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.”
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.”
Indigenous Math
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.