From Cultural Practice to Formal Geometric Reasoning: A Pre-Empirical Hypothetical Learning Trajectory Through Nias Stone- Jumping

Mathematics is often taught as a collection of universal truths that exist independently of human life, a set of rules written in the stars rather than in the soil. Yet, for decades, researchers in the field of ethnomathematics have argued that mathematical ideas actually grow out of the specific cultures, tools, and daily practices of people around the world. This perspective suggests that a community's way of building, weaving, or farming contains deep mathematical logic, even if that logic is never written down in a textbook. The challenge for educators has been figuring out how to bridge the gap between these rich, lived experiences and the formal, abstract geometry taught in schools. The goal is not to simply point out that a cultural object looks like a shape, but to understand how a person can move from knowing an object through its cultural use to understanding it through the strict rules of mathematical proof.

In a study published in October 2026, a team of researchers from Universitas Pendidikan Indonesia explored this bridge using a striking cultural tradition from the island of Nias in Indonesia. They focused on Hombo Batu, a massive stone monument used for centuries in a traditional stone-jumping competition. In this practice, young men leap over the stone structure to prove their strength and courage, a rite of passage that has been passed down through generations. The researchers did not simply look at the stone and say, "It is a pyramid." Instead, they asked a more difficult question: How can the specific way this stone is built, the reasons for its shape, and the cultural stories attached to it be transformed into a lesson that leads a student from simple observation to complex geometric reasoning?

To answer this, the team traveled to Bawomataluo Village in South Nias, where the tradition is still maintained. They did not bring a classroom of students with them; instead, they brought cameras, notebooks, and a deep respect for the local knowledge. They spoke with three elders who knew the history and construction of the stones intimately. These informants explained that the stone is not just a random pile of rocks. It has a wide, heavy base to keep it steady, a narrower top to serve as the obstacle for the jumpers, and sides that slope inward. The elders described how the proportions are passed down not through written measurements, but through the hands of builders who have learned the craft from their ancestors. The researchers also took detailed photographs from every angle, noting the symmetry and the way the stone sits in the landscape.

The core of the study was a careful, step-by-step process of translation. The researchers first listened to the cultural stories and observed the physical stone, separating the cultural meaning from the physical shape. They noted that the wide base was for stability and the narrow top was for the jump. Only after understanding these functional and cultural reasons did they begin to translate these observations into the language of geometry. They realized that the wide base could be thought of as a large rectangle, the narrow top as a smaller rectangle, and the sloping sides as trapezoids. By connecting the cultural purpose to the physical shape, they built a mental model of the stone as an idealized geometric solid, specifically a rectangular truncated pyramid. This was not a claim that the villagers thought of the stone as a pyramid, but rather a demonstration of how a researcher can use cultural evidence to construct a mathematical model.

With this model in hand, the team then applied a well-known theory of how people learn geometry, developed by a Dutch educator named Pierre van Hiele. This theory suggests that people do not jump straight into complex math; they move through distinct stages of thinking. First, they see the whole object. Next, they notice its parts, like edges and corners. Then, they start to see how the parts relate to one another. After that, they can use those relationships to prove things logically. Finally, they can think about the rules in a very abstract way, applying them to many different situations. The researchers mapped their cultural stone onto these stages to create a "hypothetical learning trajectory." This is a theoretical roadmap that suggests how a student might learn about geometry if they started with the stone-jumping tradition.

The proposed path begins with the student simply looking at the stone and recognizing it as a whole object used in a game. As they move forward, they might examine the stone's corners and flat surfaces, learning to name them as vertices and faces. They would then explore how the top and bottom are parallel and how the sides connect them. Eventually, they could use these relationships to calculate the total surface area of the stone, not by memorizing a formula, but by understanding how the shape is built from its parts. The final step would be to realize that the rules they learned from this one stone apply to many other shapes, allowing them to think about geometry in a broad, general way. Throughout this journey, the stone remains the anchor, shifting from a cultural symbol to a mathematical tool as the student's thinking becomes more formal.

The researchers are careful to state that this is a theoretical proposal, not a proven fact. They did not test this path with actual students in a classroom. Instead, they constructed a logical argument based on their deep analysis of the stone and the cultural context. They argue that this approach is superior to simply using a cultural object as a colorful picture to illustrate a math problem that has nothing to do with it. By keeping the cultural meaning and the physical construction at the center of the process, the study suggests that culture can be a true foundation for mathematical thinking, rather than just a decoration. The study concludes that for this specific path to become a real teaching method, it must be tested in schools to see if students actually follow this route of understanding. Until then, the work stands as a detailed blueprint for how culture and mathematics might be woven together, showing that the path from a stone jumper's leap to a geometric proof is not a leap of faith, but a series of small, understandable steps.