### Dana Ernst

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Dana Ernst

Works at Northern Arizona University

Attended George Mason University

Lives in Flagstaff, AZ

36,791 followers|930,360 views

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The Grammar According to West. Grammar tips for mathematicians. Thanks +Nandor Sieben and +Bret Benesh!

The Grammar According to West. by Douglas B. West. Summary. I have been accumulating these observations for many years. Writing textbooks has led me to think about how best to present mathematics. I have also noted writing errors commonly made by my thesis students and in papers submitted to ...

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Robert Jacobson

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This is brilliant!

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It is time to use evidence-based teaching practices at all levels by providing incentives and effective evaluations, urge Stephen E. Bradforth, Emily R.

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This is fun to read. I can't help being reminded of a recent post by +Richard Elwes about how we can learn from how babies learn. Conway, it seems to me, has benefited enormously from a conscious decision to adopt a childlike attitude to mathematics, following whatever he finds interesting without paying too much attention to what others will think of him.

The long read: John Horton Conway is a cross between Archimedes, Mick Jagger and Salvador Dalí. For many years, he worried that his obsession with playing silly games was ruining his career – until he realised that it could lead to extraordinary discoveries

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That's an excellent story!

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The Academy of Inquiry-Based Learning has a well established mentoring program for IBL practitioners.

The purpose of the Mentoring Program is to provide advice, support, and encouragement to those interested in using the IBL in their teaching. Individuals who request assistance are paired with mentors who are experienced practitioners of IBL. Typically, mentoring is conducted by email. Group email mentoring is also possible, and several groups have been formed around specific topics or cohorts of workshop groups.

If you are interested in a mentor, fill out the form on the page below.

The purpose of the Mentoring Program is to provide advice, support, and encouragement to those interested in using the IBL in their teaching. Individuals who request assistance are paired with mentors who are experienced practitioners of IBL. Typically, mentoring is conducted by email. Group email mentoring is also possible, and several groups have been formed around specific topics or cohorts of workshop groups.

If you are interested in a mentor, fill out the form on the page below.

The purpose of the Mentoring Program is to provide advice, support, and encouragement to those interested in using the IBL in their teaching. Individuals who request assistance are paired with mentors who are experienced practitioners of IBL. Typically, mentoring is conducted by E-mail.

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"Impartial avoidance games for generating finite groups" by +Bret Benesh, +Dana Ernst, and +Nandor Sieben now on the arXiv.

#CombinatorialGameTheory #spnetwork arXiv:1506.07105

#CombinatorialGameTheory #spnetwork arXiv:1506.07105

Abstract: We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making the set of jointly-selected elements into a ...

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In his circles

1,093 people

"Early encounters with math can be misleading. The subject seems to be about learning rules — how and when to apply ancient tricks to arrive at an answer. Four cookies remain in the cookie jar; the ball moves at 12.5 feet per second. Really, though, to be a mathematician is to experiment. Mathematical research is a fundamentally creative act. Lore has it that when David Hilbert, arguably the most influential mathematician of fin de siècle Europe, heard that a colleague had left to pursue fiction, he quipped: ‘'He did not have enough imagination for mathematics.'"

The Singular Mind of Terry Tao via +The New York Times nyti.ms/1OCpgEB

The Singular Mind of Terry Tao via +The New York Times nyti.ms/1OCpgEB

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Drew Armstrong

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It's so hard to get my students to experiment. They just have this instinct to sit there and wait until someone tells them what to do. My diagnosis is that elementary, middle, and high school must not encourage experimentation.

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Excited for the IBL Workshop to kick off on Tuesday morning. Looking forward to seeing +Stan Yoshinobu, +Matthew Jones, and +Kyle Petersen.

The next IBL Workshop is in San Luis Obispo, CA, hosted at Cal Poly. The workshop will be held July 7-10, with lodging and most meals covered by the workshop. Early career faculty are eligible for travel scholarships up to $500. SPIGOT (Supporting a Pedagogical Innovation for a Generation of ...

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Brian Loft

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I wish I could be there. Maybe next summer I won't have other obligations....

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Come on over.

The Mathematical Association of America has special interest groups for members to organize around a topic or area of mathematics or mathematics education. A special interest group of the MAA is called a SIGMAA . The IBL community has decided to apply to ...

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New at Math Ed Matters: Knowing What to Do is not Doing.

In this guest post, Bob Klein (Ohio University) reflects on his first year fully embracing inquiry-based learning (IBL).

In this guest post, Bob Klein (Ohio University) reflects on his first year fully embracing inquiry-based learning (IBL).

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John Meuser

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The Moore Method, or IBL, separates mathematical behavior from mathematical knowledge.

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Paper with +Bret Benesh and +Nandor Sieben submitted. Boom.

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A little puzzle for the math folks on Google+.

Behind the walls at Emerson High School in Oklahoma City, construction workers found old chalkboards with drawings and class lessons, written almost a century ago and in remarkable condition.

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Antonia Malchik

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I'm finding it interesting to note the different takes on this. I've seen it posted by writing groups and education groups, both with different focuses on what's important about the story (discovery, content, preservation, history, handwriting, etc.). Curious what mathematicians make of the arithmetic lesson methods!

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People

In his circles

1,093 people

Communities

18 communities

Education

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

Work

Occupation

Assistant Professor of Mathematics

Employment

- 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

Places

Currently

Flagstaff, AZ

Previously

Williamsville, NY - Fairfax, VA - Flagstaff, AZ - Boulder, CO - Plymouth, NH

Links

YouTube

Contributor to

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

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