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Our World, Our Place, Our Home, Our Responsibility

Our World, Our Place, Our Home, Our Responsibility

Carlos LópezLeiva, Silvia Llamas-Flores, Dee Crescitelli, and Kyndall Brown

Our life experiences can talk to our bodies about how the world is all interconnected. The basic elements of our world speak to us through their embodied constant collaboration or interconnectedness. Take the fire; it grows and moves, dancing with the wind. Feel the water in the rain in synchronous rhythmic movements coordinated by the wind. Admire a little cascade of water that is animated by the capricious shape of the earth and rocks under the water. Their collaboration makes the beauty of the cascades that are decorated by plants that thrive in the context where earth and water collaborate. Take the power of the fire and the earth combined to generate the most beautiful and precious colorful stones. As these collaborations take place to create beauty that we admire and use, they can also work together to change landscapes and keep the earth transforming and evolving. Earth moves, and it is alive! It works as an integrated system. This integrated system is coordinated and developed in many ways, and many of these ways are inherently mathematical.

As previously alluded to (discussed), we are all interconnected. This includes the air, water, fire, earth [and all life therein]. If we truly value all life and act according to this ethos, not only would “[earth] take care of us,” but we would do our part to “take care” of the Earth. Interconnectedness, value, and care toward the Earth and all life on Earth are Indigenous core values. Recently, these values have been referred to as either the 4 Rs (Harris & Wasileski, 2004; Kirkness & Barnhardt, 2001) or 5 Rs (Das & Strong, 2018, November 27; Dow, 2019, Summer; Tessaro et al., 2018). For example, in discussing Indigeneity and its contribution to and challenging of globalization (Harris & Wasileski, 2004), four values were identified from the many conversations by representatives of various Indigenous tribes during meetings facilitated by the Americans for Indian Opportunity, an advocacy organization that promotes self-determination of Indigenous people in the United States. The common values were Relationships, Responsibility, Reciprocity, and Redistribution. Relationships refers to our “kinship… to all living things, animals, plants, and rocks… [and] to the very stuff that stars are made of” (Harris & Wasileski, 2004, p. 4). Similarly, responsibility describes the “obligation… to take care of our relatives” (Harris & Wasileski, 2004, p. 4). Reciprocity describes kinship and obligation as “cyclical” or mutual and not one of “uneven… exchange obligations” (Harris & Wasileski, 2004, p. 5). Lastly, redistribution refers to a sharing obligation or “generosity [as] the most highly valued human quality” (Harris & Wasileski, 2004, p. 5). These 4 Rs broadly describe an ethos or a way of life that is in opposition to individualism, selfishness, the profit-motive, and exploitation of the Earth and its resources. In education settings, how have the 4 or 5 Rs been applied?

In an often-cited study, the 4 Rs were used to critique the lack of responsiveness and cultural sensitivity of indigenous students by the University of Alaska (Kirkness & Barnhardt, 2001). In this context, the 4Rs were Respect, Relevance, Reciprocal Relationships, and Responsibility. In this schooling context, these values referred to the need for faculty and staff of universities and colleges to respect the “cultural integrity” of First nations (Kirkness & Barnhardt, 2001, p. 6) to provide university experiences (content and practices) that are relevant to indigenous students and considerate of indigenous worldview; for faculty to engage in the “give-and-take” (Kirkness & Barnhardt, 2001, p. 13) exchange of knowledge (reciprocity) and learn alongside and even from First nation students; lastly, for faculty and staff to take on the responsibility for supporting Indigenous students to participate in traditional activities and for faculty and staff to attend Indigenous community events, discuss Indigenous worldviews in courses, and/or engage in outreach to Indigenous (tribes) and leaders. In this context, the expectation was for the faculty and staff of the university system to engage in practices that value and “care” for indigenous students.

Similarly, in the context of online professional development for principals of Indigenous schools across Canada (Tessaro et al., 2018), the previously discussed 4 Rs (Kirkness & Barnhardt, 2001) was expanded to 5 Rs. They decided to include Relationships because it “underlies” (Tessaro et al., 2018, p. 139) the 4 Rs. Because these researchers worked with principals, they wanted to make sure they made conscious efforts to “fortify relationships with teachers, students, family members, the local community, and the land.” (Tessaro et al., 2018, p. 139). Another example from education is how the 5 Rs were applied during K-12 science lessons (e.g., climate change, sustainability, flooding) By Judy Dow, an Abenaki basket-weaver and veteran educator (Das & Strong, 2018). In this classroom context, the 5Rs were respect, responsibility, reverence, reciprocity, and relationships. These are moral and ethical values that were passed along to her by family, and her belief was that if students “learn and remember… [these values could help the students] survive the changing world” (Dow, 2019 Summer) as a result of climate change, pollution, and disregard for all life.

So, from these various 4 and 5Rs that are reflective of indigenous core values (Das & Strong, 2018, November 27; Dow, 2019, Summer; Harris & Wasileski, 2004; Kirkness & Barnhardt, 2001), we decided to focus on 4 of these Rs to help us analyze and describe the following mathematics and [science] lessons. The 4 Rs that we will be applying in this blog are relationship, reciprocity, responsibility, and respect. Similarly, we felt it was important to emphasize that we are in “kinship” (Harris & Wasileski, 2004, p. 4) or relationships with all life on Earth to remind us not to engage in “uneven… exchange obligations” (Harris & Wasileski, 2004, p. 5) but ones that are cyclical and examples of a “give-and-take” (Kirkness & Barnhardt, 2001, p. 13) dynamic or reciprocity. Closely related is responsibility. So, not only in relation to life that is mutually positive but also mindful that “we are responsible for our actions” (Dow, 2019 Summer, p. 16) that impacts all life. And in a similar vein, we must respect all life, our “kin” (i.e., human, and non-human). So, guided by these 4 Rs, we will discuss environmental issues and lesson plans that integrate these ideas for teachers and students.

In the months to come, Alerta! will share information and lessons about environmental issues that reference back to the common values (the 4 Rs): Relationships, Responsibility, Reciprocity, and Redistribution. Topics include but are not limited to, air quality, extreme weather events, littering, mining and mountain-top removal, and wildfires.

References

Das, A. & Strong, L (2018, November 27). Abolition Science Praxis Pt. 2 (Judy Dow). Abolition Science Radiohttps://www.abolitionscience.org/home/2018/11/13/abolition-science-praxis-pt-1-judy-dow.

Dow, J (2019, Summer). Going Through the Narrows. Potash Hill, 14-17. https://potash.emerson.edu/sites/default/files/2019/Spring/PotashHill-Spring-2019.pdf.

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Ethnomathematics: Mathematics de TODOS

Ethnomathematics: Mathematics de TODOS

Carlos LópezLeiva, Kyndall Brown, and Silvia Llamas-Flores

Mathematics and daily life activities are connected. For many cultures and societies mathematics is not an isolated field or subject, it is part of an encompassing knowledge or science that helps us understand and work with the world (Cajete, 2000). Mathematics is often taught and practiced at school in ways that are rarely linked to the learners’ experiences and interests, their community, their culture, their histories, and real-life applications. However, we have learned in mathematics education that mathematics is a human endeavor (Jacobs, 1970) present across human civilizations and cultural practices such as, playing, locating, measuring, counting, explaining, and designing and building (Bishop, 1988).

Ethnomathematics is a term introduced by Ubiratàn D’Ambrosio (1991) from Brazil to describe the techniques used to explain, understand, and cope with reality in order to survive across diverse communities. Ethno relates to the members of distinct groups identified by cultural traditions, codes, symbols, myths, and specific ways of reasoning and inferring (D’Ambrosio, 1985). So, ethnomathematics refers to the way that members of various cultural groups mathematize their own reality because it examines how both mathematical ideas and practices are processed and used in daily activities (D’Ambrosio and Rosa, 2017, p. 288). In fact, this approach highlights mathematics as a cultural practice existent in human activity and challenges perspectives that present mathematics mainly as a Western—Roman, Greek—knowledge commonly taught at school. An ethnomathematical approach helps us understand mathematics from a perspective wider than traditional school mathematics, of seeing mathematics as a human act. As a result, such vision can helps renovate how we teach mathematics (Lange,1996; Rosa & D’Ambrosio, 2018).

In mathematics teaching, this approach helps us expand, affirm and redistribute mathematical authorship and empowerment; draw from and expand resources to teach and learn mathematics; recognize and challenge spaces of marginality of knowledges of many communities; and strengthen the relationship between learners and mathematics (Aguirre, Mayfield-Ingram, & Martin, 2013; Kokka, 2015). Such an approach should “perpetuate and foster—to sustain—linguistic, literate, and cultural pluralism that are part of schools” (Paris, 2012, p. 93). Thus, when students and teachers use the real world as a starting point for conceptual development, mathematics teaching and learning become more complex (De Lange, 1996) as they also become doers of mathematics (NCTM, 2000) by engaging in problem solving, multi-modal representations, and communication to develop mathematical meaning making and mathematize through their own perspectives (CCSS-M, 2010; Freudenthal, 1973).

These notes and blog were developed with the goal of sharing available resources around ethnomathematics. Our hope is that mathematics teachers and educators can access and use them as needed. This blog includes three main sections:
1. How is ethnomathematics relevant and critical?
2. What has been learned and done in ethnomathematics?
3. What can be done in the classroom?

We hope you enjoy it, and if you experience some of these or new ideas in your classroom, please share with us here, so more teachers and researchers can learn about what of ethnomathematical approaches can be implemented in the mathematics classroom.

How Is Ethnomathematics Relevant and Critical?

Ethnomathematics presents implications for classroom teachers by asking us to re-examine our beliefs and practices about what counts as legitimate mathematics, how mathematical concepts are to be taught, and how to assess children’s knowledge of mathematics. With these ideas in mind, let’s listen to a conversation between Ubiratàn D’Ambrosio and Paulo Freire as they discuss the relevance of ethnomathematics by its connection with the community thus mediating a culturally-responsive approach of teaching mathematics.

What Has Been Learned and Done in Ethnomathematics?

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