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Social semiotic discussions about the role played by representations in effective teaching and learning in areas such as physics have led to theoretical proposals that have a strong common thread: in order to acquire an appropriate understanding of a particular object of learning, access to the disciplinary relevance aspects in the representations used calls for the attainment of representational competence across a particular critical constellation of systematically used semiotic resources (which are referred to as modes, see more on this later). However, an affirming empirical investigation into the relationship between a particular object of learning and different representational formulations, particularly with large numbers of students, is missing in the literature, especially in the context of university -level physics education. To start to address, this research shortfall the positioning for this article is that such studies need to embrace the complexities of student thinking and application of knowledge. To achieve this, both factor and network analyses were used. Even though both approaches are grounded in different frameworks, for the task at hand, both approaches are useful for analyzing clustering dynamics within the responses of a large number of participants. Both also facilitate an exploration of how such clusters may relate to the semiotic resource formulation of a representation. The data were obtained from a questionnaire given to 1368 students drawn from 12 universities across 7 countries. The questionnaire deals with the refraction of light in introductorylevel physics and involves asking students to give their best prediction of the relative visual positioning of images and objects in different semiotically constituted situations. The results of both approaches revealed no one-to-one relationship between a particular representational formulation and a particular cluster of student responses. The factor analysis used correct answer responses to reveal clusters that brought to the fore three different complexity levels in relation to representation formulation. The network analysis used all responses (correct and incorrect) to reveal three structural patterns. What is evident from the results of both analyses is that they confirm two broad conclusions that have emerged from social semiotic explorations dealing with representations in relation to attempting to optimize teaching and learning. The first, which is linked to a facilitating -awareness perspective, is that any given disciplinary visual representation can be expected to evoke a dispersed set of knowledge structures, which is referred to as their relevance structure. Thus, the network analysis results can be seen as presenting a unique starting point for studies aiming to identify such relevance structure. The second broad conclusion is that disciplinary visual representation can and often does contain more disciplinary -relevant aspects than what may be directly visible in a given representation. These are referred to as the appresent aspects that need to become part of the total awareness needed by someone to constitute an intended meaning. The results of the factor analysis can then also be seen to be a way of capturing all the disciplinary -relevant aspects (both present and appresent). Educational implications are discussed.

Working out the relations between the forces involved in circular motion in a vertical plane can be challenging for first-year students, as illustrated in this analysis of a 30 min group discussion of a textbook problem where a remote-control model car moves with constant speed inside a cylinder. The analysis includes timelines of semiotic resources used, as well as of topics brought up by individual students. Questions from the students include: what is that force you drew on the paper? Does it act on the car or on the wall? What keeps the car from falling down? The normal force and the 'centripetal force' both point to the center-does it mean they are the same? Is it only a gravitational force at the top? Does the normal force at the bottom just cancel gravity or does it need to be larger? What is 'normal' about the normal force? Arriving at the correct numerical result is insufficient evidence for student understanding of forces in circular motion! Can students with fragmentary understanding bring their pieces together to solve the puzzle? From the timelines, we can identify a few critical moments where the discussion changes focus. This happens when one of the students in the group introduces a new dimension of variation, e.g. a reminder about the force of gravity, a free-body diagram drawn, as well as diagrams drawn in other parts of the circle than the top or bottom, where the centripetal and normal forces are no longer in the same direction. Embodied experiences are invoked, but only at a very late stage in the discussion. For teachers, an awareness of the different ways students use terms and think about the forces can be a guide to offering a larger variation in the interventions, as well as in problems assigned.

This article revisits and expands upon a previous phenomenographic study characterising the qualitatively different ways in which South African undergraduate physics students may experience the use of +/- signs in one-dimensional kinematics (1DK). We find the original categorisation as applicable for interpreting Swedish university-level students' responses to 1DK questions. However, by way of a typology of potential learning outcomes associated with +/- signs in 1DK, our review of the topic reveals that the original study's treatment misses the implications of +/- signs related to time rate of change and graphical shape. We also add to the description of students' experience of +/- signs in 1DK by incorporating ideas from the Variation Theory of Learning and by focusing on some of the aspects of +/- signs in 1DK that were underemphasized in the original study. Our analysis thus provides a template for physics educators to support students' conceptual understanding of sign conventions in vector kinematics.

Since visual representations play a particularly important role in the teaching and learning of chemistry, the exploration described in this article focuses on them. This is an explorative study of the qualitatively different ways that visual representations can be unpacked by Swedish upper secondary school chemistry teachers dealing with intermolecular forces. Unpacking is characterized as the ways that visual representations get used to open up the possibility of having the critical aspects and features of an intended object of learning being brought into focal awareness, initially on their own and then simultaneously. The analysis, which combines a phenomenographic and a social semiotic approach, leads to the characterizations of five qualitatively different ways that visual representations may be unpacked. These outcome categories are presented in terms of a conceptual hierarchy, where two of these ways of unpacking are characterized as being teacher-centered and the other three as student-centered. This leads to a case being made that if teachers use student-centered ways of unpacking visual representations, then their students will be more likely to gain greater access to critical aspects and features of the enacted object of learning. We argue that in terms of making theoretical and practical contributions to the phenomenographic perspective on learning, the results can be used as a tool for researchers wishing to explore how visual representations can be used effectively in science education and also provide a useful basis for discussion in teacher education and in teacher professional development programs.

A social semiotic lens is used to characterise aspects of representationalcompetence for a discipline such as physics, to providescience teachers with a practical suggestion about how studentlearning might be organised to develop representational competence.We suggest that representational competence for someareas of science can be characterised in terms of the ability toappropriately interpret and produce a set of disciplinary-scientificrepresentations of real-world phenomena, and link these to scientificconcepts. This is because many areas of science are based oncreating scientific explanations of real-world observations. We thenshow how this characterisation may be applied by performing asocial semiotic audit of what it entails to become representationallycompetent in one particular semiotic system (graphs) for one particulararea of physics (1-D kinematics). Using this audit, we generatethree open-ended tasks expected to help students develop representationalcompetence in this area and empirically demonstratetheir potential effectiveness. Building on this example, we suggestthat our description of how a disciplinary social semiotic audit maybe used to construct open-ended student learning tasks potentiallyprovides one way for teachers to think about the development ofrepresentational competence in other semiotic systems and otherareas of science.

In this paper, we show that introductory physics students may initially conceptualise Cartesian coordinate systems as being fixed in a standard orientation. Giving consideration to the role that experiences of variation play in learning, we also present an example of how this learning challenge can be effectively addressed. Using a fine-grained analytical description, we show how students can quickly come to appreciate coordinate system movability. This was done by engaging students in a conceptual learning task that involved them working with a movable magnetometer with a printed-on set of coordinate axes to determine the direction of a constant field (Earth's magnetic field).

The aim of the paper is to create a way of extending the utility of using variation theory of learning (VTL) as an analytic tool for exploring student learning in interactive environments for highly complex disciplines such as physics that aims at obtaining additional insights and understanding of students' learning challenges in physics drawing on a phenomenography perspective. To do this we propose an analytical combination of two perspectives-social semiotics and the VTL-using theoretical constructs from both. Here, in keeping with the phenomenographic perspective that underlies VTL, learning is taken to mean coming to experience things in distinctly new ways. As a case study, students were video recorded during a group problem-solving session while working on circular motion tutorial problems. Through the combined analytic approach, we were able to identify the students'relevance structureas enacted as a function of what was in focal awareness and what dimensions of variation that were presented. A social semiotic multimodal transcription is used to illustrate the proposed methodology, which is made up of the semiotic systems that the students chose to use to build their discursive engagement on. As a methodology paper, and because such discussion already exists in the literature, how this kind of analytic combination can provide additional teaching insights and how these insights could be used to enhance teachers' understanding of their students' learning are not presented in this paper.

In this paper, we examine the implementation of a digital learning environment—namely, the physics software, Algodoo—which is less-constrained in its design than the digital learning environments typically used in physics education. Through an analysis of a case study, we explore a teaching arrangement wherein physics teachers responsively guide small groups of students as they use less-constrained DLEs in a mostly self-directed manner. Our analysis leads to practical recommendations for physics teachers in terms of (1) how to glean useful information about students' existing physics knowledge through observation and (2) how to responsively intervene so as to productively guide students toward the learning of particular physics content. These recommendations stem from our use of the variation theory of learning as a lens for physics students' use of digital learning environments.

In this study we video-filmed upper-secondary physics students working with a laboratory task designed to help them learn about the Earth’s magnetic field. Students worked in pairs with a hand-held magnetometer to determine the direction of the Earth’s magnetic field. As the magnetometer is moved, the x, y and z components of the Earth’s magnetic field are displayed on a computer screen. The students were simply instructed to find the direction of the Earth’s magnetic field and mark this direction using a red paper arrow. A full multimodal transcription of the student interaction was made. In our analysis the central role of transduction (defined as the movement of semiotic material from one mode or semiotic system to another) became clear. Three separate transductions of meaning were identified. The first—transduction of the meaning potential in the room to the computer screen by themagnetometer—allowed students to interact with the invisible magnetic field. Then, as the students worked together, their coordination of resources was transducted to the red paper arrow. This allowed the students to display the results of their work in a persistent representation. The arrow then functioned as a coordinating hub for the final discussion, which resulted in transductionof meaning into student gestures. We suggest that this final transduction offers the possibility for teachers to check student learning. In conclusion, we recommend that teachers should think carefully about the resources provided in a task and the transductions that are expected to occur. The selection of a persistent resource as a coordinating hub may be useful. We also suggest that teachers should look for student transductions in their classrooms as confirmation that learning is taking place. In our analysis, when teachers noticed such transductions this often led to fruitful teacher/student discussions about the phenomenon at hand.