The Spring 2020 semester was a wild ride! The Covid-19 pandemic forced us to use remote instruction after Spring Break. Adapting to this new paradigm and coping with the state of the world was challenging for students and instructors. I could not have asked for a more awesome group of students to go through this experience with. I’m really proud of them. I asked a lot of them while investing a lot of emotional capital and they rose to the challenge.

Each semester, I ask some variation of the following question on the final exams:

Describe how your perceptions of learning, especially mathematics, have changed.

So many of the responses that I received this past semester were amazing, but the following from a student (chemistry major) in my introduction to proof course really stood out to me:

I have always enjoyed mathematics, and because of that learning math was an enjoyable process and always made me excited for future courses. However, I have never had as much fun in a math class as I did in this one. To begin with, my perception of what studying mathematics means has completely changed. While manipulating numbers and formulas has its uses, mathematics is so much more. There is a very creative and artistic beauty associated with mathematical proof and logic. Like Cantor’s Diagonalization Argument, it is incredible to think that someone was able to discover such a simple yet mind blowing process. It is just such a creative way to think and I aspire to eventually be like minded in that aspect. That is getting a little off topic, but in terms of learning, this is the first class that I have attempted homework first and then discussed it in the following class. This method is so incredibly effective that I do not understand why I am just now experiencing it. By attempting things on my own first, I am able to think of so many more questions for class and I have always believed the best way to learn is by asking questions. Math can be a difficult subject, especially proof writing, but I feel that it was made much easier by developing a true understanding rather than by force feeding people step-by-step methods or something analogous to that.


Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 226: Discrete Math
  MAT 690: CGT

About This Site

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  The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.

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Land Acknowledgement

  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.