Embodying Indigenous Relationalities with Mathematics

Abstract

Mathematical learning—understanding patterns, logic, and space—always carries ethical, relational, and political dimensions, even though these might be routinely muted at school. At the same time, Indigenous relationalities have often driven mathematics inquiry and optimization. In this paper, we highlight the co-constituted nature of Indigenous relationalities and mathematical learning and how these open up possibilities of helping us mature as humans individually and collectively. Mathematics has long been a part of practices of human maturation and the living of Indigenous relationalities. To illustrate the co-constituted nature of relationalities and mathematics, we share four stories of land-based mathematics from two urban Indigenous schools—Sahasatsuksa School in Chiang Rai, Thailand, and Nawayee Center School in Minneapolis, USA. We illuminate opportunities for human maturation and mathematics learning in four interrelated levels: (1) mathematics to cultivate a fierce love of land, (2) mathematics to regenerate unique intergenerational roles and responsibilities, (3) mathematics to learn how we are related, and (4) mathematics to better understand power in places. In conclusion, Land-based mathematics fundamentally recognizes how Land supports the systematic cultivation and transmission of mathematical knowledge and optimizes ethical learning of what it means to be human. Through these stories, we consider the power and possibility of designing mathematics education towards more relational worlds.

1. Introduction

Mathematics has long been part of cultivating systems of Indigenous relationalities that help people know how to adapt alongside a dynamic earth (Gutiérrez, 2022; Nicol et al., 2023). In contexts of changing lands, waters, and skies, mathematics support human adaptation, emerging in and embodying ethical relations to others in creation. Contexts of adaptation too, provide contexts for learning mathematics. These include attention to patterning, movement, spatial analyses, optimization, and other forms of meaning-making that are integral to learning and living out our ethical roles as individuals and collectives. This paper explores the co-constituted nature of mathematics and Indigenous relationalities, and how we might design learning towards healthier forms of living and life.

1.1. Indigenous Relationalities

Indigenous peoples have always centered the importance of ethical considerations in living and learning as embedded within particular geographies and landscapes (Deloria, 1979; Simpson, 2017). We draw from Whyte et al.’s (2018) use of Indigenous peoples to refer to the diverse “400 million people across the world whose communities, polities, and nations exercised self-determination according to their own social, cultural, and ecological systems—that is, governance systems—prior to periods in which other human groups dominated them through various combinations of imperial invasion, colonial exploitation and occupation, and settlement of their territories” (p. 155). These communities maintain distinct, continuous, and evolving cultural identities despite ongoing political, linguistic, and cultural assimilationist policies of nation-states and other outside forces. As original inhabitants of particular geographic territories, Indigenous peoples continue to exercise their sovereignty and uphold historical and relational ties embedded within their homelands (Corntassel, 2003; Prasit, 2019).

Indigenous relationalities hold entire societies together despite ongoing encroachments and exploitations. Through intimate relationships with changing Lands, (purposefully capitalized to indicate the livingness of Land), Indigenous peoples have matured vital systems of relationalities to construct societies, governance structures, and knowledge protocols based on systems of life-enhancement (Kawagley, 1995; Wilson, 2009; Wildcat, 2009; Whyte et al., 2018). Responsibilities that are maintained through generational teachings, protocols that sustain balance, diverse and equitable ecosystems in fact support 80% of the earth’s biodiversity (Garnett et al., 2018).

We use Indigenous relationalities to refer to the ethical qualities, intergenerational moral responsibilities, worldviews, governance protocols, ancestral and everyday embodied practices of living in relation with the rest of creation (See also Elliott-Groves et al., 2020; Wildcat & Voth, 2023). Nature-culture relations—where humans are seen as a part of rather apart from the natural world (Bang & Marin, 2015)—are guided by these Indigenous relationalities and reciprocal responsibilities. Ethical qualities such as consent, reciprocity, and respect, guide what it means to grow up as a person, how to treat others in the natural world (humans, plants, animals, and the spirit world), how to make decisions about what one should do, notice and stand up for what is just and good, and participate reciprocally in family and communal life. They support the continuance—the collective health, adaptation, and flourishing of cultural communities—alongside and in the midst of ongoing sociopolitical and ecological changes (Whyte, 2017).

1.2. Mathematics and Human Maturation

Strengthening Indigenous relationalities is a part of processes that Deloria (1979) and Bang (2020) call human maturation. Human maturation refers to the ways we humans cultivate capacities to take care of all systems of life, to learn our unique roles and responsibilities, act for what is good, true, and beautiful, and live in more life-giving ways. It is learning our ‘a-part-of-ness’ and our accompanying ethical commitments, reflecting and acting from our reciprocal relatedness rather than from relationships of domination, selfish accumulation, and exploitation.

Mathematical practices—the engagement with numbers, patterns, and space—have long been a part of these practices of human maturation and the embodying of Indigenous relationalities (Archibald et al., 2019; Diaz, 2019; Gutiérrez, 2022). This paper explores the co-constituted nature of Indigenous relationalities in mathematical practices, and offers ways they expand on each other towards shared goals of human maturation and the regeneration of community life. This manuscript is grounded in the following guiding question: How do mathematical practices support young people embodying and living Indigenous relationalities, and vice versa?

This paper draws on ideas of Indigenous mathematical traditions that illustrate the unity of mathematics to the rest of creation (e.g., Gutiérrez, 2022; Meixi et al., under revision; Nicol et al., 2023; Barajas-López & Bang, 2018), as an expression of the intimate bonding of a people to their place (Cajete, 2000). Through direct, personal, embodied experiences in the natural world, Indigenous people globally already have theories, stories, algorithms, and sophisticated strategies that do not dislodge ethics from STEM learning. In this sense, plants mangos, fish, creeks, lakes, and stars are all key partners in mathematics learning, human maturation, and the living of Indigenous relationalities.

These times in human history are increasingly dire. Grim IPCC reports (e.g., IPCC, 2022) state that the failure of human societies to shift their ways and implement immediate interventions within the coming decades means the planet may cross an “ecological tipping point of a 2 °C increase in global average temperature” with devastating consequences especially for Indigenous, Black, poor, disabled, and other vulnerable communities (Whyte, 2020, p. 2). At its core, human maturation is learning to do right by creation and fulfill our responsibilities as human people. Caring for and protecting plants, animals, soils, waterways, and stars is essential to a healthy society’s ability to adapt and thrive amid intensifying socioecological change (Whyte, 2017). If we have any chance at collective survival, human maturation will need to be a core purpose of human development and education (Bang, 2020)—mathematics education included. We will need a radical return to the ways that mathematics has always been part of human relationalities.

In the following sections, we share four stories of living Indigenous relationalities with mathematics from two urban Indigenous schools—Sahasatsuksa School in Chiang Rai, Thailand, and Nawayee Center School in Minneapolis, USA. We illuminate ways of living Indigenous relationalities through land-based mathematics in four interrelated levels: (1) mathematics to cultivate a fierce love of land, (2) mathematics to regenerate unique intergenerational roles and responsibilities, (3) mathematics to learn how we are related, and (4) mathematics to understand power in places.

2. Theories and Concepts: Land-Based Mathematics Towards Healing and Human Maturation

2.1. Why Mathematics?

There is still no agreed-upon definition of what counts as mathematics. Its evolving definitions typically come from the philosophers and historians who write its history (Ascher, 1994). In fact, Ascher writes that mathematics has been argued to be a Western concept—not to say that mathematizing does not exist across swaths of time and geographies, but rather “that others do not distinguish them and class them together as we do” (p. 3). We do not focus much on what mathematics is here, but rather on why mathematics is. For current purposes, we use mathematics and mathematizing to broadly refer to understanding and experiencing patterns and relations, logics, and spatial reasonings that contain ethical, spiritual, and political dimensions, part of larger intellectual systems that “our ancestors used to make sense of the world that sustained them” (Gutiérrez, 2022, p. 383).

Over the past few decades, psychological and educational studies have laid solid foundations for the continued articulation and examination of the broad scopes of mathematics practices—expanding the where of mathematics to home, community, and everyday life. This research revealed complex constellations of sophisticated family and community practices (e.g., Goldman & Booker, 2009; Cole, 1985; Lave, 2011; Saxe, 1988), the brilliance of children (e.g., Barajas-López & Bang, 2018; Carraher et al., 1985; Nasir, 2000), and the ancestral intelligences of land-based practices where mathematical reasoning and calculations have supported the survival and thriving of members of entire social groups (Barajas-López & Bang, 2018; Diaz, 2019; Rock & Gould, 2018). Expanding the where of mathematics also reveals the deep epistemic theft where these practices have been invisibilized, erased, and violently discounted at school (Joseph, 2011; Prescod-Weinstein, 2017).

Mathematics has always been a part of these dynamic endeavors. In Indigenous and place-based communities, mathematical knowledges—natural numeracies—are regenerated in direct relation with lands, waters, and skies (e.g., Barajas-López & Bang, 2018; Diaz, 2019; Lipka et al., 2011; Nicol et al., 2023; Rock & Gould, 2018). Land-based mathematics fundamentally recognizes how Lands support the systematic cultivation and transmission of mathematical knowing, and optimize our ethical engagement with lands. Each community’s intelligence system is “a series of interconnected and overlapping algorithms—stories, ceremonies, and the land itself are procedures for solving the problems of life” (Simpson, 2017, p. 23).

In this paper, we study why mathematics or practices of mathematizing are reclaimed, cherished, and embedded within and in service of relational roles and goals. We suggest that educational designs that begin with the ontological grounds of Indigenous relationalities offer tangible ways forward for cultivating community agency and reimagining schools towards human maturation and collective continuance of life.

2.2. The Axiologies of Indigenous Relationalities in Mathematics Education

Axiology refers to the ethics or morals that guide expectations of how we treat one another; our every action carries particular axiological groundings and orientations. Shawn Wilson (2009) writes that “An Indigenous axiology is built upon the concept of relational accountability” (p. 77). It is the responsibility to live in respectful, reciprocal, and reverent relationships that form the axiology of a person as they make and remake their relationships with others (Archibald, 2008). In the context of community-based design research, Bang et al. (2016) use axiologies to refer to what is valued, beautiful, and true, that “shape current and possible meaning, meaning-making, positioning, and relations in cultural ecologies” (p. 29). This means that designing towards axiological transformations supports shifts in how we make meaning of our roles and relationships to each other.

In the late 1980s, Brazilian scholar D’Ambrosio called for mathematicians to rethink their ethical contributions to a “nonkilling mathematics”, a mathematics of peace, religion, art, and toolmaking instead of violence linked to the Department of Defense (D’Ambrosio, 2009, 2016). Similarly, scholars have highlighted the dimensions of engineering ethics in computer science and latent ideologies about whose lives are grievable or not, and the explicit considerations of sociotechnical issues and individual and societal ethics of engineering (Philip et al., 2018). Yet, today ethics are routinely muted parts of STEM education so that STEM is presented as objective, apolitical, and acultural. Under narratives of objectivity, apoliticism, and aculturality (Warren et al., 2020), mathematics is often seen as abstract and without ethical implications.

Slowly, ethics and ethical decision-making are of increasing concern in STEM. The 2020 NSF STEM Education Visioning report states, as we continue to advance technologically, that “It is critical to develop STEM learners’ ability and willingness to acknowledge and resolve ethical issues in their work” (NSF, 2020, p. 18). This field-level recognition of developing ethical competencies in STEM builds on exciting advances in studies of ethics in STEM learning thus far. These include cognitive studies on regenerative nature–culture relations where children see themselves as part of, rather than apart from the natural world (Bang et al., 2012; Nxumalo et al., 2022), engage in ethical sense-making through wonder and land-based noticing (Sherry-Wagner, 2023), recognize the agencies of plant and more-than-human personhood (Barry et al., 2023), pedagogical ethics of hands and eyes in maker spaces (Vossoughi et al., 2021), mathematics for community knowledge and critical consciousness (Frankenstein, 2005; Godoy Penteado & Skovsmose, 2022; Gutstein, 2007; Gutstein, 2012) and curricular ethics to see mathematics as place and within stories (Archibald et al., 2019; Nicol et al., 2019). The field has made incisive advances in this area, and we are just beginning to uncover the ways that ethical thinking features in STEM education and to what impact.

The stories in this paper come from a keen focus on the axiological dimensions of learning and using mathematics. Following this attention to the axiological, ethical, and moral dimensions of mathematizing, we ask: How is mathematizing and mathematical knowledge gained (process)? Why is learning mathematics a worthy pursuit of our time and relations (reason)? How are the processes of mathematizing and the mathematical knowledge gained used to improve the realities and relations we are after (outcomes)?

3. Methodologies

Stories from this paper came from participatory and community-based design research traditions where we were interested in designing for particular forms of axiological transformations—namely intergenerational intersubjectivities and institutional change through attention to critical historicity and community agency (Bang et al., 2016; Bang & Vossoughi, 2016). In Chiang Rai, Thailand, participatory designing took the form of coordinating a design team of teachers (Sukanda and Panthiwa, Thai educators, Authors 5 and 6) and school leadership (Amornrat, Karen tribe and Thai, Author 7) in Sahasatsuksa School, an urban Indigenous school that Meixi (Hokkien/Hokchiu-Chinese, Author 1) and her mother Alison (Hokchiu-Chinese Author 8) have been partnering with since 2000 to support Lahu and other Indigenous educational futures. This design team of teachers continues to gather to shift normative school structures and uphold Indigenous knowledge in the city, and across the landscapes and relational knowledge systems of home and school.

Meixi’s partnership with Nawayee Center School in Minneapolis began in December 2021 through the school’s Medicine Wheel Program Director. Meixi began supporting Indigenous food and lifeway classes in 2022 as a volunteer, working in the school kitchen and garden. In August 2023, this relationship grew into a more design-based partnership under the leadership of George Spears (Author 4), through the initial organizing of Nawayee Guardian Circles, a monthly gathering of the students’ guardians and family members. Through various grants that Meixi, Racquel (Bad River Band of Ojibwe, Author 2), George Spears (Red Lake Nation & Crow Creek Dakota, Author 3), and Eileen Bass (Sac and Fox of Oklahoma, Hunkpapa Lakota, and Mvskoke Creek, Author 4) secured and ran, we organized a four-day land and water-based Nawayee Futures Camp with students and families in July 2024 and 2025.

The stories from this paper emerged from these two relational histories across place. Participatory design for us especially included intentional place-design practices with families and community members. We were guided by community forms of expertise to use our unique gifts, power, and skillsets to secure resources, strategize, repurpose, and re-appropriate institutional structures to enact the kinds of urban Indigenous relationalities and futures we hoped and strived for. Importantly, our designs did not begin with designing for mathematics education but rather centered who communities were in relation with, the role of mathematics within those relations, and the related transformations of mathematics as a discipline.

3.1. Relational Histories of Place

3.1.1. Study Context 1: Nawayee Center School in Minneapolis, USA

Nawayee Center School is located on Dakota homelands. It is a contracted 7th–12th-grade alternative school of Minneapolis Public Schools, with a yearly enrollment of approximately 50 students. Nawayee means “the Center” in Ojibwemowin, the Ojibwe language. Over 80% of Nawayee school families live in Little Earth, a 212 Housing and Urban Development subsidized housing complex a 5-min walk from the school. The only remaining “survival school” in the cities (Davis, 2013), Nawayee was founded in 1972, born of vibrant intergenerational histories of more than 50 years of community-based activism and organizing since the late 1960s. Today, Minneapolis is home to over 35,000 Native people, including Dakota, Ojibwe, Ho-Chunk, and more, and is one of the largest urban Native communities in the United States (MAIC, 2023). Minnesota is translated from Miní Sóta Makhóčhe—the land where the waters reflect the skies in Dakhóta iápi, the Dakota language.

Native families in Minneapolis are also chronically underserved (Minnesota Department of Health, 2022). Native youth under the age of 24 experience three times the average national rate for suicide (Cwik et al., 2022; National Alliance on Mental Illness, n.d.). The 4-year high school graduation rate for American Indian students in Minneapolis hovers around 40–50% (Minneapolis Public Schools, 2024). In spite of these challenges, Nawayee has never wavered in their commitment “to provide transformative education, grounded in Indigenous language and life-ways, nature and love of learning. We strive to inspire a sense of place and direction, within the Circle of Life, from which students discover strength, purpose and vision.” The school’s emphasis on the “center” comes from Black Elk, who teaches, “At the center of the universe dwells the Great Spirit, and that its center is really everywhere, it is within each of us.” Ona Kingbird from Obaashiig/Ponemah Red Lake named the school Nawayee Center School.

Native communities are continually negotiating new developments, gentrifications, and sovereignty in cities. Urban areas are fraught with histories of deep connection and deep dislocation; they require ongoing efforts to make and remake relationships to ever-changing built and natural environments. This context is a particularly special one as it speaks to the profound community-based expertise, axiological commitments, and intergenerational ethical intelligences that uphold their relationships with lands and reclaim urban spaces as Indigenous land (Bang et al., 2014). Far from a pan-Indigenous identity that often erases tribal differences, community members at Nawayee and the broader Franklin Avenue community maintain intimate relationships across urban places and their tribal nations, their tribally specific cultural and linguistic knowledge systems and ethical commitments to particular places.

Since 2023, we (Meixi, Racquel, George, and Eileen) have been working together to build and support the involvement of the Nawayee Guardian Circles. Together, guardians, students, and school staff led monthly meetings to collaboratively design and implement community activities such as Dakota and Ojibwe language bingo, gardening, and winter storytelling. These circles led to our first week-long land-based Nawayee Futures Summer Camp in July 2024. Summer camp activities included canoeing, storytelling, ethical harvesting, and restoring lakeshore and wetland plant relatives. Young people and families wrote manifestos for the future, created cyanotype prints, and produced a short film about what healthy Indigenous futures mean to them. The camp culminated in a community feast with survival school elders sharing stories and honoring the ongoing legacy of Indigenous activism in education.

The following school year, camp participants became Nawayee Guardian Circle leaders themselves and helped lead several storywalks (Meixi, submitted) around their neighborhood in the heart of the Minneapolis Native community, drawing from practices of Indigenous Storywork (Archibald, 2008). Through experiential learning with storied Lands and sacred places, we intentionally designed to ensure and cultivate community capacities for land-based intergenerational transmission of knowledges from within the community itself – especially with families, elders, and young people.

3.1.2. Study Context 2: Sahasatsuksa School in Chiang Rai, Thailand

Sahasatsuksa School is a K-12 government-funded welfare school (โรงเรียนเอกชนการกุศลประเภทการศึกษาสงเคราะห์) for about 2600 urban Indigenous children in Chiang Rai, Thailand. Students all attend for free and come from 13 different ethnic groups and over 300 villages in the north—Akha, Lahu, Karen, Hmong, Lisu, Yao, Chan, Thailue, Lawa, Chinese, Khmu, Plang, and Northern Thai.

Similar to the urban Native community in Minneapolis, Indigenous peoples of the Greater Mekong subregion have always challenged the limits of nation-state education and have found ways to maintain and advance their deep pedagogical and ethical intelligence, identities, practices, and lifeways (Prasit & Meixi, 2018). At the same time, colonial impacts in Thailand reverberate prominently through urban schooling and in the lives of Indigenous young people making their way in the city (Kwanchewan & Prasit, 2009). Sahasatsuksa, as an accredited school, has been a part of these acts of Indigenous maintenance, and yet, at the same time, has to follow the national curriculum. As such, they navigate teaching Thai to their students for translatability in the city, as well as English on top of that, while working to have programs and to support reconnecting home and for students to maintain their unique tribal identities.

More than half of Sahasatsuksa’s students live in Chiang Rai city, away from their families for nine months during the school year. Schooling has been complicit in removing Indigenous children from their homelands, languages, and knowledge systems in order to participate in a “superior present” (Kwanchewan & Prasit, 2009). This is exemplified through compulsory state education efforts to assimilate diverse ethnic–linguistic groups under “Thai-ness,” or ความเป็นไทย where heterogeneity is viewed as a threat to national security and nationhood (Thongchai, 2000). Global narratives of modernity perpetuate hierarchies of who is considered human and civilized (city versus rural, lowland versus highland), human exceptionalism and domination, and the removal of learning from meaningful lands and contexts, where settled structures of power control the bounds of permissible sense-making (Bang et al., 2012; Prasit & Meixi, 2018). Thus, intentionally reconnecting with homelands in our designs and shifting how we are in relation to one another directly refuses colonial narratives and agendas in Indigenous education in Thailand.

In 2000, Meixi’s mother started working with a group of Lahu tribal elders and Karen tribal educators who negotiated with the state to provide funding to all tribal students regardless of citizenship. As a response to deficit-oriented and dehumanizing narratives of Indigenous peoples as unintelligent, uncivilized threats to national cohesion and security, Meixi first began organizing family storywalks in six rural villages (Karen, Akha, Hmong tribes) in 2017. The two stories featured here were part of “Designing Pathways Home”, where Sukanda, Panthiwa, and Amornrat, Sahasatsuksa’s principal, were part of storywalks to design curriculum with young people and the families after walking, reading, and storying their lands together in their homeland villages (Bang & Marin, 2015). The design team and students whose families were featured on the walks then watched their storywalk videos. We also presented an initial analysis to the Sahasatsuksa teachers to ask if there were other codes or themes of interest in our analysis.

3.2. Gathering Stories and Relational Analysis

Participants used GoPros to film their time on land and water, where young people, families, and community members were sharing stories along walks of homelands. Homelands here included their specific homes as well as larger territories that included “a-long-time-ago” lands, sacred places, and pathways that held deep historical, cultural, and spiritual significance to those with whom we were storywalking. These videos were then logged with portions transcribed to stay close to the actual words and place-based context in which dialogue unfolded.

We draw from a range of analysis strategies in this paper, but all are based on stories, Indigenous storywork (Archibald, 2008), and the living of stories on Land. First, we gathered stories across cycles of education design across these two schools. We selected key stories that hold theories within them around mathematizing and land-based education. We then chose four storied moments that highlighted the presence of a diverse range of relational systems and natural world kinds (rice, waterfalls, geologic systems) and how time was inferred from within the Land—the toggling of multiple timescales within a particular place within ongoing dialogue and family/community teachings. We then presented these stories to various community members who were part of these events. We invited them to read drafts of the manuscript and invited their feedback on the ways we described our time together, on our ideas, findings, and analyses.

4. Teachings on Embodying and Living Indigenous Relationalities

The teachings we have received from these four stories illustrate four ways that mathematical practices enliven and enrich relational goals. First, mathematics cultivated a fierce love of land and territory. This occurred through a deepening of knowledge of water relations in rice fields and lake ecosystems. Second, mathematics was intertwined with the ongoing development of children’s unique roles and responsibilities in family and community life. This included practices on a mango farm and the network of responsibilities embedded within the Land as elders pass on. Third, mathematics cultivated gratitude and an understanding of interdependence, helping us learn and recognize the ways we are related to rice fields and farmers who provide us sustenance. Finally, mathematics deepened our understandings of power in places—the when and where we are in time and space that reaffirm Indigenous relations to place and ongoing presence, power, and sovereignty. Together, these illustrate how mathematics is inherently co-constituted with Indigenous relationalities. Indigenous relationalities shape possible mathematical meaning-making and activity. Mathematics also enacts and expresses gratitude, humility, reverence, and one’s personal and collective commitments to Land and each other. Here, we show how educational designs beginning with the ontological grounds of Indigenous relationalities offer tangible ways forward for cultivating community agency and reimagining schools - and mathematics education - towards human maturation.

4.1. Embodying Indigenous Relationalities 1: Mathematics to Cultivate a Fierce Love of Land, Waters, and Territory

• Minneapolis, USA

Wetlands, lakes, and waterways are central to the social, ecological, relational, and intellectual health and foundation of Miní Sóta Makhóčhe. Most recently, Friends of Lake Hiawatha, Bdé Psíŋ Collective, and the Minneapolis Parks Board have been working to clean and restore different parts of the lake. Through various conversations with Nicole Cavender (Sisseton Wahpeton descent), Sean Connaughty, and Marisa Anywaush (Upper Sioux), we began to dream of connecting Nawayee Center School guardian circles and Dakhódiapi Wahóȟpi (Dakota Language Nest preschool) to co-organize a day-long field trip to Bdé Psíŋ (renamed Lake Hiawatha in 1929) in Minneapolis. Bdé Psíŋ (Rice Lake in Dakhóta iápi) was once a lake filled with wild rice, providing centuries of sustenance for Dakota peoples (www.friendsoflakehiawatha.org/, accessed on 29 September 2025). It is the only lake that Minnehaha Creek passes through to then flow out to the Mississippi River. What was once a vibrant wetland habitat and functioning floodplain is now the most polluted lake in the Minneapolis chain of lakes1. From the reduction in the lake’s size to establishing the Hiawatha golf course in the 1930s, to routine floods and massive accumulation of trash from south Minneapolis2, Bdé Psíŋ has been central in conversations about urban waterways, wildlife, and land use.

• Mathematizing: Bathymetry

In preparation for the Bdé Psíŋ field trip event in October 2024, Nawayee’s science teacher, Walt Johnson, prepared students to understand where they might re-seed bulrushes and to appreciate community efforts to return psíŋ (wild rice) to the lake. We learned that water levels are a key factor in psíŋ returning to the lake before the field trip. Students studied the bathymetry (the measurement of the depth of water in oceans, seas, and lakes) of Bdé Psíŋ. Students discussed how bathymetry might be measured and how these kinds of measurements are one dimension of helping us be good relatives to help re-establish healthy lake ecosystems (Figure 1a,b). In a sense, mathematics in bathymetry was used to understand psíŋ (rice) as a friend and relative. They meant to get to know the kinds of waters psíŋ likes, their preferences for water quality, turbidity, water level rises and fluctuations, what other plants keep psíŋ happy and healthy, and how we as humans can learn our responsibilities to support psíŋ feeling comfortable enough to return to these waters in the future. Importantly, a love of the lake as Dakota territory was the starting grounds to begin learning mathematical concepts of depth and lake bathmetry of Bdé Psíŋ. At the same time, bathymetry was a way to cultivate a fierce love for psíŋ and to use these understandings to support the future flourishing of psíŋ as a relative that has and continues to sustain communities across generations.

• Mathematizing: Reading Cattail density and Re-seeding lakeshore bulrushes

Students from Nawayee Center School launched canoes from the southeast shore of Bdé Psíŋ to paddle the perimeter of the lake. The shores with shallower waters where psíŋ could grow were also filled with cattail stands. As we paddled, we tried to notice and read the lake’s shoreline to find suitable spots to re-seed bulrushes. Bulrushes are a plant relative who helps in wetland restoration, providing food for wildlife and shoreline stabilization while also supporting water filtration through the absorption of metals and toxins, and has cultural significance for Dakota peoples as a weaving fiber (Minnesota Historical Society, n.d.). As we were reading the shoreline to read the density of the sedges and scout openings for bulrushes, we made seedball mixes that we put into the lake to restore bulrush habitat with a seed mix sponsored by the Minneapolis Park and Recreation Board.

Strengthening Indigenous nature–culture relations directly upholds the epistemic authority of Indigenous conceptions of mathematics (Booker & Goldman, 2016 as cited in Barajas-López & Bang, 2018). Often, culturally responsive mathematics or ethnomathematics can be reduced to a means of promoting state-sanctioned goals of learning without ever naming or refusing Indigenous erasure in mathematical traditions (Gutiérrez, 2022). By drawing from long-standing lake relations across time, mathematizing on Indigenous terms unsettles colonial logics of mathematics and policed hierarchies of knowing where school-based mathematics is no longer the only yardstick of learning.

• Relationalities: Love for Territory On Psíŋ’s Time

As we considered the ecological niche of bulrushes, we too had to reflect on our collective and unique ecological niches as human people living in Dakota territory (June, 2022). Additionally, during the closing ceremony for the day, we discussed the real possibility of not seeing bulrushes or psíŋ return next year or even for a while. For both the high schoolers and preschoolers, we talked about the day they might walk back in this place and see a lake that has vibrant bulrush and psíŋ beds, and that they might tell their grandchildren that they were once a part of restoring a lake that is back to health, maybe 1 or 50 years into the future. Even if we did not witness psíŋ restored within our lifetimes, we knew we would be setting up the conditions for the generations to come. Through placing ourselves on bulrush’s and psíŋ’s time, a re-imagination of timescales helped to cultivate a longer-term love for Dakota territory and the longer-term roles we can play to restore it. Mathematics cultivated a love for, a sense of belonging with the natural world and one’s ecological niche within it to support healthier lands and waters.

4.2. Embodying Indigenous Relationalities 2: Mathematics to Regenerate One’s Unique Intergenerational Roles and Responsibilities

• Chiang Rai, Thailand

The next two stories come from Sahasatsuksa School in Chiang Rai city in northern Thailand. One key iteration of our design was when we began storywalking in homeland villages with children and their families. These storywalks served as starting points to engage students and their families in designing curricular units to be taught at school. Designing pathways home from school represented an ontological shift in the grounds of learning in a context of Indigenous education in Thailand, which had continually fragmented and separated home and school life in the name of “modernity” and “progress” (Prasit & Meixi, 2018). The first episode is from the Paj family, specifically Ti (11th grade) and Pan (Ti’s mother), as they brought us, visitors and researchers, to walk around their mango farm. The episode begins as we were walking through the mango farm, when Sukanda asked “Who measures the distance (between the mango trees)?” (Time 20:53). The episode unfolded as follows:

20:53	Noi	และใครเป็นคนวัดระยะ ล่ะคะ	Who is the person to measure the distance?
20:56	Pan	แต่ก่อนแฟน	Before, it used to be my husband
20:56	Noi	แต่ก่อนแฟนเป็นคนวัดใช่ไหมคะ	Oh before, it used to be your husband as the one who measures.
20:59	Ti	เขาจะมีแบบเป็นเชือกครับ แล้ยก็ยกไปจะมีไม้วัดครับ ก็วัดๆ วัด	We carry a rope to measure, and measure measure and then we use a stick to mark mark mark a hole.
21:03	Pan	วัดตามเชือก	Measure by rope.
21:04	Noi	เอาไม้ใช่ไหม	Use wood right?
21:06	Ti	ครับ แล้วก็เอาไม้เสียบๆ ๆ แล้ยก็	And then, we use the wooden stick to mark mark and then -
21:07	Noi	เชือก หมายความว่าเชือกนี่มัดเป็นระยะ 4 เมตร 4 เมตร ใช่ไหมคะ	Rope (.) that means the rope that’s tied and you use to measure is 4 m, 4 m right?
21:11	Ti	ไม่ใช่ครับ เอาเชือกแบบ เรามัดเป็นตุ่ม แล้วก็ดึง	No krap, we tie it into knots and then pull the rope tight.
21:15	Noi	เป็นเส้นตรงใช่ไหม	Like a straight rope right?
21:15	Ti	ใช่ครับ เส้น ยาวๆ แล้วก็มีสองคนยกๆ แล้ววัดๆ	Yeah, long rope and then two people lift it up (again and again) to measure.
21:18	Pan	ปีที่แล้ว ปลูกอีกสวนหนึ่งน่ะ เนก็ไปลง—วัด	Last year, we planted another garden that Ti also went to measure.
21.22	Noi	- ไปวัด จำได้ดีเลย โอเค	That’s good to remember. Okay.
21.28	Pan	500 ต้น	500 trees.

• Mathematizing: Patterns of distance

In this mathematical practice of the Paj family, Ti describes a practice where at least three people work together to use a long piece of rope, with knots tied at 4 m intervals. At each knot, the third person then uses a stick to mark the land for places to plant the new mango trees. Similar to Verran’s (2000) analysis on Yoruba number and measurement, numeration is treated as a relational multiple instead of a fixed linear extension from point zero. Quantities are not static and abstract, but rather involve patterns of distances in space and land. In thinking about mathematical goals, this measurement strategy for the goal of mango planting happens in the context of family responsibilities.

• Relationalities: Growing into family, community, and ancestral roles

At first, Pan (Ti’s mother) named her husband, Ti’s father, who used to be the person responsible for measuring the distances between new mango trees plantings. Ti then jumped in to explain how the measurement happens with the rope and stick (Timestamp 20:59). Pan then verbally affirmed that Ti was beginning to hold knowledge and play this role of planting new mango trees. She offered that last year, “Ti also went to measure/เนก็ไปลงวัด” and in fact planted 500 trees.

“Ti koj nqha puab hais tias ntawv (Hmong) Ti, you tell her about that there.”

Nearing the end of the walk, Ti and Pan pointed out a tuft of long grasses to us. Ti shared that “Grandfather, when he passed, was buried here… Following our beliefs, it is believed that if we bring him and bury him here, he will help look after the garden.” Mango planting for Ti was not simply a task or family chore; it was deeply embedded within intergenerational responsibilities, responsibilities that, for his grandfather, continued even after he journeyed on to the afterlife. Planting mangoes and the combination of quantity (4 m) measurements and spatial patterning in the land for Ti are part of the larger family roles and responsibilities, contributing to the flourishing of the community, and ancestral roles and relations.

In this story of the Paj family, living Indigenous relationalities was a key context of learning mathematics, problem-solving, and innovating tools like the rope in order to refine the practices of planting mangos in the larger context of shared and intergenerational family roles and goals. In addition to highlighting the ways rich mathematizing happens ubiquitously within at-home and community contexts (e.g., Goldman & Booker, 2009; Gutstein, 2012; Nasir & Hand, 2008), family is also the context in which mathematizing is engaged and expanded. Mathematics was a part of learning what it means to become a person and contributing member of the world, the specificity of where we need to be and what we need to do within a dynamic network of responsibilities across time and space, understanding our unique gifts, and enacting and fulfilling intergenerational roles and responsibilities in beloved places. These are foundational to maturing as a human and the regeneration of vibrant community life. At the same time, intergenerational responsibilities were rich contexts in which to engage with numeric patterns in space.

4.3. Embodying Indigenous Relationalities 3: Mathematics to Learn How We Are Related

• Chiang Rai, Thailand

This next story is from a teacher-student conversation with Mali (student, Grade 6) and Kru Yai after a similar walk along cultivated rice fields in northern Thailand with Mali, her grandmother, Mali’s two twin brothers, and her cousin.

Mali is a rice farmer with her family. A short walk from the back of their compound leads you to a rice field of about 10 rai3 in area (approximately 4 acres) where Mali spends time with her family planting rice twice a year. As we enter the rice fields, Mali’s grandmother proudly declares “All of them can grow rice” (referring to her grandchildren).

• Mathematizing: Embodied spatial measurements

Back at home, Mali’s grandmother shows us again how the thumb to the pinky stretched out along the forearm is used to measure the interval spacing between each new rice sapling. She first uses the spacing from thumb to pinky to measure three lengths from the tips of her fingers to her elbow (Section 3, Image 1–3), finally showing that one “elbow” length, referring to the tip of her middle finger to the elbow, is approximately the spacing of three rice saplings.

• Relationalities: Learning Nature-Culture Interconnections & Interdependence

As part of the Designing Pathway Home program at Sahasatsuksa School, Mali worked with her family to design and discuss what she should include in her lesson on rice farming to teach Kru Yai, her teacher at school. Through Mali’s lesson deisgn, Kru Yai more deeply recognized her interconnectedness with rice and rice farming, a kind of nature-culture, species interrelationality grounded in interdependence as a ethic.

At one part of the dialogue, Mali and Kru Yai conversed through the multitude of processes for rice growing, such as drying the grains, collecting the hay, and needing to store the hay when the rains come. After a long 12 second pause in their conversation, Kru Yai asked Mali, “เคยคิดว่าถ้าเราเป็นเจ้าของนา แล้วจะขายไหม? (Have you ever thought, if you were the owner of the rice field, would you sell it?)” To Kru Yai, perhaps selling the rice field sounded like an easier life, instead of needing labor at home to take care of the rice. To this, Mali responded, “ไม่ขาย ที่นาก็แพงอยู่แล้ว (I won’t sell it. A rice field is already expensive).”

Mali’s refusal to sell her rice field stood out to Kru Yai. Mali’s defense of rice farming, despite the labor required, spoke to her love for the practice. In Kru Yai’s post-interview, she spoke of this moment with Mali. She shared that the decision not to sell the field was testament to Mali’s love for tending and harvesting rice.

เพราะว่าเค้าจะมีความรู้สึกว่าเค้ารักในผืนนาของเค้าอะไรอย่างเนี่ย เค้าก็ไม่อยากจะขาย เค้าก็อยากจะเก็บไว้อย่างนี้ เค้าก็อยากจะทำอาชีพอย่างนี้ต่อ แปลว่าเค้ายังอยากทำอยู่ ถึงแม้ว่าเค้าไปเรียนวิชาอื่นๆ แต่เค้าก็ยังรู้ตัวว่ายังเป็นชาวนาอยู่ เค้ารู้ขั้นตอนวิธีทำอะไรหมด เพราะว่า... เค้าก็ยังเป็นชาวนาเค้าก็จะไม่คิดว่าจะขายมั้ย ก็ไม่ขาย ไม่ขายที่นา

Because she has the feeling of loving her rice field, she doesn’t want to sell it. She wants to keep it. She wants to continue doing this as an occupation. This means that she still wants to do it. Although she also studies other subjects, she knows from within herself that she is a rice farmer. She knows all the steps, how to do it because she is still a farmer. She won’t think of selling the field. She won’t sell it. She won’t sell her rice field.

Kru Yai shared that this dialogue with Mali allowed Mali to speak and express the “feeling of loving her rice field” and her desire to “still want to do it” into the future. This has ontological and relational implications, as from witnessing this kind of love, Mali “knows from within herself that she is a rice farmer,” prompting Kru Yai to “pay attention” to the work of rice growing around her. Kru Yai continues below, saying Mali’s relationship with rice prompted her to carry out more research about the intricate processes of growing rice. She said the following:

รู้สึกว่าดีงาม แต่ว่า เราก็อยู่คลุกคลีกับชาวนาใช่มั้ย บ้านเราก็อยู่ใกล้ท้องนา เวลาขับรถไปไหนก็เห็นแต่ทุ่งนา แต่เราไม่เคยใส่ใจว่าเออตั้งแต่เริ่มแรกเนี่ย เค้าเพาะกว่าเค้าจะมาหว่านกล้าได้เค้าต้องใช้ข้าวยังไง เค้าเพาะอะไรกี่วันเงี้ย เราไม่เคยใส่ใจ พอเราได้มาเรียนรู้เราก็ได้กลับไปค้นดูในอินเทอร์เน็ตว่าอ๋อ กว่าจะเอามาหว่านได้ต้องเอาไปแช่น้ำก่อน แล้วก็ถึงจะหว่าน แล้วหว่านก็ต้องดูแลอะไรเงี้ย รู้สึกว่าราคามันก็ถูกเนอะค่ะ มันไม่คุ้มกับที่ทำ กับแรงงานของชาวนาที่ทำ

I feel that it’s so beautiful. We live among farmers, right? Our houses are close to rice fields. When we drive anywhere, we can see only the fields around. We don’t pay attention to what they do first, how they cultivate the rice, how they sow, what kind of grain they use, how many days they cultivate the rice. I have never paid attention to these things. When I learned about them, I went back and did some research on the internet and I found that before farmers sow the rice seedlings, they have to be immersed in water first and then they are sowed. After sowing, farmers have to keep watching. Then I feel that its price is quite cheap and it’s not worth farmers’ manpower.

Kru Yai here narrates how she has begun to notice that rice and rice farming are “so beautiful.” She adds that “we live among farmers” but that she never actually paid attention to them before. Through Mali, she gained a new curiosity about the process, and a renewed appreciation for the value of effort, care, attentiveness, and energy farmers put into their work “keep watching” of their rice fields.

Living Indigenous relationalities through mathematics here are related to Kru Yai remembering and honoring her interdependence with others through rice as a plant that has sustained generations upon generations, and the rice farmers, whose everyday expertise continues to provide us with food, sustenance, and life. Through Mali and Kru Yai’s dialogue, Kru Yai was not only changed by resonating with her student’s felt desires and experiences, as well as family practices, which are important contexts for teaching and learning, but also renewed her own relationship with interdependency with others to continue to eat and be well across time. Mali reflects in her post-interview on why.

พราะว่าปัจจุบันก็ไม่ค่อยมีใครทำนาอย่างนี้เยอะ. อนาคตอาจจะไม่มีการทำนาเลยก็ได้…จะได้แบ่งปันกับคนที่ไม่เคยได้ทำ หรือว่ากำลังความคิดแตกต่างกัน ให้เขาได้รู้ว่าเป็นประเพณี (ไทย)ตั้งแต่สมัยก่อนว่า ตั้งนานแล้ว การทำนา…คือการได้แบ่งปัน ความรู้แกก่เพื่อนๆ และคนอื่น และก็ครอบครัวค่ะ เพราะว่าจะได้พัฒนาต่อเนื่องกัน

Nowadays there aren’t that many people who do rice farming like this. In the future, it is possible that there will be no rice farming anymore… so it is possible to share this with those who might never have grown rice before, or to share with people who have different ideas so they know that this is a Thai tradition since a long time ago, from way back, how people have farmed rice… sharing this knowledge to friends and other people and also families, that this (practice) can keep developing.

Mali here toys with the idea that the loss of rice farming can be imminent, that “อนาคตอาจจะไม่มีการทำนาเลยก็ได้ (in the future, it is possible that there will be no rice farming anymore).” Here, the embodied mathematics of hand and elbow measurement estimates within the family practices of rice harvesting and planting for Mali connects her to people “from way back” and her role in growing food for her people. As Mali engages in this ancestral and present-day family practice, she cultivates a fierce love for rice, for this “long time ago” tradition. Mathematizing is thus, in practice, not simply sharing this love but the renewal and continuation of a practice, where “sharing this knowledge to friends and other people and also families, that this (practice) can keep developing.” Mathematics supports the renewal of the practice of rice growing, its innovation and evolution, and learning our interdependence with so many others—rice farmers and those who eat it, rice itself, and humans—through current family practices and ancestral and future traditions in order to sustain ourselves in the future. Mathematics expresses a deepening of nature–culture relations; it is part of cultivating a deep gratitude for how we are related and interdependent with each other. At the same time, recognizing one’s interdependence can birth and deepen our curiosities to sharpen and refine our everyday mathematical algorithms and calculations as we engage and read lands.

4.4. Embodying Indigenous Relationalities 4: Mathematics to Understand Power in Places

Building on learning how we are related, this final story comes from Nawayee Futures Summer Camp with Native young people (aged 13–19) learning community stories of art and activism along sacred waterways in Minneapolis. Over four days, we followed Minneapolis lakes and streams as they made their way to the Mississippi River through Mní Ówe Sni (Cold Water Spring). This camp interwove Indigenous stories, cultural harvests for art-making, Dakhóta iápi (Dakota language), and partnerships with the Minneapolis Park and Recreation Board and the National Parks Service to carry out some plant monitoring and restoration work along the waterways.

Living Indigenous relationalities with mathematics here supported our understanding of deep space-time, not just where but also when we are in longer continuums and cycles of life. Deep time helps us consider who we are within geological and socioecological phenomena and our connected responsibilities across time and space, especially when places are threatened or come under attack. This includes hydraulic formations, plant and animal ancestors, and the deep-rooted and dynamic relationships among Indigenous nations. Mathematics has often been used to understand Lands and our place within them at multiple scales (Nicol et al., 2023; Rock & Gould, 2018; Learning in Places Collaborative, 2021). This has been particularly true with knowledge of the stars (e.g., paafu) that has helped humans to understand where we are in time and space in relation to moving islands in oceanic navigation (Diaz, 2019). Readings of lands, waters, and skies for navigational purposes and for learning about daily, yearly, and seasonal cycles for harvesting are all a part of understanding when and where we are in relation to the cosmos (Aldana, 2022; Lipka et al., 2011; Rock & Gould, 2018; Van Brummelen, 2009). When landscapes are hurting, mathematical noticings of leaf and growth patterns can help us know what to do and how to help restore and protect loved places. Mathematics is not just for reading the world (Frankenstein, 2005) but for reading Lands too.

• Nawayee Summer Camp at Mní Owe Sní

Mní Ówe Sni4 (Coldwater Spring) was the third waterway location of the Nawayee Futures Camp. Here, we see how mathematical readings of lands in terms of depth and sense of numbers through geologic time emplaced and anchored young people and families into spatiality and historicity across scales of time. It supports power and place, where power is “the living energy that inhabits and/or composes the universe, and place being the relationship of things to each other” (Deloria & Wildcat, 2001, pp. 22–23).

Mní Ówe Sni’s spring holds socioecological, cultural, and spiritual significance. The spring has long been a gathering place for various Ojibwe, Dakota, Ho-Chunk, and Ioway nations and communities (National Park Service, 2024). It is close to Bdote, the Dakota place of genesis, and settler-inflicted genocide located at the confluence of the Minnesota and Mississippi Rivers (Waziyatawin, 2008). The site is also a place of ongoing Indigenous activism. The construction of Highways 55 and 62 threatened the spring, and many Native people in the cities protested the highway in 1999. The land was transferred to the National Parks Service in 2010. Since then, the National Parks Service has been active in restoring the area into an oak savannah, filled with native prairie plants and oak trees, and protecting the ridgeline overlooking the channels from Minnehaha Creek and the spring that flows into the Mississippi River.

At the Nawayee Futures Camp, one of the teachers, Gary Spears (Red Lake Nation & Crow Creek Dakota), began his story as follows (bolded text for emphasis):

At the time here in the Coldwater Springs, before anything was here, there was a flint spear, I guess, south, just south of here stuck in a bison twice the size of what buffalo look like today. And I guess that was nine thousand years ago. So that can you tell how long human beings have been around in this area. And to skip forward, they had a hundred thousand gallons pumping out of here every day… It doesn’t freeze over… Wherever it’s coming from, it’s coming from a deep area, and it used to be clean and able to drink. Over the times here in the city and urban areas. It’s been, you know, made it really heavily contaminated for us human beings to consume it. This was an area, peaceful area where Ojibwe and Dakota people could meet and kind of talk out and resolve their conflicts, make peace treaties, make peace with each other, make trade… So if you were here 400 years ago, you would have Bdote the island and then you would have the Coldwater Springs with the water. You’d have Minnehaha Avenue, you’d have Hiawatha Avenue, go to Franklin Avenue, head west. You’d go to Bde Maka Ska and the Lake of the Isles and then Minnetonka. And those were—those were the paths, the walking paths, and then you could take the Minnehaha Creek all the way back here to the falls. So it went in one big circle. That’s really old. That’s very old. So most of these roads are just built over old trails, especially Minnehaha Avenue and Hiawatha Avenue, they are just old trails in the past. Fast forward here. I guess they rerouted Highway 55 and the tunnel that you guys drive through was made there. There’s major protests because they tore down a lot of these sacred trees here from the Mendota people in the late 90s.

• Mathematizing: Scales of time

Gary’s opening introduction to place interweaves multiple layers of time (Learning in Places Collaborative, 2021). One layer is the time when First Peoples were here by this creek. He referenced the flint spear and the bison that was twice as big, dated to nine thousand years ago, “so that can you tell how long human beings have been around in this area.” Another layer is the part of the spring that does not freeze over, coming from “a deep area,” which used to be a clean source of drinking water that sustained communities across thousands of years.

Gary then traced the 400-year-old stories of the walking paths across south Minneapolis that were “really old”, “very old”, and that made “one big circle”. He then “fast forwards”, jumping across time to support young Native—Ho-Chunk, Ojibwe, and Dakota—people continue to understand their own relationship to place, reasserting that their nations have been here for hundreds of generations. That this place is one where tribal nations enacted their sovereignty, governance, Indigenous economics, peace-making, and relationalities with one another—where they “could meet and kind of talk out and resolve their conflicts, make peace treaties, make peace with each other, make trade.” Gary then layered on the stories of more recent activism in the late 1990s protesting Highway 55, where we just came from, to protect the sacred trees and this spring.

• Relationalities: Deep time connectivities, ongoing Indigenous presence, and responsibilities to sacred waters and lands

The numerical estimates and the “fast-forwarding” used in Gary’s story and description of place reinforce deep-time relationships to Mní Ówe Sni and all the life that has been given here by the spring defy settler notions of time (Rifkin, 2017). Instead, different connectivities and temporalities come into view—the change and continuity as linked to their Indigeneity ethical commitments to Mní Ówe Sni, based on ancestral and contemporary relationships with the spring, with the medicine trees, with the creek, and old walking paths and new highways. This evidence of intergenerational longevity anchored Native young people’s sense of sovereign belonging to this particular place, the power, continuum, and constellations of co-resistance that they are stepping into (Simpson, 2017), and their future responsibilities to this place.

These understandings of where and when we were, deepened as we walked along the ridges and to the stream where the spring flowed out into the Mississippi River (Figure 2). One educator, Brett Ramey (Iowa Tribe of Kansas and Nebraska) asked, “Who has a sense of where we are right now? If you had to tell somebody where you are, what are some ways you could tell them where you are, if they were looking for you.”

After some responses, Gary shared the following:

When people are doing Ojibwe introductions, they’ll say, gakaabikaang indoonjibaa, it means I come from Minneapolis, doesn’t really mean “I’m coming from Minneapolis, it means I’m come from where the mist or rapids are”, and that’s the same thing you’re doing. You’re using that mist coming off there.

Gary drew on the Ojibwe language to reaffirm how Ojibwe people have place-based historical ties to this place. This linguistic tracing and marking illustrates how people, land, and language continue to be intertwined, and by way of introduction, people would refer to Minneapolis as the place where the mist would come off the waterfall. The sharing of place names reinforces a deep-rootedness, as demonstrated by linguistic ties to the land, through the power of the spring, and how people across time and space have protected and been given life from it.

Brett added on to broaden socioecological understandings of the falls and their power to cut rock as the waterfall moved and made their way to its current resting place, Owámniyomni or St. Anthony Falls.

Brett: So, does anybody know where that waterfall used to be? By the Stone Arch Bridge, right?... St. Anthony Falls, or Owámniyomni. That waterfall actually used to be in downtown St. Paul. And so, over time, it just, as water kind of carves out, water is the most powerful force of anything, it can carve through rock, right? And so, over time, as that waterfall was just being a waterfall, doing what it does, it carved out a channel, and it just kept moving upstream, upstream, upstream. And so, that’s why if you were to go down here, and you see these kind of steep cliffs, these bluffs that we were on were carved by that waterfall, carved by St. Anthony Falls, or Owámniyomni…You can kind of think about that not only in place, like this waterfall carves all the way up, making these bluffs all the way to downtown Minneapolis, follow it to downtown St. Paul, but also kind of connects us across time. That’s like a long time. That’s like a million years, way beyond what I can conceive of time, right? But that’s kind of where we’re at in the world, both in place and time.

Brett brought the conversation into geological time, asking “So, does anybody know where that waterfall used to be?” Timescales, velocity, and distance helped participants of the camp, the young people and their families, understand where we were in the world, the layers of historical timescales that we were in the presence of at the creek, and the active power of the waterfall Owámniyomni actively carving out a gorge to make this place (See Figure 3 for Sean Connaughty’s representation of the Falls).

Living Indigenous relationalities here meant to understanding how we are connected to place through time and space on multiple levels in humble and potent ways. This includes through the active carving of lands and bluffs by waterways, through plants that continue to reside in place and are now returning to place, to the geologic and hydraulic histories of place, to language across generations like Ojibwe people understood and introduced themselves by this stream, to histories of how people have risen up to protect these sacred place in the last few decades, and the future relational responsibilities that the young people are stepping into (See Figure 4 on Bdé Psíŋ across deep time). There is a toggling of both rootedness—a deep sense of belonging and responsibilities to specific sacred places—as well as the routedness of Indigenous mobilities where Indigenous peoples have moved and been in strategic relationships as they travel across swaths of lands, waters, and skies (Diaz, 2019). Furthermore, a continuity of Indigenous presence across multiple scales of time illustrates the ways Indigenous peoples are embedded in the landscape. Deep relationalities to place support humans to shift and change as lands and waters also change, shift, hold, protect, and regenerate. Place and water hold distinct cycled temporalities. The creek’s water and all the water that surrounded families before settler colonization at Camp Coldwater was the same water that we were standing in the presence of in Figure 2.

Coming full circle, mathematics can help us fall in love with our places and to get to know them in intimate, routine ways. Time-scale toggling can humble us and feel a deep gratitude to the waters that have sustained thousands of generations before us and is the same water that sustains us today. Cultivating this kind of love prompts us to rise up when that place is under threat, like with a poisoned spring or the threat of a highway development. They help us understand our diverse, historical, future, and everyday responsibilities in the midst of ongoing threats and impending planetary collapse, where all land is sacred. Land-based mathematical knowledge has always supported these goals and advanced mathematical philosophy and practice as they emerge through embodied experiences with specific places.

5. In Closing: Mathematics Within Relational Worlds

Mathematics holds stories and stories hold mathematics. Across these four stories, we consider how intergenerational mathematizing helps one “grow into your place in the universe” as John Trudell says in the Listening/Honor Song. This includes how we grow our responsibilities to support the health of our lands, waters, and skies, where and when we are in longer time–place cycles of family and community life, who we are to each other, how to fall in love more and more with our lands, understand the toxins that threaten their health, and how to live well in our places. Mathematizing could teach us humility, the natural numeracy and literacy of the living world, to know what Land needs, and how to live out our relationalities to the plant, animal, waters, skies, and spirit world every day. It is part of the unified experience of becoming human—for human flourishing (Su, 2017) and the flourishing of all life on earth on which we depend.

It is important to note that while mathematizing can support the living of Indigenous relationalities, the living of Indigenous relationalities on the land creates powerful contexts in which mathematizing, Indigenous, place-based thought can be re-generated (Simpson, 2017). In the embodied everyday and routine experiences, visiting our psíŋ, ทุ่งนา (rice fields), mango gardens, sacred routes, and waterways, and sharing contexts of deep love for land and territory, opens up opportunities for mathematizing and the continual regeneration of Indigenous mathematical thought and philosophy.

Mathematics and falling in love with our places, learning our intergenerational responsibilities, honoring our interdependency, and fostering a sense of belonging and responsibility in when and where we are—while narrated separately here—are deeply intertwined. Each fosters the other. Land-based mathematics fundamentally recognizes how lands support the systematic cultivation and transmission of mathematical knowledges that optimize our ethical engagement and learning with lands.

Thinking about implications for mathematics teaching and learning moving forward, the stories in this paper illustrate how mathematics (and science) is not a separate discipline. Mathematics is intimately integrated with language, community relationships, critical histories, birthing, the cosmos, and the stars (Cajete, 2000; Lipka et al., 2011; Rock & Gould, 2018). It is unsettling ontologies of what counts as mathematics, the purposes of learning and engaging in mathematics, and the very separation of the discipline from creation. Rather than beginning with state directed mathematical goals, grounding mathematics education from within nature-culture relationalities requires us as mathematics educators to first ontologically begin from family and community futures, from the regeneration of land-based knowledges, from the protection and restoration of damaged and hurting ecosystems, and then to understand the mathematics embedded and emergent within them.

Additionally, Indigenous mathematics education should involve learning alongside lands, waterways and skies. A Dakota knowledge holder reminded us that plant medicines have always been here, offering their gifts to those who will listen. We have obligations to our relatives, the plants and animals, and other natural kinds. Learning and fulfilling these obligations involves understanding Indigenous notions of time from deep time to the rhythms of our everyday lives. Opening up these experiential learning opportunities to community members outside the confines of the walls allows for more meaningful forms of learning to occur. One of our Dakota elders spoke of the connection between the cosmos and the earth, which inherently integrates and interweaves multiple layers of time and space. As they spoke of star stories, they simultaneously told stories of the Lands on which we stood, including planetary distances, the angles of the sun throughout the year, and pattern recognition through constellations. Preschoolers, high schoolers, families, and elders learned alongside one another, thus fostering intergenerational knowledge transmission of the Land. Embracing epistemic and axiological multiplicities dispels zero-sum epistemologies (Bang et al., 2012) and tensions between Indigenous approaches and standardized mathematics requirements. Instead, we begin to see how learning with Land actually requires a continual deepening of dynamic algorithms, natural numeracy, and mathematical philosophies, practices that have long been embedded within Indigenous governance and knowledge systems (Rock & Gould, 2018), albeit still not adequately recognized in our normative forms of mathematics.

Indigenous relationalities (and the mathematics within them) will be increasingly important as we navigate the complexities of climate change and colonialism. We will need renewed forms of mathematical practices and logic that emerge from an intimate land-based engagement. Indigenous relationalities are vibrant contexts to generate and inspire mathematical practices; mathematics, too, can help us better live in relation. We extend Chronaki and Yolcu (2021)’s definition of a competent subject in mathematics education—problem-solving or reasoning for sustainable solutions counters the neutrality of mathematics, using mathematics to subvert injustice, and confronts global acts of Eurocentric exportation of mathematics curricula to include growing a relational orientation to life and Land. If we have even a chance of surviving the climate crisis, every human person needs to continually learn and re-learn to live in relationships of consent and reciprocity with other forms of life. Indigenous relationalities can guide humanity there if we commit to presencing and following the leadership of Indigenous people who have already cultivated long-standing relationships that enhance and protect a biodiverse natural world (Garnett et al., 2018). Fostering dynamic intellectual systems and complex mathematical thinking has always been, and can and should continue to be, part of these relationalities—to fall deeper in love with creation, to rise up when we witness injustice and injury to waterways and violated ecosystems, and to know how to support their regeneration and flourishing.

Still, questions remain about how to make human maturation a core goal of mathematics education. How can we design mathematics learning at school on Land’s time in ways that consider our roles and responsibilities across a continuum of ancestors? How might we imagine land-based mathematics learning at school? How can we design STEM and mathematics education as part of living these relationalities? What kinds of mathematical practices and relations might emerge because of it? What relationalities might be embodied, revealed, renewed, and restored because of deepening mathematical understandings and practices? What other land-based mathematics stories might we need to listen to and study? What kinds of leaders might we grow if we imagined mathematics education through and within our relations? How can mathematics support renewing our relational worlds? As many young people and even adults shudder at the thought of learning mathematics, we look forward to gathering more stories with you to support mathematics learning that holds the highest meaning from within our relational responsibilities.