Introduction/Rationale

**Still in draft form**

This project was born out of a desire to create something meaningful for students, while combining my seemingly disjointed interests and experiences. My formal education includes the study of history, mathematics, and secondary education and my mathematics teaching career has taken me to the Navajo Nation; Albuquerque, NM; Colombia; and now, New Zealand. Each of these experiences has pushed me to think differently about what education could, and should, be for teachers and students. Although I love teaching math (or maths), I have increasingly seen a need among my students and within myself to connect to the world outside of the classroom. For me, this has meant exploring the outdoors by bike, foot, or ski and seeking opportunities to travel. These experiences have taught me lessons I could never learn from a book, though material I learned in the classroom has often provided the initial spark to embark on the next adventure. One thing that has become very apparent is math’s usefulness for communicating across cultures. Students in Colombia were able to communicate their work to me despite the language barrier we experienced due to a lack of mastery of each other’s languages.

Before going further with the idea of math being a language for international cooperation, it is important to acknowledge that mathematics breaks down into the worlds of pure and applied mathematics. Pure mathematicians ask questions and then pursue them to their logical end, caring little about application. Applied mathematicians care more about the applications of mathematics rather than why the techniques work. Fortunately, there is a place for both in this world and their work is often complementary, though the benefits of pure math research may take centuries to present itself. For example, modern cryptography is based on number theory research from centuries ago. The inventors of that math were trying to satisfy their own curiosity, obviously unable to envision applications in a field that did not yet exist. Regardless, modern society and online banking have benefited from the work of applied mathematicians putting this pure work to use in the modern world. Furthermore, the field of GIS still relies on the Pythagorean Theorem, one of math’s oldest, and most famous, theorems. Pythagoras and his followers were not interested in the applications of their theorem, but were impressed by its beauty, though it was also the source of much distress once they realized it could produce irrational numbers such as the square root of two. But this is a story for another time. Right now, this project is based on the assumption that students deserve the chance to experience both branches and pursue the one that piques their curiosity.

As globalization continues unabated, cooperation among nations becomes essential to solving the resulting issues such as climate change and environmental degradation. My students will inherit these issues, but too often they are told they must wait to engage with them until they graduate. With this project, I am arguing that public schools have the opportunity to demonstrate their relevance to the twenty-first century by guiding students on how to act as global citizens addressing pressing global issues. They can be taught to think global, but act local. I went to New Zealand to interact with lead authors on the Intergovernmental Panel on Climate Change (IPCC) because I wanted to know how to bring mathematical modeling of climate change into the classroom. At the end of the day, despite their prominence on the world stage guiding international policy, these authors recognize the need to ensure New Zealand is meeting its climate goals. These scientists are thinking global, but acting local.

Unfortunately, beyond some very simplistic models, the mathematics these scientists were using was often at the level of advanced statistics and differential equations. In other words, mathematics beyond the reach of secondary students. Thankfully, my research introduced me to the fields of science communication and geographic information systems (GIS). While science communication has shown the importance of being able to adapt content to one’s audience, GIS has proven to be a goldmine of interesting mathematical questions accessible to my students. Better yet, GIS is actively used by organizations like the National Forest Service (NFS), National Park Service (NPS), National Aeronautics and Space Agency (NASA), Jet Propulsion Lab (JPL), IPCC, and National Geographic. This means there is an opportunity  for students to produce mathematical research that can be presented to audiences made up of professionals from these organizations. Ultimately, students gain a sense of who they are and who they want to be through a combination of formal education, experience, and access to role models. Thus, this project is as much about self-discovery as mathematics.

I would like to close this introduction with a thought on human exploration. For most of human history, exploration meant journeying across oceans and lands nobody you knew had ever seen with the real possibility that you may never return. But today, most of human exploration is conducted by robots and satellites. Although space is the final frontier, robots have been able to do the exploring for us since the 1970s. So although we constantly need more individuals capable of improving these satellites and robots, there is no longer a need to risk human lives to explore the moon or Mars. Which leads to the question: what is the role of humans in exploration now? Thankfully, a quick search on Google Earth shows us that satellites can capture moments in time, but the environment is always changing, therefore we need individuals to, for example, stay at permafrost stations in the far north to conduct continuous observations. Furthermore, the Earth will not always be habitable, therefore it will be necessary to learn how to put humans on other planets to not just visit, but establish homes. And finally, beyond physical exploration, humans have the ability to search for abstract truths through the arts, humanities, mathematics, and sciences. Maybe this last point is most important because it means humans will always be relevant through their ability to imagine futures that do not yet exist. This is what I hope to instill in students. Thanks for joining me on this journey!