Bonawitz E., Gopnik A., Denison S. & Griffiths T. L. (2012) Rational randomness: The role of sampling in an algorithmic account of preschooler’s causal learning. In: Xu F. & Kushnir T. (eds.) Advances in child development and behavior. Volume 43. Academic Press, Waltham MA: 161–191.

Bonawitz E., Gopnik A., Denison S. & Griffiths T. L.
(

2012)

Rational randomness: The role of sampling in an algorithmic account of preschooler’s causal learning.
In: Xu F. & Kushnir T. (eds.) Advances in child development and behavior. Volume 43. Academic Press, Waltham MA: 161–191.
Probabilistic models of cognitive development indicate the ideal solutions to computational problems that children face as they try to make sense of their environment. Under this approach, children’s beliefs change as the result of a single process: observing new data and drawing the appropriate conclusions from those data via Bayesian inference. However, such models typically leave open the question of what cognitive mechanisms might allow the finite minds of human children to perform the complex computations required by Bayesian inference. In this chapter, we highlight one potential mechanism: sampling from probability distributions. We introduce the idea of approximating Bayesian inference via Monte Carlo methods, outline the key ideas behind such methods, and review the evidence that human children have the cognitive prerequisites for using these methods. As a result, we identify a second factor that should be taken into account in explaining human cognitive development the nature of the mechanisms that are used in belief revision.

Sarnecka B. W. & Negen J. (2012) A number of options: Rationalist, constructivist, and Bayesian insights into the development of exact-number concepts. In: Xu F. & Kushnir T. (eds.) Advances in child development and behavior. Volume 43. Academic Press, Waltham MA: 237–268.

Sarnecka B. W. & Negen J.
(

2012)

A number of options: Rationalist, constructivist, and Bayesian insights into the development of exact-number concepts.
In: Xu F. & Kushnir T. (eds.) Advances in child development and behavior. Volume 43. Academic Press, Waltham MA: 237–268.
The question of how human beings acquire exact-number concepts has interested cognitive developmentalists since the time of Piaget. The answer will owe something to both the rationalist and constructivist traditions. On the one hand, some aspects of￼numerical cognition (e.g. approximate number estimation and the ability to track small sets of one to four individuals) are innate or early-developing and are shared widely among species. On the other hand, only humans create representations of exact, large numbers such as 42, as distinct from both 41 and 43. These representations seem to be constructed slowly, over a period of months or years during early childhood. The task for researchers is to distinguish the innate representational resources from those that are constructed, and to characterize the construction process. Bayesian approaches can be useful to this project in at least three ways: (1) As a way to analyze data, which may have distinct advantages over more traditional methods (e.g. making it possible to find support for a null hypothesis); (2) as a way of modeling children’s performance on specific tasks: Peculiarities of the task are captured as a prior; the child’s knowledge is captured in the way the prior is updated; and behavior is captured as a posterior distribution; and (3) as a way of modeling learning itself, by providing a formal account of how learners might choose among alternative hypotheses.

Xu F. & Kushnir T. (2012) What is rational constructivism. In: Xu F. & Kushnir T. (eds.) Advances in child development and behavior. Volume 43. Academic Press, Waltham MA: xi–xiv.

Xu F. & Kushnir T.
(

2012)

What is rational constructivism.
In: Xu F. & Kushnir T. (eds.) Advances in child development and behavior. Volume 43. Academic Press, Waltham MA: xi–xiv.