Not sure why you think differently, because your teacher is entirely correct. Tactics are what you do "small scale", strategy is what you do "big scale". For instance, we employed a strategy of containment to halt the spread of communism. That got us involved in Vietnam. Tactics are the things we did like escalation and deploying agent orange to try to beat the VC and thus halt the spread of communism. The strategy worked even if some of our tactics were flawed.
It may be better to think of strategy and tactics in terms of war. Your strategy might be to divide and conquer the enemy, but how you actually go about doing that is going to require a series of tactical maneuvers.