My first semester at Northern Arizona University ended a little over a week ago. Well, it wasn’t my first semester at NAU. I finished my masters at NAU in May of 2000 and then worked as an instructor for the 2000-2001 academic year in the Department of Mathematics and Statistics. Returning to NAU and Flagstaff is a dream come true for me and my family.

After leaving NAU in 2001, I worked for two years as a full-time math faculty at Front Range Community College in Boulder and Longmont, CO. I loved teaching at FRCC and felt like Superman everyday when I went to work. However, I had a hankering to earn my PhD, and after my wife finished her masters, I decided to return to graduate school. I started working on my PhD at University of Colorado at Boulder in August of 2003, and under the guidance of Richard M. Green, I finished in the summer of 2008.

After completing my PhD, I spent four years as an assistant professor at Plymouth State University. PSU is a predominately teaching-oriented institution with low research expectations. Each semester, I taught 3 or 4 different courses. My teaching duties always included one section of Calculus I or Calculus II and my remaining classes usually consisted of upper-level proof-based courses.

While at PSU, I was twice awarded the Plymouth State University Distinguished Professor of Mathematics award, an honor determined by the mathematics majors. Moreover, during my last semester at PSU, I was selected as the university’s sole nominee for the NH Excellence in Education Award, which is a statewide teaching award.

It was during my second year at PSU that I first started using an inquiry-based learning (IBL) approach in my classes. My strategy has been to implement IBL in my proof-based courses first and then work my way down into the calculus sequence. Due to content pressure and class size, using a full-blown IBL approach in calculus is difficult, but not impossible. I would call my current approach in calculus IBL-lite. For me, it is a work in progress.

Despite my high teaching load, I managed to maintain a somewhat active research program. While at PSU, I published three papers and began working on a few more. In addition, I gave frequent math and math education related talks. For the last three years at PSU, I also mentored year-long undergraduate research projects.

The teaching load at NAU is much lower, by about half, but the research expectations are much higher. This past semester, I taught two sections of Calculus I. During my last semester at PSU, I taught Calculus II, Calculus III, Linear Algebra, and Logic, Proof, & Axiomatic Systems (which is an introduction to proof course). In addition, I was mentoring three undergraduate research students. You would think that with only teaching two classes with only a single prep, I would feel like I had tons of time to get things like research done! However, I never quite felt that way. I have to cut myself some slack since starting a new job does require some time to transition.

In my view, my teaching went well this past semester. Each of my sections had roughly 45 students, which is way larger than any calculus class I’ve taught before (or care to for that matter). The class met four days per week and for most weeks, one whole class meeting was devoted to students presenting problems on the board. This was well-received by the students and seemed to be beneficial. Unfortunately, I spent most of my time lecturing during the remaining three days per week. The students didn’t seem to mind this approach; it is what they are used to after all. However, I’d like to lecture a lot less.

Even though I’ve taught Calculus I numerous times, it required more effort than I expected to adapt to teaching at a new school with new expectations. Part of the issue is that calculus at NAU is somewhat coordinated and I didn’t want to stand out too much by doing something vastly different than everyone else. This seems overly cautious to me now. I have vague plans for how I can incorporate more IBL and less lecturing, but I still need to flesh out the details.

I held five hours of office hours per week, which were wildly popular. On most days, I had at least three students

for the full hour and it wasn’t uncommon for me to have close to ten. Office hours are my favorite part of my job! My approach is to get the students helping each other. The photos below illustrate a typical day in office hours.

I also supervised an independent study with one graduate student (Kirsten Davis) on the combinatorics of Coxeter groups. If all goes according to plan, Kirsten will receive approval from the graduate committee and will begin writing a masters thesis under my guidance next semester. I’m excited and nervous about supervising my first graduate student.

As for my research, it has been a mixed bag. I did not manage to get much writing done and did not submit any new articles for publication. However, I have managed to get some writing done now that the semester is over and plan to submit a paper before the spring semester starts. This will make me feel significantly better. If the break was a bit longer, I could get close to having a second paper done. The goal is to find ways to be more productive next semester.

On a more positive note, I did give several talks during the semester. In fact, I gave more talks this semester than I have ever given in a single semester. Here are the details:

- On an open problem of the symmetric group, Friday Afternoon Mathematics Undergraduate Seminar, NAU, September 12, 2012.
- Inquiry Based Learning: What, Why, and How?, UA Mathematics Instructional Colloquium, University of Arizona, October 2, 2012.
- Inquiry Based Learning: What, Why, and How?, ArizMATYC, Yavapai College, October 12, 2012.
- Designing Inquiry-Based Learning Experiences, Faculty Development Workshop, NAU, October 16, 2012.
- Inquiry-Based Learning Panel Discussion, Indiana Section NExT Panel Discussion, Fall 2012 Indiana MAA Section Meeting, October 27, 2012.
- Euler’s characteristic, soccer balls, and golf balls, Friday Afternoon Mathematics Undergraduate Seminar, NAU, November 2, 2012.
- The Futurama Theorem and some refinements, NAU Department of Mathematics and Statistics Colloquium, NAU, November 6, 2012.
- Conjugacy and reducibility in Coxeter groups, series of 5 talks, Algebra, Combinatorics, Geometry, and Topology Seminar, NAU, October-November, 2012.

In addition to giving talks, I also applied for two grants, both of which are still pending.

- Combinatorics of the CFC elements Coxeter groups, Center for Undergraduate Research in Mathematics (CURM). I requested funds to support three undergraduate students to conduct research for 2013-2014 academic year. I’ve got my fingers crossed for this one and should hear one way or the other soon.
- An open problem library for mathematics, NAU Faculty Grants Program. This was an internal grant proposal to fund the initial development of an Open Problem Library (OPL) consisting of an extensive online database of innovative, well-tested, and documented mathematics problems that instructors and students may use in a variety of contexts. I don’t anticipate this grant being funded, but it is a project that I hope to work on eventually.

During my last year at PSU, I applied for and was awarded a mini-grant from the Academy of Inquiry-Based Learning that provides summer salary to fund the development of IBL course materials for an abstract algebra course that emphasizes visualization and incorporates technology. You can read more about my plan by going here. Since I ended up leaving PSU, I arranged to have the grant postponed until the summer of 2013. So, technically, I’ve already been awarded one grant since arriving at NAU. Woot.

Here are a few other miscellaneous highlights from my first semester at NAU.

- I’ve got three students lined up to do undergraduate research next semester. The details will get sorted out as we go, but the tentative plan is for one of them to work on a project by herself and for the other two to work together on something different. Regardless, the projects will be in the general area of combinatorics of Coxeter groups. I’m really looking forward to working with these students.
- This past semester, Tatiana Shubin (San Jose State University) spent her sabbatical on the Navajo Nation. While she was there, she established several Math Circles at middle and high schools. A few weeks ago, Nandor Sieben and I traveled out to the Navajo Nation for a couple days to have Tatiana introduce us to a some of the teachers and administrators that she has been working with, as well as observe some of the circles. Beginning next semester, Nandor and I will be part of a team that will take turns visiting each of the circles in an effort to sustain what Tatiana has started and to support the local teachers that will be running them in her absence. I’m thrilled to be a part of this project.
- Last summer, Stan Yoshinobu, Angie Hodge, and I organized a contributed paper session at MathFest titled “Inquiry-Based Learning Best Practices.” A few weeks ago, we submitted an abstract to the MAA to organize a similar session and we recently found out that our proposal was accepted.
- Angie Hodge and I were recently designated as Special Projects Coordinators for the Academy of Inquiry-Based Learning. This position comes with a small annual stipend and our duties include spreading the word about IBL and organizing workshops and conferences like the one mentioned above. I’m extremely passionate about inquiry-based learning and I’m really looking forward to playing an active role in inspiring others to take a more student-centered approach to teaching.
- I’m a lot like a dog. If I don’t get out for exercise, I might start chewing the furniture. I am more productive at work and a better father and husband if I’m getting regular exercise. Up until some tendonitis in my ankle slowed me down, I was doing a great job of getting outside to run, bike, or climb. In September, I ran my first 50K trail race. Obviously this isn’t academic related, but I’m proud of the fact that I’ve been able to balance work, family, and play enough to train for such an event.

All-in-all, I’d say that I had a pretty good first semester. My one major weakness is not having submitted a paper yet, but I hope to remedy this soon. It’s unfortunate that this may be the only thing that some people care about. I really enjoy doing research, but I’ll never be the world’s strongest researcher. I’m confident that I can do enough to get by (i.e., get tenure at NAU) and I am content being a well-rounded academic.

I work too much. Period. Work is constantly competing for time with family and time for exercising and playing. I feel like this semester was an improvement over recent semesters in terms of balancing work, family, and play. However, I can do better. I need to spend more time with my wife and sons. Of course I want to be the best mathematics professor I can be, but not at the sacrifice of my family. I don’t think about tenure every day, but it’s definitely more on my mind than it used to be at PSU. Having written this reflection, I feel a lot more confident moving forward.

Mathematics & Teaching

Northern Arizona University

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MAT 123: First Year Seminar

MAT 136: Calculus I

MAT 526: Combinatorics

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Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.