Two principles guide Cowen's teaching. "First, in addition to the usual skills we try to teach them, students should also be taught to read mathematics. Secondly, they should be shown not only the finished product as it appears in textbooks, but also how mathematicians think and work."
The first principle is well explained in an article by Cowen, published in the American Mathematical Monthly 98 (1991) 50-53. The second principle is one that most teachers understand, but few embrace. For teachers to prepare in such a way that enables them to explore with a class some incorrect approaches and false starts, while at the same time covering the prescribed course material, takes an extraordinary amount of time and effort.
Cowen believes the task for teachers at all levels is the same. "From junior high school to advanced graduate courses, the challenge is to motivate students to do their best, lead them to recognize the obstacles in their road to mathematical understanding, and help them overcome these obstacles."
Cowen has contributed to the teaching of mathematics at many levels and in various ways. After growing up in Indiana and earning degrees from Indiana University and the University of California at Berkeley, he taught at Brookville (Indiana) Junior High School, Indiana University East, Earlham College, and the University of Illinois. In 1978 he came to Purdue, where he has served as Director of the Actuarial Science Program since 1992. Cowen is the author, with Barbara D. MacCluer, of the research monograph "Composition Operators on Spaces of Analytic Functions." He is currently writing on linear algebra, the subject he teaches most frequently.
Cowen has served as thesis advisor to several doctoral students in mathematics, and in recent years, has supervised research projects for 15 undergraduate students. Most of the undergraduates were supported by the NSF Research Experience for Undergraduates (REU) program. Eight of the fifteen co-authored publications resulting from their research projects. One student explains how participation in the program under Cowen's guidance impacted his future. "My decision to attend graduate school was strongly influenced by my experiences during two summers I spent at Purdue participating in an REU under the direction of Professor Cowen. An expert and canny educator, Professor Cowen has played a prominent role in encouraging me to pursue a career in mathematics."
Cowen has been extraordinarily successful in teaching a wide range of courses at the university level, from service courses for engineering students to advanced graduate courses. In 1986 he received the Purdue School of Science Outstanding Undergraduate Teaching Award. Whatever the course or level, Cowen says, "my goal is always for students to leave with a better understanding of the role mathematics can play in their work and to enjoy the application of mathematical tools, from arithmetic to linear algebra to operator theory, in their problems."
Since 1991, the MAA has awarded 19 awards for distinguished college or university teaching of mathematics. Purdue is the only institution to have had more than one recipient. Previous Purdue awardees are mathematics professor Justin J. Price (1994) and statistics professor David S. Moore (1995).