This project is constructing Lurch, a free software application for use in courses that involve rule-based symbolic manipulation, including but not limited to mathematical proofs. Lurch is a mathematics editor in which instructors choose rules and theorems for their students to use. It then allows students to manipulate expressions only according to those rules. Lurch is undergoing testing in a variety of courses at several institutions, with assessment of the outcomes and user experiences performed in each. After each course, a focus group is being held to encourage dialog and brainstorming between users and developers. An advisory panel of professors with expertise in science, technology, engineering, and mathematics (STEM) education and educational software is regularly reviewing and advising on both design and assessment.
Intellectual Merit: Under a customizable, extensible infrastructure, Lurch gives users control over arbitrary notation, definitions, rules, and their applications, thereby creating a new way to do mathematics on a computer. Lurch defaults to standard notation and conventions, but is customizable. It includes libraries of foundational rules and theorems (e.g., logic, algebra), to which users can add definitions, axioms, and theorems from their area (e.g., geometry, real analysis). Homework done in Lurch is easy to grade because Lurch verifies both the syntax and the reasoning. Research on student learning using technology affirms the pedagogical principles in the design.
Broader Impact: Dissemination includes faculty and selected student users speaking at both local and national conferences and a minicourse at a national meeting. Because a strong user community is integral to dissemination and long-term stability, instructors who have tested Lurch in their classes are being encouraged to report about their experiences at local conferences. The project is assisting instructors with adoption and adaptation and establishing and proactively growing an online community for sharing materials and ideas among instructors and students across the U.S. and worldwide. Lurch is being released as an open-source package, at no cost to users, for Windows, Macintosh, and Unix systems. Better educational tools make theoretical courses accessible to a wider audience and can therefore increase the number of students taking upper-division STEM courses. Lurch is not only for proof-based courses; many computational activities can benefit from the computer-verified, step-by-step approach Lurch makes possible.
