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### Dana Ernst

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### Dana Ernst

Shared publicly -**Math Anxiety Realities: Student Voices**

In the interest of trying to ensure things are interpreted appropriately, I need to mention some very important caveats. I deeply respect the people who work in education at all levels. No one I know, who works in education, intentionally creates or suppo...

### Dana Ernst

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### Dana Ernst

Shared publicly -Wouldn't it be nice to know how students learn math: what they think works and what they think doesn't? How do students see their math classrooms and what their teachers do to facilitate learning? This is a wonderful opportunity for new teachers as well as veterans to have a chance to hear from students about how they learn math. These students aren't necessarily math majors - but they DO take our classes and DO care about their learning!

There will be 4-6 students on the panel representing courses such as algebra for precalculus, precalculus, and first semester calculus. I'm currently drafting a set of questions to ask them.

What would you ask?

### Dana Ernst

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### Dana Ernst

Shared publicly -As a side note, nearly all of my students had 0 programming experience prior to working on this worksheet. It's interesting to see the variety of default comfort levels with working with computers and programming. Many of my female students expressed extreme doubt that they could do it without help. Of course, they did just fine, but it bothered me that this was their default reaction.

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### Dana Ernst

Shared publicly -The results have been astounding so far. Today in class, a student said the following words, which I never thought I would hear in an undergraduate classroom: "Oh, we can prove that no problem! It's just a simple application of the First Isomorphism Theorem!" She then jumped up to the board and proved a certain ideal I was prime in a ring R, by demonstrating I was the kernel of a homomorphism from R to a known integral domain.

My thanks to +Dana Ernst and +Theron Hitchman , whose frequent posts on and about IBL experiences finally got me to take the plunge.

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### Dana Ernst

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Shared publicly -Posting publicly in case there are other colorblind folks out there with insight.

### Dana Ernst

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- George Mason UniversityBS, Mathematics, 1993 - 1997
- Northern Arizona UniversityMS, Mathematics, 1997 - 2000
- University of Colorado at BoulderPhD, Mathematics, 2003 - 2008

My name is Dana Ernst and I am an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ.

My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, I study the combinatorics of Coxeter groups and their associated Hecke algebras, Kazhdan-Lusztig theory, generalized Temperley-Lieb algebras, diagram algebras, and heaps of pieces. By employing combinatorial tools such as diagram algebras and heaps of pieces, one can gain insight into algebraic structures associated to Coxeter groups, and, conversely, the corresponding structure theory can often lead to surprising combinatorial results. The combinatorial nature of my research naturally lends itself to collaborations with undergraduate students, and my goal is to incorporate undergraduates in my research as much as possible. See my scholarship page for more information.

Furthermore, I am passionate about mathematics education. In particular, I am interested in inquiry-based learning (IBL) and the Moore method for teaching mathematics. This educational paradigm has transformed my teaching. I am currently a Special Projects Coordinator for the Academy of Inquiry-Based Learning and a mentor for several new IBL practitioners. Moreover, I actively give talks and organize workshops on the benefits of IBL as well as the nuts and bolts of how to implement this approach in the mathematics classroom.

I am also interested in utilizing technology to enhance the teaching and learning of mathematics. Specifically, I choose free and open-source software and technologies when appropriate. For example, I have been incorporating Sage and GeoGebra into my teaching. Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. For examples of a few of the cool things you can do with Sage, check this page. According to their webpage, GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. There are tons of awesome GeoGebra examples located here.

In addition to using free and open-source software, I am inspired by the recent open-source textbookmovement and I strongly believe that educators should choose free, open-source, or low cost textbooks when a viable alternative exists. For a list of open-source textbooks, go here and here.

Angie Hodge and I are coauthors for Math Ed Matters, which is a (roughly) monthly column sponsored by the Mathematical Association of America. The column explores topics and current events related to undergraduate mathematics education. Posts aim to inspire, provoke deep thought, and provide ideas for the mathematics—and mathematics education—classroom. Our interest in and engagement with IBL color the column's content.

I also maintain a personal blog, which is part of the Booles' Rings network of academic home pages/blogs. On my blog, I typically write about topics related to mathematics, education, and technology. In addition, I occasionally post about my cycling, trailing running, and rock climbing adventures on my Elevation Gain blog.

Lastly, I am a husband and a father of two incredible sons. Oh, I enjoy drinking copious amounts of coffee, too.

- Northern Arizona UniversityAssistant Professor, 2012 - present
- University of Colorado at BoulderGraduate Student/Teaching Assistant, 2003 - 2008
- Front Range Community CollegeMath Faculty, 2001 - 2003
- Northern Arizona UniversityGraduate Student/Instructor, 1997 - 2001
- Plymouth State UniversityAssistant Professor, 2008 - 2012

- Dana's Blog (current)
- Math Ed Matters (current)