Teaching Summary: Numbers

Do you want to teach your students about Indigenous languages? Are you looking for a way to introduce students to working with unfamiliar grammars or counting systems?

Overview: This module is an introduction to the number system in Colonial Valley Zapotec. The lesson guides students in understanding a historical explanation of the counting system from reading movable-type printed text, breaking down the text line-by-line, and understanding the mathematical principles involved. Students learn Zapotec words for numbers and are guided through how higher numbers are formed, learning about number systems and bases. This open-access lesson also shows students that Zapotec numbers are spoken today and helps them make connections to their own language.

Grade Level Recommendations: High school and college students

Courses and Units: This module is appropriate for courses such as global studies, Indigenous knowledge and science, linguistics, morphology, and typology.

Time: This module can be taught in approximately 1.5 – 3 hours.

Major Points (by section):

• Colonial Valley Zapotec is a form of Zapotec attested in writing during the Mexican Colonial Period. Zapotec languages are threatened and discriminated against today. This module references a 1578 grammar written about Colonial Valley Zapotec in Tlacochahuaya, credited to Juan de Cordova, though many Zapotec people contributed to it. The book is printed using movable-type and students learn how to understand the letters and symbols in the first few lines of the text. Readers study numbers 1-4 and learn about the different sets of numbers.
• The lesson guides students through the composition of higher numbers in Zapotec. The section shows how numbers are put together using forms from the different sets, as well as words that can be used in bigger numbers to combine the smaller “building blocks”.
• Readers are provided with all words and word parts found in the Zapotec numbers 1-24,000. Exercises allow students to analyze the composition of numbers, practice writing Zapotec numbers, and compare the Zapotec number system to other languages.
• Number systems in the world’s languages use different bases – for example, English uses a base-10 system. The Zapotec counting system has three bases: base-10 for 10-14, base-15 for 15-19, and base-20 for 20 and above. Zapotec shares a system for number representation with other languages in the Mesoamerican cultural area.
• Zapotec numbers are still used today, and students are asked to view a video of them and consider the differences between the modern numbers and the numbers as written in the Colonial period they have viewed previously.

Guiding Questions (by section):

• Building Blocks for Numbers: What do you notice about the way numbers are built, and how is it similar or different to other languages you know?

• Number Systems and Bases: Research the Mesoamerican number representation system using bars and dots – does this reflect the number system and bases you analyzed in this section?
• Zapotec Numbers Today: What similarities and differences are there between numbers spoken today and those written in the Colonial period? What are numbers like in your language, and how do they compare to those in Colonial Valley Zapotec? Search for more examples of Zapotec counting – how do they compare to numbers in Tlacochahuaya?

Definitions: 

• Number system: A system in which numbers are expressed in a particularly language, including the words for the numbers, the linguistic and mathematical structure of those words, and the internal logic of the system as a whole
• Base: in a number system, the base is a number where all numbers greater than the base are ‘built’ upon that value, and powers of that value may have special names

Before teaching this unit: View conference presentations about the creation of Caseidyneën Saën-Learning Together

• Recovering Words, Reclaiming Knowledge, and Building Community: Ticha Conversatorios.
• Caseidyneën Saën: The collaborative creation of open educational materials as a pedagogical practice and act of resistance.
• Read a Zapotec language activist’s reflection on recovering numbers by using the Colonial texts: Recovering knowledge through forgotten words (Lopez 2020)

More resources: 

• “Numbers” – Caseidyneën Saën – Learning Together
• Caseidyneën Saën – Learning Together (full text)
• Further readings on the Mesoamerican number representation system of bars and dots, case studies of Mesoamerican mathematics and a lesson on the Mesoamerican calendar
• Academic articles on Zapotec and digital resources:
  • Considerations in the creation of an electronic database for Colonial Valley Zapotec (Broadwell & Lillehaugen 2013)
  • Ticha: Collaboration with indigenous communities to build digital resources on Zapotec language and history (Broadwell et al. 2020)
• Webseries on current day Valley Zapotec language reclamation efforts: Dizhsa Nabani
• Join in a community: Tweet about this work or read others tweeting about it!  #ZapotecoColonial