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There are ongoing debates whether logarithmic compression in number-to-space mapping reflects logarithmic encoding of large numbers (bias) or uncertainty about numeric value (noise). We tested these two hypotheses by disentangling the effect of bias and noise. When 80 adults and 80 4- to 7-year-olds were asked to estimate the number of dots on a number line, both children and adults were more logarithmic on 0-100 than 0-30 problems. Internal noise explained some of the variance in logarithmicity, but only for children. We then examined the wisdom of crowds effect by comparing accuracy of children&#39;s mean estimate with accuracy of each adult&#39;s estimates. As predicted, children as a crowd were not as accurate as individual adults, indicating that noise is not the only source of children&#39;s errors. Generally, increasing the size of a crowd also had a smaller effect on 0-100 than 0-30 problems, indicating that inaccuracy on 0-30 problems is likely due to noise. The present study provides evidence that bias and noise have an additive effect on logarithmic compression and that children&#39;s logarithmicity reflects bias in number representations, not just noise.

CogSci 2023

Children Are Not Just Noisy Adults: Disentangling Noise and Bias in Numerical Estimation

There are ongoing debates whether logarithmic compression in number-to-space mapping reflects logarithmic encoding of large numbers (bias) or uncertainty about numeric value (noise). We tested these two hypotheses by disentangling the effect of bias and noise. When 80 adults and 80 4- to 7-year-olds were asked to estimate the number of dots on a number line, both children and adults were more logarithmic on 0-100 than 0-30 problems. Internal noise explained some of the variance in logarithmicity, but only for children. We then examined the wisdom of crowds effect by comparing accuracy of children's mean estimate with accuracy of each adult's estimates. As predicted, children as a crowd were not as accurate as individual adults, indicating that noise is not the only source of children's errors. Generally, increasing the size of a crowd also had a smaller effect on 0-100 than 0-30 problems, indicating that inaccuracy on 0-30 problems is likely due to noise. The present study provides evidence that bias and noise have an additive effect on logarithmic compression and that children's logarithmicity reflects bias in number representations, not just noise.

poster

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).

Join us!

<br>[**The Program at a Glance can be found here**](https://cognitivesciencesociety.org/wp-content/uploads/2023/07/COgSci-PAAG-V2.pdf)
<br>[**The Detailed Program can be found here**](https://online.fliphtml5.com/ebtyf/mswz/)
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#### **CogSci 2023 Program Book**
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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.

We explore whether people can infer the principle of additive commutativity in the absence of cultural support—such as formal schooling and market experience. Our prior research shows that unschooled Tsimane’ adults do not succeed on abstract symbolic and word problem commutativity tasks. In a new study, we implement a concrete commutativity task with tangible tokens, including sums with specified (e.g. 2+1 vs. 1+2) and unspecified (e.g. 2+Dax vs. Dax+2) quantities. We find significantly better performance on concrete tasks than in abstract tasks, even in Tsimane’ participants with limited levels of formal schooling and other cultural supports. This suggests that cultural support is not necessary to understand the commutative principle, but is necessary to apply it to more abstract problems.

The role of cultural support on commutativity at varying levels of abstraction

People are known for their ability to learn probabilistic rewarding rules of the environment. However, the rules tested in most studies consisted of one feature dimension or a linear combination of multiple features. It is unclear how well people can learn non-linear combinatory rules where each single dimension is noninformative. In an adapted matching-pennies game, we asked participants to predict whether their opponent would choose head or tail next trial. Though the feature space for possible rules was small, including only two binary dimensions (i.e., the two players’ current choices), participants had striking failures in learning the probabilistic XOR rules (e.g., the opponent would have a probability of 0.8 to choose head if the two players had matching pennies and tail for unmatching pennies). The failure persisted in a series of experiments, even when the feature space was made explicit, after 320 trials of learning, and for different cover stories.

People fail to learn probabilistic XOR rules even in a small feature space

Despite the importance of risk attitude on decision making, its role on belief updating has been overlooked. In this paper, we aim to answer this fundamental question. We show, using economic theory, that stronger risk aversion drives more conservative actions, decreases the instrumental value of information relative to the importance of belief-based utility. Thus, with utility for clarity, stronger risk attitude yields to more belief change; whereas with updating cost, stronger risk attitude leads to less belief change. We confirm the result experimentally in two settings where subjects update their belief about their IQ and a randomly drawn number, respectively.

Belief Attitude and Belief Updating

Nudges have been shown to be successful behavioral interventions. However, nudges have also been criticized to be paternalistic and infringe upon decision makers’ (DMs) autonomy. One solution that has been proposed is self-nudges—let DMs nudge themselves. Using default nudges, we tested whether self-nudges are as effective as traditional nudges. Participants were presented with a choice between two videos. We either nudged the participants by preselecting one video as default on their behalf, or asked participants to self-nudge by preselecting a video for themselves prior to their choice. We found that a much larger percentage of participants stayed with the default option and watched the preselected video when they preselected the video themselves (82.5% on average between the two videos) than when we preselected the video for them (59.5% on average between the two videos). Our findings provide preliminary evidence for the efficacy of self-nudges.

Are self-nudges effective?

Serial dependence is a phenomenon in which the perception of current stimuli is induced by the perception of past stimuli. We examined the serial dependence when participants estimated the total number of coins, or the monetary value displayed and observed attractive effects in both tasks. We also analyzed the effect of response history, and found that the immediately prior response had an attractive effect on current responses, while the immediately prior stimuli exerted a repulsive effect. These results suggest that serial dependence depends on the response to the stimulus, rather than on the perception. In this study, we aimed to separate the effect of the stimulus and that of the response by direct experimental manipulation. Specifically, we compared the magnitude of the serial dependence between trials in which participants only saw the dots in the previous trials and trials in which participants answered the number of dots in the previous trials.

Impact of past answer on serial dependence in numerosity perception

Decades of research has demonstrated that people do not make economically rational decisions when risk is involved. While research has focused on how and why people’s decisions differ from economic rationality, an unanswered question is whether people can learn to improve their risky decision making in response to feedback on similar past decisions. In an experiment, we test whether people’s risk preferences change after they received either natural (a single outcome), or idealised (the average outcome) feedback about similar decisions in the past. Crucially, unlike studies of decisions from experience, they received feedback on several different decisions from description, rather than repeated feedback about a single choice. Compared to a control, who received no feedback, both forms of feedback led to an increase in choice of the higher Expected Value gamble. Modelling suggests, for natural feedback, this may be due to changes in how they treat probability information.

Effects of learning and feedback on risk preferences

On-line decision problems – in which a decision is made based on a sequence of past events without knowledge of the future – have been extensively studied in theoretical computer science. A famous example is the Prediction from Expert Advice problem,
in which an agent has to make a decision informed by the predictions of a set of experts. An optimal solution to this problem is the Multiplicative Weights Update Method (MWUM).
In this paper, we investigate how humans behave in a Prediction from Expert Advice task. We compare MWUM and several other algorithms proposed in the computer science literature against human behavior. We find that MWUM provides the best fit to people’s choices.

Comparing Human Predictions from Expert Advice to On-line Optimization Algorithms

Developmental dyscalculia (DD) is a neurodevelopmental disorder characterized by persistent poor math performance despite normal intelligence and education opportunities. Existing behavioral and neuroimaging studies have demonstrated that quantity processing deficits in DD are accompanied by aberrant brain functions and neurobiological alterations. Although theories have argued that the behavioral impairments observed in DD result from neurobiological deficiency and imbalance of excitatory and inhibitory signals in the brain, these hypotheses are difficult to test in human subjects. Therefore, in the current study, we implemented convolutional neural network models and tested the causal influence of neural capacity (i.e., number of units) and system excitability (i.e., the slope of activation) during the learning of quantity information. For both symbolic and non-symbolic processing, we observed that reducing the number of units did not lead to changes in learning performance. In contrast, increased excitability largely impaired the accuracy of learning, especially for the non-symbolic representations. Therefore, our model simulations provided direct evidence that increased excitability in the brain could result in behavioral impairments in learning quantity information, potentially suggesting a neurobiological basis for DD.

Limited Neural Capacity and Hyper-Excitability Affect Quantity Processing: A Computational Account

Active learning techniques enhance understanding and engagement in the learner, but these techniques can be difficult to teach to instructors. The pedagogy of active learning typically either describes abstract concepts or it relies heavily on case studies of what other instructors have created. Because it can be difficult for interested instructors to put theory into practice without a concrete structure, active learning techniques can be hard to implement in the classroom. Behaviorism, cognitivism, constructivism, and connectivism can be used to describe ideas about how learning is occurring, but they do not accurately categorize commonly used teaching activities, which instead often contain elements of multiple learning theories. I propose a novel functional categorization of active learning techniques that is both brain-based and student-centered, placing emphasis on the knowledge journey. This work describes these seven evidence-based “knowledge catalysts” as a new user-friendly framework for both understanding, using, and teaching active learning techniques.

Knowledge Catalysts: A Structure to Promote Incorporation of Active Learning Techniques

This study investigates how individuals collaboratively constructed shared knowledge during a group activity. The dataset was collected from group activities for pre-service teachers in professional development. Participants designed body poses and action sequences that could help their students’ mathematical conceptualization. Using k-means clustering and principal component analysis, patterns of individuals’ contributions based on their verbal and gestural behavior identified two groups of individuals: (1) Those who contributed to the discussion by speaking and gesturing frequently (~ 25% of the participants), and (2) those who mostly listened and focused on design ideas presented by others. Furthermore, epistemic network analysis corroborated significant differences in discourse patterns between the clusters, the results of which has significant implications for collaborative embodied learning and application for teacher education and professional development.

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Children Are Not Just Noisy Adults: Disentangling Noise and Bias in Numerical Estimation

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The role of cultural support on commutativity at varying levels of abstraction