Related papers: Proof Assistants for Teaching: a Survey
Interactive proofs are often considered as costs of formal modelling activity. In an incremental development environment such as the Rodin platform for Event-B, information from proof attempts is important input for adapting the model. This…
We formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use…
The role of conversational assistants has become more prevalent in helping people increase their productivity. Document-centered assistance, for example to help an individual quickly review a document, has seen less significant progress,…
Students who serve as Learning Assistants (LAs) and have the opportunity to teach the content they are learning, while also studying effective teaching pedagogy, have demonstrated achievement gains in advanced content courses and positive…
Digital innovation in education has revolutionized teaching and learning processes, demanding a rethink of pedagogical competence among educators. This study evaluates the preparation of instructors to use digital technologies into their…
The automation offered by modern program proof tools goes hand in hand with the capability to interact with the tool when the verification fails. The SPARK proof tool tries to help the user by providing the right information, so that the…
A large body of research demonstrates how teachers' questioning strategies can improve student learning outcomes. However, developing new scenarios is challenging because of the lack of training data for a specific scenario and the costs…
Large language models (LLMs) are rapidly transforming knowledge work by improving the quality and efficiency of tasks such as writing, coding, and data analysis. However, their growing use in education has exposed a learning-performance…
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 shortage of people trained in STEM fields is becoming acute, and universities and colleges are straining to satisfy this demand. In the case of computer science, for instance, the number of US students taking introductory courses has…
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…
Artificial intelligence (AI) applications to support human tutoring have potential to significantly improve learning outcomes, but engagement issues persist, especially among students from low-income backgrounds. We introduce an AI-assisted…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical…
Recent advances in large language models (LLMs) have shown promise for scalable educational applications, but their use in dialog-based tutoring systems remains challenging due to the need for effective pedagogical strategies and the high…
This paper introduces ProofCloud, a proof retrieval engine for verified proofs in higher order logic. It provides a fast proof searching service for mathematicians and computer scientists for the reuse of proofs and proof packages. In…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
Aiming to offer a framework for blended learning to the teaching of proof theory, the present paper describes an interactive tutorial, called \textsc{TryLogic}, teaching how to solve logical conjectures either by proofs or refutations. The…
This article describes a prototype implementation of a web interface for the Matita proof assistant. The interface supports all basic functionalities of the local Gtk interface, but takes advantage of the markup to enrich the document with…
Computational reductions are an important and powerful concept in computer science. However, they are difficult for many students to grasp. In this paper, we outline a concept for how the learning of reductions can be supported by…