1 Introduction

As educators, we are always invited to reflect on our teaching to assess how our goals are being met. This manuscript presents a teachers-researchers dialogue recalling and retelling our experiences of teaching Mesoamerican numbers in monolingual (Spanish) and bilingual (Ixil and Spanish) contexts. “Tellings” of our previous work revived our memories and feelings during those experiences. Through a framework of Indigenous circles of dialogue, and a deep desire to reconnect to Mesoamerican onto-epistemologies in Ixil, we responded to each other’s “tellings” with remarks that highlighted the forces that moved through our teaching and learning of this vigesimal numerical system weaving in Indigenous cosmovision, mathematical thought, and language. This analysis and accompanying reflections are shared in our findings. These highlight the aspects that helped us honor the language embedded in this system, as well as some shortcomings that have provided insight into future healing, and affirmative and decolonizing actions in our teaching.

From an Indigenous onto-epistemological perspective, the language and thought patterns of the Mesoamerican number system are intricately interconnected and integrated in a system of knowing and being rather than to a discrete separation between sciences and language (Absolon, 2022; Cajete, 2000; Morales Aldana, 1994; Yojcom Rocché, 2013). Efforts on promoting mathematical and linguistic epistemologies and ontologies are present around the world. For example, mathematical curricular approaches that have included decolonial culturally sustaining and reviving languages and pedagogies have been developed with the Yup’ik people in Alaska (Lipka et al., 2005), Yakama people in the US (Ruef et al., 2020), Mi’kmaw people and other Nations in Canada (Lunney Borden, 2013; Robinson et al., 2023), and Maori people in New Zealand (Meaney et al., 2012). Specific to the Mesoamerican numbers, children of Mayan descent in the US learned about Mayan numerals using technology and creating ‘manipulatives’ for operating Mayan numbers (Furner et al., 2021). Also in the US, several curricula were developed to support children’s exploration of how the Mayan calendar works (Taylor et al., 2015), explore preservice teachers’ rediscovery of the intricacies of the Mayan numerals in historic contexts (Farmer & Powers, 2005), facilitate the exploration of multiples of twenty and linguistic patterns (Lara-Alecio et al., 1998); and support the learning of Mayan numbers through a set of pedagogical activities (Overbay & Brod, 2007). In Mexico, links between dancing and Nahuatl mathematics were studied (Lara González, 2015). In Guatemala, a Spanish–Ixil monograph describes relations of basic operations and counting in Ixil (ALMG, 2018); and an ethnographic study documented Mayan mathematical practices in Tzu’tujil linked to socioepistemological practices (Yojcom Rocché, 2013).

The work in this paper moves across languages which, on the one hand, can help us note assumptions about concepts and, on the other, unveils related ontologies. For example, in English a person “is” a certain number of years of age: Marta is five years old. In Spanish, a person “has” a certain number of years of age: Marta tiene cinco años. In Ixil, one “reaches” a certain number of years of age: Tz’ajyu oval un ya’b’ Marta. Naming a person’s age changes across languages and cultures, and at times this practice might not even exist. These differences reflect the multiple onto-epistemologies of each language and community. We hope that our dialogue on the Mesoamerican numerical and linguistic system may inspire reconnections in our educational practices.

2 The Mesoamerican numbers in Ixil

In this section, we describe the Mesoamerican number system with attention to their onto-epistemological and linguistic features. The Mesoamerican numbers originated in southern Mexico and Central America. This study focuses specifically on the teaching and learning of these numbers in Ixil.

2.1 Guatemalan languages

Guatemala has 25 languages, including Spanish. 24 of these languages are Indigenous to the region which include: 22 languages of Mayan origin (Ixil is included in this linguistic group), and two more (Xinca and Garifuna). Ixil is spoken in the department of Quiché, Guatemala (ALMG, 2018).

2.2 Ontological forces in the Mesoamerican numbers

The Mesoamerican numbers as a vigesimal number system originated from a metaphoric symbolism rooted in an ontological view of understanding and counting in the world and the Universe. The Mesoamerican numbers are linked to counting. In counting, we use our “entire body of our senses in direct participation with the natural world perspective” (Cajete, 2000, p. 2). Counting was developed by observers of natural phenomena, tlamatinime, who “realized the stars in the firmament always move in certain order […] that the sun appeared in one place and hid in another. They labeled this cycling translation movement semilhuitl (day)” (Lara González, 2015, p. 25).

2.2.1 Twenty = a person/vinqil = unity

The concept of twenty is associated with a whole person or unity, who has four limbs and five fingers (in Spanish toes are also called fingers) in each limb. So, each fingertip is associated with one and the five fingertips are associated with a limb (i.e., wrist or ankle). A limb (q’e’lich) would animate (or bring to “life”) the concept of five. Then, two wrists plus one ankle would animate the concept of 15. If another ankle is included, then it would imply a whole person, a unit. As such, 19 is the highest digit, because if one more fingertip (tz’etkin-in Ixil) or pebble is added to 19, it would give completion to a whole woman or man. The terms winaq in K’iche and vinquil in Ixil mean a person, a man. And the term juwinaq means twenty; because “jun” means one, one person, embodying twenty. Thus, the word juwinaq for twenty also means one person. “When picturing the straight dimension of human expansion upwards towards the universe, the fingers and the toes represent the being in complete fullness; whole and integrated” (Lara González, 2015, p. 43). In Nahuatl this is called cempohualli, or the whole body. The vigesimal nature of the Mesoamerican numbers is rooted in an ontological concept of one, or unity, which is achieved through 20, an embodied measure of wholeness.

2.2.2 Zero/Iya = shell, seed

The concept of zero was ontologically developed within the Mesoamerican system. In this system, a zero is animated through the symbol of a shell. A shell embodies the cycle of life because it was left from a previous life, and it can also transcend to a new start in a cycle (Lara González, 2015). Iya is a term in Ixil that means seed or shell. A seed symbolizes the beginning (birth) and the end (death). Zero is also linked to the term U Ixi’m, which means a kernel of corn in the hand before planting it (ALMG, 2018). A seed is evidenced after a fruit that has fallen on the ground decomposes; and as the seed falls, it also rises. It sprouts again into a new life cycle. A seed, like a zero, embodies the essence of the past and what is next. As such, zero is evident in harmony. Zero represents a state of harmony with others; but if the relationship or people change, it breaks the harmony and requires the tearing apart of the current state, so that a new order and level of consciousness and harmony can be reached. Harmony lasts just enough until “it has to be revised as people and their circumstances change” (Cajete, 1994, p. 210).

2.2.3 Mutx’ul/eighty = fist

As described above, the human body and the Mesoamerican number system are ontologically related. Just as the fingertips animate the concept of 1 and limbs animate the concept of 5, the shape of a fist animates the value of 80. As the four fingers are enfolded by the thumb, a shape of a shell (the symbol of zero) is created, with the four elevated knuckles resembling the four dots (the symbol for four groups of 20).

figure a

The Mesoamerican system, as other numerical systems, evolved “from finger and spoken counting in a hunter-gatherer stage, to pebble counting in a herder-farmer stage, to written additive numbers, and finally to written positional numbers in an urban stage” (Rudman, 2007, p. 118). Below, we describe the positional organization of this numerical system.

2.3 Positional system of Mesoamerican numbers

Humans, inherently mathematical, have developed multiple numerical systems around the globe, such as base-2, base-10, base-16, base-20, base-60, etc. (Closs, 1986; Joseph, 2011; Smith, n.d.). These systems help to describe, count, measure, shape, or program objects important for social, cultural, and academic practices, situations, or lived experiences. The decimal number system has become the default number system in Westernized societies which obscures the fact that other ways of making sense of numbers exist.

The Mesoamerican numbers, commonly referred to as Mayan numbers, are a base-20 numerical system. Since 36 BCE, the Mesoamerican numbers (Smith, n.d.) are recognized by its symbols (stick, pebbles, shells). The Mesoamerican numerals between 0–20 are created through a combination of symbols that have specific values such as pebbles (dots), each with a value of 1; sticks (rods), each with a value of 5; and shells, each with a value of zero. A Mesoamerican numeral cannot include more than three rods or four dots (Díaz Díaz, 2006).

As seen in Fig. 1, sticks (rods), pebbles (dots), and shells are combined in different patterns to animate the concept of number in the Mesoamerican system. Each of these numerical symbols can be placed at different positions in the base-20 system, which will affect their value. For example, Table 1 below depicts how a value of 68 would be organized in a vigesimal system. Since the positional value of the Mesoamerican units is vertical, the value of the number 68 would be animated by raising three (dots) groups of 20 to an upper position (201) for a value of sixty (20 × 3 = 60); and leaving a group of 5 (one rod) and 3 (dots) units on the lower position (200) for a value of eight (1 × 8 = 8). The Mesoamerican symbols of “3” and “8” in these specific positions animate the value of 68, as presented below:

Fig. 1
figure 1

Mesoamerican numbers 0–20

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Table 1 Positional value in the vigesimal system
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figure b

The example of the value of ‘68’ can be animated across different numerical systems. In a decimal system this value is expressed and organized as 6810 (six groups of ten and eight ones), and in a vigesimal system the value of ‘68’ is expressed and organized as 3820 (three groups of twenty and eight ones).

Furthermore, the positional value of Mesoamerican numbers can be arranged either vertically or horizontally (as shown below). In the vertical arrangement the lowest value or position (200) is at the bottom, in the horizontal arrangement the lowest value or position (200) is on the right. The examples below present how these arrangements are portrayed.

figure c

Literature informs that the spatial organization of values in the Mesoamerican numbers has evolved over the years (Díaz Díaz, 2006). Earlier versions of the system included an additive organization of values. In this format, different types of glyphs animate the different powers of 20, which would be added to finally yield the value of a number. This format does not include calendar applications (Farmer & Powers, 2005).

2.4 Linguistic Ixil forces

The symbols and language used in Mesoamerican numbers animate the mathematical and onto-epistemological concepts organized in this system. Each Mayan language uses similar mathematical and linguistic patterns with some word variation across these languages. The table below portrays how the Ixil linguistic pattern in the group of numbers (1–9) repeats in the next group of numbers (11–19). In the second group (11–19), the names end in laval or ten. For example, oxlaval or thirteen, “ox” relates to three and “laval” to ten. Oxlaval could be translated as three and ten. This name highlights the combination “ox” (three dots) placed over “laval” (two rods, the value of 10).

Since Mesoamerican numbers are a vigesimal system, the system has 20 digits or units from 0–19, included in Table 2. The number twenty is animated by the symbol of one dot ascended to the second positional level of the numerals, meaning 1 × 201 = 20; and the symbol of zero at the lower level. Twenty in Ixil is named in two ways: ma’l k’al with m’al meaning one and k’al indicating that ma’l is placed at the second positional level; or vinquil which means one woman or man (with 20 fingers).

Table 2 Numbers 1–20 in Ixil
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After 20, the pattern of the digits 1–19 repeats in the numbers between 21–40, but with a suffix ika’k’al added at the end of each number name. In ika’k’al the prefix “i” means of or its, and “ka’” means two; then “k’al” indicates that “ika’” is placed at the second positional level. This sequence of numbers ends in ka’k’al (animated through two dots at the second level and a zero at the lower level), which is the number forty. The symbolic and linguistic patterns observed continue at each positional value.

3 Theoretical frame

Our work stems from our communal desire for reconnecting in our teaching and learning with the Indigenous mathematical onto-epistemologies and language, especially Ixil, not only because of the Mesoamerican numbers, but the children we worked with (Kashatok & Wyman, 2022; Smith, 2012). Our frame is sustained by a desire to reconnect to and engage with Indigenous onto-epistemologies through dialogue on our experiences of teaching and learning of Mesoamerican numbers.

3.1 Longing to reconnect our teaching with Indigenous epistemologies

Our work acknowledges and builds on the brilliance of Indigenous epistemologies. Our desire-based research approach to Mathematics Education (Gutiérrez, 2022) is linked to how people see unity in all things and draw on tradition to heal and remake ourselves. We desire to heal our teaching of Mesoamerican numbers through their links with nature, our bodies, the animacy of objects, and the Ixil words of the numbers to honor their Indigenous onto-epistemologies (Cajete, 2000).

Reflections on our teaching and learning practices of the Mesoamerican numbers helped us (re)member and center our desire to new collective actions. As Tuck (2009) states, desire is “about longing, about a present that is enriched by both the past and the future […, it] is involved with the not yet and, at times, the not anymore” (p. 417). The “tellings” of our teaching and learning experiences envision a change on what is not yet there, but could be manifested in our classrooms. This is due to a desire-based research framework which, while it “accounts for the loss and despair”, it analyzes “the hope, the visions, the wisdom of lived lives and communities” (Tuck, 2009, p. 422). This framework is future focused as it calls for what could be built through resistance and revitalization (Gutiérrez, 2022; Jacob, 2014; Simpson, 2017).

A desire-based research frame aims at understanding the intricacies of people’s lives and practices to point towards pathways to become more of us and reconnect within (Anzaldúa, 1987). Anzaldúa uses conocimiento as a metaphor to redeem oneself by living in a world that constructs us as divided and separate. She invites us into a process of conocimiento, which starts by recognizing our current state, being broken, and moving forward on the process of “re-membering” oneself into a consciousness that reconnects within to all that we are. Our hope is to reconnect in our teaching and within to philosophies, the Ixil language, and onto-epistemologies that animate the concepts of the Mesoamerican numbers. Arts and science manifest through myths, stories, and cosmologies of our practices and techniques (Athayde et al., 2017). The Mesoamerican numbers provide a context where Indigenous languages, beliefs and cosmologies are present. Our work aims at reconnecting ourselves to these sources of knowledge. The goal is that in this process of reconnection we can ask our own ‘eyes’ what has changed during our respective processes of decolonization (Wilson & Yellowbird, 2005).

3.2 Reconnecting with Indigenous onto-epistemologies through dialogue

We drew on the process of dialogue to promote a reconnecting force to Indigenous mathematical epistemologies, ontologies, and languages. It can help us reconnect because it provides a basis and a source for learning. Cajete (2015) writes that dialogue and relations encapsulate a pathway to knowledge. It is our goal that the dialogic recalls from memories of our teaching experiences may help us nurture and sustain emergent knowledges or remember old ones (Cajete, 1994). A community learns in cycles in the “telling and retelling of their stories,” reflecting on their meaning, and reinforcing or questioning elements of their cultural orientation. Dialogue potentializes opportunities for a “second thought” to emerge in the co-creation of ideas derived from our own culture, history, and social experiences. Learning is a creative process “that we create and that creates us” (Cajete, 2015, p. 211).

Under forces of mutual creation, we view research and dialogue as relational. Wilson (2008) notes that an “Indigenous research paradigm is relational and maintains relational accountability” (p. 71). The ontologies and epistemologies in a community “are based upon a process of relationships that form a mutual reality” (pp. 70–71). Wilson uses chapan, a Cree word, to describe a relationship between a great-grandparent and a great-grandchild in an ontological view. In this balanced relationship both relatives can call the other chapan, a practice that disrupts hierarchies (Wilson, 2008). Wilson also notes how Cree uses more than a single word (i.e., “the thing that you sit on”) to name one single object (chair). In other languages, single objects are named with single words. These differences reveal multiple ontological realities that are relational and contextual. Wilson notes that ontologies and epistemologies are inseparable in Indigenous research views. As such, our dialogue is guided by an onto-epistemological view to understand relational forces (e.g., language, symbols, mathematics, and objects) that move our teaching and learning experiences of the Mesoamerican numbers.

4 Methodology

Our methodology derives from our theoretical framework. Dialogue within an Indigenous epistemology acknowledges more than just the people involved. A circle of dialogue encompasses the community members and their relations and communication, including the places of ‘communion’ where we live. Cajete (2015) reminds us that a land-inclusive dialogue deepens an ecological and an ethical relationship to a place, and a homeland; the places also include acting forces such as language, symbols, artifacts, and the collective psychic energy of the people involved. In the light of this energy, we are deeply grateful to the lands that have given us the opportunity to engage in educational practices (Martin, 2017). We first acknowledge the beautiful mountains, with banana and orange trees, corn and coffee plants, cascades, rivers, and the ancestors and inhabitants of Santa Avelina, Quiché, Guatemala. This land hosted the birth of María, Domingo, and Juan, the authors participating in this work, and is where they are currently educating children. Second, we acknowledge Quetzaltenango, Guatemala, and its original name of Re-Xelajuj-noj (beneath the ten gods) or commonly called Xela, which is surrounded by the volcanos of Siete Orejas, Santa María, Chikabal, and Cerro Candelaria. It is a place where apples, potatoes, corn, pine trees, and many more plants grow. This land has hosted the K’iche and Mam people. Xela was the birthplace for one of the authors, where he worked with the children mentioned here. We honor the land of Albuquerque, New Mexico, homeland of the Pueblo Sandia and Tiwa; and the Sandia, the Manzano Mountains, and the Rio Grande, which hosts Carlos.

Our circle of dialogue focused on the sharing of our stories while teaching and learning the Mesoamerican numbers in our classrooms. Drawing on ethnographic approaches (Ellen, 1984), we named these “tellings”, the sharing of our stories. Our “tellings” described our goals, feelings, activities, forces, and relations that we witnessed during our teaching of lessons on the Mesoamerican numbers in Ixil (Martin, 2017). Our “tellings” focus more on describing than on examples (Coles & Sinclair, 2019), and included 2–3 lessons based on how we (i.e., students, objects, languages, symbols, teachers, etc.) felt we related to one another in ways that impacted our bodies and hearts (Absolon, 2022). Learning happens in the “telling and retelling of [our] stories, reflecting on [our] meaning, and reinforcing the vital elements of [our] cultural orientation [… this] process stimulates [our] thinking” (Cajete, 1994, pp. 217–218). The sharing of our “tellings” in our dialogue was a ceremony where everyone stepped out of the ordinary (Wilson, 2008). As Cajete (1994, 2015) suggests, in a dialogue, a research team learns to create new meanings and apply insights derived from their culture, history, and social experience in their life about the issue at hand.

Our circles of dialogue focused not only on “telling”, but also on both the listening with our bodies, hearts, and minds to the stories that we shared about our teaching and learning of the Mesoamerican numbers as well as to responding to one another on what resonated within our bodies, hearts, and minds about our stories (Absolon, 2022). Our “tellings” served as a source of generative dialogue in the analysis of our relations with the language and mathematical concepts in Mesoamerican numbers and with one another. We recorded our “tellings” and dialogues (over zoom) through field notes, audio recordings, and collective notes on a shared digital document. We revisited the notes on our “tellings”/dialogues focusing on the following question: How do we reconnect with the forces of Indigenous mathematical thought and language during the teaching and learning of the Mesoamerican numbers?

Our analysis included a desire inspired by Tuck’s (2009) work to account for the losses, hope, and wisdom of our communities to help us identify the forces that move through our teaching. Accordingly, we decided to tell the stories of the teaching of the Mesoamerican numbers in two contexts, Xela and Santa Avelina. We chose to do so because we think that the contrast between a predominantly Spanish speaking context versus an Ixil-Spanish context can help us describe and learn about the forces we sensed in each setting. In the section for each context, we included 2 “tellings” on specific lessons or issues, and excerpts of our dialogue that helped us recognize and give a “second thought” to the forces and relations that we experienced in our teaching and learning.

4.1 Places of research and participants

The work in this manuscript is linked to two educational places where the authors have taught. Below, we briefly describe both.

4.1.1 Santa Avelina

The school is in the village of Santa Avelina in the Cotzal Ixil speaking region. The children and teachers at the school are from Mayan background and raised in Ixil-Spanish bilingual homes and communities. Most households predominantly speak Ixil at home, and Spanish is more common at school and among children. Most teachers are female. Most children have studied at this school since first grade, and all live in the village. Juan, María, and Domingo, with active participation in this work, teach Ixil-Spanish bilingual lessons in all school subjects, including mathematics. The teachers identify as Indigenous Ixil, and they live in the village where the school is located. María teaches fourth grade, Juan fifth grade, and Domingo sixth grade. There are about 20–25 students in each class. The teaching of Mesoamerican numbers in Ixil is part of the mathematics curriculum and it is included in the national content standards. Children study the Mesoamerican numbers in a curricular unit once a year. The content includes learning the base-twenty system. The curriculum also requires that students perform operations with these numbers. While most of the teaching of mathematics takes place in Spanish, the Mesoamerican numbers are taught in Ixil and Spanish because the goal is for students to learn the names of the numbers in Ixil as well. María, Domingo, and Juan describe that it is a common practice for people in the village to use decimal numbers and name them in Spanish. However, Ixil is used for numbers between 1–10 in regular conversations. Ixil speakers often switch to Spanish when naming numbers beyond ten. This practice might be related to the pervasive use of decimal numbers in Guatemalan society and the relegation of the use of the Mesoamerican numbers as an Indigenous “cultural” practice.

4.1.2 Xela

The school in Xela is a place located in the Western highlands of Guatemala. There are about ¾ million people living in Quetzaltenango’s metropolitan area. 50% of the population are from a K’iche’ background. About 40% of the student population at the school where Carlos taught were from Indigenous backgrounds. He had an average of 20–30 students per class. At the time Carlos taught at the school, he was not required, nor encouraged to teach the Mayan numbers. Carlos included these numbers in the curriculum as a way of being place and culture responsive. While K’iche’ is spoken in the town, K’iche’ was not taught in schools at the time.

4.1.3 Researcher’s background as an outsider

Carlos is the son of Alfonso and Lucy. Carlos honors that Alfonso’s family is native to Quetzaltenango from K’iche’ people with multiracial marriages from different backgrounds including German, Mexican Indigenous, and European. Lucy’s ancestors are also from diverse origins, Salvadorean, Guatemalan Afro-Indigenous, and Spanish. As a result, Carlos identifies as a mestizo (Indigenous (K’iche’) and European) man born in Guatemala. He is a Spanish–English bilingual speaker and does not speak any Indigenous language fluently. Carlos’ relatives live in Guatemala. He lived in Guatemala for thirty-two years and taught K-11 grades for 15 years. Carlos learned some K’iche’ as a child, but language stigmatization discouraged him from continuing to learn it. He never learned the Mayan numbers at school, but he taught them as a teacher attempting to reconnect to his Guatemalan native roots and knowledges. Carlos studied in the U.S. to become a mathematics educator and researcher. His work focuses on understanding bilingual mathematics teaching and learning approaches that sustain students’ personal connections with their mother language, culture, and mathematics. This focus has encouraged him to embrace ethnomathematical approaches and Indigenous epistemologies in his work. Working with teachers from the Ixil community aligns with this focus. He lives in Albuquerque U.S. He acknowledges that he is an outsider to the Ixil community, but his collaborative work co-developing lessons since 2015 with the teachers in Santa Avelina has nurtured a sense of reconnection with this community.

5 Results from our epistemological dialogue

We present excerpts of the dialogues that took place among the four of us sharing the “tellings” of our teaching of Mesoamerican numbers in a monolingual and a bilingual context. In each “telling”, we describe the goals, activities, successes, and challenges related to our practice-based reconnections with Indigenous mathematical ideas, thought, and language.

5.1 Reconnecting with the Mesoamerican numbers in a monolingual context

Carlos shared with the Santa Avelina teacher his recollection of his experiences of trying to reconnect the first-grade curriculum, his teaching in Spanish, and students with Mesoamerican knowledge and numbers in Xela. He had two main goals in teaching Mayan numbers. First, to develop an inclusive curriculum of Indigenous Guatemalan knowledge. Many of the students in the groups he worked with came from an Indigenous background. This goal emerged as he noticed comments with negative stereotypes that some students in his class made about Indigenous people in Guatemala. Some of the Indigenous children in Carlos’ class cried and felt hurt due to these negative comments about Indigenous people. Carlos explained in SpanishFootnote 1:

Carlos::

I had a student whose family is from a Mam Indigenous background, and he told me that the other children were making fun of him for being Indigenous.

Juan::

That is very common; that is why it is necessary that our Indigenous boys and girls develop acceptance and pride of who they and their families are, and where they come from.

Carlos::

That’s why I thought I had to do something to highlight the knowledge of our ancestors.

Carlos then described that the second goal was that all children, regardless of their background, could learn about and appreciate the brilliance of the mathematics of the Mesoamerican numbers because these numbers were developed by Indigenous people in Guatemala. Carlos also hoped that the teaching of the Mesoamerican numbers could help reaffirm and expand children’s mathematics experiences. The unit was taught after the decimal system and students were familiar with identifying, naming, and writing numbers 0–100, as well as with the concepts of positional value of ones and tens. In the following section we share two practices that we identified as reconnections between the Mesoamerican numbers with our body and the reading and writing of these numbers.

5.1.1 Reconnecting the Mesoamerican numbers with our body

Carlos described making connections to the body to teach and learn the Mayan numbers. Carlos shared how he and the children “played” at counting numbers using all dedos del cuerpo. In Spanish, toes are also called “dedos” but dedos del pie, which could be translated as “foot fingers”. We will use the word fingers indistinctly from toes because the discussion took place in Spanish. Carlos shared with Juan, Domingo, and Maria how he used a poster (included below) with the written Mesoamerican numbers from 0–19 and counted each number using his fingers (Fig. 2).

Carlos::

Children and I used our fingers to animate the dots and a hand for a line. I also asked them to notice the difference between 4 and 5 (i.e., moving from dots to a line). I asked the children to count these numbers using their hands. Then, we moved on to animate each number with our bodies (fingers/toes, hands/feet).

Domingo::

It seems so easy to me like this because the numbers can be seen in our body and thus it is difficult to forget how to count.

Juan::

The important thing about all this is that what the number twenty really means in Ixil is a person or a man. For twenty we say ma'l k'al which relates to one or m'al. But twenty can also be said vinquil which literally means "man."

María::

Yes, we know what the word vinquil means and that it is a person, a man or a woman, but when we teach the Mayan numbers, we do not do it using the body.

Carlos::

At that time, I did not know the word to say twenty, neither in Ixil nor in K’iche’, but it occurred to me because with base ten numbers we always use our fingers to count. But in base twenty we are already afraid to use all our fingers.

Domingo::

And it is that the number twenty is written as a point in the second box and a zero in the first. It is as if the dots in the first box are fingers and then in the second box the dots are people.

Fig. 2
figure 2

Poster of the Mayan numbers 0–19

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The discussion on our “tellings” about Carlos’ teaching helped all of us notice how the physical vertical placement or positional value of a Mesoamerican numeral at the second level cell (groups of twenties) can be linked to the inclusion of a whole body, (ma’l k’al) of twenty fingers, or a whole person, vinquil; and in the first cell (ones) to the digits or fingers with values that are 19 or less. Such ontology of the numbers is embedded within the core of the concepts of the Mesoamerican Number system and its related naming in Ixil, and our dialogue helped us deepen our reconnection with this number system and the Ixil language used to name this system (Fig. 3).

Fig. 3
figure 3

Equivalent values: one human body is equivalent to ma’l k’al/vinquil or 20

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In the Mesoamerican system, the dot at the second position is assigned the value of one group of twenty, or one whole person with twenty fingers. Below the one dot there is a shell, which means that there are zero units or fingers besides the twenty of the one dot or person. Carlos also shared with the group another “telling” about a later lesson that focused on counting beyond twenty. Carlos, still drawing on the connection between bodies and the Mesoamerican numbers, asked children to connect and differentiate between the Arabic decimal numeral of 22 and write its equivalent in Mesoamerican numbers. Carlos described to the teachers how the group agreed that 22 in Mesoamerican numbers will be written as follows:

figure d
Carlos::

When I noticed that children wrote 22 in Mesoamerican numbers as depicted above, I tried to prompt the conversation by remembering what we had talked about our bodies and groups of twenty, and by thinking of the value of 22 in each numeral system. For example, in decimal numbers, “the value of the digit 2 on the left has the value of twenty, and the value of the digit 2 on the right has the value of two”. Then, for the Mayan numbers, the pair of dots at the second positional value are linked to our bodies. As soon as I said “bodies,” I remember seeing their eyes go bright and their hands go up. As they took turns speaking, one child said, “the dots above are bodies, and the dots below are fingers; so, two bodies and two fingers!”.

María::

I believe that by connecting the Mayan numbers with our body, everything becomes easier. Children can see and feel it. And the sticks and dots have another meaning. And in Ixil forty you can also say ka’vinqil which is “two men or people”.

Carlos::

Yes, that’s true, but I noticed that it was easier for children to think of two people than forty. To get everyone there, I had to ask a few more questions, such as: “if two points are two people and each one has twenty fingers then how many fingers are the two people together?”.

Domingo::

It seems to me that the complicated thing here is that the children now have to count in twenties and they are not used to doing that.

Our dialogue helped us identify again the conceptual benefit of making connections between the Mesoamerican numbers and our bodies. We agreed that these connections help us because we can feel and see the concept of twenty in our bodies. Quantities need conversion across systems. And connections to our body seemed helpful to translate this information. This ease of the connection to our body seems so natural because the Mesoamerican numerical system stemmed from this embodiment of quantities of twenty (Lara González, 2015). Beside the concept of twenty and its embodiment, connections are also evident in the language used. We have become aware that Mesoamerican languages articulate this epistemological and ontological relationship between the body and a counting system (Lara González, 2015). These connections help us think of new practices, such as counting in fives, tens, or twenties. We desire to be more intentional and strategic in our teaching.

5.1.2 Reconnecting with the reading and writing of the Mesoamerican numbers

The last lesson that Carlos recalled and shared with Maria, Juan, and Domingo was a “telling” about his goal of reconnecting with the Mesoamerican numbers by writing and reading the numbers. In this lesson students had to read, write, and ‘create’ Mesoamerican numbers to become familiar with the numerals. First, students used toothpicks as if they were sticks or lines, beans as dots, and bottle caps as shells. With these props, students practiced ‘writing’ the numbers of 1–20. Carlos mentioned:

Carlos::

I asked each student to randomly come up with a number by using and “write” dots (beans), sticks (toothpicks), and shells (bottle caps). Then each student had to explain and justify to a partner the value of the number they had just created. As we created the numbers, the goal was to make connections between numbers and the body, meaning the number of fingers and hands for a specific number. One interaction that stayed with me was when a student created the number six using six beans. The student partner agreed with the argument that six beans had the value of six.

Through our dialogue, we were able to realize that the use of materials such as beans and toothpick was helpful. However, materials affect bodies differently. As Wilson (2008) argues, relationality, or how materials and people meet, affects the concept or meaning that evolves at the moment. Also, we noticed the onto-epistemological relation of counting the six beans and counting of six fingers under the paradigm of a base-20 Mesoamerican number system; a greater relationality was needed since the beans are not tied in groups of five as the fingers in the hand; so that the counting by fives could be linked to a toothpick (stick) or a hand.

As a final goal, the teaching and learning of the Mesoamerican numbers was extended to counting to one hundred. The goal was to practice reading the numbers in everyday contexts, through artifacts such as calendars, clocks, and currency. For example, the name of the Guatemalan currency is quetzal, to honor the Maya origins of the country, since the quetzal is the sacred bird of the Maya. This bird is depicted on the upper left corner of the front face of every bill. This bill also includes a Mesoamerican number related to the bill’s value. Below, there is a picture of the one-hundred-quetzal Guatemalan bill. The goal of reading the Mesoamerican numbers on the Quetzal bills was to reconnect children with various contexts of use of these numbers. As homework, children with their parents examined the value of each bill by identifying the Mesoamerican and Arabic numbers (Fig. 4).

Carlos::

Students’ homework was to work with their parents and collect different kinds of bills and identify, read, and explain the value of the Mesoamerican number on each bill. I received comments from parents commenting how some of them had never noticed this feature on the Quetzal bills.

María::

I think that this is very important for children of any ethnicity to work with their parents and notice that the Mayan numbers are useful in the society.

Fig. 4
figure 4

One-hundred-quetzal Guatemalan bill

Full size image

We learned that the link between bodies and groups of twenties was a strong force to animate the second position in the vigesimal system. Similarly, the processes of reading the Mesoamerican numbers on the different bills at home nurtured participation of the family, promoted curiosity, and asserted identities and the ‘real’ application of the numbers. The use of six beans instead of a stick and a bean helped us realize the multiple ontologies at play during teaching and how crucial it is to build relationality between object, concept, person, and language.

5.2 Reconnecting with the Mesoamerican numbers in an Ixil–Spanish bilingual context

In this section, we first present María, Juan, and Domingo’s shared views on the importance of teaching Mesoamerican numbers in Ixil. Then, we include two subsections related to these teachers’ efforts in reconnecting the Ixil language, symbols, and mathematical concepts during the teaching and learning of Mesoamerican numbers. The goal of learning and teaching Mesoamerican numbers is to reconnect onto-epistemologically to the linguistic and mathematical contexts that are endogenous to the Indigenous Ixil community, and not simply because the Ixil–Spanish bilingual school includes such goals in the curriculum. This process is also linked to the larger goal of revitalizing—not only maintaining—the language, culture, and epistemologies of Ixil people. Domingo, María, and Juan describe how important it is for them as schoolteachers to plan for lessons and experiences for children to learn about the Mesoamerican numbers in Ixil.

Juan::

It is important for me to learn and teach the Mayan numbers in Ixil because it is a complex knowledge that we inherit from our ancestors. Students can realize that the ancestors were smart and that their language is useful.

María::

When I was a child, I didn’t learn this at school. So, today’s children have the opportunity to reconnect to this knowledge from a young age and appreciate who we are and where we come from.

Carlos::

When I taught the Mayan numbers in Xela, the students said they were proud of their country.

Domingo::

That’s right, this knowledge is important for the children and inhabitants of Santa Avelina to feel proud of their origins. But it is also important that other countries hear about the Mayan numbers in Ixil Cotzal.

The following sub-sections describe reconnections between the mathematics and language of the Mesoamerican number system, and its symbols, values, and numerals.

5.2.1 Reconnecting with the mathematics and language in Mesoamerican numbers

Juan shared a lesson he uses to focus on the language of Mesoamerican numbers with Domingo, María, and Carlos. Children count objects in Ixil with the goal of practicing the sequence of numbers. Juan mentioned how the counting of a set of objects in Ixil is often done with corn seeds.

Juan::

When the children count, they touch each kernel and say: ma’l, ka’va’l, oxva’l, kaava’l, ova’l, vaajil, jujva’l, vaaxajil, beluval, laval, junlaval, kab’laval, oxlaval, and […]? When they finish counting, they arrive at a number, which tells them how many corn seeds they have, then they must write that number down. In this case it was fourteen or [kaalaval corn seeds]. Children learn the sequence of number words. Upon reaching the final number, the idea is for them to write the number with symbols, but also to connect the symbols with the words. In this case, the number kaalaval is composed of “kaa” which means four or four loose corn seeds, and “laval” which means ten and is represented by the two lines, each with the value of five or a total of ten, ten little corn seeds.

María::

I also do this exercise, but sometimes I adapt it too. For example, a girl takes a handful of corn seeds from a basket. Then she puts them on the table, and she estimates how many corn seeds she thinks there are in the group. Her partner counts the handful or group of corn seeds that the girl estimated in Ixil. After counting, the peer finds the difference between what the girl said and the number counted. The roles switch, and the child with the best estimates wins.

Carlos::

So, is it easy for children to count in Ixil?

Domingo::

Sometimes numbers 0–20 are more common, and you know them well. The problem is when larger numbers are used, then it is more difficult to remember the names of the numbers.

Carlos::

And what could be done to help them remember the linguistic patterns of Maya numbers in Ixil?

María::

[shakes head no] It’s very difficult.

As a result of our dialogue, we learned that Juan, María, and Domingo have developed creative ways in their classes for students to practice the counting sequence of the Mesoamerican numbers in Ixil. However, it was also discussed how difficult it is for Ixil children to name numbers higher than 20. To develop new ways for students to engage with the number names in Ixil, we collaborated creating videos that presented the symbols for each number, the written name of the number in Ixil, and the pronunciation of each number in Ixil. We developed several videos that focus on different number sequences and patterns. We are working on the use of these videos. Our future goal is to develop more opportunities for Ixil children to name the Mesoamerican numbers and use them more fluently. Here is the link to one of these videos: (https://drive.google.com/file/d/12Br1FrRIk4vGfn9ZI-wBSUyyjY9c0-Bv/view?usp=sharing).

In the construction of these videos, we identified and included mathematical linguistic patterns helpful to understand the mathematical thought animated in the Ixil words. For example, a linguistic pattern we included is k’al. K’al is included in the names of the numbers at the second positional place value. When looking up the meaning of k’al, we realized that it is an Ixil suffix that translates as faja or “belt” and indicates the second-place value, or groups of twenty. Noticing these linguistic features can guide ways of animating the concept and make the process of naming the numbers in Ixil easier. Another example of linguistic patterns we discussed was ika’ and itox. In these markers, the “i” and “it” are prefixes placed before the word numbers “ka” (two) and “ox” (three), respectively. And when we linked these words to the numerals or number symbols, these linguistic markers (ika and itox) of the numerical sequence appear before the numbers with two or three dots (40 and 60 respectively) at the second positional level. The dialogue below describes this situation in detail.

Carlos::

I am confused because the name for the numbers between 21 and 39 end with ika’k’al, and ka’k’al means forty. And after forty, the numbers continue to include the word ika’k’al or forty; the numbers between 41-59 end with itoxk’al, and the name for 60 is oxk’al. Why?

Juan::

It's that numbers work differently in Ixil. It does not go backwards, they go forwards.

Carlos::

With Arabic numbers, if we are at 30, we count one by one until we reach 40; and then when we reach 40, we begin to add one by one over the forty, and we go forty-one, forty-two, and so on. But in Ixil, if we are at twenty and we start counting with 21, and we do not add another one (ma'l) after twenty (ma'l ka'l), instead, we have a one (ma'l) that is going to forty (ika'k'al).

María::

Yes, ma'l ika'k'al is 21. We do not say ma'l ima'l'k'al (one of the next twenty) because ma'l ka'l is 20 and 20 has already passed. So, the one in the 21 is on its way to becoming forty or two groups of twenty, ma'l ika'k'al.

Carlos::

[scratches head] Uhhhh? …21, one of forty, ma’l ika’k’al?

Domingo::

What if we think with the body? If we have 20 fingers it is equal to a person, and if we have one more finger; That finger belongs to someone else, right?

Carlos::

Oh! And if there are two people which make 40 fingers, ka'k'al; but with 21 we do not completely have another person, only one finger, ma'l, of the second person, ika'k'al. And if we think after forty, 42 for example [draws two sets of hands and feet on a piece of paper (see Figure below)]. It takes 3 people, but in 42 you have only two fingers of the third person. That’s why to say 42, you say ka'va'l itoxk'al; which is two, ka'va'l, of a third person or of sixty, itoxk'al.

Domingo::

Ah yes, I had not thought of it like that, but I understand you.

Our dialogue about the language to name the Mesoamerican numbers helped us notice more clearly how the Ixil language organizes the number names in vigesimal patterns, which may be also linked to our bodies. Ixil words provide insight about the concept of numbers not being static, instead they become the next group of twenty. They have animacy. This linguistic connection helps us differentiate from and connect with the base-ten system we are most familiar with. In the base-10 system in English and in Spanish, the numbers are counted one by one, and when they reach a group of ten, the name for the new group of ten works as a base to which the next units are added. For that reason, we can think of 42 as four tens with two extra ones added on. It is like building on already reached milestones. In the Mesoamerican numbers, however, the language marks a different animation by considering milestones to be reached while counting; the numbers “become” that announced group of twenty (Fig. 5).

Fig. 5
figure 5

Three bodies to represent 42

Full size image

Furthermore, our dialogue helped us feel the ontological connection of the Mesoamerican numbers with the body (20 fingers). When we counted one-by-one the Mesoamerican numbers using our fingers, we noticed that: (a) when we reached a multiple of 20, the count included a full body or 20 fingers; (b) when we counted a number above a multiple of 20, the count included a new person’s fingers, and the number names were linked to a new group of 20. The counting in Ixil, with our voices and bodies, precisely animated the connection between the number counting and becoming into groups of 20. For example, we took turns counting out loud until we reached the value of 42 (i.e., ka'va'l itoxk'al). First, Maria counted the first group of twenty using her fingers and reached, ma’l k’al (20, ma’ = one). Next, Juan counted after twenty using his fingers; as he spoke the number names, they ended with ika’k’al (40, ka’ = two, or 2 people), and not with ma’l k’al (20); for example, ova’l ika’k’al or 25. Juan’s finger counting ended at ka’k’al (40). Finally, when Domingo counted his fingers after 40, he said, ma’l itoxk'al (41), then ka'va'l itoxk'al (42). After 40, Domingo did not use the ending ika’k’al anymore, instead he used itoxk'al (sixty, which is oxk'al, ox = three, or 3 people).

This exercise helped us listen with our body by using and counting with our fingers while speaking in Ixil words that named the count of each finger and included the collective of our bodies, context where the groups of twenty and their names became alive. Thus, we argue that when Ixil animates the value of 42, the two ones (ka’va’l) in 42, while seemingly standing alone; they are not; they are tacitly embedded in a third person (itoxk'al). One by one, the value of 42 (ka'va'l itoxk'al) becomes the value of three full persons or sixty (oxk'al) fingers. At the second positional level, the Ixil naming of the Mesoamerican numbers animates the links between the language for each set of twenty and the body; they provide an onto-epistemological relationship of numbers becoming groups of 20, or, completing the 20 fingers of a person.

5.2.2 Reconnecting with the symbols and base-20 of the Mesoamerican numbers

Domingo shared “tellings” about some of his lessons on the Mesoamerican numbers with older grades. The lessons included activities of counting or using larger numbers, or even combining smaller groups into one number. One tool that has been deemed helpful by Domingo, María, and Juan is the creation of “cells” (“casillas” in Spanish), which are aligned vertically to follow the vertical positional value of the Mesoamerican numbers. Domingo described how children used the cells to place symbols, whose values would change depending on their cell placement (Table 3). The cells included a vigesimal system pattern, such pattern is not linked to contextual uses of the Mayan numbers (Farmer & Powers, 2005). Based on that, he posed the problem below to the group:

Juan:

To determine the value of this number, children would need to multiply 5 × 400 = 2000; 5 × 20 = 100; and 5 × 1 = 5; giving us the number 2105. It means that the number created with three lines positioned in the first three cells is the number 2105.

María::

Yes, these cells can be fun and flexible. For example, if the three sticks were in the first cell, the number or value would be 15. If the three sticks were at the second level cell, the value would be 20 × 15 = 300, or three hundred in words.

Domingo::

I also use two sets of cells to create a number in each of them and then add them together. This helps students not only practice addition, but also think about the conventions to write the Mesoamerican numbers.

Table 3 Place value cells
Full size table

The Table 4 below exemplifies the activity that Domingo described.

Table 4 Adding Mesoamerican numbers
Full size table

In the activity, children added 2408 + 512. This process can be completed by first bringing together all sticks and dots within the same level. However, as illustrated, at the lowest cell, a re-grouping of values was needed. When units at this level add up to 20, they have to be regrouped as 20, thus becoming a dot and a shell, instead of three sticks and five dots. Once regrouped, the lowest cell gets occupied by the value of zero. After Juan, Domingo, and María described these activities, Carlos asked their perspectives on how students view these tasks.

María::

I can see how this becomes like a game for the students and they want to guess and find out, “what happens if I do this?” Children can play and create different numbers by picking the symbols they want to add, where to place them and create specific numbers. For example, if you had three lines or sticks, four dots, and one shell, how many numbers can you create with these symbols?

Domingo::

Yes, it helps them to write the numbers and it helps them become more fluent with addition as well. Also, what I do sometimes is to ask students to also write the Arabic numbers next to the number they created. I ask them to write the names of the numbers in Ixil. In this way, students can go view the list later.

Carlos::

And do all activities take place in Spanish or Ixil?

Juan::

Mainly in Spanish.

Carlos::

I wonder how could these lessons connect more to Mayan cosmovision or concepts and be less related to regular school mathematics?

Teachers described how they provided multiple opportunities for students to symbolize and “create” numbers in their lessons. In all these processes, the positional place value cells figured as a central tool. Through their “tellings”, teachers elaborated on each other’s ideas describing how they use and adapt the use of cells in the process of reading and writing Mesoamerican numbers. However, we felt regretful when we realized that we were replicating colonizing school mathematical practices in our teaching. What if these conversions could be linked to understanding time or students’ ages in conjunction to the Mayan calendar and used in our classrooms? We desire to plan for greater reconnections to these Indigenous onto-epistemologies.

Unfortunately, our work was done mainly in Spanish. In the teaching and learning of Mesoamerican numbers, Ixil is mainly practiced in the counting of the numbers by using either objects or cells on small white boards. The names of the numbers in Ixil had to be memorized. This situation creates tensions with our desire to reconnect more fully with Ixil, given the colonial legacy that continues to function in schools that privilege the decimal system. We stress our desire to re-indigenize this practice in the community. How could this be done? We cannot say, but it would require the work and decision of the entire community (Jacob, 2014; Simpson, 2017).

6 Concluding remarks

Our epistemological dialogue started with the strong desire to reconnect with the forces of Indigenous mathematical thought and language that move in and through our teaching and learning of Mesoamerican numbers. Our collective dialogue and reflections on our “tellings” helped us note some unforeseen forces (Absolon, 2022; Wilson, 2008) of non-linguistic input that were at play during our teaching and learning experiences (Cajete, 2015). This force nurtured the “re-membering” and making reconnections between the numbers and our bodies during teaching (Absolon, 2002; Anzaldúa, 1987; Cajete, 1994). The concept of twenty animated through our body (i.e., 20 dedos or 10 fingers and 10 toes) was a force that helped us re-connect the language and the symbols associated with the numbers. The Indigenous onto-epistemology of Mesoamerican numbers re-engaged our bodies in our teaching. The embodiment of our “fingers” and careful attention to associated linguistic patterns nurtured our listening to an Indigenous vigesimal mathematical thought. These numbers are ontologically linked with our bodies. In fact, Cajete (2000) asserts, “Native science is based on the perception gained from using the entire body of our senses in direct participation with the natural world" (p. 2). This quote conveys how a wholistic sensorial experience, beyond just language, helps us understand, feel, and express a concept more fully. Sometimes we can express more with a gesture, or an undecipherable sound than with a well-constructed sentence. There are studies on the richness of our expression and concept animation (Coles & Sinclair, 2019; Dominguez, 2021; Dominguez et al., 2023), but still require further exploration.

Regarding language, this onto-epistemological relationship also helped us to animate the number concepts and appreciate the links of an ontological foundation between the number names and the numerals themselves more fully. For example, ova’l itoxka’l (45); a translation or interpretation of this number name would be “five that belong to the third group of twenty”. We can paraphrase it as “five towards three twenties”. These linguistic interpretations that animate the concept of 45 are clarified when we reconnect the Ixil number names and the mathematical concepts with our bodies. These reconnections bring 45 alive! Reinterpreting ova’l itoxka’l as linked to its ontological source helps us to see it as the five fingers of a third person. With this linguistic force, the concept of forty is animated through the collective of the first- and second-person’s bodies even though they are just implicit, they are acknowledged by the inclusion of the third person. Note that in 45 we only include five fingers from the third person. The relationship between the body, the naming of Mesoamerican numbers in Ixil, and the symbols altogether onto-epistemologically animate these number concepts in a vigesimal system. This way of understanding numbers as becoming groups of twenty in the Mesoamerican system is also reflected on the concept that in Ixil a person neither is of nor has an age; rather, a person reaches an age. Thus, in the learning and teaching of Mesoamerican numbers, the invocation of onto-epistemological relationships helps us animate their concepts in ways that are felt, seen, and touched, and their names heard. As Cajete (1994) has beautifully articulated, the naming of these numbers help us ‘listen’ to the ancestors’ mathematical thought. Ixil worked as a linguistic force that made us feel more deeply, in our individual and collective bodies, the relations between the Mesoamerican number names and numerals in a base-20 system that our ancestors developed. When we teach the Mesoamerican numbers using only symbols and numerals while excluding their names in the original languages, this context limits the onto-epistemological links that harbor the meaning of these numerical concepts. The linguistic and onto-epistemological forces in the Mesoamerican numbers speak about how mathematical concepts are constantly non-universal across lands. It is our desire that our dialogue may awaken desires to heal mathematical practices and reconnect with the learner’s and community’s sensitivities and histories in teaching and learning.

Finally, regarding the issue of reconnecting with Indigenous languages, we raised the question about how to re-indigenize the practice of using and naming the Mesoamerican numbers beyond 1–10 at the school, given that it is a common practice in the community. The realization about the onto-epistemological relationship between the Mesoamerican numbers and their naming could guide our future actions. In fact, these numbers were expressed with different names, symbols, and patterns depending on the context of use, for example in medicine and everyday practices (Joseph, 2011; Yojcom Rocché, 2013). Furthermore, the Mesoamerican numbers help explain astronomic concepts and time cycles (Closs, 1986; Farmer & Powers, 2005; Grisby, 2004; Lara González, 2015). So, by being aware that Ixil-speaking students are not naming and using the Mesoamerican numbers in Ixil; we—the authors ask—how may genuine reconnections be promoted when teaching this Indigenous curriculum (Farmer & Powers, 2005; Kashatok & Wyman, 2022; Wilson & Yellowbird, 2005; Yojcom Rocché, 2013)? In the teaching of Mesoamerican numbers, we should resist (Absolon, 2022; Gutiérrez, 2022; Jacob, 2014) using these numbers to teach regular school Mathematics. Such approach would only promote superficial connections to the onto-epistemologies in these numbers. Instead, we could more intentionally decolonize and indigenize our teaching and learning (Absolon, 2022; Wilson & Yellowbird, 2005) by including contexts of practice (e.g., tracking time and seasons) for teaching and learning (Anzaldúa, 1987) that are onto-epistemologically closer (Cajete, 2000; Wilson, 2008) to how these numbers emerged and were used in the first place (Farmer & Powers, 2005; Taylor et al., 2015; Yojcom Rocché, 2013). Then, in these contexts the different versions, uses, and names of the Mesoamerican numbers will flow more naturally. It is our deep desire (Gutiérrez, 2022; Tuck, 2009) to engage in such practices.