This question is extremely wide open. It is narrowed down in the fact that you are told to write about a specific movie; however, everything else is completely open. Some writers might find this a breath of fresh air, but other writers might find it frustrating to be given so...
This question is extremely wide open. It is narrowed down in the fact that you are told to write about a specific movie; however, everything else is completely open. Some writers might find this a breath of fresh air, but other writers might find it frustrating to be given so little guidance. An argumentative paper might sound intimidating, but all that it means is you have to make an argumentative statement about the film and support your position with evidence.
Your argument looks like it could be about anything. You could make an argument about Crowe's exceptional acting, the filming techniques used, the film's themes, the film's portrayal of characters, etc. It's up to you to decide how broad or narrow your focus is going to be. If you have a length requirement, let that be your guide. If the length requirement is fairly short, pick a narrow topic and use 3-4 examples from the film that explain and support your topic. If the length requirement is somewhat lengthy, then try to blend together a couple of the previous thesis ideas. Generally speaking, themes and characters blend well with each other. This is because characters are often used to show audiences/readers the theme. For this particular film, there are themes of madness and perseverance, and John Nash is the character centrally involved with both themes. It's entirely possible for you to highlight the theme and character development by explaining how certain film techniques that Ron Howard uses further enhances the audience's experience with the theme and character. For example, Howard is intentional about the use of high and low angle shots as well as how tightly the camera is framed on Crowe's face. Much of the film's emotional impact rests on Crowe's ability to deliver his inner struggles via his face.
Start the entire paper with an interesting hook that leads into the argumentative thesis statement, and then make sure that every paragraph that follows is devoted to proving that initial statement. The statement could be something like the following statement
"Although A Beautiful Mind is focused on John Nash, it is Alicia Nash that truly gives audiences the deep emotional impact of John's struggles."