Section 2 Proposed Activities
Sabbatical leave is requested for Spring 2024. This timing is requested to complement Clontz's anticipated NSF-funded release from teaching duties in Fall 2023.
The American Institute of Mathematics (AIM) located in San Jose, California will serve as host for this sabbatical, connecting Clontz with other likeminded scholars engaged in the work of developing cyberinfrastructure for mathematics research and education. To support these activities, AIM has offered Clontz office space for the duration of the sabbatical, as well as funding to cover travel to San Jose and local expenses.
Subsection 2.1 Cyberinfrastructure for Mathematics Research
A current shortcoming of the pi-Base application is lack of tooling to preview work on the actual web application (or a facsimile thereof) by both contributors and referees. Instead, numerical IDs for each object in the database must be manually looked up and compared across several files, and this process allows plenty of room for human error. The main development goal for the pi-Base is to add functionality via GitHub Actions that will automatically provide an online preview of how individual contributions will change the overall database, which can be used by both contributors and referees to catch such mistakes before they are published to the public. Such features will also assist new contributors in making improvements by providing a more graphical user interface compared to the current editing of text files.
To begin to make these improvements, Clontz will collaborate with the pi-Base's lead developer James Dabbs for one week at the beginning of the sabbatical for a focused development sprint. Note that the pi-Base is developed using the same technologies (particularly, the Svelte Javascript framework) as Clontz's CheckIt and Scratchee projects, and is used by Dabbs in his daily work as a software engineer. As such, this meeting will have cascading effects across the rest of the work performed throughout the sabbatical, by providing time and support for Clontz to pick up more advanced Javascript programming techniques fueled by best industry practices. In addition, this training will enable Clontz to serve not only as the pi-Base's lead mathematical editor, but also as a co-developer of the platform itself, ensuring that an academic researcher is capable of maintaining the platform in case of future technical issues.
Additionally, Clontz will use time granted by sabbatical to become fluent in the Lean proof assistant language, and contribute his expertise in general topology to the mathlib library. Collaborating with Jim Fowler at Ohio State University, Clontz will also work to integrate the \(\pi\)-Base and mathlib databases to connect computer-verified results in mathematics to an easily-accessible semantic search enginer for use by researchers.
Subsection 2.2 Cyberinfrastructure for STEM Higher Education
Throughout 2023, Clontz will be working on the development of an Open Source Ecosystem for PreTeXt software products used to develop Open Educational Resources for STEM higher education classrooms. In particular, Clontz's NSF-funded teaching release in Fall 2023 will allow him to hold virtual office hours for community members, iterate on security infrastructure for PreTeXt products, and develop a Software-as-a-Service solution for authoring, building, and deploying PreTeXT documents in the cloud. A $1.5M Phase II proposal will be submitted to the NSF around October 2023; sabbatical release in Spring 2024 will facilitate the continued development of this Open-Source Ecosystem while this proposal is under review.
After preliminary development for two years for Clontz's personal use, the CheckIt Platform received its first public release in June 2021. Two dozen instructors participated in an introductory authoring workshop, and as of August 2022 randomized exercise banks have be published or are in development for calculus, linear algebra, differential equations, introductory statistics, quantitative reasoning, introduction to proofs, and mathematics for liberal arts courses, and were been used in classrooms across the country throughout 2021 and 2022. This quick evidence of productivity witnesses the utility of the platform, and it has also generated many requests for new features and bugfixes to be worked on during this sabbatical.
An alpha version of the Scratchee app for creating and sharing virtualized scratch cards for IF-AT was released in late July 2021. This prototype was created in response to developments related to Clontz's NSF grant for supporting Team-Based Inquiry Learning; while physical IF-AT cards are not incredibly expensive, they introduce logistical friction for implementing TBIL (ordering the cards, waiting for shipment, aligning multiple-choice questions with the predetermined correct responses printed on the card). Multiple TBIL instructors have used Scratchee throughout 2021 and 2022; their experiences will be used to determine the necessary enhancements required for a public release of the platform for the broader Team-Based Learning community.
Subsection 2.3 External Grant Activity
The primary external mechanism used to fund proposed activities related to the infrastructure of STEM higher education is the NSF POSE solicitation. As noted, a $1.5M two-year Phase II proposal will be submitted in Fall 2023, to begin following the requested Spring 2024 sabbatical.
Another relevant solicitation is Research Experiences for Undergraduates (REU) [23]. In particular, the research data used as the basis for the pi-Base was originally developed as part of an NSF-funded REU [15], which resulted in the reference text Counterexamples in Topology. In this spirit, a new REU program would allow students to extend this work using the pi-Base, expanding its coverage of the literature and making the platform more useful by researchers. Additionally, unlike some traditional mathematics REUs, students would gain knowledge of the cyberinfrastructure powering the pi-Base platform, and relevants skills that would extend to careers across STEM. This proposal is anticipated to be submitted in Summer 2024, developed as part of a Spring 2024 sabbatical.
Subsection 2.4 Additional Activites
Sabbatical leave from instruction is requested to facilitate progress on the above activities while allowing Clontz to continue his active line of traditional mathematics research on the game-theoretic characterization of topological properties. Briefly, a topological space models data points along with neighborhoods that describe nearby data; for example, the Euclidean line uses real numbers \(x\in\mathbb R\) as points, and intervals \((x-r,x+r)\) of radius \(r>0\) as neighborhoods. At the time of writing, Clontz is investigating how to characterize topological dimension (as simple examples, a square is two-dimensional and a cube is three-dimensional) in terms of which player in a certain game defined for each topological space has a winning strategy. Recent results by Babinkostova and Scheepers published in the Proceedings of the Americian Mathematical Society have established three such games [3]; however, these results are only guaranteed when a metric measuring distance between points as non-negative real numbers is known to exist (for example, \(|x-y|\) is the distance from \(x\) to \(y\) on the Euclidean line of real numbers). When such a measurement is not guaranteed, the two common definitions of dimension no longer are equivalent, making the study of non-metrizable spaces difficult. This also illustrates the utility of a more robust pi-Base, as finding literature on dimension in the context of non-metrizable spaces is very difficult when only using search engines and chasing citations, so this work will also be incorporated into the pi-Base as it is completed to assist future scholars.