Section 2 Proposed Activities
Sabbatical leave is requested for Fall 2022. While further delay of these proposed activities will lessen their broader impact, the applicant recognizes the need for flexibility in reallocating duties to the department, and thus Spring 2023 is also acceptable if necessary. Either way, it's anticipated that these activities will extend into the adjacent summer semester, modulo Clontz's obligations to ongoing grant activity.
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. Most of the collaborative work planned is alternatively able to be done virtually as needed via AIM's online collaboration platform developed during the COVID-19 pandemic, so sabbatical activities may be performed independent of public health concerns related to travel.
The activities proposed involve the development of several software packages, preparation of grant proposals, traditional mathematics research, and more. Given the rapid development of such technologies and research, and the length of time between this application and the start of the sabbatical, it's difficult to pinpoint the precise work that will best fit a Fall 2022 or Spring 2023 semester leave. Therefore, this section describes a wide range of activities to be undertaken between now and the end of the 2022-23 academic year, assuming one semester of sabbatical.
Subsection 2.1 FOSS 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 meet with the pi-Base's lead developer James Dabbs for one week at the beginning of the sabbatical for a focused development sprint. During this visit, Clontz will give a talk to a Javascript development organization Dabbs belongs to on the use of Javascript programming in academia. 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 collaborate with the steering committees of two major mathematics conferences, the Spring Topology and Dynamics Conference and the Summer Conference on Topology and its Applications, to begin development of a replacement to the now-defunct Topology Atlas platform. While some features of the Atlas (such as forums for posing and answering questions on mathematical research) are well-replicated by existing solutions (such as MathOverflow), there remains no elegant solution for handling abstract submissions and scheduling, so Clontz's work will focus on that vacuum. Some of this functionality has been roughly imitated through the use of Google Apps; it's anticipated that these can be wired together by designing new Javascript programs that recreate the automated workflows previously provided by the Atlas.
Subsection 2.2 FOSS Cyberinfrastructure for Mathematics Instruction and RUME
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 2021 randomized exercise banks have be published or are in development for calculus, linear algebra, differential equations, introductory statistics, quantitative reasoning, and mathematics for liberal arts courses, many of which will be used to facilitate Fall 2021 instruction. This quick evidence of productivity witnesses the utility of the platform, and it has also generated many requests for new features and bugfixes.
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 are using Scratchee in Fall 2021; 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.
Beginning in Summer 2020, Clontz partnered with Prof. Oscar Levin to develop PreTeXt-CLI, a command-line user interface for quickly generating PreTeXt template projects, authoring new materials, and publishing them to freely available internet hosts. AIM provided support for Clontz and Levin to continue this work in Summer 2021, and in August 2021 the PreTeXt-CLI became the canonical interface for authoring textbooks and research manuscripts in PreTeXt. The CLI is significantly simpler to install and use compared with previous tools; however, more work remains to integrate the tool with the VS Code graphical web application, with the ultimate goal of creating an elegant web browser-based authoring experience akin to using Google Docs or Overleaf, but producing documents accessible by both sighted and blind students. Additionally, there have been requests to directly integrate the CheckIt Platform into the PreTeXt ecosystem, allowing textbook authors to directly create randomized exercises for the end of each section.
Subsection 2.3 External Grant-Seeking
The work described above is well-aligned with two specific NSF solicistations. The first is Improving Undergraduate STEM Education: Education and Human Resources [19]. Clontz is currently funded as part of an IUSE program on Team-Based Inquiry Learning, and served as a consultant for another IUSE program studying the use of open-source textbooks in undergraduate mathematics education, particularly those authored in PreTeXt. In January 2022, Clontz will submit a new IUSE proposal focusing on the cyberinfrastructure needs of these projects and related RUME work. If this grant is not funded, sabbatical leave would be very useful to revise and resubmit in Spring 2023, based upon reviews from the NSF.
The other is Research Experiences for Undergraduates (REU) [20]. In particular, the research data used as the basis for the pi-Base was originally developed as part of an NSF-funded REU [14], 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 July 2022; sabbatical leave in Fall 2022 would free Clontz's time from usual sememster preparations to invest in this proposal.
Clontz is also engaged with additional NSF grant-writing in association with the Mathematical Puzzle Programs outreach organization, described below. He served as co-PI for an Advancing Informal STEM Learning (AISL) [18] proposal submitted in January 2021; while not funded, the proposal received promising reviews, and a new proposal will be submitted in 2022.
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.
Clontz is also heavily involved in mathematics outreach. He serves as director of Mathematical Puzzle Programs, which organizes fun escape-room-like experiences for the general public at nine college campuses across the country, whose puzzles incorporate contemporary mathematics research. Likewise, Clontz previously consulted with the new Alabama School of Cyber Technology and Engineering (ASCTE) statewide magnet high school in Huntsville to develop their technology-integrated freshman mathematics curriculum, and often collaborates with the Alabama School of Mathematics and Science (ASMS) statewide magnet high school local to Mobile as well. Sabbatical leave will give Clontz increased flexibility to support MaPP activities across the country, as well as visit ASCTE and ASMS to provide support integrating modern technologies into their mathematics curricula and promote the University to their talented students.