Indigeometry Planetarium brings a Navajo perspective to math education

Second-year doctoral student Jessica Benally remembers many nights of her childhood lying outside on her trampoline in rural New Mexico, feeling in awe of the expanse of the cosmos. At times, her grandmother would tell Navajo stories of the different constellations that were more than just celestial patterns in the night sky.

The Navajo strong connection to constellations, her grandmother said, helped with many aspects of life on earth, such as determining the planting seasons. Benally didn’t realize it back then, but in academic terms, she was learning archaeoastronomy.

It wasn’t until Benally’s years as an undergraduate at the University of New Mexico that she began thinking about the stars in terms of both Navajo culture and mathematical concepts.

“To understand the rotation of the stars, like in Navajo archeoastronomy, you first become familiar with placing yourself as the origin to look at the stars. By doing this, you are orienting yourself to multiple layers of the environment by recognizing distances between stars and shapes to form constellations. From there you can map changes of the constellations' rotation from season to season.

“The rotational change of Náhookos Bi'ka' (Ursa Major) around Náhookos Biko' (Polaris) cut by seasons is similar to the 90 degree increments on the unit circle,” Benally says. “It first calls for a perspective change, being able to see an angle project from yourself out – toward the stars and constellations – rather than just seeing angles on paper."

Jessica Benally assembles the Indigeometry Planetarium, a mobile, tent-like, icosahedron structure.

This is far from the way she learned math growing up in Tohatchi, New Mexico, on the Navajo Reservation, and not how she studied applied mathematics at the University of New Mexico. Benally’s math education was mostly lectures and worksheets. Yet she excelled, in part because of early support her father provided in her mathematical learning.

“I remember I was trying to figure out multiplication. I just couldn't get it. He got some marbles and we had a seat cushion where it had little dimpled sections, this made it easier to divide up the marbles. Multiplication finally made sense when I was able to physically separate the marbles and visually see the different sets,” she said.

And her math identity was cemented.

Benally also became more aware of her classmates who didn’t have the support at home, nor did they feel confident in their math knowledge. That stuck with her.

During college, she tutored at a high school in New Mexico that focuses on incorporating Indigenous perspectives throughout the curriculum, except when it came to math. She decided to introduce math lessons with storytelling about the constellations, drawing on some of her grandmother’s archaeoastronomy stories.

Benally’s doctoral research involves her Indigeometry Planetarium, a mobile tent-like icosahedron structure that she constructed in Professor Dor Abrahamson’s Embodied Design Research Laboratory (EDRL). The planetarium is built from a series of dowels linked together with rubber joints and a black cloth to enclose the space.

Inside the Indigeometry Planetarium students engage with Navajo archaeoastronomy and math.

Elementary students sit inside to gaze at the stars affixed to the planetarium’s sky. To orient themselves, students begin with their small outstretched arms, seeing and feeling the distance between stars in front of them, to the side, and behind.

Benally then hands them a measuring instrument fashioned out of a protractor with two dowels attached, allowing the young students to visually become a vertex of a triangle. Holding the protractor near their chest, students then measure the distances between the stars again, this time being able to read the angle’s degree.

“This leverages the Indigenous perspective in an elementary math classroom where Euclidean geometry is the privileged view. Geometry is now no longer just static lines drawn on paper,” Benally said.

“For Navajo students, this work introduces the students' environment -- bright stars, dark night and a wide sky -- and their orientation to it physically and also starts the tasks with a story of how the stars came to be from the Navajo perspective,” she said.

Benally also notes that non-Navajo students will benefit as well, as they learn about Indigenous culture and are physically engaged in math.

“The Indigeometry Planetarium puts students at the center,” she said. “They feel and see math.”