Mayans and Tigers and Bears, OH MY!

Week 2

A great article from nctm.org explores the difficulty young students have with understanding the base ten place values system in the Hindu-Arabic number system.  The article first gives some informative, but startling statistics.  A study referenced in the article states that of the first graders in their sample group, none of them identified that the 1  in 16 corresponded with a physical representation of ten ones.  That number only went up to 50 percent by the fourth grade.  The authors of the article decided to explore place values using the Mayan and Egyptian number systems, rather then Hindu-Arabic.  Their theory was that students would more easily understand place values using a different number system from their own.

Egyptian numbering is complicated, it is a series of symbols that I can't insert in this blog.  The system is the same base-ten that Hindu-Arabic uses, but each tens position is represented by a different symbol.  The ones position is a vertical line (that looks like a one), tens are represented by an arch (upside down U), hundreds are represented by a twisted rope (looks like the letter P) and finally thousands are represented by a flower.  Students were given the task of writing numbers using these symbols.  As you can imagine, writing 101 was much easier then writing the number 9, which was just a series of nine ones.  Students agreed with the authors that the Hindu-Arabic way of writing was much easier and more efficient.  Students were asked to perform an exercise where they thought of "mystery numbers" and had to decipher each others numbers.  When asked to write the number 248, students found it took 14 symbols using the Egyptian number system.

The Mayan number system uses a base-twenty system, so every number up to 20 is designated by a different set of dots and lines (check out figure 2 in the article).

(check out the video below)

This system required fewer symbols, but position of the dots was vital.  In order for the Mayans to differentiate the number six and 120 (both would be a dot with a line under it) the Mayans would place a clam symbol under the number symbol to signify that it was the ones position and not twenty.  Students understood the importance of zero's in the Hindu-Arabic number system after attempting to write numbers in both the Mayan and Egyptian number systems. 

The article concluded with a great geography exercise, having students identify the locals where Hindu-Arabic, Mayan and Egyptian originated.  The students were already aware that Hindu was from India, but needed assistance finding the Arabian Peninsula and needed to be guided to the location of the Mayans.  This interdisciplinary approach to math enforces both topics and makes it interesting for students and teachers.