Q&A with Patrick Rault, associate professor and Haddix Community Chair of Mathematics, at the University of Nebraska at Omaha. Before joining UNO, Dr. Rault spent eight years at the State University of New York at Geneseo and two years as program director of mathematics for the distance college at the University of Arizona.
Q: What brought you to UNO?
A: I was offered the position of Haddix Community Chair of Mathematics, which is one of UNO’s five STEM Community Chair positions. These positions have a unique tradition within academia of breaking through barriers to make things happen. My new team of colleagues has experience with directing large projects to improve the K-16 experience through a variety of different initiatives, using inquiry as a key instrument to uplift students and lifelong learners. In short, this was my dream job.
Q: What is your favorite math class or lesson to teach?
A: Number theory class. I teach it as a very deep experience in inquiry, starting with the axioms of the integers and working up to Quadratic Reciprocity. My students, who may only be familiar with geometric axioms and proofs, learn about proofs in an algebraic setting where we develop a definition of the integers from scratch and use it to develop everything there is to know about these discrete number systems. There are more “a-ha moments” in this class than I can count!
Q: When did you discover your affinity for math? Who helped you discover it?
A: My parents were very supportive of me from an early age. I was never good with speed tasks like “Do as many of these 100 questions as you can in the rest of the class period,” so I was not identified as gifted. But my parents could see me working on the homework of my sister, who was 4 years older than me, so they worked with my teachers to find the right balance. In high school my calculus teacher encouraged me to start doing more by attending the PROgram in Mathematics for Young Scientists (PROMYS) summer camp. After that experience, I knew that I was going to be a mathematician.
Q: What are the hardest and most rewarding parts of teaching math?
A: The hardest part is related to the most rewarding part: making it fun and engaging for students. When it works, you can really see a lasting transformation in them that will stick with them for the rest of their lives, similarly to what happened to me at PROMYS. I think I knew that I wanted to teach mathematics when I started discussing pedagogy with my instructors while I was in college. Inquiry stuck out to me as the key to motivating students, whether it was me or my classmates. This led to some great collaborative working groups as an undergraduate.
Q: What is your favorite math memory?
A: My favorite math memory as a student was in pre-calculus class, when I learned how the limit of secant lines (defined algebraically) is the tangent line (which until then I had only seen geometrically). I was so amazed that I actually told my parents what I had learned in school that day! As a teacher, my favorite memory was about a student of mine. He figured out something in my own research: I had asked him to try to find an algebraic solution to a given problem, and he came back with a very elegant geometric proof that I would never have thought of myself. He came from a disadvantaged background and the pride in this accomplishment really stuck out to him – we are still in touch. I guess the unifying theme here is that I am still amazed at how the different subdisciplines of mathematics interact together. Doing math really is a social endeavor, as otherwise we can get stuck trying only the methods we can think of at the moment. And it is more fun to problem solve together.
Q: On your website, you say, "In Mathematics, relationships with advisers are analogous to those with significant others: long-term relationships will get you further than short flings." Tell me about some of these long-term relationships that pushed you to become a better mathematician and teacher. (Who had the greatest impact (positive and/or negative)? What other lessons did they teach you?)
A: This is a common saying about Ph.D. advisors: You have to start getting to know them before committing to working closely with them over your five-year doctoral thesis. While at the University of Wisconsin I started working with my own Ph.D. advisor Jordan Ellenberg (author of the popular book “How Not to be Wrong”), only after not clicking with a few other potential advisors. But then Jordan and I met regularly about a project to improve a known theorem by removing an unnecessary assumption. His humor made him easy to work with – for example he regularly called me his “epsilon removal service” (since the aforementioned assumption was that a certain epsilon was needed in an equation). Working on a project over so many years does not always pay off: in mathematics we don’t know that we are close to the end until we’re there. So many drop out of these programs, and I considered doing the same on more than one occasion. I could not have given my first conference talks, let alone completed my Ph.D., if not for his extensive support.
Q: How do you intend to build these relationships at UNO and with Nebraska teachers?
A: That is a good question. I cannot give a blanket answer, as so much depends on unique personalities. Since I moved to Nebraska in August, I’ve begun a “listening tour” where I am getting to know the key constituencies and what sorts of projects we can work on together. Collaborations on projects tend to develop rich long-lasting relationships, so I am beginning with several of those. I am starting by bringing my own experience to the table, with inquiry experiences both in the classroom and for research by undergraduates – including education research for our pre-service teachers. This is already leading to some discussions of positive tweaks to how we organize Math Teacher Circles. Similarly, I aim for the discussions initiated through my listening tour to blossom into longer relationships resulting in continuous projects.
Q: What are some of the most beneficial professional development opportunities you’ve experienced?
A: The most significant PD that I did as a teacher was a four-day residential workshop on Inquiry-Based Learning (IBL) at the University of Texas at Austin. It gave me the tools to teach effectively, with a focus on transforming the lives of students in a way that would last 20 years into the future. I now lead these residential workshops each summer for the Academy for IBL. At UNO, I have already given a mini workshop of the same variety and am working on creating several communities of practice around teaching. The first was started this fall around calculus. Another is being formed around IBL in college mathematics across the Midwest to mirror similar communities that I created in Upstate New York and Southern Arizona – the Upstate New York one is the subject of a recent article in the journal PRIMUS.
Q: Of the projects you are working on now, which one is your favorite?
A: I’m currently writing a grant to support the aforementioned regional IBL communities, which has been a long-term goal. There are about a dozen such communities in formation, replicating some of the aspects of our pioneering Upstate New York community. This has the potential to change the way that college mathematics courses are taught around the world. Another project on my mind is to introduce a scaffolded research experience to permeate the college curriculum. I was working on this in my previous job, as the leader of the University of Arizona’s team on the Council on Undergraduate Research’s (CUR) Transformations Project. That project focused on the lab sciences, but as chair of both the CUR Math & Computer Science Division and the Mathematical Association of America’s Special Interest Group on Undergraduate Research, my focus is on quantitative and education research. I am in the process of piloting several components of this and gathering a team to make it a success.
Q: What are you most looking forward to in your future in math learning and teaching?
A: I am very much looking forward to the day when lecture is a rarity, used for specific situations where information needs to be transferred efficiently, while most classes are taught in a student-centered framework that focuses on how the student can grow in place of how the student is deficient. Teaching is a lifelong learning endeavor, in part because every student we ever interact with is different – and we need to inquire into their thinking to see how we can best help them to succeed.