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We conducted a study with introductory and upper-division physics students in a Mexican university to learn how students independently recognize the electric field's main characteristics in the electric field lines diagram and as a source or target representation in conversion processes. We used the theory of registers of semiotic representations and a phenomenographic approach as a framework to analyze data. The recognition and conversion abilities were explored through interpretation and construction tasks. We identified students' main difficulties in recognition and conversion in the interpretation and construction tasks. In conversion processes, we found that when the electric field lines diagram is the source representation, students do not interpret the field lines' density as the magnitude of the electric field. The difficulties of interpretation that arise in these conversion processes depend partially on the target representation. We also found that constructing electric field lines is especially difficult for students at both introductory and upper-division levels. Most students would prefer to draw vector field plots instead. We recommend that electricity and magnetism teachers and researchers be aware of the difficulties that the recognition and conversion in interpretation and construction tasks may represent for their students in understanding the electric field concept.

Inquiring about students' learning and their difficulties understanding the concepts and models of physics is a familiar challenge in physics education research. Researchers have developed various methodologies, such as phenomenography, to address it. Phenomenography is an empirical approach to determining how people experience and understand aspects of their surroundings and the physical world in qualitatively different ways. Rigorous phenomenographic analysis can be used to define categories to describe general ways the students experience the research phenomenon. The phenomenographic analysis process focuses on critical aspects of the collective experience rather than the richness of individual experience, assuming that there are a limited number of categories to describe the variations of experience for a given phenomenon. The possibility of defining a limited number of categories for experiencing a phenomenon on a collective level is one characteristic that makes phenomenographic analysis particularly appropriate for research that aims to enhance teaching and learning. We shall critically examine the strengths and weaknesses of phenomenographic research in this paper. The strengths include integral and holistic descriptions of people's conceptions. Weaknesses include the risks of equating participants' experiences with their descriptions of their own experiences. Our contribution weighs up the literature's warnings about the validity and reliability of phenomenographic research. To provide an overview of phenomenography in physics education research, we conducted a literature review which identified and analyzed different approaches to data collection, data analysis, rigor, presentation of the results, and scope. We conclude by considering phenomenography as a research approach to learn how students perceive a concrete learning phenomenon, thus, providing an essential teaching design and preparation guide for instructors.

Textbooks play a fundamental role in teaching and learning in school science classrooms. In this paper, we investigate the presentation of the nature of the electromagnetic field in a dozen of the world's most popular introductory university physics textbooks. We analyze, from an epistemologically based teaching approach, the didactic treatment of the electromagnetic field in relation to its sources, Maxwell's laws and electromagnetic waves. With this objective, we elaborate a rational reconstruction of the developments that led to the formulation of the nature of the electromagnetic field, Maxwell's laws and their meaning, as well as electromagnetic waves. Next, we formulate criteria based on the key aspects derived from the reconstruction that are useful in the evaluation of electromagnetism textbooks at the introductory level and apply them to the sample of selected books. In light of the results, we reflect on their consequences for teaching. Our analysis indicates the existence of certain inconsistencies in the approach to the electromagnetic field and its relationship with its sources, Maxwell's laws and electromagnetic waves in many of the books analyzed.

In this work we present the application of design based research (DBR) methodology to conduct a systematic iterative study of the design and implementation of a teaching-learning sequence (TLS) on emf (electromotive force). This work is the final part of a broader study that started with the analysis of students' difficulties with emf in the contexts of transitory current, direct current, and electromagnetic induction. We complete our research by investigating to what extent students see emf as a cross-cutting concept. We establish the design parameters based on an epistemological analysis and the empirical data, and describe how we devised and implemented the first version of the TLS that takes 4.5 h of classroom time. We analyze the data obtained in the first implementation and describe the redesign process that resulted in a second version of the TLS that takes 1.5 h of classroom time. We conclude that both versions of the TLS effect a similar boost in student attainment of learning objectives compared to the control group.

We conducted a study with introductory and upper-division level physics students in a Mexican and a Spanish university to learn how students recognize the main characteristics of the electric field in three of its more widely used representations, namely, algebraic notation, vector field plot, and electric field lines, and how the students do conversions of them. The students' abilities to recognize the three representations of the electric field and do conversions gave insight into their understanding of this concept. We used the "theory of registers of semiotic representations" as a framework to analyze the data. Our results showed that the direction of the conversion is an essential factor in determining the students' success in performing conversions of electrical field representations. We found close synergy between the vector field plot and the algebraic notation of the electric field. However, we found that the conversions that involve electric field lines do not present synergy. The electric field lines representation is especially difficult for students, both as a "source" and as a "target" representation, specifically, the interpretation and representation of the magnitude of the field through the density of field lines. We recommend that teachers and researchers of electricity and magnetism be more conscious of the difficulties that some conversion tasks may present to their students. We specifically invite instructors to be attentive to how they approach the representation of electric field lines and be explicit when performing conversions that involve electric field lines.

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] We argue that teaching learning sequence (TLS) design needs to be further developed through the explicit articulation of methodology, which comprises the theoretical commitments regarding research and how those give rise to methods for design, implementation and assessment. In this study we propose design based research (DBR) as a methodology to conduct systematic and iterative studies of the design and assessment of educational interventions (such as materials and strategies) as solutions to complex problems in educational practice. This methodology does not specify theoretical commitments regarding the nature of learning and how those give rise to teaching strategies, but the articulation of those commitments is expected as part of the justification for decision making in the design process. In order to demonstrate the framework, we present an example of TLS development in the context of introductory electrostatics and dc circuits. We describe the evaluation of the TLS over three years of implementation, addressing both the capacity of the TLS for involving students in learning the topic and the students' learning itself.

In this work, we explore how undergraduate students use classical field theory when describing physical phenomena in the context of introductory electromagnetism. We have extracted five key characteristics of the electric and magnetic field from a historical analysis of the topic. These characteristics informed the creation of a questionnaire comprising six free-response conceptual questions. The questionnaire instrument was administered to undergraduate students in three European countries. Phenomenographical analysis of the students' responses shows that many undergraduates do not have a coherent idea of field theory. We conclude that, rather than focusing on teaching rules with which to calculate, more attention should be paid to the specific characteristics of field theory and the difference between fields and forces, with particular emphasis on the conceptual interpretation of the interaction process.

In this paper we put forward a proposal for the design and evaluation of teaching and learning sequences in upper secondary school and university. We will connect our proposal with relevant contributions on the design of teaching sequences, ground it on the design-based research methodology, and discuss how teaching and learning sequences designed according to our proposal relate to learning progressions. An iterative methodology for evaluating and redesigning the teaching and learning sequence (TLS) is presented. The proposed assessment strategy focuses on three aspects: (a) evaluation of the activities of the TLS, (b) evaluation of learning achieved by students in relation to the intended objectives, and (c) a document for gathering the difficulties found when implementing the TLS to serve as a guide to teachers. Discussion of this guide with external teachers provides feedback used for the TLS redesign. The context of our implementation and evaluation is an innovative calculus-based physics course for first-year engineering and science degree students at the University of the Basque Country.

This study examines the causal reasoning that university students use to explain how dc circuits work. We analyze how students use the concepts of electric field and potential difference in their explanatory models of dc circuits, and what kinds of reasoning they use at the macroscopic and microscopic levels in their explanations. This knowledge is essential to help instructors design and implement new teaching approaches that encourage students to articulate the macroscopic and microscopic levels of description. A questionnaire with an emphasis on explanations was used to analyze students' reasoning. In this analysis of students' reasoning in the microscopic and macroscopic modeling processes in a dc circuit, we refer to epistemological studies of scientific explanations. We conclude that the student explanations fall into three main categories of reasoning. The vast majority of students employ an explanatory model based on simple or linear causality and on relational reasoning. Moreover, around a third of students use a relational reasoning that relates two magnitudes current and resistance or conductivity of the material, which is included in a macroscopic explanatory model based on Ohm's law and the conservation of the current. In addition, few students situate the explanations at the microscopic level (charges or electrons) with unidirectional cause-effect reasoning. This study looks at a number of aspects that have been little mentioned in previous research at the university level, about the reasoning types students use when establishing macro-micro relationships and some possible difficulties with complex reasoning.

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.