Grant: Research Tools and Instruments - Category 1 (<$150,000)

How do people solve mathematical problems?  Cognitive science explores the mental processes that people use to perform many cognitive tasks.  Of special interest are activities that we use every day.  Numbers are an integral part of the modern world and people are constantly confronted with problems that require mathematical decisions, from how much of a tip to leave in a restaurant to how to manage debt.  Mathematical problem solving involves a great deal of thinking time:  The challenge for cognitive scientists is to try and understand what the mind is doing.  I have requested an eye-tracking system to allow me to study in great detail patterns of gaze during the solution process.  Eye-tracking data has proven very useful in a wide variety of related areas, such as reading and visual perception, and has enhanced our understanding of a variety of complex real-world tasks such as driving.  Application of this methodology to mathematical cognition is overdue.  It will allow me to decompose solution times and connect patterns of looking to other behaviours, thus extending existing ideas about how thinking relates to problem solving.  By carefully manipulating the types of problems that people are given and the tasks they are asked to perform, I will integrate eye gaze information, solution times, and patterns of errors to develop a better understanding of mathematical problem solving and mathematical skill.