Related papers: Practical Online Assessment of Mathematical Proof
As educational systems move from onsite to online due to the COVID-19 pandemic, teachers face the difficulty of designing online examination formats which minimise opportunities for dishonesty. In this paper, we expose our design of such a…
Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we…
We present IntelliProof, an interactive system for analyzing argumentative essays through LLMs. IntelliProof structures an essay as an argumentation graph, where claims are represented as nodes, supporting evidence is attached as node…
Humans engage in informal debates on a daily basis. By expressing their opinions and ideas in an argumentative fashion, they are able to gain a deeper understanding of a given problem and in some cases, find the best possible course of…
In contemporary research, data scientists often test an infinite sequence of hypotheses $H_1,H_2,\ldots$ one by one, and are required to make real-time decisions without knowing the future hypotheses or data. In this paper, we consider such…
In this article we address the problem of automatic answer checking in interactive learning systems that support mathematical notation. This problem consists of the problem of establishing identities in formal mathematical systems and hence…
This article reports the argumentation work of a group of trainee mathematics teachers in an experiment carried out in a virtual class (due to the emergence of COVID-19) during 2020. They worked with a task on fractions in an online…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
In parallel to the ever-growing usage of mechanized proofs in diverse areas of mathematics and computer science, proof assistants are used more and more for education. This paper surveys previous work related to the use of proof assistants…
The past decade has seen a substantial rise in the amount of mis- and disinformation online, from targeted disinformation campaigns to influence politics, to the unintentional spreading of misinformation about public health. This…
Fact-checking has become increasingly important due to the speed with which both information and misinformation can spread in the modern media ecosystem. Therefore, researchers have been exploring how fact-checking can be automated, using…
Adaptive online testing efficiently assesses examinee proficiency by dynamically adjusting the difficulty of test items based on their performance. To achieve this, items are selected so that their difficulty closely matches the test…
One of the core applications of machine learning to knowledge discovery consists on building a function (a hypothesis) from a given amount of data (for instance a decision tree or a neural network) such that we can use it afterwards to…
Mathematical proofs should be paired with formal proofs, whenever feasible.
People learn whenever and wherever possible, and whatever they like or encounter--Mathematics, Drama, Art, Languages, Physics, Philosophy, and so on. With the bursting of knowledge, evaluation of one's understanding of conceptual knowledge…
We report on an exploratory analysis of the forms of plagiarism observable in mathematical publications, which we identified by investigating editorial notes from zbMATH. While most cases we encountered were simple copies of earlier work,…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
The evaluation of recommendation systems is a complex task. The offline and online evaluation metrics for recommender systems are ambiguous in their true objectives. The majority of recently published papers benchmark their methods using…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.