Do I have to include references in my profile after signing up?
Much like with a typical hiring process, you will only need to provide references if you have been contacted by Teach Away or a school in regards to your application and they ask for references.
Having references attached to your profile early on certainly doesn't hurt. Sometimes, getting in touch with a reference can take longer than you expect, so if you already have some contacts you'd like to reach out to then send them a reference request at your convenience.
But not having references already part of your profile does not impact your chances of obtaining a job offer.