Why inappropriate in another class? All classes are supposed to be educating the children. Several of my English teachers used interesting quotes and phrases from classic works and elsewhere to help us think critically. In the 9th grade I was identifying and utilizing the universal truths from Shakespeare's "Julius Caesar" and I was making A's from one of the schools toughest teachers by reputation.
Even in math class, a good teacher can help students understand concepts that go beyond the core numbers. For instance:
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A simple statement loaded with all sorts if nuances and applications that could be applicable to critical thinking from math class, poli-sci, biology, health class, many others.