I’m a student making a logo for a particular elementary school, and I can’t figure out what to do, other than a bear paw (in which many other schools based around bears have). Do you think there is any other ideas, I’ve already tried sketching a picture of one, didn’t work.
One sketch? Unfortunately that doesn’t cut it. As a student there are a million sketches in your future. It’s a large part of how you learn.
Is this for practice or are you really trying to design a new logo for this school?
This is a professional forum and folks here get paid for their ideas. Your job is to come up with the idea if you want to be a Graphic Designer. Once you throw out YOUR ideas we would d be happy to help you improve and guide you in what’s not working and what is.
Other than that you have given no information of what you need other than a logo for a school and you thought of a bear paw. Why a bear paw? What type of school is it?
These are just my first thoughts 
btw … welcome aboard. We are here to help even if it seems a bit stern at times. But, as I said be aware … we will help … we won’t do the work for you 
I wouldn’t for a moment suggest copying anything you find at this link, but it does give you an idea of what’s possible in bear logos other than bear paws.
You need to write a brief for yourself, or if there is a client ask them to help you fill a questionnaire to answer essential questions. I put together a list of brief questions for you here: Branding Brief Template
Brainstorm time! If you’re not quick or strong at drawing, brainstorm by writing down words. Write down the first 20-50 words that come to mind. Then start drawing them and see what shapes work or could be worked upon further.
As a student, you should rely heavily on process. Don’t skip the brainstorming and research portion.