Goodyear began his museum career in 1969 as curator at the Rhode Island Historical Society. He spent 21 years at the Pennsylvania Academy of Fine Arts in Philadelphia, first serving as curator and then as director and president. Prior to joining the Heard Museum, Goodyear served as director of planning and development at the Buffalo Bill Historical Center in Cody, Wyo. Goodyear received a Bachelor of Arts degree from Yale University and a Master of Arts degree in the Winterthur Program in Early American Culture at the University of Delaware. He also attended executive training and management programs at Columbia University Business School and the University of Chicago Business School.