This series contains materials resulting from Abel's long career teaching philosophy in two university divisions.

The "Graduate Faculty" folders document Abel's activities in that division. Materials include correspondence with students concerning their theses, recommendation letters for former students, Philosophy Department meeting minutes and memoranda, correspondence with administrators concerning course proposals, and internal reports issued to all faculty members. A great deal of correspondence concerns Abel's self-advocacy regarding hiring, reappointment, titles, increased pay, and, finally, retirement benefits. These files cover the end of his doctoral work, when he was already teaching in the Graduate Faculty, through his final years, although the 1980s and 1990s are not as well-documented as earlier decades.

The "New School" folders document Abel's activities outside of the Graduate Faculty, teaching in what was formerly known as the Adult Division and, as of 2016, the Schools of Public Engagement. The referenced "Senior College" is the forerunner of the current undergraduate Eugene Lang College. Records consist of memoranda and reports primarily concerning administrative matters, particularly faculty compensation and a multi-year dispute between the American Association of University Professors (AAUP) and the New School for Social Research over contracts. Additionally, Abel served on the school's Curriculum Committee. Abel's primary correspondent in these files is Dean William Birenbaum and Birenbaum's successor, Allen Austill. Although Abel continued to teach outside of the Graduate Faculty, these files are concentrated in the 1960s.