Related papers: How students blend conceptual and formal mathemati…
We are investigating cognitive issues in learning quantum mechanics in order to develop effective teaching and learning tools. The analysis of cognitive issues is particularly important for bridging the gap between the quantitative and…
Expert problem solvers are characterized by continuous evaluation of their progress towards a solution. One characteristic of expertise is self-diagnosis directed towards elaboration of the solvers' conceptual understanding, knowledge…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
We are interested in better understanding ways that students collaborate to solve conceptual physics problems in the context of spherical unit vectors in upper-level E&M, especially problems that have been shown to be difficult for students…
Most students struggle when faced with complex and ill-structured tasks because the strategies taught in schools and universities simply require finding and applying the correct formulae or strategy to answer well-structured, algorithmic…
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we…
Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments…
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…
We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and…
We discuss the effect of administering conceptual and quantitative isomorphic problem pairs (CQIPP) back to back vs. asking students to solve only one of the problems in the CQIPP in introductory physics courses. Students who answered both…
Many studies have investigated students' epistemological framing when solving physics problems. Framing supports students' problem solving as they decide what knowledge to employ and the necessary steps to solve the problem. Students may…
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…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
While large models pre-trained on high-quality data exhibit excellent performance on mathematical reasoning (e.g., GSM8k, MultiArith), it remains challenging to specialize smaller models for these tasks. Common approaches to address this…
An appropriate diagram is a required element of a solution building process in physics problem solving and it can transform a given problem into a representation that is easier to exploit for solving the problem. A major focus while helping…
We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games…
Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify…
A primary goal of science and engineering (S & E) education is to produce good problem solvers, but how to best teach and measure the quality of problem-solving remains unclear. The process is complex, multifaceted, and not fully…
We discuss the development of interactive video tutorial-based problems to help introductory physics students learn effective problem solving heuristics. The video tutorials present problem solving strategies using concrete examples in an…
This work examines student meaning-making in undergraduate physics problem-solving. We use a social semiotic perspective to sketch a theoretical framework. The social semiotic approach focuses on all types of meaning-making practices that…