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On Friday, June 14 I gave a 15 minute talk in one of the parallel session at the Legacy of R.L. Moore Conference in Austin, TX. The Legacy Conference is the inquiry-based learning (IBL) conference. In fact, it’s the only conference that is completely devoted to the discussion and dissemination of IBL. It’s also my favorite conference of the year. It’s amazing to be around so many people who are passionate about student-centered learning.
This was my fourth time attending the conference and I plan on attending for years to come.

Here is the abstract for the talk that I gave.

In this talk, the speaker will relay his approach to inquiry-based learning (IBL) in an introduction to proof course. In particular, we will discuss various nuts and bolts aspects of the course including general structure, content, theorem sequence, marketing to students, grading/assessment, and student presentations. Despite the theme being centered around an introduction to proof course, this talk will be relevant to any proof-based course.

The target audience was new IBL users. I often get questions about the nuts and bolts of running an IBL class and my talk was intended to address some of the concerns that new users have. I could talk for days and days about this, but being limited to 15 minutes meant that I could only provide the “movie trailer” version.

Below are the slides from my talk.

One of my goals was to get people thinking about the structure they need to put in place for their own classes. When I wrote my slides, I had a feeling that I couldn’t get through everything. I ended up skipping the slide on marketing, but in hindsight, I wish I would have skipped something else instead. Two necessary components of a successful IBL class are student buy-in and having a safe environment where students are willing to take risks. Both of these require good marketing and I never had a chance to make this point. Maybe next year, I will just give a talk about marketing IBL to students.

Dear College Instructors,

Matthew Leingang (NYU), Ron Taylor (Berry College), and I are interested in how college instructors utilize social media. In particular, we are curious how teachers interact with their current and past students on social networks like Facebook and Google+. How do you interact with your current and former students on social media? Do you have policies about this interaction? We have put together a short survey to gather some data regarding this often sensitive issue. The intent is to summarize the results in a short article that will likely be submitted to MAA FOCUS. We would be thrilled if you would take a few minutes to complete our short survey.


Dana, Matthew, & Ron

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On Saturday, May 5, 2013, I was joined by TJ Hitchman (University of Northern Iowa) for the Michigan Project NExT Panel Discussion on Teaching Strategies for Improving Student Learning, which was part of the 2013 Spring MAA Michigan Section Meeting at Lake Superior State University. The title of the session was “Teaching Strategies for Improving Student Learning” and was organized by Robert Talbert (Grand Valley State University). The dynamic looking guy in the photo above is TJ.

Here is the abstract for the session.

Are you interested in helping your students learn mathematics more effectively? Are you thinking about branching out in the way you teach your courses? If so, you should attend this panel discussion featuring short talks from leaders in higher education in employing innovative and effective instructional strategies in their mathematics classes. After speaking, our panelists will lead breakout discussions in small groups to answer questions and share advice about effective instructional strategies for college mathematics. Panelists will include Dana Ernst (Northern Arizona University) and Theron Hitchman (University of Northern Iowa), both noted for their effective use of the flipped classroom and inquiry-based learning.

Sweet, I guess running my mouth often enough about inquiry-based learning (IBL) gets me “noted.”

Each of TJ and I took about 10-15 minutes to discuss our respective topics and then we took the remaining time to chat and brainstorm as a group. The focus of my portion of the panel was on “Inquiry-Based Learning: What, Why, and How?” My talk was a variation on several similar talks that I’ve given over the past year. For TJ’s portion, he discussed his Big “Unteaching” Experiment that he implemented in his Spring 2013 differential geometry course.

Here are the slides for my portion of the panel.

Despite low attendance at the panel, I think it went well. Thanks to Robert for inviting TJ and me!

Montessori Observations

April 30, 2013 — 3 Comments

This morning I spent an hour observing my boys’ classrooms at Haven Montessori. Wow. My wife and I sat in the corner and just watched for 30 minutes in each classroom. My younger son (age 5) is in a Primary Classroom, which is for children 3 years to 6 years (including Kindergarten). My older son (age 7) is in Lower Elementary, which is for 1st–3rd grades. Both of our boys started Montessori in January of this year and we have been thrilled with the outcome. We were hesitant to move them mid-school year, especially after having moved to Arizona less than a year ago, but we have no regrets about our decision.

This wasn’t my first observation of a Montessori classroom, but each time I do it, I am blown away. Here are a few quick observations:

  • All of the students were working quietly and respectfully.
  • Students were either working independently or collaboratively with another student or two.
  • There were a variety of different things going on at the same time.
  • Students were freely moving about the room, but always focused on their respective task.
  • Students were smiling and enjoying themselves, but not goofing off.
  • Students appeared to be working on stuff because they genuinely seemed interested.
  • There were no incentives and no grades!

I could go on and on, but you get the idea. It seems like a Utopia. If you’ve never seen a Montessori classroom, go check it out. I’m sure the success of each classroom has a lot to do with the teacher, so we are tremendously grateful that our boys ended up with great teachers.

There are a lot of similarities between Montessori and inquiry-based learning (IBL), which is the approach that I try to take (to various degrees) in the classes that I teach. All of the wonderful things that I witnessed this morning are exactly the kinds of things that I strive for in my own classrooms. Sometimes it works and sometimes it doesn’t. But I keep trying.

While I was observing, I kept daydreaming; “What if students were provided with this type of experience throughout their entire education?” In particular, I spent quite a bit of time pondering my last observation above about grades and incentives. As a teacher, I try to de-emphasize grades as much as possible, but our educational system is so entrenched in their use. Is it possible to eliminate the need for incentives? Is there something that happens in our development that diminishes our curiosity flame?

Math Ed Matters is Live!

April 12, 2013 — 2 Comments


Angie Hodge and I are excited to announce that Math Ed Matters went live earlier today. Math Ed Matters is a (roughly) monthly column sponsored by the Mathematical Association of America and authored by me and Angie. The column will explore topics and current events related to undergraduate mathematics education. Posts will aim to inspire, provoke deep thought, and provide ideas for the mathematics—and mathematics education—classroom. Our interest in and engagement with inquiry-based learning (IBL) will color the column’s content.

Our first post is isn’t terribly exciting; it’s just an introduction to who we are. Here’s a sample of what we hope to discuss in future posts:

  • How did Angie and I meet and how did we end up collaborating on this blog?
  • History and impact of Project NExT
  • Inquiry-Based Learning: What, Why, and How?
  • How and why did Angie and Dana start implementing an IBL approach?
  • What’s the Buzz? (Calculus Bee)
  • A recap of the 16th Annual Legacy of R.L. Moore Conference (June 13-15, 2013 in Austin, TX)
  • A recap of MathFest 2013 (July 31-August 3, 2013 in Hartford, CT)
  • Pivotal Moments: How did Dana and Angie get to where they are now?
  • Utilizing open-source technologies and text-books

We’d love for you to follow along and join in the conversation. What other topics would you like for us to discuss?

Thanks to the MAA for giving us the opportunity to share our musings with you!

The best teachers are those who show you where to look, but don’t tell you what to see.

Quote by Alexandra K. Trenfor

Several weeks ago I was asked to take part in the Project NExT Alternative Assessment Techniques panel discussion at the 2013 Joint Mathematics Meetings, which recently took place in San Diego, CA. I was extremely honored to be considered for the panel, but at the time I was not planning on attending the JMM, so I declined the invitation. A couple weeks later, it turned out that I was going to make it to the JMM after all. At about 11PM the night before I was going to fly to San Diego, I received an email from the organizers of the panel discussion indicating that one of the panelists was unable to make it and that they heard was going to be there. They asked if I could fill in at the last minute and I accepted.

Here is the abstract for the panel.

Since classroom assessment is used to determine a student’s level of mastery, how can we vary our methods of assessment to accurately reflect the diversity of ways that students learn and understand the material? Traditional methods of assessment, such as exams, quizzes, and homework, may not accurately and robustly measure some students’ understanding. In this panel, we will propose alternative methods and discuss the following questions:
– What assessments exist besides the traditional ones and how can I use them for my course?
– How can I determine the validity of an alternative assessment?
– How can I develop my own alternative assessments?
– How can alternative assessments help me evaluate the effectiveness of a non-traditional classroom?

It is worth pointing out that I’m not an assessment expert by any stretch of the imagination. Also, given that I had less than 48 hours to prepare amidst a pretty full schedule, I didn’t have a lot of time to come up with something new and creative for my talk. Inquiry-based learning (IBL) is one of my passions and I’ve given quite a few IBL-related talks in the past few months, so I decided to “twist” the ideas from some of my recent talks into a talk about assessment. In my talk, I propose implementing IBL not only as a pedagogical approach but also as an assessment strategy. This isn’t really a stretch since in my view, an effective IBL class is all assessment, all the time.

My fellow panelists included Theron Hitchman (University of Northern Iowa), Bonnie Gold (Monmouth University), and Victor Odafe (Bowling Green State University). Theron gave a talk on using Standards Based Assessment (you can find his slides here), Bonnie spoke on a variety of summative assessment techniques, and Victor shared his experience with oral assessment. It turns out that the person that I was filling for is mathematics education superstar Jo Boaler. Me filling in for her is ridiculous.

Here are the slides for my portion of the panel.

Thanks to the organizers of the panel (Cassie Williams (James Madison University), Jane Butterfield (University of Minnesota), John Peter (Utica College), and Robert Campbell (College of Saint Benedict and Saint John’s University)) for providing me with the opportunity to speak on the panel.

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.

What have I been up since I was last at NAU?

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.

Reflection on the past semester at NAU

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.

Office Hours

More 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:

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

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.

Miscellaneous Highlights

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.

That student is taught the best who is told the least.

Quote by R.L. Moore in 1966

Producing learners

December 21, 2012 — Leave a comment

Robert Talbert (Grand Valley State University) recently posted an article titled “We need to produce learners, not just students” on his Casting Out Nines blog that really resonates with me. In the article, Robert expresses what he feels is the goal of higher education and states in general terms how an educator can get on the path to achieving this goal.

There are so many wonderful nuggets in the article. Here’s one of my favorites.

I even care about this more than students’ grades. In my mind, and I think in the minds of most people who employ my students later in life, if you graduate from university and don’t have the skills or dispositions necessary to teach yourself new things for the rest of your life, it doesn’t really matter what your GPA says: You’re not educated. And if I shepherd a student through the university without putting them in a position time and again to hone these skills and dispositions, it doesn’t matter what my title or my course evaluations say: I’m not an educator.

This quote summarizes exactly why I started incorporating inquiry-based learning (IBL) and the Moore method into my courses. IBL is not a magic bullet, but the experiences that I have had watching students transform into independent learners is why I am so passionate about it. I want students to have life-changing experiences! Learning the content of mathematics is just a bonus.

Robert ends the article with the following statement.

But it doesn’t matter whether we use the flipped classroom, IBL, PBL, or what-have-you — what counts is whether we are training people to be able to learn on their own. Doing education without this in mind is just irresponsible.


If you haven’t already, please go read Robert’s article.