Before you do ANYTHING, drop the moonlight sonata. There's a ton of underlying challenge that leads to beginners completely butchering it. You have to voice the top melody while letting the triplets in the left hand fade, except the third and bottom voice, it's much harder than people think.The best way to start recognizing chords, is to play a lot of those basics. Having a goal in mind is great, but you need to do those things you're teacher is giving you. What is helpful, is to ask around and find out what the challenges are for the pieces you want to play, then ask your teacher if you two could make challenges to help with that.. Mostly, ask your teachers how to make practicing more fun. He or she likely (if they are an experienced teacher) has dealt with this problem before. But before you do, put a lot of meaningful practice into those 2 boring pieces of music, and she'll be impressed, likely giving you more complex work. Those kinds of things tend to show through