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Dana Ernst
Works at Northern Arizona University
Attended George Mason University
Lives in Flagstaff, AZ
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Dana Ernst

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Yes!
 
Elegant reason-poems (AKA "proofs")

Paul Lockhart waxing lyrical about mathematics. In a way, this video captures, for me, exactly what matheamatics is

https://www.youtube.com/watch?v=V1gT2f3Fe44

This is a kind of trailer for his book Measurement:

http://www.hup.harvard.edu/catalog.php?isbn=9780674057555

Don't miss the wonderful excerpts at

http://www.brainpickings.org/index.php/2012/09/25/measurement-paul-lockhart/

 +David Butler , you should love this!

#mathematics  
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My brother, Brandt Christopher Ernst, was born on this day in 1971.  He passed away from leukemia at 11 years old.  In honor of my brother, my boys celebrate Brother's Day on this day.  Happy Brother's Day!   #fuckcancer  
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fuck cancer, indeed
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The Klein Four group is back!  

"Get Tenure" set to Daft Punk / Pharrell Williams' "Get Lucky".
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On that note, I am going to bed.
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Dana Ernst

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Great IBL post.
 
"Activation Energy" and IBL Uptake
Here's a basic question.   What does it take to switch from traditional to IBL teaching?   This question can be answered in many ways.  I'm going to come at this from an education system reform angle.  Essentially the general problem is the implementation c...
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Dana Ernst

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Here is the kit for my recent graph theory project:

Math for eight-year-olds: graph theory for kids! 
http://jdh.hamkins.org/math-for-eight-year-olds/

Print out to double-sided, and then fold each page in half. Place the folded pages one after the other (not nested) inside the cover page.
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The call for papers for the PRIMUS special issue on "Inquiry-Based Learning in First-Year and Second-Year Courses” is now posted on the PRIMUS website:

http://explore.tandfonline.com/cfp/est/inquiry_based_learning

If you are interested in submitting a paper for consideration, the deadline is June 1, 2015.

If you are not planning on submitting a paper, then please consider volunteering to referee for the special issue.  If you are willing to sign up to referee, you should first let me, +Angie Hodge, and/or +Theron Hitchman know and then follow the instruction below.

Instructions to create a PRIMUS referee account:

1.  Go to http://mc.manuscriptcentral.com/upri

2.  Under “New User?”, click “Register here”.

3.  Enter your name and email as prompted.  Click “Next”.

4.  Enter your primary address information.  Click “Next”.

5.  Select a password and enter at least two keywords for yourself that indicate your interests.  More keywords are especially helpful to us.  For example, if you have interests in the teaching of calculus and using technology and the inverted classroom and inquiry based learning, you might write include “calculus,” “technology,” “IBL,” and “inverted classroom.”  If you had additional interests in undergraduate research, you could add keywords to that effect, etc.

6.  Click “finish”.

Now you can return to the main page at http://mc.manuscriptcentral.com/upri and log in.  Your email address that you entered in the system is your username; your password is the password you entered.  You should receive an automatically generated email from Joanna Ellis-Monaghan that confirms your account creation, username, and password.

If you have any questions, please let us know.

Dana, Angie, and TJ
An inquiry-based learning (IBL) approach challenges students to create mathematics by providing tasks requiring them to conjecture, experiment, explore, and solve problems. Rather than showing facts or a clear, smooth path to a solution, the instructor guides students via well-crafted problems ...
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Dana Ernst

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Welcome to spring in Flagstaff, AZ. 
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No thanks.
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Holy spam bots!
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It can't be true... can it?

Yes, it is indeed true that the square root of 2 and two thirds is equal to 2 times the square root of two thirds. This particular equation is an example of a prompt on the UK-based website Inquiry maths. The website explains:

Inquiry maths is a model of teaching that encourages students to regulate their own activity while exploring a mathematical statement (called a prompt). Inquiries can involve a class on diverse paths of exploration or in listening to a teacher's exposition. In inquiry maths, students take responsibility for directing the lesson with the teacher acting as the arbiter of legitimate mathematical activity.

Remarkably, this particular prompt was found by a year 10 student of teacher Rachael Read. It is recommended for students with high prior attainment in years 10 and 11. Reportedly, students are quickly hooked in to the prompt, particularly when one of them claims it “works” after checking on a calculator. 

Relevant links

There is more discussion of the educational value of this equation, and on the teaching of surds in general, in the original blog post on this topic: http://www.inquirymaths.co.uk/home/number-prompts/surds

The word “surd”, referring to n-th roots, is a Latin translation of a term tracing back to the 9th century Persian mathematician al-Khwārizmī, after whom algorithms are named. He also invented the term algebra (al-jabr in Arabic).

Surds: http://en.wikipedia.org/wiki/Nth_root

al-Khwārizmī: http://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi

(Seen via Cliff Pickover on Twitter.)

#mathematics #education  
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Following my confusion about what is meant by the left hand side which I shared with many comments on the original post, I opened a poll at https://plus.google.com/u/0/101584889282878921052/posts/3BjYRf8Eg8f
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Playing in the dirt. San Francisco Peaks, Flagstaff, AZ in the distance. 
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New at Math Ed Matters: "Calculating Community: The Running Equation"

In this post, +Angie Hodge connects some lessons she has learned in her life as a runner to her life in academics.

Check out her TedX talk: https://www.youtube.com/watch?v=W6JG9-MWCKA
How does one do something they perceive to be so difficult that they never thought they would even consider doing it? How does one go from being a non-athlete to running 100 miles at elevation? And, how does this have anythin...
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Boy and dog needed some exercise. 
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In his circles
1,078 people
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36,682 people
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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
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Currently
Flagstaff, AZ
Previously
Williamsville, NY - Fairfax, VA - Flagstaff, AZ - Boulder, CO - Plymouth, NH
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