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By Andrew Misseldine

A referatory is simply an online database that collects bibliographic information for literature on a specific topic as well as supporting information such as reviews, external links, and descriptions. Because OER in mathematics is continuously evolving, finding the right OER can be a challenge. Of course, key players like OpenStax and Lumen catalog their own OER collections through their websites, but many searchers will need to look elsewhere for an objectively curated and fully up-to-date list of high quality open math textbooks. While many online databases for OER exist that intend to be comprehensive, the goal is not to find *all* OER presently available on the internet. Instead, potential users seek an index of only those OER of a high caliber. As new OER textbooks are developed and improved, these texts should eventually migrate to one of the referatories mentioned below. Among all online options, there are three primary referatories particularly suited for mathematics: the Open Textbook Library, the Approved Textbooks List by AIM, and the OpenTextbookStore.

Chief among all OER referatories is the Open Textbook Library (OTL), a product of the Center for Open Education from the University of Minnesota and the Open Textbook Network. The OTL is fairly comprehensive in its indexing of high quality OER textbooks, covering many academic disciplines. Under the mathematics subject, all indexed textbooks are listed in alphabetical order with the option of filtering by two subheadings: applied and pure (a somewhat coarse filtration option, frankly). Of course, this list is also searchable by keyword, although the keyword is only useful for searching titles, authors, and descriptions as opposed to filtering by subcategory. Presently, this list contains about sixty textbooks ranging over all branches of mathematics. Displayed on the list screen is an image of the textbook cover, title, author(s), a brief summary, a rating of the text (out of a possible five stars), the number of reviews posted (by which the rating is calculated), and a link to more information on the textbook’s profile page. The profile page provides complete bibliographic information, including publisher, date, ISBN, and the type of open license. Each book’s profile also contains a complete table of contents, a more detailed synopsis about the book and author(s), reviews posted by professionals, and links for accessing the textbook in a downloadable format or for purchasing a print edition if desired. The reviews are truly what makes the OTL such a valuable resource, as interested users can find substantive feedback from faculty who have already adopted the text. Unfortunately, the OTL’s major drawback, other than not being specifically designed for mathematics, is the that the link to the textbook’s home page—nearly every high quality OER has a regularly maintained webpage—is hidden under the “Publisher” label; many users who mistakenly think this link will take them elsewhere may attempt to search the web for the link on their own. A related drawback is that links to printed copies connect to a single seller, even if more than one exists.

Although the OTL is the best respected referatory for general high quality OER, the Approved Textbooks list operated by AIM is the best dedicated mathematics referatory. What is especially lacking from the OTL—that is, the ability to search textbooks by subject—is exactly what the Approved Textbooks list offers. It includes eighteen categories consisting of about fifty textbooks (about three books per category). Again, this list is highly curated: AIM lists only those books which pass their rigorous evaluative criteria (described in detail on their website). Because of these evaluative criteria, the Approved Textbooks list should be the first place a mathematics professor turns when considering an OER textbook for undergraduate teaching. It should be noted that the list only contains textbooks for undergraduate math courses (besides graduate mathematics, development math is likewise omitted). Like the OTL, this list contains profiles for each approved textbook containing bibliographic information, a table of contents, summaries, etc. Unlike OTL, links to the textbooks’ home pages are much easier to find, and pricing information for print editions is listed directly on the profile. The Approved Textbooks list does not provide peer reviews; but according to AIM’s criteria, only texts with a track record of multi-institutional adoption and positive peer review make the list.

The third referatory to make this list is the OpenTextbookStore (OTS). OTS is similar to the others in that it lists approximately forty-five curated math textbooks; it divides these into eight categories. This website’s mission is to aid “educators frustrated with the time involved in finding adoptable open textbooks, with the hope to make open textbook adoption easier for other faculty.” Each textbook has a profile and features similar to the others mentioned above, and thus fails to offer anything beyond the other referatories besides a slightly different list of textbooks (the overlap between lists is substantial, however). Its main weakness is that the textbooks on OTS are mostly focused on developmental and general education mathematics; the “Higher Mathematics” section currently lists just three titles.

If a librarian or mathematician fails to find a quality OER after searching through these three referatories, they may try one of many other online databases, although a simple web search for the specific course name may prove more satisfactory.