Organizers: Breeanne Swart, The Citadel (bbaker2@citadel.edu); Antara Mukherjee, The Citadel (mukherjeea1@citadel.edu)
This session seeks to contribute to the conversation of mentoring undergraduate research in all of its forms. Proposals topics can include, and are not limited to, descriptions of projects worked on with students, unique techniques for working with students, how you determine which students are a good fit for your projects, and what your expectations are of students given a variety of factors such as length of project (semester, year, summer, etc), academic commitments, personal commitments, etc.
Course-based Undergraduate Research Experiences (CURE) provide an opportunity to engage students in undergraduate research, particularly in settings where external research support is limited. However, integrating this high-impact practice into coursework presents several challenges: while courses require structured syllabi and clear assessment criteria, research often demands flexibility to explore unplanned directions. Additionally, research is typically an open-ended and lengthy process, but in a course-based setting, projects must be completed within the constraints of a single semester. In this talk, I’ll share my experience incorporating student research into a mathematical modeling course, highlighting strategies to balance these competing needs and challenges. I will discuss how a scaffolded approach helped students navigate the research process while developing mathematical models using foundational frameworks. This approach to structuring student research is adaptable and can be applied to other courses or areas of mathematics to foster inquiry-driven learning.
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As educators, our role extends far beyond simply teaching course content; we are also mentors who help students navigate the complex landscape of research, career development, and personal growth. This talk will explore strategies for mentoring students in mathematics, focusing on undergraduate research projects, internships, and career preparation. Drawing from 20 years of experience, I will share insights on how to support students in various research areas and finding REU's and internship opportunities. By cultivating trust and creating lasting relationships with students, mentors can help students not only excel academically but also prepare for success in their careers.
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Mathematical puzzles and games offer rich opportunities for faculty seeking to develop student research projects. By exploring math in a recreational context, students can naturally notice patterns, ask questions, make hypotheses, and delve deeper into mathematical investigations. We have used card games such as $\textit{Quads}$ and $\textit{Spot It!}$ to generate accessible projects for students at a variety of levels. We discuss the successes and challenges of both virtual and in-person research groups, highlighting the dynamics of collaborative work in different settings.
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In this talk, we will consider several projects that undergraduates have worked on in the past several years. We will discuss how the problems were chosen as well as what the students were expected to accomplish in various time frames.
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In this talk, we explore strategies for engaging students with basic mathematical knowledge in research projects. This approach leverages open problems from respected academic journals. We will discuss methods for guiding students through problem--solving, publishing their results, and ultimately presenting their findings publicly. This technique can also benefit educators without prior research experience who wish to begin exploring research themselves. We discuss how to stimulate students' curiosity through visual tools, including classic experiments involving the Mo\"bius strip and the Klein bottle. These experiments involve constructing the objects, observing their properties, and using hands-on activities to show how altering the objects by cutting disrupts their inherent properties. At the end of the presentation, we will discuss problems our students have solved from journals as well as original problems related to our own research topics. Additionally, we will provide a list of current problems along with recommended books and articles to help students prepare for future projects. Join work with Drs. Chen, Mukerjee, and Swart.
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This is a personal tale of how I have directed undergraduate research at MTU and ETSU via NSF-REU awards. I was the sole advisor from 1991 to 2018, and have worked with Fernando Piñero and Pamela Harris since then. I retired in 2024. Some aspects of my talk are *How I used undergraduate research as a springboard to solidify and define my own research; *How I learned so much from my students while teaching them sophisticated and bread-and-butter techniques; and *The illustrious careers of my students.
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Team Bromeliad is an ongoing seven-year interdisciplinary collaboration Dr.~Erin N.~Bodine (biomathematician) and Drs.~Rachel Jabaily, Brad Oberle, and Brian Sidoti (botanists) to study the growth, reproduction, and population dynamics of bromeliads (a plant family of rosette-structured flowering plants that includes the pineapple and Spanish moss) using greenhouse and field experiments in conjunction with mathematical modeling. The long lifespan of many bromeliads (up to 100 years in some species) can make it difficult to study individual rosettes \textit{in situ} over their lifetime. However, this provides fertile ground for developing mathematical and computational models that can simulate and predict growth, reproduction, and population dynamics over many decades. These models have the additional benefit of allowing for simulations that consider the impact of changing environmental conditions, such as climate change or the introduction of invasive species. In this talk, we will tour a selection of mathematical models of bromeliad growth, reproduction, and population dynamics that have been developed and analyzed in collaboration with undergraduate students from a variety of institutions. From simple single equation continuous functions and discrete difference equations to more intricate models of systems of differential equations and agents-based models, each model provides a different lens from which to view and understand bromeliad growth and reproduction. Additionally, this talk will reflect on the elements of this collaboration that have enabled it to persist and evolve over time, and to provide research opportunities for over 20 undergraduate students.
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This presentation shares my experiences and insights from undergraduate research mentoring at my current institution, UT Martin. I discuss the challenges and successes of integrating multiple disciplines, navigating the mentor-mentee relationship and promoting student autonomy in team-based research. This reflective analysis aims to contribute to best practices in undergraduate research mentorship, highlighting the benefits and complexities involved and challenges faced as an entry-level faculty member.
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