Related papers: Providing Hints, Next Steps and Feedback in a Tuto…
We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…
We investigate how automated, data-driven, personalized feedback in a large-scale intelligent tutoring system (ITS) improves student learning outcomes. We propose a machine learning approach to generate personalized feedback, which takes…
Proof Blocks is a software tool that provides students with a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. In this paper we describe a…
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…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
While state-of-the-art LLMs have shown poor logical and basic mathematical reasoning, recent works try to improve their problem-solving abilities using prompting techniques. We propose giving "hints" to improve the language model's…
We introduce real induction, a proof technique analogous to mathematical induction but applicable to statements indexed by an interval on the real line. More generally we give an inductive principle applicable in any Dedekind complete…
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…
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…
Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing…
Learning basic programming with Scratch can be hard for novices and tutors alike: Students may not know how to advance when solving a task, teachers may face classrooms with many raised hands at a time, and the problem is exacerbated when…
Block-based environments such as Scratch are increasingly popular in programming education. While block syntax reduces surface errors, semantic bugs remain common and challenging for novices to resolve. Existing debugging workflows…
Intelligent tutoring systems (ITSs) that imitate human tutors and aim to provide immediate and customized instructions or feedback to learners have shown their effectiveness in education. With the emergence of generative artificial…
Recent studies have integrated large language models (LLMs) into diverse educational contexts, including providing adaptive programming hints, a type of feedback focuses on helping students move forward during problem-solving. However, most…
Proof assistants offer tactics to facilitate inductive proofs. However, it still requires human ingenuity to decide what arguments to pass to those induction tactics. To automate this process, we present smart_induct for Isabelle/HOL. Given…
The field of Artificial Intelligence in Education (AIED) focuses on the intersection of technology, education, and psychology, placing a strong emphasis on supporting learners' needs with compassion and understanding. The growing prominence…
Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…
Large language models (LLMs) have created new opportunities to assist teachers and support student learning. While researchers have explored various prompt engineering approaches in educational contexts, the degree to which these approaches…
Large language models (LLMs) have demonstrated the ability to generate formative feedback and instructional hints in English, making them increasingly relevant for AI-assisted education. However, their ability to provide effective…
Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…