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Student understanding of eigenvalue equations in quantum mechanics: Symbolic blending and sensemaking analysis 学生对量子力学中特征值方程的理解:符号混合和感性分析
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-06-18 DOI: 10.1103/physrevphyseducres.20.010153
A. R. Piña, Zeynep Topdemir, John R. Thompson
As part of an effort to examine students’ mathematical sensemaking (MSM) in a spins-first quantum mechanics course during the transition from discrete (spin) to continuous (position) systems, students were asked to construct an eigenvalue equation for a one-dimensional position operator. A subset of responses took the general form of an eigenvalue equation written in Dirac notation. Symbolic blending, a combination of symbolic forms and conceptual blending, as well as a categorical framework for MSM, were used in the analysis. The data suggest two different symbolic forms for an eigenvalue equation that share a symbol template but have distinct conceptual schemata: A transformation that reproduces the original and to operate is to act. These symbolic forms, when blended with two sets of contextual knowledge, form the basis of three different interpretations of eigenvalue equations modeled here as conceptual blends. The analysis in this study serves as a novel example of, and preliminary evidence for, student engagement in sensemaking activities in the transition from discrete to continuous systems in a spins-first quantum mechanics course.
在自旋第一量子力学课程中,为了考察学生从离散(自旋)系统到连续(位置)系统过渡期间的数学感知(MSM),要求学生构建一维位置算子的特征值方程。一部分回答采用了用狄拉克符号书写的特征值方程的一般形式。分析中使用了符号混合、符号形式和概念混合的组合以及 MSM 的分类框架。数据表明,特征值方程有两种不同的符号形式,它们共享一个符号模板,但具有不同的概念图式:一种是再现原式的变换,另一种是操作即行动。这些符号形式与两组情境知识相融合,构成了对特征值方程的三种不同解释的基础,并在此作为概念混合模型。本研究的分析是一个新颖的例子,初步证明了在自旋第一量子力学课程中,学生在从离散系统向连续系统过渡的过程中参与了感性认识活动。
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引用次数: 0
Exploring generative AI assisted feedback writing for students’ written responses to a physics conceptual question with prompt engineering and few-shot learning 探索生成式人工智能辅助反馈写作,用于学生对物理概念问题的书面回答,并进行提示工程和少量学习
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-06-13 DOI: 10.1103/physrevphyseducres.20.010152
Tong Wan, Zhongzhou Chen
Instructor’s feedback plays a critical role in students’ development of conceptual understanding and reasoning skills. However, grading student written responses and providing personalized feedback can take a substantial amount of time, especially in large enrollment courses. In this study, we explore using GPT-3.5 to write feedback on students’ written responses to conceptual questions with prompt engineering and few-shot learning techniques. In stage I, we used a small portion (n=20) of the student responses on one conceptual question to iteratively train GPT to generate feedback. Four of the responses paired with human-written feedback were included in the prompt as examples for GPT. We tasked GPT to generate feedback for another 16 responses and refined the prompt through several iterations. In stage II, we gave four student researchers (one graduate and three undergraduate researchers) the 16 responses as well as two versions of feedback, one written by the authors and the other by GPT. Students were asked to rate the correctness and usefulness of each feedback and to indicate which one was generated by GPT. The results showed that students tended to rate the feedback by human and GPT equally on correctness, but they all rated the feedback by GPT as more useful. Additionally, the success rates of identifying GPT’s feedback were low, ranging from 0.1 to 0.6. In stage III, we tasked GPT to generate feedback for the rest of the students’ responses (n=65). The feedback messages were rated by four instructors based on the extent of modification needed if they were to give the feedback to students. All four instructors rated approximately 70% (ranging from 68% to 78%) of the feedback statements needing only minor or no modification. This study demonstrated the feasibility of using generative artificial intelligence (AI) as an assistant to generate feedback for student written responses with only a relatively small number of examples in the prompt. An AI assistant can be one of the solutions to substantially reduce time spent on grading student written responses.
教师的反馈对学生概念理解和推理能力的发展起着至关重要的作用。然而,对学生的书面回答进行评分并提供个性化的反馈可能需要花费大量时间,尤其是在招生人数较多的课程中。在本研究中,我们探索使用 GPT-3.5 撰写学生对概念问题的书面回答的反馈,并采用了提示工程和少量学习技术。在第一阶段,我们使用了一小部分(n=20)学生对一个概念性问题的回答来反复训练 GPT 生成反馈。其中四个与人工撰写的反馈配对的回答被作为 GPT 的示例包含在提示中。我们让 GPT 为另外 16 个回答生成反馈,并通过多次迭代完善了提示。在第二阶段,我们向四名学生研究员(一名研究生和三名本科生研究员)提供了 16 个回复以及两个版本的反馈,其中一个由作者撰写,另一个由 GPT 撰写。我们要求学生对每个反馈的正确性和有用性进行评分,并指出哪个反馈是由 GPT 生成的。结果显示,学生对作者和 GPT 的反馈的正确性评价不相上下,但他们都认为 GPT 的反馈更有用。此外,识别 GPT 反馈的成功率很低,从 0.1 到 0.6 不等。在第三阶段,我们要求 GPT 为其余学生的回答(n=65)生成反馈信息。反馈信息由四位指导教师根据他们向学生提供反馈所需的修改程度进行评分。所有四位指导教师都对大约 70% 的反馈语句(从 68% 到 78% 不等)进行了评分,认为只需稍加修改或无需修改。这项研究证明了使用生成式人工智能(AI)作为助手,为学生的书面回答生成反馈的可行性,而提示中的例子数量相对较少。人工智能助手是大幅减少学生书面回答评分时间的解决方案之一。
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引用次数: 0
Vector representations and unit vector representations of fields: Problems of understanding and possible teaching strategies 场的向量表示和单位向量表示:理解问题和可行的教学策略
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-06-05 DOI: 10.1103/physrevphyseducres.20.010150
Christoph Hoyer, Raimund Girwidz
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when describing real fields such as magnetic and electric fields, as the vector arrows can overlap. The present study investigates vector understanding at the end of secondary education. In particular, the extent to which the geometry of the field can be derived from conventional unit vector representations and representations with centered unit vectors was examined. To support this understanding, two exercises were compared. The unirepresentational exercise argued within the conventional unit vector representation, while the multirepresentational exercise attempted to support the link between centered and conventional unit vectors. The results show that almost all test subjects solved the items for generating vector representations correctly, but significant difficulties were encountered in interpreting vector representations. Drawing and interpreting vector representations therefore appear to be different skills that should be practiced intensively and in an integrated way. Various problems could be identified when interpreting vector representations. For example, the number of vectors is often erroneously used to estimate the strength of the field, although more vectors per surface element actually only increase the resolution of the representation. Here, however, the results suggest that the longitudinal density and the transverse density of the drawn vectors are perceived differently by the learners. Furthermore, the learners recognized the field’s geometry much more readily from centered unit vectors than from conventional unit vectors. Errors occur especially when interpreting the geometry of conventional unit vector representations of rotational fields and fields containing both sources and sinks while the geometries of fields containing only sinks were interpreted quite well. The comparison between the two training exercises showed that a promising approach to deepen students’ understanding would be to use an exercise that contrasts conventional and centered unit vector representations and explains how to translate from one representation to the other, rather than describing the main elements of only a single representation. Finally, based on the results of the study, we propose a strategy for teaching vector representations in schools. Given the significantly improved readability of the representation with centered unit vectors, the results even raise the question of whether this type of representation could possibly replace the conventional representation in textbooks and learning materials in the future.
矢量场是一个高度抽象的物理概念,通常采用可视化的方式进行教学。虽然矢量表示法特别适用于定量数据的可视化,但由于矢量箭头可能会重叠,因此经常令人困惑,尤其是在描述磁场和电场等实际场时。本研究调查了中学教育结束时对矢量的理解。特别是,研究了在多大程度上可以从传统的单位矢量表示法和带有居中单位矢量的表示法中推导出场的几何形状。为了支持这种理解,我们对两种练习进行了比较。非线性练习在传统单位矢量表示法的范围内进行论证,而多重表示法练习则试图支持居中单位矢量和传统单位矢量之间的联系。结果表明,几乎所有受测者都正确地解决了生成向量表象的题目,但在解释向量表象时却遇到了很大的困难。因此,绘制矢量图和解释矢量图似乎是两种不同的技能,应该以综合的方式进行强化练习。在解释向量表象时,可以发现各种问题。例如,矢量的数量经常被错误地用来估计场的强度,尽管每个表面元素的矢量越多,实际上只会提高表征的分辨率。然而,这里的结果表明,学习者对绘制矢量的纵向密度和横向密度的感知是不同的。此外,与传统的单位矢量相比,学习者更容易从居中的单位矢量中识别出实地的几何形状。特别是在解释旋转磁场和同时包含源和汇的磁场的常规单位向量几何图形时,会出现错误,而解释只包含汇的磁场的几何图形时则相当好。对两种训练练习的比较表明,加深学生理解的一种可行方法是使用一种练习,对比传统的和居中的单位矢量表示法,并解释如何从一种表示法转换到另一种表示法,而不是只描述一种表示法的主要元素。最后,根据研究结果,我们提出了在学校教授矢量表示法的策略。鉴于居中单位矢量表示法的可读性明显提高,研究结果甚至提出了这样一个问题:这种表示法将来是否有可能取代教科书和学习材料中的传统表示法。
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引用次数: 0
Exploring techniques to improve machine learning’s identification of at-risk students in physics classes 探索改进机器学习识别物理课上问题学生的技术
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-05-31 DOI: 10.1103/physrevphyseducres.20.010149
John Pace, John Hansen, John Stewart
Machine learning models were constructed to predict student performance in an introductory mechanics class at a large land-grant university in the United States using data from 2061 students. Students were classified as either being at risk of failing the course (earning a D or F) or not at risk (earning an A, B, or C). The models focused on variables available in the first few weeks of the class which could potentially allow for early interventions to help at-risk students. Multiple types of variables were used in the model: in-class variables (average homework and clicker quiz scores), institutional variables [college grade point average (GPA)], and noncognitive variables (self-efficacy). The substantial imbalance between the pass and fail rates of the course, with only about 10% of students failing, required modification to the machine learning algorithms. Decision threshold tuning and upsampling were successful in improving performance for at-risk students. Logistic regression combined with a decision threshold tuned to maximize balanced accuracy yielded the strongest classifier, with a DF accuracy of 83% and an ABC accuracy of 81%. Measures of variable importance involving changes in balanced accuracy identified homework grades, clicker grades, college GPA, and the fraction of college classes successfully completed as the most important variables in predicting success in introductory physics. Noncognitive variables added little predictive power to the models. Classification models with performance near the best-performing models using the full set of variables could be constructed with very few variables (homework average, clicker scores, and college GPA) using straightforward to implement algorithms, suggesting the application of these technologies may be fairly easy to include in many physics classes.
我们利用 2061 名学生的数据构建了机器学习模型,用于预测美国一所大型赠地大学机械入门课的学生成绩。学生被分为有挂科风险(获得 D 或 F)或无挂科风险(获得 A、B 或 C)。模型的重点是开课前几周的变量,这些变量有可能为帮助高风险学生进行早期干预提供帮助。模型中使用了多种类型的变量:课内变量(平均家庭作业和点击测验分数)、机构变量[大学平均学分绩点(GPA)]和非认知变量(自我效能)。该课程的及格率和不及格率严重失衡,只有约 10%的学生不及格,因此需要对机器学习算法进行修改。决策阈值调整和上采样成功地提高了问题学生的成绩。逻辑回归与决策阈值相结合,最大限度地提高了平衡准确率,从而产生了最强的分类器,DF 准确率为 83%,ABC 准确率为 81%。对变量重要性的衡量涉及平衡准确率的变化,结果发现作业成绩、点击成绩、大学平均学分绩点和成功完成的大学课程比例是预测物理入门学习成功与否的最重要变量。非认知变量对模型的预测作用很小。使用简单易行的算法,只需使用很少的变量(作业平均分、点击器成绩和大学平均学分绩点)就能构建分类模型,其性能接近于使用全套变量的最佳模型,这表明这些技术的应用可能很容易被纳入许多物理课程中。
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引用次数: 0
Assessment of preservice physics teachers’ knowledge of student understanding of force and motion 评估职前物理教师对学生理解力和运动的掌握情况
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-05-31 DOI: 10.1103/physrevphyseducres.20.010148
Lan Yang, Leheng Huang, Xianqiu Wu, Jianwen Xiong, Lei Bao, Yang Xiao
In physics education, a number of studies have developed assessments of teachers’ knowledge of student understanding (KSU) of specific physics concepts with modified versions of existing concept inventories, in which teachers were asked to predict the popular incorrect answers from students. The results provide useful but indirect information to make inferences about teachers’ knowledge of the misconceptions that students may be using in answering the questions. To improve the assessment of teachers’ KSU, a new instrument is developed using a three-tier item design. The items were adapted from 17 questions from the Force Concept Inventory on force and motion. Each item was designed in three tiers, with tier 1 asking for teachers’ own answers to the question to test their content knowledge, tier 2 asking for teachers’ predictions of popular students’ incorrect answers, and tier 3 asking for teachers’ explanations of students’ incorrect answers in an open-ended form. The three-tier design captures teachers’ content knowledge, predictions, and explanations in a single item to allow explicit measures of teachers’ own content knowledge and their KSU on students’ misconceptions. The instrument was validated with preservice physics teachers, who were master-level graduate students in a normal university in China. The assessment results also suggest that the preservice teachers’ KSU of force and motion was only moderately developed, and their content knowledge was uncorrelated with their KSU. In addition, a four-level progression scale of KSU was also developed, which categorized the preservice teachers into five proficiency groups.
在物理教育中,许多研究利用现有概念清单的修订版,对教师对学生理解特定物理概念的知识(KSU)进行了评估,其中要求教师预测学生的常见错误答案。这些结果为推断教师对学生在回答问题时可能使用的错误概念的了解提供了有用但间接的信息。为了改进对教师 KSU 的评估,我们开发了一种采用三层题目设计的新工具。这些题目改编自力概念量表中有关力和运动的 17 个问题。每个项目均设计为三层,第一层要求教师自己回答问题,以测试其内容知识;第二层要求教师预测学生的错误答案;第三层要求教师以开放式形式解释学生的错误答案。三层设计将教师的内容知识、预测和解释包含在一个项目中,以便明确测量教师自身的内容知识和他们对学生错误认知的 KSU。该工具在中国一所普通高校的硕士研究生职前物理教师中进行了验证。评估结果还表明,职前教师对力和运动的 KSU 仅有中等程度的发展,他们的内容知识与其 KSU 不相关。此外,还建立了四级 KSU 进阶量表,将职前教师分为五个能力组别。
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引用次数: 0
Utilizing network analysis to explore student qualitative inferential reasoning chains 利用网络分析探索学生定性推理链
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-05-29 DOI: 10.1103/physrevphyseducres.20.010147
J. Caleb Speirs, MacKenzie R. Stetzer, Beth A. Lindsey
Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of scaffolded questions to step students through a qualitative inferential reasoning chain. It is often tacitly assumed that, in addition to building conceptual understanding, such materials improve qualitative reasoning skills. However, clear documentation of the impact of such materials on qualitative reasoning skills is critical. New methodologies are needed to better study reasoning processes and to disentangle, to the extent possible, processes related to physics content from processes general to all human reasoning. As a result, we have employed network analysis methodologies to examine student responses to reasoning-related tasks in order to gain deeper insight into the nature of student reasoning in physics. In this paper, we show that network analysis metrics are both interpretable and valuable when applied to student reasoning data generated from reasoning chain construction tasks. We also demonstrate that documentation of improvements in the articulation of specific lines of reasoning can be obtained from a network analysis of responses to reasoning chain construction tasks.
在以微积分为基础的物理入门课程中,学生通常需要建立对概念的理解,并发展和完善解决问题和定性推理的技能。在过去的 30 年中,物理教育研究界开发了许多基于研究的教材,这些教材使用一系列支架式问题来引导学生进行定性推理。人们通常默认,除了培养概念理解能力,这些教材还能提高定性推理技能。然而,明确记录此类材料对定性推理技能的影响至关重要。我们需要新的方法来更好地研究推理过程,并尽可能地将与物理内容相关的过程与所有人类推理的一般过程区分开来。因此,我们采用了网络分析方法来研究学生对推理相关任务的反应,以便更深入地了解学生物理推理的本质。在本文中,我们展示了网络分析指标在应用于推理链构建任务生成的学生推理数据时,既可解释又有价值。我们还证明,通过对推理链构建任务的响应进行网络分析,可以获得在阐明特定推理思路方面有所改进的记录。
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引用次数: 0
Modeling novel physics in virtual reality labs: An affective analysis of student learning 在虚拟现实实验室中模拟新颖的物理学:学生学习的情感分析
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-05-28 DOI: 10.1103/physrevphyseducres.20.010146
Jared P. Canright, Suzanne White Brahmia
[This paper is part of the Focused Collection on Instructional labs: Improving traditions and new directions.] We report on a study of the effects of laboratory activities that model fictitious laws of physics in a virtual reality environment on (i) students’ epistemology about the role of experimental physics in class and in the world; (ii) students’ self-efficacy; and (iii) the quality of student engagement with the lab activities. We create opportunities for students to practice physics as a means of creating and validating new knowledge by simulating real and fictitious physics in virtual reality (VR). This approach seeks to steer students away from a confirmation mindset in labs by eliminating any form of prior or outside models to confirm. We refer to the activities using this approach as Novel Observations in Mixed Reality (NOMR) labs. We examined NOMR’s effects in 100-level and 200-level undergraduate courses. Using pre-post measurements, we find that after NOMR labs, students in both populations were more expertlike in their epistemology about experimental physics and held stronger self-efficacy about their abilities to do the kinds of things experimental physicists do. Through the lens of the psychological theory of flow, we found that students engage as productively with NOMR labs as with traditional hands-on labs. This engagement persisted after the novelty of VR in the classroom wore off, suggesting that these effects were due to the pedagogical design rather than the medium of the intervention. We conclude that these NOMR labs offer an approach to physics laboratory instruction that centers the development of students’ understanding of and comfort with the authentic practice of science.
[本文是 "教学实验重点文集 "的一部分:改进传统和新方向]。我们报告了一项关于在虚拟现实环境中模拟虚构物理定律的实验活动对以下方面影响的研究:(i) 学生对物理实验在课堂和世界中作用的认识论;(ii) 学生的自我效能感;以及 (iii) 学生参与实验活动的质量。我们通过在虚拟现实(VR)中模拟真实和虚构的物理现象,为学生创造物理实践的机会,将其作为创造和验证新知识的一种手段。这种方法通过消除任何形式的先前或外部模型来确认,从而引导学生在实验中摆脱确认思维。我们将使用这种方法的活动称为 "混合现实中的新观察"(NOMR)实验室。我们考察了 NOMR 在 100 级和 200 级本科课程中的效果。通过前后测量,我们发现在 NOMR 实验后,这两个群体的学生在实验物理的认识论方面更像专家,并对自己做实验物理学家所做的事情的能力有了更强的自我效能感。通过 "流动 "心理学理论的视角,我们发现学生参与 NOMR 实验与参与传统动手实验一样富有成效。在课堂上使用虚拟现实技术的新奇感消失后,这种参与感依然存在,这表明这些效果是由教学设计而非干预媒介造成的。我们的结论是,这些 NOMR 实验为物理实验教学提供了一种方法,它以培养学生对真实科学实践的理解和舒适感为中心。
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引用次数: 0
Cheat sites and artificial intelligence usage in online introductory physics courses: What is the extent and what effect does it have on assessments? 在线物理入门课程中作弊网站和人工智能的使用:程度如何,对评估有何影响?
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-05-23 DOI: 10.1103/physrevphyseducres.20.010145
Gerd Kortemeyer, Wolfgang Bauer
As a result of the pandemic, many physics courses moved online. Alongside, the popularity of Internet-based problem-solving sites and forums rose. With the emergence of large language models, another shift occurred. One year into the public availability of these models, how has online help-seeking behavior among introductory physics students changed, and what is the effect of different patterns of online resource usage? In a mixed-method approach, we investigate student choices and their impact on assessment components of an online introductory physics course for scientists and engineers. We find that students still mostly rely on traditional Internet resources and that their usage strongly influences the outcome of low-stake unsupervised quizzes. We empirically found distinct clusters of help-seeking and resource-usage patterns among the students; the impact of students’ cluster membership on the supervised assessment components of the course, however, is nonsignificant.
由于大流行病的影响,许多物理课程都搬到了网上。与此同时,基于互联网的解题网站和论坛也越来越受欢迎。随着大型语言模型的出现,出现了另一种转变。在这些模型公开提供一年后,物理入门学生的在线求助行为发生了怎样的变化,不同的在线资源使用模式又产生了怎样的影响?我们采用混合方法,调查了学生的选择及其对科学家和工程师在线物理入门课程评估部分的影响。我们发现,学生仍然主要依赖于传统的互联网资源,而且他们的使用对低风险无监督测验的结果有很大影响。我们从经验中发现,学生在寻求帮助和资源使用模式上存在明显的群集;然而,学生群集成员身份对课程监督评估部分的影响并不显著。
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引用次数: 0
Editorial: Coauthor! Coauthor! 社论:共同作者合著者
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-05-21 DOI: 10.1103/physrevphyseducres.20.010002
Randall D. Kamien, Daniel Ucko
DOI:https://doi.org/10.1103/PhysRevPhysEducRes.20.010002
DOI:https://doi.org/10.1103/PhysRevPhysEducRes.20.010002
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引用次数: 0
Learning difficulties among students when applying Ampére-Maxwell’s law and its implications for teaching 学生在应用安培-麦克斯韦定律时遇到的学习困难及其对教学的影响
IF 3.1 2区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2024-05-16 DOI: 10.1103/physrevphyseducres.20.010143
Álvaro Suárez, Arturo C. Marti, Kristina Zuza, Jenaro Guisasola
We investigate learning difficulties among second-year students in electromagnetism courses when they apply Ampère-Maxwell’s law. Using phenomenography, we analyzed written answers from 65 undergraduate physics students to four questions on Ampère’s and Ampère-Maxwell’s laws. We complemented our research by interviewing 12 students. To design the questionnaire, we ran an epistemological analysis of classical electromagnetism which helped us to identify a set of key essential concepts to understand this theory, guided the definition of learning objectives, and drew up the questions. The results revealed that the students found it hard to recognize the validity framework from Ampère’s law and to apply Ampère-Maxwell’s law. They face particular difficulties to recognize the appearance of the displacement current and the relationship between the circulation of the magnetic field and an electric field that is variable over time.
我们研究了电磁学课程二年级学生在应用安培-麦克斯韦定律时遇到的学习困难。我们使用现象学方法,分析了 65 名物理系本科生对四个有关安培定律和安培-麦克斯韦定律问题的书面答案。此外,我们还对 12 名学生进行了访谈。为了设计问卷,我们对经典电磁学进行了认识论分析,这有助于我们确定理解这一理论的一系列关键基本概念,指导我们确定学习目标,并拟定问题。结果显示,学生很难从安培定律中认识有效性框架,也很难应用安培-麦克斯韦定律。他们在认识位移电流的出现以及磁场环流与随时间变化的电场之间的关系方面尤其困难。
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引用次数: 0
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Physical Review Physics Education Research
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