Why does my ex always stare at me?

We dated for 9 months and he broke it off for some unknown reason. Few months later he dated some girl for about 2 weeks and it was over. Even when he was dating that girl; he would always stare at me. Especially when they called it off all he does is stare! Sometimes I even look at him to show that I noticed but he doesn't even look away. The last couple weeks I've noticed that whenever I'm in the same hall as him, he walks to the bathroom (which actually consist of him going into the bathroom, walking RIGHT back out, and then looking at me by my locker on his way back to class). Our last class of the day is kinda by each other and I can see him turning back every few seconds to look at me. He walks slower and randomly stops like he's waiting on someone, looks at me, and walks slowly again. He's always been kinda shy when it comes to interactions with me for some reason, but I don't really want to go up to him and start a conversation. I'm not sure if he even wants to talk to me. Should I just smile or something to let him know it's okay? I'm so confused