"See the big picture" is itself a little ambiguous.
If you're thinking of seeing how all the parts fit together at a given point in time, consider astute, perceptive, observant, or insightful:
astute (adj.) having or showing shrewdness and an ability to notice and understand things clearly
perceptive (adj.) characterized by sympathetic understanding or insight
observant (adj.) Keep, perceptive
insightful (adj.) exhibiting or characterized by the power or act of seeing into a situation
However, the student-teacher example makes me thing that you may be looking for an adjective that means the teacher can see how a situation may play out over time.
In that case, consider perspicacious, far-sighted, or even plain-old wise:
perspicacious (adj.) of acute mental vision or discernment
far-sighted (adj.) having or showing foresight or good judgment : SAGACIOUS
wise (adj.) characterized by wisdom : marked by deep understanding, keen discernment, and a capacity for sound judgment.
(All definitions are from Merriam-Webster online: https://www.merriam-webster.com/)