Embodied Science Learning: Students Enacting Complex ... - CiteSeerX

Embodied Science Learning: Students Enacting Complex Dynamic Phenomena with the HubNet Architecture Uri Wilensky Departments of Learning Sciences and Computer Science Center for Connected Learning & Computer-Based Modeling Northwestern University Tel: 847 467-3818 Email: [email protected]

Walter M. Stroup Department of Curriculum and Instruction The University of Texas at Austin Tel: 512 232-9683 Email: [email protected]

Abstract: The participatory simulations project brings together three lines of research—student understanding of complex dynamic systems, the use of participatory activities to augment student experience and the use of computerbased technologies to enable exploration of and reflection upon a domain of inquiry. These trio of goals can be significantly enabled and advanced through emerging network technologies. We argue that the study of dynamic systems stands as a new form of literacy – enabling us to track and make sense of the evolution of systems across time. Participatory Simulations Activities (PSA), on their own, are a powerful means for studying dynamic systems. But PSA can also support new forms of classroom interaction and can serve to prepare the way for engagement with computer-based systems modeling. To accomplish these goals, we introduce a new architecture, HubNet. HubNet is an open client-server architecture, which enables many users at the “Nodes” (typically handheld devices) to control the behavior of individual objects or agents and to view the aggregated results on a central computer known as the Hub. This network of nodes is integrated with a powerful suite of modeling, analysis and display tools that together give users the capacity to run the system in real-time mode, to reflect on the emergent result of their simulation and, also, to encode their strategies as rules which the system can then run independently. The HubNet system is in use in several middle and secondary classrooms. The results from this classroom work is analyzed using the framework of a design experiment. Two illustrative cases from the classroom use of this embodied approach to science learning are then presented and analyzed. Aspects of HubNet activity design and classroom pedagogical design are also discussed. Keywords: Simulations, modeling, emergence, mathematics education, science education, experiential education, computer-supported collaboration Introduction In this paper, we describe a new network-based architecture, HubNet, designed for enabling students to engage in participatory simulations of complex dynamic systems. Working together with a commercial partner, we are engaged in an iterative design and test cycle to refine the HubNet system and its associated activities. Early versions of HubNet have been in use in classrooms in Boston Massachusetts, Austin Texas. Chicago Illinois, Berrin County Michigan, and Salt Lake City Utah. This work is being undertaken under the auspices of the Participatory Simulations Project (PSP) – an NSF-funded collaboration between Northwestern University’s Center for Connected Learning and Computer-Based Modeling and the School of Education at University of Texas at Austin.

Embodied Science Learning

In the following sections of this paper, we introduce our project and illustrate two cases of its use in school settings. We begin with a brief history of the use of participatory simulations in math/science education, move on to describe the HubNet architecture and its design rationale. We then present the pedagogical principles and practice that govern our use of HubNet in classrooms. In the body of the paper, we present and analyze two classroom scenarios using HubNet. The first of these, the “Gridlock” activity recruits class members to control traffic lights in a city traffic grid. The collaborative goal of the activity is to optimize traffic flow. In the second activity, “PeopleMolecules”, students play the role of individual gas molecules in a chamber. Students’ goal in this activity is to pay close attention to the relationship between their own individual speed, as they move in the “chamber”, and the distribution of speeds in the class collective. We conclude by summarizing the cognitive and social affordances of the HubNet technology and then outline future directions for technology development, activity design and cognitive research. What’s a Participatory Simulation? Students engaged in a participatory simulation act out the roles of individual elements of a system and then observe how the behavior of the system as a whole can emerge from these individual behaviors. The emergent behavior of the system and its relation to individual participant actions and strategies can then become the object of collective discussion and analysis. While such participatory role-playing activities have been commonly used in social studies classrooms, they have been infrequently used in science and mathematics classrooms. Our use of the term participatory simulations is intended to refer to such role-playing activities aimed at exploring how complex dynamic systems evolve over time. Our focus is primarily on learning in science and mathematics classrooms For example, each class member could play the role of a predator or prey in an ecology and engage in a classwide discussion of the resultant global population dynamics. A wide ranging set of sample content areas for participatory simulations include the spread of a disease, the flow of traffic in a grid, the distribution of goods in an inventory system, the diffusion of molecules through a membrane, or the emergence of an algebraic function from a set of points (Wilensky & Stroup, 1999a). Why do Participatory Simulations and Emergent Activities Matter? A principal goal of the PSP is to research the use of participatory simulations as a way into complex systems thinking as a new form of literacy for the public at large. During recent decades, there has been a recognition of the importance of understanding the behavior of complex dynamic systems—how systems of many interacting elements change and evolve over time and how global phenomena can arise from local interactions of these elements. New research projects on chaos, self-organization, adaptive systems, nonlinear dynamics, and artificial life are all part of this growing interest in complex systems. The interest has spread from the scientific community to popular culture, with the publication of general-interest books about research into complex systems (Gleick, 1987; Kauffman, 1995; Kelly, 1994; Holland, 1995; Waldrop, 1992). Several educational projects have recently arisen with the goal of incorporating new complex systems content into science curriculum (e.g., Jacobson, 200x; Hmelo, 200x). These projects offer exciting new content. In our view, however, focusing on complex systems content misses a major opportunity-- the study of dynamic systems is not just a new area of study for scientists. Our stance is that the study of dynamic systems stands as a new form of literacy, a new way of describing, viewing, and symbolizing phenomena in the world. As such, a complex dynamic systems approach transforms virtually the entire curriculum, reconceptualizing traditional content and opening it up to an account of dynamics. The language of the current mathematics and science curriculum employs static representations. Yet, our world is constantly changing. This disjunct between the world of dynamic experience and the world of static representations stands as one source of student alienation from the current curriculum (Chen & Stroup 1994; Wilensky & Reisman, 1998). By enabling the study of dynamics, we empower students to gain powerful access to understanding phenomena as diverse as weather, evolution and origin of life, food web ecologies, or kinetic molecular reactions. Research in mathematics/science education and cognitive science (Chi et al, in press; Jacobson & Angulo, 1998; Mandinach & Cline, 1994; Resnick, 1994; Wilensky, 1997b; Wilensky & Resnick, 1999) has documented that students have considerable difficulties in making sense of complex systems. In particular, Resnick and Wilensky (1993) have documented the considerable difficulties people have in making sense of emergent phenomena, global patterns that arise from distributed interactions, central to the study of complex systems. This constellation of -2–


difficulties in understanding emergent phenomena and constructing distributed explanations of such phenomena has been labeled the “deterministic/centralized mindset” (Resnick & Wilensky, 1993; Wilensky & Resnick, 1999; Resnick, 1996). Our aim in the PSP and in developing the HubNet system is to be catalytic in helping secondary and post-secondary students move beyond the deterministic/centralized mindset and advance their understanding of how systems unfold and develop over time. By acquiring the facility with systems thinking, modeling and emergence they gain fluency in thinking about change and complexity. The theoretical and computer-based tools arising out of the study of dynamic systems can describe and display the changing phenomena of science and the everyday world. A core conjecture of the PSP is that the affordances of participatory simulations, as supported by networked modeling and analyses tools discussed below, provide a powerful way into systems related sense-making that can help realize the vision of systems learning for all students. What’s New in the Participatory Simulations Project? The PSP is breaking new ground in two important areas: On the design and implementation side, we are developing and deploying innovative networked classroom-based technologies to enable learners to have new kinds of experiences – experiences that connect their evolving intuitions with powerful modeling and analysis tools. On the learning research side, we are pursuing fundamental research into the kinds of learning about systems and complexity that can be achieved through the use of such network-based interactivity. By interconnecting the artifacts created from learner activity with powerful modeling and analysis tools the enactive aspects of participatory simulations stand to be deepened and extended. Additionally, learners working in the networked environment make overt and visible their strategies in relation to generating different kinds of emergent behavior. In so doing, these strategies become increasingly well-articulated and refined in ways that scaffold both learner understanding of complex systems and the actual use by learners of the tools themselves. Through the participation in and analysis of emergent activities, we expect learners to come to see the tools as increasingly useful in helping them to further articulate their insights into the emergent behavior of complex systems. These tools enable them to analytically understand these systems, in effect working with the mathematics of change without needing to master the formalisms of differential equations. Additionally, the technology enables the students to back up the activity and go down a “road not taken”, examining what-if scenarios. For researchers, the network-based activity enables data collection and capture and the saving and replaying of classroom activities, making visible learners’ ideas and ways of organizing their experiences, which should significantly advance our understanding of these forms of emergent learning. A Brief History of Participatory Simulations The first major instance of which we are aware where a participatory simulation was used in the context of systems dynamics and systems learning was The Beer Game as developed by Jay Forrester and his systems dynamics group at MIT in the early 1960’s. There is a significant literature related to The Beer Game and interest in this participatory simulation has been recently revitalized as a result of its appearance in Senge’s widely read The Fifth Discipline (1990). The game does much to highlight the ways in which costly unintended behaviors of a system (in this case beer inventory in a distribution system) can emerge from participants attempting to act rationally in their localized role (e.g., as beer retailer, wholesaler, distributor, or producer). A number of other such PSA were developed at this time. One popular PSA, FishBanks (Meadows, 1986) was developed by Meadows as an “interactive, role-playing simulation in which groups are asked to manage a fishing company.” Students try to maximize their assets in a world with renewable natural resources and economic competition. More recently, a new generation of so-called “agent-based” (aka object-based) participatory simulation activities have been developed (Resnick & Wilensky, 1993; 1998; Wilensky & Resnick, 1995). In these so-called “StarPeople” activities, participants typically play the role of “ants” in an anthill simulation, moving around the room and exchanging “messages.” After participating in these StarPeople activities students observe the emergence of global patterns from their local interactions. These pattern become the objects of reflection and whole group discussion. Participatory Simulations Activities and Computational Tools Throughout much of the fifty-year history of participatory simulations computational technologies have played a central role. The systems dynamics group at MIT developed a class of computational “flight simulators” to be used by individuals and groups of managers to gain experience flying a complex dynamic system like a modern business. -3–


More recently, multi-player networked versions of the beer game have been implemented (Coakley et al, 1995) and it is now even possible to immerse oneself in multi-player versions of the game over the Internet (Powersim Corporation, 1998). The Participatory simulations project has also developed several multi-player versions – both a calculator-HubNet-based version (Stroup & Wilensky, 1999b) and a computer-HubNet-based version (Wilensky & Stroup, 2003) of the beer game participatory simulation have been implemented and used with both school-aged and adult learners. Management trainers have argued that there is a need for a tighter coupling between computer simulations and user experience. In possibly the first known use of the term participatory simulations, Diehl (1990) constructed systems that gave users more control over and participation within the simulations by allowing users to input more real word decisions and view output of familiar reports. These simulations were modeled using finitedifference tools like STELLA (Richmond & Peterson, 1990). In contrast to the “aggregate” finite-difference computer modeling tools used to analyze simulations like The Beer Game, a newer set of simulation activities have been designed to be further explored using agent-based computer modeling languages such as NetLogo (Wilensky, 1999) and StarLogo/StarLogoT (Resnick, 1994; Wilensky, 1995; 1997a). Borovoy, Colella and fellow researchers at MIT (Colella et al, 1998; Borovoy et al, 1996; 1998) have developed wearable computational badges (or “thinking tags”) that allow users to move freely while communicating information between badges. Disease propagation models are natural candidates for this kind of technology and have been implemented by a number of researchers and curriculum developers (Stor & Briggs, 1998; Colella et al, 1998). A significant innovation in this project is a commitment to exploring the complementarity of these two fundamental kinds of dynamical systems modeling – aggregate and agent-based approaches. This compels a careful attention to a) the relationships between understanding macro- and micro-levels of a system (Chen & Stroup, 1994; Wilensky, 1993; 1997a; b) thinking in levels (Wilensky and Resnick, 1999); c) systems thinking (Roberts et al, 1990; Mandinach & Cline, 1994); and d) the analysis of particle systems such as gases (Wilensky, 1994; Wilensky, 1999b; Wilensky, Hazzard, and Froemke, 1999; Stieff & Wilensky, 2003; Levy & Wilensky, 2004). Through the use of participatory simulations and attention to the kinds of constructs learners articulate and extend in relation to both the aggregate and agent-based modeling environment, we expect to gain deeper insights into how these kinds of distinct but interrelated forms of analyses interact and complete one another. What is HubNet? HubNet is the name we have given to a networked architecture we have designed to give students the experience of participating as elements in a simulation of a complex dynamic system. HubNet is an open client-server architecture, which enables many users at the “Nodes” to control the behavior of individual objects or agents and to view the aggregated results on a central computer known as the “Hub”. This network of nodes is integrated with a powerful suite of modeling, analysis and display tools that, together, give the capacity to “fly” the system in intuitive mode, to reflect on the emergent result of the simulation and to encode student strategies as rules which the system can then run independently.

Figure 1. Students engaged in participatory simulation using the calculator HubNet network. On the left each student sees her/his own calculator view. On the right is the projected classroom display of the emergent result.

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The HubNet architecture was developed in stages. Much of the research reported on herein employed a workable subset of full HubNet functionality. Substantially more of the full design is implemented at the time of this writing. The calculator-HubNet system consists of 1) a network of graphing calculators called TI-Navigator developed in concert with our commercial partner, Texas Instruments. 2) A server, which talks to the TI-Navigator network and 3) a multi-agent modeling language, NetLogo (a successor to the StarLogoT (Wilensky, 1997a) language). NetLogo enables users to build agent-based models of systems consisting of thousands of distributed elements. 4) A shared public display space such as a computer projection system that enables participants to observe the evolution of their simulation. We are currently extending HubNet to integrate aggregate modeling languages, such as STELLA and Model-It, extending the dialogue between agent-based and aggregate approaches.

THE HUBNET ARCHITECTURE Computer Projecting Traffic Simulation

Calculator Network Proprietary

Public NetLogo Modeling Layer NetLogo Activity Scripting Layer

Browser Interface

Low Level Control and Communication

Exposed API

Wireless Communication

Other Applications : STELLA Spread Sheets ESCOT

Other Networks of Arbitrary Clients Internet Devices Palm OS Bluetooth (planned)

Graphing Calculators Controlling Individual Traffic Lights

Figure 2. The HubNet architecture. Many more analysis and display tools will also be integrated, as well as ‘hooks’ allowing a much wider array of node hardware. In some of the research reported on herein, an early wired version of the TI-Navigator network was used. Current versions of TI-Navigator run on a wireless network. HubNet Design A potential barrier to wide-spread adoption of networked activities is the difficulties in authoring new PSA. Our Javabased development effort of NetLogo improves on and extends the agent-based modeling capabilities of StarLogoT by having the NetLogo language also serve as an authoring language for the creation of HubNet-based participatory simulations. Just as agent-based models are extensible (Wilensky, 1997b, 1999b), the network-based emergent activities created in NetLogo are extensible. Under the HubNet design, the parallelism of NetLogo as a modeling environment is being significantly extended to also serve as a way of coordinating and authoring activities for a space of networked computing devices (nodes). The HubNet architecture is designed to be open to a wide variety of node clients including many handheld devices as well as internet hosts. For a number of design reasons, we have focused our work so far using TI graphing calculators as the nodes. A significant reason for this choice is the substantial presence of such calculators in secondary school mathematics and science classrooms. There is a large user base of students and teachers. The density of such calculators in classrooms allows for easier adoption as the incremental hardware costs are manageable (each classroom need only acquire one internet-enabled computer and the Navigator network box). Other reasons for this choice include the robustness of the devices themselves (they pass the “drop test”), the low maintenance costs, the significant resident functionality and the large training and support network available for teacher professional development (e.g., T-cubed3). 3

Teachers Teaching with Technology – the Texas Instruments professional development organization. -5–


The calculator can also interact with real world devices such as sensors and motors, CBLs (calculator-based laboratories) and CBRs (calculator-based rangers), allowing for a wide range of participatory simulation activities to be implemented in the classroom. Additionally, calculators can upload and download data sets, upload and download programs (e.g., applets), monitor key-presses at the hand-held level, support real-time interaction as in network computer games, and form collaborative groups of various sizes (e.g., peer to peer, small groups, and whole class modes). These reasons for using the proprietary TI Navigator network are compelling for current classroom use. But, the HubNet architecture itself is general and can work with any network of nodes. We have started using personal digital assistant (PDA) devices such as Palm Pilots, WinCE devices, cellular phones and, of course, internet-enabled computers4 with the HubNet system. HubNet supports fully networked modes of interaction with and among learners. While synchronization between the data on the handhelds and the Hub is supported in this model, the model can also support on-going, real-time interactivity and exchange (Figure 2). In the ensuing sections of this paper, we describe two HubNet activities in detail. One of these, the Gridlock activity, involves students interacting with the network in real-time. In this activity, students assume control of stoplights in a city traffic grid. Simulated cars move through the grid and, by pressing a key on a handheld, the color of a light changes in real time. Students work to create the best traffic flow they can. The second activity, the PeopleMolecules simulation is an example of synchronized interactivity. In PeopleMolecules, students play out the role of individual gas molecules in a chamber. Each “molecule” has a motion detector attached to it, which captures its speed as it moves about the chamber. This data can then be analyzed locally on the handhelds or uploaded – synchronized with the HubNet system for replay and analysis. These activities will be discussed in detail in subsequent sections of this paper. A design goal of the HubNet network is to support a range of different topologies for collaboration among learners including person-to-person, small group and whole class interaction. This inclusive range of interactivity and richly textured forms of collaboration is vital for supporting the widest possible range of participatory simulation activities. Methods Borrowing from aeronautics where there is the need for the simultaneous interaction of research and design, Collins and Brown articulated a methodology of design experiment (Brown, 1992; Collins, 1998). In the context of research on the learning sciences, design experiments focus on an effort to create a new learning environment while simultaneously carrying out a careful investigation of the cognitive affordances of the new environment (Suter & Frechtling, 1998). Our effort to develop and extend the HubNet learning environment, while simultaneously investigating the power of participatory simulations as a way into systems learning, fits this top-level description of a design experiment. The account herein of pedagogical and activity design as well as classroom implementation results from the cyclical and sometimes simultaneous process of design and research. The research reported on herein was conducted in three eighth grade classrooms in two middle schools, an urban low SES school in Austin Texas and a suburban middle-income school in the Boston area. The participatory simulation activities were integrated into already planned mathematics and science units in these schools. In the Boston class, they were integrated into an eighth grade general science class. In the Austin school, we report on activities run over the course of a year in both an eighth grade mathematics and an eighth grade science class. All class sessions in which PSA were run were observed by the research team. We kept field notes of classroom observations and videotaped each class session. Videotapes were coded and analyzed and representative cases were then selected for further analysis. Videotapes were shot and analyzed in a way that allowed us to associate student comments and actions with the evolution of the projected simulation. We used various approaches to making students initial thinking “visible.” 4

At the time this goes to press, computer-HubNet , which works on any internet-enabled computer, has been developed and is in use in a variety of both in-school and out-of-school settings. Because computer-HubNet can rely on the client computation of a computer, it can enable large numbers of distributed users to participate in a simulation. In this paper, when we refer to HubNet, we mean what we now call calculator-HubNet to distinguish it from the computer only version. -6–


These approaches included video-taping whole-class discussions before running a simulation as well as analyzing students’ individual written responses a series of short-answer and open-ended questions. Development in thinking was evaluated both during the simulation but also afterward by reviewing videotaped post-simulation class discussions. Individual responses to questions similar to those used in advance of running the simulation were also used to extend the cycles of research and design. We have chosen two significant examples that engage challenging “content” to illustrate our findings from this ongoing design experiment. These examples highlight, to a significant degree, the development of learners’ systems related insights as situated in iterative network-based simulations. Activity Design We believe that participatory activities using HubNet can effectively support a wide range of learning activity and that, in the long run, a technology like HubNet that supports this level of interactivity will be widely adopted in classrooms. To help in our efforts to understand and support this evolution in classroom practice, our activity development has come to be structured by a set of general design principles. 1) We endeavor to strike a balance between two competing curricular agendas: the desire to help students understand important aspects of the traditional curriculum and the desire to support the introduction of fundamentally new systems ideas like emergence, feedback, and self-organization into the curriculum. Rather than develop activities that are narrowly of one kind or the other, we look to instantiate this balance in each activity. At a practical level, this means that for activities that are more transparently linked to the traditional curriculum, we try to draw out significant connections to system ideas. For activities that are more deliberately about dynamic systems, we highlight connections to important ideas in traditional curricula. In the PSP, we are targeting areas of the curriculum that are currently identified as “hard” for students to learn. It is these potential “high gain” target areas that do the most to illustrate the long range potential of HubNet supported participatory design. 2) We look to develop activities that enable learners to connect the content to be learned to their personal experience. Primarily, we do this by authoring activities that actually give new experience to the students, a kind of experience not usually available to them in their daily life -- the experience of seeing the connection between their individual (micro- level) behavior and a classwide pattern (at a macro- level). We also look for opportunities to leverage personal experience gained outside of the classroom (such as knowledge gained in navigating the world) in order to enable learners to more easily enter into a participatory simulation activity. 3) We look to develop activities that are generative. Generative activities are what we describe as “space creating” activities (Stroup, 1997; 1998). By “space-creating” we mean we try and develop opportunities for students to explore or create a space of possible responses to the activity and then to make sense of patterns that structure that space. This approach stands in sharp contrast to typical science classroom activity that seeks to collapse the space of student response to a single highly constrained response or behavior (e.g. a point in an activity space). There are, for example, lots of ways of controlling traffic in a traffic grid. Rather than immediately collapsing this multiplicity to a single “right” approach that is leading the students to “discover” the “optimal” solution, we want students to generate a space of ways of controlling traffic. 4) We aim to develop activities that highlight the process of modeling and the power of “embodied” sense making. This does not, necessarily, mean that our simulations are exact replicas of the systems they represent. The simulations model some aspect(s) of the systems they are about. But as is true for models and simulations developed at the frontiers of science, the models that often teach us the most are the models that differ in important ways from other models we know or even from the underlying reality they render. Good insights are often found in these gaps. Indeed, the recognition and understanding of the nature of these gaps is at the heart of scientific modeling and inquiry. Contrasts are as important as convergences for helping learners make the most sense of models and the modeling process and to relate the models to real word phenomena. In the PeopleMolecules activity discussed later in the paper, it is not that students moving about with motion detectors behave exactly like the molecules of a gas but rather that there are some aspects of simulating molecules in this way that will help students construct an understanding of kinetic molecular theory and how it is that one might come to believe that such a theory might be developed. We

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have found that, for the purpose of making sense of classical concepts such as the Maxwell-Boltzman distribution of gas molecule speeds, the contrasts between the distributions of speeds of the students in “PeopleMolecules” and the classical distribution are as useful as the similarities. Pedagogy Design From a pedagogical point of view, participatory simulations make good use of the social space of the classroom (or other group setting). Each student is actively involved in the simulation – taking advantage of the parallel architecture of the network. Moreover, beyond the individual students, the class as a whole is engaged in the activity through observing, modifying and discussing the publicly shared projected space. The PSP activities afford putting learners’ creations at the center of developing understandings in this social space. We extend existing approaches to learning in a social space (e.g., Abrahamson et al, 2000) by being attentive to the shape and flow of discourse in the classroom and to the ways in which individual voices interact with and co-evolve with levels of group discourse. At the same time we are attentive to the ways that such collaborative technologies can transform traditional construction of understanding in a social space by creating new forms of inter-action. New forms of computationally-mediated gestures, like turning on or off a traffic light, are supported by the system. Similarly, new kinds of computationallyrendered artifacts, like graphs of traffic flow, are generated. We have developed an iterative pedagogical design that supports both extending and transforming traditional forms of individual voice/group discourse interactivity. At the center of this design is making thoughts and ideas visible in real-time for both the teacher and the students. The pedagogical model for running PSAs in classrooms proceeds in a number of steps: The first step in our iterative pedagogical design is making the goal of the activity clear. For the Gridlock activity the goal is to prepare a report for the Mayor of the City of Gridlock on how to improve traffic flow in the city. For the PeopleMolecules activity the goal is to begin to understand important dynamic aspects of gases, including the distribution of speeds, by “becoming” gas molecules and drawing from that embodied experience to explain features of the gas behavior. Next, we have found it very important that we ask students to tell us what they know about the central element of a given simulation. This serves to both catalyze the processes of students’ exchanging ideas and as a tool of ongoing assessment for teachers and researchers. For the Gridlock traffic simulation this means asking students to brainstorm the kinds of things that they know impact traffic. For the PeopleMolecules simulation we ask them what they know about the air in the classroom. Typically we have whole chalkboards full of ideas the students generate. At the same time we also gain top-level insight into their thinking. We can then contrast features of what they know initially with the kinds of understandings that develop from participating in the simulations. We are particularly interested in the ways in which student’s understandings of systems shift from an early attention to relatively static features of a particular context to the dynamics and structural aspects of the system. With the Gridlock simulation students often begin by listing things like “potholes” and “time of day” as affecting traffic. With the PeopleMolecules simulation they begin by listing features like “transparent” or even “weightless” to describe air. These ideas are important starting places for the exchange of ideas and they are important because they highlight the ways in which their previous learning has highlighted static descriptions of their environment and backgrounded the dynamic interaction and structure of these systems (e.g., how volume of traffic associated with particular times of day creates patterns of traffic flow or how the dynamics of gas molecules create a stable “weightless” experience of air). At this point, we typically run the simulation activity. The first time through we begin by having students explore the kinds of actions and gestures they can make in the simulation before actually capturing the data from the simulation. For the Gridlock simulation we often have them become familiar with turning on and off lights before we put cars in the simulation. For PeopleMolecules we have them practice moving around in an enclosed space before turning on the motion detectors. We also draw attention to the interpretive features of the simulation like how the color of the cars might change as an indication of their speeds or how a particular graph is coordinated with aspects of the simulation itself. These interpretive features often require a round or two of running the simulation. Only then do we run the actual simulation – that is students engage in the participatory activity with instructions to pay attention to a particular aspect of the simulation. For Gridlock this means encouraging students to think about ways of improving traffic flow. For PeopleMolecules this means they being attentive to how their individual molecule behavior interacts with the behavior of the “gas” as a whole.

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Next is a reflective stage where students articulate, describe and explain what they have observed. Examples of these observations for the Gridlock simulation and the PeopleMolecules simulations are discussed later in the paper. A range of artifacts are appealed to in these reflections from the visible display of the number of cars at a traffic light to specific features of a histogram for a given “molecule”. In addition to co-evolving strategies for understanding of the system, learners at this stage will articulate conjectures about how the system works and possibilities for repeating the simulations. The use of various built-in analysis features of the calculator (e.g., histograms of one’s own movement), using analysis features of NetLogo (e.g. replaying the data from the “molecules” with the data from each molecule being associated with the motion of a particular agent in a NetLogo display), or using other analysis tools like spreadsheets to compute tables of difference. At this reflective stage learners often will begin to critique the model itself in terms of ways of making the simulation better. Because the simulations are extensible, changes can be made on the fly or – more typically – in preparation for a subsequent day. Sometimes the model might not actually have to be changed but the act of trying to clearly articulate how the behavior of the model would have to be different is itself a very powerful sense-making activity. The discourse of the classroom and the ways individual students give voice to their ideas become richer. A next step is to repeat the simulation in a way that is a refinement of earlier efforts. This refinement can be in pursuit of a particular way of replaying the simulation or a set of cases to explore (e.g., scaling some of the distinct strategies identified by learners). It is also possible to move to running models that are not participatory but with insights that come from the participatory simulations. Running PeopleMolecules can scaffold engagement with agent-based models of gases such as GasLab (Wilensky, 1999b; Wilensky et al, 2000) as students use their common simulation experience as a starting point for understanding gases as emergent from individual molecule’s behavior. The five steps of this pedagogical design can then be repeated. With each iteration the texture of interaction becomes more nuanced. Student descriptions shift to be more dynamic and structural as will be evident in the sample activities described in the next section.

HubNet in the Classroom – Illustrative Examples Most of our work in classrooms has been in middle school and high school science and mathematics classes. Typically we have worked in low SES settings. We are also committed to working with low “track” classes. Class sizes have varied from a low of eight students to a high of fifty-one. In nearly every case the teachers have had very limited familiarity with computational technologies and so these activities were quite new for them in many ways. It is also the case that participatory simulations create special challenges for teachers in terms of how to make best use of student-generated ideas. In discussing the kinds of learning occurring in relation to the two examples discussed below, we will also highlight some of the challenges for teachers. A significant focus for the recent activity of the project has been on supporting teacher learning in relation to running participatory simulations in their classes. Each simulation discussed below centers on a scenario that is meaningful to students and for which the class as a whole has a goal to accomplish. By playing a role in the simulation, the knowledge students develop is more situated and embodied than it would be from just being presented with the scenario alone. Students are not simply “active” in a participatory simulation, they are enactive5 and this stands to improve both student motivation and understanding. Student engagement and sense of ownership is further extended by the fact the students analyze the results they helped to create and can iteratively replay their actions and revisit the scenarios with ‘what-if’ questions that can be explored. Gridlock – Optimizing traffic flow through a simulated city grid Students are introduced to the Gridlock activity with the following scenario: “The mayor of the City of Gridlock is unhappy with the traffic situation in town. She has commissioned our class to improve the traffic situation in the city.” Consistent with the pedagogical design outlined above, this scenario makes it clear that the goal of the activity is for the students to find ways of optimizing traffic flow for the city. We have run the Gridlock activity in a variety of settings, from middle school science classrooms, to secondary social science classrooms, undergraduate and graduate 5

Enactive in a sense that is like the Aristotelian use of memesis – that is, enacting, representing or playing a dramatic role within a structured situation (Halliwell, 1987). -9–


education classes, and at research conferences. The responses of students reported below come from two instances of running this activity in schools. One instance is an eighth-grade classroom from a school with a relatively lowincome student population located near Austin, Texas. Twenty-four students are in this ethnically and racially diverse classroom. The second eighth grade classroom is from a moderate income, ethnically diverse school near Boston, Massachusetts. In the second school, students had significant access to computers for individual use and the use of the Gridlock participatory simulation occurred in a general science class, towards the end of a one month long special unit on modeling. As part of this special unit, students explored and constructed models of complex systems using the multi-agent modeling language StarLogoT (a precursor to NetLogo, see description above). For the school in Texas such resources were not available, and so the discussions and analysis depended on the then-current capabilities of the HubNet system. After the goal of the activity was introduced students were next asked what they know about traffic flow. The following exchange was from the Austin-area school: T: What are some of the things that you guys listed that would be indications that traffic would be good or bad to you? S: Accidents (laughter) T: (While writing accidents on the board) Oh great, now we’re going to do my spelling … Okay, raise your hand if I spell a word wrong. S2: Not enough lanes. S3: Speed bumps. T: Yah there are some speed bumps … S4: Autos S5: Pedestrians T: (laughs) “obstacles”. The listing continues until two chalkboards are filled with responses including: Construction Speed limit too high (causing more accidents) Special lanes for trucks Red lights too long HOV [high-occupancy vehicle] lanes Barrier walls too close for cars Not as many intersections The longer the light Roadwork Dangerous drivers Slow drivers Fast drivers Drunk drivers Wider lanes

Special events Getting bored Crashes Lots of cars Foot traffic Cell phone drivers Distracted drivers Storms/road conditions Debris in road (trees, trash, etc.) Stop signs Buses Animals 18-wheelers

The sense is that learners can articulate a wide range of factors that can impact complex phenomena like traffic. Some of these responses are behaviors of individual drivers and others are related to the structure of the roadways or context for the behavior (e.g., HOV lanes, lights too long, etc.). Taken collectively, this list suggests that learners do have an initial appreciation of how agent behavior in a context or environment can have consequences for the emergent features of a complex system. For traffic, this insight comes from their first person experience. Part of the purpose of participatory simulations is to leverage the learners’ first person perspective in a way that can lead to more robust, incisive and powerful understandings of complex phenomena. The teacher in both settings ran the NetLogo traffic simulation and projected the computer screen in front of the class. At first, students were not logged into the HubNet network. The projected simulation starts running with cars driving east and north through the city. The city starts off with no traffic lights (Figure 3).

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Figure 3. Traffic flow with no lights. The traffic moves in two directions, left to right or up to down. A graph depicting the number of stopped cars also dynamically updates.

Figure 4. Traffic flow with no lights. On first impressions, it looks like everything is running smoothly for this city. The average number of stopped cars is close to zero and this low number is confirmed visually by cars appearing to stop only occasionally. The problem is that the initial run of the simulation doesn’t keep track of when cars are occupying the same location on the grid.

Figure 5. Accidents quickly result.

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In real life, two (or more) cars trying to occupy the same location is called a crash. If the upfront simulation now shows these crashes – denoted with red crosses – every intersection quickly has a red cross on it (Figure 5). Traffic comes to a complete standstill. The initial introduction of the participatory simulation is continued by adding a single traffic light. When the simulation is run again, the teacher can turn the lights at the intersection green and red using a switch on the NetLogo interface (green in one direction means red in the other). It soon becomes apparent that accidents re-emerge at every intersection except for the one with the traffic light. Then additional lights are added and the accidents cease at those intersections as well. The issue then becomes: how should the traffic grid be controlled? Pedagogically the next step is to run the participatory simulation. In both classrooms students were asked to first arrange groups of desks in a grid matching the grid pattern of the projected computer grid. The first challenge for students is to figure out which light they control. Students flash the light at their intersection in order to make sure they know which light they control. Their immediate identification with the light is evidenced by the ensuing cacophony of exclamations such as “where am I?”, “that’s me that just flashed”, “where are you?” “come on , change already” and so forth. As can be seen in the following transcription from the Boston-area school, students start off exploring features of the simulation. Initially the lights are controlled manually for each of the intersections in the grid. In the transcript from the ‘run” described below, we pick up at a point early in the “run” when one light doesn’t change and cars pile up behind it. Students laugh – laughter fills the room. Student 1: Eve6 change your light A chorus of students: [exhorting] Eve! Student 2 (Eve): I’m trying, but it’s not changing. Student 1: It takes a little while. Student 2: There, it changed. Why is it so slow? Student 1: It takes a while to respond. Teacher: In real traffic, it takes a while too. Human reaction times aren’t immediate. Students get very animated and are abuzz with excitement in trying to control traffic. Student 3 (Alex): Eve, you’re blocking the cars from getting to me; you have to pay more attention. Don’t just look at your light, watch the lights near you. Researcher 1: So…, what is your name sir? Student 3: Alex Researcher 1: So, there was an interesting idea: Alex says instead of watching just your own light, you could try to watch the lights near you. Alex: If the light behind you just changed, then you should change yours. Student 4: Or maybe if you see a pack of cars coming, just change automatically? Couldn’t we write that? [meaning the program code] We could count the number of cars behind each light. Couldn’t we use ‘who-maxof-patches’ to find out which light has to change? Researcher1: you could write a reporter7 that would return that for you… Teacher: Yes, this model isn’t that much harder to write than the regular models we have been doing. The language to write this is very similar to StarLogoT, it’s called NetLogo and Student 4: Couldn’t we try to make all the lights red and just have one green? Student 3: I’m trying to write the rules Meanwhile, traffic accumulates at Alex’s light. Student 4: Alex, you’re losing it. Push a button, push a button. Researcher1: you’re getting pretty good at this real time task. Let’s make it a bit harder. Student 5: increase the number of cars? Teacher: I’ll increase the number of cars. 6

All names have been changed but gender has been kept constant. A reporter is a procedure that returns a value. In Logo languages it stands in contrast to a “command” which has an effect but returns no value. 7

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Frantic light changing ensues, but despite their best efforts, the city is gridlocked (all the cars are stopped). Student 6: It’s stopped! Teacher: This happens in real cities too. Student 7: It’s just because we’re slow to press the buttons. Teacher: But real cars don’t start and stop on a dime either. We see the students make spontaneous connections to other (non-school) areas of their knowledge and begin to generate strategies for controlling the traffic. Very subtle questions about logic, timing, phase and synchronization are engaged as students struggle both to create ways of talking about the traffic that are meaningful and to implement strategies that make use of their new traffic-language.

Figure 6. Uncoordinated Traffic

Figure 7. Lights synchronized

One of the spontaneous strategies we have seen repeatedly is to synchronize the lights with a phase shift – so that lights change at different times, but in planfully choreographed ways. Uncoordinated traffic is shown in Figure 6. In Figure 7, the lights in the top row turned green in the same direction together, then the lights in the second row wait a few seconds (phase shift) and turn green. This pattern cascades downward as traffic flow in that direction is synchronized. There are many different ways to cascade the synchronization. Choosing amongst them engages the students in an inquiry cycle of argument (for and against a strategy), implementation (of a synchronization strategy), empirical testing (of the strategy against the model output) analysis (how did the strategy do?) and revision (a new strategy) Because we had seen the coordination issue arise in many classrooms, we had implemented the capability for students to set individual phase delays for their respective lights – enabling a wide array of possible strategies8. Picking up the Boston exchange again, the students have now reached a reflective stage in the pedagogical sequence. They begin to articulate a need for this kind of “phase” coordination of the lights. Initially the students articulate manual strategies for implementing a delay between the lights. They are then introduced to this feature in the participatory simulation and proceed to use it. The pedagogy is iterative: implement a strategy, reflect on the results, articulate a modified strategy and then run the participatory simulation again. Teaching Assistant: May I say something? Teacher: Sure. Teaching Assistant: I learned in social studies that England has an amazing system of locks and barges. It was about 100-150 years ago that they centralized control of these canals so that individual land owners would no 8

While the implementation of individual phase delays does enable students to explore a diversity of possible coordination strategies, it is still a small subset of the set of possible strategies. In current versions of Gridlock, we have implemented a simple interface in which students, after having tested their strategies in “real-time” can encode these strategies to run automatically. - 13 –


longer be able to charge tolls in order to get through because if you took one route you’d be stuck at the discretion of the landholder. And they centralized, instead of doing, like we’re doing now, have 12 individual people or controls over the canal system, they made it so that there would be one overarching set of rules because a model like this creates too much screaming and too much pressure. The need to coordinate strategies becomes clear for the learners. Student 7: So, let’s see if we can coordinate the lights. Student 4: But, this way is fun. Student 5: It’s fun for them [the light controllers] but it’s not fun for the people in the barges. Researcher 1; (joking). It’s beyond the decentralized mindset. Student 5: yeah, people are not ants. Teacher: There is an auto mode. Student 8: We could change the lights every 20 seconds Student 2: Or some could change every 30. Student 9: This is so cool! Student 3: Yeah. …. Researcher 1: We have an auto mode that makes it easier to coordinate the lights [in this way]. Let me set it up in auto mode. Researcher 2 explains how to get into auto mode and segues into a discussion amongst students of what is the “phase” quantity. The feature is connected with a felt need expressed by the students. Researcher 2: Now what does phase mean? Student 8: It’s like the number of seconds maybe? Student 10: Or the number of cars that pass before the light would switch? Student 8: The number of beats…. Researcher 1: It’s now in auto mode. Researcher 2: So there’s a clock that goes 1 – 100 and whatever number you enter controls the phase of your light. Student 9: So we have to decide what numbers to put in for the phase? Teacher: Do you guys understand? It’s like a clock, say a 60-second clock. You have to decide if your light is gonna change when the second hand reaches the 1, the 2, the 3, the 4, the 5. Right now everybody’s clock changes when it gets to the 12. Student 9: Everybody could just type in 50. Teacher: But then you’re all switching at the 6 and that wouldn’t make a difference. Student 9: Yeah, we have to make ‘em different. Researcher 2: The question is what would be a good way to do this phase? Student3: We should alternate. 0, 50, 0, 50. Student7: How ‘bout we just put random numbers in? Student 9: Can’t we just do them all the same? Student7: That’s what we have been doing., we want it different this time. Let’s do the random. Researcher 2: Okay, what do you think will happen if we try random? Student7: I think it’ll be exactly the same as before – random won’t help the traffic flow. Researcher 1: Okay, why don’t you all put in your random numbers.

Students enter a phase number in their calculators and restart the simulation. The first time they try the “random” strategy, traffic gets severely backed up and gridlock swiftly ensues. They try it several more times modifying their random numbers to try and get more coordinated behavior amongst the lights. Several iterations of this activity are tried out. The students begin to discuss whether the random strategy is an improvement: Student3: See, the traffic got worse. Student7 [Carol]: But, it shouldn’t – something’s wrong. Teacher: Carol, Can you say more about why you think it should get better? - 14 –


Carol: It’ll get better ‘cause they’re [the lights] not all changing at the same time. Student3: Won’t that make it worse? Carol: No. “cause the cars will be leaving the intersections at different times, so they won’t all be bunched up – there will be less jams. The above transcript we see students reasoning about “what-if” scenarios and trying to fit their intuitions about the traffic flow with the observed model output. In evaluating the “strategies” they give to the lights, the need for metrics, or ways of comparing results, arises in a natural, contextualized way. In considering possible metrics for traffic, this group of students felt that ‘number of cars stopped’ was not the best for quantifying results. Many other metrics are considered. S: I don’t think these numbers are as good as we did on our own. Teacher: You mean when you changed the lights manually? Student: Yeah. Student2: Can we compare the graphs? Teacher: Ok, we can go to the calculators and look at the saved graphs. Student1: The graphs look about the same, but the new graph is a bit higher at the beginning a bit lower at the end. Student2: and some in the middle. Student3: that’s probably where we got tired. The computer doesn’t get tired. Student1: But the graph only tells us how many cars are stopped. That’s not the whole story. There are many other things that could make a difference. Teacher: That’s a good point. … What we choose to measure could affect our assessment of good traffic flow. Student1: Yeah. Teacher: What other measures could we use? For the next twenty minutes the class engaged in a brainstorm and discussion of what possible ‘metrics’ they could use to measure traffic flow. Some typical examples are excerpted below: Student1: It’s not just the number of cars stopped, it’s how fast they’re going. Teacher: How fast? Student1: Yeah, like we could graph the average speed of the cars. Student3: Wouldn’t that be the same thing? Teacher: What do you think? Would it be the same? Student1: No. cause there could be lots of cars stopped but the other cars could be going real fast. Student4: But if lots of cars were stopped, doesn’t that mean the other cars would have to slow down and eventually stop cause they’re blocked? Student1: it depends on where they are, you know, if they’re next to each other. …. Student6: To have good flow, we’d want to make sure that it was fair. Teacher: fair? Student6: Yeah, like if the cars going down were waiting much longer than the cars going right, that wouldn’t be fair. Student7: And you’d want to know how long each car was waiting. Student6: If all the cars were going along fine and one guy was waiting a real long time, that wouldn’t be fair either. Student8: Depends on who it is. If it were Alex, I’d say it was fair. (laughter). Student6: Yeah, and if the mayor was waiting, he’d be mad and fire us. …. Student1: Don’t we care about the size of jams? I mean a city with huge traffic jams is going to be a mess even if lots of cars are merrily on their way. Student6: And then, we could switch the light depending on the size of the jam.

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The above excerpts show students engaged in a process of mathematization. They are beginning to see that not only do they have to select an optimal strategy, but that such a selection crucially depends on the metric they choose to evaluate the selected strategy. The supplied metric of “stopped-cars” becomes problematized and the students see it as one metric from a wide range of possible metrics. The task then is to argue for the value of a metric and then to see how the strategy does against that metric. The students argue for a set of factors that should be important for measuring good traffic flow and once these are selected they must represent those factors in a mathematical form so they can get comparable outputs than can be graphed and displayed. The class from the Austin area was also animated and engaged. Even without the same agent-based modeling background, they begin to articulate strategies motivated by the felt need to develop a coordinated strategy to improve the traffic flow. Teacher: Has anybody started to think of some ideas like what are you doing at your stop light that you think is working really well? Who has some ideas of why they think maybe their stop light is working better than somebody else’s stop light. Anybody have any ideas? Anything that you’re trying to do yet? Yeah (pointing to student). Student 1: Letting one go and then the other go. Teacher: Okay, so you’re letting one go … are you letting it go for a certain amount of time? Student 1: Nah, just go this and that way. Teacher: So you’re just doing one then enter, two then enter. … Student 2: Pick a space between the line of cars to turn the light red, so that way, so then all the cars will be stuck together. Teacher: So get the cars staggered and spaced out and pick a spot between … yes, sir (pointing to a third student). Student 3: Have it like every place where I saw the cars go like this (gesturing downward) and once they’re done have them all go like that (gesturing to the side). Teacher: So have the down ones green (gesturing downward with fingers extended) and then all the side-toside ones green (similar gesturing to the side). These are just some of the strategies students generate. The first strategy is simply alternating the lights at a regular interval. The second strategy looks for open spaces to shoot for in turning the light red in that direction. Other sections of classes at this school articulated what we call a “traffic cop” strategy where you simply look locally to see in which direction there are the most cars at your intersection, and then let that direction go (i.e., like what a traffic cop might do at a busy intersection). Some students discussed the possibility of developing “smart cars”. With smart cars there might not be a need for lights, if a way could be found to “coordinate” with cars coming from the “other” direction. As was true for the Boston area students, the Austin area students came up with a phase-related strategy for “synching” the lights. The actual classroom exchange related to this strategy highlights some of the pedagogical challenges related to engaging and extending the developing strategies of students. These issues help point to possible future directions for developing the HubNet functionality. In repeatedly reviewing the tape of the Austin area classroom, it is not clear whether Student3 meant for his strategy to be only for a particular column of traffic, or whether he, in fact, meant for the strategy to be applied to all the columns in parallel. The significance of the teacher having her fingers extended was to denote all the lanes in one direction working this way and then all the lanes in the other direction. In contrast, the student used only one finger to gesture downward and then the same finger to gesture to the side. This observation is made not to highlight any shortcoming of the teacher. Rather one take-away from running these activities in classrooms is that the kinds of activity and reasoning generated in relation to these activities is comparatively complex. The pedagogical load for teachers is clearly higher than it might be in a traditional mathematics classroom. Tracking student ideas in real-time as part of the iterative pedagogy associated with using participatory simulations is clearly more challenging than asking students to “simplify 2x+3x” on the board or on a workshop. Teachers we have worked with, however, see the challenge as worth the effort as they see a clear payoff in that their students are engaged with and making sense of important systems ideas,

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As one eighth grade teacher of mathematics reported after a few weeks of running the Gridlock and the Disease activities: When I’ve used it, it’s the excitement that comes through. Students who have never once opened their mouth, the entire time they’ve been in math class, and they get involved in this. There’s excitement. The interest, the not wanting to leave the room, but when they’re forced to, telling everyone they meet in the hall, just like, [whispers excitedly] hey Jim it’s math today. You never hear that -- the wanting to do more. When you’re just using the textbook, the white board or the chalk board, how many kids have ever said, can we do another one – uh uh, never happens, But on this, they want to do it over, and new, but what if we tried this what if we try that – it opens up all these avenues – things you want to have happen in your classroom, it’s there. This increase in student motivation and understanding is balanced by the greater demand placed on the teacher to make good use of all the artifacts, gestures, and verbalizations of students. In future development of HubNet functionality, we intend to expand on the ways of capturing and rendering student-generated artifacts and simulation outcomes so that the demand is lowered on the teacher and the payoff of increased understanding of student development is made more accessible to the teacher. As part of comparing results from implementing different strategies, the handheld devices (calculators) have significant resident functionality. Data from the simulation can be distributed to the class and then every student can use a set of mathematically meaningful analytic tools (graphs, tables, histograms, etc.) to analyze the results. The flow of information and the location of the tools of analysis does not remain “centralized” in this model. Instead a multi-directional (student to student, teacher to student, student to teacher, etc.) flow and exchange of analyses is supported in the HubNet architecture. In this traffic example, various metrics for measuring the improvement in traffic flow can be developed by students and a set of final recommendations can be developed as a report (or collection of reports) to the mayor. The reports can incorporate elements of both agent-based and aggregate analyses. Although on the face of it this traffic activity seems quite distant from the traditional curriculum, it is in the process of creating these metrics that students reach for and/or make sense of traditional metrics. This understanding is deeper not only because the learners must make sense of the mechanics of computing quantities like mean, median and mode, they must also struggle with the meta-issues of which representations or renderings of the data are most useful to the task of preparing a report to the Mayor. Learners must select which quantity or quantities to measure (e.g., wait time at lights, average speed across the city, number of stops, etc.). Not only is understanding deepened, but the toplevel question of “What is math for?” is addressed in a way that is interesting and engaging precisely because participatory simulations are complex. Traditional curricula assume you must start with procedures for computing before applying them. In contrast, we use dynamicism and complexity of systems like traffic to motivate the “need” for both the formal constructs of the traditional curriculum as well as new concepts related to systems thinking.

PeopleMolecules Participatory simulations can scaffold student understanding in a wide range of contexts from abstractions, like points on a graph (Wilensky & Stroup, 1999), to the imperceptibly small, like molecules in a gas. A standard component of most introductory chemistry curricula and many introductory physics curricula is the kinetic-molecular theory of gases. A very challenging aspect of this theory is developing insight and understanding related to the distribution of particle speeds for an ideal gas. Understanding that there are characteristic distributions for these particle speeds is fundamental to understanding how macro- properties of gases such as pressure and temperature behave as well as to understanding how and when chemical reactions may occur. When asked about the movement of molecules of gas in the classroom, there is little in students’ day-to-day experience that could support any understanding of why the molecules of gas would have differing speeds and why some aspects of the distribution of these speeds might remain constant. Why wouldn’t students believe, as many do, that the uniformity of their sensory experience in moving across a classroom extends down to the molecules and that means the speeds of the molecules are nearly uniform? Or why wouldn’t students who do have a sense that molecular speeds varying, also assume that there is little or no pattern in the distribution of these varying speeds? The goal in developing the PeopleMolecules simulation is to have students make sense of two core ideas: (1) that speeds vary for individual molecules and across the population of molecules due to collisions, and (2) that there are, nonetheless, top-level invariants like the distribution of speeds for an ideal gas (the Maxwell-Boltzman distribution). These invariants are related to the uniformity of students’ normal sensory experience and are what allow us to construct macroscopic constructs like pressure and temperature. We have run the PeopleMolecules simulation in a number of different settings. Although the teachers we have worked with - 17 –


have situated the activity in a number of different curricular contexts the pedagogical sequence has been similar and the results have been relatively consistent. The accounts that follow are from two different sections of middle school science class in the same Texas school discussed earlier and from the middle school science classroom in Boston. For the first classroom, the curricular context was a standard treatment of the phases of matter, with gases being just of the phases covered in the chapter. The curricular context for the second classroom was the planetary science section of a standard middle school science curriculum. In keeping with the pedagogical design discussed earlier, students in both settings were first asked what kinds of things they knew about the air in their classroom. Students mentioned a range of properties from the transparency (e.g., “you can’t see it”) to the idea that “it has water in it”. In one of the classrooms an interesting debate developed when one student listed as a property of air that, “You can’t feel it.” Almost immediately another student said, “Yes you can!” and demonstrated this by waving his arm through the air while saying, “You can feel the wind.” After a somewhat animated exchange between different factions aligning themselves with one of these two stances, a kind of rapprochement was worked out. You can feel air if you are moving but while you’re standing still you cannot. Both students and teachers talked about the composition of air with students often emphasizing the presence of oxygen and teachers stressing the additional presence of nitrogen and trace amounts of other important gases (e.g., carbon-dioxide and water). For all of these observations, and despite the fact that elastic collisions are typically discussed as part of textbook presentations of kinetic molecular theory, no students made mention of the collisions of molecules as playing a central role in “mixing” the speeds of the molecules. Likewise, the students made no mention of how a particular kind of distribution of speeds could characterize the molecules. The information emphasized in the textbook treatment of gases tended to describe the gas as a whole, not focusing on intra-gas differences and it tended to describe the gas in terms of static constructs such as – the composition of the gas, its density, its temperature and tended to background the dynamics of the gas – the fact that the gas particles were constantly moving and changing. These same sorts of constructs and descriptions tended to manifest themselves in students’ accounts. A principal design goal of the PeopleMolecules participatory simulation is to enable students to give a more dynamic account of gases and to be able to integrate micro-behaviors like moving around faster with macroscopic experience like increased temperature. To set up the PeopleMolecules activity, a bounded space, in which people “molecules” interact, is created in the classroom. This space is created by encircling a region of the classroom with paper. Some students hold up the “walls” of this container while other students are the “molecules” placed in the container (Figure 7).

Figure 7: Students moving around an enclosed space as if they are molecules. Each student “molecule” carries a calculator connected to a motion detector (Texas Instruments’ Calculator Based Ranger [CBR]). As these students moved around in this space their speeds varied. Motion detectors and calculators sampled and recorded each student’s speeds over a fifteen-second time interval. In this way data was collected for each “molecule” (student) in this “PeopleMolecules” gas (collection of students). At the end of the time interval, each calculator displays an individual histogram of sampled speeds. These individual histograms were then compared. While students were able to identify some similarities in the shapes of the distribution (e.g., “few out on the end” [few samples of relatively high speed]), for the most part they tended to see the various distributions as mostly different from each other. Often this sense of difference was judged relative to comparatively minor variances. Consistent with the findings from probability research that students often see any variance as meaning there can be “no pattern” overall (e.g., Tversky & Kahneman, 1974; Wilensky, 1993), the results from individual calculators - 18 –


seemed to be too “rough” to highlight, in a significant way, any top-level consistency. The students were generally quick to express the sense that the molecular changes in speed came from molecules interacting with each other or with the “wall.” Yet any sense of a consistent global distribution of speeds was not seen as significant relative to the variance. It was when the results were combined to get the distribution of speeds for the whole people-gas that consistent patterns between trials became more noticeable. The students did notice an overall asymmetric shape that built up toward the middle and then trailed off near the end. Two examples of aggregate results are show in Figure 8.

Figure 8: Histograms of “molecule” speeds for two trials of the PeopleMolecules activity. As has been true for nearly every time we have run this simulation, the aggregate histograms have local maxima near the lowest values of speed (e.g. the regions indicated by the arrows in Figure 8). Students’ account of why there are these relatively high incidences of the lowest speeds is that the molecules “slow down” before “hitting” and/or changing directions. Middle school students notice that there are a number of “slow” molecules in both samples (see the arrows in Figure 8). We get a lot of slow molecules, one student explained, because “we slow up to stop in front of people … and then we have to speed up again” and both result in a lot of slow speeds. People have social conventions for “collisions” that even middle-schoolers observe and these include slowing down. The students themselves advanced the explanation that this local, individual behavior shows up in the collective results as a local maximum for low speeds. Making Sense of the Maxwell-Boltzman Distribution In the first class , the PeopleMolecules results were compared to results from a NetLogo model of an ideal gas9. In this NetLogo model the rules for elastic collisions of an ideal gas are programmed in to the molecules, allowing for the interaction of thousands of simulated gas molecules (Wilensky, 1999b, in press).

Figure 9: GasLab model of an ideal gas with histogram of speeds closely matching the Maxwell-Boltzman distribution. This use of the NetLogo language highlights the sense in which this language is both a powerful environment for agent-based modeling and an environment for authoring network-based participatory simulations, like the Gridlock PSA discussed earlier. The GasLab model was projected in front of the class for discussion. The NetLogo model of an ideal gas was introduced to the students as being like a billiard table with lots of “very hard” billiard balls colliding 9

The model is taken from the GasLab (Wilensky, 1999) Curriculum. - 19 –


(Figure 9). In this activity, all the molecules in the model are initialized to start off moving at the same speed (with randomized headings). This is like having all the balls on the idealized billiard table start off moving at the same speed. This initial condition makes salient how local rules for collisions (elastic collisions for momentum and energy being conserved) both create variation in the speeds of the molecules and a stable, top-level distribution. There is a significant literature related to using this model alone in learning about gases (Wilensky, 1999b, in press; Wilensky, Hazzard & Froemke, 2000). What is new in the context of this paper is the way the results from running the PeopleMolecules participatory simulation interacts with and deepen the student understanding of the NetLogo model and of the Maxwell-Boltzman distribution of an ideal gas. Making Sense of Atmospheres We were, at first, somewhat surprised when one of the middle school teachers we worked with suggested that she wanted to use the PeopleMolecules activity in a standard unit on planetary science. She saw an immediate connection to discussing the atmospheres of earth and the other planets in our solar system. What we came to realize in talking with this teacher and others, is that they are very aware that the standard middle school approach to this curricular unit tends to be long on memorization, and relatively short on students actually understanding how features of the planets could come into being and how such features could be mutually supportive or antagonistic. Setting aside for a moment the manifest beauty of the photographs of planets found in textbooks and teacher resource materials, there was little from a conceptual point of view that was engaging to their students. The teachers knew from experience that students tended not to find compelling a simple listing of the values for gravitational acceleration found on different planets. They also knew that part of the problems was that these planetary facts did not end up being well-connected to the larger concepts that lie at the heart of planetary science. Against this backdrop it started to make a lot more sense to us that the teachers would see in the PeopleMolecules activity the possibility of advancing a more dynamic understanding of how features of atmospheres can make sense as emerging from the microscopic behaviors of gas molecules. At this point we relaxed our own sense that PeopleMolecules had to belong in a unit on phases of matter, and instead took up the challenge of having the activity support a more engaging approach to aspects of planetary science. Given that understanding properties of atmospheres was one goal of this unit, in this second classroom, we started this replacement unit not with the PeopleMolecules activity but with a NetLogo model of an ideal gas like the one discussed above. The molecules in this version are subject to gravitational acceleration and can “escape” the box out of the top of the screen. Like the simpler model discussed above, the molecules are evenly spread in a portion of the box and are all given the same initial speed (see left portion of Figure 10 where all the molecules are green and evenly spread in the lower half of the screen). The four “monitors” count how many molecules are located in each quarter of the screen. The model is then “run” and the students were asked what they noticed about the molecules. The students noticed that there were more molecules located near the bottom of the screen. The monitors confirm this by showing that there are significantly more molecules in the lower portions of the screen (i.e., 159 molecules in the lowest fourth as compared to 36 in the next quarter of the screen).

Figure 10. Simulated molecules start off evenly distributed in the lower half of the screen and then when the model is run the molecules become more dense in the lower part of the screen. Students began to “see” and remark that the atmosphere becomes less dense the higher one goes. At this point we used NetLogo to change the mass of half of the molecules in the system (see the left portion of Figure 11) and asked the students what they thought would happen. When the model is run with these settings, more molecules with a

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higher mass end up near the bottom of the screen. The heavier molecules are shown in white and the monitors confirm that there are more molecules with the new mass near the bottom of the screen (i.e., 81 versus 37).

Figure 11. Half the molecules now significantly increase their mass and when the model is then run, the more massive molecules become concentrated near the bottom of the screen (displayed as white). Not only is the atmosphere less dense higher off the surface but more massive molecules move lower in the atmosphere. Less massive water molecules can float up in our atmosphere and, under the right conditions, form clouds. As powerful as this sequence was in beginning the conversation about properties of the atmosphere, students also noticed the color changes of the molecules and wondered about the connections to speed and temperature. Additionally, the role the collisions have in changing the speeds of the molecules and the distribution was not manifest. The changing colors of the molecules in GasLab seemed to “set up” or scaffold the kinds of inquiry supported by the PeopleMolecules participatory simulation. The teacher wanted to make connections between molecules interacting and the distribution of speed (colors) in “hotter “ and “colder” gases. To do this, she ran PeopleMolecules again, but this time she had one group of students move like a cold gas when they were PeopleMolecules, and a second group of students move like a hot gas. As was true for the students in the first class, the students in this middle school class notice that the were a number of “slow” molecules in both samples (see the arrows in Figure 8 above). “We get a lot of slow molecules”, one student explained, because “we slow up to stop in front of people … and then we have to speed up again” and both result in a lot of slow speeds. Drawing from our experiences in the first class, a new network capability, “replay” was introduced for the work in the second class. The data collected by each of the “molecules” in the PeopleMolecules gas was collected by the network and imported into a simulated molecule. The molecules were then displayed in a projected NetLogo screen. NetLogo then replayed the motion data from each student so that all could see it in the projected display.

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Figure 12: NetLogo Activity Scripting Layer can Import Student Data to be replayed in NetLogo Modeling Layer For each student “molecule” the motion detectors recorded the speed at fixed increments in time over a 15 second interval. With this data now assigned to a unique agent in the NetLogo simulation, the motions associated with fixed increments of time are acted out by these simulated molecules. As the motion data is replayed, the colors of the agents change using a convention similar to that discussed earlier for GasLab: fast molecules are red, slow are blue, and in-between speeds are green. Although the students here do not directly control the NetLogo agents in real-time, there is still a sense in which the students’ embodied movements with the motion detectors are seen to control the cybernetic agents. These cybernetic agents are confined to move in a container where their speeds come from the student motion data10. Agents “bounce” off the walls in the model. The NetLogo environment simultaneously displays two kinds of “live” (i.e., updating) histograms: the first an instantaneous histogram of the distribution of speeds of the molecules in a given time step and the second a cumulative histogram for the distribution of speeds over time(which at the end of a cycle of replaying the motions will converge to look exactly like the histogram of the whole class’s results displayed on the students’ calculators). The data suggest that this re-enactment, capturing a HubNet activity in the NetLogo environment, provides additional scaffolding between the embodied student experience, the use of histograms as an interpretive artifact, and understanding the relation between micro-level behavior and global features of a gas. To address the teachers interest in comparing gases at different temperatures, the HubNet model collected the data from both the “cold” sample and the “hot” sample of the people-molecule gas. For each sample the HubNet model displayed the simulated motion of the molecules and the distribution of speeds at a given time step (see first histogram in Figure 13). Students noticed that in most of the respective time steps there appeared to be “more molecules going fast” (see arrow below) in the hot gas than for the cold gas. The presence of “more fast” molecules in most of the time steps means that the cumulative histogram has “more fast” molecules in it (see cumulative histogram on the right of Figure 13).

10

The motion detectors are not capable of collecting vector data so directions are randomly assigned. - 22 –


Figire13: HubNet model replays motion, displays a histogram for each time step, and displays a histogram of cumulative speed distributions. Based on what they did as molecules and their analyses of the “cold” results, students were able to predict what they would see for the “hot” results. The following classroom exchange occurred in the discussion between the presentation of the “cold” results and the subsequent analysis of the “hot” results: Teacher: What’s going to happen for the hot one? [Pointing at the simulated gas molecules] Student: You probably won’t even be able to see it [one of the fast molecules]. Teachers: What will happen to these graphs? …How’s it going to be different?[Pointing first to the histogram for an individual time stamp] Student: You’ll see more of them up high … [pointing to the right side of the histogram] Teacher: Let me do it on this one [moving to the cumulative graph]. Will more of them be here [pointing to the left part of the histogram] or will more of them be up here? Student: It’s going to be higher on this side [point to right side of cumulative histogram] Teacher: Why is it going to be higher on this side? Student: because it’s like counting, let’s say … it counts five people who are going fast, so it puts them up there Teacher: So if they’re going fast they get counted up here …on this side of me [indicating to the right] Student: Yah. Teacher: If they’re going slow, where do they get counted? Student 2: That side right there [indicating the left]. Teacher: [Point to the first interval of the histogram] This one tells you that a lot were going … Student 3: Very slow Teacher: So his idea [point to a student] is if we move fast there should be more of them over here [indicating to the right]. Student 3: … it’s going to be kind of like the opposite… [pointing to a spot further to the right indicating the bump would be there] When the data for the hot gas was displayed, the discussion continued and these observations were confirmed and further refined. From this embodied experience, reflection and analysis a number of significant insights and connections were made by students. Students were able to connect nuances of their personal motions with significant features of the graph. Slowing down before and after a collision resulted in a “bump” in histogram results at slow speeds. They did begin to connect their physical motions with the motions of the simulated molecules when they made the prediction that some of the simulated molecules in the hot gas would move so fast, “you probably won’t be able to see it”. Additionally they were able to discuss qualitatively that the simulated molecules would move faster on the whole for the “hotter” People Molecules gas – e.g., “you’ll see more of them up high”. Comments like “it counts five people who are going fast” suggest the students are able to understand that for both the individual time steps and in the cumulative results the histograms counted how many molecules were moving in a certain range of speeds (e.g., “fast”). Instead of assuming that all the molecules are going the same speed the students spoke in ways that suggested they understood the idea of a distribution of speeds from slow to fast for both the hot and cold gases and that shifts in this distribution would be associated in changes in speeds. Cold gases can still have some fast moving molecules and hot gases can still have some slow moving molecules yet it is still the case there will be “more” fast molecules in the hot gas or, described in terms of the aggregate, that the shape of the distribution would “opposite” (the bump would move to the right side). The students connect the clearly observable difference in color of the - 23 –


molecules with their speed and come to see the distribution of colors/speeds in a given ensemble of molecules as a measure of the temperature of the gas. In subsequent classes, the teacher then used this new understanding of the relation between speed and temperature to revisit a feature of atmospheres related to the changes in temperature as the height in the atmosphere increased. Students understood how to connect the mechanism of collisions with changing the speeds and locations of molecules in a gas. This gave them new insights into how an atmosphere “works” and what connections could be made between micro-behaviors of molecules and global features of atmospheres including the changes in density and temperature. Before using the PeopleMolecules simulations with learners we were concerned about their limitations in terms of their fidelity to the systems they represent. We clearly don’t want students learning falsehoods. With PeopleMolecules, for example, we clearly didn’t want students learning that there was a local maximum of slow moving molecules in real gases. When we ran the simulations like PeopleMolecules we were very pleasantly surprised to find that student understanding was enhanced by the contrasts between the simulations and more traditional depictions. While it is important to have the participatory simulations be like the system being rendered in at least some significant ways and that these ways be closely associated with the learning goals of the activity, it is also the case that many of the most important insights from students come from leveraging the ways in which the simulation is not exactly like the “real” thing. The consequence of a simulation not being entirely like the thing rendered turned out to be generative at two levels: (1) The contrasts often highlight significant aspects of the standard scientific models in ways that did, in fact, deepen the understanding of the standard model, and (2) the contrasts also invited the students to develop a sense of agency relative to both the particular models presented and the activity of modeling – the rendering of experience in enactive ways – itself. When the students examined the GasLab models, the absence of a second “bump” in the Maxwell-Boltzman distribution was noticed and, significantly, assumed an importance it wouldn’t have had if the students hadn’t just examined the distribution from the PeopleMolecules activity. Moreover, the contrast or “gap” between the simulation results and the distribution for an ideal gas catalyzed an examination of the different ways of running the simulation (e.g. “What if we all tried to move slower?”) and the GasLab model (e.g., “What if we they all started moving at a slower speed). We are continuing to run PeopleMolecules in schools as there is still much more for us to learn about the interaction of simulation experiences, understanding of scientific models, and students being able to generate and take ownership of the design and implementation of both simulations and models.

Discussion The work described herein is still in its early phases of analysis. Significant effort has gone into the design of the technology, activities and pedagogy. This work prepares the way for more systematic data collection and analysis. Such data collection and analysis is underway. In this paper, we have described two fairly typical enactments of activities. The data from these cases suggests some tentative conclusions and many more questions to study. We content ourselves here with ten summary observations. Participatory Simulation Activities are powerful means for studying complex systems Participatory simulations bring together three elements - student understanding of complex dynamic systems, the use of participatory activities and the use of highly interactive computer-based technologies in group settings. As an integrated learning environment, the use of participatory simulations and the HubNet architecture are showing themselves to be powerful tools for a wide range of students to learn about complex systems. Cognitively there is a good "fit" between the ways that students can act and interact and some of the most significant properties of complex dynamic systems. Students enact local strategies and approaches in controlling traffic or behaving like a PeopleMolecule and the behavior of the larger system emerges from these interactions. These resulting behaviors can then feed back into changing local decision-making. This interaction between local behaviors and the emergent properties of the system as a whole can be used both to structure the activity of the class and as a focal point for the subsequent analyses and discussions. With participatory simulations, the class itself becomes a kind of "manipulative" for exploring these personally embodied features of complex systems and the social dimensions of learning are highlighted. Within this framework, learning is itself a kind of participation. Assuming agency and identity within the system scaffolds the students' engagement with scientific and mathematical ideas that can characterize both their involvement and the evolving behaviors of the systems. The students are the system and this advances both their sense of personal engagement and their sense that understanding is closely associated with participating in new and more

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effective ways. Knowing is situated and becomes personally meaningful and motivating as a way of better participating in larger communities of inquiry. Students learn traditional content in new ways While at some point we expect the distinction between "old" and "new" content to become strained beyond any sense of sustaining utility, at a first pass we have illustrated how using participatory simulations can support both learning traditional content in new ways and learning new content. As part of our ongoing work in schools significant aspects of the PeopleMolecules activity can be and has been mapped onto traditional curricular topics. Clearly issues related to properties of gases and various aspects of the gas laws are highlighted in relation to this particular participatory simulation. In addition, important near neighbors - all of which can be found in traditional curricula -- are implicated. Students learn, in a highly situated way, about statistics, histograms, different kinds of distributions and how to interpret their significance, conservation laws (e.g., what is an "elastic" collision) and begin to connect macroscopic and microscopic properties. Indeed we have been pleasantly surprised by the many ways in which teachers have seen connections. For example, we did not anticipate teachers' interest in connecting the PeopleMolecules activity to features of atmospheres as part of the traditional emphasis on planetary science in most middle school curricula. Many of the challenging ideas and constructs in traditional curricula can become more tractable and engaging by using the embodied approaches supported by participatory simulations. In addition, this embodied approach to classroom activity and to learning allows new kinds of tasks and important new content to be introduced. The PeopleMolecules activity enables students to explore questions about how gases "work" and how their properties emerge. The Gridlock activity centers more on questions related to how to improve the workings of a system. This task moves beyond traditional science learning to support investigations of issues of design and working with trade-offs in characterizing ways of improving traffic. Not only is this task, with its more engineering-like focus, different from traditional "how it works" science tasks, new formal content is engaged. Topics associated with operations research, connecting micro- and macro-levels of systems, feedback and design become highlighted. We expect that over time the embodied approach to science learning presented in this paper and supported by the HubNet architecture will serve to better integrate and advance both current and next-generation approaches to what content matters and how this content is engaged in classrooms. PSA are technology designed specifically for a group and to support new forms of classroom interaction We have been careful to point out in this paper that some aspects of embodied approach to science learning can be engaged with single-user technologies and even with no computing technologies. Participatory simulations like the Beer Game were originally implemented with paper and pencil. Versions of the Beer Game have been implemented for single user exploration. The power of these approaches notwithstanding, the HubNet architecture can be considered the first technology that has been optimized, from the ground up, to support group interactivity in a way that specifically supports systems learning. In its group-oriented design this architecture fits one of the most overt features of classrooms: namely that classrooms in schools are almost always group contexts. This makes the omission of this feature in most of the design work for school-based technologies problematic. Technologies designed for individuals working in relative isolation don't tend to scale well to the classroom. The possibility of a group level of activity to complement individual activity either becomes problematic or, as more often the case, is ignored. An opportunity is missed and a unnecessary tension is set up between using technology or using the social space of the classroom. In contrast, participatory simulations by their very nature are group oriented. In this way they map well onto this aspect of classrooms. Conversely, groups of elements acting out behaviors to create global phenomena maps well onto the structure of understanding complex systems. HubNet supported participatory simulations, then, resonate with both the pragmatics of what classrooms are - individuals brought together in a group setting - and with important features of new kinds of scientific knowledge -- complex, dynamic systems. HubNet supported participatory simulations as the tool and systems dynamics as the topic can co-operate in our approach to embodied science teaching and learning. New forms of interaction create new kinds of knowing. Students are very engaged with PSA It is quite evident to even a casual observer that student engagement with and enjoyment of the activities is high. Students ask their teachers when the next activity will be, they smile, laugh and show great energy and excitement when involved in the simulation itself and also when reflecting upon it in class discussion. A large proportion of the students participate in the discussion, even students who do not usually participate in class

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talk. The data suggest that active participation in a simulation increases student engagement and their belief in the validity and importance of the results of the simulation. Students show great identification with the agents in the simulation. They use phrases such as “where am I”, “that’s me”, “look at me”, “stop blocking me” to describe the agents in the simulation. This identification appears to sustain engagement and when a result is observed, it is accompanied, by phrases such “I did it” or “I couldn’t stop it” or voiced connections to situations outside of school such as talk about the traffic in town or the pressure in a tire indicating a belief that the simulation results were understood by the students to not be just fun games, but reflections of the actual behavior of systems. Classroom conversation is changed Not only are students more engaged in ways that can be characterized in terms of frequency, enthusiasm and identity ("that's me"), the conversation is changed in other significant ways. Among these is that students take greater control of the flow and direction of the classroom activity. They tend to exert much greater control over how the systems is controlled, what to try next, what ideas get generated and what features of the system to attend to. This increased agency and participation then begins to show up in terms of changes in the kinds of utterances they produce. Initially there are conversations about how to act in the system and first-level observations - "there's gridlock" to increasingly causal and hypothetical forms of discourse such as “if we stagger the start time of the lights to be the average travel time of the cars then we should improve traffic flow”. These shifts in the kinds of discourse when compared with traditional classrooms will be an important component of our future investigations. PSA provide a fertile context for student mathematizing of situations As we have seen, in both the PSA described herein, the students found the experience they had shared to be a context for mathematizing, for creating mathematical descriptions of situations. In the Gridlock activity. students constructed a variety of metrics to describe the traffic flow. In the PeopleMolecules activity, students co-constructed and analyzed a distribution of their own speeds. The need to make sense of the shared experience catalyzed the need to find shared ways of describing the experience and of evaluating its validity. This need led to a plurality of mathematical constructions that in turn led to a classroom culture of comparison and critique of mathematical representations. This recognition of mathematics as a tool they could construct to serve a communicative and analytic purpose effectively changed student perception of the mathematical formalism. Instead of seeing it as a received procedure to rigidly apply, they saw it as a design problem – how to design an optimally descriptive depiction of the system by which to persuade others and themselves that they have satisfied a goal. Engaging in PSA can prepare the way for using agent-based modeling tools Once they had gotten engaged at this level with the mathematizing, students had incipient understanding of the ‘design space’ of the activity – that is which possible directions were available for exploration and change. This understanding provided both an advance organizer and motivation for them to continue the classroom investigations in standalone NetLogo modeling. After the students had run and discussed the PeopleMolecules activity, they were interested in and able to explore individually with the NetLogo GasLab models to make further progress in understanding the distribution of speeds. The key to being able to make these transitions is that students need to “invent” ways of speaking and acting in the participatory simulations that map onto key aspects of the syntax and semantics of NetLogo as a modeling language. NetLogo centers on giving agents rules or behaviors in ways that are closely akin to what the students were asked to do in the participatory simulations. Lessons for HubNet activity design Our experience with conducting HubNet-based PSA in secondary (and advanced elementary) classrooms suggests a set of heuristics for activity design. To optimally take advantage of the affordances of HubNet, activities should a) integrate new systems ideas such as feedback, emergence and self-organization into traditional curricular topics, giving students a new perspective on the traditional content as well as introducing them to the broad organizing principles of dynamic systems b) connect the content of the activities to personal experience of the learners so they can build on that experience in trying to build understandings of the new content c) be generative and space creating. That is they should include opportunities for students to explore or create a space of possible responses to the activity and then to make sense of patterns that structure that space. This approach stands in sharp contrast to typical science classroom activity that seeks to collapse the space of - 26 –


student response to a single highly constrained response or behavior. d) highlight the process of modeling enabling students to make progressively more refined models learning from the differences between their models and the phenomena as well as the similarities. Lessons for pedagogical design We have employed a five-step procedure for enacting PSA in the classroom. The five steps consist of a) setting or negotiating a shared and clearly understood goal for the activity b) eliciting students initial knowledge about the phenomena to be simulated. This serves both to catalyze the processes of students exchanging ideas as well as a tool of ongoing assessment for teachers and researchers c) run the simulation in its default mode and engage students in trying to achieve the agreed upon goal d) Students reflect upon, describe, and analyze what happened in the simulation and make predictions about how the outcome would be different under different conditions, strategies or rules e) Re-run the simulation in a way that is a refinement of earlier efforts and discuss/analyze how and why different results emerge. These 5 steps of this pedagogical sequence can then be repeated. With each iteration the texture of interaction becomes more nuanced. Participatory Simulations of Complex Systems is a new form of literacy In an increasingly interconnected world, it is no longer sufficient to study isolated content. The skills needed for literacy in today’s world, be it the world of science, business or the tools of an informed citizenry demand understanding of large systems with complex and highly interconnected relations. These kinds of complex problems are usually not best studied by individuals working in isolation, but by collaborative teams working in concert. These two features, complexity and collaborative interaction, are the hallmarks of participatory simulations. The work described herein suggests that such PSAs are accessible, motivating and engaging for a large range of students. We argue therefore that the symbolic forms, characteristic patterns and insights developed from working with PSA might serve as a new form of literacy – one that needs to be made accessible to all students. New pedagogical demands and possibilities All the teachers involved in this study reported great enthusiasm about the transformation of their classrooms while engaged in PSA. They reported seeing great gains in student learning, improved attitudes towards science learning and more active and engaged participation by a more diverse group of students. However, the teachers whose classes we worked with in these activities were sometimes quite challenged by conducting a PSA. The unpredictability of the flow of discussion generated by students, often put teachers in a position of having to think on their feet and respond to arguments, predictions and analyses they had not seen before. This kind of challenge, endemic to project-based classrooms is particularly thorny in PSA where the results are produced in real-time giving the teacher little time to get ahead of the students. At first, some teachers reported discomfort with their uncertainty about the “correct analyses”. They worried also that the students might walk away from the PSA with misconceptions about the content domain. Further study will be needed to determine if this danger is indeed evidenced in students engaged with PSA. and, if it is, what pedagogical strategies could mitigate the potential for this to occur. However, in the cases described here and subsequent work with classrooms in Chicago, Austin and Salt Lake, we have observed students testing and “debugging” such incipient misconceptions (usually in the social space of the classroom) and coming to sophisticated and reasoned arguments for rejecting them. This kind of peer review and group evaluation of the merit of ideas closely mirrors the kinds of correctives found in the larger communities of mathematical and scientific practice. Even if problematic ideas are introduced the ways in which they come to be rejected or changed is an important feature of our sense of participatory learning. Learning this “lesson” of community review and tentative embrace of novel ideas, we feel, is worth the price of potentially problematic ideas lingering for longer than they might in a traditional, lecture oriented, classroom.

Future Directions As indicated above, the HubNet architecture is in a preliminary stage. Significant project resources are allocated to developing HubNet and completing the fully networked architecture. Alongside this iterative design research, we will continue to conduct both implementation and curricular research with successive versions of HubNet. We have begun

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to design and test a set of PSA that make use of sophisticated new content domains11. This fundamental research is being carried out in economically challenged inner-city schools. Significant resources from the PSP Project are going toward site-based support and innovation. We are working alongside the teachers in targeting and implementing network-based participatory simulations that can transform students’ understanding of core concepts of the current curriculum (e.g., the concept of function) even as fundamentally new systems-understandings and content areas are introduced. In this context, we seek to gain a better understanding of how a PSA can significantly advance student understanding of the unfolding dynamics of systems. We hope to shed light on how learners' intuitive understandings and ways of responding interact with rule-based/agent-based, embodied (e.g., NetLogo) and rate-based aggregate (e.g., STELLA) modeling environments. To these ends, we are now conducting a detailed analysis of classroom data, pre- and posttests, as well as student and teacher interviews. Results from this systematic analysis will feed back into the next implementation round in Chicago and Texas. Through this design, implementation and curricular research, we hope to further the goal of advancing systems related understanding as a form of literacy for all students. Acknowledgements The preparation of this paper was supported by the National Science Foundation (Grants REC-9814682, REC9632612), The ideas expressed here do not necessarily reflect the positions of the supporting agency. We are also grateful for additional support provided by Texas Instruments Corporation. We wish to thank Sarah Davis, Matt Goto, Ed Hazzard, Geoff Matthews, and Seth Tisue for their contributions to the development of the HubNet technologies, activities and associated materials used in this research. Thanks also to Dor Abrahamson, Matthew Berland , Sharona Levy and Josh Unterman for their valuable comments on drafts of this paper. References Abrahamson, L, Davidson, A & Lipppai, A. (2000). Wireless Calculator Networks – why they work, where they come from, and where they’re going. Paper presented at the 13th International Conference on Technology in Collegiate Mathematics, Atlanta, GA, Nov 16 – 19, 2000. Borovoy, R., McDonald, M., Martin, F., & Resnick, M. (1996). Things that Blink: Computationally Augmented Name Tags. IBM Systems Journal, 35(3). Chen, D., & Stroup, W. (1993). General Systems Theory: Toward a conceptual framework for science and technology education for all. Journal for Science Education and Technology Colella, V., Borovoy, R., and Resnick, M. (1998) Participatory Simulations: Using Computational Objects to Learn about Dynamic Systems. Proceedings of the Computer Human Interface (CHI) '98 conference, Los Angeles, April 1998. Forrester, J. W. (1968). Principles of Systems. Norwalk, CT: Productivity Press. Jackson, S., Stratford, S., Krajcik, J., & Soloway, E. (1996). A learner-centered tool for students building models. Communications of the ACM, 39(4), 48-49. Jacobson, M. J., & Angulo, A. J. (1998). Complex systems, cognition, and problem solving: A preliminary investigation of differences between novices and experts. Proceedings of the Second International Conference on Complex Systems. Nashua, NH: New England Complex Systems Institute. Levy, S. T. & Wilensky, U. (2004). Making sense of complexity: Patterns in forming causal connections between individual agent behaviors and aggregate group behaviors. In U. Wilensky (Chair) and S. Papert (Discussant) Networking and complexifying the science classroom: Students simulating and making sense of complex systems using the HubNet networked architecture. The annual meeting of the American Educational Research Association, San Diego, CA, April 12 - 16, 2004. Mandinach, E. B., & Cline, H. F. (1994). Classroom dynamics: Implementing a technology-based learning environment. Hillsdale, NJ: Lawrence Erlbaum Associates Meadows, D. (1986). Fish Banks, LTD. In Durham, NH: Institute for Policy and Social Science Research. http://www.unh.edu/ipssr/index.html/ipssr/lab/fishbank.html Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books. Papert, S. (1993). The Children's Machine. New York, NY: Basic Books. Papert, S. (1996). An Exploration in the Space of Mathematics Educations. International Journal of Computers for Mathematical Learning 1(1): 138-142. 11

See ccl.northwestern.edu/isme/. - 28 –


Resnick, M. (1994). Turtles, Termites and Traffic jams. Explorations in massively parallel microworlds. Cambridge, MA: MIT Press. Resnick, M., & Wilensky, U. (1998). Diving into complexity: Developing probabilistic decentralized thinking through role-playing activities. Journal of the Learning Sciences, 7(2), 153-171. Resnick, M., & Wilensky, U. (1993). Beyond the deterministic, centralized mindsets: New thinking for new sciences. Presented at the annual conference of the American Educational Research Association, Atlanta, GA. Richmond, B., & Peterson, S. (1990). Stella II. Hanover, NH: High Performance Systems, Inc. Roberts, N. (1978). Teaching dynamic feedback systems thinking: an elementary view. Management Science, 24(8), 836-843. Senge, P. (1990). The Fifth Discipline. New York: Doubleday/Currency. Stieff, M & Wilensky, U. (2003). The Connected Chemistry Modeling Environment: Incorporating Interactive Simulations into the Chemistry Classroom. Journal of Science Education and Technology. Stor, M. & Briggs, W. (1998). Dice and disease in the classroom. The Mathematics Teacher, v. 91, no. 6. Pp 464468. Stroup, W. (1995). Dynamics and calculus for the young learner. Teacher’s Lab, 16-18. Stroup, W. (1996). Embodying nominalist constructivism: Making graphical sense of learning the calculus of how much and how fast. Doctoral Dissertation. Harvard Graduate School of Education. Cambridge, MA. Stroup, W. & Wilensky, U. (1999b). The Distribution Simulation. Center for Connected Learning & Computerbased Modeling. Northwestern University. Evanston, IL. Tversky, A. & Kahneman, D. (1974). Judgment Under Uncertainty: Heuristics and Biases. Science, 185, pp. 1124–1131. Wilensky, U. (1997b). What is Normal Anyway? Therapy for Epistemological Anxiety. Educational Studies in Mathematics. Volume 33, No. 2. pp. 171-202. Wilensky, U. (in press). Statistical Mechanics for secondary school: The GasLab Multi-agent Modeling Toolkit. International Journal of Computers for Mathematical Learning. In Wilensky, U. (Ed.) Special Issue on agent-based modeling. Wilensky, U. (2001) Modeling Nature’s Emergent Patterns with Multi-agent Languages. Proceedings of EuroLogo 2001. Linz, Austria. Wilensky, U. (2000). GasLab Curriculum. Evanston, IL, Center for Connected Learning and Computer Based Modeling, Northwestern University. ccl.northwestern.edu/cm/GasLab/ Wilensky, U. (1992). Gas-in-a-Box Model. Evanston, IL, Center for Connected Learning and Computer Based Modeling, Northwestern University. ccl.northwestern.edu/netlogo/models/GaslabGasinabox/ Wilensky, U. (1999a). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computerbased Modeling, Northwestern University, Evanston, IL. Wilensky, U. (1999b). GasLab—an extensible modeling toolkit for exploring micro- and macro- views of gases. In N. Roberts, W. Feurzeig, & B. Hunter (Eds.), Computer Modeling and Simulation in Science Education. Berlin: Springer Verlag. Wilensky, U. (1997a). StarLogoT. http://ccl.northwestern.edu/cm/starlogot/. Center for Connected Learning and Computer-based Modeling, Northwestern University, Evanston, IL. Wilensky, U. (1997b). What is Normal Anyway? Therapy for Epistemological Anxiety. Educational Studies in Mathematics. Volume 33, No. 2. pp. 171-202 Wilensky, U. (1993). Connected Mathematics: Building Concrete Relationships with Mathematical Knowledge. Doctoral Dissertation. Massachusetts Institute of Technology. Cambridge: Ma. Wilensky, U. & Reisman, K. (1998). Learning Biology through Constructing and Testing Computational Theories – an Embodied Modeling Approach. In Y. Bar-Yam (Ed.), Proceedings of the Second International Conference on Complex Systems. Nashua, NH: New England Complex Systems Institute. Wilensky, U. & Resnick, M. (1999). Thinking in Levels: A Dynamic Systems Perspective to Making Sense of the World. Journal of Science Education and Technology. Vol. 8 No. 1. Wilensky, U. & Resnick, M. (1995). New Thinking for New Sciences: Constructionist Approaches for Exploring Complexity. Presented at the annual conference of the American Educational Research Association, San Francisco. Ca. Wilensky, U. & Stroup, W. (2003). The Beer Game Participatory Simulation. Center for Connected Learning & Computer-based Modeling. Northwestern University. Evanston, IL. http://ccl.northwestern.edu/netlogo/models/hubnetbeergame/

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