Making Mathematics Meaningful on the 2021 SciFest All Access STEM Stage

By Padmanabhan Seshaiyer

The USA Science & Engineering Festival (USASEF) continued its bi-annual exposition with the SciFest All Access event from October 18-24, 2021. SciFest All Access offered a free virtual science, technology, engineering, and mathematics (STEM) exposition for K-12 students, educators, and their families. SIAM has participated in USASEF since it commenced more than a decade ago. This year’s events included STEM learning experiences, online field trips, exhibit zones, scavenger hunts, student project displays, and “STEM Stage” performances by well-known speakers on a variety of topics.

Once again, USASEF invited me to speak on the virtual STEM Stage about “Making Mathematics Meaningful.” I was glad to engage listeners with important pedagogical frameworks and practices—such as computational thinking and mathematical modeling—that serve as valuable problem-solving strategies for the application of mathematics to real-world problems. Participants learned how to navigate complex scenarios by employing strategies like problem decomposition, pattern recognition, abstraction, and algorithmic thinking. Specifically, I described the use of computational and modeling skills to both solve textbook problems (such as calculating the number of squares on a chessboard) and address global challenges (such as food waste in school cafeterias). Figure 1 illustrates these concepts.

Figure 1. At the SciFest All Access event, which took place virtually in October as part of the USA Science & Engineering Festival, Padmanabhan Seshaiyer spoke about the value of computational and modeling techniques when calculating the number of squares on a chessboard or estimating the amount of food waste in school cafeterias. Figure courtesy of the author.

To tackle these types of problems, I introduced simple tools like Fermi problem-solving approaches; such methods encourage users to think algorithmically and estimate answers via back-of-the-envelope calculations [3]. For example, estimates of food that is wasted by K-12 students in pounds per week can help one calculate larger approximations of waste based on the number of students per class, number of classes per school, number of schools per district, number of districts per state, and number of states per country. Attaching a dollar value to a wasted food item then allows one to apply simple calculations to roughly determine the amount of food that is wasted in the country each week in school cafeterias alone. These tactics build students’ understanding and appreciation of mathematics when they wonder, “When am I ever going to use this?” I also utilized games to engage students in mathematical modeling and prompted them to think about the meaning of “best” in terms of optimal problem solving.

In addition, I had the exciting opportunity to speak to K-12 teachers and university educators about meaningful mathematics through USASEF’s “Spark of STEM Coffee Break Series.” This free online series provides 15-minute “sparks” of inspiration for STEM teaching in the classroom and is meant to inspire and equip teachers with innovative STEM learning tools. Future vignettes will take place on Thursdays in December 2021 and are available on demand. Educators who are interested in participating can register online.

Ultimately, the goal of such outreach and engagement activities is to help students ask bold questions and persist through creatively imagined and calculated solutions. These exercises also provide students with the tools to collect, interpret, visualize, and predict data, which is an important transferable competency. Most institutions are beginning to recognize the importance of engaging students beyond a content-based education and are thus seeking to provide a competency-based education that includes data, computation, and global awareness — all of which involve mathematics as a key component. Along with these subjects are 21st-century lifelong competencies like communication, collaboration, critical thinking, and creativity. However, educators must start introducing appropriate contexts and relevant frameworks if they want the next generation of mathematicians to build upon and develop these competencies [1].

Figure 2. Students can apply mathematics to real-world scenarios in the context of the United Nations Sustainable Development Goals, which are designed to help society achieve a more sustainable future. Figure courtesy of the author.

One way to encourage students to employ mathematics in real-world contexts is via the United Nations Sustainable Development Goals — a collection of 17 interlinked global goals that are designed as a “blueprint to achieve a better and more sustainable future for all” (see Figure 2). Educators can have students select a goal (i.e., Goal 2: Zero Hunger) towards which they would like to make an impact, then introduce them to the art of model development. Students should understand and define a problem statement that allows them to generate a mathematical model from a physical context. This could be an algebraic or differential equation model that describes the dynamics associated with quantities of interest (e.g., growth of a population, size of a spread, etc.) in the problem.

After developing a model, students must learn to analyze it in order to investigate and theorize appropriate behaviors with rigorous mathematical tools. This kind of analysis frequently yields important estimates or bounds that are useful for comparison purposes. Because most models that represent the real world may not admit exact solutions, educators should promote the use of numerical methods to test these complex models. The testing step often involves simulation, validation, and prediction, all of which evaluate a model’s predictive capability. Working through these steps automatically helps students develop their essential habits or competencies as an integrated and sustained process. This framework can contribute to the organization of mathematical problem solving and the creation of agents of change at the student, faculty, and institutional levels [2].

Padmanabhan Seshaiyer is a professor of mathematical sciences at George Mason University and chair of the SIAM Diversity Advisory Committee. He works in the broad area of computational mathematics, data science, biomechanics, design and systems thinking, and STEM education. Seshaiyer also serves as vice chair of the U.S. National Academies Commission on Mathematics Instruction. Earlier this year, he was officially appointed to the newly formed Virginia STEM Advisory Board to the Governor of Virginia.