Related papers: Clear Thinking, vague thinking and paradoxes
Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semi-structured interviews…
It is a fact of our existence, that no matter where we are, we most often find ourselves either hearing, seeing, talking, or even engaged in design related activities. Despite this reality, the notion of 'design', and in particular…
In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…
Physics students can encounter difficulties in physics problem solving as a result of failing to use knowledge that they have but do not perceive as relevant or appropriate. In previous work the authors have demonstrated that some of these…
Scientists who study how the brain solves problems have recently verified that, because of stringent limitations in working memory, where the brain solves problems, students must apply facts and algorithms that have previously been well…
Recent investigations have been carried out on critical analyses of beginning physics teachers confronted with questionable explanations. These studies raise the question of the choices made by teachers for their teaching once they have…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…
Philosophical thinking has a side effect: by aiming to find the essence of a diverse set of phenomena, it often makes it difficult to see the differences between them. This can be the case with Mathematics, Programming, Writing and…
Paradoxes are a very frequent phenomenon in processes of thought which strive towards the intelectual and cognitive shifts. They occur in all areas of human spiritual activites. What we are interested here in, are the paradoxes in physics.…
In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…
The learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which…
Expanding our knowledge of student difficulties in advanced undergraduate electromagnetism is essential if we are to develop effective instructional interventions. Drawing on an analysis of course materials, in-class observations and…
Experimental activities are an essential part of physics education. In addition to conveying scientific knowledge, they play a significant role in developing scientific literacy, inquiry skills, and critical thinking. In today's world,…
What would you teach if you had only one course to help students grasp the essence of computation and perhaps inspire a few of them to make computing a subject of further study? Assume they have the standard college prep background. This…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Teaching logic effectively requires an understanding of the factors which cause logic students to struggle. Formalization exercises, which require the student to produce a formula corresponding to the natural language sentence, are a good…
Helping students become proficient problem solvers is a major goal of many physics courses from introductory to advanced levels. In fact, physics has often been used by cognitive scientists to investigate the differences between the…
Formally investigating the sources of students' difficulties around specific subjects is crucial for developing appropriate strategies to help students. We have been studying difficulties in understanding magnetism encountered by students…
As students increasingly rely on large language models, hallucinations pose a growing threat to learning. To mitigate this, AI literacy must expand beyond prompt engineering to address how students should detect and respond to LLM…