13th MathUI Workshop 2021
Mathematical User Interaction

We present a new annotation tool, called MioGatto, to efficiently build large corpora for grounding math formulae. While in documents in science, technology, engineering, and mathematics, math identifiers can be used in multiple meanings in a single document, corpora with annotated coreference relations between identifiers are crucial for the grounding task. Using MioGatto, annotators can produce a list of math concepts for each document, associate one of the math concepts with each occurrence of math identifiers, and annotate the text span that is the source for grounding. In general, manual annotation of coreference relations is a very tough task, but this tool is specialized for building grounding corpora and can annotate them more efficiently than existing general-purpose annotation tools. The tool can be obtained from https://github.com/wtsnjp/MioGatto.

Sophize is a novel mathematics library and discussion platform with a mission to help our users find and organize mathematical proofs. We have extended the Markdown language to represent the connections between mathematical objects that exist across various sources of knowledge. Using the new language, we demonstrated an interactive interface that helps users explore mathematics content on the web. We also utilized this new language to create a novel communication system built specifically to aid mathematicians in solving problems collaboratively. This contribution sketches the basic ideas and provides links to some demos of the new functionality.

Within the MATh project, we develop explanation strategies to help first year students adapt to unacquainted workflows in university mathematics. These strategies are designed and implemented as sets of rules which are closely tied to the common practice in first year courses. In order to make the rules easily accessible to beginners it is useful to align them with commonly known concepts. Notably, the common experience with creating, continuing and reusing stories in varying situations turns out to be a promising starting point. We present a story-based approach for generating and structuring mathematical content within the MATh language and demonstrate that it entails various mathematical notions like theorem, set, function, theory and model. Due to this intimate relation between stories as structuring constructs and associated mathematical objects, the approach differs from other systems.

Traditionally, technical documents have been designed for print delivery in letter, A4, or similar sizes. Even the change to digital delivery using PDF has not changed the basic layout strategy and desktop screens can cope well. With the advent of mobile connected devices, it becomes natural to read technical documents (like everything else) e.g. on smartphones, which may demand other layout tradeoffs.
The document components most affected by this are diagrams and formulae, which -- unlike text -- cannot simply be reflowed to a new screen size. In this paper, we discuss an experimental study design that helps the investigation of the effect of linebreaking in mathematical formulae for reading efficiency using eye-tracking experiments.

Similarly to simple text, mathematical formulæ are a widely accepted language to represent ideas. Other representation of mathematical knowledge exist, e.g. in numeric or geometric forms. However, unlike text, mathematical objects are only transferrable (that is they can enter a transfer process) in limited and particular conditions, in part because encoding the formulæ is limited to encoding a graphical representation. An unsuccessful transfer leaves users with the task of transferring by redoing, retyping, or recreating the content.
Because automatic conversions may be working in many cases and because interoperable encoding and transfers could exist one day, this paper attempts to present scenarios of transfers of formulæ almost independently of what is doable currently. Inspired by the scenarios, a vision of interoperability could be built.

Extending the UFrameIT Framework, we propose an upgrade to the User Interface features that is directly built on the knowledge-based part, MMT. In the game engine, it suffices to interpret the output and visualize it accordingly, resulting in features that work generically and out of the box for all games built with UFrameIT.
Initially, we were using fixed text descriptions and a static UI that created unnecessary mental load when players were trying to match between the abstract problem description and concrete game situations. To improve this, we introduce dynamic UI synchronization. We relate the progress of the player to the abstract formalized solution and give hints accordingly. These hints are generated via partial views; given a partial solution to the problem, MMT can check the dependencies and point towards the missing information. In the game, we can use this to highlight not yet assigned as well as even not yet existing facts in the game. This way, the player gets immediate feedback during the solution process.

In this study, we analyze computer-aided inquiry-based mathematics learning. A Moodle plug-in associated with the dynamic geometry software CindyJS which can record finegrained log data of learners' manipulations on the web was used. Our previous study indicates that teacher intervention can make student's inquiry systematic and exhaustive by helping them build a semantic circuit across language, symbolism, and visual images which are relevant to the targeted concept. In this study, we try to validate the impact of this kind of teacher intervention by monitoring the log data of manipulations.

While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix multiplication.