1. decide on the most appropraite definition of the term crucible in relation to the play.
2. discuss the definition in the introduction of your essay.
3. fuly explain three ways the definition applies to your understanding of the play in the body of your essay.
4. provide examples and analysis from the play to support your claims about the term.
5. conclude your essay with summary remarks.
Well, let's start with a good definition of the word crucible.
Here's Merriam Webster's definition, which comports very well with all others:
Etymology: Middle English corusible, from Medieval Latin crucibulum earthen pot for melting metals
Date: 15th century
1 : a vessel of a very refractory material (as porcelain) used for melting and calcining a substance that requires a high degree of heat
2 : a severe test
3 : a place or situation in which concentrated forces interact to cause or influence change or development <conditioned by having grown up within the crucible of Chinatown — Tom Wolfe>
The only word above that you might not be familiar with is "calcining." Calcinig is a high temperature treatment of metals or ores performed in order to bring about decomposition and to remove impurities.
In the context of Miller's play, then, what is a crucible? It's a trial by drastic, extreme and wrenching scrutiny, the purpose of which is to remove all the impurities of guile, subterfuge and nonsense in order to arrive at the purity of truth.
Now, in your essay, all you have to do is to decide who the truth seekers are and who the the impure individuals are who need to have their layers of lies burned away.