Cognitive Processes Underlying Ratio Representation Across Development

项目总结/摘要 比例推理是一项关键技能，无论是对日常决策，如评估财务和 医疗风险和学术成就。先前的工作表明，比例推理在两个不同的 关键方面：（1）比例所依据的数量类型;（2）发展。特别是， 当比例基于离散数时儿童和成人在比例推理方面更差（例如， 红色M& M的比例）与连续量（例如，果汁的比例只是水）。 此外，特别是具有离散比例的易错性能可能随着发展而变化， 婴儿和幼儿比年长的儿童和成人更不容易出错。然而，人们对 比例推理的共同认知机制以及这些机制如何变化 跨越背景和发展。目前的建议旨在弥补这一关键差距。拟建项目 将确定哪些认知机制独立于特定类型的定量背景，从而 更普遍的是，基本比例推理，以及哪些机制是特定类型的独特机制。 数量在手。使用发展和计算方法，具体目标针对三个不同的目标， 可能的机制，可能不同的离散和连续的比例：认知表征（目的 1），认知过程（目标2），和符号策略（目标2）。这种方法将提供新的理论 深入了解跨背景和发展的比例推理的认知机制， 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背景下的不同之处（目标1）。使用 作为一种计算建模方法，目标2将测试认知过程的正式数学模型， 可以解释目标1中的行为模式在R阶段，目标2还将测试经常报告的 但很大程度上未经检验的假设，即人们使用离散的，但不是连续的， 比例最后，目标3将利用先前目标中获得的关于特定认知机制的见解， 测试关于如何支持幼儿的比例推理和概率推理的新预测 成年人的决策（研究5）。 候选人的长期目标是发展一种比例理论，解释一系列行为， 背景和发展。指导阶段将在芝加哥大学心理学系进行 部门和拟议的培训理论建设，婴儿的方法（目标1），和计算建模 方法（目标2）将把候选人在一个很好的位置，成为一个方法和理论 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.