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Making introductory courses meaningful

Teaching general math and chemistry using sustainability
1 November 2022

For some undergraduates, especially those who do not plan to pursue a major in the sciences, the prospect of taking a college-level math course to fulfill a general education requirement can be rather daunting. But what if students could instead take a course on sustainability? A course that carefully weaves in mathematical concepts into the curriculum? As it turns out, students at Penn State have that very option with the Mathematics for Sustainability course, and for those who take the course, it can be a much more engaging experience.

Russ deForest stands and gestures while students sit at desks
Russ deForest teaching the Math for Sustainability course. Credit: Michelle Bixby, Penn State

“Students come into the course with a lot of interest and concerns and questions about topics in sustainability, so for us it’s an opportunity to connect the interests they already have with quantitative literacy and reasoning skills,” said Russ deForest, assistant teaching professor of mathematics who has taught the course since 2015. “We help them develop quantitative skills and see these skills as a part of their toolbox—skills that they will take with them beyond the course and apply in contexts outside of the classroom.”

The idea for MATH 33: Mathematics for Sustainability was conceived by the late John Roe, who was a professor of mathematics at Penn State for more than 20 years and department head for 5 of those years. He wanted to create a general education math course to serve students who weren’t going to be taking calculus or going into the sciences.

 “We want to teach quantitative literacy skills in a way that’s as engaging as possible to students, many of whom are frankly a bit skeptical of math,” said deForest.

But the course is more than a vehicle for math. Roe was passionate about sustainability and designed the course to prepare students to be active and engaged citizens. In a TEDxPSU talk in 2015, Roe described the natural links between math and sustainability. 

“When we talk about sustainability, we’re talking math,” he told the crowd. “Sustainable means it lasts. Math asks, ‘how long?’ When we talk about environmental change, math asks, ‘how fast?’ When we talk about risk, math asks, ‘what are the chances?’ When we talk about ecology, about the interconnected web of life, math asks, ‘how connected?’”

Roe, alongside then graduate student Sara Jamshidi, first offered the course in 2014. In the first few semesters, the course had about 20 or 30 students, but it quickly grew, and this semester the course has more than 100 students. As interest in the course increased, Roe and deForest, with support from the college, ran two workshops for math faculty from other Penn State campuses. And as the demand for resources increased, the trio adapted course notes from Jamshidi—now an assistant professor of computer science and mathematics at Lake Forest College—into a full-fledged textbook. Now Mathematics for Sustainability and similar courses inspired by the text run at several Penn State campuses and at least a dozen other universities.

This year also marks the launch of a Chemistry for Sustainability course in the college, designed and taught by Senior Associate Dean for Science Education and Professor of Chemistry Mary Beth Williams, who was inspired by the math course. 

“The students have been asking for something like this for a long time,” said Williams, who holds the James and Alvina Balog Faculty Fellowship in Science. “They want to see topics that they care about in our introductory courses. Chemistry for Sustainability is cross listed with CHEM 110, which is required for something like 4000 students every fall semester, so it has to match the rigor sufficient for CHEM 110 while putting it in a context that’s meaningful for students. I was very much inspired by the work that John Roe and Russ did in math. They absolutely led the way in rethinking how you can talk about sustainability while introducing math and science.”

Content and ethics

Many topics related to sustainability involve discussing quantities that are very small or very large—at the micro-scale and the macro-scale—so both the Mathematics for Sustainability and Chemistry for Sustainability courses begin by putting these quantities into human terms. 

After this “dimensional analysis,” the math course introduces concepts around modeling, starting with climate and ecosystem models. They also explore how these models can be used or adapted to model systems with similar dynamics. Then they turn to topics of probability and uncertainty and how these influence risk. Ultimately, the class applies the skills it has learned to decision making. 

“Over the last three years, we have been working to integrate ethical reasoning into more aspects of the course, and we use case studies to explore pertinent ethical issues,” said Raymond Friend, a graduate student who started as a teaching assistant for the course and has now served as an instructor for the last three years. “I believe the course has matured into one that challenges students to consider ethical issues related to sustainable development and how they might form and answer quantitative questions to investigate those issues.”

Meanwhile, the chemistry course explores topics like the carbon cycle and atmospheric warming, plastics, and freshwater purity. This course is framed by case studies, using sustainability topics like the construction of gas pipelines in Pennsylvania, pollution of plastic in the oceans, and lead-poisoned drinking water in Flint, Michigan, to then dive deeply into the chemistry concepts. Williams sets the stage for the course with a documentary film called ‘The Human Element,’ written by photographer and activist James Balog, son of Eberly alumnus James Balog and benefactor of both the faculty fellowship that Williams holds and the college’s integrated B.S/M.B.A. program.

“’The Human Element’ refers to the four traditional Greek elements earth, air, water, and fire, and the structure of the course parallels these elements: atoms, gases, liquids and solutions, and reactions, including combustion,” said Williams. “Balog argues that the fifth element is humans and our impact on the world. This course makes those human elements central to connect to the students’ world and experiences, motivating them to learn the chemistry that helps them to answer why and how.” 

An unusual approach to teaching

deForest acknowledges that the Mathematics for Sustainability course is an unusual math course, and that teaching a course like this may be unfamiliar to some math faculty. This idea led the instructors to produce the workshops and ultimately the textbook that has inspired similar math courses across the country.

“The hallmark of the course is that we really help students engage in real problems, beyond the superficial level, even though they may only come into the course with a background in high school algebra,” said deForest. “Many math courses are created around what we can ask students with the skills they have, but instead we really tried to start from the questions that students care about and go from there. We gave ourselves permission to engage students in sophisticated problems without requiring calculus.”

Both deForest and Williams said that designing and teaching these courses involves cutting some content, or changing the way some content is covered, compared to a typical course. This approach can be a challenge for some faculty, but both agree that it is worthwhile. 

“Recently published research suggests that student learning actually increases if you decrease course content,” said Williams. “If the students are deeply engaged and the content is meaningful to them, letting go of a little of the content is OK for student learning. Spending more time on how the chemistry is important to sustainability pays off when students not only persist but want to learn more.”

deForest added that cutting content has allowed “genuine exploration” for students, rather than asking them to learn a set of topics that they need to apply to the next course. The level of engagement, he said, is worthwhile.

“The students make this course a spectacular experience,” said Friend. “When students realize this course is not their ‘normal’ math class and that they are encouraged to pursue issues important to them, they feel very motivated to practice the mathematical and ethical decision-making skills and to participate in discussions related to our case studies. As a general education course, we pull students from almost every other discipline at Penn State, meaning they come in with a variety of perspectives and skill sets. I have been surprised by the insights they have added to our discussions.”

Friend fondly remembers his students from the Spring 2021 semester, who generated a list of resources to help undergraduate students and community members at University Park struggling with insecurities of food, healthcare, clothes, funds, or housing. 

“The list was distributed across the Eberly College of Science thanks to the two classrooms full of civically-engaged, compassionate MATH 33 students,” he said.

Teaching the course has also allowed deForest to explore active learning methods and, he said, to develop approaches that have changed the way he teaches calculus.

Williams also acknowledges that, in addition to the "Mathematics for Sustainability" book by Roe, deForest, and Jamshidi, she has benefited greatly from the teaching community in the Eberly College of Science, especially the college’s Center for Excellence in Science Education (CESE). 

“The course is a different way to teach general chemistry —a direction that I’m only just brave enough to try because of the years embedded with CESE and our broader teaching community,” she said. “I would love to partner with additional faculty inspired to consider deeply embedding sustainability in their courses. Maybe someday the college will have a suite of sustainability-focused courses across all of our disciplines as an alternative and integrative path through introductory science and math courses! After all, the jobs of the future for all science—and engineering!—students will, in some way, be focused on meeting the challenges of sustainability in our world.”