March 2025
Donna Fernandez, Co-Director of Alliance of Indigenous Math Circles
Nalyana, a high school student at Navajo Preparatory School, in New Mexico, admitted that her last school year was hard because she was behind in math. She had been staying after school to get tutoring but this made her feel “dumb”. The last thing she thought she would do for the summer was go to a math camp. She thought math camp was about getting more homework.
The Alliance for Indigenous Math Circles annually hosts a summer math camp at Navajo Preparatory School in Farmington, New Mexico. The camp, for 20 Indigenous youths, is fun and engaging. The students’ competence in math increases, as does their confidence.
This is just what happened to Nalyana when she came to the camp, in the summer of 2023. She quickly saw that she wasn’t ‘bad at math’, just that she hadn’t experienced situations where her abilities could be revealed. She readily engaged in the informal problem-solving groups that crystallized around the various problem-solving activities. In particular, she was chosen to be captain of her team in the “Math Wrangle” event. She was an effective captain, organizer, and role model, and soon earned the nickname “shimasani” – grandma in Navajo, among the younger students.
The ‘Math Wrangle’ is an adaptation to the American landscape of a Russian model, a ritualized ‘battle’ between two teams in explaining the solution to problems. Teams alternate challenging each other to solve problems, taken from a list given well in advance. Throughout math camp, students are given the problems. Teams prepare and explain solutions to the problems. The final day of camp is the Math Wrangle. Students are called up to present to both teams and a ‘jury’ of teachers and mathematicians. Students are prepared to field questions about their solutions—so they cannot simply ‘recite’ a solution they have heard. During the week they worked with their team to understand deeply the solutions.
An example of the Math Wrangle problem set at the AIMC summer camp is given below.
Making the student into the teacher in this way may seem intimidating, but the emphasis in math camp is on the process of overcoming any fears about being a mathematician-in-training. We value the process of getting the answer over the answer itself. On a deeper level, it is more than the actual process of logical argument we value, but the internal motivation of students to make logical arguments and the confidence to do so. The productive struggle allows them to do this by themselves.
Instilling a positive self-identity as an Indigenous mathematical problem-solver is integral to our camp. Dr. Henry Fowler, Navajo Technical University Dean of Graduate Studies opens the camp by telling students the Navajo Nation needs more Diné mathematicians who can think critically and solve problems. Helping students see themselves as mathematicians is important. Our camp allows students to bring their whole selves and leads to an experience that aligns with the cultural teachings of kinship. Kinship fosters a sense of community and belonging, empowering students to become innovative, creative, and effective problem-solvers that the world urgently needs. Integrating culturally relevant math problems supports students’ personal development and growth through relevance and relationships.
Does it work? Do students in math camp return to their homes with the confidence that they can master and even contribute to mathematics? Yes. Toward the end of t
he program, I was walking across campus with Nalyana. She told me that the math camp helped her to decide to go to college to pursue her career in the healthcare field. Other students made similar comments to the staff.
The AIMC Summer Math Camp is the product of the AlMC’s work in building informal educational practices in Native American communities. On a visit to the Navajo reservation in 2012, Dr. Tatiana Shubin, Emeritus Professor of Mathematics at San Jose State University in California, found colleagues in local schools and colleges who were interested in developing such programs and were looking for models. Shubin started 5 math circles, informal after-school groups in which students, teachers, and mathematicians discuss problems and engage in mathematical activities. Typically, these activities lie outside the traditional curriculum, expanding on techniques and objects that students are familiar with, but looking at them from unusual angles. (For much more about math circles see www.mathcircles.org.)
Shubin found a community eager to pursue the idea of math circles. They tapped into the growing literature of support materials and found ways to bring students together for mathematical study after school. This effort was successful even in the fragile environments of reservation life. Often, students travel two or three hours over the desert landscape to high school each day from their isolated communities. So, staying in school even for an extra half hour requires planning and dedication.
Nonetheless, math circles flourished. Over the past 15 years, a dozen or so math circles have appeared (and sometimes disappeared), involving students in mathematics in ways they would not have been exposed to. The effort is paying off.
“Diné College officially created four new schools as of Fall 2017…The schools are the School of Arts, Humanities and English, the School of Science, Technology, Engineering and Mathematics (STEM), the School of Diné Studies and Education and the School of Business and Social Science.” (dinecollege.edu, 2017)
“The most specialized majors at Dine College in 2022 are Math & Statistics (6 degrees awarded), Education (32 degrees), Social Sciences (16 degrees), Health (70 degrees), and Psychology (14 degrees) (as of 2022).” (https://datausa.io/profile/university/dine-college#:~:text=The%20most%20specialized%20majors%20at,)%20(as%20of%202022).
COVID hit the reservations hard. Schools were closed and whole villages were isolated with little or no WIFI service. Students could not meet face-to-face to enjoy mathematics.
In March 2021, AIMC launched Bluebird Math Circle, a supportive community of teachers, students, and their families–anyone who cares about or is curious about mathematics, education, and Indigenous young people’s futures. Bi-weekly Zoom meetings showcased online math activities from the newsletter, offered background information, and provided families with mathematical games, puzzles, and activities to support students’ continued learning during the pandemic. An archive of these materials can be found at https://aimathcircles.org/bluebird/.
Building community is what mathematics can do. Mathematics is inherent in all people. Indigenous people have mathematical knowledge, evidenced by complex systems of trade, environmental practices, and masterful artistic work–all evidence of being skillful mathematicians with inherent ability. Mathematicians are connecting with Indigenous mathematicians to learn from each other.
“Indigenous Knowledge is a body of observations, oral and written knowledge, innovations, practices, and beliefs developed by Tribes and Indigenous Peoples through interaction and experience with the environment. The Biden-Harris Administration has formally recognized Indigenous Knowledge as one of the many important bodies of knowledge that contributes to the scientific, technical, social, and economic advancements of the United States and our collective understanding of the natural world.” White House Office of Science and Technology Policy (Office of Science and Technology Policy, 2022)
Today in the classroom, creating innovative pedagogies in mathematics to connect Indigenous youth and educators to the teaching and learning of mathematics is a central theme. The International Congress on Mathematical Education (ICME-15) adopted this theme in their 2024 meeting in Sydney, Australia.
Thanks to the generosity of the Alfred P. Sloan Foundation Dawnlei Ben and I presented at ICME-15 to an international mathematical community about strengthening our students’ identity as Indigenous mathematicians. Dawnlei Hunter Ben, Naa’neeshte’zhi Ta’chiinii (Red Running Through the Water-Zuni Division) clan, is an Instructor of Indigenous Science at Dzil Dit’loií School of Empowerment, Action, and Perseverance (DEAP) in Navajo, NM, and an AIMC Regional Coordinator. This talk contributed to exploring global trends in mathematics education, research, and teaching on all levels. We found that world-leading mathematicians, educators, doctoral students, professors, and school administrators were interested in learning about our work.
In turn, we took great interest in the work of others. We found commonality among Aboriginal people of Australia, the First Nation people of Canada, and Chileans. Anahí Huencho, Universidad Católica de Temuco, Chile, purports that Indigenous mathematical knowledge has been historically disconnected in education, robbing the youth of rich relationships between culture and math. She presented to answer the question, “How can Indigenous mathematical knowledge be made accessible and what are its benefits for education and the preservation of indigenous culture?”. Incorporating culturally relevant mathematics preserves ancestral knowledge and provides a deeper enriching educational experience for the learner and community.
We presented our work using the geometry of California Pomo basket designs, the exponential growth of a turtle based on a creation story from Indigenous contemporary art, and the symmetric designs on Navajo blankets or Hopi pottery. A central theme emerged at ICME: Indigenous mathematics is humanizing mathematics education by integrating mathematics education and Indigenous ways of knowing. Students feel a sense of belonging in math and empowerment through cultural relevancy in mathematics. These pedagogical practices and curricula shift supports Indigenous students’ identity and educational achievement. Students begin to feel that mathematics is part of their culture, and part of their heritage. This leads to growth as students are more comfortable engaging in mathematics.
The intersectionality of math and culture requires work. Australia has developed a curriculum that includes a cross-curriculum priority based on the Aboriginal and Torres Strait Islander histories and cultures. Students now learn by exploring the rich traditions of its Indigenous people.
The process of exchanging ideas continued even after everyone returns home from the conference. Dawnlei and I are invigorated to work on future math curriculum projects. I look forward to writing the curriculum for the CA Native American Studies Model Curriculum set to be released in the fall of 2025. I am inspired to share the counting system of the Mapuche. This system makes sense. It reminds me of my Southeastern Pomo counting system which is base 10.
Another common theme that emerged at ICME was the need for inclusion. In our keynote address, Ben and I stated that the contributions of Native Americans to mathematics are routinely overlooked. Dr. Kamuela Yong, Professor of Mathematics at the University of Hawaii studied the effects of not accurately counting Indigenous mathematicians. He stated, “This not only impedes accurate representation but also perpetuates the false narrative that mathematics is devoid of Indigenous presence.”
More than half of the US states don’t even mention Native Americans in their curriculum. Of those that do, 87% make no mention of Native Americans after the year 1900. (Illuminative, 2024). Indigenous people need representation and visibility in the classroom that culturally correctly portrays history and shows the existence, contributions, and resilience of Native Americans.
This silence about the achievement—even the existence—of Indigenous cultures was echoed in other presentations, and in some of those vital side conversations. Culturally responsive mathematics is transformative and relevant for students. Kinship or relational connection is valued in most cultures, a curriculum that builds relationships and recognizes Indigenous ways of knowing will engage all students. The closing plenary session addressed whether mathematics education can help with humanity’s problems. The presenters said mathematics education can provide a necessary skill set but students need more: they need to see how math is a solution to social problems and can help them advocate for change and equity.
Mathematics, like music and poetry, is the birthright of every human, and mathematical talent is spread uniformly among all people. Thus, underrepresentation suggests that Indigenous students’ talents remain unrealized because of reasons beyond their control, and not because of a lack of capacity or interest. Moreover, Indigenous people will bring their unique viewpoint and thus will enhance and expand the professions worldwide.
References:
https://www.hawaii.edu/news/2024/01/18/jmm-invited-addresses/
INVISIBLE NATION KLEPPER DOCUSERIES VIEWERS GUIDE, pg. 5 – https://illuminative.org/resources/
MATH WRANGLE–Summer 2024
Problem 1: When two people shake hands with one another, that counts as one “handshake.” Every person in a room shakes hands with each other person in the room exactly once.
a) There are a total of 15 “handshakes”. How many people are in the room?
b) There are a total of 231 “handshakes”. How many people are in the room?
c) For any integer n, find a closed form (formula) for the number of handshakes when n people meet.
Problem 2: All the counting numbers are arranged in the triangular pattern as shown by the first four rows.
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1 |
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| 2 | 3 | 4 | ||||||||
| 5 | 6 | 7 | 8 | 9 | ||||||
| 10 | 11 | 12 | 13 | 14 | 15 | 16 | ||||
| 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
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…and so on.
a) What is the first number in the 13th row?
b) What is the sum of the numbers in the 100th row?
c) In a set of counting numbers, all have different values. Their sum is 350. Their average is 50. One of the numbers is 100. What is the greatest number that can be in the set?
Problem 3: The top of a rectangular box is 15 cm by 20 cm and its height is 4 cm. An ant begins at one corner of the box and walks along the edges. She touches all eight corners, and ends at another one of the corners. What is the shortest distance, in cm, that the ant may travel?
