MAA Focus October/November 2012 : Page 14

14 | Math Students Go into the World Internationalizing the Mathematics Curriculum with the Calculus of Sustainability By Tracy Bibelnieks, Mark Lester, John Zobitz Photographs by Stephen Geffre E very semester when advising students we (which throughout this article refers to Tracy and John) have encouraged our math majors to consider an interna-tional education experience. To our chagrin, the students inevitably balked. Their reasons ranged from meeting requirements for double majors to concerns about miss-ing required courses to language barriers. Knowing from our own undergraduate programs how transformative an international experience can be, we saw the situation as a personal challenge. We were determined to combine inter-national education and mathematics. approved to the trip. This may seem like an inordinate amount of time, but it was necessary to finalize all the trip details. John worked on designing a project for the inter-national education experience that incorporated calculus concepts. Educational goals included constructing a math-ematical model from intuition, incorporating eyewitness At Augsburg College, faculty can submit proposals for in-ternational education trips. After initial conversations with the Center for Global Education, an international educa-tion office located at Augsburg, we proposed a spring-break international experience embedded into a calculus II course. We outlined a week in Nicaragua investigating sustainable agriculture and coffee production as our focus. The proposal was accepted. Overall, there was strong stu-dent interest in the program, and we were excited to lead the trip. While the idea of pairing international travel with calculus II seemed odd, this format was the most ideal: calculus II has a broader audience of mathematics and natural science majors, and the trip would occur during a time that wouldn’t conflict with research and internships. As a large portion of students in calculus II are second-semester first-year students, we saw this travel opportunity as a starting experience for them to develop an interest in global citizenship. We had eighteen months from the time the proposal was  0$$)2&86v2&72%(5129(0%(5
vPDDRUJSXEVIRFXVKWPO (Left) White cliffs surround the area the class visited in northern Nicaragua. (Above) Coffee, which was just starting to flower, is the main cash crop for the farmers in the co-op. (Insett) Some ripe beans left over from the last harvest. knowledge, and analyzing collected data. We would expect students to communicate project results to the local com-munity. During the planning stage, we conducted extensive recruiting sessions making the target audience—calculus I students—aware of this opportunity. Unfortunately, we had few applications. We attributed this to both the cost of the trip and the sense that students felt they “could do study abroad later.” It became clear, however, that upper-level mathematics students were extremely interested in signing up for the experience. We modified the structure of the course so that upper-level students could participate. Seven students registered for the trip. Two were concurrently enrolled in calculus II. The remainder were advanced mathematics students, most of whom were pursuing double majors with physics, chemistry, or computer science. We met as a class every other week during the semester.

Math Students Go into the World

Tracy Bibelnieks, Mark Lester, John Zobitz

<br /> Every semester when advising students we (which throughout this article refers to Tracy and John) have encouraged our math majors to consider an international education experience. To our chagrin, the students inevitably balked. Their reasons ranged from meeting requirements for double majors to concerns about missing required courses to language barriers. Knowing from our own undergraduate programs how transformative an international experience can be, we saw the situation as a personal challenge. We were determined to combine international education and mathematics.<br /> <br /> At Augsburg College, faculty can submit proposals for international education trips. After initial conversations with the Center for Global Education, an international education office located at Augsburg, we proposed a springbreak international experience embedded into a calculus II course. We outlined a week in Nicaragua investigating sustainable agriculture and coffee production as our focus. The proposal was accepted. Overall, there was strong student interest in the program, and we were excited to lead the trip.<br /> <br /> While the idea of pairing international travel with calculus II seemed odd, this format was the most ideal: calculus II has a broader audience of mathematics and natural science majors, and the trip would occur during a time that wouldn’t conflict with research and internships. As a large portion of students in calculus II are second-semester first-year students, we saw this travel opportunity as a starting experience for them to develop an interest in global citizenship.<br /> <br /> We had eighteen months from the time the proposal was approved to the trip. This may seem like an inordinate amount of time, but it was necessary to finalize all the trip details. John worked on designing a project for the international education experience that incorporated calculus concepts. Educational goals included constructing a mathematical model from intuition, incorporating eyewitness knowledge, and analyzing collected data. We would expect students to communicate project results to the local community.<br /> <br /> During the planning stage, we conducted extensive recruiting sessions making the target audience—calculus I students—aware of this opportunity. Unfortunately, we had few applications. We attributed this to both the cost of the trip and the sense that students felt they “could do study abroad later.”<br /> <br /> It became clear, however, that upper-level mathematics students were extremely interested in signing up for the experience. We modified the structure of the course so that upper-level students could participate. Seven students registered for the trip. Two were concurrently enrolled in calculus II. The remainder were advanced mathematics students, most of whom were pursuing double majors with physics, chemistry, or computer science.<br /> <br /> We met as a class every other week during the semester.<br /> <br /> During these meetings, students formed teams and were responsible for developing a project they could investigate during the trip. Project topics were to investigate various mathematical models of coffee production, greenhouse gas emissions from that production, and economic markets and market factors of coffee production and trade. Tracy and John helped to refine mathematical content as the projects developed. We had frequent communication with Mark Lester, the director of the Center for Global Education in Nicaragua, using Skype and email. He is based in Managua and arranged the preliminary schedule of the trip. Faculty from the Research and Development Institute at the Central American University in Nicaragua enthusiastically answered student questions.<br /> <br /> Our travel experience included touring Granada, a historic colonial city, and a visit to an artisan community. The majority of the time was spent in the GARBO Coffee Cooperative, located in Peñas Blancas in northern Nicaragua. This area has beautiful white cliffs that are surrounded by local, family-owned coffee farms. In 2000 the cooperative was formed to gain better access to the coffee market. In the 2011–12 cycle, this cooperative produced 86,725 pounds of export-grade-quality coffee for the world market. It has certification from FLO-Cert, one of the fair-trade certifiers in Latin America.<br /> <br /> Although the area has a stunningly gorgeous setting, it is relatively unknown to tourists. Because of large price and demand fluctuations in the global coffee market, the cooperative would like to expand its outreach to develop a more sustainable income. At the same time it is also looking to incorporate more women and youth as members.<br /> <br /> One option it is exploring for achieving both objectives is farm-based eco-tourism, which would involve mostly the women in preparing the rooms and the food for the guests. Students and faculty were paired with different host families, and in addition to providing breakfast and dinner in their homes, the women took turns preparing lunch for the group as a whole. Class was held at a central building for community meetings. Our group served as a trial run for hosting groups at the cooperative.<br /> <br /> After the first few days at the GARBO Coffee Cooperative and touring a coffee plantation, we realized that we had defined sustainability academically in terms of ecological footprints and carbon emissions.<br /> <br /> The cooperative, however, would describe sustainability as maintaining the people’s livelihood, including retaining their property, continuing coffee production, and meeting basic needs of living. After meetings with cooperative members, it was clear that we needed a model to examine sustainable ways to ensure additional revenue streams to supplement income gained from the coffee harvest.<br /> <br /> Our daily schedule at the cooperative included “math boot camp.” At these sessions John and Tracy examined with the students a bioeconomic model of rural community tourism. Both of us are trained as applied mathematicians and have solid experience with such models. The students examined all the costs and revenue associated with hosting foreign visitors. We met with cooperative members to understand how they prepared for visitors and the prices of basic goods (food, toiletries, and other amenities). Our calculations showed that the cost to host a visitor for one night is equivalent to the daily wages for a coffee farmer.<br /> <br /> On the final day, our group gave a professional presentation to the community outlining the recommendations for enhancing the tourist experience and opportunities for future investments. Our recommendations included signage for self-guided tours through the farms and investment in amenities such as mattresses. We also recommended modifying the price structure for the guests to favor longer stays at a lower daily rate. Our analysis indicated the costs of these enhancements could be offset by charging a slightly higher price for the guests. The presentation was a highlight of the trip, as students communicated their results in a nonacademic setting.<br /> <br /> As an aside, we found that language barriers are not a problem for intercultural communication and learning. Only two students of the trip were comfortable Spanish speakers, but most students thoroughly enjoyed the homestays.<br /> <br /> Our visit and presentation made an impact on the local community. The cooperative has sponsored workshops on implementing our suggestions. Because of the significant role that women have to play in hosting visitors (which was an aspect of our presentation), they have been given a bigger role in the cooperative’s decision making. There is training for using social media sites to advertise the cooperative. Plus, we see the opportunity for a sustained relationship with the local cooperative. We plan to further develop the bioeconomic model. We hope to take another student group. We are also seeking connections with other departments (such as economics, marketing, biology, environmental studies) that could also contribute to the local cooperative.<br /> <br /> In summary, engagement in this international education experience has been a highlight of our careers. We encourage you to consider integrating international education experiences into your curriculum. Our recommendation is to keep the design flexible enough to handle surprises, such as when we realized we needed to redefine “sustainable.”

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