Related papers: Clear Thinking, vague thinking and paradoxes
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Astrophysical paradoxes are the paradoxes of physics. The main motivation of a formulated paradox is clearly recognized in the scientific environment because the phenomenon of a paradox itself has become interesting. There is an explanation…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
Very little is known about how the nature of expertise in introductory and advanced courses compares in knowledge-rich domains such as physics. We develop a framework to compare the similarities and differences between learning and patterns…
Effective software testing is critical for producing reliable and secure software, yet many computer science students struggle to master the foundational concepts required to construct comprehensive test suites. While automated feedback…
Developing students' ability to troubleshoot is an important learning outcome for many undergraduate physics lab courses, especially electronics courses. In other work, metacognition has been identified as an important feature of…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
When artificial intelligence mistakes memorization for intelligence, it creates a dangerous mirage of reasoning. Existing studies treat memorization and self-knowledge deficits in LLMs as separate issues and do not recognize an intertwining…
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…
That computers should be easy to learn and use is a rarely-questioned tenet of user interface design. But what do we gain from prioritising usability and learnability, and what do we lose? I explore how simplicity is not an inevitable truth…
First year calculus is often taught in a way that is very burdensome to the student. Students have to memorize a diversity of processes for essentially performing the same task. However, many calculus processes can be simplified and…
Background: Programming is a fundamental skill in computer science and software engineering specifically. Mastering it is a challenge for novices, which is evidenced by numerous errors that students make during programming assignments.…
One of the oft-cited qualities sought after in a potential future engineering employee is an analytical mind that is "continually examining things." In one sense this examination is discouraged in an instructional laboratory employing…
The rise of machine learning has brought closer scrutiny to intelligent systems, leading to calls for greater transparency and explainable algorithms. We explore the effects of transparency on user perceptions of a working intelligent…
With an investigation into how students in a physics Master of science program make sense of their whole first year study experience in one of the years following a programme reform, we try to offer insights and advice to consider when…
It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case…
Despite the recognition that reflection is an essential part of problem solving, it is often not emphasized in upper-division physics courses. In this paper, we discuss homework corrections (HWCs) as a pedagogical tool to motivate…
Higher education provides a solid theoretical and practical, but mostly technical, background for the aspiring software developer. Research, however, has shown that graduates still fall short of the expectations of industry. These…
When deploying online homework in physics courses, an important consideration is how many attempts should be allowed in order to solve numerical free-response problems. While on the one hand, the maximum number of attempts should be large…