Related papers: Teaching "Foundations of Mathematics" with the Lea…
The rapid integration of Large Language Models (LLMs) into software engineering practice is reshaping how software testing activities are performed. LLMs are increasingly used to support software testing. Consequently, software testing…
As part of a large-scale assessment project at a large university, we administered weekly pre-tests and bi-weekly post-tests in the recitation sections of our introductory classes over four semesters from Spring 2010 through Fall 2011. The…
We redesigned an advanced physics laboratory course to include a project component. The intention was to address learning outcomes such as modeling, design of experiments, teamwork, and developing technical skills in using apparatus and…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
Introductory programming courses often rely on small code-writing exercises that have clearly specified problem statements. This limits opportunities for students to practice how to clarify ambiguous requirements -- a critical skill in…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
This study explores the impact of Large Language Models (LLMs) in higher education, focusing on an automated oral examination simulation using a prototype. The design considerations of the prototype are described, and the system is…
Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements.…
Recent neural theorem provers use reinforcement learning with verifiable rewards (RLVR), where proof assistants provide binary correctness signals. While verifiable rewards are cheap and scalable without reward hacking issues, they suffer…
Chemical theory can be made more rigorous using the Lean theorem prover, an interactive theorem prover for complex mathematics. We formalize the Langmuir and BET theories of adsorption, making each scientific premise clear and every step of…
When executed well, project-based learning (PBL) engages students' intrinsic motivation, encourages students to learn far beyond a course's limited curriculum, and prepares students to think critically and maturely about the skills and…
Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires…
The progressive introduction of the flip teaching (FT) instructional model into higher education has accelerated in recent years. The FT methodology seems to be especially suitable for laboratory practice sessions: before the lab session…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
The current evaluation of mathematical skills in LLMs is limited, as existing benchmarks are either relatively small, primarily focus on elementary and high-school problems, or lack diversity in topics. Additionally, the inclusion of visual…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
This study explores student attitudes to the use of substantive on-line assessments that require mathematical answers. Our goal is to learn what are the important aspects in a design of more effective e-assessments that support learning of…
Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…
The increasing reliance on Large Language Models (LLMs) across various domains extends to education, where students progressively use generative AI as a tool for learning. While prior work has examined LLMs' mathematical ability, their…