We respect that faculty members will have a range of views on this issue. However, Dartmouth faculty are considered managers (and, concerning graduate students, supervisors) and are not covered by the National Labor Relations Act. Department and program chairs should be especially mindful that they are representatives of the institution's management who, under the law, are prohibited from negotiating directly with students or their representatives on union issues.
A graduate-student strike does not change a faculty member's obligation to perform their duties, including submitting grades or conducting class.
You are also encouraged to bring any concerns the students raise to your dean or associate dean, who will bring them to Dartmouth's bargaining team.