Related papers: Clear Thinking, vague thinking and paradoxes
If spreadsheets are not erroneous then who, or what, is? Research has found that end-users are. If end-users are erroneous then why are they? Research has found that responsibility lies with human beings' fast and slow thinking modes and…
The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…
Computational thinking is a key skill for space science graduates, who must apply advanced problem-solving skills to model complex systems, analyse big data sets, and develop control software for mission-critical space systems. We describe…
Background: Programming skills are advantageous to navigate today's society, so it is important to teach them to students. However, failure rates for programming courses are high, and especially students who fall behind early in…
Paradoxes are a relatively frequent occurrence in physics. The nature of their genesis is diverse and they are found in all branches of physics. There are a number of general and special classifications of paradoxes, but there are no…
It is quite exceptional, if it ever happens, that a new conceptual domain be built from scratch. Usually, it is developed and mastered in interaction, both positive and negative, with other more operational existing domains. Few reasoning…
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…
It is well-known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in quantitative problem-solving process can…
University courses in conceptual physics and astronomy typically serve as the terminal science experience for non-science majors. Significant work has gone into developing research-verified pedagogical methods for the algebra- and…
Philosophers have recently focused on critical, epistemological challenges that arise from the opacity of deep neural networks. One might conclude from this literature that doing good science with opaque models is exceptionally challenging,…
This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are:…
The human brain's computational prowess emerges not despite but because of its inherent "non-ideal factors"-noise, heterogeneity, structural irregularities, decentralized plasticity, systemic errors, and chaotic dynamics-challenging…
Producing code of good quality is an essential skill in software development. Code quality is an aspect of software quality that concerns the directly observable properties of code, such as decomposition, modularization, and code flow. Code…
Explainable artificial intelligence techniques are developed at breakneck speed, but suitable evaluation approaches lag behind. With explainers becoming increasingly complex and a lack of consensus on how to assess their utility, it is…
The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years \cite{aA75,nB77,aA89,gP89,sH96}. In this note, we investigate some of these paradoxes and classify them, over minimal…
How is it that humans can solve complex planning tasks so efficiently despite limited cognitive resources? One reason is its ability to know how to use its limited computational resources to make clever choices. We postulate that people…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
Students entering engineering in universities of applied sciences were tested to see whether they understood easy Science problems within the first week of the first semester. The test comprised of mathematics and physics questions in both…