Modeling Instruction for University Physics- Examining the Theory in Practice_Share with MD

running head: MODELING INSTRUCTION FOR UNIVERSITY PHYSICS Title: Modeling Instruction for University Physics: Examining the Theory in Practice Authors: Eric Brewe*, Florida International University; Vashti Sawtelle*, University of Maryland; Jared Durden, Florida International University *Drs Brewe and Sawtelle contributed equally to the development of this manuscript and should be considered co-first authors ABSTRACT: In spite of a lack of consensus about the nature of scientific models, the role of models and modeling are well established in the practice of science Students who participate in developing, validating, deploying, and refining models are engaged in authentic scientific practices Modeling Instruction developed to promote the role of models and modeling in introductory university physics classes Modeling Instruction for university physics is founded on the basis of three theoretical components, Modeling Theory of Science, Modeling Theory of Instruction, and Modeling Discourse Management, and is situated within a participationist learning framework We claim that the integration of these three components within the participationist framework supports learning in science We substantiate this claim by proposing a definition of a conceptual model and describing the modeling process We then provide evidence of the modeling process, and thus link the development of a conceptual model to the design of the learning environment, through the analysis of video data collected from a Modeling Instruction university physics class In this paper, we lay out the theoretical arguments for how and why modeling should be the basis for introductory physics instruction We present an event from a Modeling Instruction class in which students develop a scientific conceptual model We focus specifically on the development of the model in first a small student group and a later in the full class We argue in this paper that the integration of the theoretical components underlying Modeling Instruction are key supports in providing the opportunity for students to develop conceptual models and engage in the practice of doing physics Keywords: modeling, university physics, curriculum Introduction Historically, the implementation of Modeling Instruction has shown positive effects for students in introductory physics classes at Florida International University Work examining the impacts of Modeling Instruction (MI) has shown it to be effective at improving the conceptual understanding of physics (Brewe et al., 2010) when compared to traditional lecture classes, moving students toward more expert-like views on the nature of science (Brewe, Kramer, & O’Brien, 2009), and positively impacting students’ views of their own capability and success (Goertzen, Brewe, & Kramer, 2012; Sawtelle et al., 2010) However, none of these works have unpacked what the MI learning environment looks like in detail In this paper we set out to describe theoretical underpinnings of the MI classroom, and examine how the theory plays out in the learning environment to create opportunities for students to engage in the disciplinary practice of doing physics Modeling Instruction is a reformed curricular and pedagogical approach to physics that centers on the development and testing of conceptual models The reform effort can be described as the intersection of three overlapping components, as seen in Figure The first, the Modeling MODELING INSTRUCTION FOR UNIVERSITY PHYSICS Theory of Science (Halloun, 2004), posits that practicing scientists actively engage in the development and deployment of scientific conceptual models Underlying MI is the idea that students should be engaged in activities that emulate those of practicing scientists This leads to the second component, the Modeling Theory of Instruction (Halloun, 2004; Hestenes, 1987; Wells, Hestenes, & Swackhamer, 1995) Modeling Theory of Instruction guides the instructional practices that engage students in authentic scientific practices The Modeling Theory of Instruction brings a coherent set of instructional objectives that center on model development and deployment in a participationist classroom environment Finally, the third component of MI, Modeling Discourse Management, addresses the role and responsibilities of the instructor in this environment Developed by Desbien (2002) and currently being expanded upon by Durden et al (2012), Modeling Discourse Management provides tools for instructors to engage students in authentic scientific discourse and practice INSERT FIGURE HERE In the first half of this paper, we will go into further detail on each of the components of Modeling Instruction and the theory of learning as the transformation of participation we use in our work In the second half of this paper, we draw on the theoretical underpinnings of MI to describe how the pedagogy, curriculum, and organization play out in the learning environment We argue that students in the MI classroom successfully build a conceptual model through MI engaging them in the process of doing physics We explore in this paper how a curriculum designed to make explicit the roles of models and the processes of building, validating, deploying, and revising models plays out in the classroom Framing Learning as a Transformation of Participation Adopting a perspective on learning helps guide researchers on what phenomena constitute data, and what they should pay attention to within these data In this paper, we adopt a framework that views learning as transformation of participation Our choice of perspective is guided by the work of Rogoff (1990), who described the participationist framework as an apprenticeship in thinking Rogoff argues that because people are constantly participating in social interactions, their participation continually feeds back into their understanding of the world, which, in turn, influences how they participate in social activities Participationist views expand on Vygotskian notions of learning by building a strong MODELING INSTRUCTION FOR UNIVERSITY PHYSICS emphasis on the contextual nature of knowing This emphasis on context is a reaction to strict cognitive views on learning and knowledge In participationist views, knowledge is not mechanically acquired (Handley et al., 2006) and the knower is not independent of the surrounding environment (Packer and Gooicheca, 2000) Instead, knowing is distributed among knowers, artifacts, and activities (Hutchins, 1995; Latour, 1988) Sfard (1998) summarizes this perspective saying, “Indeed, PM [the Participation Metaphor] makes salient the dialectic nature of the learning interaction: The whole and the parts affect and inform each other.” Participation is central because it is through participation that identity and practice are built, where practice is meant “to be engaging in a task, job or profession” (Brown and Duguid, 2001) Lave and Wenger (1991), and Wenger (1998) describe this practice-based learning as entering a community of practice A learner begins as a legitimate peripheral participant and then moves centripetally towards greater expertise with greater understanding of the processes, norms, and practices of the discipline Thus a participationist perspective considers learning as a process of socialization or enculturation, such as that of entering a community of physics (Rodriguez, Brewe, & Kramer, 2010) Modeling Instruction takes a participationist view on learning for three primary reasons First, MI has an established goal that students engage in model building as the basic scientific endeavor This engagement in the practice of science directly aligns with the perspective of learning by participating in the practice Second, MI has taken a social constructivist approach to the design of pedagogy and discourse management As a result, the instructor role is that of an expert guide in MI, which fits well with notions of apprenticeship or legitimate peripheral participation Finally, research into teaching and learning from a participationist perspective involves investigating the unfolding of events in a context-laden learning environment The MI learning environment is a complex dynamical system, and requires a broad perspective that attends to the activities, organization, curriculum, and pedagogy, as well as to the instructors and students Learning happens as students interact with other students, with the course materials, and with the instructor Model Building in Participationist Framing The central practice in Modeling Instruction involves the building of a scientific model This process is a complex social phenomenon To analyze a model-building event, observable features such as the students, instructors, activities, and artifacts are important However, the contextual elements are not directly observable, are equally important, and are often inferred These contextual elements include answers to questions like “What the participants see as the meaning and purpose of the activity?” and “How are the goals of curriculum and pedagogy conveyed through the activity?” We consider these contextual elements through the analysis of a model-building event Models are often considered as mental objects contained in students’1 minds (Greca & Moreira, 2001; Greca & Moreira, 2000; Halloun, 1996; Nersessian, 1995) Our analysis of model building focuses not on mental objects, but on the social construct of a model As Rogoff (1990) points out cognitive functions are essential components of purposeful action Thus, we not reject that the participants have mental models, or that these mental models include connections Note that investigation of learning often focuses on students, which is only part of the participationist story in that the instructors are also critical participants in the learning environment When we refer to participants in this paper, we are referring to the people who participate in the learning environment including students and instructors MODELING INSTRUCTION FOR UNIVERSITY PHYSICS between representations and concepts, or interactions between mathematics and intuition Simply, we are not concerned with participants’ mental models in this paper Instead, we are interested in the ways in which people participate with the tools of the discipline, whether they take up the established purposes of the curriculum and pedagogy, and how their participation supports the goals of the curriculum and pedagogy This has specific methodological implications when attending to the unfolding of events in the learning environment We will be looking for the development of conceptual models in the actions of participants This is in contrast to investigations of student written works from which the researcher then infers a mental model (Halloun, 1996; Lehrer & Schauble, 2006) One may argue that evidence of students engaging in the classroom environment does not indicate that they have “learned” anything Here, we lean heavily on Rogoff who argues that cognitive processes (such as remembering or representing) are components of purposeful actions of participants As such, when we observe purposeful action from students we may infer the appropriation of particular cognitive processes The actions we look for in this work involve the building of a shared conceptual model We look for evidence in the event that students appropriate components of this shared model, and infer that later, in a new context, they will have the ability to reconstruct the model to fit the novel context In this way, examining student participation allows us to argue that the model has permanence, both in the actions of students in a learning environment and in the individualized relation of a student to the shared model Modeling Pedagogy and Discourse Management in Participationist Framework Up to this point we have focused our discussion of participants primarily on the students in the classroom Here we turn to the role of the instructor, who participates in Modeling Instruction as an expert guide In this approach the role of the instructor is different than in either instructor-centered lecture-oriented classes or student-centered discovery-learning oriented classes (Rogoff, Matusov, & White, 1996) The instructor has two main roles: the first is to select activities that promote student participation in the construction of conceptual models and the second is to facilitate and guide discourse among participants In selecting activities, the instructor must be aware of the trajectory of the class toward the basic conceptual models So, the instructor’s participation involves constant formative assessment Instructors use this formative assessment to identify relevant activities which trace the trajectory of the class toward the scientifically agreed upon basic conceptual model In selecting activities, instructors engage students in the processes of model construction For example, the instructor may choose a lab to introduce a phenomenon to be modeled In the lab, students are often introduced to a representation that is useful for describing this phenomenon A common trajectory might include activities that promote the use and interpretation of the representation in modeling the phenomenon This might be followed by an activity to help students understand how this representation relates to others that have been used previously Eventually, the instructor introduces activities that encourage the students to model new phenomena using these representations The instructor may then choose to provide an activity that introduces new phenomena beyond the scope of those the students have already seen In this way, the choices of the activities trace out the path of model development for students From a participationist framework, it is through the choices of activities that the curricular goals of model development are established As Rogoff notes, the selection of activities frame the expectations of what it means to participate in a learning environment For example, a tacit expectation that a standard approach to physics may convey is that solving large numbers of exercises is the primary activity in physics The approach to activity selection in Modeling MODELING INSTRUCTION FOR UNIVERSITY PHYSICS Instruction is one of the features that distinguish MI from other curricula by focusing the goals on the construction of models The goals of model development, while being primarily communicated through the selection of activities, are reinforced by the approach to discourse in the learning environment Desbien (2002) and Durden et al (2012) have described discourse tools and practices that promote student participation in the construction of conceptual models These practices, described more elaborately in section the section titled Enactment of Modeling Instruction: Modeling Discourse Management, communicate to students how the conceptual models are used in scientific communication and argumentation Discourse practices endorsed in the learning environment communicate norms of participation in the scientific community (Durden et al., 2012) From a participationist framework, communicating norms of discourse establishes the practice of a discipline In MI, the goal of instruction is to allow students to participate in the physics discipline’s authentic practice of model construction and use Thus aligning instruction with the practice of the discipline promotes more authentic engagement in the practice of physics We will consider the design of Modeling Instruction curriculum and pedagogy as a way of understanding the goals and purposes of the MI learning environment Further, we consider how these instructional goals overlap to shape the MI learning environment and communicate the practices of physics We will subsequently take up an event-analysis of a classroom episode as an opportunity to explore how the three elements of MI play out in the classroom environment to focus on the authentic scientific practice of model building The Three Elements of Modeling Instruction: (1) Modeling Theory of Science The theoretical framing that supports the goals and purposes of the Modeling Instruction curriculum and pedagogy and ultimately the learning environment is the intersection of Modeling Theory of Science, Modeling Theory of Instruction, and Modeling Discourse Management In this section we describe the Modeling Theory of Science and in subsequent sections the Modeling Theory of Instruction and Modeling Discourse Management, in order to establish the goals and purposes of the learning environment Attention to models and modeling are not novel in science education; a variety of researchers have proposed that modeling is essential to developing understanding (Greca & Moreira, 2001; Knuuttila, 2004; Louca, Zacharia, & Constantinou, 2011; Passmore & Svoboda, 2012; Passmore, Stewart, & Cartier, 2009; Schwarz et al., 2009; Windschitl & al, 2008) Recently, the framework for science education standards cited “developing and using models” as one of eight essential practices for scientists and engineers, stating that “Models make it possible to go beyond observables and imagine a world not yet seen (National Research Council, 2011)” This commitment to models and modeling can be seen as a commitment to the Modeling Theory of Science Modeling Theory of Science (MTS) avers that modeling is a central activity of science (Giere, 2005; Halloun, 1996; 2004; Hestenes, 1987) According to MTS, science can be seen as progressing through the iterative process of building, validating, deploying, and revising models (Brewe, 2009) While MTS has been a basis for science education research, curriculum development and instruction for decades, across a variety of researchers, a basic lack of consensus about the definition of a “model” remains Indeed, Barquero (1995), as cited in Greca & Moreira (2000), has gone so far as to ponder whether these mental models might not be better represented as ‘mental muddles’ as a result of the diversification of terms and definitions used when referring to models and modeling in science education MODELING INSTRUCTION FOR UNIVERSITY PHYSICS Greca and Moreira (2000) outline two camps for definitions of mental models The first, from Gentner and Stevens (1983), posits models as incomplete and instable, yet serving a purpose in that they allow the builder to explain and make predictions about the physical system, but that these models are disposed of when the prediction is complete The second camp align with the definition of mental-models from Johnson-Laird (1983), who posit that mental models are structural analogs of the real world or imagined situations, and act as substitutes that can be mentally manipulated to understand current phenomena or to predict what happens next Hestenes (1987, p 441), in his seminal work introducing Modeling Instruction defined a model as “a surrogate object, a conceptual representation of a real thing.” From this definition we understand that models not exist in the physical world, but are mental representations or stand-ins for what we observe happening in the physical world, which is consistent JohnsonLaird’s interpretation of a mental model In this paper we attempt to use a definition of a model, and the implementation of the learning as participation framework, to show how a coherently developed approach to content, curriculum, pedagogy, and practice of physics leads to successful participation in doing physics Our goal is to demonstrate students engaging in the disciplinary practice of physics through participation in the construction of conceptual models Distinguishing Mental and Conceptual Models Halloun (2004) has undertaken an extensive analysis of the composition of models and makes several distinctions which we take as critical and describe here First, we begin by distinguishing conceptual and mental models, as this distinction is important to the methods we utilize for investigating the learning environment Mental models, which are regularly used by psychologists and science education researchers, are taken to be structural analogs to the real world or imagined situations which can act as substitutes for predicting outcomes (Gentner & Gentner, 1983; Greca & Moreira, 2000; Johnson-Laird, 1983) These mental models are presumed to exist in the minds of individuals Regularly, research on mental models posits that the inscriptions that scientists or science students create reflect the mental models We not reject that people construct mental models, but these mental models are specific to individuals, idiosyncratic, and unstable We not feel that we have sufficient evidence of the mental model to describe its construction in the classroom setting Correspondence between inscriptions and mental models is plausible and a basis for cognitive research; instead, we focus on conceptual models These conceptual models are considered to be distributed constructions that are external to individual minds Conceptual models are developed in the discourse in a learning environment (such as the introductory physics classroom) Accordingly, for this paper we will attend to the conceptual models that are built and used in the learning environment What Makes Up a Conceptual Model? Conceptual models are different than mental models in that they are external representations that are created to aid comprehension of target systems Our notion of representation is based in a Vygotskian notion of a tool which mediates understanding (Knuuttila, 2004; Vygotsky, 1978) As such, we allow representation to take standard forms such as pictures, schematic diagrams, graphs, charts, and symbols as well as language, mathematical equations, and formula Implicit in this notion of a conceptual model is that representations mediate understanding across members of a learning community Therefore representations are shared and communicated, so the use and interpretation of the representation must be negotiated Defining a model as a representation of a target system opens questions about what is (and is not) MODELING INSTRUCTION FOR UNIVERSITY PHYSICS a model Questions such as “Is a picture a conceptual model? Is a graph a conceptual model?” arise A more formal formulation of these questions would be: how we operationalize a conceptual model? If we take the definition of a conceptual model to be an external representation that is created to aid comprehension of systems in the world, then a graph or a picture could be considered a conceptual model A picture of a hydrogen atom aids the comprehension of the structure of hydrogen by representing the composition of hydrogen as a nucleus of one proton and one orbital electron However, this liberal view of conceptual models essentially allows for everything to be a conceptual model Instead, we prefer to consider how purpose is reflected in conceptual models One of the features of conceptual models that reflect purpose is correspondence with objective reality Conceptual models should be analogous to something Further, conceptual models become more robust when multiple representations are coherently coordinated For example, a graph of energy levels in a hydrogen atom may be coordinated with a picture of the hydrogen atom to develop further insight into the structure of hydrogen Conversely, a picture of a hydrogen atom may just be intended as an object of art or design What distinguishes the art or design from the model is the purposeful creation of the representation The purpose in the models we are concerned with is to convey scientific meaning While one could consider a single graph a conceptual model, we will instead consider this to be a representational tool Representational tools can be used to describe phenomena, while the models will consist of multiple, coordinated tools representing different aspects of the phenomenon Halloun’s definition emphasizes this notion of models as systems of coordinated representations (2004, p 24) Our analysis of the construction of conceptual models will both follow the negotiation of representational tools in the learning environment, as well as the coordination of new representations with existing conceptual models Drawing on the work of Halloun and others, we adopt the following definition for a scientific conceptual model –coordinated representations of a particular class of phenomena that exist in the shared domain of discourse and are inscriptions of disciplinary knowledge In the following section, we show how instruction is designed to promote the construction of scientific conceptual models The Three Elements of Modeling Instruction: (2) Modeling Theory of Instruction A straightforward extension of the Modeling Theory of Science is that if science progresses through model development, validation, deployment, and revision, then students should be engaged in learning to develop, validate, deploy, and revise conceptual models Thus the Modeling Theory of Instruction is an epistemological framework for engaging in meaningful science learning (Halloun, 2004) MTI is epistemological in the sense that engaging with the development of conceptual models is how understanding in science develops, and that the understanding itself is comprised of sets of shared conceptual models Building a curriculum and pedagogy around the Modeling Theory of Instruction has important consequences when considered in light of a participationist framework on learning MTI helps to establish the goals of the curriculum and pedagogy and informs the design of the learning environment In the following sections we describe the interplay of the epistemological framework of Modeling Instruction with the participationist framework on learning Goals in Modeling Instruction: Develop, Validate, Deploy, and Revise Models The basic premise of the MTI is that for students to learn to develop, validate, deploy, MODELING INSTRUCTION FOR UNIVERSITY PHYSICS and revise models, the Modeling Instruction learning environment should support this goal In the design of a curriculum and pedagogy to promote the process of modeling, it is imperative to first consider how conceptual models are constructed Iterative cycle of model development: Specific to basic models Brewe (Brewe, 2008) provides an elaboration of the process of constructing scientific conceptual models by differentiating specific and basic conceptual models This distinction is reflective of the process by which basic models are developed, and informs the design of the MI curriculum and pedagogy Instruction with the goal of building basic conceptual models begins with considering phenomena to be described As Vosniadou (2002), describes models preserve aspects of the phenomena that they represent Once a target phenomenon is established, relevant representational tools are introduced and the class puts them into practice For example, learning to use velocity versus time graphs by graphing the motion of different objects moving represents a set of phenomena to be described Consistent with our definition of a model as a coordinated set of representations of a phenomenon, as students learn to graph the motion of an object, they are developing models of this specific phenomenon, or what we will call specific models By necessity, specific models are predecessors to basic models The specific models that students construct are made more robust as additional representational tools are introduced and coordinated with existing representations Introduction of tools and the subsequent negotiation of use and interpretation are motivated by specific phenomena to be modeled, so the models created are always specific models Yet Nersessian (1995; 2002) argues that the real skill of scientists is to reason based on general models, so the curriculum and pedagogy of MI are designed to support students in transitioning from specific to basic models Basic models, which are general and represent entire classes of phenomena (such as a constant acceleration model), are abstracted from a collection of specific models (Halloun, 1996; 2004) For example the general features of a basic constant acceleration model can be abstracted from specific models of objects undergoing constant acceleration, such as objects in free fall, or uniformly slowing down Basic models are useful because they are not tied to a specific phenomena, much like the Standard Model is a basic model built up and abstracted from the specific models of atomic collisions, particle interactions, etc Nersessian (1995) points to the essential role of basic models in science, as basic models promote abstract reasoning about novel phenomena; when physicists seek to understand interactions of atomic particles they start by using the Standard Model Understanding the MI curriculum and pedagogy as the instructional application of the Modeling Theory of Science establishes the goals of the curriculum In the previous section, we described how the goal of constructing basic conceptual models is designed into the curriculum In order to carry out event-analyses, we should not only look at the curriculum design, but more holistically at the learning environment In the following sections, we identify salient features of the learning environment for our analyses Re-developing scientific models The first feature of the learning environment is that the basic conceptual models are often well developed for scientists, particularly for instructors in introductory courses, yet these models are not well developed for the students in these courses As a result, the goal of the MI class is to support students in re-developing these constituent basic models within their own learning environment The role of the instructor is to guide students through the development of these basic conceptual models Within MI, the curriculum and pedagogy are designed to support guiding students through the development of these models by establishing activities and providing scaffolding to help instructors manage student discourse to promote model building and use In this way, the MI curriculum and pedagogy can be described MODELING INSTRUCTION FOR UNIVERSITY PHYSICS as a guided inquiry approach Students are not expected to discover physical laws without strong guidance from an instructor who chooses activities, introduces representational tools, and guides students toward their appropriate use and interpretation In this way, the instructor is a guide to the disciplinary norms and tools Student participation in a model-centered learning environment Accomplishing this redevelopment of basic conceptual models requires students to be active and engaged – participating in the learning environment We can identify specific ways we expect students to participate in the redevelopment of basic conceptual models First, we expect that students will be involved in identifying the way that tools such as pictures, diagrams, graphs, and equations can be used to represent phenomena They are not expected to invent or discover these tools, but instead to determine (with guidance from the instructor) how the tools can be used and how to interpret these representations For example, how does a vector representation of forces describe interactions the object is involved in, and what these forces allow us to infer about the current state of the object and its future behavior? We expect that students will be involved in the interpretation of these representational tools and drawing inferences from them as they pertain to physical laws We expect that students then deploy these established basic conceptual models by extending them to novel situations From a learning as participation perspective, we expect students to communicate basic conceptual models Moving toward greater expertise with models, and by so doing with the discipline of physics, involves developing competence at interacting with others using conceptual models Implications of MTI for research guided by participationist theory of learning Identifying the expectations for how students participate in the Modeling Instruction learning environment guides our research into the enactment of the curriculum and pedagogy We will avoid claims about the models that individual students hold at any point in time and instead use the unfolding of events in the classroom over a period of time to identify the trajectory of the participants toward an established conceptual model As such, we will include analyses of specific participants within the learning environment, but will also consider how specific participants influence each other The Three Elements of Modeling Instruction: (3) Enactment of Modeling Instruction through Modeling Discourse Management In previous sections we described the goals and expectations of the MI curriculum and pedagogy In this section, we turn our attention to the discourse management approach employed in the learning environment Our attention to the management of the discourse stems from the question, ‘How you get students to construct these basic models?’ The expectations for the discourse practices in the classroom relate strongly to the expectations for how students participate in the learning environment and how that participation is affected by and informs the instructor and the activities In short, the discourse management practices establish the course norms and expectations and shape the unfolding of events in the learning environment MTI establishes the goals of the learning environment, which are enacted through the activities and discourse in the classroom Desbien (2002) described Modeling Discourse Management as a set of discourse tools that instructors can use to promote the construction of conceptual models Durden et al (2012) have elaborated on the use of these discourse tools, providing evidence of their use in the Modeling Instruction classroom In addition to the discourse tools, the organization of the learning environment promotes the goals of the Modeling Instruction curriculum and pedagogy Together, the organization and discourse shape participation MODELING INSTRUCTION FOR UNIVERSITY PHYSICS Organizational Features of Modeling Instruction Modeling Instruction is designed for implementation in a studio-format classroom In studio physics classrooms students are able to flexibly engage in various types of activities, which may include labs, conceptual reasoning and problem solving At Florida International University, the MI class integrates both the “lecture” and “lab” components of the introductory physics course into one six-contact-hour course that meets two or three days a week The physical layout of the Modeling Instruction room, see Figure 2, sends meta-messages to students that elicit learning behaviors (Redish, 2004) Typically, students work in small groups of three to complete in-class activities The small group work is summarized on a small portable whiteboards These small whiteboards are then presented in a larger group “board meeting” where all students in the class participate INSERT FIGURE HERE Small group participation During the small group component, students work on modelbuilding activities as described in the Modeling Theory of Instruction section In these small groups, students begin the process of reaching consensus by creating whiteboards for sharing or “publishing” their lab results and/or solutions to problems The instructor’s role is to circulate through the classroom, asking questions, introducing new content, and examining the whiteboards that are being prepared for presentation This small group work allows for students to work together on a model-building activity, building understanding in a small group The instructor is able to formatively assess student trajectories in the model-building process In subsequent sections, we describe discourse management tools that can be used during small group work Large group participation The pattern of students first working in small groups on an activity and then presenting their work in a larger group on the whiteboard allows students to negotiate the meaning of the activity The large group board meeting consists of all the students in the class gathering in a circle such that every member can see every other member and every groups’ board During the board meeting, the instructor takes the role of disciplinary expert This role can be seen as the instructor guides the discourse toward a shared conceptual model by 10 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS The first thing to notice in Clip is in the contrast to Clip 3, when the students were saying they were frustrated with the movement of the idea toward pie charts When Lara suggests, in Clip 4, that they “forget the pies” Marcus actively resists what he calls “disposing the pies” (turn 113) After Lara asks how they are going to model energy in turn 108, Marcus affirms that pies are exactly how they are going to model energy (turn 111)2 As Marcus tells this story of the blue and brown pie he becomes very emphatic, gesturing vigorously with his hands and emphasizing his meaning Amy responds vocally to his emotional display (turn 116), and in other moments she and Kurt laugh and shake their heads at Marcus’ display We not try to claim that the emotion that Marcus exhibits in the telling of the brown and blue pie story is evidence of his owning the representation, but we draw the reader’s attention to the contrast between the message in this clip compared with that in Clip We claim that the contrast between these moments suggests that Marcus is not simply repeating the story offered by the instructor, but is appropriating and changing the representation for himself In the second half of this clip, we see the blue and brown pie representation developed across the group members, and in future clips we will observe the stability of this representation Marcus begins by stating that he has 12 inches of pie and that pie is all potential pie and changes into kinetic pie (turn 117) He then restates this terminology, replacing it with blue and brown pie He continues to say that the brown pie slowly changes to blue pie as the ball falls In Marcus’ account, when the ball reaches the ground it is all blue pie (turn 119), and when it hits the ground it loses some of its blue “pie-ness” In turn 120, blue changes to “blueberry”, and Marcus articulates that the blueberry is lost in heat, sound, and “all different forms of energy” (turn 123) These two turns suggest that Marcus is using the blue (blueberry) and brown to represent different forms of energy, and the pie transforms from one form to another When it hits the ground, the energy that was in the blue form is lost and goes everywhere even as it changes into other forms of energy An interesting point in this exchange is that Marcus inserts his explanation of elasticity into the blue and brown pie story as the explanation for why some energy is lost into other forms (turn 121) In the second half of the clip, after the initial story is told by Marcus, Amy and Kurt enter the discussion in turn 124-130 In this interaction, Amy and Kurt help Marcus to connect the colors blue and brown to the types of energy, kinetic and potential Lara pushes the group to explain what these words mean (turn 131), and the brief exchange that follows shows all three students describing the blue pie as kinetic pie (turns 134139) Lara clarifies what she is looking for as an explanation (in turn 140), and Marcus connects blue pie to motion and how fast the ball is moving and therefore says that pie gets more blue as it goes down (turn 143) At this point, the conceptual model has become slightly more refined, with the students connecting the canonical forms of energy (potential and kinetic) to their descriptions of blue and brown pie We also see in this section a connection between blue/kinetic pie and how fast the ball is going Finally, the idea that the pie gets more blue as it goes down suggests energy transfer We note the explicit use of the term model in this sequence and draw the reader’s attention to how both Lara and Marcus use this term easily as they move through the discussion We also appreciate Marcus’ use of “the foundation of our theory” in turn 115, but we recognize that he may be using that term in a colloquial manner 22 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS From turn 146 to the end of this clip, Amy and Marcus work together to connect all the pieces of the blue and brown pie story Marcus had articulated that the pie becomes more blue as it goes down (turn 141), and Amy picks up the thread of the story with the ball hitting the ground (turn 146) Marcus says that at that point, “It’s all blue pie (turn 147)”, which Amy interprets to mean that the blue pie is all over the floor (turn 148) Marcus’ turn in 149 is not clear as to whether he is agreeing with Amy’s restatement, or if he is saying that the entire pie is blue at that point, but they quickly move to the next piece of the story when it is coming back up At this point Amy takes over the story, saying that on the way back up, the pie changes back to brown (turn 152), representing potential (turn 155), which is affirmed by Marcus (turn 153, 155) Overlapping one another’s speech, Marcus and Amy build off one another’s sentences to construct the idea that at the highest point the pie is all brown pie (turns 156-165) They complete the cycle by considering when the ball is going back down and describing the pie “going back” into blue pie (turn 166-169) They cap the story with affirming statements from Amy (turn 170), Marcus (turn 171), and Lara (turn 172) In the restatement of the whole blue and brown pie story, we see pieces of the idea of transformation embedded in the talk from Marcus and Amy They use language of the pie “changing” (turns 152, 153), and “going back to” (turns 168, 169), suggesting the idea that the pie is transforming from blue to brown Additionally, because the entire story was recapped in this section, we see connections between moments of the ball’s path and what the pie would look like, including being completely blue just as it hits the ground (turn 141) and being completely brown as it reaches the highest point (turn 156165) We not have clear evidence in this section of the student talk of where the energy goes In other words there is no talk of transfer in this section It is possible that Amy’s comment in turn 148 is suggesting that when the ball hits the ground the energy is transferred out of the ball, but it is unclear from her talk and Marcus’ follow-up Additionally, the talk about the pie changing from blue to brown pie makes it unclear whether the students see the entire pie as a single kind of energy, or portions of the pie as different kinds of energy In other words, there is no talk of a pie that is simultaneously both blue and brown Development of a conceptual model What we see happening in this set of four clips is the development of a shared conceptual model between Kurt, Amy, and Marcus The development of the model is scaffolded through interactions with the professor and by the design of the activity, but at the end of this series of clips we see evidence that Marcus and Amy have appropriated the model as they share the ideas with Lara (the undergraduate instructor) We can see the development of the idea by starting with Marcus’s idea about elasticity, which is pushed forward (or as Marcus says, moved) by the professor into using pie charts In the first two clips, we see a negotiation of meaning taking place as Marcus articulates ideas about elasticity and the instructor proposes a representation to help them keep track of where the energy goes As they work through this representation, Marcus, Amy, and Kurt struggle to make sense of what the slices of pie represent and how forms of energy might be different from energy itself As the instructor moves away, it is unclear how much the students have gained from the interaction Looking at Clip 3, we see evidence that the students felt like the idea of pie charts was given to them, and not developed on their own However, as Lara suggests they abandon the pie charts in 23 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS Clip 4, Marcus rebels Instead, he and Amy construct their own meaning and appropriate the pie chart representation, clarifying that the “kind” or “color” of pie tells us about the form of energy, while the pie itself getting smaller represents energy leaving the system At the end of Clip 4, we have the sense that Marcus and Amy have together constructed a conceptual model about how the energy in the system changes, and Lara warns them that they should be prepared to share this explanation in the large group discussion Day 2: The Large Group Takes Up the Conceptual Model Day ends shortly after the close of Clip with the student groups completing the ball bounce activity and tasked with thinking about how to present their work for the large group class meeting the following day On Day 2, the students begin the class by developing whiteboards for the large group meeting The process of whiteboarding their work is a non-trivial matter for the students The whiteboard serves as a place for students to publish their results to the rest of the class, and requires the small groups to spend some amount of time working towards consensus on the work they have done Three questions that the students are asked to answer on their whiteboard scaffold the development of this artifact: (1) What did you learn? (2) What rules can you make? (3) What questions you still have? At this point in the semester (approximately one third of the way through the class) students are still working to understand how best to present their work on the whiteboards, but recognize the whiteboard as place to store evidence and representations for the findings of an activity We enter Day after students have created their whiteboards of the same activity and have begun to share their findings in a large group board meeting In the large group discussion, the students gather for a board meeting and the instructor remains silent, waiting for a student group to begin presenting their work (The instructor’s implicit action communicates the message that the students are responsible for managing this time and the discussion that will take place.) The discussion opens with a student group explaining what they learned about kinematic graphs and technical issues with the motion sensors The student group finishes and 20 seconds of silence follows Finally, Ana opens up with a discussion of the energy and what makes the ball stop Clip 5: Ana presents 500 Ana: So our group, well, our group kind of learned about umm 501 502 because it doesn't have as much like energy 503 So then the next time it goes back up um…it doesn’t go up as high because it doesn’t have as much like energy and speed as before and so then with each like bounce it loses a little bit more energy until at the end it’s like has nothing, I guess, left and it stops bouncing 504 It doesn't have I guess as much potential energy cause it still has some kind of energy in the ground but we don't really know what's gonna happen if someone kicks it or you step on it We were kind of struggling with the idea of like how does the ball stop? We’re like…it stops Then after much deliberation we realized that its a change in energy of the ball Before it gets dropped it has potential energy then as you drop it when it hits the ground it transfers energy like, to the ground in the form of sound and so it loses a little bit of energy so the next time it goes back up umm it doesn't go up as high In this short clip, we see Ana articulate the difficulty her group had with determining how the ball eventually comes to a stop She describes the ball as having 24 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS potential energy when it is at some height and the ball transferring energy to the ground when it hits (turn 502) She connects the transferring energy to the ground idea to the idea of the ball losing a bit of energy each time it goes back up, until ultimately the ball has no energy left (turn 503) and it stops bouncing However, at the end of this clip Ana articulates a confusion she still has about the kind of energy that is left in the system after the ball stops bouncing She asserts that it does not have as much potential energy, but she expresses uncertainty about the kind of energy that might still remain, in turn 504 At this point, Ana’s story contains potential energy as the only energy, and while there is talk about energy being transferred Ana expresses confusion about the details of how this works In addition to Ana’s vocalized story, we note that her group’s whiteboard had a pie chart representation that showed a solid pie getting smaller each time the ball hit the ground The representation is consistent with her story of the energy getting less each time the ball hits the ground, but the solid color of the pie reinforces the inference that Ana’s story only includes one form of energy INSERT FIGURE HERE We would be remiss in telling this story if we did not mention the role the instructor plays in this discussion The students have their chairs grouped together to form a circle with their whiteboards propped on the floor in front of each small group The instructors are positioned outside of the circle and have not said anything since asking the students to form the board meeting By remaining separate from the space the students have set up for discussion, the instructor’s implicit action communicates to the students that this is their time for explaining to one another what they did in the activity We see an echo of the whiteboard prompt in Ana’s initial utterance, “Our group kind of learned about,” suggesting that the students recognize this time as an opportunity to share the consensus they reached in small group conversation Clip 6: Marta builds off Ana’s explanation 505 Marta: To go off what you said (gestures to Ana) and looking at that umm motion map which is blue and red (gestures to Marcus' group’s board), 506 So at the top it's full of potential energy and as it goes down it loses potential energy and gets full of kinetic energy? 25 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS 507 Ana: Mhmm 508 Marta: And it goes up it has, it’s going up with kinetic energy 509 Ana: Right or, or whatever potential energy it has left (shrugs) Like I kind of did the same thing in my pie charts but I didn’t put what made it go up 510 So I guess what we could define is what drives it? Is it potential energy or kinetic energy? 511 Marta: Is kinetic energy pushing it that way? (motions upward) 512 513 Ana: Yeah like what, yeah what is the energy? I mean, it’s energy but you know which type of energy is the one that makes it like go up and down, I guess, or keeps it moving? Because if it’s potential energy, this one would make sense (gestures to her group’s board) because you’re draining it of potential energy Result is it stops moving 514 (gestures to Marcus' group’s board) Unless, you're saying kinetic energy makes it not move and that’s why it goes up more blue and then stops 515 Marcus: The energy it has doesn't make it stop move, or move 516 Ana: I don't Does anyone follow what I was saying? (A few students mutter acknowledgement of her question.) 517 Ana: You know what I’m trying to say? 518 Student of camera: I understand I 519 Ana: I don't know if I’m, I feel like it makes sense to me, but I don't know if it makes sense to anyone else In the beginning of Clip we see Marta draw attention to the different descriptions of the scenario provided by the boards from Marcus’ and Ana’s groups An interesting note about this comparison is that up until this point the board from Marcus’ group has not been presented, but the structure of the board meeting is such that Marta is able to draw from not only what has been said by others, but also what the whiteboards communicate With Marcus interjecting only once in this clip, Ana and Marta focus on trying to understand how the two boards are alike and different, and what the implications of these similarities are for understanding the energy story 26 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS INSERT FIGURE HERE In making sense of the difference in the two boards, we see the focus become one of understanding the role of the forms of energy Marta draws attention to understanding the kinetic and potential energies (turn 506), and we understand from Ana’s response that her group focused primarily on potential energy (turn 509) At this point, Ana articulates a subtly different question than the one from Clip where she wanted to understand what made the ball stop In turn 510, Ana asks what drives the ball upward Marta follow up on this question, and she and Ana use words like ‘drives,’ ‘pushes,’ and ‘makes’ (turns 510, 511, 512), communicating through their talk that the focus of understanding here is on the mechanism behind the ball’s movement At the end of this segment, we see Ana articulate the difference between seeing the ball’s loss of potential energy as the cause of the ball stopping (turn 513) and seeing the kinetic energy as stopping the ball (turn 514) In this brief discussion, Marta and Ana are trying to understand which form of energy is the mechanism behind the ball moving upward or stopping Ana directly appeals to Marcus to understand the role kinetic energy is playing in his description (turn 514), and Marcus responds to this query by saying it is not energy that is the mechanism behind the ball’s movement (turn 515) In response to Marcus’ dismissal, Ana appeals to the rest of the students to see if her argument is making sense, and a few students affirm her question In the next clip, we will see Sylvia (a student from neither Marcus’ nor Ana’s group) rearticulate this question 27 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS Clip 7: Marcus explains his board 520 Sylvia: Well I’m interested in knowing why it is you guys (gesturing to Marcus’ group) did it that way versus that way (points to Ana’s board) 521 Like, your reasoning for um having kinetic ener , like I actually kind of agree with that one (Marcus’s board), just cause you have less and less kinetic more and more potential until it reaches its maximum height Which will be less than the previous maximum height because of the energy lost 528 But again you have 100% of your energy being potential and then you basically just repeat with each bounce - where you’re fully potential at the top and then you get increasingly more kinetic going down, and impact-time comes back again Basically it repeats itself in that motion I don't know if that explained everything? 529 Sylvia: Yeah, I get it 530 Marcus: You get it? 531 Sylvia: I just, I just I don't, I just get confused like this one (motions to Ana’s board) Umm… 532 Ana: We're both saying the same thing 533 Sylvia: Yeah 534 Marcus: (shakes his head side to side) 535 (other students murmur) 536 Ana: We're not even thinking about kinetic energy really 537 Sylvia: Um…Ok that’s why it’s like… 538 Ana: The way he explains it, yeah like, if it’s the same amount of ener like the change of energy, like the purpose between potential and kinetic are the same being dropped It’s just every time you have less energy cause you dissipate energy to the ground 539 Sylvia:So its just only changing the potential 540 Ana:Yeah 541 Sylvia: (points to Marcus’ board) And that’s put together…kinetic, potential 522 Instructor: (whispers to Marcus) Why don't you guys explain what you did 523 Sylvia:…Like I feel like once it hits the ground… like I don't know Just explain it 524 Marcus: Yeah, well, basically the height that you have when you’re gonna release the ball, it's at that point you have your potential energy It’s the only energy you have potential, and as you release the ball it gains kinetic energy, gets faster And because it’s reducing its height from ground your, you have less potential energy 525 So basically, you have one standard amount of energy from the time you have the ball in your hand, which is fully potential And as it falls, the potential decreases because the height is less and the kinetic increases as it gains speed, velocity, going down So there's gonna as you go down you have more and more kinetic energy, and less and less potential energy 526 When it hits the floor you have, the split second before it hits the floor its all kinetic When it hits the floor you lose energy due to sound, elasticity of the ball, heat, all the other components of energy dissipation, whatever 527 Then you have all kinetic coming, so then you have, coming off the ground it’s all again fully kinetic but you have less energy because of energy dissipated due to the impact And then as you go up it comes, This clip is dominated by Marcus explaining his reasoning about the forms of energy to the larger group However, it is significant to note that this interaction begins with Sylvia drawing a comparison between the whiteboard from Ana’s group and the board from Marcus’ group She articulates her primary question to be around the decision to include the kinetic energy (turn 521) Prompted by the instructor, Marcus enters the dialogue where he explains the model developed by his small group We note here that the professor does not explain Marcus’ board, but instead prompts Marcus to join the conversation This again is an implicit action by the instructor, demonstrating to students that they are expected to take ownership and responsibility for the discussion and 28 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS understanding Further, because the instructor has prompted Marcus’ group to present, the instructor provides a clue that students should attend to this board In Marcus’ explanation, we see him start by moving through the physical picture of the ball falling He says that at the beginning the ball has all potential energy, which gets smaller as the ball falls (turn 524) At the same time, Marcus says the ball is gaining kinetic energy because it is getting faster He pauses at this point and clarifies that there is only one amount of energy and that energy is either potential or kinetic energy (turn 525) Marcus also emphasizes that as potential energy goes down, kinetic goes up, allowing for the sum of the total energy to remain the same When Marcus gets to the point where the ball hits the ground, he notes that just prior to this point there is all kinetic energy, and when it actually makes contact with the ground, energy is lost in a list of different way (526) Then Marcus follows the track of the ball back upward and notes that, while it is again all kinetic, there is less energy because some of it was lost when it contacted the ground (527) He goes on in turn 527 to again describe the kinetic energy becoming less as the potential energy increases, emphasizing that the ball does not go as high because it lost energy Marcus finishes his explanation by highlighting that the entire process repeats again, ending by asking if he explained everything (turn 528) Sylvia, who initiated this interaction, says that she understands Marcus, but that she is still confused about Ana’s group’s board (turn 529, 531) Ana interjects (turn 532) and says that they are doing the same thing, but Ana’s group does not talk about kinetic energy Instead, she explains that her board is capturing only the idea that energy is lost when it makes contact with the floor (turn 538) She calls this energy potential, and when Sylvia asks if the difference in the two boards is only that Marcus has both kinetic and potential and Ana only has potential, Ana affirms her understanding Development of a conceptual model When we left the small group of Amy, Marcus, and Kurt in Clip 4, their description of the phenomenon only included a description of the transformation of forms of energy In Day 2, we see a question about the purpose of these forms of energy arise in the conversation When Ana and Marta articulate their question about the form of energy which is the mechanism behind the ball in Clip 6, the model of transforming forms of energy that Marcus’ group developed has not yet been shared with the larger group The discussion between potential energy being drained from the ball versus the kinetic energy stopping the ball arises from Ana, Sylvia, and Marta drawing comparisons between the presentations of Ana’s and Marcus’ whiteboards, and the question of what stops the ball’s movement is a result of comparing the forms of energy on the two whiteboards It appears that Ana’s group has focused primarily on the decrease of the energy over time, and less on which form the energy is in On the other hand, we saw in Clip that Marcus, Amy, and Kurt had concentrated mainly on how the energy changed from one form to another In bringing these two descriptions together and contrasting them, the students were able to make progress in deciding that the forms of energy are not distinctly different while, at the same time, allowing that the total amount of energy decreasing accounts for the ball not bouncing as high We argue that the large group discussion has extended the conceptual model we articulated in Marcus’ group in Clip to the large group and that Ana and Sylvia (and potentially others) have appropriated this model The appropriation is evident in Sylvia’s 29 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS contrast of Marcus’ description with the one provided by Ana, as well as Ana’s articulation of the purpose of the kinetic and potential energies in contrast to the total energy in Clip We also note that many of the elements of MI came into play to support this conceptual model development and appropriation through the use of the representations of the pie charts on the whiteboards, the whiteboards themselves as artifacts of the consensus reached by the small group, and the instructor moves which encouraged student ownership and responsibility for the discussion We not try to argue that the presence of any of these elements caused the productive model building to occur, but in understanding how this event unfolded, we want to draw attention to the role the MI elements played in shaping the event Furthermore, we not intend to claim that the students in this event were exemplars of the kind of reasoning we would like to see students demonstrate Indeed, we would have preferred to see direct reference to the pie charts in the large group conversation, and a more widely-spread shared discourse from the other students in the classroom Nevertheless, we believe that describing how the theoretical elements guiding the implementation of MI come together in this event is important for understanding how students make progress with this conceptual model Discussion In this paper we set out to describe the ways by which the three elements of Modeling Instruction interact in the unfolding of an event in the classroom While we believe that the sequence of Clips through demonstrates how these elements interact, we not mean to imply that the sequence represents excellent teaching or learning Instead, we intended to portray a sequence of events that represent the ways in which a focus on the Modeling Theory of Science can combine with the Modeling Theory of Instruction and Modeling Discourse Management to encourage student participation in the development of a conceptual model In this section, we intend to examine some of the subtle messages that analyzing these clips uncovered How is it that Clip Came to Be? Clip represents the culmination of the conceptual model being shared with the large classroom group In our description of a conceptual model, we emphasized how these models are developed in the discourse, and thereby focused our analysis on the elements that were shared amongst the class In this way, the MDM tools of arranging the discourse become central to understanding how an event like this occurred In the beginning of Day we drew the reader’s attention to the whiteboards the students had created As described in the section The Three Elements of Modeling Instruction: (3) Enactment of Modeling Instruction through Modeling Discourse Management, the whiteboards play a key role in the development of consensus in the small groups and in allowing small groups to share their findings with the rest of the class In Clip we see this play out in a way that is distinct from perspective that the whiteboards are simply an artifact of student talk Sylvia starts by comparing the boards of two individual student groups One of these groups (Ana’s) had shared their findings prior to Sylvia’s question, while the other had not We see the pedagogical tool of whiteboards being leveraged to help bring the conceptual model developed by the Marcus’ group to the discussion with the large group Furthermore, the instructor plays an important role in Clip by prompting Marcus to explain his whiteboard In doing so, the 30 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS instructor opens the floor to the students in Marcus’ group, both encouraging them to share their findings with the large group and implicitly signaling to the rest of the classroom that what Marcus is about to share is of importance We see the instructor using the tool of seeding to leverage the work done by the small group in helping the large group make progress conceptually Without these MDM tools we could imagine the students talking far less than they in these sequences of clips from Day 2, and the instructor leading much more Additionally, we notice the difference in the amount of talk from the instructor in the Day clips as compared to the Day clips The instructor is far more involved in the small group discussions than in the large group In this way, the instructor is able to guide the conceptual model building while still allowing students to grapple with their own ideas and participate in the model-building process In MI, and learning as participation, we not mean to imply that the instructor does no work in guiding the development of models, but instead that the work that s/he does is not focused on the delivery of information The Role of the Instructor in Modeling Instruction In the clips representing Day of this sequence, we see a distinct difference in the ways the two instructors in the classroom interact with the students The senior instructor, the professor, interacts with the students in Clips and in a way that communicates that he is trying to lead them in a particular direction His goal is to introduce them to pie charts, and he purposefully guides the conversation in the direction that helps the students see how a pie chart could be useful In direct contrast to that is Lara, the junior instructor, who encourages the students to follow their own thinking, even going so far as to say in Clip 4, “Forget the pies Because the pies don’t make sense to you at this point.” In contrasting these two instructors, we see the tension between strict guidance of ideas and following studentgenerated ideas playing out in their interactions with the small group It is not entirely clear that both roles are necessary, but it is true in this sequence of clips that both roles were present We are not sure what would have happened without these two different kinds of interaction We suspect that it is in part Lara’s dismissal of the pie charts that encourages Marcus to tell the story of the brown and blue pie When the professor is present, the students spend their time trying to figure out the point he was trying to make with the pie charts, and when he leaves, they move to a discussion of how ridiculous the representation was from their perspective However, when Lara moves to entertain the absurdity of the representation, the students rebel and push back It may have been the contrast between these two roles that allowed the students to take ownership of the pie chart representation and flesh out the idea Even so, we not mean to imply that the enactment of MI requires the presence of two separate instructors Indeed, it seems possible that a single instructor could play both roles at different times through the discourse Instead, we mean to draw attention to the tension that may exist in the MI classroom between strict guidance and the individual development of student ideas, and point out that in an MI classroom there is at times room for both kinds of interactions This tension represents one possible place of further investigation in future work What is the Curriculum? A key to understanding how the three elements of MI interact in the classroom is reconceptualizing what we mean when we say the Modeling Instruction curriculum As discussed throughout this sequence, the materials that the students interact with are only a 31 MODELING INSTRUCTION FOR UNIVERSITY PHYSICS small part of the instructional design As we have moved through discussing Days and 2, we have leaned heavily on the other elements of MI to understand the unfolding of the event The goals of the lesson, which are often communicated through the instructor guide, are important to understanding the instructor’s push toward the pie chart representation The instructor knowledge of the MTS and of the goal of having students participating in the building of the scientific conceptual models is important for understanding why he does not intervene when students are having trouble making sense of the ball stopping in the large group discussion Finally, the pedagogical content knowledge(Shulman, 1987) that the question of why the ball does not bounce as high will elicit the idea of energy contributed to the writing of the student materials and the questions the instructor uses We tend to think of curriculum as being simply a collection of the written worksheets with which students interact It is our hope that in unpacking the ways the three elements of MI interact to contribute to the unfolding of this event for the students that we have problematized this idea of curriculum Instead, we hope that individuals interested in the MI curriculum consider a deep understanding of the Modeling Theory of Science, the Modeling Theory of Instruction, and Modeling Discourse Management as essential pieces of the curriculum Conclusions An important part of the goals of Modeling Instruction has been to engage students in the practice of doing physics This practice of doing physics aligns the participationist perspective that learning involves the ongoing transformation of participation Thus, as students are engage in doing physics they are learning As we discussed in the Modeling Theory of Instruction section, we believe that an essential part of doing physics is developing and validating scientific conceptual models When we examine the practice of students in the second half of the paper, we see students doing exactly this We observe a small student group engaged in the process of negotiating the use and meaning of a representation that could help them understand the particular phenomenon in question Then we observed students comparing two specific models developed by two different groups In the board meeting the discussion leads to a consensus about the purpose of the different forms of energy This conclusion is essential to the process of developing a basic model that includes the law of energy conservation As students move through this process of developing specific models of phenomena and extending them to basic models agreed upon by the community of physicists, they are engaging in the process of doing physics The focus on models and model building encourages students to develop a deep understanding of what is important in physics, which is larger than either the concepts understood or the problem-solving skills developed We contend that a coherently developed and model-centric curriculum, pedagogy, and approach to learning promote participation in the practice of doing physics Modeling Instruction for university physics is one such example We have undertaken an analysis of classroom events to illustrate the process of students engaged in the complex process of model-building In Modeling Instruction, the instructor assumes the role of a physics expert and uses this expertise to select classroom activities, monitor and guide discourse, and promote student participation in the practice of physics We encourage instructors and researchers interested in reproducing positive results seen from the Modeling Instruction learning environment to consider the 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Science, Modeling Theory of Instruction, and Modeling Discourse Management In this section we describe the Modeling Theory of Science and in subsequent sections the Modeling Theory of Instruction. .. 1995) Modeling Theory of Instruction guides the instructional practices that engage students in authentic scientific practices The Modeling Theory of Instruction brings a coherent set of instructional... curriculum Instead, we hope that individuals interested in the MI curriculum consider a deep understanding of the Modeling Theory of Science, the Modeling Theory of Instruction, and Modeling Discourse