Collaborative Research: Undergraduate Teaching and Learning in Mathematics With Open Software and Textbooks

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This Improving Undergraduate STEM Education (IUSE) Development and Implementation project aims to address challenges in the undergraduate STEM curriculum, particularly the need to promote student learning and the development of mathematical and computational skills. Specifically, this project focuses on open source mathematics textbooks that are available in free online versions. It seeks to understand two interrelated questions: "How do instructors and students use textbooks?" and "How can we develop textbooks that better support teaching and learning?" To answer these questions, the project will complete a comprehensive educational research study that includes gathering data from multiple classrooms in a variety of settings, and subsequent analysis of that data. The development portion of the project will focus on PreTeXt, a publishing system designed to encourage the creation of free, open source textbooks. The project will examine the use of existing books created with PreTeXt, and from these observations further develop the PreTeXt platform, so that open source textbooks can have increased effectiveness. The integration of research and development activities is designed to create a continuous cycle of innovation between the research and development activities. The education research component of this project will study 49 courses taught at two-year colleges, and four-year colleges and universities. These courses include first-year calculus, second-year linear algebra, and upper-division abstract algebra. The research study will investigate the work of instructors in planning and teaching lessons drawn from an online textbook and the work of students as they use the same textbooks to learn the material. In addition, the study will contrast such work with the work that instructors and students do when using less dynamic resources, e.g., a PDF or bound copy of the same material. PreTeXt is a new authoring platform that enables authors to easily fashion a textbook for both print (static) and online (dynamic) formats, including both computational and interactive components in the online version. The project will continue the development of PreTeXt and the technical underpinnings to create high quality online versions of textbooks, while only requiring authors to concentrate on their content. The accessibility features for readers with disabilities will be further improved. The inherent technical structure of online PreTeXt books will allow automated collection of student textbook usage data, organized by individual reader, with resolution to the minute and at the level of individual components, such as viewing a video. This interplay between research and development activities will produce large amounts of high-quality data about students' use of their textbooks. The Open Textbook Initiative at the American Institute of Mathematics will continue and expand its leadership in vetting and recommending quality free and low-cost textbooks, and help other STEM disciplines to adopt its successful evaluation criteria. Workshops for instructors, authors, and software developers will blend dissemination, professional development, editorial review, and software development. A novel feature of these workshops will be teaching test-site instructors how to contribute to the improvement of the open source textbooks that they are using in their courses.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.