Language and its Application to
Games for Learning Computational Science Modelning
Eric Neumannn,Wallace Feurzeig,
Peter Garik, and Allan Collins
BBN Systems and Technologies,
Cambridge, MA 02138
We describe a visual programming language called OOTLs (object-object transformation language) that allows students to build and model dynamic systems in an developmental and non-mathematical manner. Its use by students is closely tied to the playing of epistemic games, which allow learners to explore and accrue knowledge through experience necessary for sophisticated model construction. OOTLs can also be used as an interface to a wide range of simulating engines and phenomena, allowing students to produce both continuous and discrete models that can be simulated from Mathematica™ , STELLA™ , or StarLogo. OOTLs currently exists as a Java applet, and therefore can be used over the internet from anywhere.
Visual Modeling, Dynamic Systems, StarLogo
From the time of Galileo until fairly recently there were two complementary ways of doing scienceexperiment and theory. Now there is a third way. Computer modeling, a child of our time, is a powerful new paradigm, serving as a bridge between the traditional processes of experiment and theory and as a synergistic catalyst to both. The essence of computer modelingmathematical experimentationprovides a powerful tool for connecting observed phenomena with underlying causal processes. Indeed, much of our understanding of the workings of the physical world stems from our ability to construct models of it. Models are particularly valuable mental tools because in simplifying the complexities of the real world they enable us to concentrate our attention on those aspects of it that are of greatest interest or significance for the purpose at hand, whether descriptive, explanatory, or predictive.
Coupled with dynamic visualizations of model outputs, modeling provides a central and fundamental tool for describing and exploring complex phenomena. Yet, the concepts and skills of model-based inquiry, and particularly the skills of formulating computational models of physical processes and natural phenomena, are seldom taught in school science or mathematics classrooms. The computer can be an extremely valuable tool for constructing and investigating alternative models of real-world systems, and its use for this purpose in a pedagogical context has been the subject of several research projects during the past few years. Two circumstances, however, have made progress difficult: the lack of model development tools that are accessible to students with limited knowledge and skill in mathematics, and the lack of a compelling methodology for introducing students to the notions and art of modeling as a serious part of curriculum experience.
Modeling tools have been expressly developed to address the first difficulty. One such tool, designed for "modeling without mathematics" is called IQON for "Interacting Quantities Omitting Numbers" . It represents variables and the connections between them, graphically, without the user having to specify the form of the mathematical relations. Another, recently implemented at BBN, is the Object-Object Transformation Language. OOTLs is based on an object interaction metaphor and has a wide scope of application in science research as well as education. It can also be used to relate scientific model to appropriate mathematical relations by virtue of its ability to generate formal calculus descriptions from the graphics-defined system. This is further supported by a feature within OOTLs for generating code for simulation applications such as MatLab™ , Mathematica™ , and STELLA™ .
A new approach to learning model formulation through experience and experiment has promise for addressing the second of these difficulties . This approach, called "epistemic games", comes out of research in cognitive science and education. Epistemic games are general strategies for describing and representing phenomena in order to develop particular types of models. For example, aggregate-behavior models are constructed to model behavior of small particles like molecules and electrons. The models assume random, parallel motion of a large array of particles. When the particles encounter each other, there are a number of possible interactions, such as sticking together, rebounding, or breaking apart, that occur under different conditions. When they encounter a barrier, there also are a set of possible interactions, such as penetrating it, rebounding from it, or sticking to it, under different conditions.
These kinds of behaviors are characteristic of diffusion models, chemical mixtures, statistical mechanics, origin-of-life models, and DNA replication. To play this epistemic game, the student must specify completely the set of elements, their possible interactions, and the conditions under which each type of interaction occurs. Other epistemic games have different rules and constraints that the student must learn.The successful application of this approach depends on the availability of modeling tools such as OOTLs that are mathematically accessible to students and that are capable of representing a wide variety of different types of model structures.
2 The Object-Object Transformation Language (OOTLs)
The challenge of future secondary and undergraduate science instruction will be to help students learn to formulate, at an appropriate level of representation, mathematical models of physical phenomena for use with a computer simulation engine. Students will learn to investigate the behavior of their models and test their validity and scope of application. In order to make this leap in instruction to teaching model formulation, we have to confront the fact that students typically find it very difficult to express problems in the standard formal mathematical representations. The symbolic language of differential equations, for example, is very far removed from students mental models of the objects and object interactions involved in problem situations. Another kind of representation language, mathematically equivalent and mechanically translatable to differential equations, but more natural and accessible to students, is needed to provide them with initial experiences in problem formulation. The transition to the standard formal language can be made later, after they have acquired the relevant insights.
We created OOTLs to help students acquire experience and skill in formulating problems involving dynamical processes. OOTLs is a computational modeling environment designed for describing dynamic phenomena; events in OOTLs are conceptualized as interactions among the objects identified as the key players in the model processes. The OOTLs modeling language supports the description and simulation of phenomena for which the law of mass action holds: it applies to "well-stirred" systems composed of large numbers of dynamically interacting objects. OOTLs has application to an extensive variety of phenomena in many areas of science including epidemiology (contagious disease spread), population ecology (competition, predation, and adaptation), economics (market dynamics), physics (gas kinetics), chemical dynamics (reaction-diffusion equations) and traffic flow. OOTLs provides students with a parser to construct equations describing interactions between objects. The objects, which are represented as graphic icons, may represent chemical species, gas molecules, or humans. Objects interact with each other at specified rates. The equations describe the transformations resulting from the object interactions. Objects may be created or consumed (e.g., for chemical reactions there are sources and sinks for reactants; for a biological problem, birth and death of species; for a model of an economy, imports and exports, or innovation and obsolescence).
In designing OOTLs, we have taken into consideration the visual representations that research scientists have found useful for formulating their problems. The mathematical science literature is filled with diagrammatic shorthands for equations where graphs embody the basic interactions, and at the same time specify the equations to be solved to provide a numeric solution. Selection of an appropriate representation can greatly aid problem formulation and insight. For example, Feynman diagrams are a way to think of quantum electrodynamic processes that is conceptually simpler and clearer than an equivalent formulation in terms of the expansion of an integral equation. Similar such diagrammatic techniques have been extended to many-body theory, and statistical mechanics.
When physicists, chemists, biologists, and engineers think about the time evolution of interacting systems they often invoke similar mental models in their formulations. For a physicist the code words are "mean field"; for a chemical engineer or chemist it is a "stirred reactor"; for a population biologist it is high population density or rapid activation. The common mental model is one of collisions between the interactants. The collisions give rise to specific products. In a chemical reaction the result can be new species and the destruction of some of the reactants; in a predator-prey interaction, the death of the prey, and the eventual birth of a new predator. The mental model is very concrete in both these instances and the correspondence to the OOTLs formulation is direct.
3 An Illustrative Example
As an example of how OOTLs can be used to play out an epistemic game and to develop the essential forms, we show how a student could investigate the dynamics of a disease (epidemiology). Specifically, how does one learn to comprehend the system enough in order to predict the number of individuals infected with influenza over time. One can develop an initial understanding to the causes and dynamics by playing a "game" and evolving the model over this course.
The first game would involve "building the list of players that either get the flu or transmit it, and all the possible kinds of interactions between them (e.g., "catching it"). The student would then select or construct the icons each type of individual (susceptible, infected, recovered) and arrange them into lists of transformational interactions. For instance, "when a healthy individual meets a sick individual, that individual no becomes sick also" can be specified by:
Once the transformation is defined iconically and a probabilistic rate for it is given, the student can request the system to be simulated. As defined so far, if one starts with a small number of sick and a large number of healthy, over time all the healthy will "turn into" sick individuals, reaching a stable final state. The student can be asked whether this looks at all like one observes in the real world, to which the answer is: "not quite, people do not stay sick forever". The issues now is: how do they stop being sick, and what is one way to represent recovery. Simply allowing for sick to revert back to healthy is one way to extend the model, and this is done by adding a second reaction: sick eventually recover and are immune to further infection:
The result of simulations now show that there is a peaking of infection, and that the number of infected drops. There may be conditions whereby not all the susceptible ever become sick, while in other cases all are transformed into being sick and then recovered:
Figure 1 Time plot of disease simulation as specified within OOTLs. Susceptible, infected, and recovered individuals are labelled as S, I, and R , respectively.
This "conceptual building-up" of a model, from an initial hypothesis towards an elaborate working model, follows a "game" because of the student must both describe a phenomenon completely, as well as constantly compare the results of its simulation with that of real data. A direct result of this game is the emergence of an "epistemic form", that specifies how the players need to interact (i.e., existing populations of people may change but they do not appear de novo in the SIR model), and that can also be used as a basis for future investigations. One could continue to play the game by "adding" an interaction that states recovered-immune players can become susceptible over time again, thereby causing cycles of infections to occur. Alternatively, one could assume that recovered individuals may be different from infected, but could still be carriers, thereby infecting healthy individuals without any outer symptoms. Population dynamics can also be included, allowing individuals to reproduce, die, or the subpopulations introduced with different rates for susceptibility, growth, and death.
More advanced game designs pertaining still to epidemiology, could be matching simulation results presented with a time-series data of a real influenza case, such that model development and adjustment is pursued in even more detail, relying on deeper comprehension of the disease dynamics. An example of this is increasing the incubation time of the infection by slowing their rate of recovery, which results in greater spread even though contagiousness is left untouched. Here the student can use what they have learned about basic disease dynamics, surges and oscillations.
4 Some Classes of Problems Accessible to OOTLs
OOTLs can function as a gateway to many different topics in various areas of science and mathematics. It provides a natural platform for building dynamic process models in a wide range of phenomena including:
From a pedagogical standpoint, OOTLs presents students with a common conceptual framework for thinking about different processes and a common language for expressing these processes in a precise formal way. Moreover, the OOTLs representation can provide a user interface to a variety of different simulation engines, discrete as well as continuous. OOTLs does not impose itself on how the simulation is to be implemented or realized computationally. Rather, it focuses attention on the phenomenological problem at hand. Thus it supports modeling activities by students who are not yet skilled in designing computational science models. However, discovering the appropriate structural form for a model of a real-world phenomenon calls for a practical approach to identifying, understanding, and learning how to organize, the basic elements and their relationships.
5 Discrete Modeling
Some phenomena in the sciences fall into the class of problems best posed discretely through the interaction of cellular automata. These are problems where the population may be small, complex geometry important, or global averaging buries too much information. These also include the class of problems where the time evolution of internal state variables of participating reactants are difficult to represent as time differentials. Many problems in biology and engineering fall into this class. For the purpose of solving such problems, OOTLs models can interface to simulation engines such as StarLogo (Fig. 2), that support the parallel interaction of many independent reactants . This is possible, because the object-object interaction specification in OOTLs is itself discrete, even though it can be transformed into a continuous description if one assumes mean-field (well-mixed) conditions. Therefore, the semantics supported by OOTLs can be applied to both continuous and discrete models.
Figure 2 StarLogo epidemiology simulation produced by an OOTLs description.
6 Epistemic Games
We are developing specifications for the epistemic games needed to construct the computer models we present to students in OOTLs. By categorizing models according to their epistemic game class, we can provide interface scaffolding appropriate to each type of model. Making lists, and properly identifying the appropriate members of the lists, is a common strategy of epistemic games. More elaborate games will require more complex strategies for data organization. For example, some optimization problems can be solved by finding the minimum value of a multidimensional function. Unfortunately, in seeking such a minimum, it may be discovered numerically that there are several relative minima. In the definition of the problem, the user must make a plain list of all variables on which the function depends. But in addition, for a careful scan of the phase space, the user must be provided with additional data structures, such as two- or three-dimensional graphs showing the functions dependence on some of the variables.
There may be more than one epistemic game associated with a specific instance of OOTLs. For example, we have built an OOTLs model associated with a class of dynamical systems applicable to problems in epidemiology, chemical engineering, physics, and ecology. The possible outcomes of the system of equations solved by this model range from exponential behavior, to oscillatory, to chaotic, if the user parametrizes by time alone. But if the user also investigates the system behavior in time as a function of initial conditions and parameters in the equations (e.g., reaction rates), the list of outcomes becomes very complex. Whether or not this additional complexity is necessary depends upon the purpose for which the model is to be used (e.g., for description, explanation, and/or prediction of phenomena) and its scope of application. These considerations are made explicit as part of the epistemic game prior to the OOTLs implementation process.
The choice of the type of computer model appropriate to a modeling task are determined by two primary criteria: the semantics necessary to formulate the problem, and the interface scaffolding necessary to develop a strategy for analysis of the problem using the data generated by that type of model. We are investigating OOTLs models selected from problems in linear prediction, nonlinear interpolation and extrapolation, signal extraction from noise, systems of nonlinear dynamical equations, optimization problems, and discrete local interaction based systems representable by cellular automata simulations. Problems which require different semantics will also require different object relations and manipulations at the interface level. For example, the problem of predicting economic performance as a function of time must be posed in a different object language than a time-independent problem such as determining the optimal path in the classical traveling salesman problem. In addition, phenomena which involve modeling at mulitple levels, such as how the immune system works for many individuals within a larger population, further extends the language requirements to handle processes within processes [4,5].
We are also investigating the kinds of scaffolding necessary for the nonexpert to pose and answer questions and its dependence on the nature of the problem. We believe that to successfully learn the use of a computer model, the user needs explicit support from the rules and strategies of the epistemic game played by the experts who designed the model. Computer models designed by experts can be too open-ended for the nonexpert. A novice user can define variables, run simulations and display graphical data, without a clear recognition of the constraints of the problem or a carefully defined strategy for selecting variables and analyzing the data generated. We aim to immerse the user in the model with scaffolding corresponding to the strategies employed by the expert. By preparing the interface with this intent, we hope to guide the nonexpert in the principled use of the model in pursuit of new knowledge. embodiment of OOTLs.
We eventually plan to develop an extensive set of OOTLs-based models of different types (including finite-state models, multi-level (layered) models, multi-causal models, systems dynamics models, and aggregate behavior models) and a corresponding set of epistemic games spanning a rich variety of science content areas and levels of complexity. We intend soon to explore the use of these modeling games and applications in high-school and undergraduate science classrooms, and assess their benefits in helping students learn the skills of model-based inquiry, and the notions and art of model design and formulation. We will also be connecting OOTLs to various other computational initiatives, such that it can be used as a front-end to powerful computational and visualization resources available around the world. We envision this as a possible means by which students of many diverse backgrounds will be able to develop models and hypotheses by themselves, and then accurate translate them into true computational expressions.