Related papers: Clear Thinking, vague thinking and paradoxes
This invited paper is a passionate pitch for the significance of logic in scientific education. Logic helps focus on the essential core to identify the foundations of ideas and provides corresponding longevity with the resulting approach to…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
Effective physics learning, especially in complex topics, requires balancing mathematical formalism with conceptual understanding. Conceptual problem-solving involves connecting math to physical reality, and using an epistemological…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
This paper provides an overview of common challenges in teaching of logic and formal methods to Computer Science and IT students. We discuss our experiences from the course IN3050: Applied Logic in Engineering, introduced as a "logic for…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
Common research tasks ask students to identify a correct answer and justify their answer choice. We propose expanding the array of research tasks to access different knowledge that students might have. By asking students to discuss answers…
An important goal of graduate physics core courses is to help students develop expertise in problem solving and improve their reasoning and meta-cognitive skills. We explore the conceptual difficulties of physics graduate students by…
For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
Context: Students often misunderstand programming problem descriptions. This can lead them to solve the wrong problem, which creates frustration, obstructs learning, and imperils grades. Researchers have found that students can be made to…
We propose novel evaluations for mathematical reasoning capabilities of Large Language Models (LLMs) based on mathematical misconceptions. Our primary approach is to simulate LLMs as a novice learner and an expert tutor, aiming to identify…
The ability to categorize problems is a measure of expertise in a domain. In order to help students learn effectively, instructors and teaching assistants (TAs) should have pedagogical content knowledge. They must be aware of the prior…
Research on reasoning in language models (LMs) predominantly focuses on improving the correctness of their outputs. But some important applications require modeling reasoning patterns that are incorrect. For example, automated systems that…
In this paper I discuss what, according to my long experience, every computer scientist should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
Developing expert-like problem-solving skills is a central goal of undergraduate physics education. In this study, we investigate the impact of teaching explicit problem-solving frameworks, combined with deliberate practice, on students'…