14th MathUI Workshop 2023
Mathematical User Interaction

The ALeA system (Adaptive Learning Assistant) uses a fine-grained domain model, a learner model based on it, and semantically annotated learning objects to generate user-adaptive and interactive course materials for pre-/post-paration of lectures and self-study. In this paper we propose new interactions and learning support services that enhance the learner experience without requiring new markup facilities – in essence enhancing the didactic capabilities of the system without further investment into marking up learning objects.

The ALeA system (Adaptive Learning Assistant) offers learners highly interactive learning materials, leveraging a fine-grained domain model, learner profiling, and semantically annotated learning objects, to create personalized course content.
This paper focuses on ALeA's user interface, through which learners interact with active documents. We outline the representation scheme of these documents and elucidate their features designed to enhance the learning experience. Moreover, we delve into the abstractions and complexities addressed by the client-side React (javascript) library to enable these features.

In this study, we analyze computer-aided inquiry-based mathematics learning and illustrate how the learning constructs are represented in the learning data. A Moodle plug-in associated with the dynamic geometry software CindyJS was used to record fine-grained log data of learners' manipulations of the dynamic content on the web. Our previous study indicates that some characteristic quantity calculated from the log data can serve as an indicator of the occurrence of some productive failure in learners' inquiry and teacher intervention can prompt those failures. However, the relationship between the occurrence of those failures and the learning constructs created through the whole manipulation process has not been fully investigated. In this study, we examine the temporal change of the characteristic quantity across those failures and consider how the learning constructs are represented in the log data of manipulations.

Base ten blocks used together with a grid can provide a consistent environment for modelling place value as well as arithmetic operations, such as addition, subtraction, regrouping and decomposition, which is particularly beneficial for students who struggle with mathematics. However, their physical use requires extensive teacher training and almost constant teacher supervision of a student. Digital interactions with base ten blocks and a grid allow for independent work and therefore enormous scalability of math interventions. This exploratory research aims to evaluate the feasibility of this digitisation process and identify the main challenges that need to be overcome to maintain or even improve on effectiveness of base ten blocks on a grid.

This paper discusses the enhancements we have made to the Mizar Extension for Visual Studio Code (VSCode). The first part of the paper explores the creation of the Mizar Server and client-side infrastructure, developed to support the web version of the Mizar Extension for VSCode. The latter part provides an update on the development of the formatter function and reports on the progress of our research into coding assistance using ChatGPT.

The Mizar Mathematical Library (MML) is a collection of mathematical documents formalized by the Mizar system. Visualizing the interrelationships among the MML articles can illuminate their structure and connections, but the scale and intricacy pose significant challenges. In our research, we introduce a method to illustrate these MML dependencies: we sort the MML articles according to the classifications in the Encyclopedic Dictionary of Mathematics. Moreover, we are exploring the feasibility of utilizing generative AI to automate this sorting process, aiming to lessen the need for manual labor. Finally, we also discuss a new algorithm for rendering categorized dependency graphs.

We extract mathematical concepts from mathematical text using generative large language models (LLMs) like ChatGPT, contributing to the field of automatic term extraction (ATE) and mathematical text processing, and also to the study of LLMs themselves. Our work builds on that of others, %especially~\cite{collard2022}, in that we aim for automatic extraction of terms (keywords) in one mathematical field, category theory, using as a corpus the 755 abstracts from a snapshot of the online journal \emph{Theory and Applications of Categories}, circa 2020. Where our study diverges from previous work is in
(1) providing a more thorough analysis of what makes mathematical term extraction a difficult problem to begin with;
(2) paying close attention to inter-annotator disagreements;
(3) providing a set of guidelines which both human and machine annotators could use to standardize the extraction process;
(4) introducing a new annotation tool to help humans with ATE, applicable to any mathematical field and even beyond mathematics;
(5) using prompts to ChatGPT as part of the extraction process, and proposing best practices for such prompts;
and (6) raising the question of whether ChatGPT could be used as an annotator on the same level as human experts.
Our overall findings are that the matter of mathematical ATE is an interesting field which can benefit from participation by LLMs, but LLMs themselves cannot at this time surpass human performance on it.

Mathematical formulae are a significant challenge for various services that help us access scientific publications. For example, finding relevant formulae with a search engine is difficult and screen readers struggle to verbalize them in an understandable way. We believe that such services could be improved if more semantic information is available. To automatically extract this information, we typically need manually annotated data sets for evaluation and, potentially, for the training of machine learning models. However, mathematical formulae also present a major challenge for annotation tools, as they cannot be presented well as plain text which is required by most existing tools. In this context, we present AnnoTize, a new annotation tool. It can create, display and update annotations for HTML5 documents and was specifically designed to support the fine-grained annotation of formulae encoded in MathML. As manual annotation can be tedious and time-consuming, AnnoTize offers several features to speed up the annotation process for large annotation tasks.

This paper describes an experimental framework for creating an E-Learning system. This framework is designed to be used by teachers in schools, and by utilizing HTML5 technology, can create an E-Learning system on PCs without the need for a special server. The E-Learning system created is a web application consisting of a single HTML file, which can be used not only on a PC, but also on tablets and smartphones.
The E-Learning system created from this framework is characterized by its dual-layered screen structure. By placing existing educational materials and websites on the lower layer of the two-tier structure and adding additional textboxes and buttons on the upper layer, it is possible to convert existing educational materials and websites into an E-Learning system.
In addition, various functions can be added to the system by utilizing JavaScript libraries. For example, by incorporating Algebrite, a JavaScript library for symbolic computation, it is possible to perform symbolic computation of mathematical expressions, which can then be used to automatically grade students' answers.
In this paper, after outlining the structure of this framework, the JavaScript library used will be described. After that, the flow of actually constructing an E-Learning system using this framework will be explained step by step.