DISCOVERING BOLIVIA THROUGH MATH

By Claudia Rodas, Ph.D.

American Cooperative School of La Paz

What is the first thing that comes to your mind when someone talks about Bolivia? Some of you might say, altitude! And yes! Bolivia is located high up in the heart of South America. In La Paz, you have to be prepared for about 4000 meters above sea level.

Now, imagine a classroom full of middle schoolers when their math teacher tells them to combine the culture, geography and diversity of a beautiful country with mathematics. Picture a middle school math project that not only displays numbers on a page, but also brings a more tangible resource, which is a unique country with vibrant landscapes providing a good opportunity to showcase math skills.

By incorporating geography into a math project that not only provides scale drawing and basic geometry concepts like surface area and perimeter, we as educators can promote student engagement through the curiosity and excitement of discovering a South American gem.

The Uniqueness of Bolivia

Bolivia has countless places where visitors are amazed by the vast cultural diversity, stunning landscapes, and rich history stretching from the Andes mountains to the Amazon rainforest. One of the highest cities in the world and the largest salt flat in the world are just some of the gifts that Bolivia offers the world.

La Paz is actually two adjacent cities high in the Andes mountains: La Paz and El Alto. The latter is the higher of the two, rising to around 4,000 meters with La Paz sitting 400 meters lower.  And yes, the difference in the altitude is wild! One of the key tourist attractions linking these two cities is the cable car system, with its 10 lines spanning across La Paz, transporting 300,000 people daily. Since 2014, it has become an integral part of daily transportation for Paceños (residents of La Paz). 

Not many people know El Alto, but it is one of the youngest and most populous cities in Bolivia. It is a melting pot of a city where modern and ancient mix like no other place. It has provided great wealth to many families, and the new Bourgeoisie class of El Alto shows off their new prosperity through luxurious parties at their new vibrant, futuristic mansions (cholets). Cholets offer a new way of building houses through which a large marginalized population demonstrate its way of living. 

Traveling 410 km to the south, the largest salt flat in the world is located in the community of Uyuni. This is the legacy of a prehistoric lake that went dry, leaving behind a salt desert with rock formations and cacti-studded islands that goes on for about 11,000 km^2. This place captivates all who experience it with its unique habitat for pink flamingos. The Uyuni salt flats attract many tourists who stay in hotels made of salt. In these hotels, every single item is made of salt.

Do you think there are many reasons to combine such beautiful geography together with a math project? I believe there are enough reasons to start a project where a student can show their math skills in a different perspective.

A Global Classroom Experience

Introducing a real-world math project can create curiosity in the minds of students and can lead to a more engaging learning experience. The project introduces a model that can cover scale drawing, basic geometric forms, measurements (perimeter, area, surface area and volume) while using the student imagination creativity to discover the beauty of 3 tourist attractions.  In this case, the cable cars (telefericos), cholets, and the salt flats.

The Math Behind the Model

The project includes assessments based on grade level, age, and interest. The 6th grade project presents the design of a 3D model that is created using a cereal box wrapped with white paper where students create their own cholets demonstrating the Aymara style; a complex series of stepped ornamentation, made famous by indigenous artist, Freddy Mamani. Students need to know the area of each of the shapes required to build the cholets, and afterwards students must calculate the surface area and volume. 

The 7th grade project takes things one step further, requiring students to use their skills in “Minecraft Education”, an online game made up of blocks that prepares students for the future, building creativity, problem solving, and systems thinking, and nurturing a passion for design. Students must design the cabin of one of the cable cars in La Paz using the actual shape of the cabin. Students can demonstrate their learning by providing the surface area and volume of any extra element of the cable car, the stations, or even the surrounding mountains.

Last but definitely not least, the 8th grade project required some STEAM motivation by bringing art into play. Students had to design a spa/hotel built in the Uyuni salt flats using shapes like spheres, prisms, and pyramids to construct a 3D model showing the interior of the spa/hotel, as well as the landscape of the salt flats. Students use scale measurements creating proportional models, ensuring that the calculations are accurate, reinforcing the targets of ratio and proportion which are assessed in middle school.

A Celebration of Learning in a Math Class

Constructing different models of different tourist attractions in Bolivia is not only an educational exercise, but it is also a celebration of learning that makes a connection to our surroundings in Bolivia and makes for a more meaningful understanding of the real-world around them. It shows how math can be used to understand traditions, to understand cultural ways of living, and display the diversity of a country making education a truly enriching experience.

As students work on this project, not only will they enrich their math learning and their creativity skills, but they also develop a sense of appreciation of the world beyond their classroom, making math more tangible thus opening a world of possibilities, exploration and creativity.

About the Author:

Claudia Rodas holds a Bachelor's degree in Biochemistry and earned a scholarship to pursue her doctoral studies in Gothenburg, Sweden. She completed her Ph.D. in Clinical Microbiology at the University of Gothenburg and subsequently worked for a year in Malmö before returning to her home country, Bolivia. There, she began teaching as a lecturer at the public university and joined the American Cooperative School in La Paz as a chemistry tutor. She was later appointed as a Biology teacher and eventually transitioned into middle school mathematics, where she has been teaching for over a decade. With 12 years of experience in education, Claudia has also been actively involved in student life, serving in various roles such as Student Council (StuCo) advisor, Green Team coordinator, and cooking class instructor. She currently serves as the Head of the Mathematics Department. In addition to her work in education, Claudia has authored five peer-reviewed publications in the field of Clinical Microbiology.