MAA Invited Paper Session: Improving Access to Mathematical Modeling Research Abstracts

Thursday, August 6, 1:00 PM - 4:20 PM, Marriott Wardman Park, Delaware B

The picture of mathematical modeling that applied mathematics researchers have is very different from the word problems provided in textbooks for teachers. This session is dedicated to closing the gap between applied mathematics research, mathematics education research, and what goes on in classrooms around the United States. With an eye to creating environment(s) that support students and teachers at all mathematical and economic levels: How can we improve teachers' and students' understanding of modeling research, and improve access to the experience of mathematical modeling research to populations that do not typically receive graduate training in the field?

Carlos Castillo-Chavez, Arizona State University
Carlos Castillo-Garsow, Eastern Washington University

Global Disease Monitoring and Forecasting with Wikipedia

1:00 PM - 1:25 PM
Sara Del Valle, Los Alamos National Laboratory

Efforts to mitigate the impacts of infectious disease depend on accurate and timely monitoring to measure the risk and progress of disease. We examine a freely available, open data source for this use: access logs from Wikipedia. Using linear models, language as a proxy for location, and a systematic article selection procedure, we tested 14 location-disease combinations and demonstrate that these data feasibly support an approach that overcomes these challenges. Specifically, our proof-of-concept yields models with $$r^2$$ up to 0.92, forecasting value up to the 28 days tested, and several pairs of models similar enough to suggest that transferring models from one location to another without re-training is feasible. Based on these preliminary results, we close with a research agenda designed to produce a disease monitoring and forecasting system that is significantly more comprehensive than the current state of the art.

Engaging students in applied mathematics via experiential learning through research

1:30 PM - 1:55 PM
Sherry Towers, Arizona State University

In recent years, at workshops for aspiring undergraduate mathematicians, and while teaching my own courses in applied mathematics, I have developed small, encapsulated research projects that have aspects which students can understand and contribute to, even at an early stage in their studies. I also ensure that the research projects are very topically interesting (usually related to current events), and likely to be publishable. As a mentor, I assist in directing their efforts, ensuring they understand the analysis, and in bringing together the final write-up of the paper. I will discuss my methodology, the overwhelmingly positive student feedback on this process, and two publications that have resulted from this process, one of which received international media attention.

Overcoming Epistemic Obstacles to Teaching Mathematical Modeling in Calculus

2:00 PM - 2:25 PM
Patrick Thompson, Arizona State University

Poor algebra skills is one of the commonly cited culprits behind students’ poor performance in calculus. Recent research in mathematics education points to another, hidden problem that students face in learning calculus, and which contributes significantly to their “poor algebra skills.” The problem is that students in US schools learn little about how to conceptualize, reason about, and represent relationships among quantities’ values as they vary. I will share our attempt at ASU to address these problems while at the same time creating a more coherent, learnable calculus.

Mathematical Modeling Experiences in Secondary Schools

2:30 PM - 2:55 PM
Kathleen R. Fowler, Clarkson University

In the past years math modeling has been recognized as a necessary practice for students to maintain interest in STEM disciplines and build skills to succeed in school, college, and beyond. Math modeling hones problem-solving skills, fosters creativity and collaborations, and brings relevance to mathematics. We discuss initiatives at the national and local levels that support incorporating math modeling into the secondary school curriculum. We describe successful implementations on varying scales as examples for best practices.

Mathematics Education Commentary: At the Interface Between Applied Mathematics and Mathematics Education

3:00 PM - 3:25 PM
Carlos Castillo-Garsow, Eastern Washington University

Dynamical systems modeling requires nuanced ways of doing mathematics and imagining situations that are often overlooked, both by applied mathematicians who take these ways of thinking for granted, and by mathematics educators, who rarely have the experience with applied mathematics necessary to see them. In response to the above presenters, Carlos Castillo-Garsow will discuss the results of recent case study research in student thinking and their implications for the teaching of mathematics students.

Applied Mathematics Commentary: Math at Top Speed: The Role of Mathematical Modeling in Science and in My Personal Life

3:30 PM - 4:20 PM
Richard Tapia, Rice University

Mathematics is the modeling language of science. Euler and Newton first had to invent mathematical theory before they could exercise what was their true passion, the modeling of physical phenomena. For many years the speaker was involved in BMX bicycle racing as a supportive father for his son. In this talk the speaker will use several lively videos to identify and illustrate what he calls the Fair Lane Assignment Problem in BMX Bicycle racing. He then uses his mathematical training to mathematically model the problem and solves this problem using a computer and a mathematical algorithm. The speaker has been involved in drag racing throughout his life. In this talk the speaker uses his mathematical training to study the age old question how can a “slow” car beat a “fast” car. This exciting study leads him a mathematical model and in turn what he calls the Fundamental Theorem of Drag Racing”.