Grounded and Transferable Knowledge of Complex Systems using Computer Simulations

Grounded and Transferable Knowledge of Complex Systems Using Computer Simulations

(supported by IES and NSF)

These projects concern the use of interactive computer simulations to teach scientific concepts governing complex adaptive systems. The formal principles underlying these systems are applicable across a wide range of domains. Although the broad applicability of these principles speaks to their importance, it also represents a challenge to educators to convey these principles in a way that students can appreciate the principle at a sufficiently abstract level that the student can transfer the principle across superficially unrelated domains. The current research addresses the question of when and how do students transfer what they have learned about scientific principles to new situations. Our research explores methods for teaching students about scientific principles in a manner that leads to grounded yet transportable knowledge.

Our research methods involve both controlled laboratory experiments and classroom-based studies, both investigating the role of perceptually-based simulations in fostering students’ scientific understanding. By observing how active exploration of one simulation benefits understanding of a subsequently presented simulation based on the same principle, we can assess whether the scientific principle has been successfully abstracted. Experiments explore the roles of graphical concreteness, narrative contextualization, language specificity, and diagrams on students‚Äô implicit and explicit knowledge of scientific principles. One research outcome is prescriptions for how and when concrete and highly contextualized materials should be used, compared to idealized and decontextualized materials. We also follow up on our previous research suggesting that grounded yet transferable knowledge can be achieved by gradually replacing concrete graphical elements within computer simulations with progressively idealized elements. Several extensions of this ‚Äúconcreteness fading‚ÄĚ technique are implemented and assessed: shifts from specific to general terminology, shifts from first-person to third-person perspectives, and linking diagrams to domain-specific graphical elements and gradually deemphasizing the domain-specific elements.

Initial studies focus on laboratory-controlled experiments on college students‚Äô acquisition of domain-general complex systems principles such as simulated annealing, competitive specialization, and diffusion in networks. Further studies explore students‚Äô use of the simulations in middle-schools and a freshman college course on complex systems. The middle-school population includes students in 8th grade science classes in the Monroe County Community School Corporation. The college-age population includes freshman students at Indiana University from all majors in the College of Arts and Sciences who take the PI‚Äôs ‚ÄúComplex Adaptive Systems‚ÄĚ course.

The scientific goal of the inquiry is to gain an understanding of how perceptual experience can lead to abstract conceptual understanding, and how conceptual understanding can change perceptual experience. The practical goal is to translate this understanding into general educational principles for integrating computer simulations into classroom activities.




Robert Goldstone, Ph.D. – principal investigator
Linda Smith, Ph.D. – co-investigator
Ji Son – graduate research assistant
Robin Kramer – research scientist
Nancy Martin – consultant (teacher at Jackson Creek Middle School)
Uri Wilensky, Ph.D. – consultant (professor at Northwestern University)


Software, Worksheets, etc.

Analogical Transfer of Complex Systems Principles using Netlogo Simulations (Robert Goldstone and Robin Kramer):

NetLogo Code
how a thermostat works [negative feedback]
how hunger and eating affect each other [negative feedback]
how a product can come to dominate in the marketplace [positive feedback]
how global warming can lead to the ice caps melting [positive feedback]
(Instructions/worksheets with analogies for all these simulations [DOC])
  • Ball attached to two rubber bands. (applet) (nlogo code available¬†here)
  • City popularity and population size. (applet) (nlogo code available¬†here)


Competitive Specialization Demonstrations using Netlogo Simulations (Robert Goldstone, Ji Son, and Thomas Hills):

Competitive specialization reflects a general complex adaptive system principle: individual agents can organize themselves without the use of a supervisor or a plan (Resnick, 1994; Resnick & Wilensky, 1993). Self-organization is important to a number of systems such as ants efficiently covering a food resource, soccer defenders efficiently covering the offensive field, waitstaff efficiently covering a cocktail party, and even neurons efficiently covering a stimulus space.

One of the research questions we are interested in is how perceptual simulations should be described for effective teaching. In these simulations, you can see ant-shaped agents covering over green patches of ‚Äúfood‚ÄĚ resources but they are described in a number of ways: (1) as ants and food, (2) as coverers and resources, and (3) as defenders and shooter regions. There is also a simulation of little defenders (people) being described as defenders too because the defender description may be a better analogy to competitive specialization than ants and food. Lastly we‚Äôve included a far transfer situation of sensor neurons.

  • Defender-shapes covering green blobs described as defenders and shooter regions. (applet) (nlogo code available¬†here)
  • Ant-shapes covering green blobs described as ants and food resources. (applet) (nlogo code available¬†here)
  • Transfer situation: sensor neurons covering several stimuli. (applet) (nlogo code available¬†here)
  • Worksheets for these simulations [DOC]


Software for Demonstrating Complex Adaptive Systems (Robert Goldstone)


Related Taught Courses

Complex Adative Sytems


Understanding Complex Systems by Joining in Them

Group Experiment Environments (GEE) project:

Rather than exploring scientific concepts by controlling various features of simulations to gain an understanding of the underlying principles, this project allows participants to actually immerse themselves within the simulated environments. Each experiment sees groups of agents interacting with each other and their world, while individual participants are given control over their own agents. In this way, the behaviors produced by the group as a whole lead to interesting hypotheses about how processes operate at a higher level than that of the individual.


Publications Stemming from Project

Learning and Understanding Science:

These papers range from explorations of the nature of science itself, to more specific topics such as how we learn, and how this learning process can be improved. By utilizing computer simulations, models, and other such tools, this collection of work attempts to better understand how we can further science as a whole, as well as each individual’s understanding of it.

1. Goldstone, R. L. (2006). The Complex systems see-change in education. The Journal of Learning Sciences, 15, 35-43.

The day when scientists have time to read broadly across chemistry, biology, physics and social sciences is long gone. Journals, conferences, and academic departmental structures are becoming increasingly specialized and myopic. As Peter Csermely (1999), one of the organizers of the International Forum of Young Scientists expresses it, ‚ÄúThere is only a limited effort to achieve the appropriate balance between the discovery of new facts and finding their appropriate place and importance in the framework of science. Science is not self-integrating, and there are fewer and fewer people taking responsibility for ‚Äėnet-making‚ÄĚ (p. 1621). One possible response to this fragmentation of science is to simply view it as inevitable. Horgan (1996) argues that the age of fundamental scientific theorizing and discoveries has passed, and that all that is left to be done is refining the details of theories already laid down by the likes of Einstein, Darwi n, and Newton. Complex systems researchers, and learning scientists more generally, offer an alternative perspective, choosing to reverse the trend toward increasing specialization.
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2. Goldstone, R. L., & Wilensky, U (submitted). Promoting Transfer through Complex Systems Principles.

Understanding scientific phenomena in terms of complex systems principles is both scientifically and pedagogically important. Situations from different disciplines of science are often governed by the same principle, and so promoting knowledge transfer across disciplines makes valuable cross-fertilization and scientific unification possible. Although evidence for this kind of transfer has been historically controversial, experiments and observations of students suggest pedagogical methods to promote transfer of complex systems principles. One powerful strategy is for students to actively interpret the elements and interactions of perceptually grounded scenarios. Such interpretation can be facilitated through the presentation of cases alongside general principles, and by students exploring and constructing computational models of cases. The resulting knowledge can be both concretely grounded yet highly perspective-dependent and generalizeable. We discuss methods for coordinating computational and mental models of complex systems, the roles of idealization and concreteness in fostering understanding and generalization, and other complementary theoretical approaches to transfer.
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3. Landy, D., & Goldstone, R. L. (2005). How we learn about things we don’t already understand. Journal of Experimental and Theoretical Artificial Intelligence, 17, 343-369.

The computation-as-cognition metaphor requires that all cognitive objects are constructed from a fixed set of basic primitives; prominent models of cognition and perception try to provide that fixed set. Despite this effort, however, there are no extant computational models that can actually generate complex concepts and processes from simple and generic basic sets, and there are good reasons to wonder whether such models may be forthcoming. We suggest that one can have the benefits of computationalism without a commitment to fixed feature sets, by postulating processes that slowly develop special-purpose feature languages, from which knowledge is constructed. This provides an alternative to the fixed-model conception without radical anti-representationlism. Substantial evidence suggests that such feature development adaptation actually occurs in the perceptual learning that accompanies category learning. Given the existence of robust methods for novel feature creation, the assumption of a fixed basis set of primitives as psychologically necessary is at best premature. Methods of primitive construction include (a) perceptual sensitization to physical stimuli, (b) unitization and differentiation of existing (non-psychological) stimulus elements into novel psychological primitives, guided by the current set of features, and (c) the intelligent selection of novel inputs, which in turn guides the automatic construction of new primitive concepts. Modeling the grounding of concepts as sensitivity to physical properties reframes the question of concept construction from the generation of an appropriate composition of sensations, to the tuning of detectors to appropriate circumstances.
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4. Son, J. Y., & Goldstone, R. L. (2005). Relational words as handles: They bring along baggage. Proceedings of the Twenty-seventh Annual Conference of the Cognitive Science Society. Hillsdale, New Jersey: Lawrence Erlbaum Associates.

Two experiments examined the role of relational language on analogical transfer. Participants were taught Signal Detection Theory (SDT) embedded in a doctor story. In the experimental condition, relational words accompanied the story. Relational words that shared superficial similarity with the contextual elements facilitated transfer. Without the shared semantics, relational words were detrimental to transfer performance. A computational model lends a more structured perspective on how language changes cognition.
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5. Goldstone, R. L., Feng, Y., & Rogosky, B. (2005). Connecting concepts to the world and each other. In D. Pecher & R. Zwaan (Eds.) Grounding cognition: The role of perception and action in memory, language, and thinking. Cambridge: Cambridge University Press. (pp. 292-314).

How can well tell that two people both have a concept of dog, gold, or car despite differences in their conceptual knowledge?  Two kinds of information can be used to translate between the concepts in two persons’ minds: the internal relations between concepts within each person’s mind, and external grounding of the concepts.  We present a neural network model called ABSURDIST (Aligning Between Systems Using Relations Derived Inside Systems Themselves) that integrates internal and external determinants of conceptual meaning to find translations across people or other systems.  The model shows that appropriate translations can be found by considering only similarity relations among concepts within a person.  However, simulations also indicate synergistic interactions between internal and external sources of information. ABSURDIST is then applied to analogical reasoning, dictionary translation, translating between web-based ontologies, subgraph matching, and object recognition.  The perf ormance of ABSURDIST suggests the utility of concepts that are simultaneously externally grounded and enmeshed within a conceptual system.
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6. Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientific principles using concrete and idealized simulations. The Journal of the Learning Sciences, 14, 69-110.

Participants in two experiments interacted with computer simulations designed to foster understanding of scientific principles governing complex adaptive systems.¬† The quality of participants‚Äô transportable understanding was measured by the amount of transfer between two simulations governed by the same principle.¬† The perceptual concreteness of the elements within the first simulation was manipulated.¬† The elements either remained concrete throughout the simulation, remained idealized, or switched midway into the simulation from concrete to idealized or vice versa.¬† Transfer was better when the appearance of the elements switched, consistent with theories predicting more general schemas when the schemas are multiply instantiated.¬† The best transfer was observed when originally concrete elements became idealized.¬† These results are interpreted in terms of tradeoffs between grounded, concrete construals of simulations and more abstract, transportable construals.¬† Progressive idealization (‚ÄúConcreteness fading‚ÄĚ) allows originally grounded and interpretable principles to become less tied to specific contexts and hence more transferable.
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Models and Experiments of Complex Systems:

These papers focus on behaviors at the level of the group, rather than that of the individual itself. By utilizing computational models and collecting data from human participants, this body of work explores collective behaviors and how these can be related to adaptation, cooperation, and other real-world phenomena.

1. Goldstone, R. L., Jones, A., & Roberts, M. E. (2006). Group path formation. IEEE Transactions on System, Man, and Cybernetics, Part A, 36, 611-620.

When people make choices within a group, they are frequently influenced by the choices made by others. We have experimentally explored the general phenomenon of group behavior where an early action facilitates subsequent actions. Our concrete instantiation of this problem is group path formation where people travel between destinations with the travel cost for moving onto a location inversely related to the frequency with which others have visited the location. We compare the resulting paths to optimal solutions [Minimal Steiner Trees (MSTs)] and the “Active Walker” model of pedestrian motion from biophysics. There were systematic deviations from beeline pathways in the direction of MST. These deviations showed asymmetries (people took different paths from A to B than they did from B to A) and varied as a function of the topology of the destinations, the duration of travel, and the absolute scale of the world. The Active Walker model accounted for many of these results, in addition to correctly predicting the approximate spatial distribution of steps.
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2. Mason, W. A., Jones, A., & Goldstone, R. L. (2005). Propagation of innovations in networked groups. Proceedings of the Twenty-seventh Annual Conference of the Cognitive Science Society. Hillsdale, New Jersey: Lawrence Erlbaum Associates.

A novel paradigm was developed to study the behavior of groups of networked humans searching a problem space. We examined how different network structures affect the diffusion of information about good solutions. Participants made numerical guesses and received scores that were also made available to their neighbors in the network. When the problem space was monotonic and had only one optimal solution, groups were fastest at finding the solution when all of the groups’ information was presented to them. However, when there were good but suboptimal solutions (i.e., local maxima), the group connected via a small-world network (Watts & Strogatz, 1998) was faster at finding the best solution than all other network structures.
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3. Mason, W. A., Jones, A., & Goldstone, R. L. (in press). Propagation of innovations in networked groups. Journal of Experimental Psychology: General.
A novel paradigm was developed to study the behavior of groups of networked people searching a problem space. We examined how different network structures affect the propagation of information in laboratory-created groups. Participants made numerical guesses and received scores that were also made available to their neighbors in the network. The networks were compared on speed of discovery and convergence on the optimal solution. One experiment showed that individuals within a group tend to converge on similar solutions even when there is an equally valid alternate solution. Two additional studies demonstrated that the optimal network structure depends on the problem space being explored, with networks that incorporate spatially-based cliques having an advantage for problems that benefit from broad exploration, and networks with greater long-range connectivity having an advantage for problems requiring less exploration.
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4. Roberts, M. E., & Goldstone, R. L. (2005). Explaining resource undermatching with agent-based models. Proceedings of the Twenty-seventh Annual Conference of the Cognitive Science Society. Hillsdale, New Jersey: Lawrence Erlbaum Associates.

We propose two agent-based models of group foraging for two perceptual conditions. These models exhibit complex group-level behavior using only a simple rule set with a homogeneous group of agents. The models are shown to replicate results from Goldstone and Ashpole (2004), and we describe a series of simulations that test the sources of the resource undermatching often found in group foraging experiments. After testing the effects of travel costs, the number of agents, and uniform variance food distributions, we conclude that many group foraging studies have overlooked the interplay of spatial constraints with food rates in causing undermatching.
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5. Goldstone, R. L., & Janssen, M. A. (2005). Computational models of collective behavior. Trends in Cognitive Science, 9, 424-430.

Computational models of human collective behavior offer promise in providing quantitative and empirically verifiable accounts of how individual decisions lead to the emergence of group-level organizations. Agent-based models (ABMs) describe interactions among individual agents and their environment, and provide a process-oriented alternative to descriptive mathematical models. Recent ABMs provide compelling accounts of group pattern formation, contagion, and cooperation, and can be used to predict, manipulate, and improve upon collective behavior. ABMs overcome an assumption underlying much of cognitive science ‚Äď that the individual is the critical unit of cognition. The advocated alternative is that individuals participate in collective organizations that they may not understand or even perceive, and that these organizations affect and are affected by individual behavior.
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6. Feng, Y., Goldstone, R. L., & Menkov, V. (2005). A Graph Matching Algorithm and its Application to Conceptual System Translation. International Journal on Artificial Intelligence Tools, 14, 77-100.

ABSURDIST II, an extension to ABSURDIST, is an algorithm using attributed graph matching to find translations between conceptual systems. It uses information about the internal structure of systems by itself, or in combination with external information about concept similarities across systems. It supports systems with multiple types of weighted or unweighted, directed or undirected relations between concepts. The algorithm exploits graph sparsity to improve computational efficiency.We present the results of experiments with a number of conceptual systems, including artificially constructed random graphs with introduced distortions.
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7. Goldstone, R. L., Ashpole, B. C., & Roberts, M. E., (2005). Knowledge of resources and competitors in human foraging. Psychonomic Bulletin & Review, 12, 81-87.

The allocation of human participants to resources was studied by observing the population dynamics of people interacting in real-time within a common virtual world. Resources were distributed in two spatially separated pools with varying relative reinforcement rates (50-50, 65- 35, or 80-20). We manipulated whether participants could see each other and the distribution of resources. When participants could see each other but not the resources, the richer pool was underutilized. When participants could see the resources but not each other, the richer pool was overutilized. In conjunction with prior experiments that correlated the visibility of agents and resources (Goldstone & Ashpole, in press), these results indicate that participants’ foraging decisions are influenced by both forager and resource information. The results suggest that the presence of a crowd at a resource is a deterring rather than attractive factor. Both fast and slow oscillations in the harvesting rates of the pools across time were revealed by Fourier analyses. The slow waves of crowd migration are most prevalent when the resources are invisible, whereas the fast cycles are most prevalent when the resources are visible and participants are invisible.
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8. Gureckis, T. M., & Goldstone, R. L. (in press). Thinking in groups. Pragmatics and Cognition.

Is cognition an exclusive property of the individual or can groups have a mind of their own? We explore this question from the perspective of complex adaptive systems. One of the principle insights from this line of work is that rules that govern behavior at one level of analysis (the individual) can cause qualitatively different behavior at higher levels (the group). We review a number of behavioral studies from our lab that demonstrate how groups of people interacting in real-time can self-organize into adaptive, problem-solving group structures. A number of principles are derived concerning the critical features of such ‚Äúdistributed‚ÄĚ information processing systems. We suggest that while cognitive science has traditionally focused on the individual, cognitive processes may manifest at many levels including the emergent group-level behavior that results from the interaction of multiple agents and their environment.
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Human Learning:

This collection of work explores how people learn about, and understand, the things that they come across in the world around them. In particular, exploration of the various aspects of stimuli, such as their origins or their similarity to other stimuli, provides insight into what processes might be taking place, and how we might usefully incorporate this knowledge when attempting to assist everyday learning.

1. Corneille, O., Goldstone, R. L., Queller, S., & Potter, T. (in press). Asymmetries in categorization, perceptual discrimination, and visual search for reference and non-reference exemplars. Memory & Cognition.

Two studies examined the representation, treatment, and attention, devoted to the members of reference (i.e., Club members) and non-reference (i.e., Not-Club members) categories. Consistent with prior work on category interrelatedness (e.g. Goldstone, 1996; Goldstone, Steyvers, & Rogosky, 2003), the findings reveal the existence of asymmetric representations for reference and non-reference categories which, however, decreased as expertise and familiarity with the categories increased (Experiment 1 and Experiment 2). Participants also more readily judged two reference than two non-reference exemplars as being the same (Experiment 1), and were better at detecting reference than non-reference exemplars in a set of novel, category-unspecified,exemplars (Experiment 2). These findings provide evidence for the existence of a feature asymmetry in the representation and treatment of exemplars from reference and non-reference categories. Membership in a reference category acts as a salient feature, thereby increasing the perceived similarity and detection of faces that belong in the reference, compared to nonreference, category.
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2. Hockema, S. A., Blair, M. R., & Goldstone, R. L. (2005). Differentiation for novel dimensions. Proceedings of the Twenty-seventh Annual Conference of the Cognitive Science Society. Hillsdale, New Jersey: Lawrence Erlbaum Associates.

Two experiments are reported that provide evidence for perceptual differentiation between a pair of novel, integral dimensions, in contrast to previous attempts that failed to differentiate these same two dimensions (Op de Beeck,Wagemans, & Vogels, 2003). In Experiment 1, an acquired distinctiveness effect was created on the category-relevant dimension through a categorization training regimen that gradually increased in difficulty. Response times for correct trials were faster across the category boundary. This effect was replicated in Experiment 2 using a new training procedure where participants had to predict category boundaries while watching an animation in which shapes transformed along the category-relevant dimension. Furthermore, the accuracy results of Experiment 2 also indicated that discriminability was changed on the category-relevant dimension relative to the irrelevant dimension across the entire range of the dimension, not just at the category boundary.
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3. Landy, D., & Goldstone, R. L. (2005). Relational reasoning is in the eyes of the beholder: How global perceptual groups aid and impair algebraic evaluations. Proceedings of the Twenty-seventh Annual Conference of the Cognitive Science Society. Hillsdale, New Jersey: Lawrence Erlbaum Associates.

Relational reasoning‚ÄĒreasoning that depends on the interactions of multiple elements, rather than on the intrinsic properties of the elements‚ÄĒis both ubiquitous and challenging. For example, children find it difficult to respond to relational commonalities when object-based similarities are present (Gentner & Rattermann, 1991). Since overt symbol systems such as algebra are external constructs, their terms can contain perceptual regularities. Models of symbolic reasoning, however, typically ignore perceptual regularities (Anderson, in press). It is reasonable to wonder whether people make use of available domaingeneral grouping processes when parsing mathematical structures.

The purpose of the experiments described here is to evaluate whether algebraic grouping is sensitive to visual grouping. If processing is strictly symbolic, then the manipulation of perceptual regularities should not affect judgments; however, if people use visual grouping to help them parse expressions, then they should make more errors in cases where the perceptual grouping gives an incorrect answer, and be more accurate when visual grouping supports the standard order of operations.
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4. Rogosky, B. J., & Goldstone, R. L. (2005). Adaptation of perceptual and semantic features. In L. A. Carlson & E. van der Zee (Eds.), Functional features in language and space: Insights from perception, categorization and development. (pp. 257-273). Oxford, England: Oxford University Press.

This chapter examines the role of feature in theories of concepts, perception, and language. The authors define features as psychological representations of properties in the world that can be processed independently of other properties and that are relevant to a task, such as categorization. They discuss the classic view of features as entities that do not change over time. They argue for an alternative view in which features are created and adapted according to the immediate goals and context of tasks, and over longer time periods in terms of perceptual and conceptual learning and development. The authors also distinguish pairs of dimensions in terms of whether the dimensions can be processed separately (i.e. either dimension can be attended independently of the other) or integrally (i.e. the dimensions cannot be processed independently). They present a study of the classification of linguistic stimuli according to rules based on semantic features (e.g. ferocity and socialness of animals). The results indicate that changes in the integral processing of the dimensions can be induced by tasks that favor the separate processing of one dimenion. The findings support the authors’ claim that, like perceptual features, semantic features can be adapted during learning.
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5. Goldstone, R. L, & Son, J. (2005). Similarity. In K. Holyoak & R. Morrison (Eds.). Cambridge Handbook of Thinking and Reasoning. Cambridge: Cambridge University Press. (pp. 13-36).

Human assessments of similarity are fundamental to cognition because similarities in the world are revealing.¬† The world is an orderly enough place that similar objects and events tend to behave similarly.¬† This fact of the world is not just a fortunate coincidence.¬† It isbecause¬†objects are similar that they will tend to behave similarly in most respects.¬† It is because crocodiles and alligators are similar in their external form, internal biology, behavior, diet, and customary environment that one can often successfully generalize from what one knows of one to the other.¬† As Quine (1969) observed, ‚ÄúSimilarity, is fundamental for learning, knowledge and thought, for only our sense of similarity allows us to order things into kinds so that these can function as stimulus meanings.¬† Reasonable expectation depends on the similarity of circumstances and on our tendency to expect that similar causes will have similar effects (p. 114).‚Ä̬† Similarity thus plays a crucial role in making predictions because similar things usually behave similarly.
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