When I saw your question, a very specific passage came to me. When Scout figure's out that she's literate, we readers see an incredible thought process in the words on page 18, chapter 2 in my book. It reads:
"I mumbled that I was sorry and retired meditating upon my crime. I never deliberately learned how to read, but somehow I had been wallowing illicitly in the daily papers. In the long hours of church - was it then I learned? ... Now that I was compelled to think about it, reading was something that just came to me ... Until I feared I would lose it, I never loved to read."
This shows an incredibly naive but intelligent little girl. As with so many other things in her life, Scout has so little awareness that she is on the right track. She sometimes just goes about the wrong way on it. Learning naturally happens for Scout when she thinks. She doesn't even realize it is going on. This occurs for her at Cal's church as she is exposed to a new culture, it occurs as she learns about her father from Miss Maudie, and in this situation with learning to read, she had no idea it happened. True to her character though, she is passionate about reading as she is justice.