Related papers: Blending Mathematical and Physical Negative-ness
The ability to express scientific concepts in mathematical terms and integrate scientific and mathematical reasoning about a phenomenon is a foundational cognitive process involved in scientific thinking. This process called blended…
Learning physics requires understanding the applicability of fundamental principles in a variety of contexts that share deep features. One way to help students learn physics is via analogical reasoning. Students can be taught to make an…
The classical number system encodes magnitude using a single scalar value whose sign positive or negative has remained conceptually unchanged for centuries. This work introduces Multisign Algebra, a mathematical generalization of the sign…
Questions of participant understanding of the nature of an activity have been addressed in anthropology and sociolinguistics with the concepts of frames and framing. For example, a student may frame a learning activity as an opportunity for…
Developing expertise in physics requires appropriate integration and assimilation of physics and mathematics. Instructors and students often describe physics courses in terms of their emphasis on conceptual and quantitative problem-solving.…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem…
Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
Energy is an abstract science concept, so the ways that we think and talk about energy rely heavily on ontological metaphors: metaphors for what kind of thing energy is. Two commonly used ontological metaphors for energy are energy as a…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
It is now widely accepted that the concept of negative absolute temperature is real one and not just theoretical curiosity. In this brief report, by combining the formalism used in the statistical mechanics and thermodynamics, we have…
In recent years, natural language processing (NLP) has become integral to educational data mining, particularly in the analysis of student-generated language products. For research and assessment purposes, so-called embedding models are…
The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…
Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…
We demonstrate how students' use of modeling can be examined and assessed using student notebooks collected from an upper-division electronics lab course. The use of models is a ubiquitous practice in undergraduate physics education, but…
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…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
The research documents the impact of a teaching experiment designed in order to make students consider not only the spectral composition of light but also its intensity when they interpret colour phenomena. The analysis of eight recorded…
Physics education researchers have argued that authentic physics education includes computation as part of a physics student's training, and many parties have made efforts towards this goal. However, most research on this teaching modality…