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Categorization and Representation of Physics Problems by Experts and Novices
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The representation of physics problems in relation to the organization of physics knowledge is investigated in experts and novices. Four experiments examine (a) the existence of problem categories as a basis for representation; (b) differences in the categories used by experts and novices; (c) differences in the knowledge associated with the categories; and (d) features in the problems that contribute to problem categorization and representation. Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifiably different problem categories, and completion of the representations depends on the knowledge associated with the categories. For, the experts initially abstract physics principles to approach and solve a problem representation, whereas novices base their representation and approaches on the problem's literal features.
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... Several studies in history education have shown, for instance, that students tend to privilege short-term and proximate causes over long-term and distant ones (Nersäter, 2018;Voss et al., 1994). In problem-solving more generally, novices struggle to expand the problem space beyond the problem statement (Chi et al., 1981;Voss et al., 1983) and are less likely to question whether further knowledge is needed (Voss & Post, 1988). As a result, novices tend to construct smaller problem spaces, often neglecting important conditions and stakeholders (Grotzer & Basca, 2003;Grotzer et al., 2015;Voss et al. 1983). ...
... For example, she argued that a lack of government regulations (Factor 2, see Appendix C) made it "so the businesses could be selfish… and make as much profit for themselves and just not care for workers." Avery's focus on localized factors and agentic intent was similar to novice approaches to other types of problems (e.g., Chi et al., 1981;Grotzer & Basca, 2003;Grotzer et al., 2015;Voss et al., 1983;Voss & Post, 1988). ...
... Some of the student-participants, like Avery, developed relatively small problem spaces as anticipated in prior studies on novice problem-solving (e.g., Chi et al., 1981;Grotzer & Basca, 2003;Grotzer et al., 2015;Voss et al., 1983;Voss & Post, 1988). Others, like Robert, greatly expanded the time and geographic scale of the problem. ...
Problem framing is an essential yet under-explored aspect of problem-based historical inquiry. This study investigated how tenth-grade students in one AP US History class framed an ill-structured historical causal reasoning problem. Data included students’ written brainstorms, students’ responses to open-ended interview questions, and researcher-created causal diagrams. The analysis, grounded in both empirical data and existing literature on historiography and problem-solving, reveals three key dimensions for researching and teaching problem framing: (a) establishing the scale of the problem space, (b) identifying relevant agents and structures, and (c) establishing causal interactions. The findings underscore the importance of metacognition, particularly the need to weigh the affordances and constraints of alternative framings. The study concludes by offering relevant instructional interventions, such as explicitly teaching problem framing concepts, designing tasks to elicit problem framing, and using prompts and visualizations to help students reflect on their problem framing.
... Past research has shown that experts and novices tend to classify physics problems differently [10,11]. Problems that novice students, who are developing expertise in physics, consider as similar due to surface features may involve very different physics principles and concepts, requiring quite different approaches to solve correctly. ...
... By contrast, experts may group problems together because the same physics principle or concept can be used to solve them. For example, a study on the categorization of introductory mechanics problems [10] based upon similarity of solutions indicates that, while experts are likely to place two problems in different categories because the best or most straightforward solutions involve different physics principles (e.g., energy conservation and Newton's second law), novice students may group the same two problems together because-they say-they both involve a pulley with hanging blocks. The findings suggest that novices are more likely to be distracted by surface features of problems, often leading them to choose unproductive solution pathways. ...
... Research shows that both the robustness of the students' knowledge structure and the specific setting in which the student originally acquired the knowledge can affect a student's ability to apply knowledge flexibly across different problem types [10][11][12][13][17][18][19]. For this reason, prior studies have used various scaffolding mechanisms to assist students in learning to transfer their knowledge effectively [20,21]. ...
We use a validated conceptual multiple-choice survey instrument focusing on thermodynamic processes and the first and second laws of thermodynamics at the level of introductory physics to investigate the problem-property dependence of introductory and advanced student responses to introductory thermodynamics problems after traditional lecture-based instruction. The survey instrument has qualitative problems involving the same concepts across multiple problems related to internal energy, work, heat transfer, and entropy. The concepts for which we investigated problem-property dependence include, among others, (i) internal energy and entropy are state variables while work and heat transfer are path-dependent variables, (ii) internal energy is proportional to the absolute temperature for an ideal gas, (iii) work corresponds to the (signed) area under the curve on a PV (pressure-volume) diagram, and (iv) internal energy is constant but entropy increases in isolated systems undergoing spontaneous and irreversible processes. This study used survey data from over 1000 college students in introductory-level algebra-based and calculus-based physics courses as well as upper-level thermodynamics courses; the survey was administered after traditional instruction in relevant concepts for each group. Think-aloud interviews were carried out to gain additional insight into students’ thinking as they responded to the survey problems. For concepts related to internal energy, heat transfer, and work, student responses for different concepts investigated often showed strong problem-property dependence, but advanced students, as a group, generally performed better than introductory students across different problems. For entropy concepts, introductory students consistently performed poorly across problem types, reflecting a persistent belief in the constancy of entropy. By contrast, upper-level students struggled consistently in cases where entropy was increasing (e.g., net entropy change in a cyclic process). Our systematic investigation of problem-property dependence of student responses is novel for thermodynamics, made possible by the use of a survey that includes multiple varied problem scenarios involving the same underlying concept. In addition to yielding many previously unreported results regarding problem-property dependence in thermodynamics, our work confirms and extends, to new problem settings and student groups, findings previously reported through the study of more limited problem settings and student groups.
Published by the American Physical Society 2025
... Problem solving has long been studied in disciplinebased education research (DBER) and cognitive science [12,[16][17][18][19][20]. It is defined in the 2012 National Academies report on DBER as being "required whenever there is a goal to reach, and attainment of that goal is not possible either by direct action or by retrieving a sequence of previously learned steps from memory" [21,22]. ...
... It is defined in the 2012 National Academies report on DBER as being "required whenever there is a goal to reach, and attainment of that goal is not possible either by direct action or by retrieving a sequence of previously learned steps from memory" [21,22]. Researchers further draw a distinction between well-defined and ill-defined problems [19]. In well-defined problems, the initial conditions, goal, and constraints on the solution are all specified clearly. ...
... Many studies have shown that students often learn how to solve quantitative problems by plugging values into algorithmic equations and pattern matching, and thus are not developing the necessary skills to transfer their understanding to unseen situations [29][30][31][32][33][34]. There is also substantial research on the use of representations in physics problem solving [19,25,35,36]. Representations describe the depth of consideration of the problem solver (whether they are representing only the surface features of the problem or the deeper physics?). ...
One of the greatest weaknesses of physics education research is the paucity of research on graduate education. While there are a growing number of investigations of graduate student degree progress and admissions, there are very few investigations of at the graduate level. Additionally, existing studies of learning in physics graduate programs frequently focus on content knowledge rather than professional skills such as problem solving. Given that over 90% of physics Ph.D. graduates report solving technical problems regularly in the workplace, we sought to develop an assessment to measure how well graduate programs are training students to solve problems. Using a framework that characterizes expert-like problem-solving skills as a set of decisions to be made, we developed and validated such an assessment in graduate quantum mechanics (QM) following recently developed design frameworks for measuring problem solving and best practices for assessment validation. We collected validity evidence through think-aloud interviews with practicing physicists and physics graduate students, as well as written solutions provided by physics graduate and undergraduate students. The assessment shows strong potential in differentiating novice and expert problem solving in QM and showed reliability in repeated testing with similar populations. These results show the promise of measuring expert decision making in graduate QM and provide baseline measurements for future educational interventions to more effectively teach these skills.
Published by the American Physical Society 2025
... Στον Πίνακα 1 παρουσιάζεται η δομή της αλυσίδας σκέψης (CoT) στην οποία εμπλέκονται οι μαθητές βήμα-βήμα κατά την επίλυση προβλημάτων Φυσικής. Περιλαμβάνει δεξιότητες όπως η αναγνώριση των φαινομένων που πραγματεύεται το προς επίλυση πρόβλημα, η αναγνώριση αρχικών και τελικών συνθηκών του συστήματος (Chi et al., 1981), η διατύπωση υποθέσεων και αναγνώριση αιτιακών σχέσεων (Lawson, 2000), η αναγνώριση και ο έλεγχος των μεταβλητών (Lawson, 1978˙ Chi et al., 1981, ο συσχετιστικός συλλογισμός, ο παραγωγικός συλλογισμός, η εξαγωγή αποτελεσμάτων και η αξιολόγηση (Zimmerman, 2007). ...
Η παρούσα έρευνα εξετάζει τον ρόλο της μηχανικής προτροπών (prompt engineering) με τα μεγάλα γλωσσικά μοντέλα (Large Language Models-LLMs), όπως το ChatGPT-4, ως μαθησιακό εργαλείο για την ανάπτυξη δεξιοτήτων επιστημονικού συλλογισμού και την ενίσχυση της ικανότητας επίλυσης προβλημάτων Φυσικής σε μαθητές δευτεροβάθμιας εκπαίδευσης. Βασικός στόχος της έρευνας είναι να ενσωματώσει τα μοντέλα τεχνητής νοημοσύνης στις παραδοσιακές μεθόδους διδασκαλίας, ως ¨υποστηρικτές¨ στη μάθηση σε ένα μαθητοκεντρικό περιβάλλον. Αξιοποιώντας στρατηγικές της μηχανικής προτροπών όπως η αλυσίδα σκέψης (Chain of Thought-CoT), επιδιώκεται η ενίσχυση της κριτικής σκέψης των μαθητών και η κατανόηση θεμελιωδών αρχών της Φυσικής.
... Once the schema is retrieved, they solved the problem in a forward-working manner, by writing the general equations and then solving for the appropriate unknowns until the goal variable is calculated. The results have been corroborated by the famous Chi study [21], where both experts and novices were asked to categorize mechanics problems based upon similarity of solutions. As opposed to experts, novices categorized problems based on superficial aspects of problems (such as inclined plane problems, pulley problems, block problems, etc). ...
... The set of possible student learner states is theoretically infinite, though. Empirical learning sciences work shows that the effects of a specific learning activity may depend on many individual features such as motivation, intelligence, and prior knowledge (Schneider & Stern, 2010)-these factors can further differentially influence whether learners are active or passive (Chi & Wylie, 2014), exhibiting surface or deep learning (Chi et al., 1981), engaging in cognitive or emotional conflict (Asterhan & Schwarz, 2016), etc. It maybe therefore tempting as an AIED designer to value what can be easily measured and develop sophisticated learner models to offer greater personalization. ...
I nudge reevaluation of the idea that artificial intelligence for education (AIED) is merely about using artificial intelligence (AI) tools to automate understanding and responding to learning processes. Instead, I advocate for a human-centered approach to AIED that emphasizes the importance of personal connections, relationship-building, and scaffolding that goes beyond simplifying tasks to push students in their critical thinking. This approach calls for curating multimodal data from ecologically valid learning settings to train AIED systems, and maintaining flexibility in expectations around rational learner behavior when analyzing data from such systems. Given that the definition of good AIED is often discipline-specific and influenced by the underlying pedagogical models of student learning, the article calls on learning sciences researchers to integrate their complementary yet often competing theoretical lenses in rigorously studying AI-supported learning phenomena at scale.
Although a sizable body of knowledge is prerequisite to expert skill, that knowledge must be indexed by large numbers of patterns
that, on recognition, guide the expert in a fraction of a second to relevant parts of the knowledge store. The knowledge forms
complex schemata that can guide a problem's interpretation and solution and that constitute a large part of what we call physical
intuition.
Expert problem-solving programs have focused on working problems which humans consider difficult Oddly, many such problem-solvers could not solve less difficult versions of the problems addressed by their expertise This shortcoming also contributed to these program's inability to solve harder problems. To overcome this 'paradox' requires multiple representations of knowledge, inferencing schemes for each, and communication schemes between them. This paper presents a program, NEWTON, applying this idea to the domain of simple classical mechanics. NEWTON employs the method of envisionment, whereby simple questions may be answered directly, and plans produced for solving more complex problems. Envisioning enables NEWTON to use qualitative arguments when possible, with resorts to mathematical equations only if the qualitative reasoning fails to produce a solution.
This paper develops a technique for isolating and studying the per- ceptual structures that chess players perceive. Three chess players of varying strength - from master to novice - were confronted with two tasks: ( 1) A perception task, where the player reproduces a chess position in plain view, and (2) de Groot's ( 1965) short-term recall task, where the player reproduces a chess position after viewing it for 5 sec. The successive glances at the position in the perceptual task and long pauses in tbe memory task were used to segment the structures in the reconstruction protocol. The size and nature of these structures were then analyzed as a function of chess skill. What does an experienced chess player "see" when he looks at a chess position? By analyzing an expert player's eye movements, it has been shown that, among other things, he is looking at how pieces attack and defend each other (Simon & Barenfeld, 1969). But we know from other considerations that he is seeing much more. Our work is concerned with just what ahe expert chess pIayer perceives.
A fundamental aspect of the structure of material contained within a large, intelligent memory system is that the contexts, in which units of the stored information are accessed, are critically important in determining the way that information is interpreted and used. Most of the schemes, currently under active consideration, can be viewed as variants of list structures or semantic network structures. This chapter discusses some implications of these memory structures in regard to how the connections among different memory units are formed and interpreted, and some of the issues of processing that arise when these memory structures are used. It also discusses the nature of memory reference processes that can lead automatically, without particular effort, to the richness of the retrievals that it is believed to be a fundamental property of human memory. When two or more processes use the same resources at the same time, they may both interfere with one another, neither may interfere with the other, or one may interfere with a second without any interference from the second process to the first. The important principle is that a process can be limited in its performance either by the amount of available processing resources, such as memory or processing effort, or by the quality of the data available to it. Competition among processes can affect a resource-limited process, but not a data-limited one.
The recent cognitive skills literature is reviewed and several principles of skilled performance are derived. One of the central issues in cognitive skills concerns the organization of knowledge and it was concluded that in a variety of domains, spatial knowledge is hierachically organized. This issue was explored in a map-drawing study and it was found that the most serious errors were due to a normalizing error, an error that is symptomatic of hierarchical organization. It was concluded that normalizing errors in large-scale environments are caused by incorrect representations at higher levels in the hierarchy (global errors). Finally, from an information processing analysis of spatial knowledge, the paper addresses the question of what are the cognitive processes underlying cognitive maps and cognitive mapping. (Author)
This chapter discusses production systems and the way in which they operate. A production system is a scheme for specifying an information processing system. It consists of a set of productions, each production consisting of a condition and an action. It has also a collection of data structures: expressions that encode the information upon which the production system works—on which the actions operate and on which the conditions can be determined to be true or false. The chapter discusses the possibility of having a theory of the control structure of human information processing. Gains seem possible in many forms such as completeness of the microtheories of how various miniscule experimental tasks are performed, the ability to pose meaningfully the problem of what method a subject is using, the ability to suggest new mechanisms for accomplishing a task, and the facilitation of comparing behavior on diverse tasks. The chapter presents a theory of the control structure.