Related papers: Towards understanding and characterizing expert co…
Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even…
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…
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels.…
Top-K sparse softmax gating mixture of experts has been widely used for scaling up massive deep-learning architectures without increasing the computational cost. Despite its popularity in real-world applications, the theoretical…
Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics…
Background: As traditional coding tasks in education become increasingly vulnerable to the use of Generative AI, there is a critical need for authentic, project-based assessments that evaluate students' scientific inquiry. To address this…
In a recent report, the American Association of Physics Teachers has developed an updated set of recommendations for curriculum of undergraduate physics labs.1 This document focuses on six major themes: constructing knowledge, modeling,…
With the advent of high-level programming languages capable of quickly rendering three-dimensional simulations, the inclusion of computers as a learning tool in the classroom has become more prevalent. Although work has begun to study the…
The paper describes two general problems encountered in computational assignments at the introductory level. First, novice students often treat computer code as almost magic incantations, and like novices in many fields, have trouble…
We conduct the convergence analysis of parameter estimation in the contaminated mixture of experts. This model is motivated from the prompt learning problem where ones utilize prompts, which can be formulated as experts, to fine-tune a…
One of the common ways children learn is by mimicking adults. Imitation learning focuses on learning policies with suitable performance from demonstrations generated by an expert, with an unspecified performance measure, and unobserved…
We describe how graduate students categorize introductory mechanics problems based on the similarity of their solutions. Graduate students were asked at the end of a teaching assistant training class to categorize problems from their own…
Student learning in upper division thermal physics has not been studied to the same extent as in other courses like electromagnetism and quantum mechanics. Studies addressing reasoning and learning at the graduate level are even more…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
A problem of incorporating the expert rules into machine learning models for extending the concept-based learning is formulated in the paper. It is proposed how to combine logical rules and neural networks predicting the concept…
This paper uses classical high-rate quantization theory to provide new insights into mixture-of-experts (MoE) models for regression tasks. Our MoE is defined by a segmentation of the input space to regions, each with a single-parameter…
The ability to flexibly transform between different representations (e.g., from mathematical to graphical representations) of the same concept is a hallmark of expertise. Prior research suggests that many introductory physics students show…
Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…
The perspectives of introductory classical physics students can often negatively influence how those students later interpret quantum phenomena when taking an introductory course in modern physics. A detailed exploration of student…
Previous research has found that introductory physics students perform far better on numeric problems than on otherwise equivalent symbolic problems. This paper describes a framework to explain these differences developed by analyzing…