What are some of the patterns you've used when hiring students to ensure they fit into the company and become productive as quickly as possible?

Two filters could be conducted for help identifying students fit your team.
1. Pre-work or After-word to the interviews. Sometime I require the student candidate to do some work before or even after the interview, to know some special aspects of their ability, and most important, how they treat work.
2. Internship before actual official work, this can give both student and the company better insights each other.

When I was applying for engineering internships at startups last Summer I chose Shoptiques because I thought the post-interview project was interesting. Additionally, I felt like they valued me more because they gave me a non-trivial project that I knew they were going to potentially use in production.

I hadn't used any of the libraries before so the project gave me a quick preview to figure out whether or not I was going to enjoy working there and I think it gave them a good evaluation of my ability to learn quickly. It also showed them that I wanted to work there bad enough to do nothing else for a weekend (since they only gave me Friday night and Saturday morning to do the project).

1. Have they used your product? In my case, have the tried any of the free-to-play games we make?
1a. What do they think of the product? Can they communicate what they feel are the pros and cons? (Yes, for all disciplines.)
2. What have they done outside of standard coursework? Internships? Clubs? Volunteer work?
3. How many group projects have they completed at school? This is important because 99%+ of work today is collaborative.
3b. What did they learn about group dynamics, communication and conflict?
4. Communication: Can they explain a difficult concept to you in the interview? It can be (should be) something they say they know well so their understanding isn't an issue. Can they adapt their message for the specific audience?

Becoming productive:
A. What's their learning style? (Do they know their learning style?) How do they best learn new concepts? How do they learn compared to classmates and peers?
B. Are they a good blend of confident and humble? Confident enough not to be scared off of learning new things quickly and humble enough to realize they are just starting and have a lot to learn.
C. What is they experience being a coach, mentor, teacher? What is their experience being coached or an apprentice? What have they learned from both sides of this type of relationship?
D. What resources do they use to learn? Ideally something beyond Google searching. :-)
E. Can they evaluate their own performance after a project? Are they reflective? Identify lessons?