Our Team
Principal Investigators
Rachel Arnold is a mathematician with a passion for understanding students' mathematical reasoning as they transition to proof-based mathematics. She serves as PI on the NSF grant and Co-PI on the 4VA grant, which fund The Proofs Project. She designs research-based instructional tools for supporting students' abstraction of logical reasoning that is fundamental for advanced STEM study.
Andy Norton conducts research on the nature of logical-mathematical knowledge and how we, as humans, develop such knowledge. He serves as co-PI on the NSF grant and PI on the 4VA grant, which fund the Proofs Project. His main interest on the project concerns students' constructions of logical reasoning.
Team Members
Vlad Kokushkin was a graduate research assistant on the project and is currently a postdoc at Colorado State. His research focuses on high-level mathematical cognition and cognitive offloading. Within the scope of the project, he is interested in understanding what cognitive challenges undergraduate students experience while working with mathematical proofs and determining how they can successfully navigate these challenges.
Joe Antonides is a postdoc at Virginia Tech. His research focuses on mathematical knowing and learning, particularly the mental actions and processes that students use in combinatorics and geometry. Within the Proofs Project, his main interest is in students' reasoning about logical implications, especially using Euler diagrams.
Graduate Member(s)
Matthew Park
Matt Park is a graduate student in the Math Department at Virginia Tech, specializing in math education. His research interests include the learning of complex analysis and symplectic geometry. He has served as a GRA on the Proofs Project and has contrbuted to several papers and presentations.
Corinne Mitchell
Corinne Mitchell is a PhD student in mathematics at Virginia Tech. Her research focuses on the pedagogical practices of mathematicians and how they support high-level classroom discourse in proof-based math courses. Corinne’s master’s thesis investigated the facilitation of a professional development designed to support teachers taking up the Inquiry-Oriented Abstract Algebra curriculum materials. She is currently serving as a graduate research assistant on the Proofs Project.
Undergraduate Members
Emma is an undergraduate student majoring in mathematics and minoring in computer science. Within the proof's project, her role is to assist professors from partnered universities with implementing proofs research within their classrooms and interpreting data through the lens of epistemological obstacles.
Michael is a junior, majoring in mathematics and minoring in finance. Within the Proofs Project, his main role is to analyze EOs within course instruction at a partnering institution, particularly those that occurred during proof by cases. He also assisted with analyzing connections between EOs that occurred during classroom discussions.
Andy Miller - George Mason University
Andy is a Computer Science and Math double major at George Mason University, graduating Spring 2025. His role within the project is to assist Dr. Chowdhury in researching undergraduate math students’ understanding of proofs.
Alejandro is an undergraduate student majoring in Mathematics, with focus on education. Within the proofs project, his role is to analyze and capture selected visual data that shows students' critical thinking and understanding of several topics from the introductory proofs class.
Alex is a third-year undergraduate student majoring in mathematics, with a minor in Computer Science. Within the Proofs Project, he conducted a self-study on the development of logical structures for prood and proving, including the connections and epistemological obstacles he experienced.
Key was a CMDA major at Virginia Tech, minoring in CS and math. His interests lie in web development, computer programming, and mathematical theory behind algorithm efficiency. He contributed to the development of the project's website.
Paul Dawkins - Texas State University, San Marcos
Paul Christian Dawkins is an associate professor of mathematics education in the Department of Mathematics at Texas State University. He studies the teaching and learning of proof-based mathematics at the undergraduate level. He focuses particularly on real analysis, geometry, and logic. His teaching experiments focus on modeling student thinking about mathematical proofs and developing teaching sequences and learning trajectories by which students can learn the epistemology of mathematical proving. He received the Selden Award for research in undergraduate mathematics education from the Mathematics Association of America.
Paul enjoys his family, his church, his job, food, beer, whiskey, video games, and reading. He also runs quite a bit, but “enjoy” might be too strong a word in that regard.
Guershon Harel - University of California at San Diego
Guershon Harel is a professor of mathematics at the University of California, San Diego. He has contributed greatly to the mathematics education research community through his work on advanced mathematical thinking, including the introduction of constructs directly relevant to our project, such as intellectual need and quasi-inductive reasoning. Dr. Harel will advise the research team on the role of such constructs in addressing epistemological obstacles.
Barbara Shipman - University of Texas, Arlington
Barbara Shipman is an Associate Professor and Distinguished Teaching Professor in the Department of Mathematics at The University of Texas at Arlington. She completed her doctoral studies in mathematics at the University of Arizona, where she initiated the Department's student-led graduate seminar. Before coming to Texas, she held a three-year position at the University of Rochester in New York.
Dr. Shipman has received support from the National Science Foundation as well as teaching awards for her mentoring and creative work in the classroom, including the 2010 Regents' Outstanding Teaching Award from The University of Texas System. She is a member of the University of Texas System Academy of Distinguished Teachers. To complement her work in differential geometry, Dr. Shipman enjoys rethinking foundational concepts and definitions in new and creative ways. She regularly teaches seminar-style capstone courses, where she likes to look for deep answers to simple questions together with curious students.
Barbara enjoys running, hiking, cooking, and birding, and plays the violin and viola. She also likes to learn about nature and the chemistry and biology of how healthy foods work.
Sarah Barreto is an advanced instructor at Virginia Tech. She received her PhD in mathematics in 2015 from North Carolina State University. She began teaching the introduction to proofs course at VT in 2022 and has since been interested in finding effective ways to engage students in the topics of the course.
Ahsan Chowdhury is a term assistant professor at George Mason University in Fairfax, VA. He earned his PhD in Mathematics from Virginia Polytechnic Institute and State University. His research focuses on the teaching and learning of undergraduate mathematics, with the goal of better understanding how mathematics can be made meaningful for students as well as how innovative instructional approaches are implemented.
Brent Cody is an Associate Professor of Mathematics at Virginia Commonwealth University. His research is in the field of set theory and involves using forcing and large cardinals to prove that statements are independent of the usual axioms of mathematics. A lot of his work has been concerned with using the technique of forcing to arrange various behaviors of the continuum function to hold while preserving large cardinals.
David Duncan began teaching mathematics in 2004 and he received his PhD in mathematics in 2013. He is now an assistant professor at James Madison University, where he has been since 2018.
Rani Satyam is an Assistant Professor at Virginia Commonwealth University (VCU). She earned her PhD from Michigan State University. Her research focuses on undergraduates' development in transition to proof courses and student affect, in particular emotions. She is currently a co-PI on an NSF project supporting graduate students in learning how to teach, PI for a geometry summer camp to foster middle schoolers' engagement, and is a member of the Creativity Research Group.
Jessica Schmale is a Senior Instructor and Academic Advisor for undergraduate mathematics majors at Virginia Tech. Successful mathematicians are inquisitive, creative problem solvers, and effective communicators. Jessica is passionate about cultivating these traits while developing mathematical knowledge, particularly as students transition to proofs-based courses.