A school assignment that doesn't have a specific context set for it will look like school writing: it's written to the teacher (captive audience) to demonstrate that students can string together some appropriate evidence or analysis to make a point. Depending on where students are in the curriculum, you might still get what looks essentially like a high-schooler's five-paragraph essay. Students have practiced this kind of writing for 12 years before they appear in our college classrooms, and they've been successful with their strategies for generalized academic writing. After all, they wouldn't be in college if they couldn't produce this kind of writing with at least some proficiency.
But most of us aren't satisfied with a "high school" approach to writing. We're trying to get students to deepen their analysis, refine their critical thinking, and, in many cases, begin to think as a specialist in a particular discipline asking and answering certain kinds of questions appropriate to the disciplinary context.
If you keep in mind that writing is always situated in a context - that is, written for a particular audience with a particular goal or purpose and appropriate content - then you'll more likely think about particular audiences, levels of language, and even genre expectations for that context. Perhaps as you imagine your writing assignments, you might think about a specific publication context or venue. If you can show students that publication, they'll get a much fuller picture of the expectations readers have within that context, and they'll begin to adapt their writing for that context. But if you don't set up a specific context, students will either guess or fall back on the generalized academic context they've become so comfortable with.
How can you set a workable context for students?
Think about the kinds of writing you do. Can you find ways for students to write within those same contexts even though they don't have the disciplinary expertise you have?
Think about the audiences you write to - other specialists, other folks with some knowledge of your field, clients, nonacademic readers. Can any of these groups become the target readers for student writing?
Think about students writing to other students. Even though the writing will still fall within the academic context, students will not use the "teacher" style if they know that you aren't the primary audience for the writing. This approach works better with introductory classes that are not yet immersed in disciplinary conventions.