By Tejvir Kaur Grewall
This blog features scholarship and research from Dr. Tejvir Kaur Grewall’s recently published dissertation, “Students' Mathematical Understandings of Fraction División with an Ethnomathematics/STEM Framework .”
June 2021. Lahaina, Maui. Apprentice, myself, Pwo (Samoan Master Navigator)
Micronesian ocean navigator and ancestor Mau Pialug’s (1932-2010) legacy taught the next and future generations the ancient wisdom of “traditional wayfinding, [which] is guided by the sun, moon, stars, winds, currents, and mathematical modeling” (Furuto & Phillips, 2021, p.263). As a Polynesian master navigator, or Pwo, he teaches apprentices the concepts and procedures for precision engineering when preparing, mending, upgrading, and voyaging canoes. He uses an indigenous perspective, a genealogy of knowledge, which dates back in the Pacific waters to around 3,000 years ago (New Zealand History, 2023). Embedded in his language and the Pwo’s teachings of today are the answers to the three questions that continue to manifest in the process of precision engineering and mathematical modeling: What is changing? How is it changing? and Why is it changing?
The triage for understanding the dynamics of changing conditions–what, how, and why–are central to indigenous ways of knowing, navigation, and problem-solving. They are taught by Pwos in the Polynesian Voyaging Society (PVS), an organization that has worked since the 1970’s to:
…ignite a movement of 10 million ‘planetary navigators’ who will pursue critical and inspiring ‘voyages’ to ensure a better future for the earth…by developing young leaders and engaging communities around the world while amplifying the vital importance of our oceans, nature, science and indigenous wisdom. (Hōkūle’a, n.d.)
Grounded in this mission, from 2023-2027 the PVS carried out a worldwide voyage, “move[ing] from exploration and understanding to mālama, or caring, and kuleana, or taking responsibility” in an effort to deepen the organization’s values of building “a future good enough for our children” (Hōkūle’a, n.d.). As a secondary mathematics teacher living in California, I learned about the work of PVS through the worldwide voyage and marveled at the way ocean navigation requires an immense amount of mathematical thinking and problem-solving that undergirds the required skills of precision engineering. I wondered: How can I teach the principles of engineering through ocean navigation?
As a 21st century progressive educator, I believe it's imperative that we exercise decolonizing practices to counter those that have colonized, discredited, and ignored ancient cultural contributions of indigenous peoples who have been stewards of planet Earth for thousands of years. In doing so, we can learn from Pwo’s pedagogy: What is changing? How is it changing? Why is it changing? This is one of the connections between progressive education and ethnomathematics, which is the study of the relationship between culture and mathematics. As a progressive secondary math teacher I continually push myself to study and learn how to apply decolonizing practices to design mathematics teaching and learning that is grounded in culture.
To pursue this work, I find it helpful to draw from the work of Rosa and Orey (2019) who state:
Ethnomathematics opposes a dominant and Eurocentric discourse in mathematics education, which emphasizes the school curricula developed by colonizing countries and imposed on local communities during the process of colonization…the development of an ethnomathematics program can be interpreted, to some extent, as a reaction to the cultural imperialism world-widely spread during the expansion of the Great Navigations in the beginning in the fifteenth century (D’Ambrosio, 1985).
Similar to anthropological approaches to teaching, ethnomathematics (Rosa & Orey, 2019) is based on a sociological framework that teaches the three components of culture: artifacts, mentifacts, and sociofacts (Fantini & Fantini, 1997). Artifacts are tools, or material expressions and manifestation; sociofacts are customs or social expressions that are the axiom of practices; and mentifacts are ideas or concepts, and value expressions that are the axiom of knowledge (Fantini & Fantini, 1997). The sociological framework with the three components of culture is important because historically mathematics education has been Eurocentric (i.e. Greek ‘origins’), whereby Eurocentrism has behaved as a dominant worldview that invalidates the possible significance of other culturalist arguments (Amin, 1989).
So, how did I connect my passion for progressive education and ethnomathematics with my interest in voyaging? As a doctoral student in 2021, I was awarded a travel and research grant to go to Maui. As a part of this research project I volunteered with the PVS under the leadership of Captain Timi Gilliom of the double-hull canoe Mo'okiha O Pi'ilani and an elder Samoan Pwo. Prior to my visit, I had studied math education through a cognitive psychology lens (e.g., human memory), and upon my return from the trip I was inspired to reflect on my own metacognition that occurred both during and after my experiences. I wanted to investigate how I had learned the utmost in those hours with Captain Timi and Pwo, compared to any other educational setting in my recent history. I then realized that two out of three aspects of ‘change’ (what, how, why) were always presented, and flowed into reasoning the third, which then connected itself to another aspect, and so forth–altogether, producing an immense amount of knowledge in a remarkably short period of time given the complexity of the precision engineering being taught as they worked with ropes and the mast.
The impact of this experience was so great that I layered the three components of change (what, how, why) with the three components of culture (artifacts, mentifacts, sociofacts) and generated a reflection framework for the sixth-grade math students that I was working with in my dissertation study. I applied the Pwo’s pedagogy and focused on students’ mathematical understandings of fraction division with an Ethnomathematics/STEM framework. After all, fraction division is a rate of change, just like calculus with the instantaneous speed that voyagers use. For four days, I asked students to individually reflect on the day’s math lesson by asking: What is changing? How is it changing? and Why is it changing? Each day had a different topic (e.g., calculating knots for estimating voyaging speed, etc.).
In my study, I served as both researcher and interventionist (specific to design research methodology). As I taught, I made research notes in my daily reflection log. These notes documented how the student’s responses to the three questions developed in fluency over the four days. For example, the students demonstrated ongoing productivity in the content of their responses as each day passed of the short study. During post-interviews for the study, some of the students mentioned that at first they struggled to understand how they should answer the questions. They then shared that they saw what the pattern meant by the second and third days, and that overall the why question was the most challenging question for them to answer.
Since this particular research study and teaching investigation, the application of this “Pwo pedagogy” has inspired more research on the framework. I am now wondering, how might progressive educators who work with younger children apply this math reflection protocol in classrooms of their own? I also wonder how this Pwo pedagogy may support managing the cognitive load with students studying various subjects by generating the ‘look fors’ when students are learning new materials, about the what, how, and why the dynamics change in various real-world contexts? How can the reflection questions also be used to make interdisciplinary connections between content areas? I recognize that more work is needed to develop this framework. As I move forward in my inquiry, I commit to dedicating the framework to the indigenous perspectives of Pwo’s teachings and Polynesian navigators for their scientific, technological, engineering, and mathematical wisdoms in advancing learning for progressive educators and students everywhere.
The design of the students’ daily reflection log after each Ethnomathematics/STEM lesson.
Works Cited:
Amin, S. (1989). Eurocentrism. Monthly Review Press
D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the learning of Mathematics, 5(1), 44-48.
Fantini, A. E., & Fantini, A. (1997). Artifacts, sociofacts, mentifacts: a sociocultural framework. New ways in teaching culture, 56-59.
Furuto, L., & Phillips, M. (2021). Knowledge and Action for Change Toward the 4th Industrial Revolution Through Professional Practice in Ethnomathematics. Khon Kaen, Thailand 19-22 July 2021.
Hōkūle’a. (n.d.). Moananuiākea: A voyage for oceans, a voyage for Earth, 2023-2027. https://www.hokulea.com/moananuiakea-voyage/
New Zealand History. (2023). Pacific Voyaging and Discovery. Ministry for Culture and Heritage, New Zealand History. https://nzhistory.govt.nz/culture/encounters/polynesian-voyaging
Rosa, M., & Orey, D. C. (2019). Ethnomathematics and the responsible subversion of its pedagogical action: an investigation based on three anthropological approaches. Revista Brasileira de Estudos Pedagógicos, 100, 191-210.
ABOUT THE AUTHOR:
Tejvir Kaur Grewall, PhD is a former high school math and visual arts teacher in Los Angeles Unified School District, and a former Math Coach. She has conducted research nationally and internationally (i.e. Hawai’i, Cuba, Library of Congress, etc.) that focuses on secondary math education, and earned her doctorate in STEM Education, focusing on secondary mathematics education. She taught an Introduction to Teaching course at the University of Nevada, Reno. She completed two B.A. degrees from UC Santa Barbara in Global and International Studies with an emphasis on cultural ideologies of South/East Asia and in Art Studio, and later earned her M.A.Ed from CSU Dominguez Hills in Curriculum and Instruction. Since 2009, she has been a public radio broadcast journalist in educational radio at KPFK 90.7FM with the Pacifica Radio Network station in Los Angeles, which has existed since 1959, and where she was elected annually to chair their Local Station Board from 2013-2015. She is multilingual in English, Spanish, Punjabi, and Hindi. Her passion for education as a tool for liberation encompasses multicultural perspectives, Ethnomath/math/STEM, social justice, visual arts and progressive pedagogies.
