"Mathematical Cognition: Effects of Educational Experience, Language, and Working Memory"

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Most people are confronted with decisions that require quantitative skills on a daily basis: Banking, cooking, and shopping are obvious examples, but math is also involved in health maintenance (weight loss, exercise), gambling, and in understanding world issues such as population control and climate change. Because people experience a daily barrage of quantitative data, understanding the cognitive processes that are involved and the variability of such processes across individuals is relevant to individuals' participation in society and thus is of immediate practical benefit. Theoretically, mathematics is a tractable domain in which to test theories about how, for example, thinkers are able to manage multiple mental tasks. My ongoing research program addresses questions about how people store and access their mathematical knowledge. The present proposal is focused on how people use limited mental resources to manage complex mathematical activities. Consider the following: You need to estimate the square footage of a room that measures 13 x 8.5 m. You have several options. You could use the solution algorithm taught in school. You could use a calculator. You might visualize the numbers and mentally calculate. Or, you could estimate by rounding 8.5 to 10 and responding with an approximate answer, "about 130 square metres". Which solution approach you choose will depend on the situation, on your mathematical competencies, and on the precision required for the answer. In my research, we combine arithmetical tasks with other tasks known to require specific mental resources to determine how people solve mathematical problems. For example, participants might be asked to remember visual or verbal information while solving the above problem and then we test how their mental processes are affected by the specific memory demands. I am particularly interested in individual differences in mathematics. Over the last 25 years, my research on mathematical cognition has provided insights into the flexibility and diversity of mental processes that adults use on numerical tasks. These insights and the further research described in this proposal will allow advances in our understanding of how people solve mathematical problems.