Suparna Sinha^a, Steven Gray^b, Cindy E. Hmelo-Silver^a, Rebecca Jordan^a, Catherine Eberbach^a, Ashok Goel^c, Spencer Rugaber^c

^aRutgers University, United States of America

^bUniversity of Hawaii, United States of America

^cGeorgia Institute of Technology, United States of America

               

Article received 10 March 2013 / revised 15 May 2013 / accepted 23 May 2013 / available online 27 August 2013

 

 

Abstract

A primary goal of instruction is to prepare learners to transfer their knowledge and skills to new contexts, but how far this transfer goes is an open question.  In the research reported here, we seek to explain a case of transfer through examining the processes by which a conceptual representation used to reason about complex systems was transferred from one natural system (an aquarium ecosystem) to another natural system (human cells and body systems). In this case study, a teacher was motivated to generalize her understanding of the Structure, Behaviour, and Function (SBF) conceptual representation to modify her classroom instruction and teaching materials for another system. This case of transfer was unexpected and required that we trace back through the video and artefacts collected over several years of this teacher enacting a technology-rich classroom unit organized around this conceptual representation. We provide evidence of transfer using three data sources: (1) artefacts that the teacher created (2) in-depth semi-structured interview data with the teacher about how her understanding of the representation changed over time and (3) video data over multiple years, covering units on the aquatic ecosystem and the new system that the teacher applied the SBF representation to, the cell and body. Borrowing from interactive ethnography, we traced backward from where the teacher showed transfer to understand how she got there. The use of the actor-oriented transfer and preparation for future learning perspectives provided lenses for understanding transfer. Results of this study suggest that identifying similarities under the lens of SBF and using it as a conceptual tool are some primary factors that may have supported transfer.

 

Keywords: Transfer; Technology; Teacher learning; Systems thinking

 

1.             Introduction

          The aim of transfer research is to identify instructional conditions that prepare learners to apply what they have learned to new contexts. As designers of learning environments, we seek to create tools to facilitate transfer. We argue that one such tool is the use of conceptual representations to organize instruction by allowing students to develop a means to think about conceptual elements in a more generalised way (Liu & Hmelo-Silver 2009). In addition, our prior research suggests that use of certain conceptual representations can promote understanding of complex systems.

          Helping students and their teachers develop an understanding of complex systems is a difficult yet important component of scientific literacy (Sabelli 2006).  Given the ubiquity of complex systems in the natural world, transferring ideas about complex system learning in one context to another is critical for the development of scientific thought.  In many cases the behaviour of system components can affect its overall function, through emergent processes and localized interactions (Jacobson & Wilensky s2006). These interactions are often dynamic and invisible which make them difficult for learners to understand and present instructional challenges for teachers (Feltovich et al. 2001; Hmelo-Silver et al. 2007).

          Here we define systems thinking as being able to understand how bounded phenomena arise through considering the interactions and relationships among these interdependent structures, behaviours, and functions (Hmelo-Silver et al., 2007; NRC, 2012). There is evidence to suggest that students find it especially challenging to think about: (1) the interactions between visible and invisible structures, (2) the effect of their dynamic behaviours on overall functions, and (3) being able to extend their thinking beyond direct causality of complex systems (Grotzer & Bell-Basca 2003; Hogan 2000; Hogan & Fisherkeller 1996; Jacobson & Wilensky, 2006; Leach et al. 1996; Reiner & Eilam 2001).

          In the research presented here, we investigate an unexpected case of transfer in a teacher - as the learner - who had been involved in a long-term classroom research project and appropriated the conceptual representation from the researcher-developed units to develop new instruction. This is particularly notable because learning about complex systems is often difficult (Hmelo-Silver et al., 2007).

          Although our research focuses on the use of conceptual representations as a tool for learners, it also appears that it can be a tool for teachers to deepen their own understanding of complex systems (Liu & Hmelo-Silver 2009; Goel et al., 1996). Specifically we discuss how Structure-Behaviour-Function (SBF) served as a conceptual representation that promoted transfer across different complex systems (Goel et al., 1996). Structures are defined as the components of a system, behaviours as the mechanisms or processes that occur within a system and functions as system outcomes (Goel et al., 1996; Machamer et al., 2000). We developed technological tools using the SBF representation that make these features of complex systems salient (Hmelo-Silver et al., 2007; Liu & Hmelo-Silver 2009; Vattam et al. 2011). Our study draws attention to a teacher’s journey of understanding SBF as a conceptual tool, using it in the context of a technology-intensive science curriculum and her initiative to appropriate SBF as a conceptual representation beyond what we designed it for and use it meet local curricular needs.

 

2.             Research goals

This study focuses on two main research questions:

1.         How does a middle school science teacher develop her understanding of SBF as a representational tool?

2.         How does generalization of SBF prepare her to make sense of a new complex system?

          Specifically the focus of this study is to understand the means by which the teacher takes up opportunities to generalise her understanding of SBF as a representational tool to view similarities between two systems; one provided by researchers and one designated by the teacher. To understand the conditions that facilitated transfer, we need to view it through a lens that magnifies this teacher’s learning trajectory. To focus on the dynamic nature of transfer, we did not see a traditional model of transfer as a productive lens. Traditional transfer researchers consider decontextualised expert knowledge, independent of how learners construe meaning in situations (Cobb & Bowers, 1999; Greeno, 1997). Because our objective was to highlight the processes the teacher used to understand and transfer a conceptual representation, we needed to consider alternative transfer models.  Such models should illuminate the interactions that were meaningful and engaging for the teacher and subsequently, led her to generalize her learning experience.

 

2.1     Transfer through alternative lenses

We consider transfer from both an actor oriented approach (AOT; Lobato 2004, 2006) and a preparation for future learning perspective (Bransford & Schwartz 1999) to investigate a teacher as a learner applying knowledge in a new curricular unit.Lobato (2003, 2006) proposes that shifting from the observer’s (expert’s) perspective to considering how the actor (learner) perceives similarities between the new problem scenarios to prior experiences is a useful tool to understand transfer. Evidence for transfer from this perspective is found by scrutinizing a given activity for any indication of influence from previous activities.

Moreover, we investigate how a greater understanding of SBF representations might have contributed to transfer from a preparation for future learning (PFL; Bransford & Schwartz, 1999) perspective.  The PFL perspective focuses on the strategies used by learners in knowledge rich environments and their ability “to learn a second program as a function of their previous experiences” (Bransford & Schwartz, 1999, p. 69). This provides a framework for evaluating the quality of particular kinds of learning experiences and the feedback they provide. Feedback is a powerful factor in preparing students to make sense of instructional materials, to help them in knowledge construction and as a result facilitate transfer of skills needed to unpack novel problems (Moreno, 2004; Tan & Biswas, 2006).  Like other alternative perspectives on transfer (e.g., Konkola, Tuomi-Grohn, Lambert, & Ludvigsen, 2007), the classroom context and activity is an important factor in promoting transfer.

We add to the transfer literature by exploring use of the SBF conceptual tool for abstracting systems thinking. That is, the conceptual tool can be used to make sense of complex systems by thinking about macro and micro level connections either independently or at multiple levels of intersections. We make the conjecture that SBF as a conceptual tool can serve as a focusing phenomenon, which makes it suitable for integrating the AOT and PFL lenses of transfer as we describe in the next section. In this study, we investigate how the experiences that led to successful generalization of SBF as a conceptual tool prepared the teacher to keep refining her systems thinking.

                         

2.2     Supporting transfer through focusing phenomena

Lobato et al (2003) propose that focusing phenomena supports transfer by prompting students to generalize their learning. As a concept they define focusing phenomena as "observable features of the classroom environment that regularly direct attention to certain mathematical properties or patterns" (p.2). They attribute a combination of factors such as curriculum materials, artefacts, teacher’s instructions as important for directing and focusing students' attention towards the intended content. In the context of this study, we extend the notion of focusing phenomena to science.

We propose that SBF serves as focusing phenomena  (Figure 1) to advance systems thinking. It helps the teacher focus her attention on understanding connections between multiple structures, their functional roles within the complex system and the behaviours they exhibit. Here we consider the importance of generalizing SBF as a tool for transfer.

        From an AOT perspective, SBF as a focusing phenomena highlights what is similar between two complex systems i.e. the aquatic ecosystem (introduced by the researcher) and human digestive system (introduced by the teacher). It helps concretize the idea that biological systems are similar to ecosystems in terms of interacting at multiple levels. Using this framework affords the teacher opportunities to focus on the connections that exist between various organs of the digestive system. Specifically, it directs the teacher’s attention to the ways that “structure and function in biological systems are causally related through behavioural mechanisms” (Hmelo-Silver et al., 2007, p. 308). The teacher’s understanding of SBF in the classroom mirrors her understanding of systems thinking. This is important for us, as researchers, as it lets us trace the teacher’s learning trajectory.  From a PFL perspective, thinking in terms of SBF prepares learners to understand that behaviours are mechanisms and processes that enable structures to achieve their functions in biological systems (Bechtel & Abrahamson, 2005; Machamer, Darden, & Craver, 2000).  In the remainder of the paper, we present a case study that considers how several aspects of the learning environment influenced the teacher’s generalization of SBF as a conceptual tool.

                                            

Figure 1. SBF as Focusing Phenomena. (see pdf file)

 

3        A case of transfer: The instructional context

          This study is part of a larger research program, which is a technology-intensive curriculum unit centred on an aquarium based aquatic ecosystem. The curriculum provides multiple opportunities for learners to develop and deepen their understanding of SBF as a conceptual tool.  First, technological tools such as the RepTools toolkit (Hmelo-Silver et al., 2011) and the Aquarium Construction Toolkit (ACT; Vattam et al., 2011) were designed: (1) to help learners think about aquatic ecosystems in terms of structures, the functions they perform within the system and the behaviours they exhibit to perform the functions, (2) teach about the aquarium ecosystems using SBF as a conceptual tool for a period of 4 years, and (3) engage in active discussions about the concept and ways to teach it with the research team present daily in the classroom and at the annual professional development workshops.

 

3.1     SBF tools

          The RepTools toolkit includes a function-oriented hypermedia (Hmelo-Silver et al., 2007; 2009; Liu & Hmelo-Silver, 2009) organized in terms of SBF representation and Net Logo computer simulations (Wilensky & Reisman, 2006). The hypermedia (Figure 2) introduces the aquarium system with a focus on functions and provides linkages between structural, behavioural and functional levels of aquariums. It is organized around what, how, and why questions which correspond to structures, behaviors, and functions.

 

                                                                               Figure 2. Aquarium Hypermedia. (see pdf file)

 

          Two NetLogo simulations allow learners to explore macroscopic processes of fish reproduction  (i.e., the fishspawn simulation, Figure 3a) as well as microscopic processes (the nitrification simulation, Figure 3b) that represent the chemical and biological processes in the aquarium. The simulations provide a context for learners’ investigation of the aquatic ecosystem.  They afford opportunities for designing experiments, manipulating variables, making predictions, and discussing conflicts between predictions and results. Each simulation allows learners to explore key features that are relevant to the process of fish spawn or nitrification cycle.

 

                                                                Figure 3a. Macro level- Fish spawn simulation. (see pdf file)

 

                                                                  Figure 3b. Micro level – Nitrification simulation. (see pdf file)

 

          The second component to the learning environment, ACT is designed to promote construction of SBF models (Vattam et al., 2011). Models can be constructed either in a table (Figure 4a) or graph (Figure 4b) format. The model table focuses learners’ attention on thinking about various structures in an ecosystem. The three column table affords the opportunity for learners to think about the structural components, their multiple behaviours and functions. This is valuable because learners get an opportunity to understand both individual mechanisms in the system and the meta-level concepts related to complex systems.

 

                                                        Figure 4a. Sample ACT Model Table. (see pdf file)

 

                                                               Figure 4b. Sample ACT Model Graph. (see pdf file)

           

The ACT model graph is a platform for learners to create models of their evolving understanding of ecosystem processes in terms of SBF. As students read through the hypermedia, generate and test their hypotheses with the simulations, they integrate the critical structures with their behaviours and functions in ACT models.

           

3.2     Methods

          We used a case study approach to characterize how a science teacher, Ms. Y, appropriated her understanding of SBF as a representational tool and applied it to make sense of a new complex system. Case study methodology allowed us to use multiple data sources to study this complex phenomenon in context (e.g., Stake, 1998; Yin, 2009). Borrowing from interactional ethnography (Castanheira, Green, & Yeager, 2009) we began at the end—the SBF hypermedia that Ms. Y constructed. The unit of analysis for this case is the individual teacher in her classroom context over several years. Through this approach, we used multiple sources of data to trace the social and cognitive events that occurred over time and led Ms. Y to see SBF as a tool she could appropriate for her teaching practice.  Although this was not an ethnography we borrowed the logic of this inquiry approach to understand how an individual within a social context constructed particular knowledge over time (Bridges, Botelho, Green, & Chau, 2012).

 

3.3     Context

       Ms. Y taught seventh grade science at a public middle school in North East United States. She had been teaching science for 26 years and had a Bachelor’s degree in Elementary Education. This study was part of a larger 4-year study focused on teaching middle school science students about aquatic ecosystems.  Ms. Y participated in annual professional development (PD) workshops. The PD focused on concepts related to aquatic ecosystem, analysis in terms of SBF and the technological tools that she would need to use in her classroom. During the PD, Ms. Y. had the chance to share her pedagogical challenges and experiences, such as difficulties in using the software or teaching about SBF as a conceptual tool.

          Ms. Y had been using the RepTools and ACT in an aquarium curriculum for four years when she informed us that she wanted to develop her own instructional tools using the SBF representation to teach about cell and human body systems.  This prompted her to collaborate with her colleague, another science teacher, Ms. T. Together they used Microsoft Power Point to create a human body system presentation, modelled after the function-centred aquatic hypermedia. We refer to it as the teacher-created hypermedia. Given their limitations in terms of technical knowledge in designing a hypermedia similar to the one we had created, the teachers hyperlinked key words in their power point presentation and follow up questions to point to relevant slides.

          Ms. T also taught seventh grade science in the same school. She was a new teacher with one year of teaching experience. Ms. T had a science education background. While she collaborated with Ms. Y, she also attended the annual PD and implemented the same technology intensive curriculum on aquatic ecosystem in her classroom.

          Each teacher taught four diverse seventh grade classes with approximately twenty-five students in each section. During the curriculum implementation the students were grouped together in small heterogeneous groups.

 

3.4     Data sources

We had three primary sources of data.  First was the artefact that the teacher created (this indeed was the impetus for our research).  Second, we conducted an hour-long semi-structured interview with the two teachers, Ms. Y & Ms. T. Finally we collected video data of classroom interactions. These videos were drawn from classroom data from a long-term (i.e., four year) research project. These helped us to understand: (1) why the teacher transferred her generalizations of SBF representations to new instructional domains and (2) how she transferred these understandings. We interviewed Ms. Y & Ms T approximately two months after Ms. Y completed teaching about both systems. The primary focus of the interview was to understand how she conceived the idea of extending the computer-based representational tools beyond what was expected from her, the influence of her prior knowledge during this process, and her attempts to prepare herself to solve new challenges.

          Following Powell, Francisco and Maher’s (2003) recommendations for video analysis, we reviewed video data to identify critical events.  In an attempt to trace and track the nature of Ms. Y’s generalizations of SBF we selected representative clips of critical events from her classroom that demonstrated evidence of her developing understanding and generalization of SBF representations as a tool to teach about another complex system. These video clips included whole class discussions that Ms. Y had with her students while: (1) introducing the SBF representation for the aquatic ecosystem in Year 3 (i.e., the year before she created the digestive system unit), (2) introducing the SBF representation for the aquatic ecosystem in Year 4 i.e. the year she employed the digestive system unit, and (3) explanation of SBF representations and modelling of the digestive system unit. We viewed a total of nine clips that consisted of three classroom interactions for each of the three kinds of whole class discussions.

 

3.5     Analysis

          We examined classroom interactions that highlight Ms. Y’s learning trajectory with SBF as a representational tool. The video data were analysed using Interaction Analysis (IA; Jordan & Henderson 1995), which involved collaborative viewing of video clips by six members of the interdisciplinary research team. We successively conducted nine IA sessions to collaboratively review the selected video clips, describe observations, and generate hypotheses. Any differences in opinions were resolved by discussions.

 This helped ensure the trustworthiness of our interpretations through the initial independent interpretations of the IA session participants and the subsequent discussions.

          During the IA sessions we focused our attention on two specific aspects of Ms Y’s practice. First, we paid attention to patterns and variations in the ways that she introduced the SBF as a conceptual tool in relation to the aquatic ecosystem across the four years. Specifically, we examined her explanation of the concept, the analogies she presented and whether or not she sought help from any external resources, such as researchers in the classroom or Ms T.

          Second, we focused on how she introduced SBF as a conceptual tool in the context of the human body unit. At this time we made comparisons between the ways the topic was introduced in the aquatic ecosystem with the human body system. We also looked for similarities in terms of analogies. In particular, we wanted to understand if and how her prior knowledge of SBF prepared her to discuss this particular complex system with ease and confidence.

          To gain a holistic perspective of the teacher’s journey we also examined the interview transcript. We looked for themes related to the mechanisms by which transfer occurred in the ways in which the teacher constructed similarities between aquarium and digestive systems.  This allowed us to triangulate the teacher’s perspective with the IA and artefact analysis.

 

4.       Findings

         Based on our analysis of the interview and video data we identified themes related to AOT or PFL perspectives. These findings helped strengthen our understanding of the processes Ms. Y used to generalize SBF as a representational tool and observe how it prepared her for the transfer.  The AOT perspective provided a framework to trace Ms. Y’s evolving understanding of using the SBF lens as a tool to make sense of aquatic ecosystem. The PFL perspective demonstrated how Ms. Y transferred and used her knowledge of SBF to make sense of a complex system that was outside the scope of our research.

 

4.1     Tracing and tracking Ms Y’s Understanding of SBF from an AOT lens

                       

4.1.1  Orientation to the SBF representation led by the teacher

          Ms Y’s journey began with using the ACT tool. The ACT technology enabled construction of SBF representations using the Model Table (Figure 4a). The tool introduced the students and Ms. Y to the language of SBF representations.  Initial data analysis of the whole class video revealed that the teacher’s introduction of the SBF representation played a critical role in students’ conceptual understanding of the complex system. She presented the idea that the SBF representations captured interconnected entities within a complex system while completing the ACT table:

1. Ms. Y: Alright, so the first thing yours say is fish right? So, lets go back and tell me what is the behaviour of the fish?
2. Student: Releases waste.
3. Ms Y. OK. So the fish releases waste. Right? Alright, so it, it releases what kind of waste?
4. Students (in unison): Ammonia.
5. Ms. Y: Right, so you have that in there right? Now. What is the function?
6. Students (in unison): Remove toxins from the body.
7. Ms. Y: Okay. So we want to get these things out of the fishes’ body. Now next, the next one is what?
8. Students: Ammonia.
9. Ms. Y: Ammonia. So, put, put ammonia here. Alright, so now, what is, what is the behaviour of the ammonia? What’s it do if you look at it in the tank?
10. Student: Water?
11. Ms. Y: Yeah, it’s just floating around right? What’s its function do? It’s food for bacteria. So it has its purpose right? So the next one on our list which is blank on yours will be what?

In this excerpt, Ms. Y drew the students' attention to the functions and behaviours of various structures present in the aquarium. The students identified structures such as fish (turn 1) and ammonia (turn 8). Next she prompted them to think about their behaviours and functions. In turn 2, the students responded that the behaviour of the fish is to release waste. She pushed them to think in detail about the kind of waste (turn 3) and the function or overall purpose of this behaviour (turn 5).  In turn 11, she clearly articulated that structures have a function within complex systems.  Although this is a somewhat mechanical application, it also allowed her to begin to see how the SBF lens might serve as a tool for understanding systems. 

We speculate that this discussion prepared both the students and Ms Y. to use the SBF conceptual representation to understand the interconnectivity between various structures within complex systems. This initial understanding of SBF as a representation may have prepared Ms. Y to appropriate SBF as tool when she collaborated with her colleague to create a new learning tool i.e. (the teacher-created hypermedia).

 

4.1.2  Teacher-created hypermedia 

    Just as the orientation to SBF was the starting point, the artefact that Ms. Y created at the other end bound the case study. Ms Y., in collaboration with her colleague Ms. T, created new hypermedia in the form of an interactive PowerPoint of the cell and body systems mirroring the aquarium hypermedia developed by the research team (Figures 5a and 5b). The teachers’ hypermedia outlined the different structures in the system along with orienting why and how questions. The how questions were directed towards behaviours of system components and the why questions focused on functions. The teachers created this hypermedia as a learning resource to help students connect cell systems to larger body systems. The research team did not plan either the body system hypermedia or the use of modelling these systems using the ACT software; the teachers did this of their own volition.

                                                                   Figure 5a. Researcher-developed hypermedia.    (see pdf file)
                                                                Figure 5b. Teacher-developed Hypermedia.   (see pdf file)

 

The development of the cell hypermedia demonstrated multiple ways by which Ms. Y generalized and transferred her understanding of SBF as a conceptual tool. First, understanding the SBF of the aquatic ecosystem prepared her to teach it better in successive years and second, she was able to modify the learning environment (i.e., by changing them physically–from an aquarium hypermedia to a cell hypermedia and by seeking resources) into something that was more compatible with her current goals.

           

4.1.3  Identifying similarities through SBF representations

          Ms. Y’s initiative to extend and appropriate our research and develop additional classroom instruction suggested that the SBF representation was becoming a tool for her to see similarities across complex systems.  Adopting an AOT perspective helped us understand how she constructed similarities between what she had been teaching for several years (the aquatic ecosystem) to the current unit she developed (cell and body systems).  This perspective helped us recognize which connections she made, on what basis, and how and why those connections were productive (Lobato, 2004).  For example, consider Ms. Y’s response when asked about the utility of their hypermedia during the interview session:

Right, and it's a hard concept to get. So, what we were thinking about is like the kids actually think when they eat food it breaks down and then leaves the body. They don't get that the food has to go to the cells and the cell actually works and creates energy from this food and then there's a waste and it sends that back to the body for it to be excreted. So we're trying to give them not only the names of the parts and what each part does individually but how it needs to work-...And we're doing the behaviour not only of the cell itself but behaviour of all the systems and then the behaviour of the whole body. And the cells are all part of that whole body.

This highlights that Ms. Y understood that the cells were an integral part of the body systems and could not be taught in isolation. Earlier, she noted that systems in the body are not disconnected and have complex mechanisms that allows for higher order operation. This provided evidence that she now understood how structures within a system perform multiple behaviours in order for it to function effectively. The IA results showed how Ms. Y introduced the SBF representation and refined her thinking over multiple years.

 

4.1.4  Refining the SBF representation as a conceptual tool

From an AOT perspective we needed to track Ms. Y’s transition from her initial naïve ideas about SBF representations to a more expert conception. The results from the IA indicated that Ms. Y’s understanding of the SBF representation as a conceptual tool changed. She used several distinct strategies to introduce the topic of complex systems ranging from discrete (i.e., in Years 1, 2 and 3), to acknowledging complexity (in Year 4), and finally providing a systems perspective with her new cell/body unit. In the first three years, she introduced to the SBF representation to her students by mentioning the new terminology being used to understand the aquatic system.  However, she introduced structures, behaviours, and functions as discrete constructs. In Year 4, she espoused a coherent view of SBF representation as a conceptual unit. Later that year, while introducing SBF in the context of the unit on cells and body she explained SBF as a system, complete with nested and interconnected subsystems.

 

4.1.4.1   Year 3: SBF representations

          Ms. Y’s early introduction to SBF representation suggested a focus on linear connections. This was shown by the way in which she filled out the ACT SBF table (Figure 4a) in front of the classroom. As a way to connect ideas about SBF she drew clear conceptual lines between one structure at a time and all the behaviours exhibited by that structure as the following example shows:

We just named them all yesterday. The heater, the fish, the plants. Those things are called the ‘structure’. The next word we're gonna use is ‘behaviour’. The behaviour is what the fish do. What do the things do in the tank? And the next word we're gonna use is ‘function’ okay? So what I want to do today is to start with structure and behaviour.  So, I made a chart and the first column is the structure, or the parts. So everyone write down one of the things in the fish tank is fish and the second column I wrote was behaviour, and the third column I wrote was function. We're going to start with this second column that is behaviour. When I ask you the behaviour of something, I want to know is what does it do? "What do fish do?" Swims, eats, breathes, and poops. Okay, all fish swim. That is their behaviour okay. They swim. What else do fish do?

       Here Ms. Y. described the meaning of the term “behaviour” somewhat superficially as “what fish do” rather than the more expert mechanistic view. She established linear connections between the structure (fish) and the multiple behaviours (swims, eats, breathes, poops) that this structure exhibits. After promoting an understanding of the behaviour exhibited by the structure (fish), she then drew another relationship between each individual behaviour in the last column to indicate the behaviour’s function.

 

4.1.4.2   Year 4: SBF representations are interconnected

Over time, Ms Y’s introduction to the SBF representation became richer and more complex.  In the excerpt below taken from a whole class discussion in year 4 she described structures, behaviours and functions as interconnected entities within a system, rather than discrete elements on a worksheet:

1. Ms. Y: Okay, now, let's do the filter. I'm gonna do the filter with you and then you're gonna do one on your own. All right, so what does the filter do?  What does the filter do? Jim what does the filter do?
2. Jim: Um, cleans out the tank
3. Ms. Y: Cleans the tank. Or cleans the “what part of the tank?”
4. Jim: The water in the tank?
5. Ms. Y: All right, so the filter will clean the water. Okay? Now, why does it clean the water?
6. Jim: So it can put more oxygen into the water?
7. Ms. Y: No. That's another thing that it does. It actually, because it's spinning around, because it's spinning like this, it's actually, one of the things it does…is it adds oxygen to the water. Now, this part here, why does it do it? First of all, I want to stop right here. The filter is this big grey thing here. Right? Now, first of all, how does it work? What's this big tube doing? [Points to picture of filter on the screen.]
8. Pat: Sucking up the water
9. Ms. Y: Sucking up the water. Then the water comes up here, right? And it gets sucked up and it goes back here and it pours back down. When it flushes back over that's when the oxygen from the air can get pulled back into the water. Okay, so how- you said it cleans the water- how does it do this?
10. Pat: Well, it has the filter. The filter has like chemicals and stuff.
11. Ms. Y: What do you think is in this bag?
12. Pat: Bad stuff
13. Ms. Y: Well, eventually the bad stuff is going to get in here, but actually there's charcoal in here, gravel in here. And then when the water flows through it, can it catch all the big chunks? Maybe the fish faeces and stuff like that? So, and then see how it spins back down here? Water splashes and it's pulling in the oxygen. So now, all right so now, why does it clean the water? What is the point of cleaning the water?

After turn 13, the class went on to discuss the fish and the plants, how the filter aerates the tank and how it affects the whole system. In turns 3 and 5 when Ms. Y discussed the behaviours (the mechanism that cleans water in tank) and function of the filter (by collecting faeces from fish) she was guiding students’ answers to structure, behaviour, and function simultaneously and filling in the chart appropriately, stressing relationships rather than focusing on any one aspect in isolation. Turns 6-12 show that Ms. Y used student response to generate more questions that linked what and why questions throughout her classroom discussion, highlighting the system complexity.