The significance of human actions upon observed global warming patterns is the topic of much debate in the media, politics, and popular culture. In the past sixty years, average winter temperatures in the Arctic region have increased by nearly seven degrees Fahrenheit. Significant change, both qualitative and quantitative, has been observed in the structure of Arctic ice sheets. Some climate models even predict that by 2013 the Arctic region will be entirely free of ice in the summer months. Land that has been frozen solid year-round in the past has now been freed for agriculture. The changes occurring in the Arctic region are stunning and, if climate models are to be believed, likely to continue and perhaps even accelerate in the coming years.
The reasons for these changes remain the subject of intense debate. Some scientists and world leaders are skeptical that human beings can have any real effect on global climate, while others are of the mind that global behavior and attitudes must be immediately changed if catastrophic and irreversible change to our planet is to be avoided. In its attempts to shed light on this question, the scientific community is in general agreement that human society does at least some role in shaping the overall character and future of the Arctic environment. Regardless of the cause the rise in Arctic temperatures is undeniable and significant. Thus while continued investigation into the cause of rising temperatures is critically important to the planning of long-term policies and strategies, it remains only one aspect of a broad spectrum of new issues. Aside from understanding why changes to the Arctic are occurring, attention must be devoted to how to best handle and adapt to the concerns, questions, and possibilities that arise from a new, warmer reality.
The young people of today will inevitably be drawn into the process of adapting to this reality. Global warming, and mankind's response to it, will truly be one of the defining issues of their lives. It is therefore important that young people are exposed to the types of opportunities and challenges that will emerge in the coming years. With climate models predicting continued increases in temperature, the question of how humanity as a whole is to come to terms with a warming world will only become more salient with the passage of time. Far from being confined to any one region, this question will come to dominate all levels of human society in all areas of the globe. Individuals, governments, and global institutions will all have to play a role in adapting - economically, politically, and socially - to an uncertain and precarious future.
Nowhere is new reality more evident than in the Arctic regions. There a population in the millions must witness and grapple daily with the changes brought about by warmer temperatures. Melting permafrost, disruptions in transportation routes, and shifts in animal- and plant-life are only a few indicators of the new reality imposing itself upon traditional modes of existence in the Arctic. As these changes are occurring right now in dramatic fashion, the Arctic offers a focused context in which students can discuss and think critically about some of the pressing dilemmas of our time. Furthermore, an investigation of warming-induced changes in the Arctic can provide students with a meaningful example of how mathematics is used to understand and address real concerns that have an impact on individuals, governments, and environment. In linking mathematics to a problem as vast and complex as global warming, students will be able to understand how mathematics and the many facets of human existence are intertwined. They will come to see mathematics and science as tools to clarifying the future of their generation and the world they will inherit.
This unit will focus on the three major dimensions of global warming as it pertains to the Arctic region: the environmental, the economic, and the geopolitical. Though these three will be considered separately, connections between the three will be reinforced throughout the unit. Breaking up the unit in this way is essential to giving students a solid understanding of the myriad issues that have arisen from global warming. The unit itself will be geared towards geometry students, though elements of the content will likely lend themselves to use in my precalculus classes as well.
Students will be involved in three engineering-related investigations. These activities are meant to strike a balance between reinforcing mathematical concepts and furthering students' understandings of the environmental, economic, and geopolitical issues which underlie this unit. Students will, for example, examine how melting sea ice will impact the routes taken by supertankers on journeys across the world. They will also analyze the mathematics of pumping crude oil through pipes. Concepts utilized in the three-lesson sequence (each lesson will take two 45-minute periods or one 90-minute block) include area, volume, distance/rate/time problems, direct measurement using rulers, analyzing the scale of a map, and converting between units. More detail can be found in the instructional design strategy below.
Care has been taken to ensure that the unit's overall purpose and specific learning objectives align with new mathematics guidelines established as part of the Common Core curriculum overhaul. In keeping with the Common Core emphasis on depth rather than depth, this unit is designed with only the truly core areas of geometric content in mind. Thus emphasis is placed on volume, area, and direct measurement as opposed to the large quantity of small properties and factoids which characterizes so much of the study of geometry. While geometric properties are indeed important, this unit is intended to help students grasp how the main ideas of geometry can be used to visualize, explain, and understand a profoundly important real-world problem.
