Difficult: The most difficult part of this section for me was trying to conceptualize all of the various properties of rings. I know that the theorems are quite familiar to me with rings like R, Z, and others, but I tried to think "outside the box." Instead of familiar elements of R, Z, Q, etc., I tried to think of a, b, and other elements used as elements of any ring. This confused me sometimes. It is hard to remember what theorems and axioms we can use to prove other theorems and corollaries.
Reflective: If I can understand the properties of rings, I think I will be a better math teacher. I will be better equipped to help students to understand why and how math works. Understanding rings in general will help me to understand well-known rings on a deeper level. In addition, as we move to performing algebraic actions on elements in rings, I think algebra will get harder! I will be able to understand my students better when they "can't understand" algebra because it is "symbolic" or "abstract." I am excited to learn more so that I can connect with my future students.
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