Undergraduate Teaching and Learning with Mathematics Open-Source Textbooks (UTMOST)

Vilma Mesa
University of Michigan

Free, open-source, dynamic textbooks for university mathematics courses are easily available for students and instructors and have been praised as being great news for teaching and learning. However, these claims have not been empirically investigated. Not only we do not know how these textbooks are used by teachers or students, nor whether there is any advantage over static (PDF) formats of the same textbooks, but neither do we know whether they can be vehicles for supporting change in instructional practices. One branch of this project investigates the affordances and challenges of dynamic textbooks in teaching undergraduate mathematics courses, seeking to answer three questions: §How do instructors and students use these textbooks as they teach and learn?§How can the features in the textbooks support instructional change?§Are there benefits of dynamic textbooks (HTML) over static (PDF) textbooks?We used a concurrent mixed methods design that involved nearly 60 instructors and their students (over 1000) from close to 30 states and in a variety of institutions, including community colleges. We used three textbooks, Active Calculus (Boelkins, 2021), First Course in Linear Algebra (Beezer, 2021), and Abstract Algebra Theory and Applications (Judson, 2021) that were written in PreTeXt (https://pretextbook.org/), which allowed including interactive features that collect student responses and the tracking of user activity in real time. The textbooks were chosen to represent different entry levels of students into a mathematics program. We have identified several distinct uses of textbooks by teachers and students, specifically regarding the interactive features embedded in the textbooks, some uses that were not anticipated by the authors nor the designers of the textbooks, and others that were surprising to the teachers (Mesa et al., 2021, Quiroz et al., 2022); we have identified a potential path for supporting changes in teaching practices that can be fostered by the textbooks and a marginal advantage of HTML textbooks over PDF textbooks, although more empirical evidence needs to be collected to ascertain this last claim.The first obvious societal benefit is that an open textbook may be read freely by anyone with an Internet connection. The cost of an education is significantly reduced, thus expanding access to higher education. The PreTeXt textbook system enables a variety of interactive features without requiring authors to have extensive technical knowledge. Findings from our research study, workshop activities with instructors and authors, discussions in the online PreTeXt forums, and meetings with authors and researchers at many venues (e.g., Joint Math Meetings, International Conference of the Mathematics Textbook), suggest that technical design decisions and pedagogical practices can be supported directly in PreTeXt. We have addressed needs of accessibility features in online versions of textbooks. Studying student use of textbooks presently requires students to self-report their activity, or places students in artificial environments involving mechanical devices such as eyeball trackers. The nature of our student textbook-use data, both in its detail and its unobtrusive and accurate collection, could offer new tools for research into an important component of student learning.


David Farmer, Kent Morrison, American Institute of Mathematics; Robert Beezer, University of Puget Sound, Thomas Judson, Stephen F Austin State University; Megan Littrell, University of Colorado Boulder