Priors, Progressions, and Predictions in Science Learning: Theory-Based Bayesian Models of Children’s Revising Beliefs of Water Displacement

Abstract

Despite sometimes noisy evidence (e.g., perceptual processing errors), young children are capable of predicting and evaluating events based on complex causal representations. Children rapidly revise their beliefs and learn scientific conceptssometimes without prior knowledge of an underlying causal system. What might we need in our computational models of belief revision to similarly simulate children's behaviors when learning such causal systems? Building from experimental data of elementary school children's intuitive beliefs and predictions of water displacement, we propose three aspects of human inference and belief revision that warrant attention within the subfield of computational cognition. Each aspect is described by identifying the gaps between empirical findings and current computational implementations. Then, specific implementations of these aspects are built using models of Theory-based Bayesian inference. First, we construct children's prior beliefs at the individual level based on their prior behavior. Second, we approximate children's learning using an "optimal" Bayesian model, revealing the dynamics of belief revision trial-by-trial. Third, we investigate the role prediction may have in facilitating learning. By performing these key computational steps, we find support for contemporary claims that children may be approximately "Bayesian" learners and increase awareness of the importance of generating predictions in active learning.

Seeing the Error in my “Bayes”: A Quantified Degree of Belief Change Correlates with Children's Pupillary Surprise Responses Following Explicit Predictions

“…This highlights that there are instances where pupillary surprise might be more likely to occur when making predictions -as proposed by other recent empirical work (e.g., [28]). Second, in line with the original paper that we draw our model from [11], the current model accounts for individual differences among children's prior beliefs and the processes by which they update. In of Kayhan et al [45], children's behaviors are modeled to all follow the same inferred computational model 5 .…”

“…Children's causal beliefs of water displacement were chosen as children frequently have the misconception that water displacement depends on the weight of an object or a combination of weight and size rather than on its size only (e.g., [58]), providing an appropriate domain for the investigation of variability across individual children's beliefs, as well as their impact on children's subsequent learning. Furthermore, previous work has modeled this experimental data for investigation of children's learning during a belief revision task [11] and found very strong fits between "optimal" Bayesian learning and children's performance on the task.…”

“…However, two alternative hypotheses are also considered here regarding which of the model estimates better fits their responses. Recent interpretations of prediction suggest that actively making a prediction entails leveraging one's prior beliefs and extrapolating potential outcomes given these beliefs (e.g., [11,27,28,40]). Both Shannon Information and Kullback-Leibler divergence accounts are consistent with this proposal because they both leverage prior beliefs towards predictions.…”

“…The Ideal Bayesian learning model that we employ for our investigations builds on a recent investigation of individual differences in children's belief revision (the Optimal Bayesian model described in [11]). Here, the Bayesian model constructed computational representations of children's beliefs based on their task responses.…”

“…Psychological and philosophical work suggests that two interrelated components of human intelligence are the ability to deploy abstract, causal, "intuitive theories" to support inference and the ability to revise these theories in light of evidence [3,5,6]. Contemporary approaches in the Cognitive Sciences align empirical work with computational implementations, typically finding that Bayesian models can provide a framework with which to understand human inference from, and learning of causal beliefs [7][8][9][10][11]. These models provide an account of how learners can draw rich inferences relatively rapidly even when data is limited or ambiguous and have been extended to account for the ways in which learners form and revise more abstract intuitive theories as well [12][13][14][15][16][17][18].…”