Energy, Climate, Environment

Strategies

The most important thing to have in mind about using environmental context is that it is exceptionally scalable. As teachers we can make many different adaptations to our instruction of math, and we can make them short-and-sweet or deep-and-embedded. We can use a little or a lot of context, and it may make more sense to do one or the other at specific times.

For instance, at a very basic level, we can validate a lesson full of raw skills practice in calculating the area of polygons by providing one example that briefly references human expansion into forests. On the other end of the spectrum, we could assign a long-term project in which students continuously develop geometry skills by modeling urbanization and deforestation of a region of the earth (e.g. Irian Jaya, the Indonesian state on the island of New Guinea). So, there are many ways in which, and "levels" at which, climate change issues can be added to instruction, or used as organizing themes, to make math lessons more meaningful for students. To keep this manageable, I focus on three levels - simply referred to as low, middle, and high.

Levels of Environmental Context

The first, low level of environmental context is to provide simple, limited reference to an issue that falls within the broad realm of climate change. Examples might include representing the exponential growth or decay of a species population in equation form, graphing the rate of change in crop yields for a given region, or calculating the average number of commuters per vehicle entering the downtown area of your city during a weekday morning rush hour from given information on the estimates of automobile, bus, and other traffic. These contexts, while valid, merely give a backdrop to the raw mathematics skills that students are developing within the curriculum. They might be employed in warm up exercises to quickly set a tone of environmental context or be used to build up a basis of tangibility in specific moments anywhere throughout a lesson. To maintain their integrity, these contexts should be drawn from real data as much as possible, and creating overly contrived scenarios should be avoided.

The next, middle level that can be employed might take on many appearances. Short reading excerpts from scientific journals, or articles of environmental interest from the local newspaper, might be used to broach a mathematical concept and/or skill set that the class will focus on that day. Video clips of research activities in progress may serve an identical purpose. More significantly, a sequence of word problems might be written to use the numeric data from an environmental contextual source in order to practice skills, and the context referred to continually throughout the tasks that comprise the lesson. This context can also be referred back to as a reflection of "what do these numbers mean?" when the computations and other tasks are completed to provide numeric results.

Providing problem scenarios that require students to creatively apply mathematics skills to find solutions may necessitate the inclusion of more writing exercises. Such writing can effectively be placed in advance of, in parallel with, or following after students' application of math skills (as I mention above in reference to facilitating the teacher's assessment of objectives). Student writing may also fit in at multiple points throughout coursework, with reference to and building from their earlier observations of math skills practice.

Expanding the role of organized group discussion at this moderate level will also strengthen students' conceptualization of the connectivity between the mathematics skill set they are practicing and the given environmental context that is being implemented. Such discussion can be used in both small and whole class arrangements, with serious thought toward the objectives of improving students' skill application and decision making relative to which skills are best to apply in a given situation.

The final, high level of context is something that I envision as a project-based series of activities. The overarching structure of such projects (the format and actual skills applied) may rely heavily on which of many environmental subjects are providing the context. The timing of introducing this high level, robust context is very important. It is imperative that the content works with students' prior knowledge as well as with the current curricular priorities. In general, I would make any such project-based course work inclusive of a series of readings, discussions, and mathematics skills application based on real data from the chosen context. A project will be more valid for students' learning if it involves ongoing data collection, communication, and management on the part of students themselves - to the end that they actually discuss and document findings in their own words. ¹⁶ Ideally projects can also include high level features such as field studies and guest experts, who can give anecdotal and practical examples of how they use mathematics skills in their fields.

The choice of context level may depend more on student preparedness and prior achievement, or more on the content to which the context will be applied. The best implementations of environmental context to a mathematics course will incorporate some composition of all three levels. From the outset of a math course, an understanding should be established, that the students and the teacher are working together toward a valid and meaningful set of educational objectives. As the course progresses, day-to-day lessons can regularly use low and moderate levels of context to relate all of the different, and seemingly disparate, skills and concepts of the course toward some central environmental theme (this is key because a single math curriculum can contain a wide range of concepts and skills). A high-level project structured over these daily activities can provide continuity between subtopics of the given curriculum so that students can see how the many different math skills they learn within a course are actually linked to one another. In this way, the context works symbiotically with content.

Before truly bringing any level of environmental contexts to my mathematics instruction, I have to first face one serious reality check. In the Pittsburgh Public Schools, mathematics curricula have come to contain increasingly scripted materials, which math teachers are mandated to follow on a strict basis. As this is also the case for many of my colleagues, the guidelines to adapt lessons that I have developed above require some creative manipulation. The key to this for my purposes will be the direct variation of levels of context to scripted materials.

I will use low level contexts to build some validity into the math exercises and activities that my curricula mandate and most thoroughly script. In this way it is possible to remain compliant with district guidelines and still provide the urgent engagement in real application for students. In the instances where the curricula expressly give the teacher options to choose problem sets or sections of the course textbook to draw assignments from, I will use middle level contexts to fortify validity in my students' skill practice and reflective exercises. Middle level contexts can also add a dimension of legitimacy to my teacher created assessments, such as periodic quizzes and take home assignments that contribute significantly to measuring students' independent proficiency at applying math skills. I see the greatest opportunity for high level contexts, again, in multi-part projects that tie together the various skills that sum up to a course.

Choosing Valid Environmental Contexts

As to choice of environmental contexts, a teacher should look to her or his own interests as well as the interests of the students. In making choices of context that are most specifically valid, a holistic consideration of the school, community, and city can inform the process very well. Our choice of context for mathematics can actually be guided by a metaphorical consideration of the principles of green design. With a nod to Frank Lloyd Wright's architectural philosophy of using local, indigenous materials in building, I recommend favoring the use of environmental context that is immediately visible and accessible for students. It is largely to the discretion of individual teachers to interpret the "environment" of their city just as much as the curriculum of their course. It is also important to be cautious because the first interest of the teacher may not always be the "greenest choice for development" in developing lessons.

For instance, I would personally love to focus context on wind and solar power as the future of renewable energy sources, however, significant examples of these technologies are largely lacking in the urban environment of Pittsburgh. Wind and solar technologies will most certainly enter in my use of low-level context, but for the sake of moderate to higher-level problem solving I will guide my students to work with topics that they can "reach out and touch" on an experiential level. Given my surroundings in Pittsburgh this will include two major topical foci: air quality and green building.

Pittsburgh is historically associated with rust belt pollution and has gained infamy in the last year with a worst national air quality ranking for short-term (daily levels) particulate matter, and a second worst national ranking for long-term (annual levels) particulate matter from the American Lung Association. ¹⁷ This situation is all the worse for my particular school because it is based in our downtown area, amid the exhaust of two interstate highways and several other major traffic routes. However the real story of our air quality is highly impacted by coal burning power plants to the west of the city. The small particle pollution, PM 2.5, which is emitted from their smoke stacks wafts for miles, over relatively flat land, to converge in the steep river valleys that form the primary topography of Pittsburgh. ¹⁸ Many mathematical principles and skills of the math courses that I teach will be applicable to this context.

On a more progressive note, there are several opportunities to implement the environmental context of intelligent design and green building in Pittsburgh. Immediately adjacent to my school is the LEED Gold certified Pittsburgh Convention Center. In our urban center we also have the Pittsburgh Children's Museum and the national headquarters of PNC (Pittsburgh National Corporation) Bank, each of which is LEED certified and may offer models for students to study the relevance of logical argument and geometric principles in green architecture. Also, as of late July 2009 the Pittsburgh City Council is holding votes on implementing LEED standards on all new construction and development within the city. Even more compelling than all of these contextual resources is the fact that my school is currently undergoing the final phases of major renovation for the 2009/2010 school year - making it possible for my students to observe our own school building through the lens of environmental health and green construction.

These two topics are the best starting point for me. The best opportunities for other teachers, in either other Pittsburgh schools or other cities, may well be different. For instance, some school districts, or individual buildings, may have visible solar arrays and in a variety of places around the nation wind farms have become prominent. In these cases there is every reason to create context around these technologies and to organize valid mathematical exercises around these observable structures and industries. In areas with significant agriculture a focus on the use of pesticides, herbicides, and fungicides may be more appropriate environmental context for math teachers. In areas where significant construction is ongoing, where alternate forms of transportation exist, or where other specific industries are prevalent, different choices should probably be made to offer the most valid and immediate contexts for students.

Of course there are also ubiquitous contexts that will work in most any American city to create connections between mathematics studies and the environment for students. Water use, electrical infrastructure, the materials science and life cycle of consumer products, food distribution, and many other environmental contexts are common frameworks for any of us to teach mathematics from. There are also social climate change issues, as alluded to above with reference to Darfur. Most any teacher may use such dramatic climate issues to engage students and validate math instruction for them.