Po-Shen Loh at Carnegie-Mellon is perhaps best known for his success coaching the US Math Olympiad team. However, he is equally passionate about a project he started called Expii that he hopes will provide self-directed learning of mathematics using open-source contributions and a sophisticated dynamic learning system.

Mathematical subject matter is organized in a collection of nodes that are determined by a core group of editors at Expii. Navigating through the nodes eventually leads to a specific topic node. Within that topic node resides a collection of explanations and exercises for that specific topic written by a volunteer contributor. Explanations are constructed on the site's easy to use editor which recognizes LaTeX. The site also allows one to embed instructional YouTube videos. Exercises too are easily constructed within the site's builtin editor.

There are two aspects to Expii that separate it from other open source on-line learning systems, the editorial approach and the dynamic learning algorithm.

First, unlike the Wikipedia editorial approach, contributors do not typically edit other contributors' work. Factual corrections to an existing contribution are welcome, but stylistic re-writes are discouraged. Rather, if a contributor does not like the style of a particular explanation, that contributor is encouraged to submit a competing explanation in the style that they prefer. Subsequently, the two (or more) explanations then compete with each other by receiving upvotes/downvotes from users of the site. Explanations with more votes are listed first when a learner visits a particular node. Prof. Loh hopes that this approach will provided a variety of explanations on different topics that will resonate with different learners.

Second, the learning algorithm is a novel application of the ELO ranking system that is used in international chess competition. In a sense, learners and exercises are in competition with each other and are ranked using an ELO-type system. In this way, when a learner requests an exercise on a particular topic, their ranking is matched to an exercise with a nearby ranking. As the learner improves, their ranking improves and they are presented with increasingly challenging exercises.

At the moment, the Expii effort is funded by private investors and is a for-profit entity. However, Prof. Loh says that the future business model will not include a paywall for access to the site. Rather, one possible business model would be mediating the pairing of contributors and learners on Expii into paid, adhoc, teaching and tutoring relationships. The core group is looking for investors and applying for federal grant money to keep the 3-year effort going. There has been steady growth in both users and contributors, but it seems to not have reached "critical mass" yet.

The site welcomes the addition of existing open-source materials as long as they are appropriately licensed. For example, a Creative Commons license that allows commercial use would work.

Prof. Loh states that a lot of his motivation for starting the site came from his work with the Math Olympiad and other mathematics competitions. He recognizes that for the US (and other countries) to compete, there needs to be a large pool of talented mathematics students. He hopes that Expii can deepen that pool. Indeed, he hopes that it can take a struggling mathematics student that may not be getting quite what he/she needs in their home classroom and provide just the right kind of learning experience to turn them into future Math Olympians. And, as a great side benefit, Expii will elevate the mathematical literacy across the board.

If you have OERs that you have developed and would like a venue, Expii may be a good choice for you. The ranking system may be the kind of objective assessment of your work that could be used in tenure, promotion and merit considerations at your institution.

# Open Mathbook

A place to promote, discuss, and develop free and open source mathematics textbooks.

## Thursday, August 4, 2016

## Thursday, June 16, 2016

### Interesting OER Article in the Washington Post.

Interesting and encouraging that the nation's community colleges are really taking OERs to heart. Good article here: College courses without textbooks? These schools are giving it a shot. By Danielle Douglas-Gabriel

## Thursday, June 2, 2016

### University of North Carolina Press OER Initiative

The effort by the University of North Carolina Press to provide formal support throughout the UNC system for open educational resources (OER) development described in this Chronicle article is really promising. It's wonderful to see institutional support for these kinds of efforts.

I followed up with John McLeod, Director of the Office of Scholarly Publishing Services at UNC Press about whether there were any math related efforts within the office right now. While there aren't any current projects, they have applied for NSF funding to support OER development in service level mathematics classes within the UNC system. They are also in conversation with the NC School of Science and Math, a high school that is part of the UNC system, about OER for mathematics at the secondary level.

I followed up with John McLeod, Director of the Office of Scholarly Publishing Services at UNC Press about whether there were any math related efforts within the office right now. While there aren't any current projects, they have applied for NSF funding to support OER development in service level mathematics classes within the UNC system. They are also in conversation with the NC School of Science and Math, a high school that is part of the UNC system, about OER for mathematics at the secondary level.

## Tuesday, April 26, 2016

### AIM Open Textbooks in Mathbook XML Workshop (almost live updates)

David Farmer, Rob Beezer and others are developing an open markup language, Mathbook XML, to typeset mathematical texts in a way that facilitates publication in a variety of formats (e.g. html, pdf, e-book). As part of that development, they seek authors willing to engage the new platform and provide feedback for development.

The American Institute of Mathematics is hosting a workshop with the developers and open texbook authors this week that is focused around open textbooks and Mathbook XML. Rob Beezer and Tom Judson are both posting daily reports on the workshop at their blogs:

The American Institute of Mathematics is hosting a workshop with the developers and open texbook authors this week that is focused around open textbooks and Mathbook XML. Rob Beezer and Tom Judson are both posting daily reports on the workshop at their blogs:

The posts so far have been pretty informative. I wish I was there.

### Lakeland and Lorain Community Colleges Support Open-Source Textbook

Jeff Zeager recently shared the following news:

We look forward to the next edition of the text.

Carl Stitz and I have been granted sabbaticals from our respective institutions for Fall 2016 to edit and enhance the Stitz-Zeager Precalculus book. It is our intention to have the 4th edition ready by January 2017.

Of course, this is good news for their project, but it also shows that their respective institutions, Lorain County Community College and Lakeland Community College, are willing to commit resources to support and advance an open-source textbook. Both institutions should be applauded for their support. If you find yourself in a similar position--trying to justify a sabbatical to work on an open-source project--perhaps point at these two colleges as precedent.The .pdf version of the book along with all of the LaTeX code will be posted on our website www.stitz-zeager.com when we're done with the revisions.

We look forward to the next edition of the text.

## Monday, January 25, 2016

### Elementary Abstract Algebra: Examples and Applications

Elementary Abstract Algebra: Examples and Applications is a new open-source abstract algebra text by a number of contributors: Justin Hill, Chris Thron (eds), Thomas Judson, Dave Witte Morris, Joy
Morris, A. J. Hildebrand, Holly Webb, Johnny Watts and David Weathers.

According to editor Chris Thron:

If you have used the text in its current form, please consider writing a review for the MAA Reviews website. The previous blog posting describes best practices for doing so.

As a follow up to this blog posting, I hope to get some insight into how this large number of collaborators managed to work together.

According to editor Chris Thron:

The link above will lead to both on-line (html) and pdf versions of the text. Print-on-demand copies are available through Lulu. There is also a series of supporting YouTube videos."The treatment is far more elementary than any other book on abstract algebra that we've seen. The text is designed for students who are planning to become secondary-school teachers. We particularly emphasize material that has relevance to high-school math, as well as practical applications."

If you have used the text in its current form, please consider writing a review for the MAA Reviews website. The previous blog posting describes best practices for doing so.

As a follow up to this blog posting, I hope to get some insight into how this large number of collaborators managed to work together.

## Thursday, January 14, 2016

### MAA Reviews of Open Source Texts

The Mathematical Association of America (MAA) maintains a book review site called MAA Reviews where volunteers review math-related texts. The site hosts reviews of traditionally published texts, but also accepts reviews of open-source texts. For example, Vic Reiner and I wrote a review of Guichard's Calculus text a while back.

The editor of MAA Reviews, Fernando GouvĂȘa, is quite supportive of including reviews of open-source texts on the site. Though he lightly lamented in an email exchange with me:

After a while, other things made claims on my time, leaving me less active in this pursuit. However, this is a good way to get open-source texts some exposure. Further, a favorable review in MAA Reviews might help the author(s) get some credit for their work at their home institutions.

The editor of MAA Reviews, Fernando GouvĂȘa, is quite supportive of including reviews of open-source texts on the site. Though he lightly lamented in an email exchange with me:

For a while, I went on a one-man mission to recruit reviews of open-source texts for the site. My self-imposed best practice was that the reviewer not be an author of the text and had to have taught at least one class using the text. Here's a list of some of the MAA Reviews I "recruited" during this period:We are definitely willing and interested. The difficulty is that

usually the only reward I can offer my reviewers is a free copy of the

book they are to review; as a result, it is always harder to find

reviewers for open-source texts.

- Abstract Algebra: Theory and Applications by Thomas W. Judson, reviewed by Chris Thron.
- A First Course in Linear Algebra by Robert Beezer reviewed by Mike Daven and Tanya Leise.
- Calculus for Life Sciences: a Modeling Approach by J. L. Cornette and R. A. Ackerman reviewed by Steven Deckelman and George Jennings.
- Book of Proof by Richard Hammack reviewed by David Offner.
- Linear Algebra by Jim Hefferon reviewed by Robert W. Hayden.
- Precalculus: An Investigation of Functions by David Lippman and Melonie Rasmussen reviewed by Mike Kenyon.

After a while, other things made claims on my time, leaving me less active in this pursuit. However, this is a good way to get open-source texts some exposure. Further, a favorable review in MAA Reviews might help the author(s) get some credit for their work at their home institutions.

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