Cognitive Processes Underlying Ratio Representation Across Development

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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.