United States

Commutativity–the fact that changing the order of operands in an operation does not change the results–is a fundamental principle of mathematics. How does its understanding develop in children? While this question has mostly been addressed for addition, here we focus on multiplication. We ask whether children’s formal learning of multiplication commutativity relies on pre-existing non-symbolic intuitions, or whether it is first learnt symbolically and only later elaborated as a general principle that extends to concrete situations. 2nd and 3rd graders received an intervention on commutative multiplication, before and after which they played a number comparison game testing their understanding of commutativity in symbolic and non-symbolic contexts. Our results suggest that the commutative principle of multiplication may not be available to intuition before formal teaching: perceiving that 2 groups of 3 dots and 3 groups of 2 dots contain the same number of dots requires mastering commutativity symbolically first.

CogSci 2023

Do school-age children learn that 2 x 3 = 3 x 2 relying on previous intuitions?

technical paper

The 45th Annual Meeting of the Cognitive Science Society will take place in Sydney, Australia as a modified hybrid conference. Presentations from the main-session room will be live-streamed every day for all events. This will include all invited talks and award sessions. Recordings of all CogSci 2023 sessions will be made available for on-demand viewing after the conference.<br>
The in-person component will be held at the International Convention Centre Sydney at Darling Harbour. The Conference will take place Wednesday July 26th – Saturday July 29th, 2023 (Wednesday, July 26th is the Workshops Day).

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<br>[**The Program at a Glance can be found here**](https://cognitivesciencesociety.org/wp-content/uploads/2023/07/COgSci-PAAG-V2.pdf)
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The 45th Annual Meeting of the Cognitive Science Society presents the latest research across cognitive science and highlights the theme of Cognition in Context.

Infants are born into rich social networks and are faced with the challenge of learning about them. Previous research shows that infants learn about the individuals in observed social interactions, but it is not clear whether they infer their individual dispositions or their relationships to one another. The current studies address this question in 12-month-old infants and 16- to 18-month-old toddlers who observe social interactions involving imitation. In Studies 1 and 3, infants and toddlers expected that imitators, compared to non-imitators, would respond to their social partners’ distress. Likewise, they expected the targets of imitation, compared to non-targets, to respond to their partner’s distress. In Study 2, these expectations did not generalize to interactions with a new partner, providing evidence for learning about the original individuals’ relationship. In Study 3, infants’ expectations did not generalize to responses to laughter, suggesting a focus on established social relationships. Together, these results provide evidence that infants and toddlers learn about the social relationships of unknown individuals by observing interactions involving imitation.


Infants Infer Social Relationships between Individuals who Engage in Imitative Social Interactions

Can one person tell, just from observing how another person’s body moves, what that person is trying to learn? Here, we explore this question through several experiments on “epistemic action recognition”. We filmed volunteers playing a box-shaking game in which they attempted to determine either (a) the number of objects hidden in an opaque box, or (b) the shape of the objects hidden in the opaque box. Then, independent subjects watched these videos and were asked to determine which videos came from which task: Who was shaking for number and who was shaking for shape? Across 3 experiments, observers successfully determined what an actor was trying to learn about the contents of the box, based only on their observed actions (i.e., how they shook it). These results demonstrate that humans have the ability to infer epistemic intent from physical behaviors, adding a new dimension to research on action understanding.

What does learning look Like?: visual Recognition of epistemic intent

Successful social coordination requires being able to predict how the other people that one depends on are likely to behave. One solution to this dilemma is to establish social conventions, which constrain individuals' behavior but make prediction easier. Here, we develop a multi-agent deep reinforcement learning environment to investigate the costs associated with these conventions. In our produce-and-trade task, agents have varying production skills, but their actions must be predictable in order to be rewarded. Stronger norms improve the overall success of the group by improving the average rewards of the majority, but also systematically disadvantage agents whose specialization is in the minority of the group. Critically, this outcome is magnified by population size: as larger groups make it potentially more difficult to develop individualized representations of agents, minority agents become more likely to conform to a norm that is disadvantageous to them.


Unequal Norms Emerge Under Coordination Uncertainty in Multi-Agent Deep Reinforcement Learning

Humans are remarkably effective social learners, with several recent studies formalizing this capacity using computational models. 
However, previous research has often been limited to tasks where observer and demonstrator share the same reward function. In contrast, humans can learn from others who have different preferences, skills, or goals. To study social learning under individual differences, we introduce the socially correlated bandit, where participants have personalized rewards, which are correlated with but not identical to those of others. Social information can still be useful, but not when used verbatim.
We present a model of social generalization that integrates individual and social information into the generalization process, but assumes social information to be noisier and thus less informative. This model out-competes previous models, with it being the dominant strategy in evolutionary simulations.
Our findings expand on previous models of social learning, showing humans can integrate social information more flexibly than previously assumed.


Social learning with a grain of salt

Many cultures share common constellations and common narratives about the stars in the night sky. Previous research has shown that this overlap in asterisms, minimal star groupings inside constellations, is clearly present across 22 distinct culture groups and can be explained in part by properties of individual stars (brightness) and properties of pairs of stars (proximity) (Kemp, Hamacher, Little and Cropper, 2022). The same work, however, found no evidence that properties of triples (angle) and quadruples (good continuation) predicted constellation formation. We developed a behavioural experiment to explore how individuals form constellations under conditions that reduce cultural learning. We found that participants independently selected and connected similar stars, and that their responses were predicted by two properties of triples (angle and even spacing) in addition to the properties of brightness and proximity supported by previous work. Our findings lend further evidence to the theory that commonality of constellations across cultures is not a result of shared human history but rather stems from shared human nature.


Visual perception principles in constellation creation in individuals

Computational models of multiple object tracking (MOT) presuppose the existence of non-conceptual indexes in visual perception, and as a result predict that identification performance on MOT tasks should be no worse than tracking performance for the same stimuli. However, empirical evidence suggests that identification performance is worse than tracking performance in MOT. We propose a computational model of MOT that is able to account for several empirical results related to tracking performance without the use of indexes and thus avoids yoking tracking performance to identification performance. We also test our model empirically and show that it accounts well for the variation in identification performance with increasing number of targets in MOT with visually identical objects. By employing an explicit (rather than an implicit) mechanism for the maintenance of correspondence between attended locations and object identities, our model accounts for the tracking vs ID performance disparity.


Tracking Multiple Objects without Indexes

The inverse base-rate effect is a robust irrational bias that arises when people face ambiguity. The most prominent theories of this irrational bias depend on prediction error.
In this study, we gradually removed elements of a predictive learning design to test the extent to which error-driven processes underly this bias. In our first experiment, we removed explicit feedback by implementing the inverse base-rate effect in an observational learning procedure. In our second study, we further removed any causal relationship between stimulus features and category labels by moving towards an unsupervised learning procedure. This removed any information participants could use to identify category labels. In both experiments, the inverse base-rate effect persisted and remained robust. This outcome suggests that this irrational bias is independent of supervised learning procedures. We propose that any theories and models of the inverse base-rate effect must manage information encoding and connection updates without explicit prediction error. We end by proposing two clear paths for future investigations.


Errorless irrationality: removing error-driven components from the inverse base-rate effect paradigm

Recent studies suggest that errors facilitate learning in certain conditions. Despite this, reinforcement paradigms dominate learning methods, subscribing to the narrative that errorless learning is the foundation of an ideal learning environment. If we continue to view learning from this restrictive perspective, we may fail to capture and apply the benefits of errors. In this paper, we investigate two potential mechanisms of post-error learning. Participants (N = 61) learned word pairs in either a study or error trial before taking a final test. Supporting past error learning literature, errors before a study opportunity led to better performance on a final test. Differences in reaction times between conditions support the theory that errors increase learning by acting as a mediator, or secondary cue, to the correct answer on subsequent tests.


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Do school-age children learn that 2 x 3 = 3 x 2 relying on previous intuitions?

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Infants Infer Social Relationships between Individuals who Engage in Imitative Social Interactions