This is something that you will ultimately have to ask your teacher. That being said, I would say that it is not necessary to do this, but I'd also say that you should be able to write more than three paragraphs to make your points. If you're looking to illustrate maturity, you must select the three points that you want to make about Scout's maturity and then organize them into your three paragraphs. For instance, if you wanted to make one paragraph about how Scout has good interpersonal communication skills, you could give three example quotes that illustrate her abilities to speak to each of three characters. In your paragraph, you could have her talk to Jem, Atticus and then Boo. I guess she would talk about Boo, really. At any rate, you could break it down like that and that would be your structure.
If you don't use quotations, you do have to watch "re-telling" or summarizing the story, but you can stay away from that by giving your analysis between the examples. In my opinion, you can paraphrase now and again, but don't make a habit of it. Use it when you need to, but go for those really poignant and illustrative quotes. Those are the key.