How, and how well, do people switch between exploration and exploitation to search for and accumulate resources? We study the decision processes underlying such exploration/exploitation trade-offs using a novel card selection task that captures the common situation of searching among multiple resources (e.g., jobs) that can be exploited without depleting. With experience, participants learn to switch appropriately between exploration and exploitation and approach optimal performance. We model participants’ behavior on this task with random, threshold, and sampling strategies, and find that a linear decreasing threshold rule best fits participants’ results. Further evidence that participants use decreasing threshold-based strategies comes from reaction time differences between exploration and exploitation; however, participants themselves report nondecreasing thresholds. Decreasing threshold strategies that “front-load” exploration and switch quickly to exploitation are particularly effective in resource accumulation tasks, in contrast to optimal stopping problems like the Secretary Problem requiring longer exploration.
Best, R. M., & Goldstone, R. L. (2019). Bias to (and away from) the Extreme: Comparing Two Models of Categorical Perception Effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 7, 1166-1176.
Categorical Perception (CP) effects manifest as faster or more accurate discrimination between objects that come from different categories compared to objects that come from the same category, controlling for the physical differences between the objects. The most popular explanations of CP effects have relied on perceptual warping causing stimuli near a category boundary to appear more similar to stimuli within their own category and/ or less similar to stimuli from other categories. Hanley and Roberson (2011), on the basis of a pattern not previously noticed in CP experiments, proposed an explanation of CP effects that relies not on perceptual warping, but instead on inconsistent usage of category labels. Experiments 1 and 2 in this paper show a pattern opposite the one Hanley and Roberson pointed out. Experiment 3, using the same stimuli but with different choice statistics (i.e., different probabilities of each face being the target), obtains the same pattern as the one Hanley and Roberson showed. Simulations show that both category label and perceptual models are able to reproduce the patterns of results from both experiments, provided they include information about the choice statistics. This suggests two conclusions. First, the results described by Hanley and Roberson should not be taken as evidence in favor of a category label model. Second, given that participants did not receive feedback on their choices, there must be some mechanism by which participants monitor their own choices and adapt to the choice statistics present in the experiment.
Humans show a striking penchant for creating tools to benefit our own thought processes. Andy Clark (2003, 2008) has convincingly argued that the tools that we as humans recruit become integrated parts of an extended cognitive system that includes us as just one component. By extending cognition beyond our brains, Clark presents an “embiggened” perspective on what it means to be a cognizer and a person more generally. This perspectival shift runs counter to some recent forms of argumentation that in effect work to minimize personhood. For example, arguments for lack of personal culpability can take the form of “It wasn’t my fault. It was the fault of my ___ ” to be filled in, perhaps, by “upbringing,” “genes,” “neurochemistry,” “diet,” or “improperly functioning amygdala.” Instead, Clark (see also Dennett 1989) offers the opposite line of argumentation, according to which we consist not only of our amygdalae and hippocampi but also potentially our glasses, notebooks, friends, supporting technologies, and culture.
Andrade-Lotero, E., & Goldstone, R. L. (2019). Self-Organized Division of Cognitive Labor. Proceedings of the 41st Annual Conference of the Cognitive Science Society. (pp. 91-97). Montreal, Canada: Cognitive Science Society.
The division of labor phenomenon has been observed with respect to both manual and cognitive labor, but there is no clear understanding of the intra- and inter-individual mechanisms that allow for its emergence, especially when there are multiple divisions possible and communication is limited. Situations fitting this description include individuals in a group splitting a geographical region for resource harvesting without explicit negotiation, or a couple tacitly negotiating the hour of the day for each to shower so that there is sufficient hot water. We studied this phenomenon by means of an iterative two-person game where multiple divisions are possible, but no explicit communication is allowed. Our results suggest that there are a limited number of biases toward divisions of labor, which serve as attractors in the dynamics of dyadic coordination. However, unlike Schelling’s focal points, these biases do not attract players’ attention at the onset of the interaction, but are only revealed and consolidated by the in-game dynamics of dyadic interaction.
Lara-Dammer, F., Hofstadter, D. R., & Goldstone, R. L. (2019). A Computational Model of Scientific Discovery in a Very Simple World, Aiming at Psychological Realism. Journal of Experimental & Theoretical Artificial Intelligence, 1-22. 10.1080/0952813X.2019.1592234
We propose a computational model of human scientific discovery and perception of the world. As a prerequisite for such a model, we simulate dynamic microworlds in which physical events take place, as well as an observer that visually perceives and makes interpretations of events in the microworld. Moreover, we give the observer the ability to actively conduct experiments in order to gain evidence about natural regularities in the world. We have broken up the description of our project into two pieces. The first piece deals with the interpreter constructing relatively simple visual descriptions of objects and collisions within a context. The second phase deals with the interpreter positing relationships among the entities, winding up with elaborated construals and conjectures of mathematical laws governing the world. This paper focuses only on the second phase. As is the case with most human scientific observation, observations are subject to interpretation, and the discoveries are influenced by these interpretations.
Carvalho, P. F., & Goldstone, R. L. (2019). When does interleaving practice improve learning? In J. Dunlosky & K. A. Rawson (Eds.) The Cambridge Handbook of Cognition and Education. Cambridge, England: Cambridge University Press. (pp. 411-436).
As you flip through the pages of this handbook you will notice that the content does not seem to be randomly organized. The content of the handbook is sequenced in a particular way: foundations before general strategies, background before applications, etc. The editors envisaged a sequence of topics, the authors of each topic envisaged a sequence of information in each chapter, and so on. We selected a particular sequence because we considered it to be effective. Deciding how to sequence information takes place all the time in educational contexts, from educators deciding how to organize their syllabus to educational technology designers deciding how to organize a piece of educational software, from handbook editors and writers deciding how to organize their materials, to students making decisions as to how to organize their study. One might imagine that as long as all students study the same materials, regardless of the sequence in which they study it, they will all learn the same information. This could not be further from the truth. In this chapter, we will review evidence of how and why the sequence of study changes what is learned. In doing so, we will try to uncover the powerful ways in which sequence can improve or deter learning.
Motz, B. A., Carvalho, P. F., de Leeuw, J. R., & Goldstone, R. L. (2018). Embedding experiments: staking causal inference in authentic educational contexts. Journal of Learning Analytics,5, 47-59. doi: 10.18608/jla.2018.52.4
To identify the ways teachers and educational systems can improve learning, researchers need to make causal inferences. Analyses of existing datasets play an important role in detecting causal patterns, but conducting experiments also plays an indispensable role in this research. In this article, we advocate for experiments to be embedded in real educational contexts, allowing researchers to test whether interventions such as a learning activity, new technology, or advising strategy elicit reliable improvements in authentic student behaviours and educational outcomes. Embedded experiments, wherein theoretically relevant variables are systematically manipulated in real learning contexts, carry strong benefits for making causal inferences, particularly when allied with the data rich resources of contemporary e-learning environments. Toward this goal, we offer a field guide to embedded experimentation, reviewing experimental design choices, addressing ethical concerns, discussing the importance of involving teachers, and reviewing how interventions can be deployed in a variety of contexts, at a range of scales. Causal inference is a critical component of a field that aims to improve student learning; including experimentation alongside analyses of existing data in learning analytics is the most compelling way to test causal claims.
McColeman, C., Michal, A., Goldstone, R. l., Schloss, K., Kaminski, J., & Hullman, J. (2018). Data visualization as a domain to research areas in cognitive science. Proceedings of the 40th Annual Conference of the Cognitive Science Society. (pp. 35-36). Madison, Wisconsin: Cognitive Science Society.
How people are able to turn information in the environment into meaning is a critical question for cognitive science. That environment is increasingly data-driven. Using data to inform decisions and improve understanding of the world is a valuable component of critical thinking, and serves as the foundation of evidence-based decision making. Designing graphical representations can make those data more accessible, such that users may engage the visual system and capacity for visual pattern recognition to discern regularities and properties of data. We ultimately want to understand the connection between the initial perception of data visualizations and conceptual understanding of information. Data visualizations, broadly, are the representation of recorded values in visual form, including scientific visualizations such as brain scans, or live visualizations such as stock market monitoring; the work discussed through this symposium is of the type used in science, business, and medical settings to display data abstractly.
Yu, J., Landy, D., & Goldstone, R. L. (2018). Visual flexibility in arithmetic expressions. Proceedings of the 40th Annual Conference of the Cognitive Science Society. (pp. 2750-2755). Madison, Wisconsin: Cognitive Science Society.
We investigated whether, and in what, ways people use visual structures to evaluate mathematical expressions. We also explored the relationship between strategy use and other common measures in mathematics education. Participants organized long sum/products when visual structure was available in algebraic expressions. Two experiments showed a similar pattern: One group of participants primarily calculated from left to right, or combined identical numbers together. A second group calculated adjacent pairs. A third group tended to group terms which either produced easy sums (e.g., 6+4), or participated in a global structure. These different strategies were associated with different levels of success on the task, and, in Experiment 2, with differential math anxiety and mathematical skill. Specifically, problem solvers with lower math anxiety and higher math ability tend to group by chunks and easy calculation. These results identify an important role for the perception of coherent structure and pattern identification in mathematical reasoning.
Yu, J., Goldstone, R. L., & Landy, D. (2018). Experientially grounded learning about the roles of variability, sample size, and difference between means in statistical reasoning. Proceedings of the 40th Annual Conference of the Cognitive Science Society. (pp. 2744-2749). Madison, Wisconsin: Cognitive Science Society.
Despite its omnipresence in this information-laden society, statistics is hard. The present study explored the applicability of a grounded cognition approach to learning basic statistical concepts. Participants in 2 experiments interacted with perceptually rich computer simulations designed to foster understanding of the relations between fundamental statistical concepts and to promote the ability to reason with statistics. During training, participants were asked to estimate the probability of two samples coming from the same population, with sample size, variability, and difference between means independently manipulated. The amount of learning during training was measured by the difference between participants’ confidence judgments and those of an Ideal Observer. The amount of transfer was assessed by the increase in accuracy from a pretest to a posttest. Learning and transfer were observed when tailored guidance was given along with the perceptually salient properties. Implications of our quantitative measures of human sensitivity to statistical concepts were discussed.
Goldstone, R. L., Rogosky, B. J., Pevtzow, R., & Blair, M. (2017). The construction of perceptual and semantic features during category learning. In H. Cohen & C. Lefebvre (Eds.) Handbook of Categorization in Cognitive Science. (pp. 851-882). Amsterdam: Elsevier.
Category learning not only depends upon perceptual and semantic representations; it also leads to the generation of these representations. We describe two series of experiments that demonstrate how categorization experience alters, rather than simply uses, descriptions of objects. In the first series, participants first learned to categorize objects on the basis of particular sets of line segments. Subsequently, participants were given a perceptual part/whole judgment task. Categorization training influenced participants’ part/whole judgments, indicating that whole objects were more likely to be broken down into parts that were relevant during categorization. In the second series, correlations were created or broken between semantic features of word concepts (e.g., ferocious vs. timid and group-oriented vs. solitary animals). The best transfer was found between category learning tasks that shared the same semantic organization of concepts. Together, the experiments support models of category learning that simultaneously create the elements of categorized objects’ descriptions and associate those elements with categories.
Motz, B.A., de Leeuw, J.R., Carvalho, P.F., Liang, K.L., Goldstone, R.L. (2017). A dissociation between engagement and learning: Enthusiastic instructions fail to reliably improve performance on a memory task. PLoS ONE, 12(7): e0181775. doi: 10.1371/journal.pone.0181775
Despite widespread assertions that enthusiasm is an important quality of effective teaching, empirical research on the effect of enthusiasm on learning and memory is mixed and largely inconclusive. To help resolve these inconsistencies, we conducted a carefully-controlled laboratory experiment, investigating whether enthusiastic instructions for a memory task would improve recall accuracy. Scripted videos, either enthusiastic or neutral, were used to manipulate the delivery of task instructions. We also manipulated the sequence of learning items, replicating the spacing effect, a known cognitive technique for memory improvement. Although spaced study reliably improved test performance, we found no reliable effect of enthusiasm on memory performance across two experiments. We did, however, find that enthusiastic instructions caused participants to respond to more item prompts, leaving fewer test questions blank, an outcome typically associated with increased task motivation. We find no support for the popular claim that enthusiastic instruction will improve learning, although it may still improve engagement. This dissociation between motivation and learning is dis- cussed, as well as its implications for education and future research on student learning.
Goldstone, R. L., Kersten, A., & Carvalho, P. F. (2017). Categorization and Concepts. In J. Wixted (Ed.) Stevens’ Handbook of Experimental Psychology and Cognitive neuroscience, Fourth Edition, Volume Three: Language & Thought. New Jersey: Wiley. (pp. 275-317).
Concepts are the building blocks of thought. They are critically involved when we reason, make inferences, and try to generalize our previous experiences to new situations. Behind every word in every language lies a concept, although there are concepts, like the small plastic tubes attached to the ends of shoelaces, that we are familiar with and can think about even if we do not know that they are called aglets . Concepts are indispensable to human cognition because they take the “blooming, buzzing confusion” (James, 1890, p. 488) of disorganized sensory experiences and establish order through mental categories. These mental categories allow us to make sense of the world and predict how worldly entities will behave. We see, hear, interpret, remember, understand, and talk about our world through our concepts, and so it is worthy of reflection time to establish where concepts come from, how they work, and how they can best be learned and deployed to suit our cognitive needs.
Trench, M., Tavernini, L. M., & Goldstone, R. L. (2017). Promoting spontaneous analogical transfer by idealizing target representations. Proceedings of the 39th Annual Conference of the Cognitive Science Society. (pp. 1206-1211). London, England: Cognitive Science Society.
Recent results demonstrate that inducing an abstract representation of target analogs at retrieval time aids access to analogous situations with mismatching surface features (i.e., the late abstraction principle). A limitation of current implementations of this principle is that they either require the external provision of target-specific information or demand very high intellectual engagement. Experiment 1 demonstrated that constructing an idealized situation model of a target problem increases the rate of correct solutions compared to constructing either concrete simulations or no simulations. Experiment 2 confirmed that these results were based on an advantage for accessing the base analog, and not merely on an advantage of idealized simulations for understanding the target problem in its own terms. This target idealization strategy has broader applicability than prior interventions based on the late abstraction principle, because it can be achieved by a greater proportion of participants and without the need to receive target-specific information.
Marghetis, T., Goldstone, R. L., & Landy, D. (2017). Even when people are manipulating algebraic equations, they still associate numerical magnitude with space. Proceedings of the 39th Annual Conference of the Cognitive Science Society. (pp. 2675-2680). London, England: Cognitive Science Society.
The development of symbolic algebra transformed civilization. Since algebra is a recent cultural invention, however, algebraic reasoning must build on a foundation of more basic capacities. Past work suggests that spatial representations of number may be part of that foundation, but recent studies have failed to find relations between spatial-numerical associations and higher mathematical skills. One possible explanation of this failure is that spatial representations of number are not activated during complex mathematics. We tested this possibility by collecting dense behavioral recordings while participants manipulated equations. When interacting with an equation’s greatest [/least] number, participants’ movements were deflected upward [/downward] and rightward [/leftward]. This occurred even when the task was purely algebraic and could thus be solved without attending to magnitude (although the deflection was reduced). This is the first evidence that spatial representations of number are activated during algebra. Algebraic reasoning may require coordinating a variety of spatial processes.
Carvalho, P. F., & Goldstone, R. L. (2017). The most efficient sequence of study depends on the type of test. Proceedings of the 39th Annual Conference of the Cognitive Science Society. (pp. 198-203). London, England: Cognitive Science Society.
Previous research has shown that the sequence in which concepts are studied changes how well they are learned. In a series of experiments featuring naturalistic concepts (psychology concepts) and naïve learners, we extend previous research by showing that the sequence of study changes the representation the learner creates of the study materials. Interleaved study leads to the creation of relatively interrelated concepts that are represented by contrast to each other and based on discriminating properties. Blocked study, instead, leads to the creation of relatively isolated concepts that are represented in terms of their central and characteristic properties. The relative benefits of these representations depend on whether the test of conceptual knowledge requires contrastive or characteristic information. These results argue for the integrated investigation of the benefits of different sequences of study as depending on the characteristics of the study and testing situation as a whole.
Learners often struggle to grasp the important, central principles of complex systems, which describe how interactions between individual agents can produce complex, aggre-gate-level patterns. Learners have even more difficulty transferring their understanding of these principles across superficially dissimilar instantiations of the principles. Here, we provide evidence that teaching high school students an agent-based modeling language can enable students to apply complex system principles across superficially different domains. We measured student performance on a complex systems assessment before and after 1 week training in how to program models using NetLogo (Wilensky, 1999a). Instruction in NetLogo helped two classes of high school students apply complex sys-tems principles to a broad array of phenomena not previously encountered. We argue that teaching an agent-based computational modeling language effectively combines the benefits of explicitly defining the abstract principles underlying agent-level interac-tions with the advantages of concretely grounding knowledge through interactions with agent-based models.
Goldstone, R. L., Marghetis, T., Weitnauer, E., Ottmar, E. R., & Landy, D. (2017). Adapting perception, action, and technology for mathematical reasoning. Current Directions in Psychological Science, 1-8. DOI: d1o0i.1or1g7/170/.01197673/70926134712717410747808488
Formal mathematical reasoning provides an illuminating test case for understanding how humans can think about things that they did not evolve to comprehend. People engage in algebraic reasoning by 1) creating new assemblies of perception and action routines that evolved originally for other purposes (reuse), 2) adapting those routines to better fit the formal requirements of mathematics (adaptation), and 3) designing cultural tools that mesh well with our perception-action routines to create cognitive systems capable of mathematical reasoning (invention). We describe evidence that a major component of proficiency at algebraic reasoning is Rigged Up Perception-Action Systems (RUPAS), via which originally demanding, strategically-controlled cognitive tasks are converted into learned, automatically executed perception and action routines. Informed by RUPAS, we have designed, implemented, and partially assessed a computer-based algebra tutoring system called Graspable Math with an aim toward training learners to develop perception-action routines that are intuitive, efficient, and mathematically valid.
Meagher, B. J., Carvalho, P. F., Goldstone, R. L., & Nosofsky, R. M. (2017). Organized simultaneous displays facilitate learning of complex natural science categories. Psychonomic Bulletin & Review, DOI 10.3758/s13423-017-1251-6.
Subjects learned to classify images of rocks into the categories igneous, metamorphic, and sedimentary. In accord with the real-world structure of these categories, the to-beclassified rocks in the experiments had a dispersed similarity structure. Our central hypothesis was that learning of these complex categories would be improved through observational study of organized, simultaneous displays of the multiple rock tokens. In support of this hypothesis, a technique that included the presentation of the simultaneous displays during phases of the learning process yielded improved acquisition (Experiment 1) and generalization (Experiment 2) compared to methods that relied solely on sequential forms of study and testing. The technique appears to provide a good starting point for application of cognitive-psychology principles of effective category learning to the science classroom.
Carvalho, P. F., & Goldstone, R. L. (2017). The sequence of study changes what information is attended to, encoded and remembered during category learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 43, 1699-1719.
The sequence of study influences how we learn. Previous research has identified different sequences as potentially beneficial for learning in different contexts and with different materials. Here we investigate the mechanisms involved in inductive category learning that give rise to these sequencing effects. Across 3 experiments we show evidence that the sequence of study changes what information learners attend to during learning, what is encoded from the materials studied and, consequently, what is remembered from study. Interleaved study (alternating between presentation of 2 categories) leads to an attentional focus on properties that differ between successive items, leading to relatively better encoding and memory for item properties that discriminate between categories. Conversely, when learners study each category in a separate block (blocked study), learners encode relatively more strongly the characteristic features of the items, which may be the result of a strong attentional focus on sequential similarities. These results provide support for the sequential attention theory proposing that inductive category learning takes place through a process of sequential comparisons between the current and previous items. Different sequences of items change how attention is deployed depending on this basic process. Which sequence results in better or worse learning depends on the match between what is encoded and what is required at test.
Transfer of knowledge is the application of knowledge learned in one context to new, dissimilar problems or situations where the knowledge would be useful. Teachers, coaches, camp counselors, parents, and learners often have the experience of a learner showing apparent understanding when questioned about a topic in a way that closely matches how it was initially presented but showing almost no understanding when queried in a new context or with novel examples. This entry further explains the concept of knowledge transfer. It then discusses several different strategies used to support knowledge transfer.
An individual can interact with the same set of people over many different scales simultaneously. Four people might interact as a group of four and, at the same time, in pairs and triads. What is the relationship between different parallel interaction scales, and how might those scales themselves interact? We devised a four-player experimental game, the Modular Stag Hunt, in which participants chose not just whether to coordinate, but with whom, and at what scale. Our results reveal coordination behavior with such a strong preference for dyads that undermining pairwise coordination actually improves group-scale outcomes. We present these findings as experimental evidence for competition, as opposed to complementarity, between different possible scales of multi-player coordination. This result undermines a basic premise of approaches, like those of network science, that fail to model the interacting effects of dyadic, triadic, and group-scale structure on group outcomes.
Carvalho, P.F., Braithwaite, D.W., de Leeuw, J.R., Motz, B.A., & Goldstone, R.L. (2016). An in vivo study of self-regulated study sequencing in introductory psychology courses. PLoS ONE 11(3): e0152115.
Study sequence can have a profound influence on learning. In this study we investigated how students decide to sequence their study in a naturalistic context and whether their choices result in improved learning. In the study reported here, 2061 undergraduate students enrolled in an Introductory Psychology course completed an online homework tutorial on measures of central tendency, a topic relevant to an exam that counted towards their grades. One group of students was enabled to choose their own study sequence during the tutorial (Self-Regulated group), while the other group of students studied the same materials in sequences chosen by other students (Yoked group). Students who chose their sequence of study showed a clear tendency to block their study by concept, and this tendency was positively associated with subsequent exam performance. In the Yoked group, study sequence had no effect on exam performance. These results suggest that despite findings that blocked study is maladaptive when assigned by an experimenter, it may actually be adaptive when chosen by the learner in a naturalistic context.
Below is an index of supplemental videos for the manuscript:
Lara-Dammer, F., Hofstadter, D. R., & Goldstone, R. L. (under review).An Integrated Computational Model of Perception and Scientific Discovery in a Very Simple World, Aiming at Psychological Realism
Free Space in a Circle (Tricycle)
Boyle’s Law Sophisticated A (Tricycle)
Boyle’s Law Sophisticated B (Tricycle)
Boyle’s Law Sophisticated C (Tricycle)
Non-ideal Gas A (non-success, Tricycle)
Non-ideal Gas B (Tricycle)
Non-ideal Gas C (Tricycle)
Understanding Noise (Tricycle)
Failed Discovery (Tricycle)
Thinking in Groups A (Tricycle)
Thinking in Groups B (Tricycle)
Without ever explicitly discussing it, groups often times establish norms. A family or committee might develop a norm about when it is acceptable or not for members to interrupt each other. People greeting each other in different countries have very different norms for whether to shake hands or kiss, and if to kiss, how many times and in what cheek order. In some countries, tipping is not the norm, but if it is, violating the tipping norm could make you a persona non grata at a restaurant. We (Hawkins & Goldstone, 2016) were interested in how social norms emerge in a group without its members explicitly deciding on them, and the factors that promote effective norms.
To help explore these questions, we started by considering a simple scenario we call “Battle of the Exes.” You and your romantic partner live in a small town and both love coffee. Your shared loved of coffee was not, alas, enough to keep you together, and you have now broken up. There are only two coffee shops in your town, one with much better coffee than the other. Both you and your ex want to go every day for coffee during your simultaneously occurring coffee breaks, but if you pick the same place and run into one another, neither of you will enjoy your break at all.
Neither you nor your ex want to sit down to negotiate a schedule, but can you nonetheless develop a satisfactory routine? One of you could always go to the better coffee shop, but that would not be fair. Each of you could choose randomly, but that would end up with you and your ex often seeing each other, which would not maximize your duo’s happiness, and would not provide a stable solution in the long run.
These three features — fairness, happiness maximization, and stability are generally useful ways to assess the quality of a group’s behavior. To study scenarios like “Battle of the Exes” in the laboratory, we developed an interactive, real-time, online game. On each of the 60 rounds of the game, two players are given the choice of moving their avatar to one of two circles — one that they can visibly see will give them a small monetary prize and one that will give them a large payoff. The only catch is that if both players move to the same circle, then neither player gets anything for that round. For half of the groups, there was a small discrepancy between the prizes (1 cent vs 2 cents), and for the other half, there was a large discrepancy (1 cent versus 4 cents). Also, for half of the groups, each of the players could see the other player’s moment-to-moment position as they moved to the circles (Dynamic movement), while for the other half of the groups, the players only see the final choice that the other player made (Ballistic movement).
568 players were matched together to create 284 two-player groups. Some groups developed behaviors that were fair and stable, and led to both players earning a lot of money. These groups tended to develop social norms even without explicit communication. For example, the players A and B would alternate over rounds who got the large payoff, first A then B then A…., leading to a pattern like ABABABABAB.
In terms of maximizing happiness, the dynamic condition led to better earnings for the players than the ballistic condition. When the players can see each others’ moment-to-moment inclinations, that helps them coordinate. The dynamic condition also led to fairer solutions than the ballistic condition, with players earning similar amounts of money. An implication of these results is that giving the members in a group more information about what each person in the group is currently thinking about doing can help the group achieve well-coordinated, fair and happy solutions. This is something for politicians, social network providers, and amusement parks to consider when they are trying to design social spaces for their groups. Mutual visibility of group members is often an effective way to promote coordination.
In terms of developing stable strategies, there was a striking interaction between payoffs and movement type. When there was not a large difference in payoffs, choices in the ballistic condition were more stable than in the dynamic condition. When the stakes were low, players in the dynamic condition simply relied on moment-to-moment visual information to figure out who should get the larger payoff on any given round. They did not feel a strong pressure to develop a norm because they could use their continuous information as a crutch to help them coordinate. However, when the stakes were high, with one circle earning four times what the other circle earned, then the dynamic condition developed significantly more stable solutions than the ballistic condition. For these particularly contentious, high stakes situations, it is useful for the players to develop strong norms to help them coordinate, and the moment-to-moment information about player positions helps to create these norms.
One clear measure of how much contention there is in a group is how long both players move toward the same high payoff option before one “peels off” and lets the other player have the high payoff prize. Using this objective measure, groups have more contention at the beginning of the experiment session than the end. The higher stakes condition has more contention early on than the lower stakes condition, but by the end of the experiment, that ordering is flipped. Groups that have more contention at the beginning of the experiment tend to have less contention by the end of experiment, and are more likely to develop clever strategies like alternating who gets the high payoff option from round to round. A take-home message from this result is that contention in groups is not something to be avoided. For the groups in our “Battle of the Exes” game, early contention gives rise to well-coordinated, fair, efficient, and happiness maximizing solutions by the end of the experiment. It may be tempting to try to pave over contention and disagreement in a group, but letting the group work through these contentions is often key to giving them the motivation and insight that they need to develop creative, well-coordinated norms like alternating who gets the better payoff over rounds. So, although it may have been contention that broke you and your ex up in the first place, there is hope that this kind of early contention may allow you to enjoy your superior cup of coffee in peace. At least on Mondays, Wednesdays, and Fridays.
Why are some behaviors governed by strong social conventions while others are not? We experimentally investigate two factors contributing to the formation of conventions in a game of impure coordination: the continuity of interaction within each round of play (simultaneous vs. real-time) and the stakes of the interaction (high vs. low differences between payoffs). To maximize efficiency and fairness in this game, players must coordinate on one of two equally advantageous equilibria. In agreement with other studies manipulating continuity of interaction, we find that players who were allowed to interact continuously within rounds achieved outcomes with greater efficiency and fairness than players who were forced to make simultaneous decisions. However, the stability of equilibria in the real-time condition varied systematically and dramatically with stakes: players converged on more stable patterns of behavior when stakes are high. To account for this result, we present a novel analysis of the dynamics of continuous interaction and signaling within rounds. We discuss this previously unconsidered interaction between within-trial and across-trial dynamics as a form of social canalization. When stakes are low in a real-time environment, players can satisfactorily coordinate `on the fly,’ but when stakes are high there is increased pressure to establish and adhere to shared expectations that persist across rounds.
The idea that cognitive development involves a shift towards abstraction has a long history in psychology. One incarnation of this idea holds that development in the domain of mathematics involves a shift from non-formal mechanisms to formal rules and axioms. Contrary to this view, the present study provides evidence that reliance on non-formal mechanisms may actually increase with age. Participants – Dutch primary school children – evaluated three-term arithmetic expressions in which violation of formally correct order of evaluation led to errors, termed foil errors. Participants solved the problems as part of their regular mathematics practice through an online study platform, and data were collected from over 50,000 children representing approximately 10% of all primary schools in the Netherlands, suggesting that the results have high external validity. Foil errors were more common for problems in which formally lower-priority sub-expressions were spaced close together, and also for problems in which such sub-expressions were relatively easy to calculate. We interpret these effects as resulting from reliance on two non-formal mechanisms, perceptual grouping and opportunistic selection, to determine order of evaluation. Critically, these effects reliably increased with participants’ grade level, suggesting that these mechanisms are not phased out but actually become more important over development, even when they cause systematic violations of formal rules. This conclusion presents a challenge for the shift towards abstraction view as a description of cognitive development in arithmetic. Implications of this result for educational practice are discussed.
Recent research in relational learning has suggested that simple training instances may lead to better generalization than complex training instances. We examined the perceptual encoding mechanisms that might undergird this Simple advantage by testing category and perceptual learning in adults with simplified and traditional (more complex) Chinese scripts. In Experiment 1, participants learned Chinese characters and their English translations, performed a memorization test, and generalized their learning to the corresponding characters written in the other script. In Experiment 2, we removed the training phase and modified the tests to examine transfer based purely on the perceptual similarities between simplified and traditional characters. We found the simple advantage in both experiments. Training with simplified characters produced better generalization than training with traditional characters when generalization relied on either recognition memory or pure perceptual similarities. On the basis of the results of these two experiments,we propose a simple processmodel to explain the perceptual mechanism that might drive this simple advantage, and in Experiment 3 we tested novel predictions of this model by examining the effect of exposure duration on the simple advantage. We found support for our model that the simple advantage is driven primarily by differences in the perceptual encoding of the information available from simple and complex instances. These findings advance our understanding of how the perceptual features of a learning opportunity interact with domain-general mechanisms to prepare learners for transfer.
Prior research has established that while the use of concrete, familiar examples can provide many important benefits for learning, it is also associated with some serious disadvantages, particularly in learners’ ability to recognize and transfer their knowledge to new analogous situations. However, it is not immediately clear whether this pattern would hold in real world educational contexts, in which the role of such examples in student engagement and ease of processing might be of enough importance to overshadow any potential negative impact. We conducted two experiments in which curriculum-relevant material was presented in natural classroom environments, first with college undergraduates and then with middle-school students. All students in each study received the same relevant content, but the degree of contextualization in these materials was varied between students. In both studies, we found that greater contextualization was associated with poorer transfer performance. We interpret these results as reflecting a greater degree of embeddedness for the knowledge acquired from richer, more concrete materials, such that the underlying principles are represented in a less abstract and generalizable form.
Schwartz, D. L, & Goldstone, R. L. (2016). Learning as coordination: Cognitive psychology and education. In L. Corno & E. M. Anderman (Eds.) Handbook of Educational Psychology, 3rd edition. New York: Routledge (pp. 61-75).
The chapter follows a central thesis: A major task of teaching and instruction is to help learners coordinate categories of cognitive processes, capabilities, and representations. While nature confers basic abilities, education synthesizes them to suit the demands of contemporary culture. So, rather than treating categories of learning and instruction as an either–or problem, the problem is how to coordinate learning processes so they can do more together than they can alone. This thesis, which proposes a systems level analysis, is not the norm when thinking about teaching and learning. More common is the belief that learning involves strengthening select cognitive processes rather than coordination across processes. Our chapter, therefore, needs to develop the argument for learning as coordination. To do so, we introduce findings from the field of cognitive psychology.
Learning abstract concepts through concrete examples may promote learning at the cost of inhibiting transfer. The present study investigated one approach to solving this problem: systematically varying superficial features of the examples. Participants learned to solve problems involving a mathematical concept by studying either superficially similar or varied examples. In Experiment 1, less knowledgeable participants learned better from similar examples,while more knowledgeable participants learned better from varied examples. In Experiment 2, prior to learning how to solve the problems, some participants received a pretraining aimed at increasing attention to the structural relations underlying the target concept. These participants, like the more knowledgeable participants in Experiment 1, learned better from varied examples. Thus, the utility of varied examples depends on prior knowledge and, in particular, ability to attend to relevant structure. Increasing this ability can prepare learners to learn more effectively from varied examples.
Cavalho, P. F., Braithwaite, D. W., de Leeuw, J. R., Motz, B. A., & Goldstone, R. L. (2015). Effectiveness of learner-regulated study sequence: An in-vivo study in introductory psychology courses. Proceedings of the Thirty-Seventh Annual Conference of the Cognitive Science Society. (pp. 309-314). Pasadena, CA: Cognitive Science Society.
Study sequence can have a profound impact on learning. Previous research has often shown advantages for interleaved over blocked study, though the reverse has also been found. Learners typically prefer blocking even in situations for which interleaving is superior. The present study investigated learner regulation of study sequence, and its effects on learning in an ecologically valid context – university students using an online tutorial relevant to an exam that counted toward their course grades. The majority of participants blocked study by problem category, and this tendency was positively associated with subsequent exam performance. The results suggest that preference for blocked study may be adaptive under some circumstances, and highlight the importance of identifying task environments under which different study sequences are most effective.
Kost, A., Cavalho, P. F., & Goldstone, R. L. (2015). Can you repeat that? The effect of item repetition on interleaved and blocked study. Proceedings of the Thirty-Seventh Annual Conference of the Cognitive Science Society. (pp. 1189-1194). Pasadena, CA: Cognitive Science Society.
Three experiments explore differences between blocked and interleaved study with and without item repetition. In the first experiment we find that when items are repeated during study, blocked study results in higher test performance than interleaved study. In the second experiment we find that when there is no item repetition, interleaved and blocked study result in equivalent performance during the test phase. In the third experiment we find that when the study is passive and includes no item repetition, interleaved study results in higher test performance. We propose that learners create associations between items of the same category during blocked study and item repetition strengthens these associations. Interleaved study leads to weaker associations between items of the same category and therefore results in worse performance during test when there are item repetitions.
de Leeuw, J. R., & Goldstone, R. L. (2015). Memory constraints affect statistical learning; statistical learning affects memory constraints. Proceedings of the Thirty-Seventh Annual Conference of the Cognitive Science Society. (pp. 530-535). Pasadena, CA: Cognitive Science Society.
We present evidence that successful chunk formation during a statistical learning task depends on how well the perceiver is able to parse the information that is presented between successive presentations of the to-be-learned chunk. First, we show that learners acquire a chunk better when the surrounding information is also chunk-able in a visual statistical learning task. We tested three process models of chunk formation, TRACX, PARSER, and MDLChunker, on our two different experimental conditions, and found that only PARSER and MDLChunker matched the observed result. These two models share the common principle of a memory capacity that is expanded as a result of learning. Though implemented in very different ways, both models effectively remember more individual items (the atomic components of a sequence) as additional chunks are formed. The ability to remember more information directly impacts learning in the models, suggesting that there is a positive-feedback loop in chunk learning.
Ottmar, E. R., Landy, D., Goldstone, R. L., & Weitnauer, E. (2015). Getting from here to there: Testing the effectiveness of an interactive mathematics intervention embedding perceptual learning. Proceedings of the Thirty-Seventh Annual Conference of the Cognitive Science Society. (pp. 1793-1798). Pasadena, CA: Cognitive Science Society.
We describe an interactive mathematics technology intervention From Here to There! (FH2T) that was developed by our research team. This dynamic program allows users to manipulate and transform mathematical expressions. In this paper, we present initial findings from a classroom study that investigates whether using FH2T improves learning. We compare learning gains from two different instantiations of FH2T (retrieval practice and fluid visualizations), as well as a control group, and investigate the role of prior knowledge and content exposure in FH2T as possible moderators of learning. Findings, as well as implications for research and practice are discussed.
Weitnauer, E., Landy, D., Goldstone, R. L., & Ritter, H. (2015). A computational model for learning structured concepts from physical scenes. Proceedings of the Thirty-Seventh Annual Conference of the Cognitive Science Society. (pp. 2631-2636). Pasadena, CA: Cognitive Science Society.
Category learning is an essential cognitive mechanism for making sense of the world. Many existing computational category learning models focus on categories that can be represented as feature vectors, and yet a substantial part of the categories we encounter have members with inner structure and inner relationships. We present a novel computational model that perceives and learns structured concepts from physical scenes. The perception and learning processes happen simultaneously and interact with each other. We apply the model to a set of physical categorization tasks and promote specific types of comparisons by manipulating presentation order of examples. We find that these manipulations affect the algorithm similarly to human participants that worked on the same task. Both benefit from juxtaposing examples of different categories – especially ones that are similar to each other. When juxtaposing examples from the same category they do better if the examples are dissimilar to each other.
Inductive category learning takes place across time. As such, it is not surprising that the sequence in which information is studied has an impact in what is learned and how efficient learning is. In this paper we review research on different learning sequences and how this impacts learning. We analyze different aspects of interleaved (frequent alternation between categories during study) and blocked study (infrequent alternation between categories during study) that might explain how and when one sequence of study results in improved learning. While these different sequences of study differ in the amount of temporal spacing and temporal juxtaposition between items of different categories, these aspects do not seem to account for the majority of the results available in the literature. However, differences in the type of category being studied and the duration of the retention interval between study and test may play an important role. We conclude that there is no single aspect that is able to account for all the evidence available. Understanding learning as a process of sequential comparisons in time and how different sequences fundamentally alter the statistics of this experience offers a promising framework for understanding sequencing effects in category learning. We use this framework to present novel predictions and hypotheses for future research on sequencing effects in inductive category learning.
Various kinds of assistance, including prompts, worked examples, direct instruction, and modeling, are widely provided to learners across educational and training programs. Yet, the effectiveness of assistance during training on long-term learning is widely debated. In the current experiment, we examined how the extent and schedule of assistance during training on a novel mouse movement task impacted unassisted test performance. Learners received different schedules of assistance during training, including constant assistance, no assistance, probabilistic assistance, alternating assistance, and faded assistance. Constant assistance led to better performance during training than no assistance. However, constant assistance during training resulted in the worst unassisted test performance. Faded assistance during training resulted in the best test performance. This suggests that fading may allow learners to create an internal model of the assistance without depending upon the assistance in a manner that impedes successful transfer to unassisted circumstances.
Research on how information should be studied during inductive category learning has identified both interleaving of categories and blocking by category as beneficial for learning. Previous work suggests that this mixed evidence can be reconciled by taking into account within- and between-category similarity relations. In this paper we present a new moderating factor. Across two experiments, one group of participants studied categories actively (by studying the objects without correct category assignment and actively figuring out what the category is), either interleaved or blocked. Another group studied the same categories passively (objects and correct category assignment were simultaneously provided). Results from a subsequent generalization task show that whether interleaved or blocked study result in better learning depend on whether study is active or passive. One account of these results is that different presentation sequences and tasks promote different patterns of attention to stimulus components. Passive learning and blocking promote attending to commonalities within categories, while active learning and interleaving promote attending to differences between categories.
Perceptual modules adapt at evolutionary, lifelong, and moment-to-moment temporal scales to better serve the informational needs of cognizers. Perceptual learning is a powerful way for an individual to become tuned to frequently recurring patterns in its specific local environment that are pertinent to its goals without requiring costly executive control resources to be deployed. Mechanisms like predictive coding, categorical perception, and action-informed vision allow our perceptual systems to interface well with cognition by generating perceptual outputs that are systematically guided by how they will be used. In classic conceptions of perceptual modules, people have access to the modules’ outputs but no ability to adjust their internal workings. However, humans routinely and strategically alter their perceptual systems via training regimes that have predictable and specific outcomes. In fact, employing a combination of strategic and automatic devices for adapting perception is one of the most promising approaches to improving cognition.
When a musical tone is sounded, most listeners are unable to identify its pitch by name. Those listeners who can identify pitches are said to have absolute pitch perception (AP). A limited subset of musicians possesses AP, and it has been debated whether musicians’ AP interferes with their ability to perceive tonal relationships between pitches, or relative pitch (RP). The present study tested musicians’ discrimination of relative pitch categories, or intervals, by placing absolute pitch values in conflict with relative pitch categories. AP listeners perceived intervals categorically, and their judgments were not affected by absolute pitch values. These results indicate that AP listeners do not infer interval identities from the absolute values between tones, and that RP categories are salient musical concepts in both RP and AP musicianship.
Weitnauer, E., Carvalho, P. F., Goldstone, R. L., & Ritter, H. (2014). Similarity-based ordering of instances for efficient concept learning. Proceedings of the Thirty-Sixth Annual Conference of the Cognitive Science Society. (pp. 1760-1765). Quebec City, Canada: Cognitive Science Society.
Theories in concept learning predict that interleaving instances of different concepts is especially beneficial if the concepts are highly similar to each other, whereas blocking instances belonging to the same concept provides an advantage for learning low-similarity concept structures. This suggests that the performance in concept learning tasks can be improved by grouping the instances of given concepts based on their similarity. To explore this hypothesis, we use Physical Bongard Problems, a rich categorization task with an open feature space, to analyze the combined effects of comparing dissimilar and similar instances within and across categories. We manipulate the within- and between-category similarity of instances presented close to each other in blocked, interleaved and simultaneous presentation schedules. The results show that grouping instances to promote dissimilar within- and similar between category comparisons improves the learning results, to a degree depending on the strategy used by the learner.
Braithwaite, D. W., & Goldstone, R. L. (2014). Benefits of variation increase with preparation. Proceedings of the Thirty-Sixth Annual Conference of the Cognitive Science Society. (pp. 1940-1945). Quebec City, Canada: Cognitive Science Society.
Abstract concepts are characterized by their underlying structure rather than superficial features. Variation in the examples used to teach abstract concepts can draw attention towards shared structure and away from superficial detail, but too much variation can inhibit learning. The present study tested the possibility that increasing attention to underlying structural relations could alleviate the latter difficulty and thereby increase the benefits of varied examples. Participants were trained with either varied or similar examples of a mathematical concept, and were then tested on their ability to apply the concept to new cases. Before training, some participants received pre training aimed at increasing attention to the structural relations underlying the concept. The relative advantage of varied over similar examples was increased among participants who received the pretraining. Thus, preparation that promotes attention to the relations underlying abstract concepts can increase the benefits of learning from varied examples.
Through perceptual learning, perceptual systems are gradually modified so as to better fit an organism’s environment and frequently occurring needs. We consider psychological and neurophysiological evidence that changes to perception can be early in the stream of information processing. Three specific mechanisms of perceptual learning are described: attentional tuning, unitization, and attribute differentiation. These mechanisms allow organisms to emphasize important perceptual information, to construct single functional units that are activated when a familiar complex configuration arises, and to isolate perceptual attributes that were originally psychologically fused. We describe ways by which people modify their perceptual systems so as to better meet their goals, and the implications of these modifications for the cognitive penetrability of perception, relations between perception and higher-order reasoning, and education.
How does perceptual learning take place early in life? Traditionally, researchers have focused on how infants make use of information within displays to organize it, but recently, increasing attention has been paid to the question of how infants perceive objects differently depending upon their recent interactions with the objects. This experiment investigates 10-month-old infants’ use of brief prior experiences with objects to visually organize a display consisting of multiple geometrically-shaped three-dimensional blocks created for this study. After a brief exposure to a multi-part portion of the display, each infant was shown two test events, one of which preserved the unit the infant had seen and the other of which broke that unit. Overall, infants looked longer at the event that broke the unit they had seen prior to testing than the event that preserved that unit, suggesting that infants made use of the brief prior experience to (a) form a cohesive unit of the multi-part portion of the display they saw prior to test and (b) segregate this unit from the rest of the test display. This suggests that infants made inferences about novel parts of the test display based on limited exposure to a subset of the test display. Like adults, infants learn features of the three-dimensional world through their experiences in it.
Studying different concepts by frequently alternating between them (i.e., interleaving), improves discriminative contrast between different categories, while studying each con- cept in separate blocks emphasizes the similarities within each category. Interleaved study has been shown to improve learning of high similarity categories by increasing between- category comparison, while blocked study improves learning of low similarity categories by increasing within-category comparison. In addition, interleaved study presents greater temporal spacing between repetitions of each category compared to blocked study, which might present long-term memory benefits. In this study we asked if the benefits of temporal spacing would interact with the benefits of sequencing for making comparisons when testing was delayed, particularly for low similarity categories. Blocked study might be predicted to promote noticing similarities across members of the same category and result in short-term benefits. However, the increase in temporal delay between repetitions inherent to interleaved study might benefit both types of categories when tested after a longer retention interval. Participants studied categories either interleaved or blocked and were tested immediately and 24 h after study. We found an interaction between schedule of study and the type of category studied, which is consistent with the differential emphasis promoted by each sequential schedule. However, increasing the retention interval did not modulate this interaction or resulted in improved performance for interleaved study. Overall, this indicates that the benefit of interleaving is not primarily due to temporal spacing during study, but rather due to the cross-category comparisons that interleaving facilitates. We discuss the benefits of temporal spacing of repetitions in the context of sequential study and how it can be integrated with the attentional bias hypothesis proposed by Carvalho and Goldstone (2014a).
Carvalho, P. F., & Goldstone, R. L., (2014). Putting category learning in order: category structure and temporal arrangement affect the benefit of interleaved over blocked study. Memory & Cognition, 42(3), 481-495.
Recent research in inductive category learning has demonstrated that interleaved study of category exemplars results in better performance than does studying each category in separate blocks. However, the questions of how the category structure influences this advantage and how simultaneous presentation interacts with the advantage are open issues. In this article, we present three experiments. The first experiment indicates that the advantage of interleaved over blocked study is modulated by the structure of the categories being studied. More specifically, interleaved study results in better generalization for categories with high within- and between-category similarity, whereas blocked presentation results in better generalization for categories with low within- and between-category similarity. In Experiment 2, we present evidence that when presented simultaneously, between-category comparisons (interleaved presentation) result in a performance advantage for high-similarity categories, but no differences were found for low-similarity categories. In Experiment 3, we directly compared simultaneous and successive presentation of low-similarity categories. We again found an overall benefit for blocked study with these categories. Overall, these results are consistent with the proposal that interleaving emphasizes differences between categories, whereas blocking emphasizes the discovery of commonalities among objects within the same category.
A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and combines their advantages. Specifically, we recommend beginning with concrete materials and then explicitly and gradually fading to the more abstract. Theoretical benefits of this “concreteness fading” technique for mathematics and science instruction include: (1) helping learners interpret ambiguous or opaque abstract symbols in terms of well-understood concrete objects, (2) providing embodied perceptual and physical experiences that can ground abstract thinking, (3) enabling learners to build up a store of memorable images that can be used when abstract symbols lose meaning, and (4) guiding learners to strip away extraneous concrete properties and distill the generic, generalizable properties. In these ways, concreteness fading provides advantages that go beyond the sum of the benefits of concrete and abstract materials.
Here are some reports of our PLoS One paper on human collective behavior studying cyclic patterns in a generalization of the familiar rock-scissors-paper game. We find situations in which groups of people grow increasingly predictable as they cycle around a set of choice options in a game similar to rock-scissors-paper but with 24 rather than 3 choices.
When making decisions, humans can observe many kinds of information about others’ activities, but their effects on performance are not well understood. We investigated social learning strategies using a simple problem-solving task in which participants search a complex space, and each can view and imitate others’ solutions. Results showed that participants combined multiple sources of information to guide learning, including payoffs of peers’ solutions, popularity of solution elements among peers, similarity of peers’ solutions to their own, and relative payoffs from individual exploration. Furthermore, performance was positively associated with imitation rates at both the individual and group levels. When peers’ payoffs were hidden, popularity and similarity biases reversed, participants searched more broadly and randomly, and both quality and equity of exploration suffered. We conclude that when peers’ solutions can be effectively compared, imitation does not simply permit scrounging, but it can also facilitate propagation of good solutions for further cumulative exploration.
The terms concreteness fading and progressive formalization have been used to describe instructional approaches to science and mathematics that use grounded representations to introduce concepts and later transition to more formal representations of the same concepts. There are both theoretical and empirical reasons to believe that such an approach may improve learning outcomes relative to instruction employing only grounded or only formal representations (Freudenthal, 1991; Goldstone & Son, 2005; McNeil & Fyfe, 2012; but see Kaminski, Sloutsky, & Heckler, 2008). Two experiments tested the effectiveness of this approach to instruction in the mathematical domain of combinatorics, using outcome listing and numerical calculation as examples of grounded and formal representations, respectively. The study employed a pretest-training, posttest design. Transfer performance, that is, participants’ improvement from pretest to posttest, was used to assess the effectiveness of instruction received during training. In Experiment 1, transfer performance was compared for 4 types of instruction, which differed only in the types of representation they employed: pure listing (i.e., listing only), pure formalism (i.e., numerical calculation only), list fading (i.e., listing followed by numerical calculation), and formalism first (i.e., listing introduced after numerical calculation). List fading instruction led to transfer performance on par with pure formalism instruction and higher than formalism first and pure listing instruction. In Experiment 2, an enhanced version of list fading training was again compared to pure formalism. However, no difference in transfer performance due to training was found. The results suggest that combining grounded and formal representations can be an effective approach to combinatorics instruction but is not necessarily preferable to using formal representations alone. If both grounded and formal representations are employed, the former should precede rather than follow the latter in the instructional sequence.
Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a ‘‘hopping’’ behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.
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See a movie of actual humans (shown as Xs) playing the Mod Game. Notice the clumping of their moves and their regular progression around the circle of choices.
Unlike how most psychology experiments on learning operate, people learning to do a task typically do so in the context of other people learning to do the same task. In these situations, people take advantage of others’ solutions, and may modify and extend these solutions, thereby affecting the solutions available to others. We are interested in the group patterns that emerge when people can see and imitate the solutions, innovations, and choices of their peers over several rounds. In one series of experiments and computer simulations, we find that there is a systematic relation between the difficulty of a problem search space and the optimal social network for transmitting solutions. As the difficulty of finding optimal solutions in a search space increases, communication networks that preserve spatial neighborhoods perform best. Restricting people’s access to others’ solutions can help the group as a whole find good, hard-to-discover solutions. In other experiments with more complex search spaces, we find evidence for several heuristics governing individuals’ decisions to imitate: imitating prevalent options, imitating options that become increasingly prevalent, imitating high-scoring options, imitating during the early stages of a multiround search process, and imitating solutions similar to one’s own solution. Individuals who imitate tend to perform well, and more surprisingly, individuals also perform well when they are in groups with other individuals who imitate frequently. Taken together, our experiments on collective social learning reveal laboratory equivalents of prevalent social phenomena such as bandwagons, strategy convergence, inefficiencies in the collective coverage of a problem space, social dilemmas in exploration/exploitation, and reciprocal imitation.
Jones, M., & Goldstone, R. L. (2013). The structure of integral dimensions: Contrasting topological and Cartesian representations. Journal of Experimental Psychology: Human Perception and Performance, 39, 111-132.
Diverse evidence shows that perceptually integral dimensions, such as those composing color, are represented holistically. However, the nature of these holistic representations is poorly understood. Extant theories, such as those founded on multidimensional scaling or general recognition theory, model integral stimulus spaces using a Cartesian coordinate system, just as with spaces defined by separable dimensions. This approach entails a rich geometrical structure that has never been questioned but may not be psychologically meaningful for integral dimensions. In particular, Cartesian models carry a notion of orthogonality of component dimensions, such that if 1 dimension is diagnostic for a classification or discrimination task, another can be selected as uniquely irrelevant. This article advances an alternative model in which integral dimensions are characterized as topological spaces. The Cartesian and topological models are tested in a series of experiments using the perceptual-learning phenomenon of dimension differentiation, whereby discrimination training with integral-dimension stimuli can induce an analytic representation of those stimuli. Under the present task design, the 2 models make contrasting predictions regarding the analytic representation that will be learned. Results consistently support the Cartesian model. These findings indicate that perceptual representations of integral dimensions are surprisingly structured, despite their holistic, unanalyzed nature.
Typical disjunctive artificial classification tasks require participants to sort stimuli according to rules such as “x likes cars only when black and coupe OR white and SUV.” For cate-gories like this, increasing the salience of the diagnostic dimensions has two simultaneous effects: increasing the distance between members of the same category and increas-ing the distance between members of opposite categories. Potentially, these two effects respectively hinder and facilitate classification learning, leading to competing predictions for learning. Increasing saliency may lead to members of the same category to be consid-ered less similar, while the members of separate categories might be considered more dissimilar. This implies a similarity-dissimilarity competition between two basic classifica-tion processes. When focusing on sub-category similarity, one would expect more difficult classification when members of the same category become less similar (disregarding the increase of between-category dissimilarity); however, the between-category dissimi-larity increase predicts a less difficult classification. Our categorization study suggests that participants rely more on using dissimilarities between opposite categories than finding similarities between sub-categories.We connect our results to rule- and exemplar-based classification models.The pattern of influences of within- and between-category similarities are challenging for simple single-process categorization systems based on rules or exem-plars. Instead, our results suggest that either these processes should be integrated in a hybrid model, or that category learning operates by forming clusters within each category.
Brunel, L., Goldstone, R. L., Vallet, G. Riou, V., & Versace, R. (2013). When Seeing a Dog Activates the Bark: Multisensory Generalization and Distinctiveness Effects. Experimental Psychology, 60, 100-112.
The goal of the present study was to find evidence for a multisensory generalization effect (i.e., generalization from one sensory modality to another sensory modality). The authors used an innovative paradigm (adapted from Brunel, Labeye, Lesourd, & Versace, 2009) involving three phases: a learning phase, consisting in the categorization of geometrical shapes, which manipulated the rules of association between shapes and a sound feature, and two test phases. The first of these was designed to examine the priming effect of the geometrical shapes seen in the learning phase on target tones (i.e., priming task), while the aim of the second was to examine the probability of recognizing the previously learned geometrical shapes (i.e., recognition task). When a shape category was mostly presented with a sound during learning, all of the primes (including those not presented with a sound in the learning phase) enhanced target processing compared to a condition in which the primes were mostly seen without a sound during learning. A pattern of results consistent with this initial finding was also observed during recognition, with the participants being unable to pick out the shape seen without a sound during the learning phase. Experiment 1 revealed a multisensory generalization effect across the members of a category when the objects belonging to the same category share the same value on the shape dimension. However, a distinctiveness effect was observed when a salient feature distinguished the objects within the category (Experiment 2a vs. 2b).
Carvalho, P. F., & Goldstone, R. L. (2013). How to present exemplars of several categories? Interleave during active learning and block during passive learning. Proceedings of the Thirty-Fifth Annual Conference of the Cognitive Science Society. (pp. 1982-1987). Berlin, Germany: Cognitive Science Society.
Research on how information should be presented during inductive category learning has identified both interleaving of categories and blocking by category as beneficial for learning. Previous work suggests that this mixed evidence can be reconciled by taking into account within- and between-category similarity relations. In this paper we present a new moderating factor. One group of participants studied categories actively, either interleaved or blocked. Another group studied the same categories passively. Results from a subsequent generalization task show that active learning benefits from interleaved presentation while passive learning benefits from blocked presentation.
Weitnauer, E., Carvalho, P. F., Goldstone, R. L., & Ritter, H. (2013). Grouping by Similarity Helps Concept Learning. Proceedings of the Thirty-Fifth Annual Conference of the Cognitive Science Society. (pp. 3747-3752). Berlin, Germany: Cognitive Science Society.
In inductive learning, the order in which concept instances are presented plays an important role in learning performance. Theories predict that interleaving instances of different concepts is especially beneficial if the concepts are highly similar to each other, whereas blocking instances belonging to the same concept provides an advantage for learning lowsimilarity concept structures. This leaves open the question of the relative influence of similarity on interleaved versus blocked presentation. To answer this question, we pit withinand between-category similarity effects against each other in a rich categorization task called Physical Bongard Problems. We manipulate the similarity of instances shown temporally close to each other with blocked and interleaved presentation. The results indicate a stronger effect of similarity on interleaving than on blocking. They further show a large benefit of comparing similar between-category instances on concept learning tasks where the feature dimensions are not known in advance but have to be constructed.
After more than 100 years of interest and study, knowledge transfer remains among the most challenging, contentious, and important issues for both psychology and education. In this article, we review and discuss many of the more important ideas and findings from the existing research and attempt to bridge this body of work with the exciting new research directions suggested by the following articles.
Understanding how to get learners to transfer their knowledge to new situations is a topic of both theoretical and practical importance. Theoretically, it touches on core issues in knowledge representation, analogical reasoning, generalization, embodied cognition, and concept formation. Practically, learning without transfer of what has been learned is almost always unproductive and inefficient. Although schools often measure the efficiency of learning in terms of speed and retention of knowledge, a relatively neglected and subtler component of efficiency is the generality and applicability of the acquired knowledge. This special issue of Educational Psychologist collects together new approaches toward understanding and fostering appropriate transfer in learners. Three themes that emerge from the collected articles are (a) the importance of the perspective/stance of the learner for achieving robust transfer, (b) the neglected role of motivation in determining transfer, and (c) the existence of specific, validated techniques for teaching with an eye toward facilitating students’ transfer of their learning.
Son, J. Y., Smith, L. B., Goldstone, R. L., & Leslie, M. (2012). The Importance of Being Interpreted: Grounded Words and Children’s Relational Reasoning, Frontiers in Developmental Psychology, 3, 1-12.
Although young children typically have trouble reasoning relationally, they are aided by the presence of relational words (e.g., Gentner & Rattermann, 1991). They also reason well about commonly experienced event structures (e.g., Fivush, 1984). Relational words may benefit relational reasoning because they activate well-understood event structures. Two candidate hypotheses were tested: (1) the Schema hypothesis, according to which words help relational reasoning because they are grounded in schematized experiences and (2) the Optimal Vagueness hypothesis, by which words benefit relational reasoning because the activated schema is open enough (without too much specificity) so that it can be applied analogically to novel problems. Four experiments examine these two hypotheses by examining how training with a label influences schematic interpretations of a scene, the kinds of scenes that are conducive to schematic interpretations, and whether children must figure out the interpretation themselves to benefit from the act of interpreting a scene as an event. Experiment 1 shows the superiority of schema-evoking words over words that do not connect to schematized experiences. Experiments 2 and 3 further reveal that these words must be applied to vaguely related perceptual instances rather than unrelated or concretely related instances in order to draw attention to relational structure. Experiment 4 provides evidence that even when children do not work out an interpretation for themselves, just the act of interpreting an ambiguous scene is potent for relational generalization. The present results suggest that relational words (and in particular their meanings) are created from the act of interpreting a perceptual situation in the context of a word grounded in meaningful experiences.
Braithwaite, D. W., & Goldstone, R. L. (2012). Inducing mathematical concepts from specific examples: The role of schema-level variation. Proceedings of the Thirty-Fourth Annual Conference of the Cognitive Science Society. (pp. 138-143). Sapporo, Japan: Cognitive Science Society.
Previous research suggests that comparing multiple specific examples of a general concept can promote knowledge transfer. The present study investigated whether this approach could be made more effective by systematic variation in the semantic content of the specific examples. Participants received instruction in a mathematical concept in the context of several examples, which instantiated either a single semantic schema (non-varied condition) or two different schemas (varied condition). Schema-level variation during instruction led to better knowledge transfer, as predicted. However, this advantage was limited to participants with relatively high performance before instruction. Variation also improved participants’ ability to describe the target concept in abstract terms. Surprisingly, however, this ability was not associated with successful knowledge transfer.
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Carvalho, P. F., & Goldstone, R. L. (2012). Category structure modulates interleaving and blocking advantage in inductive category acquisition. Proceedings of the Thirty-Fourth Annual Conference of the Cognitive Science Society. (pp. 186-191). Sapporo, Japan: Cognitive Science Society.
Research in inductive category learning has demonstrated that interleaving exemplars of categories results in better performance than presenting each category in a separate block. Two experiments indicate that the advantage of interleaved over blocked presentation is modulated by the structure of the categories being presented. More specifically, interleaved presentation results in better performance for categories with high within- and between-category similarity while blocked presentation results in better performance for categories with low within- and between-category similarity.
This interaction is predicted by accounts in which blocking promotes discovery of features shared by the members of a category whereas interleaving promotes discovery of features that discriminate between categories.
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Hendrickson, A. T., Carvalho, P. F., & Goldstone, R. L. (2012). Going to extremes: The influence of unsupervised categories on the mental caricaturization of faces and asymmetries in perceptual discrimination. Proceedings of the Thirty-Fourth Annual Conference of the Cognitive Science Society. (pp. 1662-1667). Sapporo, Japan: Cognitive Science Society.
Recent re-analysis of traditional Categorical Perception (CP) effects show that the advantage for between category judgments may be due to asymmetries of within-category judgments (Hanley & Roberson, 2011). This has led to the hypothesis that labels cause CP effects via these asymmetries due to category label uncertainty near the category boundary. In Experiment 1 we demonstrate that these “within-category” asymmetries exist before category training begins. Category learning does increase the within-category asymmetry on a category relevant dimension but equally on an irrelevant dimension. Experiment 2 replicates the asymmetry found in Experiment 1 without training and shows that it does not increase with additional exposure in the absence of category training. We conclude that the within-category asymmetry may be a result of unsupervised learning of stimulus clusters that emphasize extreme instances and that category training increases this caricaturization of stimulus representations.
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Hendrickson, A. T., Kachergis, G., Fausey, C. M., & Goldstone, R. L. (2012). Re-learning labeled categories reveals structured representations. Proceedings of the Thirty-Fourth Annual Conference of the Cognitive Science Society. (pp. 1668-1673). Sapporo, Japan: Cognitive Science Society.
How do people learn to group and re-group objects into labeled categories? In this paper, we examine mechanisms that guide how people re-represent categories. In two experiments, we examine what is easy and what is hard to relearn as people update their knowledge about labeled groups of objects. In Study 1, we test how people learn and re-learn to group objects that share no perceptual features. Data suggest that people easily learn to re-label objects when the category structure remains the same. In Study 2, we test whether more general types of labeling conventions — words that do or do not correspond with object similarities — influence learning and re-learning. Data suggest that people are able to learn either kind of convention and may have trouble switching between them when re-structuring their knowledge. Implications for category learning, second language acquisition and updating representations are discussed.
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Ottmar, E., Landy, D., & Goldstone, R. L. (2012). Teaching the Perceptual Structure of Algebraic Expressions: Preliminary Findings from the Pushing Symbols Intervention. Proceedings of the Thirty- Fourth Annual Conference of the Cognitive Science Society. (pp. 2156-2161). Sapporo, Japan: Cognitive Science Society.
We describe an intervention being developed by our research team, Pushing Symbols (PS). This intervention is designed to encourage learners to treat symbol systems as physical objects that move and change over time according to dynamic principles. We provide students with the opportunities to explore algebraic structure by physically manipulating and interacting with concrete and virtual symbolic systems that enforce rules through constraints on physical transformations. Here we present an instantiation of this approach aimed at helping students learn the structure of algebraic notation in general, and in particular learn to simplify like terms. This instantiation combines colored symbol tiles with a new touchscreen software technology adapted from the commercial Algebra Touch software. We present preliminary findings from a study with 70 middle-school students who participated in the PS intervention over a three-hour period.
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Goldstone, R. L., Kersten, A., & Cavalho, P. F. (2012). Concepts and Categorization. In A. F. Healy & R. W. Proctor (Eds.) Comprehensive handbook of psychology, Volume 4: Experimental psychology. (pp. 607-630). New Jersey: Wiley.
Issues related to concepts and categorization are nearly ubiquitous in psychology because of people’s natural tendency to perceive a thing as something. We have a powerful impulse to interpret our world. This act of interpretation, an act of “seeing something as X” rather than simply seeing it (Wittgenstein, 1953), is fundamentally an act of categorization. The attraction of research on concepts is that an extremely wide variety of cognitive acts can be understood as categorizations (Murphy, 2002).
Goldstone, R. L., Braithwaite, D. W., & Byrge, L. A. (2012). Perceptual learning. In N. M. Seel (Ed.) Encyclopedia of the Sciences of Learning. Heidelberg, German: Springer Verlag GmbH. (pp. 2616-2619).
Perceptual learning consists of long-lasting changes to an organismʼs perceptual system that improve its ability to respond to its environment in specific ways. These changes persist over time; more ephemeral perceptual changes are typically considered to be adaptation, attentional processes, or strategy shifts, rather than perceptual learning. These changes are due to environmental inputs; perceptual changes not coupled to the environment are considered maturation, rather than learning. Perceptual learning benefits an organism by tailoring the processes that gather information to the organismʼs needs for and uses of information.
One of the challenges for perceptually grounded accounts of high-level cognition is to explain how people make connections and draw inferences between situations that superficially have little in common. Evidence suggests that people draw these connections even without having explicit, verbalizable knowledge of their bases. Instead, the connections are based on sub-symbolic representations that are grounded in perception, action, and space. One reason why people are able to spontaneously see relations between situations that initially appear to be unrelated is that their eventual perceptions are not restricted to initial appearances. Training and strategic deployment allow our perceptual processes to deliver outputs that would have otherwise required abstract or formal reasoning. Even without people having any privileged access to the internal operations of perceptual modules, these modules can be systematically altered so as to better subserve our high-level reasoning needs. Moreover, perceptually-based processes can be altered in a number of ways to closely approximate formally sanctioned computations.
We implemented a problem-solving task in which groups of participants simultaneously played a simple innovation game in a complex problem space, with score feedback provided after each of a number of rounds. Each participant in a group was allowed to view and imitate the guesses of others during the game. The results showed the use of social learning strategies previously studied in other species, and demonstrated benefits of social learning and nonlinear effects of group size on strategy and performance. Rather than simply encouraging conformity, groups provided information to each individual about the distribution of useful innovations in the problem space. Imitation facilitated innovation rather than displacing it, because the former allowed good solutions to be propagated and preserved for further cumulative innovations in the group. Participants generally improved their solutions through the use of fairly conservative strategies, such as changing only a small portion of one’s solution at a time, and tending to imitate solutions similar to one’s own. Changes in these strategies over time had the effect of making solutions increasingly entrenched, both at individual and group levels. These results showed evidence of nonlinear dynamics in the decentralization of innovation, the emergence of group phenomena from complex interactions of individual efforts, stigmergy in the use of social information, and dynamic tradeoffs between exploration and exploitation of solutions. These results also support the idea that innovation and creativity can be recognized at the group level even when group members are generally cautious and imitative.
‘Brain Calisthenics for Abstract Ideas’ article in the New York Times (June 6, 2011)
Goldstone, R. L., Son, J. Y, & Byrge, L. (2011). Early perceptual learning. Infancy, 16, 45-51.
Bhatt and Quinn (2011) present a compelling case that human learning is early in two very different, but interacting, senses. Learning is developmentally early in that even infants show strikingly robust adaptation to the structures present in their world. Learning is also early in an information processing sense because infants’ adapt their perceptual encodings and organizations at an early stage of neural processing. Both senses of ”early” speak to the importance of learning because they imply that learners are adapting their representations of their environment in a way that affects all ”down-stream” processing. Developmentally speaking, the learning that an infant enacts serves as the groundwork for all subsequent learning. In terms of information processing, adapting early-stage sensory and perceptual processes in turn affects all subsequent cognitive processes. There is evidence from neuroscience that interactions with an environment do cause early changes to primarysensory cortices (Goldstone, 1998; Vogels, 2010). One might generally suppose that it is advisable to be conservative in making such environment driven cortical changes, given the ripples of influence caused by early learning in both senses. Manipulating grounding representations is a risky proposition. However, the evidence indicates that systems that need to respond effectively to their environment need to engage in both kinds of learning.
Sang, K., Todd, P. M., & Goldstone, R. L. (2011). Learning near-optimal search in a minimal explore/exploit task. Proceedings of the Thirty-Third Annual Conference of the Cognitive Science Society. (pp. 2800-2805). Boston, Massachusetts: Cognitive Science Society.
How well do people search an environment for non-depleting resources of different quality, where it is necessary to switch between exploring for new resources and exploiting those already found? Employing a simple card selection task to study exploitation and exploration, we find that the total resources accrued, the number of switches between exploring and exploiting, and the number of trials until stable exploitation becomes more similar to those of the optimal strategy as experience increases across searches. Subjects learned to adjust their effective (implicit) thresholds for exploitation toward the optimal threshold over 30 searches. Those implicit thresholds decrease over turns within each search, just as the optimal threshold does, but subjects’ explicitly stated exploitation threshold increases over turns. Nonetheless, both the explicit and learned implicit thresholds produced performance close to optimal.
Son, J. Y., Smith, L. B., & Goldstone, R. L. (2011). Connecting instances to promote children’s relational reasoning. Journal of Experimental Child Psychology, 108, 260-277.
The practice of learning from multiple instances seems to allow children to learn about relational structure. The experiments reported here have focused on two issues regarding relational learning from multiple instances: (1) what kind of perceptual situations foster such learning and (2) how particular object properties, such as complexity or similarity, interact with relational learning. Two kinds of perceptual situations were of interest here: simultaneous view, where instances are viewed at once, and sequential view, instances are viewed one at a time, one right after the other. We examine the influence of particular perceptual situations and object properties using two tests of relational reasoning: a common match-to-sample task (where new instances are compared to a common sample) and a variable match-to-sample task (where new instances are compared to a sample that varies on each trial). Experiments 1 and 2 indicate that simultaneous presentation of even highly dissimilar instances, one simple and one complex, effectively connects them together and improves relational generalization in both match-to-sample tasks. Experiment 3 showed simple samples are more effective than complex ones in the common match-to-sample task. However, when one instance is not used a common sample and various pairs of instances are simply compared (Experiment 4), simple and rich instances are equally effective at promoting relational learning. These results bear on our understanding of how children connect instances and how those initial connections affect learning and generalization.
Day, S. B., Manlove, S., & Goldstone, R. L. (2011). Transfer, and the effects of context outside of the training task. Proceedings of the Thirty-Third Annual Conference of the Cognitive Science Society. (pp. 2637-2642). Boston, Massachusetts: Cognitive Science Society.
While the use of concrete, contextualized and personally relevant examples can benefit learners in terms of comprehension and motivation, these types of examples can come with a cost. Examples may become too bound to their particular context, and individuals may have a difficult time recognizing when the underlying principles are relevant in new situations. In the current study, we provide evidence that contextualization may impair knowledge transfer even when that context occurs outside of the training example itself. Specifically, when students were taught about positive feedback systems in the context of polar ice-albedo effects, those individuals that had previously learned about the effects of global warming on polar bear populations showed reliably poorer transfer performance.
Day, S., & Goldstone, R. L. (2011). Analogical transfer from a simulated physical system. Journal of Experimental Psychology: Learning, Memory, and Cognition, 37,551-567.
Previous research has consistently found that spontaneous analogical transfer is strongly tied to concrete and contextual similarities between the cases. However, that work has largely failed to acknowledge that the relevant factor in transfer is the similarity between individuals’ mental representations of the situations, rather than the overt similarities between the cases themselves. Across several studies, we find that participants are able to transfer strategies learned from a perceptually concrete simulation of a physical system to a task with very dissimilar content and appearance. This transfer is reflected in better performance on the transfer task when its underlying dynamics are consistent rather than inconsistent with the preceding training task. Our data indicate that transfer in these tasks relies on the perceptual and spatial nature of the training task, but does not depend on direct interaction with the system, with participants performing equally well after simply observing the concrete simulation. We argue that participants in these studies are using the concrete, spatial, dynamic information presented in the training simulation as the basis for a concretely similar mental model of the dissimilar transfer task. Unexpectedly, our data consistently showed that transfer was independent of reported recognition of the analogy between tasks: while such recognition was associated with better overall performance, it was not associated with better transfer (in terms of applying an appropriate strategy). Together, these findings suggest that analogical transfer between overtly dissimilar cases may be much more common—and much more relevant to our cognitive processing—than is generally assumed.
Byrge, L. A., & Goldstone, R. L. (2011). Distinguishing levels of grounding that underlie transfer of learning. Proceedings of the Thirty-Third Annual Conference of the Cognitive Science Society. (pp. 2818-2823). Boston, Massachusetts: Cognitive Science Society.
We find that transfer of learning from a perceptually concrete simulation to an isomorphic but superficially dissimilar text- based problem is sensitive to the congruence between the force dynamics common to both systems and the kinesthetic schema induced via action in the first, perceptually concrete, simulation. Counterintuitively, incompatibility between the force dynamics and the kinesthetic schema has a beneficial effect on transfer, relative to compatibility as well as an unrelated control. We suggest that this incompatibility between action and system dynamics may make the system’s relational structure more salient, leading to a more flexible conceptualization that ultimately benefits transfer. In addition, we suggest that too much “action concreteness” in hands-on learning may actually limit transfer, by fostering an understanding that is tied to that action and therefore less available for transfer in situations where that action is no longer relevant.
Braithwaite, D. W., & Goldstone, R. L. (2011). Effects of grounded and formal representations on combinatorics learning. Proceedings of the Thirty-Third Annual Conference of the Cognitive Science Society. (pp. 3431-3436). Boston, Massachusetts: Cognitive Science Society.
Two experiments examined the differential effects of ground- ed and formal representations on learning of mathematics. Both involved combinatorics, using outcome listing and com- binatorics formulas as examples of grounded and formal rep- resentations, respectively. Experiment 1 compared perfor- mance on near and far transfer problems following instruc- tions involving listing or formulas. Instruction in formulas led to more near transfer, while far transfer performance did not differ by condition. Experiment 2 compared performance fol- lowing four types of instruction: listing only, formulas only, listing fading (listing followed by formulas), and listing intro- duction (formulas followed by listing). The listing fading condition led to performance on par with the formulas only condition, and for near transfer problems, significantly higher than the listing introduction and pure listing conditions. The results support the inclusion of grounded representations in combinatorics instruction, and suggest that such representa- tions should precede rather than follow formal representations in the instructional sequence.
Carvalho, P. F., & Goldstone, R. L. (2011). Sequential similarity and comparison effects in category learning. Proceedings of the Thirty-Third Annual Conference of the Cognitive Science Society. (pp. 2977-2982). Boston, Massachusetts: Cognitive Science Society.
Order effects in category learning have been previously demonstrated. Specifically, alternation between exemplars of two categories has been shown to improve category learning and discrimination, compared to presenting exemplars of each category in separate blocks. However, the mechanisms under- lying order effects are still not completely known. Remaining issues pertain to the relevance of within and between category similarities, and the role of comparing sequentially presented objects. We present two experiments: in Experiment 1 within- and between-category similarity are manipulated simultane- ously with presentation schedule. In Experiment 2, alternation between categories is compared to two blocked conditions: one in which very similar stimuli are presented successively, and another in which they are dissimilar. Our results show a clear overall advantage of low similarity in categorization performance, but no effect of presentation schedule. Also, al- ternation between categories is shown to result in better per- formance than the blocked condition with more dissimilar stimuli.
Day, S., & Goldstone, R. L. (2010). The Effects of Similarity and Individual differences on Comparison and Transfer. Proceedings of the Thirty-Second Annual Conference of the Cognitive Science Society. (pp. 465-470). Portland, Oregon: Cognitive Science Society.
Prior research has found that while people are generally quite poor at recognizing when a new situation is structurally similar to a known case, comparison of two analogous cases greatly improves the likelihood of achieving such recognition. Our study examines the effects of varying the similarity between these compared cases, both featurally and structurally. We find that between-case similarity has a significant impact on transfer, and that these effects interact with characteristics of the learner.
Goldstone, R. L., Hills, T. T., & Day, S. B. (2010). Concept formation. In. I. B. Weiner & W. E. Craighead (Eds.) The Corsini Encyclopedia of Psychology. New York: John Wiley & Sons. (pp. 381-383).
A concept is a mentally possessed idea or notion that can be used to categorize information or objects. Over the course of each person’s lifetime, thousands of concepts are learned, for nouns like corkscrew, justice, and doorknob, adjectives like green, symmetric, and beautiful, and verbs like kick, climb, and eschew. While some philosophers have maintained that we do not genuinely learn new concepts through induction (Fodor, 1988), most psychologists believe that concepts can be learned, and that the representational capacity of the learner increases as they acquire new concepts. Most efforts have been spent developing accounts of how people acquire and represent concepts, including models based on: rules, prototypes, exemplars, boundaries, and theories.
Goldstone, R. L., & Landy, D. H. (2010). Domain-creating constraints. Cognitive Science.
The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how something will behave, a learner must know what kind of thing it is. While this has led previous researchers to argue for domain-specific constraints that are tied to different kinds/domains, an exciting possibility is that kinds/domains themselves can be learned. General cognitive constraints, when combined with rich inputs, can establish domains, rather than these domains necessarily pre-existing prior to learning. Knowledge is structured and richly differentiated, but its “skeleton” must not always be pre-established. Instead, the skeleton may be adapted to fit patterns of co-occurrence, task requirements, and goals. Finally, we argue that for models of development to demonstrate genuine cognitive novelty, it will be helpful for them to move beyond highly pre-processed and symbolic encodings that limit flexibility. We consider two physical models that learn to make tone discriminations. They are mechanistic models that preserve rich spatial, perceptual, dynamic, and concrete information, allowing them to form surprising new classes of hypotheses and encodings.
Goldstone, R. L. (2010). Foreward. in I. Gauthier, M. J. Tarr, & D. Bubb (Eds.) Perceptual expertise: Bridging brain and behavior. Oxford, England: Oxford University Press. (pp. v – x).
perceptual learning is important for two reasons—because it is perceptual and because it is learning. Changes to perception are particularly important because they affect all subsequent cognitive processes that occur downstream. There is good evidence, both neurophysiological and behavioral, that perceptual learning can involve early changes to the primary visual, auditory, and somatosensory cortices. One might feel that the early perceptual system ought to be hardwired—it is better not to mess with it if it is going to be depended upon by all processes later in the information processing stream. There is something right with this intuition, but it implicitly buys into a ‘‘stable foundations make strong foundations’’ assumption that it is appropriate for houses of cards, but probably not for flexible cognitive systems. For better models of cognition, we might turn to Birkenstock shoes and suspension bridges, which provide good foundations for their respective feet and cars by flexibly deforming to their charges. Just as a suspension bridge provides better support for cars by conforming to the weight loads, perception supports problem solving and reasoning by conforming to these tasks.
If perceptual learning is crucially perceptual, it is also crucially learning. Consistent with the ripples of downstream influence that early perceptual changes exert, perceptual systems should generally be designed to change slowly and conservatively, so as not to disrupt their downstream consumers. For this reason, this book’s focus on perceptual expertise is appropriate. Expertise typically requires at least 10 years to attain (Ericsson, Krampe, & Tesch-Römer, 1993), sufficient time to influence perception, not simply decision trees or explicitly memorized strategies. The protracted time course of acquiring new perceptual tools is certainly frustrating for those in the business of judging wines, rock samples, cell structures, dives, or manufacturing flaws. One of the reasons why wisdom can’t be simply told (Bransford, Franks, Vye, & Sherwood, 1989) but rather must be lived is that wisdom is frequently perceptual and thus must be built into one’s neurological wiring.
Goldstone, R. L., Landy, D. H., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2, 265-284.
While the field of perceptual learning has mostly been concerned with low- to middle-level changes to perceptual systems due to experience, we consider high-level perceptual changes that accompany learning in science and mathematics. In science, we explore the transfer of a scientific principle (competitive specialization) across superficially dissimilar pedagogical simulations. We argue that transfer occurs when students develop perceptual interpretations of an initial simulation and simply continue to use the same interpretational bias when interacting with a second simulation. In arithmetic and algebraic reasoning, we find that proficiency in mathematics involves executing spatially explicit transformations to notational elements. People learn to attend mathematical operations in the order in which they should be executed, and the extent to which students employ their perceptual attention in this manner is positively correlated with their mathematical experience. For both science and mathematics, relatively sophisticated performance is achieved not by ignoring perceptual features in favor of deep conceptual features, but rather by adapting perceptual processing so as to conform with and support formally sanctioned responses. These “Rigged Up Perceptual Systems” (RUPS) offer a promising approach to educational reform.
Hendrickson, A. T., Kachergis, G., Gureckis, T. M., & Goldstone, R. L. (2010). The effect of verbal interference and the internal structure of categories on perceptual discrimination.Proceedings of the Thirty-Second Annual Conference of the Cognitive Science Society. (pp. 1216-1221). Portland, Oregon: Cognitive Science Society.
Recent research has argued that categorization is strongly tied to language processing. For example, language (in the form of verbal category labels) has been shown to influence perceptual discriminations of color (Winawer et al., 2007). However, does this imply that categorical perception is essentially verbally mediated perception? The present study extends recent findings in our lab showing that categorical perception can occur even in the absence of overt labels. In particular, we evaluate the degree to which certain interference tasks (verbal, spatial) reduce the effect of learned categorical perception for complex visual stimuli (faces). Contrary to previous findings, our results show that a verbal interference task does not disrupt learned categorical perception effects for faces. Our results are interpreted in light of the ongoing debate about the role of language in categorization. In particular, we suggest that at least a sub-set of categorical perception effects may be effectively “language-free”.
Hills, T. T., Todd, P. M., & Goldstone, R. L. (2010). Priming a Central Executive Search Process: Exploration and Exploitation in Generalized Cognitive Search Processes. Journal of Experimental Psychology: General, 139, 560-609.
The trade-off between exploration and exploitation is common to a wide variety of problems involving search in space and mind. The prevalence of this trade-off and its neurological underpinnings led us to propose domain-general cognitive search processes (Hills, Todd, & Goldstone, 2008). We propose further that these are consistent with the idea of a central executive search process that combines goal-handling across subgoal hierarchies. In the present study, we investigate 3 aspects of this proposal. First, the existence of a unitary central executive search process should allow priming from 1 search task to another and at multiple hierarchical levels. We confirm this by showing cross-domain priming from a spatial search task to 2 different cognitive levels within a lexical search task. Second, given the neural basis of the proposed generalized cognitive search process and the evidence that the central executive is primarily engaged during complex tasks, we hypothesize that priming should require search in the sense of a self-regulated making and testing of sequential predictions about the world. This was confirmed by showing that when participants were allowed to collect spatial resources without searching for them, no priming occurred. Finally, we provide a mechanism for the underlying search process and investigate 3 alternative hypotheses for subgoal hierarchies using the central executive as a search process model (CESP). CESP envisions the central executive as having both emergent and unitary processes, with one of its roles being a generalized cognitive search process that navigates goal hierarchies by mediating persistence on and switching between subgoals.
Landy, D. H., & Goldstone, R. L. (2010). Proximity and precedence in arithmetic. The Quarterly Journal of Experimental Psychology, 63, 1953-1968.
How does the physical structure of an arithmetic expression affect the computational processes engaged in by reasoners? In handwritten arithmetic expressions containing both multiplications and additions, terms that are multiplied are often placed physically closer together than terms that are added. Three experiments evaluate the role such physical factors play in how reasoners construct solutions to simple compound arithmetic expressions (such as “2 + 3 × 4”). Two kinds of influence are found: First, reasoners incorporate the physical size of the expression into numerical responses, tending to give larger responses to more widely spaced problems. Second, reasoners use spatial information as a cue to hierarchical expression structure: More narrowly spaced subproblems within an expression tend to be solved first and tend to be multiplied. Although spatial relationships besides order are entirely formally irrelevant to expression semantics, reasoners systematically use these relationships to support their success with various formal properties.
Son, J. Y., Doumas, L. A., & Goldstone, R. L. (2010). When do words promote analogical transfer? The Journal of Problem Solving, 3, 52-92.
The purpose of this paper is to explore how and when verbal labels facilitate relational reasoning and transfer. We review the research and theory behind two ways words might direct attention to relational information: (1) words generically invite people to compare and thus highlight relations (the Generic Tokens [GT] hypothesis), and/or (2) words carry semantic cues to common structure (the Cues to Specific Meaning [CSM] hypothesis). Four experiments examined whether learning Signal Detection Theory (SDT) with relational words fostered better transfer than learning without relational words in easily alignable and less alignable situations (testing the GT hypothesis) as well as when the relational words matched and mismatched the semantics of the learning situation (testing the CSM hypothesis). The results of the experiments found support for the GT hypothesis because the presence of relational labels produced better transfer when two situations were alignable. Although the CSM hypothesis does not explain how words facilitate transfer, we found that mismatches between words and their labeled referents can produce a situation where words hinder relational learning.
Barab, S., Scott, B., Siyahhan, S. Goldstone, R. L., Ingram-Goble, A., Zuiker, S., & Warren, S. (2009). Transformational play as a curricular scaffold: Using videogames to support science education Journal of Science Education and Technology, 18, 305-320.
Drawing on game-design principles and an underlying situated theoretical perspective, we developed and researched a 3D game-based curriculum designed to teach water quality concepts. We compared undergraduate student dyads assigned randomly to four different instructional design conditions where the content had increasingly level of contextualization: (a) expository textbook condition, (b) simplistic framing condition, (c) immersive world condition, and a (d) single-user immersive world condition. Results indicated that the 3D-dyad and 3D-single user conditions performed significantly better than the electronic textbook group on standardized items. The immersive-world dyad condition also performed significantly better than either the expository textbook or the descriptive framing condition on a performance-based transfer task, and performed significantly better than the expository textbook condition on standardized test items. Implications for science education, and consistent with the goals of this special issue, are that immersive game-based learning environments provide a powerful new form of curriculum for teaching and learning science.
Day, S. B., & Goldstone, R. L. (2009). Analogical transfer from interaction with a simulated physical system. Proceedings of the Thirty-First Annual Conference of the Cognitive Science Society, 1406-1411. Amsterdam, Netherlands: Cognitive Science Society.
In two studies, we find that participants are able to transfer strategies learned while interacting with a simulated physical system to a dissimilar and less perceptually-concrete domain. Interestingly, performance on the transfer task was completely unrelated to explicit knowledge of the structural correspondences between the systems. We suggest that direct interaction with a concrete system may lead to a kind of procedural knowledge that provides a good basis for analogical transfer.
Landy, D. H., & Goldstone, R. L. (2009). How much of symbolic manipulation is just symbol pushing? Proceedings of the Thirty-First Annual Conference of the Cognitive Science Society, 1072-1077. Amsterdam, Netherlands: Cognitive Science Society.
This paper explores the hypothesis that schematic abstraction—rule following—is partially implemented through processes and knowledge used to understand motion. Two experiments explore the mechanisms used by reasoners solving simple linear equations with one variable. Participants solved problems displayed against a background that moved rightward or leftward. Solving was facilitated when the background motion moved in the direction of the numeric transposition required to solve for the unknown variable. Previous theorizing has usually assumed that such formal problems are solved through the repeated application of abstract transformation patterns (rules) to equations, replicating the steps produced in typical worked solutions. However, the current results suggest that in addition to such strategies, advanced reasoners often employ a mental motion strategy when manipulating algebraic forms: elements of the problem are “picked up” and “moved” across the equation line. This demonstration supports the suggestion that genuinely schematic reasoning could be implemented in perceptual-motor systems through the simulated transformation of referential (but physical) symbol systems.
Son, J. Y., & Goldstone, R. L. (2009). Fostering General Transfer with Specific Simulations.Pragmatics and Cognition, 17, 1-42.
Science education faces the difficult task of helping students understand and appropriately generalize scientific principles across a variety of superficially dissimilar specific phenomena. Can cognitive technologies be adapted to benefit both learning specific domains and generalizable transfer? This issue is examined by teaching students complex adaptive systems with computer-based simulations. With a particular emphasis on fostering understanding that transfers to dissimilar phenomena, the studies reported here examine the influence of different descriptions and perceptual instantiations of the scientific principle of competitive specialization. Experiment 1 examines the role of intuitive descriptions to concrete ones, finding that intuitive descriptions leads to enhanced domain-specific learning but also deters transfer. Experiment 2 successfully alleviated these difficulties by combining intuitive descriptions with idealized graphical elements. Experiment 3 demonstrates that idealized graphics are more effective than concrete graphics even when unintuitive descriptions are applied to them. When graphics are concrete, learning and transfer largely depends on the particular description. However, when graphics are idealized, a wider variety of descriptions results in levels of learning and transfer similar to the best combination involving concrete graphics. Although computer-based simulations can be effective for learning that transfers, designing effective simulations requires an understanding of concreteness and idealization in both the graphical interface and its description.
Son, J. Y., & Goldstone, R. L. (2009). Contextualization in perspective. Cognition and Instruction, 27, 51-89.
Instruction abstracted from specific and concrete examples is frequently criticized for ignoring the context-dependent and perspectival nature of learning (e.g., Bruner, 1962, 1966; Greeno, 1997). Yet, in the effort to create personally interesting learning contexts, cognitive consequences have often been ignored. To examine what kinds of personalized contexts foster or hinder learning and transfer, three manipulations of perspective and context were employed to teach participants Signal Detection Theory (SDT). In all cases, application of SDT principles was negatively impacted by manipulations that encouraged participants to consider the perspective of the signal detector (the decision maker in SDT situations): by giving participants active detection experience (Experiment 1), biasing them to adopt a first-person rather than third-person perspective (Experiment 2), or framing the task in terms of a well-known celebrity (Experiment 3). These contexts run the risk of introducing goals and information that are specific to the detector’s point of view, resulting in sub-optimal understanding of SDT.
Searching in space and minds: IU research suggests underlying linkarticle in E Science News (September 12, 2008),UPI, Scientific American and Science Daily
Goldstone, R. L., & Wilensky, U. (2008). Promoting Transfer through Complex Systems Principles. Journal of the Learning Sciences, 17, 465-516.
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.
Goldstone, R. L., Landy, D., & Son, J. Y. (2008). A well grounded education: The role of perception in science and mathematics. In M. de Vega, A. Glenberg, & A. Graesser (Eds.) Symbols, embodiment, and meaning. Oxford Press (pp . 327-355).
One of the most important applications of grounded cognition theories is to science and mathematics education where the primary goal is to foster knowledge and skills that are widely transportable to new situations. This presents a challenge to those grounded cognition theories that tightly tie knowledge to the specifics of a single situation. In this chapter, we develop a theory learning that is grounded in perception and interaction, yet also supports transferable knowledge. A first series of studies explores the transfer of complex systems principles across two superficially dissimilar scenarios. The results indicate that students most effectively show transfer by applying previously learned perceptual and interpretational processes to new situations. A second series shows that even when students are solving formal algebra problems, they are greatly influenced by non-symbolic, perceptual grouping factors. We interpret both results as showing that high-level cognition that might seem to involve purely symbolic reasoning is actually driven by perceptual processes. The educational implication is that instruction in science and mathematics should involve not only teaching abstract rules and equations but also training students to perceive and interact with their world.
Landy, D. H., Jones, M. N., & Goldstone, R. L. (2008). How the appearance of an operator affects its formal precedence. Proceedings of the Thirtieth Annual Conference of the Cognitive Science Society, , (pp. 2109-2114). Washington, D.C.: Cognitive Science Society
Two experiments test predictions of a visual process-driven model of multi-term arithmetic computation. The visual process model predicts that attention should be drawn toward multiplication signs more readily than toward plus signs, and that narrow spaces should draw gaze comparably to multiplication signs. Although both of these predictions are verified by behavioral response measures and eye-tracking, the visual process model cannot account for patterns of early looking. The results suggest that people strategically deploy visual computation strategies.
Son, J. Y., Smith, L. B., & Goldstone, R. L. (2008). implicity and generalization: Short-cutting abstraction in children’s object categorizations. Cognition, 108, 626-638.
Development in any domain is often characterized by increasingly abstract representations. Recent evidence in the domain of shape recognition provides one example; between 18 and 24 months children appear to build increasingly abstract representations of object shape [Smith, L. B. (2003). Learning to recognize objects. Psychological Science, 14, 244– 250]. Abstraction is in part simplification because it requires the removal of irrelevant information. At the same time, part of generalization is ignoring irrelevant differences. The resulting prediction is this: simplification may enable generalization. Four experiments asked whether simple training instances could shortcut the process of abstraction and directly promote appropriate generalization. Toddlers were taught novel object categories with either simple or complex training exemplars. We found that children who learned with simple objects were able to generalize according to shape similarity, typically relevant for early object categories, better than those who learned with complex objects. Abstraction is the product of learning; using simplified – already abstracted instances – can short-cut that learning, leading to robust generalization.
Ionescu, T., & Goldstone, R. L. (2007). Introduction to a special issue on the Development of Categorization, Cognition, Brain, and Behavior, 11, 629-633.
Categorization is indubitably an important cognitive process for humans (as well as other animals, Murai, Kosugi, Tomonaga, Tanaka, Matsuzawa, & Itakura, 2005), one that we constantly engage in to adapt to a very rich environment. We have a powerful impulse to interpret our world. This act of interpretation is fundamentally an act of categorization. We can go back in history at least to Aristotle (see his work on Categories, 350 B.C.E.) and along this way we find discussions of categories often appearing in philosophers’ books. The issue of categorization is also an historically early topic in psychology (see Hull’s experiment in 1920), and a considerable amount of research has been continuously dedicated to it up until the present. One could ask then: Why a special issue on categorization at this point in time? Although the general topic of categorization is venerable, relatively recently we cognitive scientists have changed our view about categorization. We have moved from considering taxonomies (or categories based in logic) as the “real,” mature kind of categorization to understanding that there are multiple kinds of similarities that are taken into account when one groups items (Barsalou, 1993, 2003; Medin, Goldstone, & Gentner, 1993; Ross & Murphy, 1999).
Landy, D., & Goldstone, R. L. (2007). Formal notations are diagrams: Evidence from a production task. Memory & Cognition, 35, 2033-2040
Although a general sense of the magnitude, quantity, or numerosity of objects is common both in untrained people and in animals, the abilities to deal exactly with large quantities and to reason precisely in complex but well-specified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations employ typically complex, hierarchically embedded structures, which all extant analyses assume are constructed by concatenative, rule-based processes. The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that the some of the same cognitive resources involved in representing spatial relations and proximities are also involved in representing symbolic notations: in short, formal notations are a kind of diagram. We examine self-generated productions in the domains of handwritten arithmetic expressions and typewritten statements in a formal logic. In both tasks, we find substantial evidence for spatial representational schemes even in these highly symbolic domains.
Landy, D. & Goldstone, R. L. (2007). How abstract is symbolic thought? Journal of Experimental Psychology: Learning, Memory, & Cognition, 33, 720-733.
In 4 experiments, the authors explored the role of visual layout in rule-based syntactic judgments. Participants judged the validity of a set of algebraic equations that tested their ability to apply the order of operations. In each experiment, a nonmathematical grouping pressure was manipulated to support or interfere with the mathematical convention. Despite the formal irrelevance of these grouping manipulations, accuracy in all experiments was highest when the nonmathematical pressure supported the mathematical grouping. The increase was significantly greater when the correct judgment depended on the order of operator precedence. The result that visual perception impacts rule application in mathematics has broad implications for relational reasoning in general. The authors conclude that formally symbolic reasoning is more visual than is usually proposed.
Landy, D. & Goldstone, R. L. (2007). The alignment of ordering and space in arithmetic computation. Proceedings of the Twenty-ninth Annual Conference of the Cognitive Science Society. (pp. 437-442). Nashville, TN: Cognitive Science Society.
In 4 experiments, the authors explored the role of visual layout in rule-based syntactic judgments. Participants judged the validity of a set of algebraic equations that tested their ability to apply the order of operations. In each experiment, a nonmathematical grouping pressure was manipulated to support or interfere with the mathematical convention. Despite the formal irrelevance of these grouping manipulations, accuracy in all experiments was highest when the nonmathematical pressure supported the mathematical grouping. The increase was significantly greater when the correct judgment depended on the order of operator precedence. The result that visual perception impacts rule application in mathematics has broad implications for relational reasoning in general. The authors conclude that formally symbolic reasoning is more visual than is usually proposed.
Landy, D. & Goldstone, R. L. (2007). How space guides interpretation of a novel mathematical system. Proceedings of the Twenty-ninth Annual Conference of the Cognitive Science Society.(pp. 431-436). Nashville, TN: Cognitive Science Society.
This paper investigates how people build interpretations of compound expressions in a novel formal system. In traditional arithmetic, interpretations are guided by an order of precedence convention (times and division precede addition and subtraction). This order is supported by alignment with the order of precedence. In the experiment described here, participants learned computation tables of two simple novel operators, and then were asked to discover a precedence order between them. The operators were presented with a physical spacing convention that either aligned with the precedence order, opposed it, or randomly opposed or aligned with the precedence order. Participants were more likely to reach a criterion of successful performance when the order of operations aligned with the precedence order, and did so more quickly than either other group. The results indicate that reasoners integrate salient perceptual cues with formal knowledge following particular conventions, even on novel systems.
Landy, D. & Goldstone, R. L. (2007). Grounding symbol structures in space: Formal notations as diagrams. Proceedings of the Twenty-ninth Annual Conference of the Cognitive Science Society.(pp. 425-430). Nashville, TN: Cognitive Science Society.
[Winner of the 2007 Marr Prize for Best Student Paper at the 2007 Meeting of the Cognitive Science Society]
Although a general sense of the magnitude, quantity, or numerosity is common both in untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but well-specified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations employ typically complex, hierarchically embedded structures, which all extant analyses assume are the product of concatenative, rule-based processes. The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that the some of the same cognitive resources involved in representing spatial relations and proximities are also involved in representing symbolic notations. In short, formal notations are used as a kind of diagram. We examine selfgenerated productions in the domains of handwritten arithmetic expressions and typewritten statements in a formal logic. In both tasks, we find substantial evidence for spatial processes even in these highly symbolic domains.
Son, J. Y., Smith, L. B., & Goldstone, R. L. (2007). Re-representation using labels: Comparison or replacement. Proceedings of the Twenty-ninth Annual Conference of the Cognitive Science Society. (pp. 677-682). Nashville, TN: Cognitive Science Society.
The practice of labeling seems to allow children to make difficult relational similarity matches. Two experiments explore the cognitive processes of comparison and replacement that have been implicated in the beneficial effects of linguistic labeling. Since linguistic labels may be implicated in a number of these processes, our experiments used traditional non-linguistic labels (post-its) to promote either the process of comparison or replacement. Results from two relational matching tasks suggest that comparison is more influential than replacement.
Son, J. Y., Smith, L. B., & Goldstone, R. L. (2007). Words that evoke schemas: The need for optimal vagueness. Proceedings of the Workshop on Analogies: Integrating Multiple Cognitive Abilities (AnICA07). Nashville, Tennesse.
Although young children typically have trouble reasoning relationally, they are aided by the presence of relational words (e.g., Gentner & Rattermann, 1991) and can reason well about commonly experienced event structures (e.g., Fivush, 1984). Two experiments examine how schema-evoking words help preschool-aged children generalize relational patterns. Experiment 1 shows the superiority of schema-evoking words and Experiment 2 further reveals that these words must be applied to vaguely related events in order to draw attention to structure.
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, “There 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 ‘net-making” (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, Darwin, and Newton. Complex systems researchers, and learning scientists more generally, offer an alternative perspective, choosing to reverse the trend toward increasing specialization.
Son, J. Y., Smith, L. B., & Goldstone, R. L. (2006). Generalizing from simple instances: An uncomplicated lesson from kids learning objects categories. Proceedings of the Twenty-eighth Annual Conference of the Cognitive Science Society. Hillsdale, New Jersey: Lawrence Erlbaum Associates. (2174-2179)
Abstraction is the process of stripping away irrelevant information so that learners can generalize on relevant similarities. Can we shortcut this process by directly teaching abstractions in the form of simplified instances? We tested this prediction in the domain of shape-based generalization and found that young children were able to generalize better when taught with simplified shapes rather than complex detailed ones. Simplicity during training allowed shape novices to generalize like shape experts.
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.
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. (pp. 2509)
Relational reasoning—reasoning that depends on the interactions of multiple elements, rather than on the intrinsic properties of the elements—is 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.
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. (pp. 2050-2055)
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.
Participants in two experiments interacted with computer simulations designed to foster understanding of scientific principles governing complex adaptive systems. The quality of participants’ 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 (“Concreteness fading”) allows originally grounded and interpretable principles to become less tied to specific contexts and hence more transferable.
The external world must be filtered through our perceptual systems before it can have an impact upon us. That is, the world we experience is formed by our perceptual processing. However, it is not viciously circular to argue that our perceptual systems are reciprocally formed by our experiences. In fact, it is because our experiences are necessarily based on our perceptual systems that these perceptual systems must be shaped so that our experiences are appropriate and useful for dealing with our world.
In what follows, I will argue that the “building blocks” an observer uses for construing their world depends on the observer’s history, training, and acculturation. These factors, together with psychophysical constraints, mold one’s set of building blocks. Researchers who have proposed fixed sets of hard-wired primitives are exactly right in one sense — the combinatorics of objects, words, scenes, and scenarios strongly favor componential representations. However, this does not necessitate that the components be hard-wired. By developing new components to subserve particular tasks and environments, a newly important discrimination can generate building blocks that are tailored for the discrimination. Adaptive building blocks are likely to be efficient because they can be optimized for idiosyncratic needs and environments.
Goldstone, R. L., & Sakamoto, Y. (2003). The Transfer of Abstract Principles Governing Complex Adaptive Systems. Cognitive Psychology, 46, 414-466.
Four experiments explored participants’ understanding of the abstract principles governing computer simulations of complex adaptive systems. Experiment 1 revealed better transfer between computer simulations when they were governed by the same abstract principle, even when the simulations’ domains were dissimilar. Experiments 2 and 3 showed better transfer of abstract principles across simulations that were relatively dissimilar, and that this effect was due to participants who performed relatively poorly on the initial simulation. In Experiment 4, participants showed better abstract understanding of a simulation when it was depicted with concrete rather than idealized graphical elements. However, for poor performers, the idealized version of the simulation transferred better to a new simulation governed by the same abstraction. The results are interpreted in terms of competition between abstract and concrete construals of the simulations. Individuals prone toward concrete construals tend to overlook abstractions when concrete properties or superficial similarities are salient.