SENCER educators in mathematics and other STEM disciplines can make use of a new report called GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) for ways to incorporate applied mathematics into K-12 through undergraduate level curricula. Among the writing team is Sol Garfunkel, a member of the Engaging Mathematics advisory board.
The report, developed jointly by the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and its Applications (COMAP), is available to view and/or print at no cost. Professionally printed copies will also be available for $20 through the SIAM bookstore.
Victor Donnay’s plenary address during the 2015 SENCER Summer Institute had a clear goal—to show the connection between mathematics and the issues people care about.
Victor, who is the William R. Kenan, Jr. Chair of Mathematics at Bryn Mawr College and an advisory board member for NCSCE’s Engaging Mathematics initiative, has the same goal for his students.
Victor uses various assignments to make the connection between mathematics and real world issues clear. During his plenary, Victor shared three examples of such assignments with the audience.
In the first assignment Victor shared, students are instructed to take a homework problem and describe in one paragraph how the mathematics involved might be used to address a real world issue. Students post their paragraphs online and read three others posted by their classmates. From this assignment, something like the concept of related rates in calculus transforms from a general question about how quickly two planes move away from each other into a question about how vocabulary growth rates differ for children born into different socioeconomic classes.
In Victor’s second assignment, students find an article about mathematics in a newspaper or on the web and post it to the class website with a one-paragraph summary. They then read three other summaries and write comments on them. This assignment exposes students to real-world, relevant, and newsworthy mathematics.
In the third assignment, which serves as a final project in Victor’s multivariable calculus course, students pick a world topic that interests them and a topic they learned from the course and show how they are connected. Students present their work at a reception where they can discuss their projects with a general audience.
Victor is also highly focused on issues of environmental studies and sustainability. He chairs the college’s Sustainability Leadership Group, directs the Environmental Studies program, and has taught numerous courses that integrate sustainability with mathematics.
In his mathematics of sustainability courses, he focuses on social, economic, and environmental issues, because all three have an impact on sustainability. His students have studied the Rwandan genocide, population growth models, and tipping points.
Victor worked with TED-Ed to create a short animated video on how tipping points relate to the mathematics of climate change. In the video, titled “Our Chaotic Climate,” chaotic billiard motion explains how a two-degree increase in Earth’s average temperature can lead to substantial consequences.
Victor also incorporates service learning into his mathematical modeling and sustainability course, allowing students to work to make a real difference on their campus and in their community. Student projects range from examining the energy footprint for a renovation of the science building to measuring the level of safety of bike routes. Two of Victor’s students were publicly recognized for their efforts in helping Haverford Township apply for a grant from the Pennsylvania Energy Department Authority to help fund a geothermal energy system for the Community Recreation Environmental Center, a direct result of their service-learning project that explored the center’s options for alternative energy sources.
Students react well to being able to make a difference through their course work. As one of Victor’s students said, “The end results of all the projects were pretty satisfying; it made you feel like you were making a contribution and that you might actually be able to affect something.”
Reactions from the plenary audience were largely positive as well. Overheard were comments from attendees along the lines of, “I never knew this was math!” Victor’s plenary did a great job of showing how mathematics relates to current world problems and topics in many other disciplines, from environmental sustainability to social justice. He helped SSI 2015 attendees see that mathematics is accessible, exciting, and important.
For more from Victor’s plenary, please access these resources:
What does it take to be outstanding at mathematical modeling, and how does modeling relate to real world issues across disciplines of study? For 16 years, teams of high school students and college undergraduates have competed in the Consortium for Mathematics and Its Applications’ (COMAP’s) Interdisciplinary Contest in Modeling (ICM) to find out.
COMAP recently published a book about the contest edited by Drs. Chris Arney and Paul J. Campbell. Chris is an ICM director, United States Military Academy math professor, and advisory board member for the Engaging Mathematics initiative. In addition to co-editing the book, Chris also wrote a number of the book’s chapters. Paul is a mathematics professor at Beloit College.
The book, titled The Interdisciplinary Contest in Modeling: Culturing Interdisciplinary Problem Solving, presents a history of the ICM, including descriptions of past problems, a list of outstanding teams, and commentary from participants, advisors, judges, and directors. Also included is advice on how to prepare a team for the contest and how to develop curricula on modeling, as well as discussions on the current state of interdisciplinary education. Wm. David Burns, the executive director of NCSCE and principal investigator for Engaging Mathematics, authored one of the book’s chapters on interdisciplinarity titled “‘Multidisciplinary Trouble’ and Learning: A SENCER Approach.”
In the book’s preface, Dr. Solomon Garfunkel, the executive director of COMAP and an Engaging Mathematics affiliate, writes:
All of us who do this work [of the ICM] appreciate mathematics for its beauty. But all of us also appreciate the power of mathematics to help us understand and deal with the complexities of our world. We are educators and we want our students to see knowledge not compartmentalized into a discrete set of disciplines, but with all of its interconnections.
For more information on the book, including instructions about how to purchase it, click here. Click here to register for the 2015 ICM.
Why is the climate like a billiard game? This isn’t a riddle from Alice in Wonderland, but a question Dr. Victor J. Donnay used math to help answer.
This summer, Victor, who is the William R. Kenan, Jr. Chair of Mathematics at Bryn Mawr College, worked with TED-Ed to create a short animated video on the mathematics of climate change. In the video, titled “Our Chaotic Climate,” chaotic billiard motion explains how a two-degree increase in Earth’s average temperature can lead to substantial consequences, including “more extreme and intense weather events, less predictability, and … less hospitability to human life.”
“Our Chaotic Climate” is a good example of how mathematics can help us understand the most complex and compelling civic issues of our time. Consider the video’s closing comments:
The hypothetical models that mathematicians study in detail may not always look like actual situations, but they can provide a framework and a way of thinking that can be applied to help understand the more complex problems of the real world. In this case, understanding how slight changes in the constraints impacting a system can have massive impacts gives us a greater appreciation for predicting the dangers that we cannot immediately perceive with our own senses, because once the results do become visible, it may already be too late.