A student exhibiting signs of stress, depression or mental illness is truly an impossible case for academics to handle, particularly in the context of an already taxing daily workload. Yet the fact that the academic is "there", rather than the parent, means that being able to react (listen) appropriately, and know which professional service to refer the student to, is essential - not as an academic, but as a human being, as a caring member of society. The job of an academic can be immensely stressful. Being the parent of a child suffering from mental illness is, depending on the severity, far more stressful and upsetting. One thing your article did not address is the question of when that parent is also an academic.
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