Profile

Cover photo
Dana Ernst
Works at Northern Arizona University
Attended George Mason University
Lives in Flagstaff, AZ
36,524 followers|884,631 views
AboutPostsReviews

Stream

 
Great day of rock climbing today in Flagstaff. 
7
Add a comment...

Dana Ernst

Shared publicly  - 
 
I'll be attending the 2015 MAA/CURM Conference the next couple days at Brigham Young University. Any other G+ math folks going to be there? +Sean Raleigh?
3
Theron Hitchman's profile photo
 
Have fun!
Add a comment...

Dana Ernst

Shared publicly  - 
 
Another important post by +Stan Yoshinobu. I've heard variations of all the student quotes over the years.
 
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...
View original post
4
Add a comment...

Dana Ernst

Shared publicly  - 
 
This what my students do at math conferences. I'm behind camera egging them on. 
11
Theron Hitchman's profile photoDana Ernst's profile photo
2 comments
 
The task I set them on was to pick up the top cup with their mouth while standing on one foot and without using hands. One student was able to do just a stack with one cup. Most could only do a stack with 4 cups. 
Add a comment...

Dana Ernst

Shared publicly  - 
 
Next week I am moderating a student panel in our department's Teaching Showcase.  Here is the abstract:

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?
Teaching Showcase. The Teaching Showcase provides an opportunity for professional development focused on the best practices of teaching. It is our hope that all attendees will learn from the expertise of their colleagues and be in a state of continuous improvement in the classroom as an ...
9
1
Drew Armstrong's profile photoCathleen Goodell's profile photoKatie Springer's profile photo
2 comments
 
Describe a classroom environment, including teaching methods, that optimizes your learning performance.
Add a comment...
 
Had a great day visiting with +Bret Benesh.  Bret visited my IBL problem solving class and then we got to work on some math over coffee/hot cider.  Looking forward to his two talks tomorrow and an opportunity for work on some more math.
9
Bret Benesh's profile photoTheron Hitchman's profile photo
3 comments
 
If only I could. 
Add a comment...
In his circles
1,072 people
Have him in circles
36,524 people
Jennifer Frazier's profile photo
Eddie Hayes's profile photo
Ronnie Giles's profile photo
Shane Hansen's profile photo
Jenell Scott's profile photo
Carlisha Smith's profile photo
Emily J's profile photo
Richard Green's profile photo
Tod Fuller's profile photo

Dana Ernst

Shared publicly  - 
 
Paper number 2 with the the CURMies submitted. Skidoosh.
7
Dana Ernst's profile photoRichard Green's profile photo
3 comments
 
More good CV points for you!
Add a comment...

Dana Ernst

Shared publicly  - 
 
I recently made a worksheet in +The SageMathCloud that introduces for loops and conjecture testing to my students.  I borrowed lots of ideas from a blog post by +Vincent Knight.  Check it out.  

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. 
6
1
Robert Talbert's profile photoDana Ernst's profile photoHamilton Carter's profile photoWilliam Rutiser's profile photo
4 comments
 
Thanks for the great example sheet!  I was under the impression that files couldn't be shared from +The SageMathCloud.  Way cool!
Add a comment...

Dana Ernst

Shared publicly  - 
 
 
This semester, I am teaching a second-semester abstract algebra course on rings, fields, and Galois theory. So far, I have delivered only one 30 minute lecture. The rest of the time has been student presentations, and an occasional in-class group  project. I have only six students -- I don't know if I could manage this format with a larger group, but it has been an enjoyable change of pace for the students and the instructor alike.

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.
1 comment on original post
14
Richard Green's profile photoRoice Nelson's profile photo
2 comments
 
Wish I was in this class!
Add a comment...

Dana Ernst

Shared publicly  - 
 
One of my students just introduced me to the following website that contains interesting problems to solve.  I've only tinkered around a little bit and it seems a bit like Project Euler, but without the emphasis on programming.
8
Dana Ernst's profile photo
2 comments
 
Now, it accepted the answer.
Add a comment...

Dana Ernst

Shared publicly  - 
 
+William Stein and +The SageMathCloud, I keep meaning to tell you that I have two colorblind students this semester and they've indicated to me that the color palette for SMC is really difficult for them.  Any chance some changes can be made? I have no idea what a good choice would be, but perhaps my colorblind students could point you in the right direction.

Posting publicly in case there are other colorblind folks out there with insight.
4
William Stein's profile photoDana Ernst's profile photo
4 comments
 
Thanks +William Stein. I'm not sure the students have fiddled with editor settings. I'll look into it. 
Add a comment...

Dana Ernst

Shared publicly  - 
 
 
This article does a perfect job of explaining what's going on in academia right now. We need to get back to teaching; there will always be a market for that. If universities continue to ignore what goes on in the classroom, then they really deserve what's about to happen to them.
The professoriate needs to refocus on students or face extinction.
2 comments on original post
4
1
Dana Ernst's profile photoDrew Armstrong's profile photoTheron Hitchman's profile photoJoerg Fliege's profile photo
4 comments
 
I am with +Drew Armstrong and +Cathy O'Neil on this one. Stand and fight the bear.
Add a comment...
People
In his circles
1,072 people
Have him in circles
36,524 people
Jennifer Frazier's profile photo
Eddie Hayes's profile photo
Ronnie Giles's profile photo
Shane Hansen's profile photo
Jenell Scott's profile photo
Carlisha Smith's profile photo
Emily J's profile photo
Richard Green's profile photo
Tod Fuller's profile photo
Education
  • George Mason University
    BS, Mathematics, 1993 - 1997
  • Northern Arizona University
    MS, Mathematics, 1997 - 2000
  • University of Colorado at Boulder
    PhD, Mathematics, 2003 - 2008
Basic Information
Gender
Male
Story
Tagline
Father of two boys, husband, mathematician, cyclist, trail runner, rock climber, and coffee drinker.
Introduction

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 algebrasKazhdan-Lusztig theory, generalized Temperley-Lieb algebrasdiagram 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.

Work
Occupation
Assistant Professor of Mathematics
Employment
  • Northern Arizona University
    Assistant Professor, 2012 - present
  • University of Colorado at Boulder
    Graduate Student/Teaching Assistant, 2003 - 2008
  • Front Range Community College
    Math Faculty, 2001 - 2003
  • Northern Arizona University
    Graduate Student/Instructor, 1997 - 2001
  • Plymouth State University
    Assistant Professor, 2008 - 2012
Places
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Currently
Flagstaff, AZ
Previously
Williamsville, NY - Fairfax, VA - Flagstaff, AZ - Boulder, CO - Plymouth, NH
Links
YouTube
Contributor to
Best bike shop on the planet run by the best people in the universe.
Quality: ExcellentAppeal: ExcellentService: Excellent
Public - 2 years ago
reviewed 2 years ago
1 review
Map
Map
Map