the mayans and math

I decided to spend this blog today digging deeper into the ideas of mathematics from the past. Based on the title of my blog, you can conclude that we will be exploring Mayan Mathematics. While I could have spent my time and words exploring many different histories revolving around mathematics, I decided to explore Mayan Mathematics as a follow-up to a class I took a year and a half ago. In MATH - 222, Math for Elementary Teachers, my professor, Dr. Nancy Mack, introduced Mayan Math, specifically the ideas surrounding their number system, when we were exploring our own number system with base ten blocks. She introduced, but did not give too much insight into the ideas of this ancient civilization, therefore, my interest has been peaked ever sense and here I am today writing about what I found. 

Before we dive into the math, here is a little backstory behind the Mayans. The Mayan civilization was established around 2000 BCE in Central America. They were known for being "one of the most densely populated and culturally dynamic societies in the world" (Mastin). Apart from mathematics, these people were known for several interesting facts. For example, the Mayan society set very interesting standards for physical 

beauty. They found flat foreheads to be attractive, therefore, when babies were born, it was normal to press a board to the babies head to create this culturally ideal flattened surface. The same goes for having cross eyes, therefore, the Mayan's would dangle objects in front of newborns eyes until they became permanently cross eyed. I think we can all agree that Americans have set far different standards about what they consider to be "beauty." Do you think the Mayan's think we are crazy, just as we may think about their qualifications for physical attractiveness? Aside from physical appearance, the Mayan culture took lots of pride in providing excellent medical practices. "Health and medicine among the ancient Maya was a complex blend of mind, body, religion, ritual, and science" (Top 10 Fascinating Facts About The Mayans). Therefore, only a few select would be thoroughly educated to carry the title of "shamans." There are many other fascinating things about this society, but its now time to take a look at the mathematical system they developed. Due to the importance of astronomy and calendar calculations to the Mayan civilization, the development of a mathematical system was not only wanted by absolutely required. The Mayan civilization was very resourceful of what they had. Therefore, they developed a number system using everyday materials that 

surrounded them. To the right, you see a series of symbols. This represents the "vigesimal number system" created by the Mayans themselves (Mastin). What does this mean? Well, "vigesimal" (according to Google) is an adjective related to or based on the number twenty. So, the Mayans developed a number system based on the number 20. It is inferred that the Mayan 

based vigesimal number system off the number of fingers and toes on the individual. As the image depicts, they used a shell to represent the value "0," a dot/stone to represent the value "1," and a stick/horizontal bar to represent the value "5." For larger sequences of numbers, the Mayans used a vertical stick/bar to represent any power of 20. Based on this number system, the Mayans were able to develop calendars as well as make impressive astronomical observations. For example, they were able to use their mathematical system to measure the length of a solar year. The calculation that they found ended up being more accurate than what Europe had calculated. The same results exist for the lunar month, which I find to be quite astounding. 

Why does this matter? 

So, why do we care? Well, I don't know about you, but I find learning a new (and historical mind-you) counting system to be quite valuable as an up and coming teacher. I could see myself introducing this alternative counting system as a way to integrate history and mathematics in the classroom. I found an amazing resource that would not only educate students on the Mayan past, but also navigate them towards perfecting this number system, using the Mayan materials to create the number. Check out a screen shot below...

I can already see my future students eating up a program like this. Learning about a new counting system can only help solidify the ideas revolving around the counting system we use in the United States (base ten). When thinking about my own K-12 education, I rarely recall learning about the "history" behind the subject. I believe that teaching students where the math from today has evolved from is not only informative, but valuable. 
After exploring the Mayan number system, I can finally return to my Final Exam Extra Credit for MATH - 222 and answer the question. Too bad it's a little late to actually get extra credit. ​

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RESOURCES: 
Mastin, Luke. “Mayan Mathematics.” The Story of Mathematics,   www.storyofmathematics.com/mayan.html. Accessed 19 Sept. 2017.
 
“Top 10 Fascinating Facts About The Mayans.” Listverse, 16 June 2014, listverse.com/2009/09/21/top-10-fascinating-facts-about-the-mayans/. Accessed 19 Sept. 2017.

Here is the link to the online "Maya Math Game"