemologically and through the lesson plan/unit plan he shared with me along with his thoughts behind the creation of the unit of study.

• RQ (1): What contradictions and tensions must C-VMTOC’s occupy and confront if they wish to bring de/colonial and/or ethno-mathematical practices into their teaching praxis?

A lesson plan is more than just a plan; it is an act of creation, shaped by the teacher’s guiding epistemology and the teaching community to which they are connected. What happens when these epistemologies are in tension or outright conflict with one another? Analysis related to the second research question about contradictions and tensions Kahiau occupied and confronted while bringing de/colonial and/or ethno-mathematical practices into their teaching praxis revealed the following themes: (1) concerns about standardized testing, (2) Kahiau realizing that this concern is layered with his own Native Hawaiian identity, and (3) interrogating how mathematics and testing culture intertwine in ways that other subjects do not necessarily experience at the same intensity.

Kahiau noted this issue on what it meant to be involved in a school that committed to de/colonizing its practices and curriculum and having to continue to adhere to the demands of a pervasive testing culture.

…I’m still held to this darn standardized test. And that’s the one that every teacher now that we’re in this decolonization process, every teacher is trying to dismantle. Stop making required standardized test scores…like, stop it…I want to see the progress for sure. But don’t hold it against us. Me and the ELA teacher go back and forth on it…math is not just here’s a score, the score will dictate that if you can maintain this trajectory… you will have the opportunity to get into Stanford or Princeton. You can get to it regardless of that. …I think that’s what I want to be known for. And it just sucks that there’s parts of me that I have to hold it down because I’ve got to teach to the test a little bit.

[Int. 1 (pt 2), 4 February 2024]

• The lesson plan Kahiau shared with me reflects his own grappling with the powerful statement he made earlier in our conversation: “I’m fighting to de/colonize. But I don’t recognize that I am colonized myself” [Int. 1, 17 December 2023].

In the contradictions and tensions of teaching a subject matter like mathematics, Kahiau’s experiences align and map onto the fourth aspect of complex mathematical personhood—that people might experience mathematics as a straightforward process and simultaneously a subtle reality where there is the possibility to (un)learn, transform, reject, liberate, and alchemize. The latter can be experienced unconsciously, without acute awareness until other actions bring that to the forefront. This also aligns with Gutiérrez’s explanation of ‘living mathematx’, whereby it… “means both that we live a version of mathematx as well as we are a living version of mathematx...Living mathematx means moving through the world with other living beings, acknowledging, appreciating, and reciprocating the patterns produced (Gutiérrez, 2017, pp. 17–18).”

It is notable that Kahiau mentions that he feels the pressure to ‘teach to the test a little bit’, a common experience for many teachers working in schools in the United States that are held to standardized measurements to demonstrate purported efficacy. I view this as an example of CMP attributes of learning and (un)learning [CMP 4], along with navigating the very real socio-historical and socio-cultural practices [CMP 3] embedded within mathematics education. Here, Kahiau is grappling with colonial approaches to measuring children and placing them in competition with one another—practices that are in tension with his belief in mathematics as a collaborative, inclusive discipline meant to serve and uplift all people and the world around them.

Building on this initial theorization, Kahiau’s narrations helped me observe how his experiences in co-creating curriculum with other colleagues committed to de/colonizing the curriculum were instrumental in the experiences his students were able to attain—that this act of (un)learning, transforming, rejecting, liberating, and alchemizing is a process that is built intentionally as a learning community. I have shared the unit plan below specifically related to mathematics3. Kahiau affirms this here:

…our school is, I think I mentioned [this]…we’re trying to decolonize our efforts or the histories that we have. So, my team, also last year was our first year of our pilot to Indigenize the school.

[Int. 1 (pt 1), 17 December 2023]

• RQ (2): How do the ‘contradictions and tensions’ referred to in RQ1 impact C-VMTOC’s own burgeoning critical consciousness and complex mathematical personhood

In the next section of this portrait, I respond to the third research question and share Kahiau’s observations of how his middle school students took on this learning and the subsequent connections to Kahiau’s understandings of his own complex mathematical personhood (Rezvi, 2025). Looking through the unit plan made it clear that significant efforts had been made to create interdisciplinary connections to both Indigenous Hawaiian knowledge and specific content strands. He shared some of the successes of some aspects of that collaboration with me here:

Our most successful cornerstone last year that we’re trying to duplicate this year was the Socratic seminar. Because that’s one of the skills for English and they had to debate. If Hawaii had one sustainable food crop, what would it be and why? So they have to take my skills of ratios and, and rates to talk about yields of crops, how much it can feed and how much calories for family and health they learn about calories and the balanced diet. What is a calorie? What is this? Science? They also learn about calories but also…the scientific part: the burning rate? How does it affect your body?

[Int. 1 (pt 2), 4 February 2024]

• When describing the unit and the underlying affective goals of what he hoped students would attain out of this experience, Kahiau shared the following:

Students need to play. Students need to value feedback. Students need to have multi-generational teaching practices… We know our ancestral roots; we know our genealogies. And that’s integral in every classroom. And there’s even voice and choice. Every child. Every lesson is personalized to every child, they can do this, this is, and we took that document and we’re like, Hey, what are we going to do for our sixth graders?

[Int. 1 (pt 1), 17 December 2023]

• Part of the act of CMP 4 (learning and (un)learning) and CMP 1 (remembrance and forgetting) Kahiau is describing in this narration is the importance of honoring the humanity and ancestral ties of every single child in his mathematics classroom. As readers who have been in the K12 classroom might attest, this is easier said than done; those that are the most vulnerable are the ones who are most often invisibilized daily in mathematics spaces. For middle and high school mathematics teachers, the desire to fully see and personalize the teaching experiences for every child can be in direct tension with the structural reality of scheduling and attempting to create these spaces for upwards of a 100+ children daily. It was the school’s explicit commitment to de/colonizing that made interdisciplinary planning possible, allowing Kahiau and his colleagues to engage in this level of intentional collaboration as a team, rather than attempting to do so in isolation.

9.2. Complex Mathematical Personhood: Harm and Joy

• RQ (3): How do teachers of color work within (and simultaneously subvert) colonial systems of education?

One of the main tenets that Kahiau repeatedly espoused in our conversations together was the concept of community and interconnectedness as a form of subversion to colonial systems of education. In this section, I respond to the first research question by offering Kahiau’s thoughts on Indigenous Hawaiian pedagogical practices and how he weaves them into his own ethno-mathematics teaching practice in more formalized school settings. Kahiau describes the importance of these concepts and the impact on his own teaching praxis briefly here:

I learned that in Hawaiian pedagogy, it’s… usually the Elder, the Kūpuna, the ancestor, grandparent, that teaches the child, while the adult parent is the one hunting or fishing or farming or doing that…all those things. And learning was always one on one, or one on two, very small, very small ratio. And I’m like, I can’t teach this class of 25 with these struggles, like there’s gotta be something better. And that’s how I stumbled upon ethnomath.

[Int. 1 (pt 1), 17 December 2023]

• When describing the actual enactment of the unit plan summarized in

  Table 2. Kahiau’s Critically Oriented Lesson Plan.

  Unit Title	Examining Indigenous Sustainable Food Practices
  Developed by:	Kahiau and School Community
  Suggested Course/Grade Level	MS Mathematics
  Mana’o Nui/Big Idea:	A firm foundation in my identity sets the stage for future success. [What is] required for thriving industries and economies in the land?
  Essential Question	Who am I and what role can I play as the lāhui [Hawaiian nation] seeks to reestablish kuapapa nui [the genealogy of Great Kaua‘i]?
  Hākilo (Process Look Fors):	Students are responsibly and accurately using data and research. Students are talking about lāhui-centered issues as a means of creating a thriving industry and economy. Students are using accurate vocabulary to refer to lāhui-centered issues and discuss their benefits. Students are respectfully engaging in discussion. Their voice and ideas have value for the greater lāhui. Students have agency.
  Goal	To convince audience members of the effectiveness of canoe plants as a means of bolstering Food Security in Hawai’i.
  Situation	Currently 90% of Hawaiʻi’s food comes from external sources, which is not a sustainable practice.
  Products	Students will participate in a Socratic seminar in which they use data gathered through the lens of their core classes to argue for the native plant that they believe could best be leveraged by our local communities to improve Hawaii’s Food Security.

  , Kahiau noted the powerful line from one of his students emphasized below:

We had our Socratic seminar. The kids were doing their thing. I was like, wow, these kids were amazing…They’re sixth graders, and they’re debating about whether we want kalo [taro plant in the Hawaiian language] or [not]... And we’re amazed…And watching some of these kids have good audience technique to present in front of their entire class [of more than a hundred] sixth graders, and they watched every single debate…it was amazing. And one of the comments that made us like… (Kahiau stops and gets visibly emotional) one student said, I have permission to be smart (emphasis added). You see why? Okay, that was like, oh my god, this works. We teach an Indigenous way that works.

[Int. 1 (pt 2), 4 February 2024].

• I am reflecting on a question Gutiérrez asks regarding the embedded ways in which Western/Eurocentric mathematics serves as a site of dispossession. She wonders: ‘What is lost in mathematics as a whole, and in global society, if we continue to dispossess people of valuable knowings that support them to be whole—to continually remake themselves and fulfill their responsibilities—and that have the potential to enrich the lives of others, including our other-than-human relatives? (Gutiérrez, 2019, p. 5).’

In Kahiau’s retelling of the facilitation of this lesson plan, the student’s joy in learning—and in claiming the agency to embrace their own ‘smartness’—offers a glimpse of what wholeness can look like in mathematics education. Too often, the permission to be smart is stolen in classrooms, especially for children of color, whether through low expectations or by making mathematical learning inaccessible and disconnected to their lives. Yet, as evidenced in Kahiau’s teaching praxis, when a classroom is deliberately insubordinate to colonial ways of teaching mathematics, the space for students to share their brilliance and the impact on mathematical identity is profound. For those who have witnessed such moments, the beauty of a child confidently expressing their mathematical thinking is something sacred and powerful, and could not have been made possible without Kahiau’s own desire to reclaim Indigenous ways of teaching that translate daily into his classroom.

9.3. Complex Mathematical Personhood as Revolution

Robin DG Kelly observes that, “...without new visions, we don’t know what to build, only what to knock down. We not only end up confused, rudderless, and cynical, but we forget that making a revolution is not a series of clever maneuvers and tactics, but a process that can and must transform us” (2002, p. xii). I view how teachers evolve their complex mathematical personhood as a form of joyful revolution. It is an act of de/colonizing one’s internalized socialization within ongoing systems of oppression—as CMP 4 notes, an (un)learning process that requires awareness of past/present/future time. This is particularly potent given how mathematics has long been used to dehumanize and categorize people into hierarchies of inferiority and superiority. And while I am not a historian by training, I am aware that revolutions begin by being able to first name what is wrong, what is unjust, and what troubles the spirit. For me, this has always been most viscerally embodied through the medium of poetry; for Kahiau, his primary mediums have been weaving and hula-dancing as he reconnects with his Indigenous Hawaiian heritage. When I requested a piece of art or poetry that resonated with him in some way, not only did he share the beautiful woven piece pictured below, but also offered the accompanying explanation as well. It is both appropriate and relevant that Kahiau’s voice is centered in the final portion of this section. His words flow in, through, and between the three research questions that I attempted to respond to in this piece.

Kahiau: In regards to the art piece that relates to education, I present to you a flower vase [Figure 2] that I recently wove with hala (pandanus leaf). This contemporary weaving technique is based on traditional Hawaiian round mat weaving/plaiting techniques. The hala leaves are gathered dry and each one is carefully cleaned, rolled, and flattened. With my students, this is the process to build their kahua (foundation) together. Once all leaves are properly flattened over a period of time, they are then stripped into specific widths (in this picture, they are ⅛” strips). Each leaf has its own identity so we can choose to mix colors or try to match colors to make a particular pattern. With students, sometimes heterogeneous grouping is needed and other times we select homogeneous grouping.

When I was taught to weave, my kumu [teacher] said not to fight the lau [leaf]. Let the lau do what it wants to do and I am merely there to guide the leaf into place. The same goes for our students, I do my very best not to indoctrinate and try to just guide them. Once the weaving project is complete, the interconnectedness of each leaf creates a beautiful artifact and with our students, we always connect them and network with them with their peers, their families, and the community. Ultimately, we want them to network with each other because this creates our beautiful lāhui [nation] and kaiāulu [community]. Our Hawaiian values are built upon community and proactive planning rather than the individual nuclear families and selfish behavior. I also wove three flowers (in order from L to R, loke [rose], anthurium, and putiputi [Māori flower]. These flowers are three different techniques that come with networking with people from outside our community. We can still learn from people that are different from us and that will only make us more beautiful. I also took this photo on my front patio. I have been learning to become more patient every time I work in my front yard which in turn is helping me become more patient with my 6th graders.

[Personal Correspondence, 5 March 2024]

In the liminal spaces of teaching that Kahiau’s portrait espouses, we can find acts of healing, rejuvenation, and reconnection and simultaneously the profound sorrow of the past, present, and future colliding within the young people Kahiau serves in his quest for de/colonizing his teaching practices. I think of his sixth graders, who have known no other world besides the land that is currently occupied by a settler-colonial government entity; the parents of these young people, who have also grown up watching the increased impact of tourism as both a continuation of the colonial project on Hawaiian lands and the dependency on tourist income many have to rely upon; and the previous generations that were dispossessed of their own language, cultural traditions, and land. Kahiau describes the ways in which he has begun to reclaim his Indigeneity through hula as a sacred ritual and cultural practice here:

My teacher of hula would always tell us when we do particular chants for either rain or the sun for inspiration. She always tells us…when you get your answer, don’t be surprised. You asked for it. And if you are genuine, it’s going to come to you. So don’t be surprised when it actually happens. Every time I ask for my prayer, I do my chanting. I’m not shocked anymore.

~[Int. 3, 3 March 2024]

• Kahiau’s reclamation of spiritual traditions like hula, weaving, and ethnomathematical teaching practices are prayers answered for him. In our final interview together, we both wept from our corners (and digital screens) in the world at the beauty and grief of bearing witness to our respective experiences and for allowing the universe to connect us together. In the writing of this portrait, I am grateful for my own prayers answered on what it means to be a principled remainer in our current socio-political realities.

9.4. Limitations of the Study

There are a few limitations to the study that are important to mention: (1) sample size, (2) member checks, and (3) data corroboration/authentication. Given that this article solely focuses on the experiences of one Native Hawaiian mathematics teacher, it would be both inappropriate and problematic to make larger claims of what ‘best practices’ are in serving Native Hawaiian students and/or professional development for Native Hawaiian teachers that center ethno-mathematical knowledge building. Secondly, despite my original aspirations to ground this study in participatory action research, in which Kahiau could have more actively contributed as a co-researcher, neither of us had the time or capacity to engage in that work together due to a variety of factors, including, but not limited to, time difference, impact of COVID, and personal capacities. Thus, the analysis presented here is solely my own and not member-checked beyond the data checks I asked during the interviews with Kahiau. A future study could weave elements of portraiture with participatory action research to create a more robust dataset and analysis. Finally, the narratives and anecdotes that Kahiau so openly and generously shared with me were not experiences I could independently verify or corroborate due to funding limitations. In future studies, I hope to play a more active role in direct observations of teachers in their classroom spaces to support a richer analysis. Finally, as a non-Native Hawaiian researcher, I acknowledge that despite my best intentions, the absence of member checking with Kahiau and/or other Native Hawaiian scholars means that aspects of my analysis may not fully capture the cultural knowledge and experiences he shared in our interviews. I recognize that I have much to learn in this space. My niyaat—my intention—is to approach the possibilities and limitations of this work with humility and listening, allowing it to continue orbiting around what becomes realized when we collectively imagine, reach for, and dream a different mathematical de/colonial future into being.

9.5. Further Discussion

Martin (2013) has described how mathematics education in the United States can be viewed as a site of interrogating race and racial projects. He notes that “an examination of modern mathematics education reforms…shows that they have been aligned not only with neoliberal and neoconservative market-focused projects but these reforms have also been aligned with new right, neoliberal, and neoconservative racial projects” (2013, p. 328). In the interwoven threads of neoliberal and neoconservative projects, which are themselves marked by extensions of colonial and imperial policies and practices, I continue to reflect upon the ways in which mathematics spaces continue to be a site where these constructs can be rejected, subverted, and alchemized.

Kahiau’s portrait evidencing his complex mathematical personhood offers larger insights into what mathematics spaces have the possibility of becoming and being from an explicitly de/colonial stance. I also hoped to offer a view within a view of how mathematics educational research might be presented. In the writing of this piece, I wanted to understand how I could share Kahiau’s truths as a critical veteran mathematics teacher of color, along with how he interweaves his Indigeneity, mathematiXical identity, and complex mathematical personhood into the daily work of teaching. For this to occur, I needed to lean into scholarship that centers both feminist and Indigenous knowings, methodologies, epistemologies, and theoretical frameworks. As is evident in all colonial institutions, and particularly true of academia, it is a deliberate act to foreground Black and Indigenous women’s scholarship. Lawrence-Lightfoot and Davis’ (2002) work on portraiture as a Black feminist qualitative methodology allowed me to reorient my own understandings of what can be possible in terms of practicing relationality between researcher and research participant and recognizing that there are limitations and boundaries that must also be respected.

Elsewhere, Gutiérrez and Bhattacharya’s conceptualization of MathematX and de/colonial as something that is ongoing, hybridized, and a continuous event helped me situate Kahiau’s own ways of navigating the both/and of his experiences. His recognition of and subsequent intention to de/colonize himself, along with building community with others in his workplace, are deeply interconnected, unfolding in ways that are not bound by a linear sense of time. As Bhattacharya clarifies, ‘the term de/colonizing represents both the continuous desire for and imagination of a utopia wholly free from colonization, and the (im)possibilities of such a dream that keep us shuttling between oppressive and liberatory ontoepistemic states of being and knowing.’ (p. 177). In Kahiau’s portrait, the various components of complex mathematical personhood (remembrance and forgetting, harm and joy, socio-historical and socio-cultural navigations, learning and (un)learning) are entangled with the fluidity of knowing and being Bhattacharya describes.

Perhaps part of engaging in the work of mathematX (Gutiérrez, 2019) and constructing one’s own complex mathematical personhood is figuring out what to pray for, what to hope for, and what it can teach us about how to be in relation to one another in mathematics educational spaces.