The curriculum detailed in this article was developed for use in a pre-college algebra course, MATH 101 Exploring Functions, offered at Metropolitan State University (2009), an urban institution with a strong commitment to civic engagement. The new curriculum was developed with the objective of engaging students' interests in the study of mathematics and improving mathematical learning.

During the early 1990s, a formal study assessing the impacts on student learning of a college algebra curriculum (Earth Algebra ) integrating civic/environmental issues was undertaken by Christopher Schaufele and Nancy Zumoff at Kennesaw State College. The Earth Algebra text, developed by Schaufele et al. (2003), applies algebraic content and data analysis to a quantitative exploration of anthropogenic greenhouse gas emissions and global warming. In their 1996 report to the Office of Post Secondary Education, U.S. Department of Education, they provide a detailed description of their study (Schaufele and Zumoff 1996). Pre- and post-course tests assessing algebraic skill, data analysis achievement, mathematical modeling capability, and personal attitudes were administered to students enrolled in both traditional sections of college algebra and those enrolled in sections using the Earth Algebra text. Statistical analyses revealed that Earth Algebra had no different effect on students' knowledge of algebra when compared to traditional sections of college algebra, despite the decreased emphasis on traditional algebraic skills and concepts in the Earth Algebra course. Sections using the Earth Algebra curriculum did show statistically significant gains in the areas of data analysis, mathematical modeling, and attitudes toward mathematics over traditional sections of the course.

Other existing lower-level mathematics texts integrating environmental issues include Environmental Mathematics in the Classroom edited by Fusaro and Kenschaft (2003) and Mathematical Modeling in the Environment by Charles Hadlock (1999). These texts, appropriate for use in general education or mathematical modeling courses, apply mathematical modeling techniques to a diverse range of environmental issues.

In light of the Kennesaw State College project and other existing mathematics curriculum integrating environmental issues, the significance of the present project described in this report can be summarized in the following two points:

1. The MATH 101 curriculum is the first curriculum to integrate environmental sustainability issues, quantitative reasoning, and mathematical modeling into pre-college algebra level mathematics.

2. The MATH 101 assessment study supports the gains observed in the Kennesaw study. The MATH 101 study furthermore suggests that mathematical performance may be enhanced by teaching course content from a modeling perspective and integrating real-world applications.

Curriculum Development

The MATH 101 curriculum consists of a workbook — which serves as the textbook for the course — and two sustainability projects. The workbook has been in the development process since Spring 2008. By Fall 2008, the organization of the book had stabilized, and most revisions were minor. Beginning Fall 2008, two sustainability projects exploring ecological footprints were added. Between Fall 2008 and Summer 2009, six sections of MATH 101 piloted the workbook. The two projects were incorporated into all of these later sections except for one concentrated summer session course. Each project was completed outside of class over a three-week period.

The workbook begins by introducing four key modeling concepts: (1) functions, (2) unit analysis, (3) measurement of change, and (4) linear and exponential trends. Unit analysis, or rather, deriving mathematical relationships (equations) between quantities by using their units, serves several functions in this course. It is used for (1) motivating fraction arithmetic, (2) making "back-of-the-envelope" quantitative estimates, and (3) deriving and correcting mathematical models (linear and rational functions). In this first segment of the course, students also explore how change is measured over time. Students calculate and interpret average rates of change as well as percentage changes in a diverse range of real-world contexts. Students then proceed to study trends resulting from quantities that exhibit either a constant rate of change or a constant percentage change, that is, linear and exponential trends.

These four modeling concepts come together to derive equations for linear and exponential functions. The remaining sections of the workbook focus on modeling with linear and exponential functions, interpreting rates of change in other contexts, introducing inverse functions and logarithms, and developing and applying algebraic skills.

The two sustainability projects were designed to enable students to apply the quantitative reasoning, mathematical modeling, and algebraic skills acquired to the topic of ecological footprints and biocapacities. (The Global Footprint Network (2010) defines the ecological footprint as a measure of the demand a country places on its biological resources, while a country's biocapacity represents the supply of biological resources available (World Wide Fund for Nature 2009.)

The first project focuses on estimating ecological footprints, as defined by the Global Footprint Network. Students use unit analysis to create a per capita carbon footprint calculator for gasoline-powered automobiles. The calculator they derive is a rational function with four independent variables, namely the fuel efficiency of the vehicle, the average daily miles driven, the ridership of the automobile, and the average rate of carbon dioxide uptake (tons per acre per year). Students use their function to study the affects of each variable on the carbon footprint, and to estimate their own carbon footprint. In the second part of this project, students use unit analysis to estimate the amounts of cropland required per capita to meet current U.S. demand for a few food staples. Comparisons of all of the footprint estimates (for food and carbon sequestration) give students a relative measure of which demands require the greatest land use.

The second project explores the impact of population growth in the United States on per capita biocapacity and the hypothetical policies to eliminate U.S. overshoot by the year 2050. Students use a linear regression population model, obtained from U.N. data, to project population growth out to 2050 (U.N. 2007). They also use this model to create a per capita biocapacity model, a rational function, which they use to project the decrease in land availability up through the year 2050. In the second half of the project, the students create mathematical models, exponential functions, to explore hypothetical policies for reducing the total U.S. carbon and forest footprint, the two largest components of the U.S. ecological footprint, to sustainable levels by the year 2050.

Assessment

During the summer of 2008, the Human Subjects Review Board for Metropolitan State University approved an assessment study to evaluate the new curriculum. Nine sections of MATH 101 participated in the study between Fall 2008 and Summer 2009. Six sections piloted the new curriculum and three used a more traditional curriculum. Of the thirty-two students originally enrolled in eight of the sections, the number completing the course varied from seventeen to twenty-two in the sections using the piloted curriculum and from nineteen to twenty-one in sections not using the piloted curriculum. One section of MATH 101 using the piloted curriculum was offered during Summer 2009; it enrolled nine students of which eight completed the course. Ultimately, 167 students both completed the course and consented to participate in the study. Of these students, sixty-one were enrolled in the three sections that were not using the piloted curriculum. Of the six sections using the piloted curriculum, five sections were taught by the author of the curriculum.

The following assessment tools were used:

- SENCER math SALG pre-course and post-course surveys. These surveys collect demographic information about the students, and evaluate changes in student interest and confidence in using mathematics (SENCER 2009). The surveys were administered in all sections of MATH 101 using the piloted curriculum. Of the 106 students completing both surveys, pair-wise comparison was possible for only ninety-seven students. Only the results from these ninety-seven students are included in the study. Of these students, thirty-six identified themselves as males, sixty identified themselves as females, and seventeen students identified themselves as African American, Asian, or Hispanic.

- Pre-course quizzes. Quiz content focused on making plausible estimates, solving linear equations and inequalities, and determining rates of change and percentage change. These closed-book quizzes were collected after 15 minutes and were not returned to the students. The quizzes were administered in five of the six sections of MATH 101 using the piloted curriculum.

- Final examinations. Pre-course quiz questions were embedded within the final examination for sections of MATH 101 taught by the curriculum author. Instructors teaching three sections of MATH 101 who were not using the piloted curriculum, were asked to choose questions on this final examination that they felt were appropriate for their students and embed these questions on their final exams.

Figure 1 compares the percentage of correct responses to questions on the pre-course and post-course mathematics assessments. Questions 6a–6c evaluate students' abilities to solve linear equations and inequalities. Questions 9 and 10 are quantitative literacy/reasoning questions. Questions 9a and 9b ask students to calculate the percentage increase and the average rate of change of the world's population, respectively, between 1970 and 2005. For question 10, students are asked to estimate the total cost to the taxpayers of a city for environmental hazards resulting from the disposal of plastic bags.

Figure 2 compares the percentage of correct responses on selected final examination questions between students enrolled in sections of MATH 101 using the piloted curriculum and sections not using the new curriculum. Because instructors were free to select which questions they wanted to include in their final examinations, the sample size varied by question. For all questions, the sample size for the sections using the new curriculum ranged from eighty-nine to 106, while the sample size for the sections not using the new curriculum ranged from foty to sixty-one.

Question 2 assesses students' understanding of slope. Questions 3a–4b ask students to determine equations of lines and exponential functions. Questions 7a–8d evaluate students' understanding of function notation. Questions 6, 9, and 10 are described above, with the exception of 9c. This question asks students to provide a one-sentence practical interpretation of the average rate of change obtained in question 9b.

Figure 1. Percentage of Correct Responses, Pre-course and Post-course Mathematics Assessments

Figure 2. Percentage of correct responses on selected final examination questions between students in MATH 101 using the new curriculum and those using the standard curriculum.

Figures 3–6 highlight the results from administering the SENCER math SALG in six sections of MATH 101 using the piloted curriculum. Questions 1.2–1.10 solicit information regarding students' confidence in using mathematics. Questions 2.2–2.11 solicit information about students' interest in learning and using mathematics. For each question, students rate either their confidence level or their interest level on a scale from 1 (not confident or interested) to 5 (extremely confident or interested). The figures show the p`.

Conclusions

Trends in the data obtained from this study do suggest that the MATH 101 curriculum integrating civic/environmental issues is (1) at least as effective as a traditional mathematics curriculum at building students' mathematical skills, (2) increasing students' confidence at using mathematics, and (3) increasing students' interest in learning and applying mathematics.

Figure 3. Percentage of students who rate their confidence level or their interest level in MATh 101 at 3 or higher, aggregate results.

Figure 4. Percentage of male students who rate their confidence level or their interest level in MATh 101 at 3 or higher.

Figure 5. Percentage of female students who rate their confidence level or their interest level in MATh 101 at 3 or higher.

Figure 6. Percentage of African-American, Asian, and/or Hispanic students who rate their confidence level or their interest level in MATH 101 at 3 or higher.

In future assessments, the following additions would be made to make the overall assessment more effective:

- The SENCER math SALG should be administered in sections of MATH 101 not using the piloted curriculum. In the present study, the math SALG was administered only in sections using the new curriculum.

- There should be a common set of final examination questions that all MATH 101 instructors participating in the study agree to use. In the present study, instructors were free to choose which questions they felt were appropriate for their classes.

The curriculum detailed in this article, originally developed for MATH 101, is currently being expanded for use in a new course MATH 102, Mathematics of Sustainability, piloted in Fall 2009. The improvements noted above for the MATH 101 study will be incorporated into a similar study for MATH 102.

About the Author

Rikki Wagstrom is currently assistant professor of mathematics at Metropolitan State University in Saint Paul, MN. She earned her Ph.D. in applied mathematics from the University of Nebraska–Lincoln in 1999. Her primary interests lie in undergraduate mathematics education. Although she teaches all levels of undergraduate mathematics, in recent years, she has focused her attention on introductory-level courses, developing curriculum and pedagogies integrating civic issues into mathematics courses.

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Hadlock, C. 1999. Mathematical Modeling in the Environment. Washington, D.C.: Mathematical Association of America.

Metropolitan State University. 2009. Center for Community-Based Learning. Retrieved on October 13, 2009 from http://www.metrostate.edu/msweb/community/ccbl/index.html .

Schaufele, C., N. Zumoff, M. Sims, and S. Sims. 2003. Earth Algebra. Boston, MA: Pearson Custom Publishing.

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