Cognitive Processes Underlying Ratio Representation Across Development

项目摘要/摘要 比例推理是一项关键技能，无论是对于日常决策，如评估财务和 医疗风险，以及学业成就。先前的工作表明，比例推理在两种情况下是不同的 关键维度：(1)比例所依据的数量类型和(2)发展。特别是， 当比例基于离散数字时，儿童和成人的比例推理能力较差(例如， 红色的M&M的比例)与连续的量(例如，仅为水的果汁的比例)。 此外，特别是离散比例的容易出错的性能可能会随着发展而变化， 婴幼儿比年龄较大的儿童和成年人更不容易出错。然而，人们对此知之甚少。 比例推理不足的共同认知机制以及这些机制可能如何变化 跨越各种背景和发展。目前的提案旨在解决这一关键差距。拟议中的项目 将确定哪些认知机制独立于具体类型的量化语境，因此 更普遍的欠比例推理，以及哪些机制是特定类型的唯一的 手头的数量。使用发展和计算方法，具体目标针对三个不同的目标 在离散和连续比例上可能不同的可能机制：认知表征(目标 1)、认知过程(目标2)和象征策略(目标2)。这一方法将提供新的理论 洞察跨背景和发展的比例推理不足的认知机制，如 以及如何利用这些机制来更普遍地支持比例推理(目标3)。 在项目的K阶段，候选人将描述婴儿、儿童和 成人代表比例信息，以及它在离散和连续情况下的不同(目标1)。vbl.使用 作为一种计算建模方法，Aim 2将测试认知过程的正式数学模型 可以解释在目标1中发现的行为模式。在R阶段，目标2还将测试经常报告的 但在很大程度上未经检验的假设是，人们使用离散而不是连续的符号数策略， 比例。最后，目标3将利用在之前的目标中获得的关于特定认知机制的见解来 测试关于如何支持幼儿比例推理和概率推理的新预测 成人的决策(研究5)。 候选人的一个长期目标是发展一种比例理论，解释一系列 在不同背景和不同发展阶段。指导阶段将在芝加哥大学心理学学院进行 在理论建设、幼儿方法(目标1)和计算建模方面的拟议培训 方法(目标2)将使候选人处于一个极好的位置，成为方法论和理论界的 认知发展领域的领导者。

PROJECT SUMMARY/ABSTRACT Proportional reasoning is a critical skill, both for every day decision making, such as evaluating financial and medical risk, and for academic achievement. Prior work reveals that proportional reasoning varies across two critical dimensions: (1) the type of quantity on which the proportion is based and (2) development. In particular, children and adults are worse at proportional reasoning when the proportion is based on discrete number (e.g., the proportion of M&Ms that are red) versus continuous amount (e.g., proportion of juice that is just water). Furthermore, error-prone performance with discrete proportion in particular may vary developmentally, with infants and young children being less error-prone than older children and adults. However, little is known about the shared cognitive mechanisms that underly proportional reasoning and how these mechanisms may vary across contexts and development. The current proposal aims to address this critical gap. The proposed project will identify which cognitive mechanisms are independent of the specific type of quantitative context, and thus underly proportional reasoning more generally, and which mechanisms are unique to the specific type of quantity at hand. Using a developmental and computational approach, the Specific Aims target three distinct possible mechanisms that may differ across discrete and continuous proportion: cognitive representations (Aim 1), cognitive processes (Aim 2), and symbolic strategies (Aim 2). This approach will provide novel theoretical insight into the cognitive mechanisms that underly proportional reasoning across contexts and development, as well as how these mechanisms can be leveraged to support proportional reasoning more generally (Aim 3). During the K-Phase of the project, the candidate will characterize the precision with which infants, children, and adults represent proportional information, and how it differs in discrete and continuous contexts (Aim 1). Using a computational modeling approach, Aim 2 will test formal mathematical models of cognitive processes that could explain the behavioral patterns found in Aim 1. During the R-Phase, Aim 2 will also test the often-reported but largely untested hypothesis that people use symbolic number strategies with discrete, but not continuous, proportion. Lastly, Aim 3 will leverage insights about specific cognitive mechanisms gained in the prior aims to test novel predictions about how to support both young children’s proportional reasoning and probabilistic decision making in adults (Study 5). A long-term goal of the candidate is to develop a Theory of Proportion that explains behavior across a range of contexts and across development. The mentored phase will take place in the University of Chicago’s Psychology Department and the proposed training in theory-building, infant methods (Aim 1), and computational modeling approaches (Aim 2) will put the candidate in an excellent position to become a methodological and theoretical leader in the field of cognitive development.