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The university is considering disestablishing the programme in 2020, which would allow the 18.7 equivalent full-time students (Efts) enrolled in the programme time to finish their degrees.
Numbers have dropped by more than 75% in the past four years.
Enrolments were at 80.9 Efts in 2014, and have declined steadily since then, falling to 31.6 last year.
Two of the programme’s five teaching staff left in 2014 and were not replaced, although two part-time teaching fellows were appointed. Another staff member left in 2017 and a lecturer left this year to take up a post elsewhere, leaving only one full-time staff member.
Consultation on the change is running until September 4 with the Tertiary Education Union and affected parties.
Art school director Clive Humphreys said considering the way the humanities were being treated in the tertiary education sector, the move was "possibly predictable".
"But I’m sad to see the [demise] of the art history department, which we’ve had a long association with," he said.
Art history gave budding artists a context in which to work, which was important, he said.
The art history department was established in the university in 1999 and was incorporated into the history department in 2001, forming the Department of History and Art History.
The School of Art had a history component in its qualification, so the subject would not "cease forever in Dunedin". However, the School of Art and the art history programme tended to attract "two different kinds of student" so he did not think the polytechnic would pick up students who would otherwise have gone to the University of Otago, Mr Humphreys said.
Graduates took to social media on Thursday to share their memories of the programme. One former student said "the pull away from humanities and focus on sciences will be a detriment beyond the departments themselves or even the university".
"It is well documented in history that happy and healthy societies had flourishing arts and humanities."
Humanities cuts in 2018
• Earlier this month Victoria University announced three academic and three professional positions would be disestablished to bring staffing in line with student enrolment numbers.
• The University of Auckland also proposed to cut 5.5 full-time jobs from its School of Cultures, Languages and Linguistics in August; a four-week consultation process is now taking place.
• Five staff lost their jobs in the University of Auckland’s music department in June.