Role of mental representations in problem solving: students’ approaches to nondirected tasks

In this paper, we report on a project concerned with the role of cognition during problem solving. We specifically explore the categories of mental representations that students work with during problem solving of different representational task formats. The sample, consisting of 19 engineering students taking a calculus-based physics course, attempted tasks from the topics of kinematics and work. Profiles were designed to capture the overall actions and reasoning of individual students across the various tasks. Two main profiles emerged from each topic under consideration. They were related to the Johnson-Laird cognitive framework to infer about the kinds of mental constructs. The results indicate that, for both topics, students work primarily at the level of propositional mental representation. When handling the kinematics tasks, a few students construct mental images and none of them can be categorized as using a mental model. In contrast, in the context of work, none of the participants generated a mental image while a minority of the sample was classified as using a mental model. Moreover, a comparison across the two topics indicates the predominance of propositional mental representation

Distinguishing between “change” and “amount” infinitesimals in first-semester calculus-based physics

From the perspective of an introductory calculus course, an integral is simply a Riemann sum: a particular limit of a sum of small quantities. However, students connect those mathematical quantities to physical representations in different ways. For example, integrals that add up mass and integrals that add up displacement use infinitesimals differently. Students who are not cognizant of these differences may not understand what they are doing when they integrate. Further, they may not understand how to set up an integral. We propose a framework for scaffolding students' knowledge of integrals using a distinction between “change” and “amount” infinitesimals. In support of the framework, we present results from two qualitative studies about student understanding of integration

Investigating students\u27 mental models and knowledge construction of microscopic friction. I. Implications for curriculum design and development

In this paper, we discuss the first phase of a multiphase study aimed at investigating the dynamics of students\u27 knowledge construction in the context of unfamiliar physical phenomenon-microscopic friction. The first phase of this study involved the investigation of the variations in students\u27 mental models of microscopic friction. Clinical interviews were conducted with 11 students enrolled in conceptual modern physics to elicit their ideas and generate themes of explanations. A phenomenographic approach of data analysis was employed to establish the variations in students\u27 explanations. Results show that students\u27 mental models of friction at the atomic level are dominated by their macroscopic experiences. Friction at the atomic level according to most students is due to mechanical interactions (interlocking or rubbing of atoms). © 2011 American Physical Society

Integrated STEM: Impact of Engineering Design and Computer Science in STEM Labs

By integrating physics laboratories with engineering design and computer science, students apply physics principles to ill-structured and complex problems, engage in knowledge transfer, and gain interest in STEM. The introductory physics labs at Purdue have been updated to include engineering design and computer science principles that ground physics in authentic problems. Integrated labs have been evaluated using student perception post-surveys, student course performance, interviews, and case-study observations. Preliminary results indicate that integrated physics labs promote transfer, enhanced metacognitive skills, student interest, and motivation

Linking attentional processes and conceptual problem solving: visual cues facilitate the automaticity of extracting relevant information from diagrams

This study investigated links between visual attention processes and conceptual problem solving. This was done by overlaying visual cues on conceptual physics problem diagrams to direct participants’ attention to relevant areas to facilitate problem solving. Participants (N = 80) individually worked through four problem sets, each containing a diagram, while their eye movements were recorded. Each diagram contained regions that were relevant to solving the problem correctly and separate regions related to common incorrect responses. Problem sets contained an initial problem, six isomorphic training problems, and a transfer problem. The cued condition saw visual cues overlaid on the training problems. Participants’ verbal responses were used to determine their accuracy. This study produced two major findings. First, short duration visual cues which draw attention to solution-relevant information and aid in the organizing and integrating of it, facilitate both immediate problem solving and generalization of that ability to new problems. Thus, visual cues can facilitate re-representing a problem and overcoming impasse, enabling a correct solution. Importantly, these cueing effects on problem solving did not involve the solvers’ attention necessarily embodying the solution to the problem, but were instead caused by solvers attending to and integrating relevant information in the problems into a solution path. Second, this study demonstrates that when such cues are used across multiple problems, solvers can automatize the extraction of problem-relevant information extraction. These results suggest that low-level attentional selection processes provide a necessary gateway for relevant information to be used in problem solving, but are generally not sufficient for correct problem solving. Instead, factors that lead a solver to an impasse and to organize and integrate problem information also greatly facilitate arriving at correct solutions

Student and AI responses to physics problems examined through the lenses of sensemaking and mechanistic reasoning

Several reports in education have called for transforming physics learning environments by promoting sensemaking of real-world scenarios in light of curricular ideas. Recent advancements in Generative-Artificial Intelligence has garnered increasing traction in educators' community by virtue of its potential in transforming STEM learning. In this exploratory study, we adopt a mixed-methods approach in comparatively examining student- and AI-generated responses to two different formats of a physics problem through the cognitive lenses of sensemaking and mechanistic reasoning. The student data is derived from think-aloud interviews of introductory students and the AI data comes from ChatGPT's solutions collected using Zero shot approach. The results highlight AI responses to evidence most features of the two processes through well-structured solutions and student responses to effectively leverage representations in their solutions through iterative refinement of arguments. In other words, while AI responses reflect how physics is talked about, the student responses reflect how physics is practiced. Implications of these results in light of development and deployment of AI systems in physics pedagogy are discussed

Students' Models of Newton's Second Law in Mechanics and Electromagnetism

We investigated students' use of Newton's second law in mechanics and electromagnetism contexts by interviewing students in a two-semester calculus-based physics course. We observed that students' responses are consistent with three mental models. These models appeard in mechanics contexts and were transferred to electromagnetism contexts. We developed an inventory to help instructors identify these models and direct students towards the correct one.Comment: 15 pages, 3 figues and 4 table

Impacts of the Tropical Pacific/Indian Oceans on the Seasonal Cycle of the West African Monsoon

The current consensus is that drought has developed in the Sahel during the second half of the twentieth century as a result of remote effects of oceanic anomalies amplified by local land–atmosphere interactions. This paper focuses on the impacts of oceanic anomalies upon West African climate and specifically aims to identify those from SST anomalies in the Pacific/Indian Oceans during spring and summer seasons, when they were significant. Idealized sensitivity experiments are performed with four atmospheric general circulation models (AGCMs). The prescribed SST patterns used in the AGCMs are based on the leading mode of covariability between SST anomalies over the Pacific/Indian Oceans and summer rainfall over West Africa. The results show that such oceanic anomalies in the Pacific/Indian Ocean lead to a northward shift of an anomalous dry belt from the Gulf of Guinea to the Sahel as the season advances. In the Sahel, the magnitude of rainfall anomalies is comparable to that obtained by other authors using SST anomalies confined to the proximity of the Atlantic Ocean. The mechanism connecting the Pacific/Indian SST anomalies with West African rainfall has a strong seasonal cycle. In spring (May and June), anomalous subsidence develops over both the Maritime Continent and the equatorial Atlantic in response to the enhanced equatorial heating. Precipitation increases over continental West Africa in association with stronger zonal convergence of moisture. In addition, precipitation decreases over the Gulf of Guinea. During the monsoon peak (July and August), the SST anomalies move westward over the equatorial Pacific and the two regions where subsidence occurred earlier in the seasons merge over West Africa. The monsoon weakens and rainfall decreases over the Sahel, especially in August.Peer reviewe