Our primary methodological/theoretical goal is to develop models that integrate models of how information is represented with models of how decisions are made. The domain of application will be numeracy: how numeracy is represented in the cognitive system and how it is used in making decisions. The specific goals for numeracy are to understand the basic processes involved in numeracy skills and to produce measures with which to understand the relationships between basic processes and higher-level skills. We will examine statistical properties of the integrated models and work with the authors of publicly available diffusion-model fitting packages to make the integrated models widely available. The decision model we will use is the well-established diffusion decision model, which provides a unified explanation of the full range of data for simple two-choice tasks of the kinds we will use, including the distributions of response times for correct and incorrect responses, how the distributions and accuracy change with manipulations of independent variables, and how they change with differences among individuals and groups of individuals. The representation models we will test assume distributed representations over numerosity and they will produce the measures of numeracy that drive decision processes. A successful representation model will be one for which the measures accurately predict, when translated through the diffusion model, response time and accuracy data. The proposed research will examine low-level skills, as measured by applying the models to simple numeracy discrimination and memory tasks. Relations will then be examined between these skills, working memory, and speed-of-processing and also between the skills and performance on standardized tests of higher-level math abilities, financial numeracy abilities, and health numeracy abilities. All of these tasks and measures will be tested with college-age adults, adults with Mild Cognitive Impairment, adults with early and moderate Alzheimer's disease, and cognitively unimpaired age-matched adults. Questions will include how numeracy abilities decline with normal aging and how they are impacted by cognitive impairment. It may be that impairments in numeracy abilities precede memory impairments and if so, lead to earlier treatments and earlier interventions in health and financial decision making. 1
Models of the representation and processing of numerical information will be developed and tested. The models will be applied to data from standardized tests of math abilities and health and financial literacy for older adults and Alzheimer's and Mild Cognitive Impairment patients. The aim is to examine relationships between low-level numeracy skills and the decline of numeracy skills in old age and disease.
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