How much slime can one man need?!

I am doing the quest for the science teacher. Supposedly he gave me a vial with which to collect slime. I have proceeded to explore and collect some. However there is no like, counter or gauge to let me know how much slime I need to collect. I just keep going back to the school in New Orsa to be belittled by the teacher I am supposed to be helping.

Is there an end in sight?
Is there somewhere I can see what quests I'm on?

Content removed by user request.

When you have collected all the goo a little message appears after battle

Aha! I needed 10. Thanks, ya'll

This is a big complaint with newbies. I will add functionality to it right now.