Introduction

There is now strong research interest in the links between science activity, meaning-making processes by students, and representational choices that support learning science in upper primary and junior secondary school. This research is variously guided by semiotic perspectives of science as a multi-modal discourse, where learning entails integrating meanings across different modes (diSessa 2004; Halliday and Martin 1993; Lemke 2003, 2004; Peirce 1931), second generation cognitive science perspectives on science learning as perceptual, contextual mapping (Klein 2006; Tytler et al. 2006), and socio-cultural theories of science learning as induction into the knowledge production practices of science communities (Ford 2008; Ford and Forman 2006; Gee 2004; Lemke 2003, 2004; Lunsford et al. 2007).

Researchers now broadly agree that the discipline of science should be understood historically as the development and integration of multi-modal discourses (Kress et al. 2001; Lemke 2004; Norris and Phillips 2003), where different modes serve different needs in relation to reasoning and recording scientific inquiry. In this way, mathematical, verbal and graphic modes have been used individually and in coordinated ways to represent the knowledge claims of science discourse, with more recent technology-mediated representations of science consistent with, rather than a deviation from, this evolution of science as a discipline. By implication, students need to learn about the multi-modal nature of the representations entailed in scientific inquiry, and the different modes in which the same concepts in science can be represented as part of students’ general development of science literacy.

While there is broad agreement across these perspectives about the general nature and challenges of learning tasks for learners, there is less consensus about which particular teaching and learning practices maximize learning opportunities for different learners, and why particular practices work. Debate has focused on (a) the role of natural language in this learning; (b) the value, purpose and scope of student-generated representations; and (c) effective ways for students to learn the representational conventions of science discourse. In this paper, we seek to contribute to this debate, drawing predominantly on semiotic theories proposed by Lemke (2003) and Peirce (1931).

Much recent research on learning with representations generally, and in science in particular, has focused on either (a) identifying key design features of effective representations that act as advance organizers to promote successful student interpretation and learning (Ainsworth 1999, 2006; Schnotz and Bannert 2003), or (b) analysing the conditions under which students’ construction of representations promotes learning (diSessa 2004; Prain and Waldrip 2006; Tytler et al. 2006). The first approach assumes that felicitous design features in representations can optimize student learning opportunities. However, the highly complex nature of multiple representation environments poses many intractable questions for effective design. As noted by Ainsworth (2006) and others, design researchers are beginning to wrestle with many issues including the following typical questions. What number, type, style, and sequence of representations will maximize learning outcomes for different students? To what extent does brevity or redundancy of information in and across representations enhance learning, and under what conditions? To what extent do dynamic representations, such as spoken voice, animation, and dynamic graphs, enhance or impede interpretation of represented information when contrasted with static representations, and under what conditions? Are particular concepts better matched to particular representational modes, and how does the age and background knowledge of students affect learning outcomes? To what extent does interpretive constraint in a representation, such as graphic simplicity, help or hinder student understanding, and under what conditions? To what extent should science learning be focused only on domain-specific representations such as 3D models, tables, time graphs, diagrams, cross-sections, science journals, multi-modal reports, and appropriate vocabulary and measurement for specific topics? Can learning be enhanced by including more general representational practices, such as the use of everyday language, cooperative small group work, whole-class guided discussion, posters, word walls, powerpoint presentations, charts, verbal reports, roleplays, debates and narratives, and under what conditions and with what age or cultural groups might this mix be effective? These questions can also be asked of students’ own constructions in science, and their role in learning.

Our research has been guided by recent studies in cognitive science (see Hubber et al. 2010), and accounts of the nature of science as a knowledge-production practice (Ford 2008; Ford and Forman 2006; Lemke 2004). However, in this paper we focus mainly on theoretical accounts of meaning-making relevant to conceptual learning in science (Lemke 2003; Peirce 1931) and classroom studies using a representational focus (Carolan et al. 2008; diSessa 2004; Hackling and Prain 2005; Tytler et al. 2006; Waldrip et al. 2007) to develop an emergent framework to guide teachers’ use of representations to support student learning. We consider principles to guide this approach, including teacher and student roles and interactions. We consider that semiotic and sociocultural perspectives are compatible in that they link theories of science as a subject to how science can be learnt effectively, what should count as this learning, and broad factors affecting learning outcomes.

Theoretical Perspectives

Our theoretical focus has been guided in part by semiotic accounts of the representational nature of the learning task in science (diSessa 2004; Lemke 2003, 2004; Peirce 1931). Drawing on Peirce (1893-1910), Lemke (2003) claimed that all disciplinary meaning-making practices, including mathematics and science, can be represented by a triadic account of how signs have meaning (Fig. 1).

Fig. 1
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Peirce’s triadic model of a sign system

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In Peirce’s model, distinctions are made in science, or any other field, between a representation in a sign or signifier (e.g., a flow-chart depiction of energy), the interpretation or sense made of this sign by the interpreter (the scientific idea of energy), and its referent, or the phenomena to which both the interpretation and signifier refer (examples of the operation of energy on objects in the world). As Peirce also noted, every new interpretation of a representation re-activates a new interplay of this triad, becoming a fresh interpretation of an existing interpretation. Anderberg et al. (2008, p. 15) make the compelling point that for learners this “interplay of conceptions, meanings and expressions” is inevitably “ambiguous and dynamic.” With any topic in science, students’ understandings will change as they seek to clarify relationships between their intended meanings, key conceptual meanings within the subject matter, their referents in the world, and ways to express these meanings. These researchers argue that teachers need to recognize and build on students’ intended meanings as they seek to justify their causal accounts of phenomena, using the literacies of science as tools for this reasoning.

In engaging with scientific meanings that are new to them, learners are expected to recognize the differences between an idea or concept, the different ways this idea can be represented, and the phenomena to which it refers. This implies that all attempts by learners to understand or explain concepts in science entail representational work in that they have to use their current cognitive and representational resources to make sense of science concepts that are new to them, and that are reiterated in new representations that must be freshly interpreted. Coming to know what energy or electricity mean as concepts and words in science must entail understanding and using the appropriate representational resources to make cognitive links between appropriate phenomena and theoretical, scientific accounts of this phenomena. Therefore learning about new concepts cannot be separated from learning both how to represent these concepts as well as what these representations signify in the world.

Lemke (2003, p. 226) makes the further point that particular meanings in mathematics and science and their referents are always “dependent on being embedded in the context of natural language commentary.” In other words, the learners’ everyday language is the crucial resource for negotiating understandings of (and between) the three components of the sign system in science. By implication, as also noted by Lemke (2003, 2004), students need repeated opportunities to translate disciplinary understandings into natural language, even if such translations can only ever be partial rather than complete, because of the abstractedness of the scientific forms of representation. In supporting this view, diSessa (2004, p. 299) noted that students already bring to learning in science some understanding of the need for “conciseness, completeness and precision” in representing ideas, and that “good students manage to learn scientific representations in school partly because they can almost reinvent them for themselves.”

Peirce’s triadic model might seem to imply each part is distinct, whereas Peirce acknowledged that the components (sign or representation, reference or thing referred to, and meaning [what the recipient of the sign makes of the sign]) are interlocking, and that each part is itself a sign or representation. Therefore the meaning of a representation and the actual representation are both signs of the object or referent, one mentalistic (or cognitive) and the other material (external representation) which in turn produces or shapes a new sign (i.e., what the person thinks of the secondary or external representation) leading to an evolving infinite sequence of mental “accounts” of the original object/referent plus all subsequent representations, where a past representation becomes a referent for new interpretations. Lemke (2003, p. 228) noted that Peirce saw this process as the essential building blocks or resources of science reasoning, where signs could be understood as either iconic (where there is a close resemblance between the sign and the object, such as a map or a scale model), indexical (where a system or formula measures aspects of the object, such as a thermometer) or symbolic (where a more abstract sign stands for the subject, such as a graph or table).

For Peirce, the referent is never directly experienced, but is mediated through our perceptual sensing of it. Our resulting conscious but non-expressible representations, such as visual spatial sense, and sense of basic number, cannot be expressed inwardly to form a conception of the physical reality without some representational framework (consensual, shared, public rules and conventions) learnt through interaction with some form of representation. However, this understanding may be considered merely rote, depending on the extent to which students can interpret appropriately new sign systems of relevant referents, representations and concepts. If the student fails to extend this knowledge then they also have an incomplete understanding. This raises the question of the necessary relation between perception and action for securing “strong” as opposed to “weak” learning in science, and how each aspect of the triangle must be integrated for effective sustained learning.

A representation can function as a thinking tool or scaffold during its construction, and then becomes an artefact of this thinking, shifting from a “live” representation during the process of constructing an answer to a “dormant” representation, unless used for more re-interpretive thinking. Giere and Moffatt (2003) recommended that students should learn how to use representations in science as thinking tools for predicting, understanding and making claims, rather than memorizing “correct” representations for knowledge display. This implies that students are likely to learn more effectively in science when they see the aptness of representational conventions used in this subject, and also when they recognize the persuasive nature of particular scientific explanations.

From this semiotic perspective, and following Lemke (2003, 2004) and Peirce (1893-1910), we conceptualise learning in science as the process and outcomes whereby students come to understand how to interpret and construct scientific meanings, processes, and reasoning procedures using the representational conventions of this subject. This meaning-making process implies that students can recognize and link each of Peirce’s triadic elements conceptually and practically as a basis for thinking and acting scientifically. Further, this learning entails a reciprocal process of (a) investing “public” representational conventions with “personal” meaning and referential sense-making, and (b) using these conventions as tools for new thinking, in that representational frameworks enable students (and scientists) to construct new conceptions and practices in relation to the object. Students give new meanings to the object through a process of pattern recognition between features of the event/object and representational signs, and through the internal logic or connected meanings of the representational framework, where a taxonomic view of entities (and their interplay) is the basis for scientific reasoning about casual mechanisms. Each modal framework (such as the conventions and results in a table or a graph) provides opportunities for learners to map these links and organize their understanding of the scientific meanings claimed for attributes or processes associated with the object. Using and integrating multiple modes thus facilitates learning, where this learning is conceived of as the recognition/mapping of connections between science concepts, representations and perceptual experience.

Supporting this view, Ford (2008) argued that a major dimension of learning in science should entail students knowing how to make adequate claims in this subject, where adequacy is judged by how well students know how to use the representational tools specific to this subject generally, and specific to reasoning and investigations in particular topics. For example, students should know when and why a bar graph rather than a line graph is an appropriate representation for clarifying a pattern or making a claim, or whether a graph provides different information from a table. While concurring with this broad orientation to science as claim-making practices, we suggest in this paper that representational work where students learn how to participate in these practices needs to be richly diverse, especially for younger learners, and include a broad range of representational opportunities and modes. Further, we argue that unless learners can represent their understandings in diverse modes, then their knowledge is unlikely to be sufficiently robust or durable.

Research on Student-Generated Representations

Various studies have investigated the value of student-generated representations to promote understanding in science (Greeno and Hall 1997; Prain 2006; Prain and Hand 1996; Ritchie et al. 2008; Tytler et al. 2006). Greeno and Hall (1997) pointed out that student participation only in teacher-designed activities may constrain opportunities for students’ learning. They argued that student construction and interpretation of representations had various consequences:

  • Forms of representations can be considered as important tools for constructing and communicating understanding;

  • Constructed representations are adapted for the purposes at hand; and

  • Students need to be more actively engaged in constructing and interpreting representations by actively discussing the properties of representations, including their strengths and limitations.

Ford and Forman (2006) emphasised the construction and critique (interpretation of the persuasiveness) of a representation in developing students’ understanding. They suggested that unless students learnt to construct and interpret their observations, become active participators in the learning process, and recognise the role and function of their constructions, then learning could be constrained and superficial. They acknowledged that such an approach required students to use skills often learnt in other disciplines as they constructed and interpreted their representations of emerging understanding.

Pursuing this pedagogical focus, various researchers have sought to identify cognitive and communicative conditions that supported knowledge-building in science, and advocated that students construct a diverse range of representations to enable this learning (Gunstone 1995; Prain 2006; Prain and Hand 1996; Ritchie et al. 2008; Tytler et al. 2006). This approach asserts that students should use a more diversified range of representations, both formal and informal, to engage with the practices and intent of scientific investigation. In advocating text diversification, these researchers accept that students need to demonstrate a capacity to use accurately the current vocabulary and multi-modal representations of science discourse. However, they argue that there are motivational gains and enhanced learning opportunities when students engage in a cycle of planning and guided revision of different text types where there is a strong emphasis on clarification of claims in science and their justification for both self and others.

This approach is also supported by broader current accounts of effective classroom pedagogy. A focus on representational diversity is consistent with recent calls for more student-responsive approaches to learning in the middle years of schooling (Gough et al. 2002). Such an approach is viewed as likely to engage learners more than a traditional focus on restricted forms of representing scientific ideas evident in textbooks or usual classroom practices. This orientation is also consistent with recent research findings by Tytler and Waldrip (2002) that students learn most effectively in science, and engage more with the subject, where they are challenged to develop meaningful understandings, where individual learning needs and preferences are catered for, where a range of assessment tasks are used, where the nature of science is represented in its social, personal and technological dimensions, and where links are made between the classroom program and the local and broader community that emphasise the broad relevance and social and cultural implications of science.

Ainsworth (2006, p. 186) noted that students needed to know how science representations encode information, including interpretive procedures, or operators. They also needed to know how to construct an appropriate representation, in terms of its fit with the conventions of science discourse, including brevity, compactness, absence of ambiguity, and structural coherence, or systematicity. According to diSessa (2004), “students start with a rich pool of representational competence” based on their past experiences with interpreting visual texts, and are “strikingly good at … designing representations” (p. 298). He considered, therefore, that “rich and engaging classroom activities are relatively easy to foster” (p. 298) that are highly motivating for learners. However, like Gee (2004), Unsworth (2001) and others, he acknowledges that students also need to learn about the “sanctioned representations” (p. 294) of science, and justifiable strategies for their interpretation. In summary, past research into an explicit focus on student engagement with specific representational modes and tasks has suggested the value and potential of this approach for promoting learning and for engaging a broad range of learners.

In this way, student representations and their revision can function variously as exploratory tools for initial thinking, scaffolding for building understanding, and records of new thinking and reasoning, depending on the purpose or purposes of the representation. Ford (2008) argues that the teacher’s role is to support the operation and formation of communities that explore new knowledge claims. This means that the teacher plays the role of critiquer, and should point out problems or inconsistencies with some student knowledge claims, and also model what students should do with their classes’ knowledge claims.

Two Examples of Student-Generated Representation

The following two examples are presented as indicative of pedagogical issues around the use of student-generated representation. In the first example, “Mark,” a year 8 student, attempted to represent his understanding of attraction between particles in a unit on change of matter using a computer program. Without clear representational conventions to guide him about how to depict attraction, Mark had to attempt to develop his own. From a Peircean perspective, the referent in this case was a representation of a table and text that Mark had to re-represent through natural language commentary and conventions. He then had to re-represent this emerging understanding of the concept of attraction through a 3D model, using everyday visual conventions, that could be mapped back to, and align with, the original referent. In seeking to present the attraction of particles in solids, he decided to use pipe-cleaners (Fig. 2). As he explained, “they (the plasticine balls) are all supposed to be normal particles but I made the middle one bigger so that I could put branches and stuff off it - to make it easier to put more stuff on it,” as a way of representing the attraction.

Fig. 2
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Mark’s representation of solids

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To show a liquid, Mark claimed he would repeat the representation, but have wavy lines for the weaker attraction between particles. “I would make the pipe cleaners wavier to show that the particles move around rather than vibrate in one spot.” His reason for the use of “waviness” is not entirely clear. It may be a response to animations showing the particles circulating around each other, effectively weaving in and out in a wavy motion. It may be his invention of a symbolic representational convention, perhaps to suggest force acting laterally to the attractive force in order to move the particles as well. He explained that “the bonds would have to be doing more. They would have to keep the waviness and hold all the particles so they wouldn’t be as strong.” Another response seemed to indicate he thought that the attractive force in liquids is weaker because it has to do work in two ways. In this situation, Mark had no means to distinguish between the attractive force holding the particles together and the forces causing relative movement of particles.

For gases, Mark seemed to resort to iconic representations of particle spacing to represent an indexical (force magnitude) measure. “I’d have one pipe cleaner with one particle on the end and one in the middle because they don’t really have any attraction to each other.” He was unresolved on the use of waviness here and seemed to feel that the spacing would be sufficient. He was not concerned that he had used particle spacing to represent attraction in tandem with the waviness of the branches, and also used waviness to denote both movement and degree of attraction in relation to liquids.

He said that he made use of arrows because he remembered the animation from the website used in a class activity. He wanted to show the relative movement, and his teacher suggested that he could show direction using arrows. To meet the challenge of representing the vibrational movement of solid particles, Mark shook the camera to represent the vibrational movement of solids as a fuzzy image (see Fig. 2), introducing an indexical representation by incorporating the idea of time and its effect on the image produced.

Mark identified and resolved some other representational challenges with prompting from his teacher who noted, for example, that the particle spacing used for one of Mark’s models made it difficult to distinguish between liquid and gas states. When asked if he had recognised any possible problems of interpretation, Mark replied, “I did realize it (that the spacing was too large) but I didn’t think it would be that much of a big deal, but when the teacher pointed it out I then realized so I changed it.” Mark also chose to present his models in the context of “real world” examples of solids, liquids and gases “because having a little bunch of plasticine to represent little particles all close together then putting that on a liquid shows you what it’s made up of – to represent it in a different way.”

This example suggests that the teacher can (a) gain crucial insights into the reasoning of students as they construct and justify representations, (b) provide targeted feedback on the adequacy of the claims implied in these representations, and (c) guide the students’ reasoning as well as in a timely fashion explain the purpose of particular conventions in scientific representations. In this way, negotiation between the teacher and students of the adequacy of the representation (to the students’ understandings and to the conceptual focus of the topic) provides valuable scaffolding of learning opportunities.

In the following example of teacher and student-generated negotiated representations, “Colin,” a year-8 teacher, aimed to critique the development of student-generated representations of air pressure. He recognized the need for active participation by the learners, and teacher responsibility to coach students about the reasons behind the acceptance of representational modes, forms, conventions and interpretation. To clarify and to focus student understanding of air pressure, Colin asked the students to represent their views of air pressure within their classroom. Figure 3 shows some of their initial representations. Some students only considered the air within the classroom. All seem to recognise the random nature of the air particles.

Fig. 3
figure 3

Students’ representations of air pressure within a classroom

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Colin::

Is there anything outside this room that might effect what’s inside?

Ok, hands up if you’ve drawn some sort of specs on the page or dots in the page. (A number of students respond with hands in the air)

Ok, if you’ve drawn those things, you must have a reason for drawing those. What do they represent?

Bev::

Air molecules.

Colin::

Air molecules. Ok, has anyone drawn arrows on the page? What do those arrows represent?

Kerry::

Moving air molecules.

Colin::

Moving air molecules. Has anyone drawn those arrows going in certain directions? Are they all going in one direction or different directions? You tell me.

Joe::

They all move around differently (gesturing with both hands, pointing in a variety of directions).

Colin::

Ok, so you’re representing the different directions the air molecules are travelling in the room. Ok, I’ve seen some people with them all pointing in one direction hitting the sides of the room. Is that what actually happens with air molecules? (indicates certain fixed directions with fingers of both hands, pointing).

Class::

No

Joe::

They’re going to hit each other.

Colin::

John, did I see that you’ve drawn them all pushing against the sides?

John::

Yep.

Colin::

What were you representing?

John::

Well, I was just representing … I could have drawn them anywhere … I was just representing that air pressure is coming from any direction sort of thing.

Colin::

Ok, so you were showing the push from the pressure not necessarily the direction of the little molecules.

John::

No.

Colin::

Ok, that’s good. What you’ve done, from what I’ve seen, is you’ve shown a lot of things inside and there are some people around here who have also, when I gave a bit of a clue, showed the same thing happening outside. So there’s different things hitting the outside.

In this example, the teacher sought to clarify the current claims made by the students’ representations in the light of their intended meanings, and to use the representation as a tool for judging and developing the adequacy of their understandings. These two examples of student-generated representations indicate (a) the rich interplay for students between their intended meanings, conceptual understanding, and representational challenges, (b) the value of non-standard representations in providing both a basis for student clarification of understanding as well as ongoing teacher insights into students’ intended and realized meanings, (c) the need for students to connect science concepts to perceptual clues, and (d) the potential for non-standard representations to provide a basis for developing students’ understanding of the form/function felicities in conventional scientific representations. This example indicates that student-generated representations can support students’ conceptual learning when the teacher responds to and negotiates with the student the clarity, coherence and adequacy of their representations as causal claims.

Using Student-Generated Representations

Researchers in classroom studies where students were guided to construct their own representations of scientific ideas (diSessa 2004; Greeno and Hall 1997, Hackling and Prain 2005; Waldrip et al. 2007; Tytler et al. 2006) have identified various key principles to guide effective planning, implementation, and evaluation of student learning. Consistent with an effective focus on conceptual learning in science generally, the teacher needs to be clear at the topic’s planning stage about the key concepts or big ideas students are intended to learn. This conceptual focus provides the basis for the teacher to consider which sequence and range of representations, including both teacher- and student-generated ones, will engage learners, develop their understanding, and count as evidence of learning at the topic’s end.

This major focus on key concepts in science learning is evident in the national professional learning program, Primary Connections (Australian Academy of Science 2008), where key concepts are emphasized at the start of units of work, and students are expected to develop understanding of these concepts through engaging in guided investigations related to a sequence of representational and re-representational work. Research on the learning outcomes of this program (Hackling et al. 2007; Hackling and Prain 2005) found that students were more motivated than through past approaches, and that learning performance was also enhanced.

These studies also indicated that representations in science can serve many different purposes. While these purposes can be considered as conventional and functional for making new meanings in the science community, clearly they can also serve learning purposes for students in the science classroom. In this way, representations can be used as tools for initial, speculative thinking, as in constructing a diagram or model to imagine how a process might work, or find a possible explanation, or see if a verbal explanation makes sense when re-represented in 2D or 3D. They can be used to record precise observations, to identify the distribution of types, to classify examples into categories, to identify and explain key causes, to integrate different ideas, to contextualize the part to the whole, to identify the inner workings of a machine or object, to show key parts, to show a sequence or process in time, to identify the effects of a process, predict outcomes, sort information, clarify ideas, show how a system works, organize findings, explain how parts of a topic are connected, and to work out reasons for various effects.

These studies have also raised the question of how teachers and students might assess the adequacy of a representation. For diSessa (2004), this means that students need to understand that a single representation cannot cover all possible purposes or all aspects of a topic. Therefore they need to learn how to select appropriate representations for addressing particular needs, or making particular claims, and be able to judge their effectiveness in achieving particular purposes. He claimed that junior secondary students intuitively have an understanding of the attributes of a good scientific representation, recognizing that it must be clear, unambiguous, give minimal but sufficient information, and be comprehensive for its purpose. By implication, where students are not clear about these criteria or their rationale of producing clear communication, then these aspects need to be taught explicitly.

These studies have also identified a range of benefits from this explicit focus on representational understanding and reasoning. Waldrip et al. (2006) claimed that this approach heightened students’ sense of ownership of their work, increased student motivation and creativity, and that teachers reported improved student learning outcomes. Tytler et al. (2006) argued that this approach also had the merit of being consistent with science practices of meaning-making in the broader science community.

The IF-SO Framework

As noted by Ford (2008) and many others, a key aspect of the teacher’s role in the science classroom is to guide and respond to students’ attempts, through various representations, to make and justify causal claims about natural phenomena. Drawing on analysis of over 1,000 h of observed upper elementary and junior secondary science classrooms across a range of science topics, informed by our collaborative work with twenty teachers, and guided by the theoretical perspectives outlined in this paper, as well as other recent classroom research drawing on these perspectives, we propose the following framework to focus on key issues in topic planning (see I and F below), and teacher and student roles in learning through a sequence of refining representations during the development of a topic (S and O).

  • I: Identify key concepts. Teachers need to identify key concepts or big ideas of a topic at the planning stage to anticipate which mix of teacher- and student-constructed representations will engage learners, develop their understanding, and count as evidence of learning different dimensions of the topic. Teachers need to consider both the sequence of representational challenges posed by the topic, as well as the type of summary representational task that will enable students to consolidate their conceptual understandings at the completion of the topic.

  • F: Focus on form and function. Teachers need to focus explicitly on the function and form (or parts) of different representations. If a particular representation is crucial to the topic, such as the utilisation of ray diagrams to describe or understand reflection or refraction of light, then the nature and reasons for this convention may need to be introduced and clarified at the outset of the topic. The conventions in less crucial representations could be covered incidentally or when needed. In working with any new representation students need to learn its function or purpose, and how this function is served by its form or parts. For example, in working with graphs, students should be asked to consider why they are used in science, as well as to identify their key parts and their function, such as the purpose of each axis for establishing patterns of data for interpretation. In this way, teachers can guide students to learn a science toolkit of types of representations and their possible purposes as tools for engaging with, reasoning about, explaining and predicting causes for phenomena. Students also need to understand the limitations of any particular representation in addressing only some aspects of its target phenomena.

  • S: Sequence. Students need to face a sequence of representational challenges, which elicit their causal accounts of phenomena, enable them to explore and explain their ideas, extend these ideas to a range of new situations, and allow opportunities to integrate their representations into a meaningful summative account of the topic. Students also need to learn that different representations focus on different aspects of the topic, and therefore serve different purposes.

    1. I.

      S: student representation. Students need to have opportunities to re-represent their claims to extend and demonstrate learning. They should be challenged and supported to coordinate representations as a means to express coherent, defensible and flexible understandings. Students need to be active and exploratory in generating, manipulating and refining representations. In seeking to show the complexity of a claim, students need opportunities to express and extend their representational resources and choices, and to integrate different representational modes to show conceptual understandings.

    2. II.

      S: student interest. Activity sequences need to focus on meaningful learning through taking into account students’ interests, values and aesthetic preferences, and personal histories. For example, learning about effective use of different energy sources could be developed through designing, trailing and modifying an energy-efficient vehicle.

    3. III.

      S: student perceptions. Where appropriate, activity sequences need to have a strong perceptual context to allow students to use perceptual clues to make connections between aspects of the objects and their explanatory representations and claims. This is not to argue that all theory-building or conceptual knowledge in the science classroom is perceptually-based, but rather that some conceptual learning in science can be enhanced by focusing on relevant student perceptions.

  • O: Ongoing assessment. Teachers should view representational work by students, including verbal accounts of the topic, as a valuable ongoing window into students’ developing thinking and as part of the evidence of student learning. This assessment can be diagnostic, formative or summative, with a variety of forms of evidence contributing to judgements about students’ conceptual knowledge and capacity to transfer understandings to new contexts and problems.

    1. I.

      O: Opportunities for negotiation. There needs to be opportunities for negotiation between teachers’ and students’ understandings of the intended and expressed meanings of representations. Students need to be encouraged to make self-assessments of the adequacy of their representations. Are they adequate to their ideas on the topic as well as the features of the object, and to what extent do they achieve the students’ representational purposes and express intended meanings?

    2. II.

      O: On-time. Students should participate in timely clarification of parts and purposes of different representations. Students need opportunities to compare the conventions and improvisations they have used to make claims about a topic with the claims made through “authorised” representational conventions. Understanding the reasoning and organizational affordances of the representational tools of science, such as graphs and diagrams, enables students to understand and communicate claims more clearly, and to understand why particular representations, often embedded within a complementary text, are used for different purposes, and for making claims about different aspects of the topic.

We consider that this proposed broad framework for guiding teacher interactions with students is consistent with other research findings in this area, including Roberts’ (1996, p. 424) proposed “trialogue” style for focusing on the role of representation in learning in science. Both frameworks recognize the crucial role of students’ prior and developing ways of representing, and reconcile these accounts with new understandings entailed in engaging with “authorised” representations. Roberts’ (1996, p. 423) trialogue proposes a three-way reciprocal linkage between teacher, student and domain. In this model, guided by appropriate scaffolding, students are encouraged to generate their own representations to explain observations and predict future outcomes. They can then compare and reconcile these representations with those of their peers, and with those of their teacher, or those presented by their teacher as current within the science community. The teacher then acts as coach and negotiator of the meanings of these representations and their refinement through a range of representational tasks. The arrow from teacher to student indicates the accepted wisdom of representations, as communicated by the teacher, while the reverse arrow indicates the students’ prior or developing representations of the domain (Fig. 4). As Ford and Forman (2006) emphasize, students are directly involved in the construction and critique of the representation in developing understanding.

Fig. 4
figure 4

Teacher in trialogue

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The trialogic style affirms the students’ needs to generate their own explanations and compare these claims to peers, making the material meaningful to themselves and to others. This style both recognizes the need for active participation by the learner, and teacher responsibility to coach students about the reasons behind the acceptance of representational modes, forms, conventions and interpretation. As students move into the “community of science,” it is crucial for them to be aware of and conversant in the languages and practices of this subject. Whilst established conventions and interpretations are no longer negotiated, it is also important for students to recognise that they once were, and this is still the case for some new procedures and findings. This style makes no assumption about students’ metacognitive ability to recognize spontaneously pertinent features of the representations and their meaning, or the overall applications and limitations of a representation (as well as any of the representation’s advantages over students’ own personal representations), without some teacher guidance. Instead, the teacher guides the students to recognize each representation’s key features and, in a “precious metacognitive lesson” (Roberts 1996, p. 427), recognize how these features act as knowledge “justifiers” or “definers” in the domain.

The Trialogue Style of Teaching Using the IF-SO Framework

The IF-SO framework can be understood as combining Peirce’s (1893-1910) account of the three components of meaning-making (Fig. 1) with Roberts’ (1996) model of pedagogy (Fig. 4), and is represented as a set of interlocking triads (Fig. 5). From this perspective, teaching and learning in science entails various triads incorporating the domain (D), teacher conceptions (TC), teacher representations (TR), student conceptions (SC), and student representations (SR), where all are mutually supportive (Fig. 5). At all stages in the learning process, the teacher must rely on interpreting students’ representations as evidence of their understanding.

Fig. 5
figure 5

Triadic pedagogical model

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In the planning phase triad (IF), the teacher chooses the key concepts (TC), the aspects of the domain (D), such as physical objects, experiences, artefacts, situation/context or processes, that will be the focus of the unit, and the types and sequence of representations to use to engage students and develop their understanding (TR). The teacher also needs to consider the purpose of any student representational work.

For example, in the planning phase of a unit on “Forces,” the choice of concepts and processes to be focussed on from the domain, and the ways of representing them, will depend on the class level. For a junior class the teacher might identify the key idea as being “forces are pushes or pulls,” the focus being simple (physically) perceptible examples of force involving contact such as pulling a drawer or pushing a door, and student convergence on the use of simple symbols (perhaps arrows) functioning to represent force direction and magnitude. At this level, the symbol (arrow) directions could be approximate without really diminishing fundamental learning of the key ideas. In order to communicate their ideas, however, students will need to negotiate and define their conventions to allow common interpretation, importantly reflecting practices within the broader science community. In more advanced classes, students need to develop a more abstract view of forces, such as an understanding of how forces can balance out. In this case, following accepted conventions about the use of arrows to represent force as vectors may best facilitate communication and learning of the key ideas.

Thus, in the sequence of classroom lessons (S and O), different triadic emphases might occur, depending on stages in the topic and student knowledge, interests, and needs. Where key concepts are highly abstract, then students may need guidance in learning how to use accepted conventions to explore relevant ideas. This suggests the value of focusing on the triad of the Domain, Teacher Representations and Student Conceptions (D, TR, SC). Where students can engage initially or further with the topic because of their understanding, the teacher might facilitate student constructions, focusing on the triad of domain, student representations, and student conceptions (D, SR, SC). As stated in the IF-SO framework, we believe it is crucial that students have opportunities to create their own representations of the domain to motivate them, develop representational competence, and learn how to make convincing claims in science. The teacher and class then need to assess the convergence or compatibility of these representations with authorized ones, using a different triad (TC, D, SR). The success of this work then frames directions for subsequent lessons, establishing if there is a need for explicit teacher-guided negotiation of students’ current representational meanings. The actual use of student-generated representations in examination scripts could reflect the value that the teacher implies to student-generated representations.

While we have not focused explicitly on reasoning in science in this paper, the proposed approach also provides ways to link representational work with developing convincing explanations. Negotiating representational meaning provides many opportunities for students to consider possible claims, evidence, and reasons in developing scientific accounts of the physical world. For example, students can use representations such as organized data in graphs to identify patterns in data distribution. They can also translate ideas from one type of representation to another, thus shifting their mode of reasoning as they re-organize their understanding to take into account visual, spatial and verbal aspects of topics. As students develop a representation as a claim, the teacher and/or students can direct attention to inconsistencies of interpretation, and thus provide further opportunities for reasoning about causal factors. Constructing representations can also enable students to keep track of their progress in problem-solving in a topic, can refine and clarify first impressions, and can promote the pleasure of recognition of understanding when students see that their representation makes a clear and convincing case.