This presentation examines how mathematics is embedded within Diné spirituality through the human body, traditional Hoganconstruction, and the observation of constellations. The Hogan embodies principles of geometry, symmetry, measurement, proportion, and orientation while serving as a model of harmony and balance. It also provides a framework for understanding celestial movements, seasonal cycles, and relationships between Earth and sky. Drawing from Diné knowledge systems, the presentation demonstrates how mathematical reasoning connects people, place, and the cosmos, offering a broader understanding of mathematics as a cultural, spiritual, scientific, and relational way of knowing.

Biography: Dr. Henry Fowler is Tódich'ii'nii (Bitterwater), born for Naasht’ézhí dine’é Tábąąhí (Zuni Edgewater). His maternal grandfather is Tł’ízí lání (Manygoats), and his paternal grandfather is Táchii'nii (Red Running into the Water). Dr. Fowler’s research centers on Ethnomathematics and Navajo education. He is deeply committed to promoting mathematics literacy, advancing social justice through mathematics, and integrating culturally relevant teachings that honor Diné ways of knowing and guide meaningful instruction.

This presentation demonstrates how Diné (Navajo) cultural knowledge provides authentic contexts for teaching mathematics. The Diné kinship system teaches relationships long before students encounter formal mathematics. Identifying parents, grandparents, and clans develops recursive reasoning modeled through binary trees, exponential growth (2 to the nth power), graph theory, geometric series, and algorithmic thinking. Participants will also explore the traditional batten stick (Beeníłʼíníłtłish), a Navajo weaving tool used diagonally across the warp to create a geometric grid for finding midpoints, symmetry, proportional reasoning, and spatial visualization, illustrating Indigenous mathematics as a living system of mathematical knowledge.

I will use Indigenous knowledge to teach mathematical thinking through traditional string designs. According to Diné/Navajo teachings, spiders taught people how to create string designs, and these activities are traditionally practiced during the winter when insects are hibernating. The lesson will incorporate Navajo winter storytelling, including the teachings of Spider Woman, who represents creativity, problem-solving, and perseverance.

The game Spot-It, played with 55 cards each pair of which is known to have exactly 1 symbol in common (of the 8 symbols printed on the cards), is well-known for its design via a projective plane of order 7. A similar game can be constructed with words, each pair of which has a single letter in common, provided we can find the configuration of a projective plane within a graph constructed of words. In this talk, Professor Edward Doolittle of First Nations University of Canada will demonstrate an efficient method for searching for projective plane configurations and related configurations in graphs obtained from dictionaries in various languages, including English, French, and some of the Indigenous languages of Canada, in particular Plains Cree written in Standard Roman Orthography (SRO) and Plains Cree written in Canadian Aboriginal Syllabics.

Ten years ago, I was asked to Indigenise curriculum in Mathematics at the University that I worked for at the time. Since I didn’t know how to go about that, I began a project exploring this, supported by the mathematics research centre CARMA. We started with small teams of two or three leaders around each of half a dozen themes, with each team including at least one Indigenous person and at least one University-based Mathematician; and the IUM (Indigenising University Maths) project and knowledge community has grown from there: see https://carmamaths.org/iumproject/. I will reflect on my learnings within this journey.