Probability learning in children

Spatial evolution of regularization in learned behavior of animals

Stochastic population dynamics of learned traits are studied, where individual learners behave according to a reinforcement learner model, which is a nonlinear version of the Bush-Mosteller model. Depending on a regularization parameter (parameter a), the learners may possess different degrees of overmatching (regularization behavior, 0 ≤ a < 1), frequency matching (corresponding to a=1), or undermatching behavior (a > 1). Both non-spatial and spatial models are considered, to study the interplay of individual heterogeneity of behavior, spatial and temporal effects of learning, and the possibility of emergence of regional culture. In non-spatial models, we observe that populations of individuals learning from each other converge to a universally shared, deterministic rule (either rule "1" or rule "0"), only if they to some extent possess the ability to generalize (a < 1). Otherwise, a low-coherence solution where both rules are used intermittently by everyone, is achieved. If the evolution of the regularization ability is included, then we find that a initially evolves toward lower values, and a shared solution is established when everyone reliably uses the same rule. The spatial (2D) model has two well known limiting cases: if a=0 (the strongest degree of regularization), the model converges to a threshold voter model, and if a=1 (frequency matching), it is equivalent to the discrete diffusion equation. If 0 < a < 1 (the case where individuals regularize), spatial patterns emerge, where patches of different usage of the rule are formed. Smaller values of a lead to sharper and longer lived patches. Values of a < 1 close to unity result in probabilistic outcomes where patches only survive if they are attached to the boundary. Analytical treatment of the 1D case reveals the existence of approximate equilibria that have front structure, where spatially intermittent deterministic usage of one and the other rule are separated by interfaces whose analytical form is derived.

Skill and Chance Orientations as Determiners of Problem-Solving Behavior in Lower- and Middle-Class Children

This study was an attempt to replicate a previous finding that lower- and middle-class children of the same MA differ in their performance on a partially reinforced three-choice learning task. It was also an attempt to assess the role that skill and chance orientations play in determining this differential performance of social-class groups. The most significant finding of this study was that skill-oriented Ss showed less maximizing (correct responses) and more left, middle, right patterning of their responses than chance-oriented Ss. No main effect of social class was found but an interaction effect did occur that reflected significantly more left, middle, right patterning of responses by middle-class skill-oriented Ss than any other group.

Getting it right by getting it wrong: when learners change languages

When natural language input contains grammatical forms that are used probabilistically and inconsistently, learners will sometimes reproduce the inconsistencies; but sometimes they will instead regularize the use of these forms, introducing consistency in the language that was not present in the input. In this paper we ask what produces such regularization. We conducted three artificial language experiments, varying the use of determiners in the types of inconsistency with which they are used, and also comparing adult and child learners. In Experiment 1 we presented adult learners with scattered inconsistency - the use of multiple determiners varying in frequency in the same context - and found that adults will reproduce these inconsistencies at low levels of scatter, but at very high levels of scatter will regularize the determiner system, producing the most frequent determiner form almost all the time. In Experiment 2 we showed that this is not merely the result of frequency: when determiners are used with low frequencies but in consistent contexts, adults will learn all of the determiners veridically. In Experiment 3 we compared adult and child learners, finding that children will almost always regularize inconsistent forms, whereas adult learners will only regularize the most complex inconsistencies. Taken together, these results suggest that regularization processes in natural language learning, such as those seen in the acquisition of language from non-native speakers or in the formation of young languages, may depend crucially on the nature of language learning by young children.

Decision-making processes: sensitivity to sequentially experienced outcome probabilities

A computerized sequential event sampling decision-making task was administered to 187 5- to 10-year-olds and adults Participants made a series of choices between alternatives that differed in win probability (Study 1) or win and loss probability (Study 2). Intuitive and more explicit measures were used. Study 1 revealed that, across ages, participants demonstrated intuitive sensitivity to probability; however, adult participants evidenced greater sensitivity than did children, and younger children failed to demonstrate more explicit understanding of probability. Study 2 also revealed that children were intuitively sensitive to probability; however, the inclusion of loss had limited impact on decision processes. These findings and their relevance to cognitive developmental theory are discussed.

Early Development of Executive Function: A Problem-Solving Framework

Executive function (EF) accounts have now been offered for several disorders with childhood onset (e.g., attention-deficit/hyperactivity disorder, autism, early-treated phenylketonuria), and EF has been linked to the development of numerous abilities (e.g., attention, rule use, theory of mind). However, efforts to explain behavior in terms of EF have been hampered by an inadequate characterization of EF itself. What is the function that is accomplished by EF? The present analysis attempts to ground the construct of EF in an account of problem solving and thereby to integrate temporally and functionally distinct aspects of EF within a coherent framework. According to this problem-solving framework, EF is a macroconstruct that spans 4 phases of problem solving (representation, planning, execution, and evaluation). When analyzed into subfunctions, macroconstructs such as EF permit the integration of findings from disparate content domains, which are often studied in isolation from the broader context of reasoning and action. A review of the literature on the early development of EF reveals converging evidence for domain-general changes in all aspects of EF.

Curiosity and demographic factors as determinants of children's probability-learning strategies

Children's curiosity, gender, activity level, and socioeconomic status (SES) were related to their performance on a partially reinforced discrimination-learning task. The 38 boys and 37 girls were in the first grade and were all white. Three factors of curiosity (manipulatory, conceptual, and about the complex) were assessed. Performance on the learning task was scored for the number of correct responses (maximizing) and for the frequency of three-step sequences reflecting variability, systematic patterning, and perseveration. In general, the three curiosity factors related negatively to maximizing and perseveration and positively to variability. (The same effects were found for activity level.) Systematic patterning related positively to one curiosity type and negatively to another. Girls used less maximizing and more systematic patterning than boys. The response choices of girls were affected more by differences in conceptual curiosity and those of boys by differences in curiosity about the complex. Activity level was unrelated to gender but differed with SES. The findings demonstrate the role of different curiosity factors in shaping response sequences and suggest some reasons for children's choice of probability-learning strategies.

Influence of parental expectancies and responsiveness on achievement motivation of minimally brain-injured and normal children

16 families with minimally brain-injured children and 16 families with normal children were matched on a number of characteristics. The two groups differed in regard to mothers' expectancies for achievement, fathers' rewards for success and punishment for failure, and children's need for achievement. Moreover, parents had a significant influence on their children's achievement motivation but patterns of relationships were not the same for the two groups.