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Navajo Math Circles | Navajo Math Circles

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Navajo Math Circles follows Navajo students in a lively collaboration with mathematicians.

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Link to newsletter integrating Ethnomath into NCTM Standards http://web.nmsu.edu/~pscott/isgem51.htm

Ethnic Studies (OUSD): https://docs.google.com/document/d/1jlmJRffpX3xEq2bpRYNae1-SeNuKiZpusYu95VM80pY/edit?usp=sharing

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Chapter 17: Applications in the Teaching of Mathematics and the Sciences

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Chapter 17: Applications in the Teaching of Mathematics and the Sciences

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Assumed universality of how children develop doesn't jive with Navajo way of learning. What would it sound like to elaborate on Navajo system but integrate western system? (p. 387) "Space is finite bounded and absolute. Everything is contained in a saucer like structure." Big example that could understand: On p.389, number line, distance, numbers are distinct. If things are entangled, cannot describe distance between objects; can give it a quality. Navajo would describe this distance as: teacher has children play with rods, tries to make notion of spacial distance clear. Then made clear with trial and search, objects/sticks/steps, there is someone to explain idea of volumeness. It's relational; maybe volume is interconnected.
3 objectives: (1) teach western system and infuse components of Navajo system. Problematic bc fundamental axioms of each are different. (2) start with Navajo and use western system to elaborate. (3) True integration and still centering Navajo framework: what do we assume are the basics? In western system, start with point and line; everything goes from here. Navajo deals with volumenesses which interact somehow. On practical level, can talk about different ways/assumptions on how we do math.
Author was saying "western way should wait." Are children isolated where western way does wait? It's possible. Are they somewhat entangled at this point?
Colonization is the erasure of people who have those ideas, then appropriation of those ideas for someone else's benefit. "A big part of school math is of African and Asian origin."
Math is disconnected from stories and humans. Rehumanization.
In application part, there was community, culture and experiential learning. Even now in China and India, it's so much memorization; what led to this? Colonization, but is that related to the economics of testing

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Chp 18: Ethnomath approach to Math ed: A matter of political power

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Chp 18: Ethnomath approach to Math ed: A matter of political power

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Chapter 16: Survey of Current of Work in Ethnomathematics

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Chapter 16: Survey of Current of Work in Ethnomathematics

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Been happening since way back in terms of Western doc
Definition of math
different types of math pg. 337 the gestation of new concepts list of bullets
academic math (formal) vs. non academic math (ad hoc)
integration entry points into our own practice - what is new work and what work is left to be done
page 341 market women in mozambique - number talks recognition that people do this - different ways of calculating around the world

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Other Questions/Thoughts (please add on!)

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Other Questions/Thoughts (please add on!)

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How/is there a relationship b/t Ethnic Studies and Restorative Justice? How is this connected to "restoring the relationship with mathematics that has been stolen from [some groups of] ... students," as Crystal Proctor said?

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Target audience-
Ourselves,
Pre-service teachers
In-service teachers
Students

Documenting examples for persuasion
2+2 is not always 4 (sheep are not standard units)

Documenting examples for curriculum
star navigation
familial connections

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- revise math...expand what counts as math (but also get rid of extra stuff)
- decolonized, anti-oppression to see more robust, strength-based lens of our students

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math & ethnic studies was a principle of Radical STEMM that we couldn't really expand on or answer questions about
Wanted to bolster our own understanding and learning
Read ethnomathematics, read rethinking ethnic studies, read rethinking mathematics
Meet with Dr. Jolivette
design learning experience for adults -> attach to CBUW

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- develop/understand examples of ethnomathematics (ex: Ch2, sheep, star charts)...which could be used for student-facing, teacher-facing, etc purposes (so we can use them as tools to speak to)
- MZ: blog post
- identify next chapters

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Co: it's time to revise those statements (referring to non0-literate/primitive people). Revise really resonated. Triggered by non-literate.
Ji: p.35 "while they differ on the geometric form, the writer share their convictions with... god, nature and proper human development." All the way we fundamentally see the world in straight lines where I could see the world in curves.
Ma: the movie The Arrival. Language is so different, once she learns language, she can travel through time. Your understanding of math shapes everything about what you see. If I grew up where math was knots on strings, I would have a different way of thinking of the world. A lot of examples were hard to understand. p.35 "everything the power of the world does in the form of a circle." p.30 "2+2 is not always 4."
Va: 2+2 is not 4 goes back to the sheep (p.29). Shepherd gives a price, 2 sticks of tobacco for one sheep. Sheep are not standardized units so wouldn't sell 2 sheep for the same.
Ce: as we try to shift people's mindsets of what math is, these examples are powerful. 2 pants and 2 jackets is 2 suits. How much context matters for what we consider to be fundamental universal truths.
Co: when Maria was talking about how language affects how we interpret the world, I remember as 1st grader learning how to write numbers in Chinese. Help get place value better. One-point-two doesn't help students understands tenths, hundredths.
Martian math base 7. In Vietnam, 30 minutes mods. Spoken as 15 until, 20 until the hour. New comer students who have different type of calendar than western; in court those calendars aren't recognized, but have to prove by drawing it out. Cases for asylum are having a hard time. Calendar is not just the trip around the. some objective way of time. Corrina's grandma doesn't know what day it is, but knows which festival is coming up.
Ce: Sapiens book: agricultural revolution screwed us. Function of math: broadly across cultures and globe - practice for goods and accounting and having things. Have resistance is so tied to material and ownership

Synthesis: math is only powerful is its in this fake truth objective study. Challenge back what we tend to think of is math. Speaking to mathematicians. Left thinking in terms of PST, want them to read Chp 2? Nice examples in Chp 2.

Other chapters to focus: 3,9,10,12,13,16,18. If I wanted to read half of the book, these would be the chapters. If well versed in Eurocentric math, can skip section 2. What's our purpose? Can we catalog/documents things like familial relationship tables and star charts and make them into something that's more accessible to PST's and IST's? Purpose: to have good knowledge base to speak on ethnomath to move forward, create tools for ourselves. What's output/outlet? This is inspiring blog entry. Do we want to build on this? Publish in particular places? Putting in for conferences?

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Ce: So many different understanding of what math is - ex: teachers in one department in one school. Then layer on level of culture and history. On p.19 idea of particular math practices; Bishop named 6 practices of math across culture. How do ideas in math become cannonized? How do they become considered the way they are? (p.19) How do we expand space of intersection of ethnic studies and math?
Ma: Looking at diagrams. Look at history. Skipping over how everyone has done math conveniently reinforces math is eurocentric. Can LOOK AT Figure 1.2 and how history is present in the picture. "We" don't know our mathematical history whereas ethnic studies focuses on history of marginalized groups.
Ji: Juxtaposition between scholarly and practical math, in some places it's pure math vs applied. Notion: there's something inherently superior with pure math and practical math is not. Histories that have been erased change the way objective mathematics is; ignoring all these other histories but still calling it objective.
Ka: when we're ready to merge, she knows authors of chapters in the new ethnic studies book. Will be in the Bay during May 2-6.
Co: lens of students seeing themselves as sacred - tension experienced in the classroom where principal would say that "you're not at" the right pace to get them to this test. Skills of real life had an impact on students. To get students through gateways meant to work in eurocentric mathematics. If we know it in lived experience and lived practice, how might we use the power to elevate that? Who does pure objective math serve and who has access to that? How does practical definition empower who Freire was talking about?
Together: Ce - we're doing ideological exploration right now and very much thinking about practice. How do we grow this, how do we bleed this into the work we do everyday? The different kinds of mathematics: we have to think about our standards, content and how do we teach that? I'm trying to identify my dream. What would preK-12 look like if we were to embody this? Problem and project based, no grade levels, don't just have the math department and really true collaboration/interdisciplinary for students. Long-term: what would this look like?
Co - everyone touched on an expanded definition of "x" that is a non-Eurocentric definition and the tensions of these definitions.
Ma: So much has been erased already. Like Chicanos have math in their blood chapter in rethinking schools/math. Math has been erased.
Co: Filling in the gaps of our miseducation.

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Sacred teaching/students: systemetize helping students and teachers see more holistic definition of success. S's at continuation school haven't fit in narrow box of definition of success. White supremacy and patriarchy have defined success narrowly. See students in other ways of success. Can build valuing of who they are.
Teacher equity statement: no more bullshit, no more fear, dig deep to understand your why (Myers).
Letter to teacher: Not afraid to push against the curriculum. First, do no harm to the children; then teach math.
Letter to teacher: Show beauty of math but do it in a way without prereq of math. Most powerful thing you taught me was to create conditions for anyone to explore, understand do math withouth prereq.
Sacred teaching/learning: how to weave in humanity of students into work; teachers can take that as an easy out to not do mathematics. Students seeing possibility in themselves.