Professor Flashman has preferred to follow a career in mathematics and has been actively involved in teaching calculus since beginning his graduate work. He had taught at Mount Holyoke College, Baruch College of CUNY, and Bard College before coming to his current position at Humboldt State University(HSU) where he is Professor of Mathematics. He has taught summers at the University of California, Berkeley, and the University of San Francisco, and has been a Visiting Fellow at Yale University and a Visiting Professor at the University of Toronto in Canada and Occidental College in Los Angeles and has been an adjunct Professor at College of the Redwoods. At HSU he has been a Pre-Law advisor since 2005 and was Chair of the University Curriculum Committee, 2008-2009.

For over 25 years Professor Flashman has been working on a draft of the Sensible Calculus Book. He was book and media editor for UME TRENDS in which he wrote the column "Noteworthy Books and Such" until it ceased publication in 1996, and was a member the MAA committee on Calculus Reform And The First Two Years (CRAFTY) for 6 years ending in January, 1999. He was chair of the MAA Special Interest Group in the Philosophy of Mathematics from 2007 to 2009. In summer 2013 he started work on a resource for mapping diagrams: Mapping Diagrams from A(lgebra) to C(alculus) and D(ifferential) E(quation)s. A Reference and Resource Book on Function Visualizations Using Mapping Diagrams which he plans to make available on the internet.

His hobbies include music, tennis, chess, go, and trying to be on time.