By Andrew Misseldine

*Open Choice*. The service will feature a significant collection of critical reviews of OER materials targeted to teaching faculty, instructional designers, librarians, and university staff charged with acquiring digital tools for instruction. Check Choice’s blog (http://www.choice360.org/blog) for future updates.

As a mathematics professor who teaches at a public four-year university in the US, my office resembles the typical professor’s: a desk with computer, a whiteboard, file cabinets, a table for students, photos of family and friends, framed degrees on the wall, tall stacks of grossly unorganized papers, and a bookshelf loaded with more math books than the typical student even knew existed. Many of these relate to my research interests or are about mathematics in general. Many more are textbooks for college courses like college algebra, calculus, statistics, linear algebra, topology, or differential equations. Most are copies sent to me for free by the publishers, either at my request or in hopes that I will adopt the text for future courses. The edition numbers displayed on their spines scream a fundamental problem in academics today: Why do textbooks have so many different editions? A quick poll of my own shelf gives an average of five, with some texts reaching up to eleven editions. If the content of *Elementary Linear Algebra* is so elementary, why did it take the authors eleven tries to get it right? And why is there another edition coming out next year? What could possibly still be wrong with a book that has been revised eleven times already?

It comes as no surprise, of course, that an inspection of two recent editions of one college math textbook reveals that very little has changed between them, other than cosmetic updates, minor corrections to previous errata, and rearrangements, omissions, and insertions of exercise problem sets. The cosmetic updates make the book more attractive to the instructors who adopt the texts and to the students who—without any choice in the matter—will have to purchase and use them. The changes to problem sets serve to make old editions impractical as homework exercise repositories (which many students believe is the only purpose for their math texts). In short, late edition textbooks generate revenue for their publishers and authors but provide little for the faculty and students who use them. Lane Fischer, coauthor of a recent multi-institutional study on the impact of OER in the *Journal of Computing in Higher Education*, said in an interview, “In an introductory class like College Algebra, the textbook isn’t there to entertain, it’s there to teach a topic. Algebra hasn’t changed a lot in the past fifty years, so you don’t need the latest, most expensive book to teach it well. There are comparable free resources available, and students really appreciate saving money.”^{1}

David Wiley, another coauthor of the aforementioned study, defines OER as those educational resources—such as textbooks, syllabi, media, or any other asset useful for teaching and learning—that are licensed openly: in other words, users have permission granted by the license to retain, reuse, revise, remix, and redistribute the resources (these are called the “five Rs” of OER).^{2} OER are not merely “open/free access”; “free” designates those materials for which a digital format is freely downloadable. The open license of OER grants many more permissions besides open access, because free materials might still retain copyrights. Therefore, “free” and “open” are not synonyms here. “Free” is a consequence of “open,” but the opposite is certainly not true.^{3}

While research by Wiley, Fischer, and others has indicated great benefits for faculty and students using OER and open pedagogy,^{4} many governments and philanthropic groups have pushed for OER creation and adoption as a potential solution to the textbook dilemma presented above. Thanks to the nearly universal curriculum requirements for mathematics in education, the teaching of this discipline in particular has greatly benefited from the addition of high quality OER.

The scope of this essay will be to shine a light on the OER realm in higher education mathematics. Since this field is vast and continually expanding, it would be impossible to write an essay which covers *all* OER in mathematics—and such an essay would quickly become outdated. This discussion will therefore be restricted to open textbooks which resemble traditional texts in quality, content, and rigor—in other words, those which have been thoroughly proofed, revised, and edited, and which contain enough content, examples, and exercises to fill a typical college term. The books discussed here are readily available and have been adopted by multiple institutions with positive reviews. These textbooks will be referred to as high quality OER.

This essay will first introduce readers to some of the key players in the mathematical OER mission; these players will likely inform the future direction for OER development. Important OER referatories will be discussed as well, as they can help students, faculty, and librarians better navigate the vast collection of open resources available. Although this essay focuses on mathematical literature, some topics will be relevant to any discipline.

1. Jon McBride, “Students Who Switch to Open Source Textbooks Don’t See Grades Drop,” *BYU News,* October 19, 2015, https://news.byu.edu/news/students-who-switch-open-source-textbooks-dont-see-grades-drop

2. David A.Wiley, “Defining the ‘Open’ in Open Content and Open Educational Resources,” accessed March 20, 2018, http://opencontent.org/definition

3. David A.Wiley, “Cable on Free vs Open,” *Iterating toward Openness*, accessed March 20, 2018, https://opencontent.org/blog/archives/2596

4. David A.Wiley, “What is Open Pedagogy?” *Iterating toward Openness,* accessed March 20, 2018, https://opencontent.org/blog/archives/2975

*Andrew Misseldine is a professor of mathematics at Southern Utah University. Andrew’s mathematical background and research interests are in abstract algebra, especially group theory, representation theory, and algebraic combinatorics. His educational research interests include OER and other open pedagogies. Andrew holds a PhD in mathematics from Brigham Young University.*