Lee Michael D, Sarnecka Barbara W
Department of Cognitive Sciences, University of California, Irvine.
Cogn Sci. 2010 Jan 1;34(1):51-67. doi: 10.1111/j.1551-6709.2009.01063.x.
We develop and evaluate a model of behavior on the Give-N task, a commonly-used measure of young children's number knowledge. Our model uses the knower-level theory of how children represent numbers. To produce behavior on the Give-N task, the model assumes children start out with a base-rate that make some answers more likely a priori than others, but is updated on each experimental trial in a way that depends on the interaction between the experimenter's request and the child's knower-level. We formalize this process as a generative graphical model, so that the parameters-including the base-rate distribution and each child's knower-level-can be inferred from data using Bayesian methods. Using this approach, we evaluate the model on previously published data from 82 children spanning the whole developmental range. The model provides an excellent fit to these data, and the inferences about the base-rate and knower-levels are interpretable and insightful. We discuss how our modeling approach can be extended to other developmental tasks, and can be used to help evaluate alternative theories of number representation against the knower-level theory.
我们开发并评估了一种关于“给N任务”行为的模型，“给N任务”是衡量幼儿数字知识的常用方法。我们的模型采用了关于儿童如何表征数字的知晓者水平理论。为了在“给N任务”中产生行为表现，该模型假定儿童一开始有一个基础概率，使得某些答案在先天情况下比其他答案更有可能，但在每次实验试验中，这个概率会以一种取决于实验者要求与儿童知晓者水平之间相互作用的方式进行更新。我们将这个过程形式化为一个生成式图形模型，这样包括基础概率分布和每个儿童的知晓者水平在内的参数就可以使用贝叶斯方法从数据中推断出来。使用这种方法，我们根据先前发表的来自82名涵盖整个发展范围儿童的数据对模型进行评估。该模型与这些数据拟合得非常好，并且关于基础概率和知晓者水平的推断是可解释且有洞察力的。我们讨论了我们的建模方法如何能够扩展到其他发展任务，以及如何用于帮助对照知晓者水平理论评估数字表征的替代理论。
