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# Week 7: Ethnomathematics

Find an example of what people consider to be "ethnomathematics." Describe it briefly. How can technology help to preserve unique mathematical cultures of different peoples? Should it be done, or is it ultimately better to globalize mathematics into one universal language? Discuss these questions from the point of view of teaching.

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An example of ethnomathematics would be the golen ratio or the Khamitic numeral system. The golden ratio is a universal math that a multitude of various cultures have used and can relate to. It is also prevelant in nature and the physique of the human body. The Khamitic numeral system was one of, if not, the earliest used of a base-10 numeral system. It incorpates algebra from each glyph, called MDW NTR, represented a numerical value and basic addition skills. The people of KMT also used the golden ratio to construct pyramids.

Technology could preserve unique mathematical cultures by presenting the information in a different light. Touch screen technology could be used to develop a cultural math app where you have the ability to construct numbers using archaic number systems. Some cultures that would be highlighted are the Khamitians, Arabic, Roman, Mayan, and Asian. This would allow the information to be engaging while relating it to our current number system.

Ummmm. Yes, technology should preserve unique mathematical cultures. No, it should not be globalized into one language. We should recognize the common thread among mathematics through out the globe and I feel like the measurement system should be globalized. Everyone else should feel free to intepret math how they feel as long as they can prove their conjecture throught mathematical analysis or physical application. The unique mathematical cultures should be preserved due to the fact that each culture contributed to development and beauty of math. We would not have made the advancements of today if it was not for the previous pioneers of math.

Note: KMT (Kemet) is the original name of Egypt.
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http://www.icce2009.ied.edu.hk/pdf/c2/proceedings341-345.pdf

Ethnomathematics is described as  – the mathematics present in the cultural forms of an ethnic group.

Here is a quick summary of activity they did with elementary age students, entitled “Learning fractions by making patterns – An Ethnomathematics based approach.” Kids are taught about fractions by doing tiling. Its tied into South Indian “Kolams. ” which use graph theory ideas and traditional floor patterns that show tessellations. The students have to create patterns with a grid and a toolbox of tiles. When completed they note the different amounts of different tiles used as compared to the whole area tiled. After completing this type of task, the students did very well on their fractions test which they had done poorly on prior to the task.

Technology can easily be utilized here because creating patterns on a computer is very common and fairly simple to do. Children can color coordinate. You could use a spread sheet and have kids start with it being blank . The activity could be using 5 different colors to create a pattern within the spreadsheet. The students would enjoy coming up with their own design and you can absolutely start a get fractions discussion from this! And, they'd be introduced to a spreadsheet. Next, we'd be counting each color, the whole amount of tiles used and how that turns into fractions.

If I wanted to move this into an ethnomathmatic lesson, I’d say I’d talk about something like “subway tile.” Something Americans can relate to…part of our history and plain old excel spreadsheet can even be made to replicate tiles that are sized and shaped more like subway tile.

I really love this idea of relating math concepts to your heritage. I know its always easier for me to learn something if I can find a way to relate to it. Being able to go online and find images and games and examples of so many different historical facts and stories makes the math come to life. If the student may not use this particular math concept, its great to see how their grandfather, or cousin, or neighbor may have used it for something significant.

As far as globalizing math, in order to better communicate research, science, any kind of information and have it in the same format…whether its math or English or whatever, there is something to be said for keeping things consistent. I believe, our ability to be willing to learn a universal language of math globally is important for the us to grow as people. We should share information and solve global issues in a way that remains consistent…without loss during translation. This doesn’t mean we throw away the wonderful languages, maths and traditions we have grown accustomed to. I do so wish that us prideful Americans hadn’t thrown the whole metric system out the window....what were we thinking??

As educators, we have to keep this in mind. Just like incorporating our heritage will help us relate to the math, giving our students an understanding of the global math world that is out there is truly important as well.

• I chuckled about the lack of metric system, because I still struggle with that one even after living in the States for 20 years. The other day I was teaching and I could not remember how many yards are in a mile... 1760, really?

The US has exceptionally interesting educational challenges, because it's a country of greatly many ethnicities - and many different communities. Subway tiles or graffiti (another great ethnomath lesson I've seen) will make a lot of sense to New Yorkers, but rural Southern kids may not have first-hand experiences with those. What you said about people of the world growing through global languages very much applies within the US itself.

I guess you could program the spreadsheet so that students just select the colors of the cells, but the spreadsheet counts the cells of different colors and provides some data analysis for them. Interesting!

• After searching through different articles and websites about ethnomathematics, I kept seeing the name D’Ambrosio come up about being the founder of this mathematical idea connecting culture and history to math. I found an article on an academy of science website about ethnomathematics that included a really interesting quote from D’Ambrosio about using ethnomathematics to unite the world and providing a step towards peace. Here is the link: http://www.science.org.au/nova/073/073key.html . The article also brings up the fact that ethnomathematics is not strictly defined. It can either mean the study of mathematics in each culture group or making mathematics more streamline across different cultural groups, which would unify the subject and also celebrate the differences in each cultural. If all cultures appreciated each other and their differences, then I could see how in the long run, that would provide a good stepping stone to peace between countries.

Here is an example of what I think can be considered ethnomathematics: http://economics.mrdonn.org/money.html. This is a website that explores the concept of money and how it developed and changed over time. It includes the history of money in the US and also about the currency used around the world. I think this is a concept that has differences across the world in the way the money is printed and assigned monetary values. However, it also unites the world in a concept of math that involves currency and counting.

I think it is important for each culture to preserve their unique math culture. From the abacus used in Asia to count and operate with numbers to the different numeric systems across history that have developed into the current number systems today, the history of math is important in order to understand and appreciate the math we use today. I think that it is important to preserve these unique differences in each country’s math history in order to appreciate where different aspects of math came from. However, I do think that there is some universality to math as well. The idea of numbers, counting, money, shapes, and patterns are some concepts that are understood across different languages and cultures. Math is a language that can be universally understood because each culture uses some form of math and the subject is based on numbers, not words. This is why I think it is not only important for cultures to preserve their own unique math history, but also for people to be exposed to and learn about these different cultures in order to gain a better appreciation and understanding of other cultures. That is a job for us teachers to include in our lessons and activities. This will also really appeal to our students that are already in love with history!

• You found an interesting example of using math and math ed to change the world. Some mathematicians frown upon such political applications, and want to keep math pure and abstract. Others embrace this idea.

Money is such an interesting concept. If you look at gift economies and other local and alternative economies, the role of money (if any) there can be really different from Western-type economies. Now people talk about online currencies, game currencies and other tech currencies, such as peer-to-peer Bitcoin: http://bitcoin.org/ Currencies from Second Life and EVE online MMORPG game are convertible to hard currencies, as well. The mathematics of these virtual economies is not quite "ethnomathematics" - but you can research it using similar methods, because virtual worlds have their own cultures.

History adds so much richness to math - to everything!

• I do see why mathematicians would want to keep the subject pure and abstract considering how highly valued it was in history. Math was viewed almost as a religion in some ancient times, so I can see why mathematicians would want to preserve and continue that type of tradition. However, with math being an essential piece to being successful in society, I think it is important to make math relevant to everyday people, who are normally not mathematicians.

I took a look at the Bitcoin video on the website and was amazed! I was not aware of digital currency, but can easily believe that this is where we are headed as we move more and more into the tech savvy future. The thought of a worldwide accepted digital currency is a great example of unifying a mathematical concept.

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Ethnomathematics is the overlap of math and culture. I found this example of a math professor in Hawaii integrating Hawaiian culture and history in her math classes. She uses field studies in her teaching and students learn about math as it relates to topics such as marine biology and astronomy, and how they are related to Hawaiian culture and history.

One way technology can preserve unique cultures is by providing a place to record and access the history. One article I read talked about how when math history is incorporated in instruction, it is usually with a very Eurocentric focus, and it leaves out the contributions and history from non-Western cultures. This can be detrimental for students of color since they won't have the same opportunities to make connections between their history and meaningful mathematics. Technology can give the cultures that have historically been oppressed or ignored a voice, and also give teachers an easy and convenient way to access that information to incorporate it in instruction. I think ethnomathematics is not only important because it tells a history, but also because it gives students diverse opportunities to make connections and find relevance from their individual cultural perspective.

I do like the idea of one universal math language because I think that the bigger and more diverse a group is, the better the results. For the overall field of mathematics, global culture would provide the biggest gains. However, I think it is important to preserve the individual cultural history of mathematics and to allow students the opportunities to explore this. I also think there is a danger in the idea of globalizing mathematics, because all too often in history, "globalization" has really meant Western colonialism. Technology can help in this respect because it provides a platform and a voice for a wide range of people and cultures.

• Katherine, you bring up an issue of race and culture as they interact with history. There are similar issues concerning languages, ethnicities and cultures. For some people, country-language-ethnicity-culture-heritage means one and the same, but all these things can become decoupled. It is fascinating how much of these "extra" meanings a person can bring into their math! Who you are - your identity - determines what you do, to a large extent.

One example I wanted to share with you is the movement of math circles. The original concept came to the US from the Eastern Europe: http://en.wikipedia.org/wiki/Math_circle The subcultures that adopted the idea as their own are academic mathematicians; homeschoolers who do a lot of their work in a similar small group format; and recent immigrants from, naturally, the Eastern Europe, but also India, China and Japan. As an illustration, here is a photo from the front page of the Orange County Math Circle: http://www.ocmathcircle.org/

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Ethnomathematics attempts to customize mathematics instruction to make math relevant to the historical, cultural, and societal characteristics of a particular group of people.  Such customized lessons can be done by appealing to one or all of these characteristics, and in countless ways.  I've always loved beaded jewelry made with 'seed beads', and found a lesson plan (Virtual Bead Loom) that relates Native American beading to mathematics:  http://csdt.rpi.edu/na/loom/index.html.  This site demonstrates how a particular culture used mathematics to create art, and how mathematics influences the aesthetic value of same (students can create virtual designs by using the Cartesian Coordinate System to arrange beads of different colors).  History of North American beadwork is mentioned, and phonetic pronunciations of some Native American tribes known for beadwork are provided.

In this way, the relationship between culture, beading and mathematics is both preserved and distributed; technology (the internet) makes this information readily available to anyone who wants it.  I'm interested in beading, so I actively seek this information.  But, prior to home internet access, I needed to leave the house and spend time at the library, often waiting for inter-library loans to arrive; books and periodicals were the only way to view this art aside from travel, which was not feasible for me.  For me, tech gives accessibility; I think that those involved in ethnomathematics use tech to distribute information to create both acknowledgement and appreciation of their culture.

I personally don't feel that ethnomathematics creates barriers.  I believe that it only increases our learning - we not only learn about the mathematics themselves, but are required to learn about the sociocultural environment in which the mathematics are being applied.  I agree that this approach requires teachers to not only address math, but culture and history.  It's extra work, and may require co-teaching, which might require us to step up our interpersonal skills.  But, all of this extra work only emphasizes the global importance of math and, in today's multicultural society, being able to relate to people from different backgrounds is critical for social, economic, and spiritual happiness.

• Access via tech is an interesting topic to bring up here. We can all become both explorers of one another's cultures, and ambassadors to one another's cultures. I would like to note the shift in access that happened in the last few years, with relatively widespread mobile technology that supports video and image sharing.

For crafts like beading, video means better sharing of techniques and oral stories that carry the techniques. When I do some of the crafts I learned as a kid, like crochet, I can hear voices of people who taught me little stories and rhymes that helped to remember the techniques. An American example is the shoelace rhyme, "Here's a little rabbit, and here's a great big tree, Watch the little rabbit, run around the tree. Out pops his head, to see what he can see, how neat a knot he made around his great big tree."

Because you are interested in social justice, I would like to note that video sharing, in particular, gives another types of access: instant access to events as they unfold. I have seen it used for blended participation in educator conferences, where presenters "came" from another place via their mobile devices, and both online and physical audiences interacted together, in real time, using their phones and laptops. I also took real-time video trips to sites like the student protests during recent Middle East uprisings, or the Occupy Movement demonstrations. It was scary to watch the troops arrive, and then the camera go blank (and to hear the sounds of what was going on) - but someone else would pick up streaming most of the time. Or at least tweet, "Bye, we are all being arrested."

For a more peaceful application of access mobile tech gives and the collaboration it supports, check out the wonderful Noon Day Project where kids measure the Earth together: http://ciese.org/noonday/projectinstructions.html Instead of physically traveling like Erathosthenes did 2000+ years ago, kids use their GPS devices and share data online. Here is Carl Sagan explaining it: http://www.youtube.com/watch?v=0JHEqBLG650

• That was an interesting little video you have linked for this task. Thanks.

• From the different sites and articles I have looked, I get the feeling that there is not one clear definition for ethnomathematics. I have read a few differing ideas, that I think are linked to whether or not the person agrees with or likes the idea behind it. I believe that ethnomathematics is a way of honoring and learning the history of mathematics: the ways in which different cultures used and taught math. Today, math is a universal language. The symbols and short hands we use in proofs and teaching are the same everywhere. However, this was not always the case. Different cultures had different ways of doing math centuries before proofs. I remember in one math class a professor telling us of an algebraic proof that was credited to one man but if you look decades before another had solved the proof but for whatever reason it went unpublished so he did not get the credit of the writing of the proof. However, there is rich history here. Perhaps there was a flaw in his proof that he could not find. It would be fun as a teacher to see if my students could find such a flaw and try to fix it. I think the history of math should absolutely be taught. We teach the history of language, science, the world, why not math? If math is the universal language that ties us all together, why not learn how it came about. How were things discovered and proved.

I think technology would be an asset to teaching different cultural differences in mathematics. We talked before about virtual field trips. This would be an excellent opportunity to plan and implement one. It would be time consuming, costly, and nearly impossible to travel to different parts of the world to teach our students about culturally rich math. However it would only take time and imagination to go on a virtual field trip to these worldly destinations. I think that learning the history of math might inspire some students to really take an interest in math. Kids that love history will flourish with an opportunity to look into the history of math. They could make connections to other parts of history and perhaps bring more to the table than we anticipate as the teacher. It could surprise us.

I do like the universalality of math currently. (I know that is not a word but I think you know what I mean.) When I did my senior capstone at Arcadia, I had to read several math papers (which for those of you that have not read one, seem to be written in a secret language that only other mathematicians know) and even ones written in another language, I could use the proofs because the numbers and symbols were the same that I am used to. However, I do like the knowledge of other cultures and their math and how they use. It is fun to gain this knowledge in my opinion.

• Glad you liked the video, Meagan! Looks intriguing, doesn't it?

From what you wrote, history seems to be one of the keys to preserving ethnomathematics, and also to the value other cultures can derive from it.

The modern math language used, say, at international conferences is pretty universal. As in your examples, you can follow math papers even in languages you don't know. I have a book on trigonometry through origami, in Japanese, and I can follow most of its trigonometry without knowing any Japanese. However, notation not entirely universal. If you try to publish articles even in other English-speaking countries like Australia, you will find different requirements for notations! Paul Libbrecht has a project collecting modern math notations of the world: http://wiki.math-bridge.org/display/ntns/Home For example, here are symbols for intervals open on the left and closed on the right, taken from Dutch, UK and German textbooks:

US teachers are likely to encounter this issue with first-generation immigrant students.