Revitalizing D/Lakota Mathematics Through Language & Culture
Author: Lori Huston, Qiaochu Xu, Ariane Faria, and Cynthia Nicol
For some curriculum developers bringing math and Indigenous perspectives together involves “unfreezing” mathematics within cultural practices (for example coding in beading or cones in tipis). But for Dr. Danny Luecke it is through the perspectives of Indigenous Elders (Lakota), sharing their knowledge and worldviews through the D/Lakota language that provides opportunities for learning and revitalizing Lakota mathematics.
Growing up on Očhéthi Šakówiŋ and Anishinaabe land, now known as Fargo, North Dakota, Danny is of mixed ancestry being from the Choctaw Nation and multiple European nations. However, Danny described that most of his experiences are from “a privileged white guy” perspective. So, as a way to reconnect and honor his own Indigenous heritage, Danny decided that during graduate school he wanted to learn and work with Indigenous communities in the place he grew up.
With great pleasure, we'd like to extend our heartfelt congratulations to Dr. Danny Luecke for successfully completing his Ph.D. in Mathematics and Mathematics Education at North Dakota State University. His remarkable journey and community-based research, conducted in collaboration with Sitting Bull College on the Standing Rock Reservation have further advanced the exploration and promotion of D/Lakota-based mathematics.
"Math fluency and language fluency can grow together."
Danny’s work explores connections between language and math, local teachings, and culture. A focus is bridging mainstream math concepts and Indigenous ways of knowing.Danny described his doctoral research as co-constructing with community members and elders a mathematics curriculum to be taught in the D/Lakota language. Danny worked with the community to understand what they wanted as a result/product of his research and what should be the next steps after the research. He found that the community wished to design a sort of reference book where they could return to review what they have learned during the process and use this type of guide for future learning in the community. Danny is also working to establish details regarding the “data sovereignty” of this math community knowledge, so that the project protects and supports the work of the Standing Rock Department of Education. You can view the work in progress resource material on the Standing Rock Lanuage and Culture Institute web portal called Othokahe by creating an account and self-enrolling in the math connections course.
"[…] there is a connection between the language, culture, and personal identity […] often in Western teaching approaches, there is a math class and there is a language class, and they are pretty much separate […] So an indigenous way of teaching and learning is the opposite. And so that's kind of one big idea that I think about often that math fluency and language fluency together."
While working with math and language teachers as well as elders from the community, Danny realized that "there is a connection between the language, culture, and personal identity […] often in Western teaching approaches, there is a math class and there is a language class, and they are pretty much separate […] So an indigenous way of teaching and learning is the opposite. And so that's kind of one big idea that I think about often that math fluency and language fluency together”. Danny writes about this more fully in his recently co-authored research article titled “Dakota/Lakota Math Connections: an epistemological framework for teaching and learning mathematics with Indigenous communities and students.”
Context is Critical
"Subtraction without context lacks meaning and not everyone agrees on how to say subtraction in an abstract way. "
Another point of D/Lakota math education is related to the close connection between language and math. Danny explained that subtraction without a context lacks meaning and "not everyone agrees on how to say subtraction in an abstract way. That’s expected though because Western math terminology, like subtraction, seeks to remove context and relationships. 2+2=4 “Two of what?”, ask the fluent speakers. Depending on what it is you will say it differently. Further, there is not a single way to say subtraction in English, so why would we expect that for the D/Lakota language."Danny and team have co-developed the D/Lakota Math Connections framework. Even though there are four distinct circles, he is learning how "all of them are intertwined.”
D/Lakota Math Connections Framework
Based on this framework, Danny emphasized how context is critical in the communication of mathematical activities in the D/Lakota language system: "Everything in D/Lakota math will be in context, there isn’t a ‘seven minus three equals four’ without reference to what the seven and three are measuring". And this means that a D/Lakota math curriculum can’t just be a direct translation of a non-D/Lakota curriculum. To make sense of a problem in the D/Lakota language students need to know the context.
D/Lakota math ways of knowing
According to Danny, D/Lakota Math is embodied within the people, land, culture, and language.For instance, consider mathematical thinking within an activity (art, construction, engineering, survival, etc.). Danny concluded that “It's the mathematical thinking that is happening, logic, recognizing patterns, responding to variation...”. Danny explained that D/Lakota math concepts wouldn't have been written down because the concepts were more likely to be embodied and didn’t need to be written. In this sense, Danny concluded by saying that many traditional and cultural activities and experiences practiced by people in the community are still mathematical even if not written on paper. This is part of what Meyer and Aikenhead describe in their explanation of “Indigenous mathematizing.”
As Danny completed his doctoral dissertation he has recently taken up an instructor position at Turtle Mountain Community College on the Turtle Mountain Reservation. For this position, he is drawing upon his dissertation studies to develop a four-year math education program focused on Ojibwe mathematics, and Indigenous math more broadly, aiming to increase the number of local math teachers in the community. Danny, his students, and other community members understand that the Ojibwe language is not separate from their culture or identity. Teaching language in the Math course enriches the student's identity and supports learning from a holistic Indigenous perspective. Danny shares more about this in the Tribal College Journal article on Ojibwe Math.Professor Dr. Cynthia Nicol and Ph.D. students Qiaochu Xu, and Lori Huston from the Curriculum and Pedagogy department at the University of British Columbia conducted this inspiring conversation over breakfast while Danny Luecke was in Vancouver attending first ever Indigenous Mathematicians conference at the 2022 Pacific Rim International Mathematics Association conference.
Carol Bob, a member of the Wilps Luus in the Gitxsan territory of the Pacific Northwest, has a powerful message for teachers - that teaching math, or any subject, is all about building relationships with students and community. Carol, whose hereditary name is Sta’osta’on (helping hand) is a non-enrolling teacher on the Lax Yip of her Gitxsan Nation at Hazelton Secondary School. There Carol also teaches Workplace Mathematics 11 where she embraces the challenge of teaching students who question the need and purpose for learning mathematics.
Drawing upon Indigenous pedagogies that focus on experiential approaches to learning and oral ways of sharing teaching and learning, Carol brings math, community and culture together. She takes her students outdoors, not only to develop awareness of mathematics in all kinds of places, but also so that they can build trusting relationships with each other – so that they can learn from each other.
Being outdoors and walking provides opportunities for learning more about what her students know and what sparks their curiosity. “I ask them what kinds of plants they know, or what do they see, what did they observe. And then eventually, they start talking and actually listening and noticing” to each other and this place. It’s a way for students to learn “to stand up for themselves and think critically when needed” says Carol, and to “communicate what they want or need, to use their voice.”
a photo of Gitxsan territory by Heqs - Own work, CC SA 1.0
“communicate what they want or need, to use their voice.”
This approach honours Indigenous pedagogies of oral teaching and learning. For Carol there are “different ways the kids can show that they know. They can either do it or write on paper. Or I can observe and take note and then discuss it with them. Or I can have one-to-one verbal conferences with students.” All this builds students’ confidence and prepares them to challenge themselves. But it also requires that teachers have high expectations for their students. As Carol describes, this strategy is “adapted to make sure that students succeed. And I try to push them to do a little bit more, because they usually can do a little bit more than what they think they can.”
In what other way could a teacher develop a math lesson around Canada’s horrific and tragic Missing and Murdered Indigenous Women and Girls? A topic for investigation that was actually suggested by Carol’s students. Without a strong relationship with community and her students this would be a challenging topic to respectfully and responsibly bring to the classroom.
Yet this is what Carol and her students did. Students deepened their knowledge of the topic by reading the formal report on Missing and Murdered Indigenous Woman and Girls. Then Carol brilliantly engaged students in questioning the data reported as they discussed “whose perspective is presented, whose bias is presented, whose perspective is missing?” Students prepared scale drawings to create their own beaded red dresses, earring size. As they beaded, Carol and her students discussed the reasons behind the report and how math could be used to understand and critique the report. All this culminated in a gathering with Chiefs, students, and community members. Students were the speakers. It was very powerful and where students were encouraged, states Carol “to stand up, be proud, and recognize ‘we’re in this together’”.
“to stand up, be proud, and recognize “we’re in this together”.
What’s next for Carol? Working to continue building community relationships. “The loss of our culture and language in the last few years just because of the loss of community Elders” has had a devasting impact. So, for Carol, “connecting with math, inviting the community in, and taking kids out more into the community to learn the culture” are high priorities. “That's what I need to be thinking of while the Elders are still the knowledge holders and are still with us.”
More details on Carol's project can be found here.
Janice Novakowski, a math consultant for the Richmond School District, is a non-Indigenous educator committed to learning about Indigenous worldviews, perspectives, knowledge, and culture.
Janice sat on the Ministry’s mathematics curriculum development team and so has insight into ways to embed Indigenous ways of knowing into mathematics teaching and learning. She explains, “they were very intentional to not include Indigenous culture in the content learning standards . . . because culture is localized.” Therefore, any particular Indigenous cultural content may not be applicable to all Nations, communities, or geographical areas. “Instead, those Indigenous worldviews and perspectives and knowledge are embedded in the curricular competencies.”
“We all have a moral and ethical and human responsibility to do the work ourselves.”
One of the ways Janice and teachers in Richmond district incorporate Indigenous culture and knowledge in their teaching is through land acknowledgement and nurturing connection to the land. They made a concerted effort to dig deep into what land acknowledgement means for mathematics, for example, by exploring measurement, shape, symmetry, and mapping to identify and classify different species and features of the land.
In one particular project, students in grades 3-5 used Google Earth and Google Maps to look at the place where they live and go to school, then went out onto the land and took pictures of their place. Back inside, the students mapped their neighbourhood while focusing on mathematical concepts of spatial reasoning, positional language, proportional reasoning, scale, and measurement.
Students then accessed the Musqueam website to look at the Musqueam place names map. They explored the places around Lulu Island (Richmond) to see how those places were named. The students realized “that those places aren’t named after someone, as is so often done in Eurocentric culture. They learned those places were named after purpose or they were describing the place, like Driftwood Place or Boiling Point.” The students then started naming the places on their maps after how they use those places and not after themselves!
Janice acknowledges teachers’ hesitancy when it comes to including Indigenous knowledge in their teaching, because there have been mistakes made in the past. But she asks us to remember: “We’re doing it with good intentions. We own the mistakes [when we make them.] And then we move forward and we learn from that.”
Janice shares a tidbit of her own journey as her parting advice (and writes thoughtfully in her own blog): “We all have a moral and ethical and human responsibility to do the work ourselves. It’s a fault in our system that we didn’t learn this in schools. Therefore, we have to take that on ourselves. We need to read, listen, watch films, go to speakers and classes that are open to the public. As educators we need to see that as part of our professional responsibilities as well.”
Carolyn Roberts is an Indigenous faculty lecturer in the Faculty of Education at Simon Fraser University. Here, she talks to us about her work in decolonization and Indigenous pedagogies.
How do you support teachers interested in connecting math, community and culture?
"Math is a colonial construct and when we think of math we usually are only able to see it through a colonial lens. So when we try to put an Indigenous view point to it, it is difficult. Our ancestors used math all the time; they used it in their carving, their canoe making, their weaving, their creation of items used to create things. In order to be able to incorporate math in an Indigenous way you need to move away from the colonial constructs of math and rethink how we teach our students about the world around us. We need to get out on the land and see how the interconnectedness happens in nature, naturally. You need to get the children using their hands and minds together with weaving, carving, and drawing. Look at how the skills we learn in math are used in these different ways."
"Math is a colonial construct. We need to rethink how we teach our students about the world around us."
What do you feel teachers (and teacher candidates) can work on (read, discuss, do) that can support their learning about teaching in ways which connect with community and Indigenous perspectives and pedagogies?
"This is a good question and I feel it is harder to answer because what I worry about is students going into community looking for ways to connect and learn without knowing the protocol involved with asking this. It is more important to learn about how to approach our communities in a good way by asking first what can we do to support your community, rather than asking for them to share their knowledge and information. The reciprocity piece is what we need to teach about. How do we do this work in a good way. More so in this moment in time, we need to make sure that we all know the Truth about our history. I don’t think teachers can even start to weave Indigenous knowledges into their practice without knowing and understanding our Indigenous history here in Canada."
What are you currently working on in your school and what will you be working on next (in the future)?
"I am currently a Faculty Lecturer at SFU; my work is grounded in decolonization, Indigenous pedagogies and teaching Indigenous history within Canada. I work with undergrad programs and the Professional Development Department for new teachers. As this work evolves, it is my hope that I have more students that know the true shared history of Canada before they walk into my classroom. I bring a different way of teaching into the academy. I bring it in from an Indigenous lens in hopes to share how we can do education differently, how we can view education from another world view other than the colonial view point that we have been taught. It is my goal to create space for Indigenous voices to be heard within our education system in order for more Indigenous academics, educators, and people to move into spaces that we were never allowed to be in before. With this we can all co-create what Indigenous education looks likes and feels like within academia."
Lyn Daniels, the Director of Instruction, Aboriginal learning for Surrey Schools in BC, sees high school mathematics as a gatekeeper course. That’s why she and her colleagues have created Math Camp, a summer learning program just for Indigenous students across the district.
Indigenous students can receive a scholarship to attend this camp that uses Rahael Jalan’s Math, Yes We Can program and The Language of Mathematics workbooks to improve their mathematics skills.
Lyn acknowledges the unusual approach to this program for Indigenous students. Rather than bringing Indigenous cultural connections and contexts to the math classroom, this program focuses more directly on developing math skills and understanding through guided workbooks alongside educational supports. Cultural connections are included but the program begins with the mathematics.
“Math is a gatekeeper course.”
In Math Camp, students get quiet, persistent, one-on-one support from educators, youth and child care workers, and other volunteers. Lyn and her colleagues find different ways to engage the students. They offer a soft start each morning and a warm welcome when the students arrive. They try to relate the mathematics to the stories of students’ lives. They bring in Katzie cultural presenters at times to do weaving, beading, and other cultural activities. They offer food and instil a sense of belonging and friendship.
The success of Math Camp is obvious in its numbers. When the program started 3 years ago, they had 30 students; last year they had 60! In fact, some students who had already graduated, came back to do it again!
Most of the educators involved with Math Camp are not Indigenous. Many of the Indigenous cultural presenters and youth care workers that assist with the program are afraid of mathematics, Lyn says. In fact, some feel downright inadequate. Lyn sees this as a problem. “Math is a gatekeeper course,” she reiterates. “It keeps all of our students out of health and sciences and business." All the professions that we need math for are then closed to Indigenous students.
Lyn advises educators to keep in mind that Indigenous students may not have had exposure to mathematics in their lives. She recommends, practice, practice, practice for Indigenous students. Finding the cultural connections is not a problem but remember that the mathematics should come first.
Christine Ho Younghusband
Christine Ho Younghusband, now an assistant professor at the University of Northern British Columbia, began her inquiry into ethnomathematics 15 years ago at a time when Indigenous education wasn’t visible in the mathematics curriculum.
As a teacher of Math 8, Christine found herself with time and space in the curriculum, so decided to embark on an inquiry project with a colleague to integrate Indigenous education into mathematics. In her project, Math Embedded: A Tribute to Susan Point, students studied the work of Coast Salish artist Susan Point and her work with spindle whorls. “The ‘spindle whorl’ refers to a carved, circular plate attached to the end of a wooden spindle that acts to lend weight during the wool spinning process. In Coast Salish tradition spindle whorls are carved with powerful, symmetrical designs which blur and merge as the spindle turns” (Google Books).
"That project was life-changing because everyone had an entry point, everyone could see their mathematics."
In Christine’s project, students demonstrated their learning of linear and rotational symmetry by designing their own spindle whorl, without using a ruler, without using a calculator. Their designs reflected who they were, and even inspired some students to bring in their own artifacts from home and talk about their heritage. Christine says, “That project was career-changing and life-changing because everyone had an entry point, everyone could see their mathematics, everyone could connect in their own way that they felt was personally relevant to them.” The entry point? Indigenous education!
Further along in her career, Open School BC, a consulting agency that offers education solutions for school districts and ministries, invited Christine to work on a team with two others to create a video and learning activity to bring Indigenous perspectives into the mathematics curriculum.
Christine and her colleagues began their work by choosing an artifact, the Bentwood box, and then thought about the math questions that could be generated. Initially they thought, “How many Bentwood boxes could fit in the gym?” But they challenged themselves: “Is this a real question? Or should we ask a different question? Let’s understand what the box is for. The dimensions matter. If it’s for a blanket versus food, the dimensions change.” By thinking about the authentic purpose for the Bentwood box, Christine and her colleagues determined the rich mathematical question: “What are the dimensions of the tree that we would need to harvest in order to build this box?”
Christine considers this experience to be the best learning community she’s encountered in her career. They were scared shitless. Curious. Excited. But they were willing to try. She says, “We have to keep encouraging each other to take these risks. You can’t do it alone!”
Scared shitless. Curious. Excited. But willing to try.
Christine’s advice for teachers, schools, and districts looking to teach ethnomathematics:
1. Think about mathematics and don’t be limited to what’s in the curriculum.
2. Pick an artifact. Where does that artifact come from, what territory is it from? Why is it important? Where is the math? How would you use it in your classroom? What do you need to learn about it? Who do you need to contact to learn?
3. Not everything is a Google search. That’s not how information is held. We can’t get to the nuances without listening and observing, witnessing and experiencing.
David Sufrin, a professor of education at Vancouver Island University, is doing exciting things with his student teachers to connect mathematics with Indigenous culture.
Early in his teaching career, David lived on Haida Gwaii for 10 years and it was there that he first developed his passion for connecting math with community and culture. Teaching trigonometry and algebra, David quickly realized that these subjects, as they were traditionally taught, were “not relevant to kids’ lives” and so began to adapt curriculum to make it more hands-on and applicable.
Now, in his elementary math methods course for teacher candidates, David offers his students an assignment that requires them to get to know the local (Cowichan) First Nation. Students are asked to design a math task within a chosen cultural activity, such as games, artwork, or ceremonies. They must research their chosen cultural activity and look for a connection to mathematics, and then create a teaching resource to share with their fellow classmates or try in their practicum.
“As a non-native, I am a learner in my classroom. I practice and model First Peoples Ways of Learning. I collaborate with Elders and Knowledge Keepers.”
As well as connecting to the local Indigenous culture, David asks that these math tasks incorporate aspects of First Peoples Principles of Learning. That is, they are related to story, are holistic and interdisciplinary, and are experiential and activity-based. (For example, teacher candidates Lucas Anderson and Andrew Gait designed an activity in which students must familiarize themselves with a Trickster story, such as How Raven Made the Tides. Students must then find connections to math and graph an aspect of the story, such as the height of the tides at various times of day.)
For David, it’s about the process for his student teachers; he wants them to experience the process of connecting math to the world around them. He believes that this is an invaluable process that will transfer into their teaching career.
David acknowledges, his students are often nervous to do this kind of work with Indigenous culture. As a non-Indigenous person, he also feels this apprehension. He asks himself these difficult questions all the time: What right do I have to teach indigenous culture? And how well can I do this? How authentic is it? How much permission should I have?
To combat his doubts, he reminds himself of this important tenet: “As a non-native, I am a learner in my classroom. I practice and model First Peoples Ways of Learning. I collaborate with Elders and Knowledge Keepers.”
Now that Indigenous ways of knowing are woven into the BC curriculum, David believes all teachers “have an obligation to bring that aspect of learning and culture into their classrooms.”
David’s advice to teachers looking to connect math with indigenous culture:
1. “Believe that what you’re doing is important.”
2. Open your heart to looking at math, not just as symbols and algorithms, but as so much more than that, as connections to the world.
3. “The First Peoples Ways of Knowing: Read them. Read them again. Incorporate them into your teaching practice.”
4. Use the resources available to you!