In order to make disciplinary meanings, science students need to coordinate a large number of semiotic systems such as graphs, diagrams, spoken and written language, gesture, mathematics, etc. In this respect, it has been suggested that there is a critical constellation of semiotic resources that is necessary for holistic construction of each scientific concept (Airey, 2009). Other actors have discussed this problem in terms of building students' representational competence (Kozma & Russell 2005; Kohl & Finkelstein 2005; De Cock 2012; Linder et al. 2014). Combining this work, Volkwyn et al (2020:91) define representational competence as: “The ability to appropriately interpret and produce a set of disciplinary-accepted representations of real-world phenomena and link these to formalized scientific concepts”. In this paper we first put forward a theoretical proposal for how such student representational competence may be developed, before empirically demonstrating the usefulness of this proposal for a particular representational system (graphs) in a particular area of physics (1-D kinematics). By coordinating kinematics concepts, the three graphs, and real-world movement we show how the students begin to practice their representational competence. We also show the complexity of this apparently simple system in representational terms.

In this study we video-filmed upper-secondary physics students working with a laboratory task designed to encourage transduction (Bezemer & Kress 2008) when learning about coordinate systems.

Students worked in pairs with an electronic measurement device to determine the direction of the Earth’s magnetic field. The device, IOLab, can be held in the hand and moved around. The results of this movement are graphically displayed on a computer screen as changes in the x, y and z components of the Earth’s magnetic field. The students were simply instructed to use the IOLab to find the direction of the Earth’s magnetic field and mark its direction using a red paper arrow.

A full multimodal transcription of the student interaction was made (Baldry & Thibault 2006). In our analysis of this transcription, three separate transductions of meaning were identified—transduction of meaning potential in the room to the computer screen, transduction of this meaning to the red arrow, and finally transduction into student gestures. We suggest that this final transduction could not have been made without the introduction of the arrow, which functioned as a coordinating hub (Fredlund et al 2012).

We recommend that teachers should carefully think about the resources in a task that may function as a coordinating hub and should also look for student transductions in their classrooms as confirmation that learning is taking place.

It has been argued that for any given physics task there is a critical constellation of resources that students need to become proficient in handling in order for physics learning to take place. This is because different resources offer access to different information i.e. they have different pedagogical and disciplinary affordances. A laboratory exercise requiring coordination of multiple resources was designed to help students appreciate the movability of coordinate systems. Initially students were unable to coordinate the manipulation of a hand-held measuring device (IOLab) and observe changes in three readouts on a computer screen, whilst simultaneously drawing conclusions in their discussions with each other and the facilitator. However, the introduction of a paper arrow allowed students to quickly coordinate the resources and begin to experience the movability of coordinate systems. The study confirms earlier work on critical constellations of resources and the functioning of persistent resources as coordinating hubs.

The construction of physics knowledge of necessity entails a range of semiotic resources, (e.g. specialized language, graphs, algebra, diagrams, equipment, gesture, etc.). In this study we documented physics students' use of different resources when working with an "invisible" phenomenon--magnetic field. Using a social semiotic framework, we show how appropriate coordination of resources not only enabled students to learn something about the Earth's magnetic field, but also about the use of an abstract mathematical tool--coordinate systems. Our work leads us to make three suggestions: 1. The potential for learning physics can be maximized by designing tasks that encourage students to use a specific set of resources.  2. Thought should be put into what this particular set of resources should be and how they may be coordinated. 3. Close attention to the different resources that students use can allow physics teachers to gauge the learning occurring in their classrooms.

The construction of physics knowledge of necessity entails a range of semiotic resources, (e.g. specialized language, graphs, algebra, diagrams, equipment, gesture, etc.). In this study we documented physics students' use of different resources when working with an "invisible" phenomenon--magnetic field. Using a social semiotic framework, we show how appropriate coordination of resources not only enabled students to learn something about the Earth's magnetic field, but also about the use of an abstract mathematical tool--coordinate systems. Our work leads us to make three suggestions: 

1. The potential for learning physics can be maximized by designing tasks that encourage students to use a specific set of resources. 

2. Thought should be put into what this particular set of resources should be and how they may be coordinated.

3. Close attention to the different resources that students use can allow physics teachers to gauge the learning occurring in their classrooms.

When students are introduced to coordinate systems in their physics textbooks these are usually oriented in the same manner (x increases to the right). There is a real danger then, that students see coordinate systems as fixed. However, as we know, movability is one of the main disciplinary affordances of coordinate systems. Students worked with an open-ended task to find the direction of Earth’s magnetic field. This was achieved by manipulating a measurement device (IOLab) so as to maximize the signal for one component of the field, whilst at the same time keeping the other two components at zero. In the process of completing this task, students came to experience themselves as holding a movable coordinate system. From this point they spontaneously offer elaborations about the usefulness of purposefully setting up coordinate systems for problem solving. In our terms, they have discovered one of the disciplinary affordances of coordinate systems.

Most students will be familiar with the compass as a tool that points north. However, the compass only shows us one component—the terrestrial projection—of the Earth’s magnetic field. In contrast, the IOLab potentially gives students access to the actual direction of the field. We have designed an open-ended task in which pairs of students use the IOLab to determine the actual direction of the Earth’s magnetic field in a laboratory classroom. Without any prior instruction or step-by-step procedure to follow, students simultaneously coordinate a set of resources: speech (in groups; and with facilitator), interpretation of graphical readouts, physical manipulation of the IOLab and proprioception. By coordinating the resources available, the students in our study can be seen to quickly come to a moment of disciplinary insight, where they realize the true direction of the magnetic field.

Disciplinary learning is a multimodal endeavour that calls for achieving representational competency (Linder et al 2014), which is constituted from the coordination of disciplinary semiotic resources (Airey & Linder, in press). Examples of these semiotic resources for disciplines such as physics and chemistry are mathematics, graphs, gestures, diagrams and language. The effective learning of complex subjects such as these presents many unsolved challenges. In order to begin working towards solving these challenges much still needs to be done to deepen our understanding of how such disciplinary learning takes place. Taking the idea that formal learning is made possible through experiencing specific patterns of variation (Marton 2015), we will use our analysis of student-engagement data to present a case for seeing complex learning in terms of the multimodal emergence (Davis & Sumara, 2006) of transduction (Kress, 2010).  We use these results to propose a model of disciplinary learning that characterizes the multimodal emergence of transduction in terms of the start of a journey towards achieving fluency in a critical constellation of semiotic resources (Airey & Linder 2009; in press) for a given object of learning.

In the teaching and learning of physics, a wide range of semiotic resources are used, such as spoken and written language, graphs, diagrams, mathematics, hands on work with apparatus, etc. (Lemke, 1998). In this respect it has been argued that there is a critical constellation of semiotic resources that is needed for appropriate construction of any given disciplinary concept (Airey & Linder, 2009; Airey, 2009). In this social semiotic tradition, it is the development of “fluency” in the individual semiotic resource systems and the ease of transduction (movement and coordination of meaning) between the various semiotic resource systems that makes disciplinary learning possible. We report here findings from an interpretive study of physics students working with a laboratory task designed to encourage transduction when learning about coordinate systems. A hand-held electronic measurement device (IOLab) was used to display components of the Earth’s magnetic field in real time. Our intention was for students to experience the movability of coordinate systems by open-ended investigation of dynamic, real-time changes in the x, y and z components displayed on the computer screen as they manipulated the device. Building on earlier work of Fredlund et. al. (2012) our analysis identifies three types of transduction, the last of which is transduction of meaning to a new modality (iconic gesture) not previously used by the students. We suggest this final form of transduction is indicative of what students have learned and offers the teacher a chance to confirm/challenge student conceptions. Our data clearly demonstrates how careful, open-ended task design, coupled with timely instructor questions can leverage the pedagogical affordances (Airey, 2015) of a range of semiotic resources to make physics learning possible. We therefore claim that understanding the roles that different semiotic resources play for physics learning is vital and call for further research in this area.