This study, part of a larger study focusing on studying a human tutor to design a computer simulation of expert tutoring (i.e., a self-improving intelligent tutoring system), conducted a detailed analysis of one expert tutor's (Nancy Mack) tutorial actions as she attempted to help students learn fractions with understanding. As Mack tutored students in two different research studies, she guided students through fraction topics by drawing on her understandings of her students' understanding and her content knowledge, focusing instruction on the development of students' conceptual knowledge, and using discourse to continually assess students' knowledge and assist them in learning. Additionally, unexpectedly and on her own initiative, Mack used the analytic framework employed to study her tutoring to deepen her own understanding of her teaching. The results of the study suggest that Mack's tutorial actions were guided by the interrelationships between her instructional goals, content knowledge, pedagogical content knowledge, and knowledge of students' thinking with respect to the content domain. (Contains 23 references.) (ND)