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Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
Computation has revolutionized science and is gradually making its way into science teaching and learning. However, we currently lack theoretical frameworks to make sense of how students learn to use computation as a disciplinary tool. In…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
We are witnessing a rapid trend towards the adoption of exercises for evaluation of national research systems, generally based on the peer review approach. They respond to two main needs: stimulating higher efficiency in research activities…
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…
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…
Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or…
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
Mathematical learning environments give domain-specific and immediate feedback to students solving a mathematical exercise. Based on a language for specifying strategies, we have developed a feedback framework that automatically calculates…
Writing is a foundational literacy skill that underpins effective communication, fosters critical thinking, facilitates learning across disciplines, and enables individuals to organize and articulate complex ideas. Consequently, writing…
The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents' decision-making. Reflexion is considered as agent's beliefs about nature, opponents' beliefs…
We identify the main actors in the Isabelle and Coq communities and describe how they affect and influence their peers. This work explores selected foundations of social networking analysis that we expect to be useful in the context of the…
To enhance student learning, we demonstrate an experimental study to analyze student learning outcomes in online and in-class sections of a core data communications course of the Undergraduate IT program in the Information Sciences and…
There is a sharp disconnect between the programming and mathematical portions of the standard undergraduate computer science curriculum, leading to student misunderstanding about how the two are related. We propose connecting the subjects…
Curiosity is a vital metacognitive skill in educational contexts. Yet, little is known about how social factors influence curiosity in group work. We argue that curiosity is evoked not only through individual, but also interpersonal…
This paper presents the course design titled "Learning Management" of which the goal is to "learn collaborative learning" for a first-year undergraduate student. The objective of the class design is to help transform the student's belief of…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
Developing competency in artificial intelligence is becoming increasingly crucial for computer science (CS) students at all levels of the CS curriculum. However, most previous research focuses on advanced CS courses, as traditional…