Grant: Discovery Grants Program - Individual

Counting, arithmetic, percentage, probabilities: People use symbolic numbers, that is, digits such as 35 and number words such as seventeen, to record and communicate information about quantity. The ability to use numbers in mathematical tasks underlies computer technologies, monetary systems, engineering, and many aspects of medical science. My research is focused on the ways in which people think about and use symbolic numbers in relatively simple number tasks, for example, when they solve arithmetic problems (e.g., 3 + 4, 5 x 8) or estimate amounts (e.g., is 45 x 96 close to 4500?). In particular, I will study how people make strategic decisions when they are solving numerical problems, for example, how they simplify numbers in estimation tasks, or place numbers on unusual number lines (e.g., if the number line goes from 0 7000, where would 3421 be located?). Performance on these types of number tasks, and even simpler ones, such as deciding quickly if the numbers 3 5 4 are in order, are closely related to adults' performance on more complex mathematical tasks. These interconnections support the view that symbolic number processing in the brain is central to mathematical understanding and applications. In this proposal, I have formulated a model of the ways in which people approach numerical tasks and outlined a series of experiments to test and improve the model. I will also explore the role of cognitive abilities such as working memory and spatial skill in numerical performance. My objectives are to use the model to contribute to our understanding of the role of symbolic numbers in everyday tasks. The results of this research will help educators and parents make decisions about children's numerical experience and training. Although everyone has a fundamental understanding of quantities, the ease with which different people learn to use number symbols varies substantially. Understanding how people represent and use numbers can ensure that everyone has sufficient number knowledge for success in their personal and professional lives.