Earth Algebra: College algebra with applications to environmental issues

Aug 15th, 1995 | By | Category: 7-2: Agriculture, Media Reviews

by Christopher Schaufele, Nancy Zumoff, and Tina H. Straley
Published by HarperCollins College Publishers, 1995

Review by Ravi Srivastava

Over the years we in the mathematics and science education community have come to realize that our students’ mathematics performance is sub‑par. The cause is primarily the pedagogical approach: dry mathematical concepts (which to a student are as flavorful as unsalted cardboard) are presented, and thoughtless problem solving is stressed without any connection to reality. Consequently, students learn the mechanics of using, for example, a quadratic formula, without realizing the significance and nature of the relationships. Nor can students relate their math knowledge to reality through so‑called word problems‑‑‑the token concession teachers of mathematics make to reality. At the end of the course, one is left wondering about what might happen if the students encountered a real quadratic function on a dark, desolate road. Would they tuck their tails between their legs and flee, or would they face this foe and vanquish it?

I am not suggesting a (snake‑oil) cure‑all remedy that will forever lay to rest our college algebra troubles. Au contraire.  I am merely reporting a possible alternative that can make math more real, palatable‑‑‑even exciting‑‑‑to our students, showing them how algebra can be and is used to address real world applications. The best part is we don’t have to worry about a plane leaving Chicago for Indianapolis at “m” miles per hour and another leaving Indianapolis for Chicago at “n” miles per hour. We can tailor this text to data and issues relevant to our people in our specific geographic areas!

Earth Algebra is the creation of two mathematicians who teach mathematics at Kennesaw State College in Marietta, Georgia, and whose mathematical world is real and full of real applications. Their book is a tool that tribal college algebra courses can utilize to benefit our students.

What is Earth Algebra and how does it differ from a traditional college algebra course? Normally we would cover topics in a sequence of increasing complexity without necessarily motivating the need for the next topic. Thus, one would study linear, quadratic, and nonlinear equations and inequalities; graphing and functions; linear, quadratic, composite, inverse, polynomial, exponential, and logarithmic functions; systems of equations and inequalities and matrices‑‑‑all without ever actually using them in real world applications.

The approach identified in Earth Algebra is quite different. As the preface states, “This college algebra text focuses on modeling (primarily by curve fitting) real data concerning environmental issues, decision making, reading, writing, and oral reporting.”

The environmental issue that provides the background for the mathematics in this book is global warming, including the role of carbon dioxide. Then the text discusses functions, domain and range, and graphing before moving on to linear functions. The first application of the linear function is the increasing atmospheric carbon dioxide concentration. Similarly, introduction of composite functions leads into a discussion of ocean levels and their dependence on global atmospheric temperatures which, in turn, depend upon carbon dioxide in the atmosphere.

This pattern is followed throughout the book. The environmental applications covered include: carbon dioxide concentrations, global warming, and ocean levels; factors leading to carbon dioxide buildup; carbon dioxide accumulation; carbon dioxide, people, and $; reducing carbon dioxide emissions; and alternative energy. Also presented in this context are mathematical topics such as systems of linear equations and matrices; exponential and logarithmic functions; linear inequalities in two variables and systems of inequalities; and geometric series.

The beauty of this approach is that it deliberately weaves applications and mathematics into a fabric that is real, meaningful, and therefore strong. Concepts and results from one stage of the course create the foundation for the next stage, forming a natural progression of ideas and exercises. In the classroom, a two‑pronged approach is used: 1) classroom lectures and discussions, and 2) workshops where students perform collaborative exercises.

The text Earth Algebra can either be used as a stand‑alone text, or it can be used as a source of exercises to supplement the regular text. Navajo Community College at Shiprock, N.M., has succeeded with both. During the summer of 1994, one of the authors, Chris Schaufele, taught the course at Shiprock using a text module that he had tailored specifically for the natural environment of Northern Navajo Nation. Thus, the students were exposed to mathematical concepts in a physical realm that was familiar to them. Based on the hydrology of the Shiprock area, the students practiced exercises at workshop classes using linear, quadratic, cubic, exponential functions, matrices, and other concepts. A similar approach was used during a summer 1995 class except this course was taught by Schaufele and Dennis Price, a math instructor at NCC-Shiprock. During spring 1995, Earth Algebra exercises tailored to the Navajo Nation supplemented workshop sessions. Additionally, in the fall of 1994, NCC-Shiprock organized a special seminar to inform other math and science instructors in the NCC system to discuss how the principles of algebra were tailored to the Navajo Nation and how the algebra student workshops were conducted.

I wholeheartedly recommend Earth Algebra either as a primary or as a supplementary text for tribal college algebra courses. With a little effort, a module can be tailored to the geographical region where the course is being taught. This flexibility and connection to reality go a long way toward making college algebra meaningful and exciting to our students.

Ravi Srivastava has worked at NCC-Shiprock in the Math and Science department since fall 1993 and has collaborated with Chris Schaufele to tailor Earth Algebra to Northern Navajo Nation. In the spring of 1995 he got his first taste of teaching college algebra. He frequently encounters algebraic demons on dark and desolate reservation roads.

Srivastava and Schaufele would be willing to teach workshops for AIHEC on this approach.

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