You absolutely haven't let your class down! You're human. I'm a teacher too (though not in a conventional academic setting), and know exactly how you feel. Sometimes the stammer rears up and there's nothing we can do about it. Personally, when I really get stuck, I tend to stop, laugh, and then try again. The laugh diffuses any tension and lets the group see that I'm not bothered by it (even if I am). I've learned that most people really don't care, though it's possibly a little easier for me because I teach adults who are keen to learn from my expertise. Kids usually don't mean to be cruel, but anything different can set them off. The student was probably just laughing out of ignorance/youth. The way forward is up to you. If you want, you could use this as a teaching moment and open up a conversation about it. It's reasonably likely that someone in your class also stutters (even if covertly), and confronting this head-on could really help them. Or even if no one in the class stutters, it could help them to learn about what it's like to have a stutter and to be more tolerant. But if you don't want to mention it, that's totally valid too. Just know that you have NOTHING to be ashamed of. Stuttering is neurological/hereditary. It's the hand we were dealt and it sucks sometimes, but it doesn't have to define us or hold us back. I just posted some tips that I've found really help me over the years -- avoiding coffee, getting a good night's rest, and making sure to eat something before an event. These may not help you (everyone's different!), but just thought I'd mention them. Hang in there. I'm sure you're a great teacher, and your students are lucky to have you, stutter or no stutter.