15th MathUI Workshop 2024
Mathematical User Interaction

Considering digital ink as plane curves provides a valuable framework for various applications, including signature verification, note-taking, and mathematical handwriting recognition. These plane curves can be obtained as parameterized pairs of approximating truncated series (𝑥(𝑠),𝑦(𝑠)) determined by sampled points. Earlier work has found that representing these truncated series (polynomials) in a Legendre or Legendre-Sobolev basis has a number of desirable properties. These include compact data representation, meaningful clustering of like symbols in the vector space of polynomial coefficients, linear separability of classes in this space, and highly efficient calculation of variation between curves. In this work, we take a first step at examining the use of Chebyshev-Sobolev series for symbol recognition. The early indication is that this representation may be superior to Legendre-Sobolev representation for some purposes.

This paper reports on the development of a web application that hosts articles from the Mizar Mathematical Library (MML). In this application, explanatory articles are written in Markdown notation, and MathJax is used to render mathematical expressions and embed MML content within the articles. This approach allows for the creation of structured explanatory articles, as opposed to the traditional method of inserting annotations directly into a formalized library. The posted explanatory articles can be referenced from the corresponding HTMLized MML page. Additionally, the hosting platform for this application, emwiki, integrates a remote verification environment. This feature allows Mizar users to develop libraries without needing to install the Mizar system and editor locally, enhancing convenience. Our new application is embedded in emwiki, an integrated web platform developed to host the Mizar Mathematical Library.

In the last years, we have seen methods from flexiformal mathematics be used for making documents active, i.e. interactive and user-adaptive. The main limitation of e.g. learning assistant systems like ALeA that use active documents is that they depend on the STEX framework – a semantical variant of LATEX –. This requires the underlying domain model and the learning objects to be encoded in STEX specific standards and be suitably annotated semantically to power the knowledge management algorithms that drive active documents.
To accommodate authors of domains other than mathematics, physics, and computer science, where LaTeX is commonplace, systems like ALeA must be scaled beyond those disciplines. We need to provide ways of semantically annotating the respectively prevalent document formats; usually some flavor of office suite.
For this we present the WOIDE plugin for MS Word, which allows to embed STEX-like semantic annotations into MS Word documents as the most prevalent tool in practice. The main contribution of this paper has been to find a way to persistently store annotations in the DocX file/object format and build a minimally viable plugin.

With the wide-spread availability of high-speed internet, an HTML-based system is one of the most promising options for mathematical software in this post COVID-19 era. While many web-based software libraries are available for specific purposes, including ones for symbolic calculations and dynamic visualizations, extra elaboration is needed to integrate their capabilities so that users can perform mathematical activities on a single HTML content. Moreover, it seems that the realities and benefits derived from the use of those systems have not yet been fully investigated. Especially in the complex case of statistics learning, more precise knowledge about them will likely help maximize the effect of using newly developed systems. This research is mainly concerned with the use of our newly developed system for the learning of the 𝜓 2 test for independence. Through the comparative study of the log of simulations, which learners performed on the HTML content between experimental and control groups, it has been shown that some restrictions to the context of its use can have a large influence on learners' thinking.

Students of mathematical proofs need to understand proof steps, both individually, and as they constitute a whole proof. How can the steps be best presented, in order to facilitate study and comprehension? We examine different ways of presenting and studying proof steps in the PISE software, and consider usability questions, including: How should steps be arranged visually (list or layered layout), how should expansions be inserted (what we call unified or embedded mode), what are the most usable ways to link proof steps to enrichments (including links to original literature, narrative guides, and example exploration using a computer algebra system), and how should students be supported in actively recording and reviewing their own progress, questions, and notes as they study.

Personalization relies on user models – representations of the user's competencies, preferences, and skills to adapt the system behavior to optimize interaction. But the anticipated gain in productivity is offset by the effort involved in collecting and maintaining said user model. This is particularly pronounced in systems like ALeA (Adaptive Learning Assistant, https://courses.voll-ki.fau.de/), where the learner models contain competency estimations for thousands of concepts among multiple dimensions – here Bloom's learning levels. In this paper we present an exploratory study design that tries to determine whether close visual observation of learners can be used to elicit competency data automatically – a task human educators perform routinely when teaching small groups of learners and adaptive learning systems should be equipped to mimic – with the help of this study.