One useful perspective-realignment I’ve found useful raising to faculty, particularly those who don’t teach strictly “English,” is the that many assignments have implicit writing assumptions which must be made explicit. It is difficult sometimes to see the necessity of writing underlying even ostensibly non-“expressive,” or technical, assignments. This sounds like an easy, or superficial suggestion, but consider, for instance, courses which integrate design and writing in an integrative and mutually-informing manner — in order to produce any sort of finished, visually appealing document, the writing present within must be coherent and “finished;” yet, this expectation is often only alluded to tacitly. Further, even if one is actively grading “writing,” it is often difficult to break down this “writing” requirement into constitutive units the students can follow, or knowingly deal with on an individual, then total, basis. As an added benefit, when students are made more conscious about articulation, even in a small way regarding a tangible quality of writing, it makes them more aware of the total flow and logic of their work. (These tangible qualities are then able to compound, and inform one another.)
One possible suggestion: Perhaps (even as a sort of pedagogical thought experiment), try outlining one or two explicit qualities of writing to be graded, or paid attention to, in a non explicitly English or even humanities assignment. As we often discuss at WAC, try to scaffold, or otherwise anticipate the exact skill you would like them to exercise by introducing it earlier than the exact moment you wish them to recall or produce it. Then, see if, for example, should you ask them to pay attention to something like topic sentences, or even choosing neutral, or discipline-specific jargon for the assignment, whether the overall clarity of thought, and quality of product produced, improves.
This means of “tailoring” expectations, or honing in on required, but implicit, qualities of writing in assignments, is also transferable to other areas, such as peer review. Rather than asking students to holistically grade entire documents for “quality” or “followability,” try to hone in on two or three qualities (perhaps even breaking a “thesis” question down into a subcategory or two), and set firmly-defined timelines for how long students spend on each portion. This means of narrowing the scope of the students’ attention will likely improve the sharpness and nuance of the skills paid attention to, and overall improve the logic, thinking, and argument of the writing, and writing-reliant aptitudes, required.